Finite Group Databasebeta

← #16962913

Subgroups — #16962913

Order 4352.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762683C211yesmaximal, characteristic
2#14527051C211yesmaximal, characteristic, complemented
3#14527046C211yesmaximal, characteristic, complemented
4#14527042C211yesmaximal, characteristic, complemented
5#14527028C211yesmaximal, characteristic
6#14527026C211yesmaximal, characteristic
7#14527020C211yesmaximal, characteristic
8#14527020C211yesmaximal, characteristic
9#14527018C211yesmaximal, characteristic, complemented
10#14527016C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527012C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic
15C17×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28#11762683C418yescomplemented
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C22×C4⋊C4×C17C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C24×D17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×Dic17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C22×C4×D17—41no—
68C22×C4×D17—41no—
69C22×C4×D17—41no—
70C22×C4×D17—41no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17C2×C414yes—
74C2×C4⋊C4×C17—22no—
75C2×C4⋊C4×C17—41no—
76C2×C4⋊C4×C17—41no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—22no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—41no—
85C2×#63227—41no—
86C2×#63227—41no—
87C2×#63227—41no—
88C2×#63227—41no—
89C2×#63227—41no—
90C2×#63227—41no—
91C2×#63227—41no—
92C2×#63227C2×C414yes—
93C2×#63227C2×C414yes—
94C2×#63227Q814yes—
95C2×C4⋊Dic17—41no—
96C2×C4⋊Dic17—41no—
97C2×C4⋊Dic17C2×C414yes—
98C2×#63225—22no—
99C2×#63225—41no—
100C2×#63225—41no—
101C2×#63225—41no—
102C2×#63225—41no—
103C2×#63225C2×C414yes—
104C2×C4×Dic17—22no—
105C2×C4×Dic17—41no—
106C2×C4×Dic17—41no—
107C2×C4×Dic17—41no—
108C2×C4×Dic17—41no—
109C2×C4×Dic17—41no—
110C17×#95—22no—
111C17×#95—41no—
112C17×#95—41no—
113C17×#95—41no—
114C17×#95—41no—
115C17×#95C2×C414yes—
116#10587502—22no—
117#10587502—22no—
118#10587502—22no—
119#10587502—22no—
120#10587502—41no—
121#10587502—41no—
122#10587502—41no—
123#10587502—41no—
124#10587502—41no—
125#10587502—41no—
126#10587502—41no—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502C2×C414yes—
132C24×C17C2411yescharacteristic
133C23×D17—21no—
134C23×D17—21no—
135C23×D17—21no—
136C23×D17—21no—
137C23×D17—21no—
138C23×D17—21no—
139C23×D17—21no—
140C23×D17—21no—
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17C22×C412yes—
146C23×D17C2×Q812yes—
147C23×D17#4112yes—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17C22×C412yes—
193C22×C4×C17C22×C412yes—
194C22×C4×C17C22×C412yes—
195C22×C4×C17C2×Q812yes—
196C22×C4×C17#4112yes—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17C22×C412yes—
240C22×Dic17C22×C412yes—
241C22×Dic17C22×C412yes—
242C22×Dic17C2×Q812yes—
243C22×Dic17#4112yes—
244C22×Dic17#4112yes—
245C22×Dic17#4112yes—
246C2×C4×D17—44no—
247C2×C4×D17—44no—
248C2×C4×D17—44no—
249C2×C4×D17—44no—
250C2×C4×D17—44no—
251C2×C4×D17—44no—
252C2×C4×D17—44no—
253C4⋊C4×C17—44no—
254#63227—28no—
255#63227—44no—
256#63227—44no—
257#63227—44no—
258#63227—44no—
259#63227—44no—
260C4⋊Dic17—44no—
261#63225—44no—
262#63225—44no—
263C4×Dic17—44no—
264C4×Dic17—44no—
265#14457—171nomaximal, Sylow
266C23×C17C23×C411yescharacteristic
267C23×C17C22×Q811yescharacteristic
268C23×C17C2×#4111yescharacteristic
269C23×C17C2×#4111yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17C2×#4111yescharacteristic
272C23×C17C2×#4111yescharacteristic
273C23×C17H(5,𝔽2)11yescharacteristic
274C23×C17H(5,𝔽2)11yescharacteristic
