Finite Group Databasebeta

← #17195404

Subgroups — #17195404

Order 4352.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763281C211yesmaximal, characteristic
2#14531758C211yesmaximal, characteristic, complemented
3#14531734C211yesmaximal, characteristic, complemented
4#14531725C211yesmaximal, characteristic, complemented
5#14531722C211yesmaximal, characteristic, complemented
6#14531716C211yesmaximal, characteristic, complemented
7#14531711C211yesmaximal, characteristic, complemented
8#14531690C211yesmaximal, characteristic, complemented
9#14531682C211yesmaximal, characteristic, complemented
10#14531678C211yesmaximal, characteristic, complemented
11#14531670C211yesmaximal, characteristic, complemented
12#14531636C211yesmaximal, characteristic, complemented
13#14531634C211yesmaximal, characteristic, complemented
14#14531631C211yesmaximal, characteristic, complemented
15#14531631C211yesmaximal, characteristic, complemented
16#14531602C211yesmaximal, characteristic
17#14531602C211yesmaximal, characteristic
18#14531425C211yesmaximal, characteristic, complemented
19#14531417C211yesmaximal, characteristic, complemented
20#14531416C211yesmaximal, characteristic, complemented
21#14531390C211yesmaximal, characteristic, complemented
22#14531379C211yesmaximal, characteristic, complemented
23#14531378C211yesmaximal, characteristic, complemented
24#14531276C211yesmaximal, characteristic, complemented
25#14531244C211yesmaximal, characteristic, complemented
26#14531222C211yesmaximal, characteristic, complemented
27C2×#11762700C211yesmaximal, characteristic, complemented
28D17×#388C211yesmaximal, characteristic, complemented
29#14531143C211yesmaximal, characteristic, complemented
30C42×C22⋊D17C211yesmaximal, characteristic, complemented
31C17×#2290C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33#11763281C4116yescomplemented
34C2×C4×D68C2211yescharacteristic
35C2×D4×Dic17C2211yescharacteristic
36C2×#10587579C2211yescharacteristic
37C2×C4×C22⋊D17C2211yescharacteristic
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×C4×C22⋊D17C2211yescharacteristic
41C2×#10587567C2211yescharacteristic
42C2×#10587567C2211yescharacteristic
43C2×#10587567C2211yescharacteristic
44C2×#10587567C2211yescharacteristic
45C2×#10587578C2211yescharacteristic
46C2×#10587578C2211yescharacteristic, complemented
47C2×#10587578C2211yescharacteristic, complemented
48C2×#10587558C2211yescharacteristic
49C2×#10587563C2211yescharacteristic, complemented
50C22×#63225C2211yescharacteristic, complemented
51C2×C4⋊C4×D17C2211yescharacteristic, complemented
52C22×#63227C2211yescharacteristic
53C22×#63227C2211yescharacteristic
54C22×#63227C2211yescharacteristic
55C22×#63227C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C42×D17C2211yescharacteristic, complemented
61#11762709C2211yescharacteristic
62#11762709C2211yescharacteristic
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762706C2211yescharacteristic, complemented
66#11762706C2211yescharacteristic, complemented
67#11762704C2211yescharacteristic, complemented
68#11762704C2211yescharacteristic, complemented
69#11762703C2211yescharacteristic, complemented
70#11762703C2211yescharacteristic, complemented
71#11762702C2211yescharacteristic, complemented
72#11762702C2211yescharacteristic, complemented
73#11762701C2211yescharacteristic
74#11762701C2211yescharacteristic
75#11762701C2211yescharacteristic
76#11762701C2211yescharacteristic
77#11762700C2211yescharacteristic
