Finite Group Databasebeta

← #17202091

Subgroups — #17202091

Order 4352.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D17C211yesmaximal, characteristic, complemented
2#14533041C211yesmaximal, characteristic, complemented
3#14533026C211yesmaximal, characteristic, complemented
4#14532921C211yesmaximal, characteristic, complemented
5#14532906C211yesmaximal, characteristic, complemented
6#14532831C211yesmaximal, characteristic, complemented
7#14532816C211yesmaximal, characteristic, complemented
8#14532732C211yesmaximal, characteristic, complemented
9#14532717C211yesmaximal, characteristic, complemented
10#14532604C211yesmaximal, characteristic, complemented
11#14532530C211yesmaximal, characteristic, complemented
12#14532447C211yesmaximal, characteristic, complemented
13#14532331C211yesmaximal, characteristic, complemented
14#14532257C211yesmaximal, characteristic, complemented
15#14532176C211yesmaximal, characteristic, complemented
16#14532155C211yesmaximal, characteristic
17#14532108C211yesmaximal, characteristic, complemented
18#14532067C211yesmaximal, characteristic, complemented
19#14532041C211yesmaximal, characteristic, complemented
20#14532026C211yesmaximal, characteristic, complemented
21#14532020C211yesmaximal, characteristic, complemented
22C4×#10587632C211yesmaximal, characteristic, complemented
23C4×#10587615C211yesmaximal, characteristic, complemented
24C4×#10587625C211yesmaximal, characteristic, complemented
25C4×#10587623C211yesmaximal, characteristic, complemented
26C4×#10587623C211yesmaximal, characteristic, complemented
27#14531229C211yesmaximal, characteristic, complemented
28#14531221C211yesmaximal, characteristic, complemented
29#14531163C211yesmaximal, characteristic, complemented
30C2×C4×#63227C211yesmaximal, characteristic, complemented
31C2×C17×#529C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35C2×#10587615C2211yescharacteristic
36C2×#10587632C2211yescharacteristic
37C2×#10587625C2211yescharacteristic
38C2×#10587623C2211yescharacteristic
39C2×#10587623C2211yescharacteristic
40C2×C4×D68C2211yescharacteristic
41C2×D4×Dic17C2211yescharacteristic
42C2×#10587579C2211yescharacteristic
43C2×C4×C22⋊D17C2211yescharacteristic
44C2×C4×C22⋊D17C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic, complemented
47C2×C4×C22⋊D17C2211yescharacteristic, complemented
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C4×D4×D17—28no—
51C2×#10587612C2211yescharacteristic, complemented
52C2×C4⋊C4×D17C2211yescharacteristic
53C22×#63227C2211yescharacteristic
54C22×#63227C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C22×C4×Dic17C2211yescharacteristic, complemented
58C2×C42×D17C2211yescharacteristic
59#11762748C2211yescharacteristic, complemented
60#11762748C2211yescharacteristic, complemented
61#11762747C2211yescharacteristic, complemented
62#11762744C2211yescharacteristic, complemented
63#11762742C2211yescharacteristic, complemented
64#11762740C2211yescharacteristic, complemented
65#11762739C2211yescharacteristic, complemented
66#11762737C2211yescharacteristic, complemented
67#11762737C2211yescharacteristic, complemented
68#11762737C2211yescharacteristic, complemented
69#11762735C2211yescharacteristic, complemented
70#11762735C2211yescharacteristic, complemented
71#11762735C2211yescharacteristic, complemented
72#11762734C2211yescharacteristic, complemented
73#11762732C2211yescharacteristic, complemented
74#11762731C2211yescharacteristic, complemented
75#11762731C2211yescharacteristic, complemented
76#11762731C2211yescharacteristic, complemented
77#11762726C2211yescharacteristic
78#11762726C2211yescharacteristic
79#11762726C2211yescharacteristic
80#11762725C2211yescharacteristic, complemented
81#11762725C2211yescharacteristic, complemented
82#11762725C2211yescharacteristic, complemented
83#11762724C2211yescharacteristic
84#11762724C2211yescharacteristic
85#11762724C2211yescharacteristic
86#11762723C2211yescharacteristic, complemented
87#11762720C2211yescharacteristic, complemented
