Finite Group Databasebeta

← #17207013

Subgroups — #17207013

Order 4352.

2878 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×#11763404C211yesmaximal, characteristic, complemented
2C2×C4×D4×D17C211yesmaximal, characteristic, complemented
3#14537098C211yesmaximal, characteristic, complemented
4#14537091C211yesmaximal, characteristic, complemented
5#14537073C211yesmaximal, characteristic, complemented
6#14537070C211yesmaximal, characteristic, complemented
7#14534703C211yesmaximal, characteristic, complemented
8#14534682C211yesmaximal, characteristic, complemented
9#14534654C211yesmaximal, characteristic, complemented
10#14534624C211yesmaximal, characteristic, complemented
11#14533023C211yesmaximal, characteristic, complemented
12#14532918C211yesmaximal, characteristic, complemented
13#14532817C211yesmaximal, characteristic, complemented
14#14532778C211yesmaximal, characteristic, complemented
15#14532733C211yesmaximal, characteristic, complemented
16#14532663C211yesmaximal, characteristic, complemented
17#14532596C211yesmaximal, characteristic, complemented
18#14532593C211yesmaximal, characteristic, complemented
19#14532449C211yesmaximal, characteristic, complemented
20#14532337C211yesmaximal, characteristic, complemented
21#14532255C211yesmaximal, characteristic, complemented
22#14532239C211yesmaximal, characteristic, complemented
23#14532183C211yesmaximal, characteristic, complemented
24#14532155C211yesmaximal, characteristic
25#14532110C211yesmaximal, characteristic, complemented
26#14531485C211yesmaximal, characteristic, complemented
27#14531452C211yesmaximal, characteristic, complemented
28#14531410C211yesmaximal, characteristic, complemented
29#14531289C211yesmaximal, characteristic, complemented
30C2×#11762680C211yesmaximal, characteristic, complemented
31C17×#2443C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35#11763404—28no—
36C2×#10587565C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic, complemented
38C2×#10587575C2211yescharacteristic, complemented
39C2×#10587575C2211yescharacteristic, complemented
40C2×#10587572C2211yescharacteristic
41C2×#10587621C2211yescharacteristic
42C2×#10587621C2211yescharacteristic, complemented
43C2×#10587621C2211yescharacteristic, complemented
44C2×#10587621C2211yescharacteristic, complemented
45C2×#10587610C2211yescharacteristic, complemented
46C2×#10587582C2211yescharacteristic
47C2×#10587582C2211yescharacteristic, complemented
48C2×#10587564C2211yescharacteristic, complemented
49C2×#10587564C2211yescharacteristic, complemented
50C2×#10587625C2211yescharacteristic
51C2×#10587623C2211yescharacteristic
52C2×#10587623C2211yescharacteristic
53C2×C4×D68C2211yescharacteristic
54C2×D4×Dic17C2211yescharacteristic
55C2×D4×Dic17C2211yescharacteristic, complemented
56C2×#10587579C2211yescharacteristic
57C2×C4×C22⋊D17C2211yescharacteristic
58C2×C4×C22⋊D17C2211yescharacteristic
59C2×#10587567C2211yescharacteristic
60C2×#10587567C2211yescharacteristic
61C2×#10587567C2211yescharacteristic
62C2×#10587567C2211yescharacteristic, complemented
63C4×D4×D17—28no—
64C22×#63225C2211yescharacteristic, complemented
65C2×C4⋊C4×D17C2211yescharacteristic
66C22×#63227C2211yescharacteristic
67C22×#63227C2211yescharacteristic
68C2×C22⋊C4×D17C2211yescharacteristic
69C2×C22⋊C4×D17C2211yescharacteristic
70C2×C42×D17C2211yescharacteristic
71#11762747C2211yescharacteristic, complemented
