Finite Group Databasebeta

← #16961990

Subgroups — #16961990

Order 4352.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762699C211yesmaximal, characteristic
2C2×#11762683C211yesmaximal, characteristic
3C2×#11762671C211yesmaximal, characteristic
4#14527050C211yesmaximal, characteristic, complemented
5#14527045C211yesmaximal, characteristic, complemented
6#14527043C211yesmaximal, characteristic, complemented
7#14527041C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic
9#14527030C211yesmaximal, characteristic
10#14527022C211yesmaximal, characteristic
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527014C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27#11762699—24no—
28#11762683C418yescomplemented
29#11762671—24no—
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
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C42×C17C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×C4×D17—22no—
70C22×C4×D17—22no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17—41no—
74C22×C4×D17—41no—
75C22×C4×D17C2×C414yes—
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—41no—
79C2×C42×C17—22no—
80C2×C42×C17—41no—
81C2×C42×C17—41no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—41no—
92C2×#63227—41no—
93C2×#63227—41no—
94C2×#63227—41no—
95C2×#63227—41no—
96C2×#63227—41no—
97C2×#63227C2×C414yes—
98C2×#63227C2×C414yes—
99C2×#63227D414yes—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—41no—
102C2×C4⋊Dic17—41no—
103C2×C4⋊Dic17—41no—
104C2×C4⋊Dic17—41no—
105C2×C4⋊Dic17C2×C414yes—
106C2×#63225—41no—
107C2×#63225—41no—
108C2×#63225C2×C414yes—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—41no—
111C2×C4×Dic17—41no—
112C17×#95—22no—
113C17×#95—22no—
114C17×#95—22no—
115C17×#95—41no—
116C17×#95C2×C414yes—
117#10587502—22no—
118#10587502—22no—
119#10587502—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—41no—
126#10587502—41no—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502C2×C414yes—
134C24×C17C2411yescharacteristic
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×D17—21no—
146C23×D17—21no—
147C23×D17C22×C412yes—
148C23×D17C2×D412yes—
149C23×D17#4112yes—
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×C17C22×C412yes—
192C22×C4×C17C22×C412yes—
193C22×C4×C17C22×C412yes—
194C22×C4×C17C2×D412yes—
195C22×C4×C17#4112yes—
196C22×C4×C17#4112yes—
197C22×C4×C17#4112yes—
198C22×C4×C17#4112yes—
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×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17C22×C412yes—
245C22×Dic17C22×C412yes—
246C22×Dic17C22×C412yes—
247C22×Dic17C2×D412yes—
248C2×C4×D17—28no—
249C2×C4×D17—44no—
250C2×C4×D17—44no—
251C2×C4×D17—44no—
252C2×C4×D17—44no—
253C2×C4×D17—44no—
254C2×C4×D17—44no—
255C4⋊C4×C17—44no—
256C42×C17—44no—
257#63227—28no—
258#63227—28no—
259#63227—44no—
260#63227—44no—
261#63227—44no—
262#63227—44no—
263C4⋊Dic17—44no—
264C4⋊Dic17—44no—
265#63225—44no—
266C4×Dic17—44no—
267#14384—171nomaximal, Sylow
268C23×C17C23×C411yescharacteristic
269C23×C17C22×D411yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17C2×#4111yescharacteristic
272C23×C17C2×#4111yescharacteristic
273C23×C17C2×#4111yescharacteristic
274C23×C17C2×#4111yescharacteristic
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
281C23×C172−1+411yescharacteristic
282C23×C172−1+411yescharacteristic
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—22no—