88#11762720C2211yescharacteristic, complemented
89#11762718C2211yescharacteristic
90#11762717C2211yescharacteristic
91#11762716C2211yescharacteristic, complemented
92#11762709C2211yescharacteristic, complemented
93#11762705C2211yescharacteristic, complemented
94#11762704C2211yescharacteristic, complemented
95#11762703C2211yescharacteristic, complemented
96#11762702C2211yescharacteristic, complemented
97#11762702C2211yescharacteristic, complemented
98#11762700C2211yescharacteristic, complemented
99#11762700C2211yescharacteristic, complemented
100#11762699C2211yescharacteristic, complemented
101#11762697C2211yescharacteristic, complemented
102#11762697C2211yescharacteristic, complemented
103#11762695C2211yescharacteristic, complemented
104#11762695C2211yescharacteristic, complemented
105#11762693C2211yescharacteristic, complemented
106#11762693C2211yescharacteristic, complemented
107#11762690C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic, complemented
114#11762689C2211yescharacteristic, complemented
115#11762689C2211yescharacteristic, complemented
116#11762688C2211yescharacteristic
117#11762686C2211yescharacteristic
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic, complemented
123#11762685C2211yescharacteristic, complemented
124#11762684C2211yescharacteristic, complemented
125#11762684C2211yescharacteristic, complemented
126#11762682C2211yescharacteristic, complemented
127#11762681C2211yescharacteristic, complemented
128#11762681C2211yescharacteristic, complemented
129#11762680C2211yescharacteristic
130#11762680C2211yescharacteristic
131#11762680C2211yescharacteristic
132#11762680C2211yescharacteristic
133#11762680C2211yescharacteristic
134#11762680C2211yescharacteristic
135#11762680C2211yescharacteristic, complemented
136#11762680C2211yescharacteristic, complemented
137#11762672C2211yescharacteristic, complemented
138#11762670C2211yescharacteristic, complemented
139#11762670C2211yescharacteristic, complemented
140#11762667C2211yescharacteristic, complemented
141#11762666C2211yescharacteristic
142#11762666C2211yescharacteristic
143#11762666C2211yescharacteristic
144#11762666C2211yescharacteristic, complemented
145#11762666C2211yescharacteristic, complemented
146#11762664C2211yescharacteristic
147#11762664C2211yescharacteristic
148#11762664C2211yescharacteristic
149#11762664C2211yescharacteristic
150C4×#63225C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×#63225C2211yescharacteristic, complemented
153C4×C4⋊Dic17C2211yescharacteristic, complemented
154C4×#63227C2211yescharacteristic
155C4×#63227C2211yescharacteristic
156C4×#63227C2211yescharacteristic
157C4×#63227C2211yescharacteristic
158C4×#63227C2211yescharacteristic
159C4×#63227C2211yescharacteristic, complemented
160C4×#63227C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×#63227C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic, complemented
166C4×#63227C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169C4×C22⋊Dic17C2211yescharacteristic, complemented
170#11762655C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C17×#529—28no—
174C2×C17×#126C2211yescharacteristic, complemented
175C2×C17×#126C2211yescharacteristic, complemented
176C2×C17×#125C2211yescharacteristic, complemented
177C2×C17×#124C2211yescharacteristic, complemented
178C2×C17×#123C2211yescharacteristic
179C2×C17×#123C2211yescharacteristic, complemented
180C2×C17×C22⋊Q8C2211yescharacteristic, complemented
181C2×C17×#121C2211yescharacteristic
182C2×C4×Q8×C17C2211yescharacteristic, complemented
183C2×C4×D4×C17C2211yescharacteristic
184C2×C4×D4×C17C2211yescharacteristic, complemented
185C2×C4×D4×C17C2211yescharacteristic, complemented
186C2×C17×#117C2211yescharacteristic, complemented
187C2×C17×#117C2211yescharacteristic, complemented
188C22×C42×C17C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C2×D4×D17—24no—
210C2×D4×D17—24no—
211C2×D4×D17—24no—
212C22×D68C2311yescharacteristic
213C22×C4×D17—24no—
214C22×C4×D17—24no—
215C22×C4×D17—24no—