275C23×C17H(5,𝔽2)11yescharacteristic
276C23×C17H(5,𝔽2)11yescharacteristic
277C23×C17H(5,𝔽2)11yescharacteristic
278C23×C17H(5,𝔽2)11yescharacteristic
279C23×C17H(5,𝔽2)11yescharacteristic
280C23×C172−1+411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17—22no—
287C22×D17—22no—
288C22×D17—22no—
289C22×D17—22no—
290C22×D17—22no—
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—22no—
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—41no—
300C22×D17—41no—
301C22×D17—41no—
302C22×D17—41no—
303C22×D17—41no—
304C22×D17—41no—
305C22×D17—41no—
306C22×D17—41no—
307C22×D17—41no—
308C22×D17—41no—
309C22×D17—41no—
310C22×D17—41no—
311C22×D17—41no—
312C22×D17—41no—
313C22×D17—41no—
314C22×D17—41no—
315C22×D17C4×Q814yes—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—41no—
332C2×C4×C17—41no—
333C2×C4×C17—41no—
334C2×C4×C17—41no—
335C2×C4×C17—41no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×Dic17—22no—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—41no—
384C2×Dic17—41no—
385C2×Dic17—41no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17#11714yes—
414C4×D17—416no—
415C2×#385—171no—
416#1445—171no—
417#1443—171no—
418#1442—171no—
419#1442D1711yescharacteristic, complemented
420#1439—171no—
421#1439—171no—
422#1437—171no—
423#1437—171no—
424#1436—171no—
425#1436—171no—
426#1436—171no—
427C4⋊#95—171no—
428C22⋊#95—171no—
429C22⋊#95—171no—
430C22×C17C2×#11711yescharacteristic
431C22×C17C2×C4×Q811yescharacteristic
432C22×C17C4×#4111yescharacteristic
433C22×C17#51811yescharacteristic
434C22×C17#51811yescharacteristic
435C22×C17#51811yescharacteristic
436C22×C17#52011yescharacteristic
437C22×C17#53811yescharacteristic
438C22×C17#53811yescharacteristic
439C22×C17#53811yescharacteristic
440C22×C17#53811yescharacteristic
441C22×C17#53911yescharacteristic
442C22×C17#53911yescharacteristic
443C22×C17#53911yescharacteristic
444C22×C17#53911yescharacteristic
445C22×C17#54011yescharacteristic
446C22×C17#54211yescharacteristic
447C22×C17#54311yescharacteristic
448C22×C17#54411yescharacteristic
449C22×C17#55111yescharacteristic
450C22×C17#55111yescharacteristic
451C22×C17#55311yescharacteristic
452C22×C17#55311yescharacteristic
453C22×C17#55311yescharacteristic
454C22×C17#55311yescharacteristic
455C22×C17#55411yescharacteristic
456C22×C17#55411yescharacteristic
457C22×C17#55411yescharacteristic
458C22×C17#55411yescharacteristic
459C22×C17#55911yescharacteristic
460C22×C17#55911yescharacteristic
461C22×C17#56011yescharacteristic
462C22×C17#56011yescharacteristic
463C22×C17#56011yescharacteristic
464C22×C17H(3,𝔽4)11yescharacteristic
465C2×D17—24no—
466C2×D17—24no—
467C2×D17—24no—
468C2×D17—42no—
469C2×D17—42no—
470C2×D17—42no—
471C2×D17—42no—
472C2×D17—42no—
473C2×D17—42no—
474C2×D17—42no—
475C2×D17—42no—
476C2×D17—42no—
477C2×D17—42no—
478C2×D17—42no—
479C2×D17—42no—
480C4×C17—42no—
481C4×C17—42no—
482C4×C17—42no—
483C4×C17—42no—
484C4×C17—42no—
485C4×C17—81no—
486C4×C17—81no—
487Dic17—24no—
488Dic17—42no—
489Dic17—42no—
490Dic17—42no—
491Dic17—42no—
492Dic17—81no—
493Dic17—81no—
494C24×C4—171no—
495C22×C4⋊C4—171no—
496C22×C4⋊C4—171no—
497C22×C4⋊C4—171no—
498C22×C4⋊C4C2×D1711yescharacteristic
499C22×C22⋊C4—171no—
500C22×C22⋊C4—171no—
501C22×C22⋊C4—171no—
502C22×C22⋊C4—171no—
503C22×C22⋊C4—171no—
504C22×C22⋊C4—171no—
505C22×C42—171no—
506C22×C42—171no—
507#385—178no—
508C2×#95—171no—
509C2×#95—171no—
510C2×#95—171no—
511C2×#95—171no—
512C2×#95—171no—
513C2×#95—171no—
514C2×#95—171no—
515C2×#95—171no—
516C2×#95—171no—
517C2×#95—171no—
518C2×#95—171no—
519C2×#95—171no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95C2×D1711yescharacteristic