72#11762744C2211yescharacteristic, complemented
73#11762744C2211yescharacteristic, complemented
74#11762743C2211yescharacteristic, complemented
75#11762740C2211yescharacteristic, complemented
76#11762740C2211yescharacteristic, complemented
77#11762738C2211yescharacteristic, complemented
78#11762738C2211yescharacteristic, complemented
79#11762738C2211yescharacteristic, complemented
80#11762737C2211yescharacteristic, complemented
81#11762737C2211yescharacteristic, complemented
82#11762733C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762731C2211yescharacteristic, complemented
85#11762731C2211yescharacteristic, complemented
86#11762729C2211yescharacteristic, complemented
87#11762727C2211yescharacteristic
88#11762727C2211yescharacteristic
89#11762726C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic, complemented
94#11762724C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic, complemented
96#11762722C2211yescharacteristic, complemented
97#11762718C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762706C2211yescharacteristic, complemented
100#11762705C2211yescharacteristic, complemented
101#11762705C2211yescharacteristic, complemented
102#11762704C2211yescharacteristic, complemented
103#11762703C2211yescharacteristic, complemented
104#11762703C2211yescharacteristic, complemented
105#11762702C2211yescharacteristic, complemented
106#11762698C2211yescharacteristic, complemented
107#11762698C2211yescharacteristic, complemented
108#11762698C2211yescharacteristic, complemented
109#11762697C2211yescharacteristic, complemented
110#11762696C2211yescharacteristic, complemented
111#11762695C2211yescharacteristic, complemented
112#11762694C2211yescharacteristic, complemented
113#11762693C2211yescharacteristic, complemented
114#11762693C2211yescharacteristic, complemented
115#11762692C2211yescharacteristic, complemented
116#11762692C2211yescharacteristic, complemented
117#11762692C2211yescharacteristic, complemented
118#11762691C2211yescharacteristic, complemented
119#11762689C2211yescharacteristic
120#11762688C2211yescharacteristic
121#11762688C2211yescharacteristic
122#11762686C2211yescharacteristic, complemented
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762685C2211yescharacteristic, complemented
130#11762683C2211yescharacteristic
131#11762683C2211yescharacteristic
132#11762683C2211yescharacteristic
133#11762683C2211yescharacteristic
134#11762683C2211yescharacteristic, complemented
135#11762683C2211yescharacteristic, complemented
136#11762682C2211yescharacteristic, complemented
137#11762682C2211yescharacteristic, complemented
138#11762682C2211yescharacteristic, complemented
139#11762681C2211yescharacteristic, complemented
140#11762681C2211yescharacteristic, complemented
141#11762680C2211yescharacteristic
142#11762680C2211yescharacteristic
143#11762680C2211yescharacteristic
144#11762680C2211yescharacteristic
145#11762680C2211yescharacteristic
146#11762680C2211yescharacteristic
147#11762680C2211yescharacteristic, complemented
148#11762680C2211yescharacteristic, complemented
149#11762680C2211yescharacteristic, complemented
150#11762680C2211yescharacteristic, complemented
151#11762680C2211yescharacteristic, complemented
152#11762680C2211yescharacteristic, complemented
153#11762680C2211yescharacteristic, complemented
154#11762676C2211yescharacteristic, complemented
155#11762673C2211yescharacteristic, complemented