216C22×C4×D17—24no—
217C22×C4×D17—42no—
218C22×C4×D17—42no—
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C17×#126—24no—
229C17×#126—24no—
230C17×#125—24no—
231C17×#124—24no—
232C17×#123—24no—
233C17×#123—24no—
234C17×C22⋊Q8—24no—
235C17×#121—24no—
236C4×Q8×C17—24no—
237C4×D4×C17—24no—
238C4×D4×C17—24no—
239C4×D4×C17D418yescomplemented
240C17×#117—24no—
241C17×#117—24no—
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊C4×C17C2311yescharacteristic
244C2×C4⋊C4×C17C2311yescharacteristic
245C2×C4⋊C4×C17C2311yescharacteristic
246C2×C4⋊C4×C17C2311yescharacteristic
247C2×C4⋊C4×C17C2311yescharacteristic
248C2×C4⋊C4×C17C2311yescharacteristic
249C2×C4⋊C4×C17C2311yescharacteristic
250C2×C4⋊C4×C17C2311yescharacteristic
251C2×C4⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C22⋊C4×C17C2311yescharacteristic
261C2×C22⋊C4×C17C2311yescharacteristic
262C2×C42×C17—24no—
263C2×C42×C17C2311yescharacteristic
264C2×C42×C17C2311yescharacteristic
265C2×C42×C17C2311yescharacteristic
266C2×C42×C17C2311yescharacteristic
267C2×C42×C17C2311yescharacteristic
268C2×C42×C17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282#10587632—24no—
283#10587625—24no—
284#10587623—24no—
285#10587623—24no—
286D4×Dic17—24no—
287#10587615—24no—
288C4×C22⋊D17—24no—
289C4×C22⋊D17—24no—
290C4×C22⋊D17—24no—
291C4×C22⋊D17—42no—
292C4×C22⋊D17—42no—
293C2×#63227—24no—
294C2×#63227—24no—
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×#63227C2311yescharacteristic
320#10587612—42no—
321C2×C4⋊Dic17C2311yescharacteristic
322C2×C4⋊Dic17C2311yescharacteristic
323C2×C4⋊Dic17C2311yescharacteristic
324C2×C4⋊Dic17C2311yescharacteristic
325C2×C4⋊Dic17C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×C4×Dic17—42no—
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340C2×C4×Dic17C2311yescharacteristic
341C2×C4×Dic17C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344C2×C4×Dic17C2311yescharacteristic
345C2×C4×Dic17C2311yescharacteristic
346C2×C4×Dic17C2311yescharacteristic
347#10587579—24no—
348C4⋊C4×D17—24no—
349#10587567—24no—
350#10587567—24no—
351C22⋊C4×D17—24no—
352C22⋊C4×D17—24no—
353C4×D68—24no—
354C42×D17—24no—
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—22no—
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—41no—
404C23×D17—41no—
405C23×D17—41no—
406C23×D17—41no—
407C23×D17#4114yes—
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C2×Q8×C17—22no—
412C2×Q8×C17—22no—
413C2×Q8×C17—41no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—22no—
419C2×D4×C17—22no—
420C2×D4×C17—22no—
421C2×D4×C17—41no—
422C2×D4×C17C2×D414yes—
423C22×C4×C17—22no—
424C22×C4×C17—22no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—22no—
429C22×C4×C17—22no—
430C22×C4×C17—22no—
431C22×C4×C17—22no—
432C22×C4×C17—22no—
433C22×C4×C17—22no—
434C22×C4×C17—22no—
435C22×C4×C17—41no—
436C22×C4×C17C2×D414yes—
437C22×C4×C17C2×D414yes—
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C22×C4×C17C2411yescharacteristic
450C2×C22⋊D17—22no—
451C2×C22⋊D17—22no—
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—22no—
459C2×C22⋊D17—22no—
460C2×C22⋊D17—22no—
461C2×C22⋊D17—41no—
462C2×C22⋊D17—41no—
463C2×C22⋊D17—41no—
464C2×C22⋊D17#4114yes—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—22no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—41no—
473C22×Dic17—41no—
474C22×Dic17—41no—
475C22×Dic17—41no—
476C22×Dic17—41no—
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490D4×D17—232no—
491C2×D68—22no—
492C2×D68—22no—
493C2×D68—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—416no—
516C2×C4×D17—416no—
517C2×C4×D17—41no—
518C2×C4×D17—41no—
519C2×C4×D17—41no—
520C2×C4×D17—41no—
521C2×C4×D17—41no—
522C2×C4×D17#4114yes—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—22no—
526C4⋊C4×C17—22no—
527C4⋊C4×C17—22no—
528C4⋊C4×C17—22no—
529C4⋊C4×C17—22no—
530C4⋊C4×C17—22no—
531C4⋊C4×C17—22no—
532C4⋊C4×C17C2×D414yes—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—22no—
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—22no—