78#11762700C2211yescharacteristic
79#11762700C2211yescharacteristic
80#11762700C2211yescharacteristic
81#11762700C2211yescharacteristic
82#11762700C2211yescharacteristic
83#11762700C2211yescharacteristic, complemented
84#11762700C2211yescharacteristic, complemented
85#11762700C2211yescharacteristic, complemented
86#11762700C2211yescharacteristic, complemented
87#11762700C2211yescharacteristic, complemented
88#11762700C2211yescharacteristic, complemented
89#11762699C2211yescharacteristic
90#11762699C2211yescharacteristic
91#11762699C2211yescharacteristic
92#11762699C2211yescharacteristic
93#11762698C2211yescharacteristic
94#11762698C2211yescharacteristic
95#11762698C2211yescharacteristic, complemented
96#11762698C2211yescharacteristic, complemented
97#11762697C2211yescharacteristic, complemented
98#11762697C2211yescharacteristic, complemented
99#11762695C2211yescharacteristic, complemented
100#11762695C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762694C2211yescharacteristic, complemented
103#11762692C2211yescharacteristic, complemented
104#11762692C2211yescharacteristic, complemented
105#11762689C2211yescharacteristic
106#11762689C2211yescharacteristic
107#11762687C2211yescharacteristic
108#11762687C2211yescharacteristic
109#11762687C2211yescharacteristic
110#11762687C2211yescharacteristic
111#11762684C2211yescharacteristic, complemented
112#11762684C2211yescharacteristic, complemented
113#11762683C2211yescharacteristic, complemented
114#11762683C2211yescharacteristic, complemented
115#11762680C2211yescharacteristic, complemented
116#11762680C2211yescharacteristic, complemented
117#11762678C2211yescharacteristic, complemented
118#11762677C2211yescharacteristic, complemented
119#11762676C2211yescharacteristic, complemented
120#11762675C2211yescharacteristic, complemented
121#11762673C2211yescharacteristic, complemented
122#11762673C2211yescharacteristic, complemented
123#11762672C2211yescharacteristic, complemented
124#11762671C2211yescharacteristic, complemented
125#11762671C2211yescharacteristic, complemented
126#11762670C2211yescharacteristic, complemented
127#11762669C2211yescharacteristic, complemented
128#11762668C2211yescharacteristic
129#11762668C2211yescharacteristic
130#11762668C2211yescharacteristic, complemented
131#11762667C2211yescharacteristic, complemented
132#11762667C2211yescharacteristic, complemented
133#11762667C2211yescharacteristic, complemented
134#11762666C2211yescharacteristic, complemented
135#11762666C2211yescharacteristic, complemented
136#11762666C2211yescharacteristic, complemented
137#11762664C2211yescharacteristic
138#11762664C2211yescharacteristic
139#11762664C2211yescharacteristic
140#11762664C2211yescharacteristic
141C4⋊C4×Dic17C2211yescharacteristic, complemented
142C4×#63225C2211yescharacteristic, complemented
143C4×#63225C2211yescharacteristic, complemented
144C4×#63225C2211yescharacteristic, complemented
145C4×#63225C2211yescharacteristic, complemented
146C4×#63225C2211yescharacteristic, complemented
147#11762660C2211yescharacteristic, complemented
148#11762660C2211yescharacteristic, complemented
149#11762660C2211yescharacteristic, complemented
150C22⋊C4×Dic17C2211yescharacteristic, complemented
151C22⋊C4×Dic17C2211yescharacteristic, complemented
152C22⋊C4×Dic17C2211yescharacteristic, complemented
153C4×#63227C2211yescharacteristic, complemented
154C4×#63227C2211yescharacteristic, complemented
155C4×#63227C2211yescharacteristic, complemented