525C2×#95C2×D1711yescharacteristic
526C2×#95C2×D1711yescharacteristic
527C2×#95C2×D1711yescharacteristic
528C2×#95C2×D1711yescharacteristic
529C2×#95C2×D1711yescharacteristic
530C2×C17#231811yescharacteristic
531C2×C17#232911yescharacteristic
532C2×C17#233511yescharacteristic
533C2×C17#234511yescharacteristic
534C2×C17#235711yescharacteristic
535C2×C17#236811yescharacteristic
536C2×C17#237511yescharacteristic
537C2×C17#277811yescharacteristic
538C2×C17#278011yescharacteristic
539C2×C17#278211yescharacteristic
540C2×C17#279011yescharacteristic
541C2×C17#279611yescharacteristic
542C2×C17#279711yescharacteristic
543C2×C17#280411yescharacteristic
544C2×C17#280711yescharacteristic
545D17—44no—
546C25—171no—
547C23×C4—171no—
548C23×C4—171no—
549C23×C4—171no—
550C23×C4—171no—
551C23×C4—171no—
552C23×C4—174no—
553C23×C4—171no—
554C23×C4—171no—
555C23×C4—681no—
556C23×C4—681no—
557C23×C4—681no—
558C23×C4—681no—
559C23×C4—681no—
560C23×C4—681no—
561C23×C4C22×D1711yescharacteristic
562C23×C4C22×D1711yescharacteristic
563C23×C4C22×D1711yescharacteristic
564C23×C4C22×D1711yescharacteristic
565C23×C4C22×D1711yescharacteristic
566C23×C4C22×D1711yescharacteristic
567C23×C4C22×D1711yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—174no—
572C2×C4⋊C4—174no—
573C2×C4⋊C4—342no—
574C2×C4⋊C4—681no—
575C2×C4⋊C4—681no—
576C2×C4⋊C4—681no—
577C2×C4⋊C4—681no—
578C2×C4⋊C4—681no—
579C2×C4⋊C4—681no—
580C2×C22⋊C4—174no—
581C2×C22⋊C4—174no—
582C2×C22⋊C4—174no—
583C2×C22⋊C4—342no—
584C2×C22⋊C4—342no—
585C2×C22⋊C4—342no—
586C2×C22⋊C4—342no—
587C2×C22⋊C4—342no—
588C2×C22⋊C4—342no—
589C2×C22⋊C4—342no—
590C2×C22⋊C4—681no—
591C2×C22⋊C4—681no—
592C2×C22⋊C4—681no—
593C2×C22⋊C4—681no—
594C2×C22⋊C4—681no—
595C2×C22⋊C4—681no—
596C2×C22⋊C4—681no—
597C2×C22⋊C4—681no—
598C2×C42—342no—
599C2×C42—681no—
600C2×C42—681no—
601C2×C42—681no—
602C2×C42—681no—
603C2×C42—681no—
604#95—22no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—174no—
610#95—342no—
611#95—342no—
612#95—342no—
613#95—342no—
614#95—681no—
615#95—681no—
616#95—681no—
617#95—681no—
618#95—681no—
619#95—681no—
620#95—681no—
621#95—681no—
622#95—681no—
623#95—681no—
624#95—681no—
625#95C4×D1714yes—
626C17#1445711yescharacteristic, complemented, Sylow
627C24—172no—
628C24—172no—
629C24—172no—
630C24—341no—
631C24—341no—
632C24—341no—
633C24—341no—
634C24—341no—
635C24—341no—
636C24—341no—
637C24—341no—
638C24—341no—
639C24—341no—
640C24—341no—
641C24—341no—
642C24C23×D1711yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—341no—
695C22×C4—341no—
696C22×C4—341no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—684no—
737C22×C4—684no—
738C22×C4—684no—
739C22×C4—684no—
740C22×C4—684no—
741C22×C4—684no—
742C22×C4—684no—
743C22×C4C2×C4×D1712yes—
744C22×C4C2×C4×D1712yes—
745C22×C4C2×C4×D1712yes—
746C22×C4#6325412yes—
747C22×C4Q8×D1712yes—
748C4⋊C4—44no—
749C4⋊C4—684no—
750C4⋊C4—684no—
751C4⋊C4—684no—
752C22⋊C4—348no—
753C22⋊C4—684no—
754C22⋊C4—684no—
755C22⋊C4—684no—
756C22⋊C4—684no—
757C22⋊C4—684no—
758C42—684no—
759C42—684no—
760C23—174no—
761C23—342no—
762C23—342no—
763C23—342no—
764C23—342no—
765C23—342no—
766C23—342no—
767C23—342no—
768C23—342no—
769C23—342no—
770C23—342no—
771C23—342no—
772C23—342no—
773C23—342no—
774C23—342no—
775C23—342no—
776C23—342no—
777C23—342no—
778C23—342no—
779C23—681no—
780C23—681no—
781C23—681no—
782C23—681no—
783C23—681no—
784C23—681no—
785C23—681no—
786C23—681no—
787C23—681no—
788C23—681no—
789C23—681no—
790C23—681no—
791C23—681no—
792C23—681no—
793C23—681no—
794C23—681no—