538C22⋊C4×C17—22no—
539C22⋊C4×C17—22no—
540C22⋊C4×C17—22no—
541C22⋊C4×C17C2×D414yes—
542C22⋊C4×C17C2×D414yes—
543C42×C17—22no—
544C42×C17—22no—
545C42×C17—22no—
546C42×C17—22no—
547C42×C17—22no—
548C42×C17C2×D414yes—
549C22⋊Dic17—22no—
550C22⋊Dic17—22no—
551C22⋊Dic17—22no—
552C22⋊Dic17—22no—
553C22⋊Dic17—22no—
554C22⋊Dic17—22no—
555C22⋊Dic17—22no—
556C22⋊Dic17—41no—
557C22⋊Dic17—41no—
558C22⋊Dic17—41no—
559C22⋊Dic17—41no—
560C22⋊Dic17—41no—
561C22⋊Dic17—41no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—22no—
575#63227—22no—
576#63227—22no—
577#63227—22no—
578#63227—22no—
579#63227—22no—
580#63227—22no—
581#63227—41no—
582#63227—41no—
583#63227—41no—
584#63227—41no—
585#63227—41no—
586#63227#4114yes—
587C4⋊Dic17—22no—
588C4⋊Dic17—22no—
589C4⋊Dic17—41no—
590C4⋊Dic17—41no—
591C4⋊Dic17—41no—
592#63225—22no—
593#63225—22no—
594#63225—22no—
595#63225—22no—
596#63225—22no—
597#63225—22no—
598#63225—22no—
599#63225—22no—
600#63225—41no—
601#63225—41no—
602#63225—41no—
603C4×Dic17—22no—
604C4×Dic17—22no—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—22no—
610C4×Dic17—41no—
611C4×Dic17—41no—
612#34670—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17C22×D412yes—
631C23×C17C22×D412yes—
632C23×C17C2×#4112yes—
633C23×C17C2×#4112yes—
634C23×C17C2511yescharacteristic
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—28no—
640C22×D17—28no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—28no—
654C22×D17—44no—
655C22×D17—44no—
656C22×D17—44no—
657C22×D17—44no—
658C22×D17—44no—
659C22×D17—44no—
660C22×D17—44no—
661C22×D17—44no—
662C22×D17—44no—
663C22×D17—44no—
664C22×D17—44no—
665C22×D17C2×#4112yes—
666C22×D17C2×#4112yes—
667C22×D17C2×#4112yes—
668C22×D17C2×#4112yes—
669C22×D17C2×#4112yes—
670Q8×C17—44no—
671D4×C17—28no—
672D4×C17—44no—
673D4×C17—44no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—28no—
685C2×C4×C17—28no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—44no—
705C2×C4×C17—44no—
706C2×C4×C17—44no—
707C2×C4×C17C22×D412yes—
708C2×C4×C17C22×D412yes—
709C2×C4×C17C22×D412yes—
710C2×C4×C17C22×D412yes—
711C2×C4×C17C22×D412yes—
712C2×C4×C17C2×#4112yes—
713C2×C4×C17C2×#4112yes—
714C2×C4×C17H(5,𝔽2)12yes—
715C22⋊D17—28no—
716C22⋊D17—28no—
717C22⋊D17—44no—
718C22⋊D17—44no—
719C22⋊D17—44no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—44no—
757C2×Dic17—44no—
758C2×Dic17—44no—
759C2×Dic17—44no—
760C2×Dic17C2×#4112yes—
761C2×Dic17C2×#4112yes—
762C2×Dic17C2×#4112yes—
763D68—28no—
764C4×D17—28no—
765C4×D17—28no—
766C4×D17—44no—
767C4×D17—44no—
768C4×D17—44no—
769C4×D17—44no—
770C4×D17—44no—
771C4×D17—44no—
772C4×D17—44no—
773C2×#529D1711yescharacteristic, complemented
774C22×C4×D4—171no—
775#2481—171no—
776#2480—171no—
777#2473—171no—
778#2472—171no—
779#2467—171no—
780#2466—171no—
781#2460—171no—
782#2459—171no—
783#2450—171no—
784#2444—171no—
785#2437—171no—
786#2425—171no—
787#2419—171no—
788#2412—171no—
789#2410—171no—
790#2405—171no—
791#2398—171no—
792#2395—171no—
793#2392—171no—
794#2392—171no—
795C4×C22⋊Q8—171no—
796C4×#123—171no—
797C4×#121—171no—
798C4×#120—171no—
799C4×#120—171no—
800#2290—171no—
801#2290—171no—
802#2280—171no—
803C2×C4×C22⋊C4—171no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—22no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17—41no—
819C22×C17—41no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17#52514yes—
825C22×C17C23×D411yescharacteristic
826C22×C17C22×#4111yescharacteristic
827C22×C17C22×#4111yescharacteristic
828C22×C17C22×#4111yescharacteristic
829C22×C17C22×#4111yescharacteristic
830C22×C17C2×H(5,𝔽2)11yescharacteristic
831C22×C17#58511yescharacteristic
832C2×D17—22no—
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—22no—
837C2×D17—22no—
838C2×D17—22no—
839C2×D17—22no—
840C2×D17—22no—
841C2×D17—22no—
842C2×D17—22no—
843C2×D17—22no—
844C2×D17—416no—
845C2×D17—416no—
846C2×D17—41no—
847C2×D17—41no—
848C2×D17—41no—
849C2×D17—41no—
850C2×D17—41no—
851C2×D17—41no—
852C2×D17—41no—
853C2×D17—41no—
854C2×D17#52914yescomplemented