156C4×#63227C2211yescharacteristic, complemented
157C4×#63227C2211yescharacteristic, complemented
158C4×C22⋊Dic17C2211yescharacteristic, complemented
159C4×C22⋊Dic17C2211yescharacteristic, complemented
160C4×C22⋊Dic17C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic, complemented
164#11762656C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic, complemented
166#11762654C2211yescharacteristic, complemented
167#11762654C2211yescharacteristic, complemented
168C2×#10587502C2211yescharacteristic, complemented
169C2×#10587502C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172C42×Dic17C2211yescharacteristic, complemented
173C2×C4×D4×C17C2211yescharacteristic
174C2×C17×#117C2211yescharacteristic, complemented
175C22×C42×C17C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#385C2211yescharacteristic, complemented
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C17×#376C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C2×D4×D17—24no—
202C2×D4×D17—24no—
203C2×D4×D17C2×C418yes—
204C22×D68C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C4×D4×C17C2×C418yescomplemented
215C17×#117—42no—
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C42×C17—42no—
230C2×C42×C17C2311yescharacteristic
231C2×C42×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245D4×Dic17C2×C418yescomplemented
246C4×C22⋊D17—24no—
247C4×C22⋊D17—24no—
248C4×C22⋊D17C2×C418yes—
249C4×C22⋊D17C2×C418yescomplemented
250C2×#63227—42no—
251C2×#63227—42no—
252C2×#63227C2×C418yescomplemented
253C2×#63227C2×C418yescomplemented
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×#63225—42no—
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319#10587579C2×C418yescomplemented
320#10587578—42no—
321#10587578—42no—
322#10587578C2×C418yescomplemented
323C4⋊C4×D17—42no—
324#10587567—24no—
325#10587567—24no—
326#10587567C2×C418yes—
327#10587567C2×C418yescomplemented
328C22⋊C4×D17—42no—
329C22⋊C4×D17—42no—
330C22⋊C4×D17C2×C418yescomplemented
331C22⋊C4×D17C2×C418yescomplemented
332#10587563—42no—
333C4×D68C2×C418yescomplemented
334#10587558C2×C418yescomplemented
335C42×D17—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
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
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—22no—
381C23×D17—22no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17—41no—
390C23×D17C22×C414yes—
391C23×D17C22×C414yes—
392C23×D17C2411yescharacteristic
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C2×D4×C17—22no—
396C2×D4×C17—22no—
397C2×D4×C17C22×C414yes—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—22no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17C22×C414yes—
409C22×C4×C17C22×C414yes—
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17C22×C414yes—
426C2×C22⋊D17C22×C414yes—
427C2×C22⋊D17#4114yes—
428C2×C22⋊D17#4114yes—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17—41no—
439C22×Dic17C22×C414yes—
440C22×Dic17C22×C414yes—
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454D4×D17—232no—
455C2×D68—22no—
456C2×D68—22no—
457C2×D68C22×C414yes—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17C22×C414yes—
481C2×C4×D17C22×C414yes—
482C2×C4×D17C22×C414yes—
483C2×C4×D17C22×C414yes—
484C2×C4×D17C22×C414yes—
485C4⋊C4×C17—22no—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C4⋊C4×C17C22×C414yes—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—22no—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17C22×C414yes—
497C22⋊C4×C17C22×C414yes—
498C42×C17—22no—