795C23C22×C4×D1711yescharacteristic
796C23C2×#6325411yescharacteristic
797C23#1058769111yescharacteristic
798C23#1058769111yescharacteristic
799C23#1058769111yescharacteristic
800C23C2×Q8×D1711yescharacteristic
801C23#1058769411yescharacteristic
802C23#41×D1711yescharacteristic
803C23#41×D1711yescharacteristic
804C23#41×D1711yescharacteristic
805C23#41×D1711yescharacteristic
806C23#1058769611yescharacteristic
807C23#1058769611yescharacteristic
808C23#1058769611yescharacteristic
809C23#1058769611yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—174no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—6816no—
879C2×C4—681no—
880C2×C4—681no—
881C2×C4—681no—
882C2×C4—681no—
883C2×C4—681no—
884C2×C4—681no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C22—344no—
910C22—344no—
911C22—344no—
912C22—682no—
913C22—682no—
914C22—682no—
915C22—682no—
916C22—682no—
917C22—682no—
918C22—682no—
919C22—682no—
920C22—682no—
921C22—682no—
922C22—682no—
923C22—682no—
924C22#117×D1711yescharacteristic
925C22C4×Q8×D1711yescharacteristic
926C22C4×#6325411yescharacteristic
927C22#1176328111yescharacteristic
928C22#1176328111yescharacteristic
929C22#1176328311yescharacteristic
930C22#1176329011yescharacteristic
931C22#1176339111yescharacteristic
932C22#1176339311yescharacteristic
933C22#1176339311yescharacteristic
934C22#1176339411yescharacteristic
935C22#1176340511yescharacteristic
936C22#1176340711yescharacteristic
937C22#1176340711yescharacteristic
938C22#1176340711yescharacteristic
939C22#1176341111yescharacteristic
940C22#1176343211yescharacteristic
941C22#1176343411yescharacteristic
942C22#1176343611yescharacteristic
943C22#1176348211yescharacteristic
944C22#1176348411yescharacteristic
945C22#1176350211yescharacteristic
946C22#1176350411yescharacteristic
947C22#1176351011yescharacteristic
948C22#1176351011yescharacteristic
949C22#1176351311yescharacteristic
950C22#1176351511yescharacteristic
951C22#1176351511yescharacteristic
952C22#1176351711yescharacteristic
953C22#1176354111yescharacteristic
954C22#1176354311yescharacteristic
955C22#1176354711yescharacteristic
956C22#1176354911yescharacteristic
957C22#1176355011yescharacteristic
958C22#1176355111yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—81no—
965C4—81no—
966C4—344no—
967C4—682no—
968C4—682no—
969C4—682no—
970C4—682no—
971C4—1361no—
972C4—1361no—
973C2—684no—
974C2#1453142011yescharacteristic
975C2#1453151811yescharacteristic
976C2#1453156911yescharacteristic
977C2#1453165811yescharacteristic
978C2#1453175411yescharacteristic
979C2#1453186611yescharacteristic
980C2#1453192411yescharacteristic
981C2#1453640711yescharacteristic
982C2#1453643111yescharacteristic
983C2#1453646011yescharacteristic
984C2#1453655911yescharacteristic
985C2#1453661911yescharacteristic
986C2#1453664611yescharacteristic
987C2#1453672511yescharacteristic
988C2#1453675411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1442C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1442D17
hypocenterC17#14457
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #14527051C2semidirect
3. #14527046C2semidirect
4. #14527042C2semidirect
9. #14527018C2semidirect
10. #14527016C2semidirect
11. #14527015C2semidirect
12. #14527012C2semidirect
15. C17×#1442C2semidirect
28. #11762683C4semidirect
419. #1442D17semidirect
626. C17#14457semidirect

Maximal subgroups

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

subgroupindex
C2×#117626832
#145270512
#145270462
#145270422
#145270282
#145270262
#145270202
#145270182
#145270162
#145270152
#145270122
#145270052
C17×#14422
#1445717