855C4×C17—22no—
856C4×C17—22no—
857C4×C17—22no—
858C4×C17—22no—
859C4×C17—22no—
860C4×C17—41no—
861C4×C17—41no—
862C4×C17—41no—
863C4×C17—41no—
864C4×C17—41no—
865C4×C17—41no—
866C4×C17#54614yes—
867Dic17—22no—
868Dic17—22no—
869Dic17—22no—
870Dic17—41no—
871Dic17—41no—
872Dic17—41no—
873Dic17—41no—
874Dic17—41no—
875Dic17—41no—
876Dic17—41no—
877Dic17—41no—
878Dic17—41no—
879Dic17—41no—
880C23×D4—171no—
881C24×C4—171no—
882C24×C4—171no—
883#529—28no—
884C2×#126C2×D1711yescharacteristic, complemented
885C2×#126C2×D1711yescharacteristic, complemented
886C2×#125C2×D1711yescharacteristic, complemented
887C2×#124C2×D1711yescharacteristic, complemented
888C2×#123—171no—
889C2×#123C2×D1711yescharacteristic
890C2×#123C2×D1711yescharacteristic, complemented
891C2×C22⋊Q8—171no—
892C2×C22⋊Q8C2×D1711yescharacteristic, complemented
893C2×#121—171no—
894C2×#121C2×D1711yescharacteristic
895C2×#120—171no—
896C2×#120—171no—
897C2×C4×Q8C2×D1711yescharacteristic, complemented
898C2×C4×D4—171no—
899C2×C4×D4—171no—
900C2×C4×D4—171no—
901C2×C4×D4—171no—
902C2×C4×D4—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—348no—
909C2×C4×D4C2×D1711yescharacteristic
910C2×C4×D4C2×D1711yescharacteristic, complemented
911C2×C4×D4C2×D1711yescharacteristic, complemented
912C2×#117—171no—
913C2×#117C2×D1711yescharacteristic, complemented
914C2×#117C2×D1711yescharacteristic, complemented
915C22×C4⋊C4—171no—
916C22×C22⋊C4—171no—
917C22×C22⋊C4—171no—
918C22×C22⋊C4—171no—
919C22×C22⋊C4—171no—
920C22×C42—171no—
921C22×C42—171no—
922C22×C42C2×D1711yescharacteristic, complemented
923#400—171no—
924#400—171no—
925#400—171no—
926#399—171no—
927#398—171no—
928#398—171no—
929#398—171no—
930#397—171no—
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397—171no—
936#397—171no—
937#396—171no—
938#396—171no—
939#396—171no—
940#396—171no—
941#394—171no—
942#394—171no—
943#394—171no—
944#394—171no—
945#394—171no—
946#394—171no—
947#394—171no—
948#394—171no—
949#394—171no—
950#394—171no—
951#393—171no—
952#393—171no—
953#392—171no—
954#392—171no—
955#391—171no—
956#390—171no—
957#389—171no—
958#389—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#387—171no—
968#387—171no—
969#387—171no—
970#387—171no—
971#387—171no—
972#387—171no—
973#387—171no—
974#387—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#385—171no—
1000#385—171no—
1001#381—171no—
1002#381—171no—
1003#381—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#380—171no—
1009#380—171no—
1010#379—171no—
1011#379—171no—
1012#379—171no—
1013#379—171no—
1014C4×C4⋊C4—171no—
1015C4×C4⋊C4—171no—
1016C4×C4⋊C4—171no—
1017C4×C4⋊C4—171no—
1018C4×C22⋊C4—171no—
1019C4×C22⋊C4—171no—
1020C4×C22⋊C4—171no—
1021C4×C22⋊C4—171no—
1022C4×C22⋊C4—171no—
1023C4×C22⋊C4—171no—
1024C4×C22⋊C4—171no—
1025C4×C22⋊C4—171no—
1026C4×C22⋊C4—171no—
1027C4×C22⋊C4—171no—
1028C4×C22⋊C4—171no—
1029C4×C22⋊C4—171no—
1030C4×C22⋊C4—171no—
1031C4×C22⋊C4—171no—
1032C4×C22⋊C4—171no—
1033C4×C22⋊C4—171no—
1034#376—171no—
1035C2×#95—171no—
1036C2×#95—171no—
1037C2×C17—24no—
1038C2×C17—42no—
1039C2×C17—81no—
1040C2×C17C2×#52511yescharacteristic
1041C2×C17C2×#52911yescharacteristic
1042C2×C17#345911yescharacteristic
1043C2×C17C2×#54611yescharacteristic
1044C2×C17D4×#4111yescharacteristic
1045C2×C17#347511yescharacteristic
1046C2×C17#348111yescharacteristic
1047D17—24no—
1048D17—42no—
1049D17—42no—
1050C25—171no—
1051C25—171no—
1052C22×Q8C22×D1711yescharacteristic
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—171no—
1059C22×D4—344no—
1060C22×D4—344no—
1061C22×D4—344no—
1062C22×D4C22×D1711yescharacteristic
1063C22×D4C22×D1711yescharacteristic
1064C22×D4C22×D1711yescharacteristic
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—171no—
1075C23×C4—171no—
1076C23×C4—171no—
1077C23×C4—171no—
1078C23×C4—344no—
1079C23×C4—344no—
1080C23×C4—344no—
1081C23×C4—344no—
1082C23×C4—682no—
1083C23×C4—682no—
1084C23×C4C22×D1711yescharacteristic
1085C23×C4C22×D1711yescharacteristic
1086C23×C4C22×D1711yescharacteristic