156#11762672C2211yescharacteristic, complemented
157#11762670C2211yescharacteristic, complemented
158#11762670C2211yescharacteristic, complemented
159#11762668C2211yescharacteristic
160#11762668C2211yescharacteristic
161#11762668C2211yescharacteristic
162#11762668C2211yescharacteristic, complemented
163#11762667C2211yescharacteristic, complemented
164#11762667C2211yescharacteristic, complemented
165#11762664C2211yescharacteristic
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169C22⋊C4×Dic17C2211yescharacteristic, complemented
170#11762656C2211yescharacteristic
171#11762656C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic, complemented
175C2×C17×#121C2211yescharacteristic
176C2×C4×D4×C17C2211yescharacteristic
177C22×C4⋊C4×C17C2211yescharacteristic, complemented
178C17×#399C2211yescharacteristic, complemented
179C17×#398C2211yescharacteristic, complemented
180C17×#397C2211yescharacteristic, complemented
181C17×#394C2211yescharacteristic, complemented
182C17×#388C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C17×#385C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C2×D4×D17—24no—
209C2×D4×D17—24no—
210C2×D4×D17—24no—
211C22×D68C2311yescharacteristic
212C22×C4×D17—24no—
213C22×C4×D17—24no—
214C22×C4×D17—42no—
215C22×C4×D17—42no—
216C22×C4×D17—42no—
217C22×C4×D17—42no—
218C22×C4×D17C2311yescharacteristic
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×Dic34C2311yescharacteristic
228C17×#123—42no—
229C17×#121—24no—
230C4×D4×C17—24no—
231C2×C4⋊C4×C17—42no—
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264#10587625—24no—
265#10587623—24no—
266#10587623—42no—
267#10587621—24no—
268#10587621—24no—
269#10587621—24no—
270#10587621—24no—
271D4×Dic17—24no—
272D4×Dic17D418yescomplemented
273C4×C22⋊D17—24no—
274C4×C22⋊D17—24no—
275C2×#63227—24no—
276C2×#63227—42no—
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307#10587610—24no—
308C2×#63225—24no—
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336#10587582—42no—
337#10587582—42no—
338#10587579—24no—
339C4⋊C4×D17—24no—
340#10587575—24no—
341#10587575—24no—
342#10587572—24no—
343#10587567—24no—
344#10587567—24no—
345#10587567—42no—
346#10587567—42no—
347C22⋊C4×D17—24no—
348C22⋊C4×D17—24no—
349#10587565—24no—
350#10587565—24no—
351#10587564—24no—
352#10587564—24no—
353C4×D68—24no—
354C42×D17—24no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
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×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—41no—
418C2×D4×C17—41no—
419C2×D4×C17C2×D414yes—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—22no—
424C22×C4×C17—22no—
425C22×C4×C17—22no—
426C22×C4×C17—41no—
427C22×C4×C17—41no—
428C22×C4×C17—41no—
429C22×C4×C17—41no—
430C22×C4×C17—41no—
431C22×C4×C17—41no—
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—22no—
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—41no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17—41no—
457C2×C22⋊D17—41no—
458C2×C22⋊D17#4114yes—
459C22×Dic17—22no—
460C22×Dic17—22no—
461C22×Dic17—22no—
462C22×Dic17—22no—
463C22×Dic17—22no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17—41no—
470C22×Dic17—41no—
471C22×Dic17—41no—
472C22×Dic17C2×D414yes—
473C22×Dic17C2×D414yes—
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487D4×D17—232no—
488C2×D68—22no—
489C2×D68—22no—
490C2×D68—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—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—416no—