300C22×D17—22no—
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×D17—41no—
316C22×D17—41no—
317C22×D17C4×D414yes—
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—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
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×C4×C17—41no—
366C2×C4×C17#11714yes—
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—41no—
380C2×Dic17—41no—
381C2×Dic17—41no—
382C2×Dic17—41no—
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—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C4×D17—416no—
417C2×#388—171no—
418C2×#385—171no—
419C2×#381—171no—
420#1445—171no—
421#1443—171no—
422#1442—171no—
423#1442—171no—
424#1440—171no—
425#1439—171no—
426#1437—171no—
427#1436—171no—
428#1436—171no—
429#1436D1711yescharacteristic, complemented
430C4⋊#95—171no—
431C22⋊#95—171no—
432C22×C17C2×#11711yescharacteristic
433C22×C17C2×C4×D411yescharacteristic
434C22×C17C4×#4111yescharacteristic
435C22×C17#51811yescharacteristic
436C22×C17#51811yescharacteristic
437C22×C17#51911yescharacteristic
438C22×C17#52011yescharacteristic
439C22×C17#53411yescharacteristic
440C22×C17#53511yescharacteristic
441C22×C17#53811yescharacteristic
442C22×C17#53811yescharacteristic
443C22×C17#53811yescharacteristic
444C22×C17#53811yescharacteristic
445C22×C17#53911yescharacteristic
446C22×C17#53911yescharacteristic
447C22×C17#53911yescharacteristic
448C22×C17#53911yescharacteristic
449C22×C17#54211yescharacteristic
450C22×C17#54211yescharacteristic
451C22×C17#54611yescharacteristic
452C22×C17#54711yescharacteristic
453C22×C17#54711yescharacteristic
454C22×C17#54711yescharacteristic
455C22×C17#55111yescharacteristic
456C22×C17#55211yescharacteristic
457C22×C17#55211yescharacteristic
458C22×C17#55211yescharacteristic
459C22×C17#55311yescharacteristic
460C22×C17#55311yescharacteristic
461C22×C17#55911yescharacteristic
462C22×C17#55911yescharacteristic
463C22×C17#56211yescharacteristic
464C22×C17#56211yescharacteristic
465C22×C17#56311yescharacteristic
466C22×C17#56311yescharacteristic
467C2×D17—24no—
468C2×D17—24no—
469C2×D17—24no—
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—
480C2×D17—42no—
481C2×D17—42no—
482C4×C17—24no—
483C4×C17—42no—
484C4×C17—42no—
485C4×C17—42no—
486C4×C17—42no—
487C4×C17—42no—
488C4×C17—81no—
489Dic17—42no—
490Dic17—42no—
491Dic17—42no—
492Dic17—42no—
493Dic17—81no—
494Dic17—81no—
495Dic17—81no—
496C24×C4—171no—
497C22×C4⋊C4—171no—
498C22×C4⋊C4—171no—
499C22×C4⋊C4—171no—
500C22×C4⋊C4C2×D1711yescharacteristic
501C22×C22⋊C4—171no—
502C22×C22⋊C4—171no—
503C22×C22⋊C4—171no—
504C22×C22⋊C4—171no—
505C22×C22⋊C4—171no—
506C22×C22⋊C4—171no—
507C22×C42—171no—
508C22×C42C2×D1711yescharacteristic
509#388—344no—
510#385—178no—
511#381—344no—
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×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95C2×D1711yescharacteristic
530C2×#95C2×D1711yescharacteristic
531C2×#95C2×D1711yescharacteristic
532C2×#95C2×D1711yescharacteristic
533C2×#95C2×D1711yescharacteristic
534C2×C17#231811yescharacteristic
535C2×C17#232111yescharacteristic
536C2×C17#233211yescharacteristic
537C2×C17#234411yescharacteristic
538C2×C17#235711yescharacteristic
539C2×C17#235911yescharacteristic
540C2×C17#237811yescharacteristic
541C2×C17#270811yescharacteristic
542C2×C17#271011yescharacteristic