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—24no—
1090#126—24no—
1091#125—24no—
1092#124—24no—
1093#123—24no—
1094#123—24no—
1095#123—344no—
1096C22⋊Q8—24no—
1097C22⋊Q8—344no—
1098#121—24no—
1099#121—344no—
1100#120—344no—
1101#120—344no—
1102C4×Q8—24no—
1103C4×D4—24no—
1104C4×D4—24no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—344no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—682no—
1114C4×D4—682no—
1115C4×D4C22⋊D1718yescomplemented
1116#117—24no—
1117#117—24no—
1118#117—682no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—344no—
1136C2×C4⋊C4C22×D1711yescharacteristic
1137C2×C4⋊C4C22×D1711yescharacteristic
1138C2×C4⋊C4C22×D1711yescharacteristic
1139C2×C4⋊C4C22×D1711yescharacteristic
1140C2×C4⋊C4C22×D1711yescharacteristic
1141C2×C4⋊C4C22×D1711yescharacteristic
1142C2×C4⋊C4C22×D1711yescharacteristic
1143C2×C4⋊C4C22×D1711yescharacteristic
1144C2×C4⋊C4C22×D1711yescharacteristic
1145C2×C4⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—344no—
1185C2×C22⋊C4—344no—
1186C2×C22⋊C4—344no—
1187C2×C22⋊C4—344no—
1188C2×C22⋊C4C22×D1711yescharacteristic
1189C2×C22⋊C4C22×D1711yescharacteristic
1190C2×C22⋊C4C22×D1711yescharacteristic
1191C2×C22⋊C4C22×D1711yescharacteristic
1192C2×C22⋊C4C22×D1711yescharacteristic
1193C2×C22⋊C4C22×D1711yescharacteristic
1194C2×C22⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C42—24no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—171no—
1206C2×C42—171no—
1207C2×C42—171no—
1208C2×C42—344no—
1209C2×C42—682no—
1210C2×C42C22×D1711yescharacteristic
1211C2×C42C22×D1711yescharacteristic
1212C2×C42C22×D1711yescharacteristic
1213C2×C42C22×D1711yescharacteristic
1214C2×C42C22×D1711yescharacteristic
1215C2×C42C22×D1711yescharacteristic
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95—171no—
1243#95—171no—
1244#95—171no—
1245#95—171no—
1246#95—171no—
1247#95—171no—
1248#95—171no—
1249#95—171no—
1250#95—171no—
1251#95—171no—
1252C17#3467011yescharacteristic, complemented, Sylow
1253C24—171no—
1254C24—171no—
1255C24—171no—
1256C24—174no—
1257C24—342no—
1258C24—342no—
1259C24—342no—
1260C24—342no—
1261C24—342no—
1262C24—342no—
1263C24—342no—
1264C24—342no—
1265C24—342no—
1266C24—681no—
1267C24—681no—
1268C24—681no—
1269C24—681no—
1270C24C23×D1711yescharacteristic
1271C24C23×D1711yescharacteristic
1272C24C23×D1711yescharacteristic
1273C2×Q8—22no—
1274C2×Q8—22no—
1275C2×Q8—41no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—41no—
1284C2×D4—174no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—3432no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—342no—
1294C2×D4—342no—
1295C2×D4—342no—
1296C2×D4—342no—
1297C2×D4—342no—
1298C2×D4—342no—
1299C2×D4—342no—
1300C2×D4—681no—
1301C2×D4—681no—
1302C2×D4—681no—
1303C2×D4C2×C22⋊D1714yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—41no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—174no—
1321C22×C4—171no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—171no—
1325C22×C4—171no—
1326C22×C4—171no—
1327C22×C4—171no—
1328C22×C4—171no—
1329C22×C4—171no—
1330C22×C4—171no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—681no—
1360C22×C4—681no—
1361C22×C4—681no—
1362C22×C4—681no—
1363C22×C4—681no—
1364C22×C4—6816no—
1365C22×C4—6816no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4C2×C22⋊D1714yes—
1372C22×C4C2×C22⋊D1714yes—
1373C22×C4C23×D1711yescharacteristic
1374C22×C4C23×D1711yescharacteristic
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C22×C4C23×D1711yescharacteristic
1383C22×C4C23×D1711yescharacteristic
1384C22×C4C23×D1711yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—342no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—681no—
1405C4⋊C4—681no—
1406C4⋊C4—681no—
1407C4⋊C4—681no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4C2×C22⋊D1714yes—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—22no—
1419C22⋊C4—174no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—342no—
1427C22⋊C4—342no—
1428C22⋊C4—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—342no—