510C2×C4×D17—416no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17—41no—
515C2×C4×D17—41no—
516C2×C4×D17—41no—
517C2×C4×D17—41no—
518C2×C4×D17—41no—
519C2×C4×D17—41no—
520C2×Dic34—22no—
521C2×Dic34—41no—
522C2×Dic34—41no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—22no—
526C4⋊C4×C17—22no—
527C4⋊C4×C17—41no—
528C4⋊C4×C17—41no—
529C4⋊C4×C17—41no—
530C4⋊C4×C17—41no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—22no—
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—41no—
538C22⋊C4×C17—41no—
539C22⋊C4×C17—41no—
540C22⋊C4×C17—41no—
541C22⋊C4×C17—41no—
542C42×C17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—22no—
551C22⋊Dic17—41no—
552C22⋊Dic17—41no—
553C22⋊Dic17C2×D414yes—
554C22⋊Dic17C2×D414yes—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
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—41no—
573#63227—41no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580C4⋊Dic17—22no—
581C4⋊Dic17—22no—
582C4⋊Dic17—22no—
583C4⋊Dic17—22no—
584C4⋊Dic17C2×D414yes—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—22no—
594#63225—22no—
595#63225—22no—
596#63225—22no—
597#63225—22no—
598#63225—22no—
599#63225—41no—
600#63225—41no—
601#63225—41no—
602#63225—41no—
603#63225—41no—
604#63225—41no—
605#63225—41no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17C2×D414yes—
612#34991—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×D17H(5,𝔽2)12yes—
669C22×D172−1+412yes—
670D4×C17—28no—
671D4×C17—44no—
672D4×C17—82no—
673C2×C4×C17—21no—
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—21no—
685C2×C4×C17—21no—
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—21no—
705C2×C4×C17—21no—
706C2×C4×C17—21no—
707C2×C4×C17—44no—
708C2×C4×C17—44no—
709C2×C4×C17—44no—
710C2×C4×C17—82no—
711C2×C4×C17C22×D412yes—
712C2×C4×C17H(5,𝔽2)12yes—
713C22⋊D17—28no—
714C22⋊D17—28no—
715C22⋊D17—44no—
716C22⋊D17—44no—
717C22⋊D17—82no—
718C2×Dic17—21no—
719C2×Dic17—21no—
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—44no—
753C2×Dic17—44no—
754C2×Dic17—44no—
755C2×Dic17—82no—
756C2×Dic17—82no—
757C2×Dic17C22×D412yes—
758C2×Dic17C22×D412yes—
759C2×Dic17C22×D412yes—
760C2×Dic17C22×D412yes—
761C2×Dic17C2×#4112yes—
762D68—28no—
763C4×D17—28no—
764C4×D17—28no—
765C4×D17—44no—
766C4×D17—44no—
767C4×D17—44no—
768C4×D17—44no—
769C4×D17—44no—
770C4×D17—44no—
771C4×D17—44no—
772Dic34—82no—
773C2×#539—171no—
774C22×C4×D4—171no—
775#2852—171no—
776#2851—171no—
777#2849—171no—
778#2848—171no—
779#2638—171no—
780#2636—171no—
781#2633—171no—
782#2630—171no—
783#2480—171no—
784#2473—171no—
785#2466—171no—
786#2463—171no—
787#2460—171no—
788#2455—171no—
789#2449—171no—
790#2449—171no—
791#2443D1711yescharacteristic, complemented
792#2437—171no—
793#2425—171no—
794#2419—171no—
795#2418—171no—
796#2412—171no—
797#2410—171no—
798#2405—171no—
799#2325—171no—
800#2322—171no—
801#2318—171no—
802C4×#120—171no—
803C2×#385—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×C17C2×H(5,𝔽2)11yescharacteristic
829C22×C17C2×H(5,𝔽2)11yescharacteristic
830C22×C17C2×2−1+411yescharacteristic
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#53914yescomplemented
855C4×C17—22no—
856C4×C17—22no—
857C4×C17—41no—
858C4×C17—41no—
859C4×C17—41no—
860C4×C17—41no—
861C4×C17—41no—
862C4×C17—41no—
863C4×C17—41no—
864C4×C17—41no—
865C4×C17—41no—
866C4×C17—41no—
867Dic17—22no—
868Dic17—22no—
869Dic17—22no—
870Dic17—22no—