499C42×C17—22no—
500C42×C17—41no—
501C42×C17—41no—
502C42×C17—41no—
503C42×C17—41no—
504C42×C17C22×C414yes—
505C22⋊Dic17—22no—
506C22⋊Dic17—22no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511C22⋊Dic17C22×C414yes—
512C22⋊Dic17C22×C414yes—
513#63227—22no—
514#63227—22no—
515#63227—22no—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227C22×C414yes—
534#63227C22×C414yes—
535#63227C22×C414yes—
536#63227C22×C414yes—
537#63227C22×C414yes—
538#63227C22×C414yes—
539#63227C22×C414yes—
540#63227C22×C414yes—
541C4⋊Dic17—41no—
542C4⋊Dic17—41no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545C4⋊Dic17C22×C414yes—
546#63225—22no—
547#63225—22no—
548#63225—22no—
549#63225—22no—
550#63225—22no—
551#63225—22no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225C22×C414yes—
559#63225C22×C414yes—
560C4×Dic17—22no—
561C4×Dic17—22no—
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—22no—
565C4×Dic17—22no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17C22×C414yes—
575C4×Dic17C22×C414yes—
576C4×Dic17C22×C414yes—
577#34261—171nomaximal, Sylow
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17C23×C412yes—
589C23×C17C23×C412yes—
590C23×C17C2×#4112yes—
591C23×C17C2×#4112yes—
592C23×C17C2511yescharacteristic
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—28no—
610C22×D17—28no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—82no—
616C22×D17—82no—
617C22×D17—82no—
618C22×D17—82no—
619C22×D17—82no—
620C22×D17—82no—
621C22×D17—82no—
622C22×D17—82no—
623C22×D17C23×C412yes—
624C22×D17C23×C412yes—
625C22×D17C23×C412yes—
626C22×D17C2×#4112yes—
627C22×D17C2×#4112yes—
628D4×C17—28no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—44no—
662C2×C4×C17—44no—
663C2×C4×C17—44no—
664C2×C4×C17—44no—
665C2×C4×C17C23×C412yes—
666C2×C4×C17C23×C412yes—
667C2×C4×C17C23×C412yes—
668C2×C4×C17C23×C412yes—
669C2×C4×C17C23×C412yes—
670C2×C4×C17H(5,𝔽2)12yes—
671C2×C4×C17H(5,𝔽2)12yes—
672C22⋊D17—28no—
673C22⋊D17#117116yescomplemented
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—44no—
707C2×Dic17—44no—
708C2×Dic17—82no—
709C2×Dic17—82no—
710C2×Dic17C23×C412yes—
711C2×Dic17C23×C412yes—
712C2×Dic17C23×C412yes—
713C2×Dic17C23×C412yes—
714C2×Dic17C23×C412yes—
715C2×Dic17C2×#4112yes—
716C2×Dic17C2×#4112yes—
717D68—28no—
718C4×D17—28no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—44no—
722C4×D17—44no—
723C4×D17—44no—
724C4×D17—44no—
725C4×D17—82no—
726C4×D17—82no—
727C2×#518—171no—
728#2357—171no—
729#2354—171no—
730#2353—171no—
731#2353—171no—
732#2352—171no—
733#2352—171no—
734#2349—171no—
735D4×C4⋊C4—171no—
736#2347—171no—
737#2346—171no—
738#2342—171no—
739#2342—171no—
740#2342—171no—
741#2342—171no—
742D4×C22⋊C4—171no—
743D4×C22⋊C4—171no—
744#2319—171no—
745#2318—171no—
746#2318—171no—
747#2314—171no—
748#2312—171no—
749#2312—171no—
750#2298—171no—
751#2293—171no—
752#2290—171no—
753#2290D1711yescharacteristic, complemented
754C2×#388—171no—
755C2×#388—171no—
756#2275—171no—
757C42×D4—171no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17C2×#11714yes—
772C22×C17C24×C411yescharacteristic
773C22×C17C22×#4111yescharacteristic
774C22×C17C22×#4111yescharacteristic
775C22×C17C2×H(5,𝔽2)11yescharacteristic
776C22×C17C2×H(5,𝔽2)11yescharacteristic
777C22×C17#58511yescharacteristic
778C22×C17#58511yescharacteristic
779C2×D17—22no—
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—88no—
800C2×D17—88no—
801C2×D17C2×#11714yes—
802C4×C17—22no—
803C4×C17—22no—
804C4×C17—22no—
805C4×C17—22no—