1444C22⋊C4—342no—
1445C22⋊C4—342no—
1446C22⋊C4—681no—
1447C22⋊C4—681no—
1448C22⋊C4—681no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C22⋊C4—681no—
1453C22⋊C4—681no—
1454C22⋊C4—681no—
1455C22⋊C4—681no—
1456C22⋊C4—681no—
1457C22⋊C4C2×C22⋊D1714yes—
1458C22⋊C4C2×C22⋊D1714yes—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—342no—
1465C42—342no—
1466C42—342no—
1467C42—342no—
1468C42—342no—
1469C42—342no—
1470C42—342no—
1471C42—681no—
1472C42—681no—
1473C42C2×C22⋊D1714yes—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—172no—
1492C23—172no—
1493C23—172no—
1494C23—172no—
1495C23—172no—
1496C23—348no—
1497C23—348no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—348no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—341no—
1508C23—341no—
1509C23—341no—
1510C23—341no—
1511C23—341no—
1512C23—341no—
1513C23—341no—
1514C23—341no—
1515C23—684no—
1516C23—684no—
1517C23—684no—
1518C23—684no—
1519C23—684no—
1520C23—684no—
1521C23—684no—
1522C23—684no—
1523C23—684no—
1524C23—684no—
1525C23—684no—
1526C23#41×D1712yes—
1527C23#41×D1712yes—
1528C23C22×C22⋊D1712yes—
1529C23C22×C22⋊D1712yes—
1530C23C24×D1711yescharacteristic
1531Q8—44no—
1532D4—28no—
1533D4—44no—
1534D4—44no—
1535D4—348no—
1536D4—348no—
1537D4—348no—
1538D4—684no—
1539D4—684no—
1540D4—684no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—28no—
1552C2×C4—28no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—44no—
1572C2×C4—44no—
1573C2×C4—44no—
1574C2×C4—172no—
1575C2×C4—172no—
1576C2×C4—172no—
1577C2×C4—348no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—348no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—341no—
1606C2×C4—341no—
1607C2×C4—341no—
1608C2×C4—341no—
1609C2×C4—341no—
1610C2×C4—341no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
1615C2×C4—684no—
1616C2×C4—684no—
1617C2×C4—684no—
1618C2×C4—684no—
1619C2×C4—684no—
1620C2×C4—684no—
1621C2×C4—684no—
1622C2×C4—684no—
1623C2×C4—684no—
1624C2×C4—684no—
1625C2×C4—684no—
1626C2×C4#41×D1712yes—
1627C2×C4#41×D1712yes—
1628C2×C4#1058769612yes—
1629C2×C4C22×C22⋊D1712yes—
1630C2×C4C22×C22⋊D1712yes—
1631C2×C4C22×C22⋊D1712yes—
1632C2×C4C22×C22⋊D1712yes—
1633C2×C4C22×C22⋊D1712yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—174no—
1655C22—342no—
1656C22—342no—
1657C22—342no—
1658C22—342no—
1659C22—342no—
1660C22—342no—
1661C22—342no—
1662C22—342no—
1663C22—342no—
1664C22—342no—
1665C22—342no—
1666C22—342no—
1667C22—6816no—
1668C22—6816no—
1669C22—681no—
1670C22—681no—
1671C22—681no—
1672C22—681no—
1673C22—681no—
1674C22—681no—
1675C22—681no—
1676C22—681no—
1677C22#1176331614yes—
1678C22C23×C22⋊D1711yescharacteristic
1679C22C2×#41×D1711yescharacteristic
1680C22C2×#41×D1711yescharacteristic
1681C22C2×#41×D1711yescharacteristic
1682C22C2×#41×D1711yescharacteristic
1683C22C2×#1058769611yescharacteristic
1684C22#1176364511yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—22no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—342no—
1697C4—342no—
1698C4—342no—
1699C4—681no—
1700C4—681no—
1701C4—681no—
1702C4—681no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4#1176344714yes—
1710C2—24no—
1711C2—42no—
1712C2—81no—
1713C2—344no—
1714C2—682no—
1715C2—682no—
1716C2C2×#1176331611yescharacteristic
1717C2D17×#52911yescharacteristic
1718C2#1454219411yescharacteristic
1719C2C2×#1176344711yescharacteristic
1720C2#41×C22⋊D1711yescharacteristic
1721C2#1454233611yescharacteristic
1722C2#1454239011yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutator, socle, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#529C2
prime radical#14532155C2
hypercenterC2×#529D17
hypocenterC17#34670
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×D4×D17C2semidirect
2. #14533041C2semidirect
3. #14533026C2semidirect
4. #14532921C2semidirect
5. #14532906C2semidirect
6. #14532831C2semidirect
7. #14532816C2semidirect
8. #14532732C2semidirect
9. #14532717C2semidirect
10. #14532604C2semidirect
11. #14532530C2semidirect
12. #14532447C2semidirect
13. #14532331C2semidirect