871Dic17—22no—
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#539—348no—
884C2×#126—171no—
885C2×#126—171no—
886C2×#125—171no—
887C2×#125—171no—
888C2×#123—171no—
889C2×#123—171no—
890C2×#123—171no—
891C2×#123—171no—
892C2×#123—171no—
893C2×#123C2×D1711yescharacteristic, complemented
894C2×C22⋊Q8—171no—
895C2×C22⋊Q8—171no—
896C2×C22⋊Q8—171no—
897C2×C22⋊Q8—171no—
898C2×C22⋊Q8—171no—
899C2×#121—171no—
900C2×#121C2×D1711yescharacteristic
901C2×#120—171no—
902C2×#120—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—171no—
909C2×C4×D4—171no—
910C2×C4×D4—171no—
911C2×C4×D4—171no—
912C2×C4×D4—171no—
913C2×C4×D4—348no—
914C2×C4×D4C2×D1711yescharacteristic
915C22×C4⋊C4—171no—
916C22×C4⋊C4—171no—
917C22×C4⋊C4C2×D1711yescharacteristic, complemented
918C22×C22⋊C4—171no—
919C22×C22⋊C4—171no—
920C22×C22⋊C4—171no—
921C22×C22⋊C4—171no—
922C22×C42—171no—
923#400—171no—
924#399—171no—
925#399—171no—
926#399C2×D1711yescharacteristic, complemented
927#398—171no—
928#398—171no—
929#398—171no—
930#398C2×D1711yescharacteristic, complemented
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397—171no—
936#397C2×D1711yescharacteristic, complemented
937#396—171no—
938#396—171no—
939#396—171no—
940#396—171no—
941#395—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#394C2×D1711yescharacteristic, complemented
952#393—171no—
953#392—171no—
954#392—171no—
955#389—171no—
956#389—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#388C2×D1711yescharacteristic, complemented
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#387—171no—
976#387C2×D1711yescharacteristic, complemented
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#386C2×D1711yescharacteristic
989#386C2×D1711yescharacteristic, complemented
990#386C2×D1711yescharacteristic, complemented
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#385—171no—
1002#385—171no—
1003#385—171no—
1004#385—171no—
1005#385—171no—
1006#385—171no—
1007#385—171no—
1008#385—171no—
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385C2×D1711yescharacteristic, complemented
1016#385C2×D1711yescharacteristic, complemented
1017#383—171no—
1018#382—171no—
1019#381—171no—
1020#381—171no—
1021#381—171no—
1022#380—171no—
1023#380—171no—
1024#380—171no—
1025#380—171no—
1026#380—171no—
1027#380—171no—
1028#379—171no—
1029#379—171no—
1030#379—171no—
1031#379—171no—
1032C4×C22⋊C4—171no—
1033C4×C22⋊C4—171no—
1034C4×C22⋊C4—171no—
1035C2×#95—171no—
1036C2×#95—171no—
1037C2×C17—24no—
1038C2×C17—42no—
1039C2×C17—81no—
1040C2×C17C2×#52511yescharacteristic
1041C2×C17C2×#53911yescharacteristic
1042C2×C17#345911yescharacteristic
1043C2×C17#348411yescharacteristic
1044C2×C17#348911yescharacteristic
1045C2×C17#351311yescharacteristic
1046C2×C17#352011yescharacteristic
1047D17—24no—
1048D17—42no—
1049D17—42no—
1050C25—171no—
1051C25—171no—
1052C22×Q8—171no—
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—171no—
1079C23×C4—344no—
1080C23×C4—344no—
1081C23×C4—682no—
1082C23×C4—682no—
1083C23×C4—682no—
1084C23×C4—682no—
1085C23×C4C22×D1711yescharacteristic
1086C23×C4C22×D1711yescharacteristic
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—344no—
1090#126—344no—
1091#125—344no—
1092#125—344no—
1093#123—42no—
1094#123—344no—
1095#123—344no—
1096#123—344no—
1097#123—344no—
1098#123—344no—
1099C22⋊Q8—344no—
1100C22⋊Q8—344no—
1101C22⋊Q8—344no—
1102C22⋊Q8—682no—
1103C22⋊Q8—682no—
1104#121—24no—
1105#121—344no—