543C2×C17#271811yescharacteristic
544C2×C17#272411yescharacteristic
545C2×C17#275011yescharacteristic
546C2×C17#275111yescharacteristic
547C2×C17#276511yescharacteristic
548C2×C17#277111yescharacteristic
549D17—44no—
550C25—171no—
551C23×C4—171no—
552C23×C4—171no—
553C23×C4—171no—
554C23×C4—171no—
555C23×C4—174no—
556C23×C4—171no—
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—342no—
560C23×C4—342no—
561C23×C4—681no—
562C23×C4—681no—
563C23×C4—681no—
564C23×C4—681no—
565C23×C4C22×D1711yescharacteristic
566C23×C4C22×D1711yescharacteristic
567C23×C4C22×D1711yescharacteristic
568C23×C4C22×D1711yescharacteristic
569C23×C4C22×D1711yescharacteristic
570C23×C4C22×D1711yescharacteristic
571C23×C4C22×D1711yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—174no—
576C2×C4⋊C4—174no—
577C2×C4⋊C4—342no—
578C2×C4⋊C4—681no—
579C2×C4⋊C4—681no—
580C2×C4⋊C4—681no—
581C2×C4⋊C4—681no—
582C2×C4⋊C4—681no—
583C2×C4⋊C4—681no—
584C2×C22⋊C4—174no—
585C2×C22⋊C4—174no—
586C2×C22⋊C4—174no—
587C2×C22⋊C4—342no—
588C2×C22⋊C4—342no—
589C2×C22⋊C4—342no—
590C2×C22⋊C4—342no—
591C2×C22⋊C4—342no—
592C2×C22⋊C4—342no—
593C2×C22⋊C4—342no—
594C2×C22⋊C4—342no—
595C2×C22⋊C4—342no—
596C2×C22⋊C4—681no—
597C2×C22⋊C4—681no—
598C2×C22⋊C4—681no—
599C2×C22⋊C4—681no—
600C2×C22⋊C4—681no—
601C2×C22⋊C4—681no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—342no—
606C2×C42—681no—
607C2×C42—681no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—174no—
613#95—342no—
614#95—342no—
615#95—342no—
616#95—342no—
617#95—342no—
618#95—342no—
619#95—342no—
620#95—342no—
621#95—681no—
622#95—681no—
623#95—681no—
624#95—681no—
625#95—681no—
626#95—681no—
627#95—681no—
628#95—681no—
629#95C4×D1714yes—
630C17#1438411yescharacteristic, complemented, Sylow
631C24—172no—
632C24—172no—
633C24—172no—
634C24—341no—
635C24—341no—
636C24—341no—
637C24—341no—
638C24—341no—
639C24—341no—
640C24—341no—
641C24—341no—
642C24—341no—
643C24—341no—
644C24—341no—
645C24—341no—
646C24C23×D1711yescharacteristic
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—21no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—348no—
693C22×C4—341no—
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—341no—
737C22×C4—341no—
738C22×C4—684no—
739C22×C4—684no—
740C22×C4—684no—
741C22×C4—684no—
742C22×C4—684no—
743C22×C4—684no—
744C22×C4C2×C4×D1712yes—
745C22×C4C2×C4×D1712yes—
746C22×C4C2×C4×D1712yes—
747C22×C4#6325212yes—
748C22×C4#6325212yes—
749C22×C4D4×D1712yes—
750C22×C4#6325412yes—
751C22×C4#6325612yes—
752C4⋊C4—44no—
753C4⋊C4—684no—
754C4⋊C4—684no—
755C4⋊C4—684no—
756C22⋊C4—348no—
757C22⋊C4—348no—
758C22⋊C4—684no—
759C22⋊C4—684no—
760C22⋊C4—684no—
761C22⋊C4—684no—
762C42—44no—
763C42—684no—
764C23—174no—
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—342no—
780C23—342no—
781C23—342no—
782C23—342no—
783C23—681no—
784C23—681no—
785C23—681no—
786C23—681no—
787C23—681no—
788C23—681no—
789C23—681no—
790C23—681no—
791C23—681no—
792C23—681no—
793C23—681no—
794C23—681no—
795C23—681no—
796C23—681no—
797C23—681no—
798C23—681no—
799C23C22×C4×D1711yescharacteristic
800C23C2×#6325211yescharacteristic
801C23C2×#6325211yescharacteristic
802C23C2×D4×D1711yescharacteristic
803C23C2×#6325411yescharacteristic
804C23#1058769111yescharacteristic
805C23#1058769111yescharacteristic
806C23C2×#6325611yescharacteristic
807C23#1058769411yescharacteristic
808C23#41×D1711yescharacteristic