14. #14532257C2semidirect
15. #14532176C2semidirect
17. #14532108C2semidirect
18. #14532067C2semidirect
19. #14532041C2semidirect
20. #14532026C2semidirect
21. #14532020C2semidirect
22. C4×#10587632C2semidirect
23. C4×#10587615C2semidirect
24. C4×#10587625C2semidirect
25. C4×#10587623C2semidirect
26. C4×#10587623C2semidirect
27. #14531229C2semidirect
28. #14531221C2semidirect
29. #14531163C2semidirect
30. C2×C4×#63227C2semidirect
31. C2×C17×#529C2semidirect
46. C2×C4×C22⋊D17C22semidirect
47. C2×C4×C22⋊D17C22semidirect
51. C2×#10587612C22semidirect
57. C22×C4×Dic17C22semidirect
59. #11762748C22semidirect
60. #11762748C22semidirect
61. #11762747C22semidirect
62. #11762744C22semidirect
63. #11762742C22semidirect
64. #11762740C22semidirect
65. #11762739C22semidirect
66. #11762737C22semidirect
67. #11762737C22semidirect
68. #11762737C22semidirect
69. #11762735C22semidirect
70. #11762735C22semidirect
71. #11762735C22semidirect
72. #11762734C22semidirect
73. #11762732C22semidirect
74. #11762731C22semidirect
75. #11762731C22semidirect
76. #11762731C22semidirect
80. #11762725C22semidirect
81. #11762725C22semidirect
82. #11762725C22semidirect
86. #11762723C22semidirect
87. #11762720C22semidirect
88. #11762720C22semidirect
91. #11762716C22semidirect
92. #11762709C22semidirect
93. #11762705C22semidirect
94. #11762704C22semidirect
95. #11762703C22semidirect
96. #11762702C22semidirect
97. #11762702C22semidirect
98. #11762700C22semidirect
99. #11762700C22semidirect
100. #11762699C22semidirect
101. #11762697C22semidirect
102. #11762697C22semidirect
103. #11762695C22semidirect
104. #11762695C22semidirect
105. #11762693C22semidirect
106. #11762693C22semidirect
107. #11762690C22semidirect
108. #11762690C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
113. #11762689C22semidirect
114. #11762689C22semidirect
115. #11762689C22semidirect
122. #11762685C22semidirect
123. #11762685C22semidirect
124. #11762684C22semidirect
125. #11762684C22semidirect
126. #11762682C22semidirect
127. #11762681C22semidirect
128. #11762681C22semidirect
135. #11762680C22semidirect
136. #11762680C22semidirect
137. #11762672C22semidirect
138. #11762670C22semidirect
139. #11762670C22semidirect
140. #11762667C22semidirect
144. #11762666C22semidirect
145. #11762666C22semidirect
150. C4×#63225C22semidirect
151. C4×#63225C22semidirect
152. C4×#63225C22semidirect
153. C4×C4⋊Dic17C22semidirect
159. C4×#63227C22semidirect
160. C4×#63227C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×#63227C22semidirect
165. C4×#63227C22semidirect
166. C4×#63227C22semidirect
167. C4×C22⋊Dic17C22semidirect
168. C4×C22⋊Dic17C22semidirect
169. C4×C22⋊Dic17C22semidirect
170. #11762655C22semidirect
171. C2×#10587502C22semidirect
172. C2×#10587502C22semidirect
174. C2×C17×#126C22semidirect
175. C2×C17×#126C22semidirect
176. C2×C17×#125C22semidirect
177. C2×C17×#124C22semidirect
179. C2×C17×#123C22semidirect
180. C2×C17×C22⋊Q8C22semidirect
182. C2×C4×Q8×C17C22semidirect
184. C2×C4×D4×C17C22semidirect
185. C2×C4×D4×C17C22semidirect
186. C2×C17×#117C22semidirect
187. C2×C17×#117C22semidirect
188. C22×C42×C17C22semidirect
239. C4×D4×C17D4semidirect
773. C2×#529D17semidirect
854. C2×D17#529semidirect
884. C2×#126C2×D17semidirect
885. C2×#126C2×D17semidirect
886. C2×#125C2×D17semidirect
887. C2×#124C2×D17semidirect
890. C2×#123C2×D17semidirect
892. C2×C22⋊Q8C2×D17semidirect
897. C2×C4×Q8C2×D17semidirect
910. C2×C4×D4C2×D17semidirect
911. C2×C4×D4C2×D17semidirect
913. C2×#117C2×D17semidirect
914. C2×#117C2×D17semidirect
922. C22×C42C2×D17semidirect
1115. C4×D4C22⋊D17semidirect
1252. C17#34670semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D4×D172
#145330412
#145330262
#145329212
#145329062
#145328312
#145328162
#145327322
#145327172
#145326042
#145325302
#145324472
#145323312
#145322572
#145321762
#145321552
#145321082
#145320672
#145320412
#145320262
#145320202
C4×#105876322
C4×#105876152
C4×#105876252
C4×#105876232
#145312292
#145312212
#145311632
C2×C4×#632272
C2×C17×#5292
#3467017