806C4×C17—22no—
807C4×C17—22no—
808C4×C17—22no—
809C4×C17—41no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815Dic17—22no—
816Dic17—22no—
817Dic17—22no—
818Dic17—22no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17C2×#11714yes—
828C23×D4—171no—
829#518—1716no—
830C2×C4×D4—171no—
831C2×C4×D4—171no—
832C2×C4×D4—171no—
833C2×C4×D4—171no—
834C2×C4×D4—171no—
835C2×C4×D4—171no—
836C2×C4×D4—171no—
837C2×C4×D4—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4C2×D1711yescharacteristic
842C2×#117—171no—
843C2×#117—171no—
844C2×#117—171no—
845C2×#117—171no—
846C2×#117—171no—
847C2×#117C2×D1711yescharacteristic, complemented
848C22×C4⋊C4—171no—
849C22×C4⋊C4—171no—
850C22×C22⋊C4—171no—
851C22×C22⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855C22×C22⋊C4—171no—
856C22×C22⋊C4—171no—
857C22×C22⋊C4—171no—
858C22×C42—171no—
859C22×C42C2×D1711yescharacteristic, complemented
860#390—171no—
861#390—171no—
862#390—171no—
863#390—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388—171no—
895#388—171no—
896#388—171no—
897#388—171no—
898#388C2×D1711yescharacteristic, complemented
899#388C2×D1711yescharacteristic, complemented
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387C2×D1711yescharacteristic, complemented
907#387C2×D1711yescharacteristic, complemented
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386C2×D1711yescharacteristic
915#386C2×D1711yescharacteristic
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#385—171no—
921#385—171no—
922#385C2×D1711yescharacteristic, complemented
923#385C2×D1711yescharacteristic, complemented
924#384—171no—
925#383—171no—
926#383—171no—
927#382—171no—
928#382—171no—
929#382—171no—
930#381—171no—
931#381—171no—
932#381—171no—
933#381—171no—
934#380—171no—
935#380—171no—
936#380—171no—
937#380—171no—
938#380—171no—
939#380—171no—
940#380—171no—
941#380—171no—
942#380—171no—
943#380—171no—
944#379—171no—
945#379—171no—
946#379—171no—
947#379—171no—
948C4×C4⋊C4—171no—
949C4×C4⋊C4—171no—
950C4×C4⋊C4—171no—
951C4×C4⋊C4—171no—
952C4×C4⋊C4—171no—
953C4×C4⋊C4—171no—
954C4×C4⋊C4—171no—
955C4×C4⋊C4—171no—
956C4×C4⋊C4—171no—
957C4×C4⋊C4C2×D1711yescharacteristic, complemented
958C4×C22⋊C4—171no—
959C4×C22⋊C4—171no—
960C4×C22⋊C4—171no—
961C4×C22⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4C2×D1711yescharacteristic, complemented
975C4×C22⋊C4C2×D1711yescharacteristic, complemented
976#376—171no—
977#376—171no—
978#376C2×D1711yescharacteristic, complemented
979C2×#95—171no—
980C2×#95—171no—
981C2×#95—171no—
982C2×#95—171no—
983C43—171no—
984C2×C17—24no—
985C2×C17—42no—
986C2×C17C22×#11711yescharacteristic
987C2×C17C4×H(5,𝔽2)11yescharacteristic
988C2×C17C4×H(5,𝔽2)11yescharacteristic
989C2×C17#351311yescharacteristic
990C2×C17#351411yescharacteristic
991C2×C17#351911yescharacteristic
992C2×C17#352111yescharacteristic
993D17—24no—
994D17—42no—
995D17—42no—
996C25—171no—
997C25—171no—
998C22×D4—171no—
999C22×D4—171no—
1000C22×D4—178no—
1001C22×D4—171no—
1002C22×D4—344no—
1003C22×D4—344no—
1004C22×D4C22×D1711yescharacteristic
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4C22×D1711yescharacteristic
1019C23×C4C22×D1711yescharacteristic
1020C23×C4C22×D1711yescharacteristic
1021C23×C4C22×D1711yescharacteristic
1022C4×D4—178no—
1023C4×D4—178no—
1024C4×D4—178no—
1025C4×D4—178no—
1026C4×D4—178no—
1027C4×D4—178no—
1028C4×D4—178no—
1029C4×D4—344no—
1030C4×D4—344no—
1031C4×D4—344no—
1032C4×D4—344no—
1033C4×D4C4×D1718yescomplemented