1106#120—344no—
1107#120—682no—
1108C4×D4—24no—
1109C4×D4—178no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—344no—
1114C4×D4—344no—
1115C4×D4—344no—
1116C4×D4—344no—
1117C4×D4—682no—
1118C4×D4—682no—
1119C2×C4⋊C4—42no—
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—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—171no—
1146C2×C4⋊C4—344no—
1147C2×C4⋊C4—344no—
1148C2×C4⋊C4C22×D1711yescharacteristic
1149C2×C4⋊C4C22×D1711yescharacteristic
1150C2×C4⋊C4C22×D1711yescharacteristic
1151C2×C4⋊C4C22×D1711yescharacteristic
1152C2×C4⋊C4C22×D1711yescharacteristic
1153C2×C4⋊C4C22×D1711yescharacteristic
1154C2×C4⋊C4C22×D1711yescharacteristic
1155C2×C4⋊C4C22×D1711yescharacteristic
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—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—171no—
1189C2×C22⋊C4—171no—
1190C2×C22⋊C4—171no—
1191C2×C22⋊C4—171no—
1192C2×C22⋊C4—171no—
1193C2×C22⋊C4—344no—
1194C2×C22⋊C4—344no—
1195C2×C22⋊C4—344no—
1196C2×C22⋊C4—682no—
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C22⋊C4C22×D1711yescharacteristic
1199C2×C22⋊C4C22×D1711yescharacteristic
1200C2×C22⋊C4C22×D1711yescharacteristic
1201C2×C22⋊C4C22×D1711yescharacteristic
1202C2×C22⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4C22×D1711yescharacteristic
1204C2×C22⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C22⋊C4C22×D1711yescharacteristic
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—171no—
1214C2×C42—344no—
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#95C22×D1711yescharacteristic
1245#95C22×D1711yescharacteristic
1246#95C22×D1711yescharacteristic
1247#95C22×D1711yescharacteristic
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252C17#3499111yescharacteristic, 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—342no—
1274C2×Q8—681no—
1275C2×Q8—681no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—41no—
1283C2×D4—41no—
1284C2×D4—174no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—3432no—
1289C2×D4—342no—
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—681no—
1300C2×D4—681no—
1301C2×D4—681no—
1302C2×D4—681no—
1303C2×D4D4×D1714yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—41no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—41no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—174no—
1322C22×C4—174no—
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—681no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4—681no—
1361C22×C4—681no—
1362C22×C4—681no—
1363C22×C4—6816no—
1364C22×C4—6816no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4—681no—
1372C22×C4—681no—
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—41no—
1390C4⋊C4—41no—
1391C4⋊C4—41no—
1392C4⋊C4—41no—
1393C4⋊C4—174no—
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—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—342no—
1408C4⋊C4—342no—
1409C4⋊C4—342no—
1410C4⋊C4—342no—
1411C4⋊C4—342no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4—681no—
1416C4⋊C4—681no—
1417C4⋊C4—681no—
1418C4⋊C4—681no—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—22no—
1424C22⋊C4—22no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—41no—
1430C22⋊C4—174no—
1431C22⋊C4—174no—
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—342no—
1447C22⋊C4—342no—
1448C22⋊C4—342no—
1449C22⋊C4—342no—
1450C22⋊C4—342no—
1451C22⋊C4—342no—
1452C22⋊C4—342no—
1453C22⋊C4—342no—
1454C22⋊C4—342no—
1455C22⋊C4—342no—