809C23#1058769611yescharacteristic
810C23#1058769611yescharacteristic
811C23#1058769611yescharacteristic
812C23#1058769711yescharacteristic
813C23#1058769711yescharacteristic
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—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
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—41no—
860C2×C4—41no—
861C2×C4—41no—
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—6816no—
875C2×C4—681no—
876C2×C4—681no—
877C2×C4—681no—
878C2×C4—681no—
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—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4#1058757814yes—
913C22—344no—
914C22—344no—
915C22—344no—
916C22—682no—
917C22—682no—
918C22—682no—
919C22—682no—
920C22—682no—
921C22—682no—
922C22—682no—
923C22—682no—
924C22—682no—
925C22—682no—
926C22—682no—
927C22—682no—
928C22C2×#1058757811yescharacteristic
929C22C4×D4×D1711yescharacteristic
930C22C4×#6325211yescharacteristic
931C22#1176328111yescharacteristic
932C22#1176328311yescharacteristic
933C22#1176328511yescharacteristic
934C22#1176328811yescharacteristic
935C22#1176336711yescharacteristic
936C22#1176337711yescharacteristic
937C22#1176339411yescharacteristic
938C22#1176339511yescharacteristic
939C22#1176339811yescharacteristic
940C22#1176339911yescharacteristic
941C22#1176340111yescharacteristic
942C22#1176340311yescharacteristic
943C22#1176340611yescharacteristic
944C22#1176340811yescharacteristic
945C22#1176343011yescharacteristic
946C22#1176343111yescharacteristic
947C22#1176344911yescharacteristic
948C22#1176345911yescharacteristic
949C22#1176346211yescharacteristic
950C22#1176346411yescharacteristic
951C22#1176348811yescharacteristic
952C22#1176349311yescharacteristic
953C22#1176349711yescharacteristic
954C22#1176349811yescharacteristic
955C22#1176350511yescharacteristic
956C22#1176350511yescharacteristic
957C22#1176354411yescharacteristic
958C22#1176354411yescharacteristic
959C22#1176355511yescharacteristic
960C22#1176355611yescharacteristic
961C22#1176356111yescharacteristic
962C22#1176356311yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—682no—
971C4—682no—
972C4—682no—
973C4—682no—
974C4—1361no—
975C4—1361no—
976C4—1361no—
977C2—684no—
978C2#1453141211yescharacteristic
979C2#1453143711yescharacteristic
980C2#1453153511yescharacteristic
981C2#1453165211yescharacteristic
982C2#1453175511yescharacteristic
983C2#1453177711yescharacteristic
984C2#1453194811yescharacteristic
985C2#1453549711yescharacteristic
986C2#1453552111yescharacteristic
987C2#1453563111yescharacteristic
988C2#1453571311yescharacteristic
989C2#1453602511yescharacteristic
990C2#1453604011yescharacteristic
991C2#1453621611yescharacteristic
992C2#1453630011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#14384
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #14527050C2semidirect
5. #14527045C2semidirect
6. #14527043C2semidirect
7. #14527041C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527014C2semidirect
15. C17×#1436C2semidirect
28. #11762683C4semidirect
429. #1436D17semidirect
630. C17#14384semidirect

Maximal subgroups

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

subgroupindex
C2×#117626992
C2×#117626832
C2×#117626712
#145270502
#145270452
#145270432
#145270412
#145270322
#145270302
#145270222
#145270182
#145270152
#145270142
#145270052
C17×#14362
#1438417