1034#117—42no—
1035#117—178no—
1036#117—178no—
1037#117—682no—
1038#117—682no—
1039#117—682no—
1040C2×C4⋊C4—171no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4—171no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—682no—
1060C2×C4⋊C4—682no—
1061C2×C4⋊C4C22×D1711yescharacteristic
1062C2×C4⋊C4C22×D1711yescharacteristic
1063C2×C4⋊C4C22×D1711yescharacteristic
1064C2×C4⋊C4C22×D1711yescharacteristic
1065C2×C4⋊C4C22×D1711yescharacteristic
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—178no—
1069C2×C22⋊C4—178no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—178no—
1079C2×C22⋊C4—178no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—682no—
1107C2×C22⋊C4—682no—
1108C2×C22⋊C4—682no—
1109C2×C22⋊C4—682no—
1110C2×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C42—42no—
1119C2×C42—171no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—682no—
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139C2×C42C22×D1711yescharacteristic
1140C2×C42C22×D1711yescharacteristic
1141C2×C42C22×D1711yescharacteristic
1142C2×C42C22×D1711yescharacteristic
1143C2×C42C22×D1711yescharacteristic
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182#95C22×D1711yescharacteristic
1183#95C22×D1711yescharacteristic
1184C17#3426111yescharacteristic, complemented, Sylow
1185C24—171no—
1186C24—171no—
1187C24—171no—
1188C24—174no—
1189C24—174no—
1190C24—342no—
1191C24—342no—
1192C24—342no—
1193C24—342no—
1194C24—681no—
1195C24—681no—
1196C24—681no—
1197C24—681no—
1198C24—681no—
1199C24—681no—
1200C24—681no—
1201C24—681no—
1202C24C23×D1711yescharacteristic
1203C24C23×D1711yescharacteristic
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—174no—
1207C2×D4—174no—
1208C2×D4—174no—
1209C2×D4—174no—
1210C2×D4—174no—
1211C2×D4—342no—
1212C2×D4—342no—
1213C2×D4—342no—
1214C2×D4—342no—
1215C2×D4—3432no—
1216C2×D4C2×C4×D1714yes—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—174no—
1233C22×C4—174no—
1234C22×C4—174no—
1235C22×C4—174no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—342no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4C2×C4×D1714yes—
1280C22×C4C2×C4×D1714yes—
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—174no—
1299C4⋊C4—174no—
1300C4⋊C4—174no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—342no—
1305C4⋊C4—342no—
1306C4⋊C4—342no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4C2×C4×D1714yes—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—174no—
1325C22⋊C4—174no—
1326C22⋊C4—174no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
1329C22⋊C4—174no—
1330C22⋊C4—174no—
1331C22⋊C4—174no—
1332C22⋊C4—174no—
1333C22⋊C4—174no—
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—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4C2×C4×D1714yes—
1361C22⋊C4C2×C4×D1714yes—
1362C42—22no—
1363C42—22no—
1364C42—41no—
1365C42—41no—
1366C42—41no—
1367C42—41no—
1368C42—174no—
1369C42—174no—
1370C42—174no—
1371C42—342no—
1372C42—342no—
1373C42—342no—
1374C42—342no—
1375C42—342no—
1376C42—342no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42—681no—
1381C42—681no—
1382C42—681no—
1383C42—681no—
1384C42—681no—
1385C42C2×C4×D1714yes—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—172no—
1397C23—172no—
1398C23—172no—
1399C23—172no—
1400C23—172no—
1401C23—348no—
1402C23—341no—
1403C23—341no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—348no—
1419C23—684no—
1420C23—684no—
1421C23—684no—
1422C23—684no—
1423C23—1362no—
1424C23—1362no—
1425C23—1362no—