1456C22⋊C4—342no—
1457C22⋊C4—681no—
1458C22⋊C4—681no—
1459C22⋊C4—681no—
1460C22⋊C4—681no—
1461C22⋊C4—681no—
1462C22⋊C4—681no—
1463C22⋊C4—681no—
1464C22⋊C4—681no—
1465C22⋊C4—681no—
1466C22⋊C4—681no—
1467C42—22no—
1468C42—174no—
1469C42—342no—
1470C42—342no—
1471C42—342no—
1472C42—681no—
1473C42—681no—
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—
1526C23C2×D4×D1712yes—
1527C23C2×D4×D1712yes—
1528C23#41×D1712yes—
1529C23#41×D1712yes—
1530C23C24×D1711yescharacteristic
1531Q8—1362no—
1532D4—28no—
1533D4—44no—
1534D4—82no—
1535D4—348no—
1536D4—348no—
1537D4—348no—
1538D4—684no—
1539D4—684no—
1540D4—1362no—
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—21no—
1552C2×C4—21no—
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—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—44no—
1576C2×C4—44no—
1577C2×C4—44no—
1578C2×C4—82no—
1579C2×C4—172no—
1580C2×C4—172no—
1581C2×C4—172no—
1582C2×C4—172no—
1583C2×C4—172no—
1584C2×C4—348no—
1585C2×C4—348no—
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—341no—
1616C2×C4—341no—
1617C2×C4—341no—
1618C2×C4—341no—
1619C2×C4—341no—
1620C2×C4—684no—
1621C2×C4—684no—
1622C2×C4—684no—
1623C2×C4—684no—
1624C2×C4—684no—
1625C2×C4—684no—
1626C2×C4—684no—
1627C2×C4—684no—
1628C2×C4—684no—
1629C2×C4—684no—
1630C2×C4—1362no—
1631C2×C4—1362no—
1632C2×C4C2×D4×D1712yes—
1633C2×C4#1058769112yes—
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#1176331714yes—
1678C22C22×D4×D1711yescharacteristic
1679C22C2×#41×D1711yescharacteristic
1680C22C2×#41×D1711yescharacteristic
1681C22H(5,𝔽2)×D1711yescharacteristic
1682C22C2×#1058769111yescharacteristic
1683C222−1+4×D1711yescharacteristic
1684C22#1176364511yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—41no—
1697C4—342no—
1698C4—342no—
1699C4—342no—
1700C4—342no—
1701C4—342no—
1702C4—681no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4—681no—
1710C2—24no—
1711C2—42no—
1712C2—81no—
1713C2—344no—
1714C2—682no—
1715C2—682no—
1716C2C2×#1176331711yescharacteristic
1717C2D17×#53911yescharacteristic
1718C2#1454219111yescharacteristic
1719C2#1454241211yescharacteristic
1720C2#1454245811yescharacteristic
1721C2#1454271511yescharacteristic
1722C2#1454282611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2443C2
prime radical#14532155C2
hypercenter#2443D17
hypocenterC17#34991
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2443

Complements

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

NH ≅ G/Ntype
1. C2×#11763404C2semidirect
2. C2×C4×D4×D17C2semidirect
3. #14537098C2semidirect
4. #14537091C2semidirect
5. #14537073C2semidirect
6. #14537070C2semidirect
7. #14534703C2semidirect
8. #14534682C2semidirect
9. #14534654C2semidirect
10. #14534624C2semidirect
11. #14533023C2semidirect
12. #14532918C2semidirect
13. #14532817C2semidirect
14. #14532778C2semidirect
15. #14532733C2semidirect
16. #14532663C2semidirect
17. #14532596C2semidirect
18. #14532593C2semidirect
19. #14532449C2semidirect
20. #14532337C2semidirect
21. #14532255C2semidirect
22. #14532239C2semidirect
23. #14532183C2semidirect
25. #14532110C2semidirect
26. #14531485C2semidirect
27. #14531452C2semidirect
28. #14531410C2semidirect
29. #14531289C2semidirect
30. C2×#11762680C2semidirect
31. C17×#2443C2semidirect
36. C2×#10587565C22semidirect
37. C2×#10587565C22semidirect
38. C2×#10587575C22semidirect
39. C2×#10587575C22semidirect
42. C2×#10587621C22semidirect