1426C23—1362no—
1427C23—1362no—
1428C23—1362no—
1429C23—1362no—
1430C23—1362no—
1431C23C22×C4×D1712yes—
1432C23C22×C4×D1712yes—
1433C23#41×D1712yes—
1434C23#41×D1712yes—
1435C23C24×D1711yescharacteristic
1436D4—28no—
1437D4—1716no—
1438D4—348no—
1439D4—348no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—44no—
1473C2×C4—44no—
1474C2×C4—44no—
1475C2×C4—44no—
1476C2×C4—172no—
1477C2×C4—172no—
1478C2×C4—172no—
1479C2×C4—172no—
1480C2×C4—172no—
1481C2×C4—172no—
1482C2×C4—172no—
1483C2×C4—348no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—684no—
1517C2×C4—684no—
1518C2×C4—684no—
1519C2×C4—684no—
1520C2×C4—684no—
1521C2×C4—684no—
1522C2×C4—684no—
1523C2×C4—684no—
1524C2×C4—1362no—
1525C2×C4—1362no—
1526C2×C4—1362no—
1527C2×C4—1362no—
1528C2×C4C22×C4×D1712yes—
1529C2×C4C22×C4×D1712yes—
1530C2×C4C22×C4×D1712yes—
1531C2×C4C22×C4×D1712yes—
1532C2×C4C22×C4×D1712yes—
1533C2×C4#1058769112yes—
1534C2×C4#1058769612yes—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—174no—
1549C22—342no—
1550C22—342no—
1551C22—342no—
1552C22—342no—
1553C22—342no—
1554C22—342no—
1555C22—342no—
1556C22—342no—
1557C22—342no—
1558C22—342no—
1559C22—342no—
1560C22—342no—
1561C22—681no—
1562C22—681no—
1563C22—681no—
1564C22—681no—
1565C22—681no—
1566C22—681no—
1567C22—681no—
1568C22—681no—
1569C22—1368no—
1570C22—1368no—
1571C22#117×D1714yes—
1572C22C23×C4×D1711yescharacteristic
1573C22C2×#41×D1711yescharacteristic
1574C22C2×#41×D1711yescharacteristic
1575C22C2×#1058769111yescharacteristic
1576C22C2×#1058769611yescharacteristic
1577C22#1176364511yescharacteristic
1578C22#1176364511yescharacteristic
1579C4—22no—
1580C4—22no—
1581C4—22no—
1582C4—22no—
1583C4—22no—
1584C4—22no—
1585C4—22no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—174no—
1593C4—342no—
1594C4—342no—
1595C4—342no—
1596C4—342no—
1597C4—681no—
1598C4—681no—
1599C4—681no—
1600C4—681no—
1601C4—681no—
1602C4—681no—
1603C4—681no—
1604C4—681no—
1605C2—24no—
1606C2—42no—
1607C2—344no—
1608C2—682no—
1609C2—682no—
1610C2C2×#117×D1711yescharacteristic
1611C2C4×#1058769111yescharacteristic
1612C2C4×#1058769611yescharacteristic
1613C2#1454271011yescharacteristic
1614C2#1454273311yescharacteristic
1615C2#1454280411yescharacteristic
1616C2#1454283811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2290C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenter#2290D17
hypocenterC17#34261
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #14531758C2semidirect
3. #14531734C2semidirect
4. #14531725C2semidirect
5. #14531722C2semidirect
6. #14531716C2semidirect
7. #14531711C2semidirect
8. #14531690C2semidirect
9. #14531682C2semidirect
10. #14531678C2semidirect
11. #14531670C2semidirect
12. #14531636C2semidirect
13. #14531634C2semidirect
14. #14531631C2semidirect
15. #14531631C2semidirect
18. #14531425C2semidirect
19. #14531417C2semidirect
20. #14531416C2semidirect
21. #14531390C2semidirect
22. #14531379C2semidirect
23. #14531378C2semidirect
24. #14531276C2semidirect
25. #14531244C2semidirect
26. #14531222C2semidirect
27. C2×#11762700C2semidirect
28. D17×#388C2semidirect
29. #14531143C2semidirect
30. C42×C22⋊D17C2semidirect
31. C17×#2290C2semidirect
33. #11763281C4semidirect
46. C2×#10587578C22semidirect
47. C2×#10587578C22semidirect
49. C2×#10587563C22semidirect
50. C22×#63225C22semidirect
51. C2×C4⋊C4×D17C22semidirect
60. C2×C42×D17C22semidirect
65. #11762706C22semidirect
66. #11762706C22semidirect
67. #11762704C22semidirect
68. #11762704C22semidirect