43. C2×#10587621C22semidirect
44. C2×#10587621C22semidirect
45. C2×#10587610C22semidirect
47. C2×#10587582C22semidirect
48. C2×#10587564C22semidirect
49. C2×#10587564C22semidirect
55. C2×D4×Dic17C22semidirect
62. C2×#10587567C22semidirect
64. C22×#63225C22semidirect
71. #11762747C22semidirect
72. #11762744C22semidirect
73. #11762744C22semidirect
74. #11762743C22semidirect
75. #11762740C22semidirect
76. #11762740C22semidirect
77. #11762738C22semidirect
78. #11762738C22semidirect
79. #11762738C22semidirect
80. #11762737C22semidirect
81. #11762737C22semidirect
82. #11762733C22semidirect
83. #11762732C22semidirect
84. #11762731C22semidirect
85. #11762731C22semidirect
86. #11762729C22semidirect
93. #11762724C22semidirect
94. #11762724C22semidirect
95. #11762724C22semidirect
96. #11762722C22semidirect
99. #11762706C22semidirect
100. #11762705C22semidirect
101. #11762705C22semidirect
102. #11762704C22semidirect
103. #11762703C22semidirect
104. #11762703C22semidirect
105. #11762702C22semidirect
106. #11762698C22semidirect
107. #11762698C22semidirect
108. #11762698C22semidirect
109. #11762697C22semidirect
110. #11762696C22semidirect
111. #11762695C22semidirect
112. #11762694C22semidirect
113. #11762693C22semidirect
114. #11762693C22semidirect
115. #11762692C22semidirect
116. #11762692C22semidirect
117. #11762692C22semidirect
118. #11762691C22semidirect
122. #11762686C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
129. #11762685C22semidirect
134. #11762683C22semidirect
135. #11762683C22semidirect
136. #11762682C22semidirect
137. #11762682C22semidirect
138. #11762682C22semidirect
139. #11762681C22semidirect
140. #11762681C22semidirect
147. #11762680C22semidirect
148. #11762680C22semidirect
149. #11762680C22semidirect
150. #11762680C22semidirect
151. #11762680C22semidirect
152. #11762680C22semidirect
153. #11762680C22semidirect
154. #11762676C22semidirect
155. #11762673C22semidirect
156. #11762672C22semidirect
157. #11762670C22semidirect
158. #11762670C22semidirect
162. #11762668C22semidirect
163. #11762667C22semidirect
164. #11762667C22semidirect
169. C22⋊C4×Dic17C22semidirect
171. #11762656C22semidirect
172. C2×#10587502C22semidirect
173. C2×#10587502C22semidirect
174. C2×C17×#123C22semidirect
177. C22×C4⋊C4×C17C22semidirect
178. C17×#399C22semidirect
179. C17×#398C22semidirect
180. C17×#397C22semidirect
181. C17×#394C22semidirect
182. C17×#388C22semidirect
183. C17×#387C22semidirect
185. C17×#386C22semidirect
186. C17×#386C22semidirect
187. C17×#385C22semidirect
188. C17×#385C22semidirect
272. D4×Dic17D4semidirect
791. #2443D17semidirect
854. C2×D17#539semidirect
893. C2×#123C2×D17semidirect
917. C22×C4⋊C4C2×D17semidirect
926. #399C2×D17semidirect
930. #398C2×D17semidirect
936. #397C2×D17semidirect
951. #394C2×D17semidirect
966. #388C2×D17semidirect
976. #387C2×D17semidirect
989. #386C2×D17semidirect
990. #386C2×D17semidirect
1015. #385C2×D17semidirect
1016. #385C2×D17semidirect
1252. C17#34991semidirect

Maximal subgroups

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

subgroupindex
C2×#117634042
C2×C4×D4×D172
#145370982
#145370912
#145370732
#145370702
#145347032
#145346822
#145346542
#145346242
#145330232
#145329182
#145328172
#145327782
#145327332
#145326632
#145325962
#145325932
#145324492
#145323372
#145322552
#145322392
#145321832
#145321552
#145321102
#145314852
#145314522
#145314102
#145312892
C2×#117626802
C17×#24432
#3499117