69. #11762703C22semidirect
70. #11762703C22semidirect
71. #11762702C22semidirect
72. #11762702C22semidirect
83. #11762700C22semidirect
84. #11762700C22semidirect
85. #11762700C22semidirect
86. #11762700C22semidirect
87. #11762700C22semidirect
88. #11762700C22semidirect
95. #11762698C22semidirect
96. #11762698C22semidirect
97. #11762697C22semidirect
98. #11762697C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762694C22semidirect
102. #11762694C22semidirect
103. #11762692C22semidirect
104. #11762692C22semidirect
111. #11762684C22semidirect
112. #11762684C22semidirect
113. #11762683C22semidirect
114. #11762683C22semidirect
115. #11762680C22semidirect
116. #11762680C22semidirect
117. #11762678C22semidirect
118. #11762677C22semidirect
119. #11762676C22semidirect
120. #11762675C22semidirect
121. #11762673C22semidirect
122. #11762673C22semidirect
123. #11762672C22semidirect
124. #11762671C22semidirect
125. #11762671C22semidirect
126. #11762670C22semidirect
127. #11762669C22semidirect
130. #11762668C22semidirect
131. #11762667C22semidirect
132. #11762667C22semidirect
133. #11762667C22semidirect
134. #11762666C22semidirect
135. #11762666C22semidirect
136. #11762666C22semidirect
141. C4⋊C4×Dic17C22semidirect
142. C4×#63225C22semidirect
143. C4×#63225C22semidirect
144. C4×#63225C22semidirect
145. C4×#63225C22semidirect
146. C4×#63225C22semidirect
147. #11762660C22semidirect
148. #11762660C22semidirect
149. #11762660C22semidirect
150. C22⋊C4×Dic17C22semidirect
151. C22⋊C4×Dic17C22semidirect
152. C22⋊C4×Dic17C22semidirect
153. C4×#63227C22semidirect
154. C4×#63227C22semidirect
155. C4×#63227C22semidirect
156. C4×#63227C22semidirect
157. C4×#63227C22semidirect
158. C4×C22⋊Dic17C22semidirect
159. C4×C22⋊Dic17C22semidirect
160. C4×C22⋊Dic17C22semidirect
163. #11762656C22semidirect
164. #11762656C22semidirect
165. #11762656C22semidirect
166. #11762654C22semidirect
167. #11762654C22semidirect
168. C2×#10587502C22semidirect
169. C2×#10587502C22semidirect
170. #95×D17C22semidirect
171. #95×D17C22semidirect
172. C42×Dic17C22semidirect
174. C2×C17×#117C22semidirect
175. C22×C42×C17C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
182. C17×#385C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C17×#376C22semidirect
214. C4×D4×C17C2×C4semidirect
245. D4×Dic17C2×C4semidirect
249. C4×C22⋊D17C2×C4semidirect
252. C2×#63227C2×C4semidirect
253. C2×#63227C2×C4semidirect
319. #10587579C2×C4semidirect
322. #10587578C2×C4semidirect
327. #10587567C2×C4semidirect
330. C22⋊C4×D17C2×C4semidirect
331. C22⋊C4×D17C2×C4semidirect
333. C4×D68C2×C4semidirect
334. #10587558C2×C4semidirect
673. C22⋊D17#117semidirect
753. #2290D17semidirect
847. C2×#117C2×D17semidirect
859. C22×C42C2×D17semidirect
898. #388C2×D17semidirect
899. #388C2×D17semidirect
906. #387C2×D17semidirect
907. #387C2×D17semidirect
922. #385C2×D17semidirect
923. #385C2×D17semidirect
957. C4×C4⋊C4C2×D17semidirect
974. C4×C22⋊C4C2×D17semidirect
975. C4×C22⋊C4C2×D17semidirect
978. #376C2×D17semidirect
1033. C4×D4C4×D17semidirect
1184. C17#34261semidirect

Maximal subgroups

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

subgroupindex
C2×#117632812
#145317582
#145317342
#145317252
#145317222
#145317162
#145317112
#145316902
#145316822
#145316782
#145316702
#145316362
#145316342
#145316312
#145316022
#145314252
#145314172
#145314162
#145313902
#145313792
#145313782
#145312762
#145312442
#145312222
C2×#117627002
D17×#3882
#145311432
C42×C22⋊D172
C17×#22902
#3426117