Finite Group Databasebeta

← #16963198

Subgroups — #16963198

Order 4352.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762700C211yesmaximal, characteristic
2#14527050C211yesmaximal, characteristic, complemented
3#14527045C211yesmaximal, characteristic, complemented
4#14527042C211yesmaximal, characteristic, complemented
5#14527039C211yesmaximal, characteristic, complemented
6#14527032C211yesmaximal, characteristic
7#14527028C211yesmaximal, characteristic
8#14527020C211yesmaximal, characteristic
9#14527015C211yesmaximal, characteristic, complemented
10#14527011C211yesmaximal, characteristic, complemented
11#14527008C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic
13#14527005C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762700C418yescomplemented
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2211yescharacteristic
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×C42×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—22no—
68C22×C4×D17—22no—
69C22×C4×D17—22no—
70C22×C4×D17—41no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17—41no—
74C2×C42×C17—41no—
75C2×C42×C17—41no—
76C2×C42×C17C2×C414yescomplemented
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×#63227C2×C414yes—
95C2×#63225—41no—
96C2×#63225—41no—
97C2×#63225—41no—
98C2×#63225—41no—
99C2×#63225—41no—
100C2×#63225C2×C414yescomplemented
101C2×C4×Dic17—22no—
102C2×C4×Dic17—41no—
103C2×C4×Dic17—41no—
104C17×#95—22no—
105C17×#95—22no—
106C17×#95—41no—
107C17×#95—41no—
108C17×#95—41no—
109C17×#95—41no—
110#10587502—22no—
111#10587502—22no—
112#10587502—22no—
113#10587502—22no—
114#10587502—22no—
115#10587502—41no—
116#10587502—41no—
117#10587502—41no—
118#10587502—41no—
119#10587502—41no—
120#10587502—41no—
121#10587502—41no—
122#10587502—41no—
123#10587502—41no—
124#10587502—41no—
125#10587502—41no—
126#10587502C2×C414yescomplemented
127#10587502C2×C414yescomplemented
128C24×C17C2411yescharacteristic
129C23×D17—21no—
130C23×D17—21no—
131C23×D17—21no—
132C23×D17—21no—
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×D17C22×C412yes—
142C23×D17#4112yes—
143C23×D17#4112yes—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
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×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C22×C412yes—
191C22×C4×C17#4112yes—
192C22×C4×C17#4112yes—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
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×Dic17C22×C412yes—
238C22×Dic17C22×C412yes—
239C22×Dic17C22×C412yes—
240C22×Dic17#4112yes—
241C22×Dic17#4112yes—
242C2×C4×D17—44no—
243C2×C4×D17—44no—
244C2×C4×D17—44no—
245C2×C4×D17—44no—
246C2×C4×D17—44no—
247C2×C4×D17—44no—
248C2×C4×D17—44no—
249C42×C17—44no—
250#63227—28no—
251#63227—44no—
252#63227—44no—
253#63227—44no—
254#63227—44no—
255#63227—44no—
256#63225—44no—
257#63225—44no—
258C4×Dic17—44no—
259#14481—171nomaximal, Sylow
260C23×C17C23×C411yescharacteristic
261C23×C17C2×#4111yescharacteristic
262C23×C17C2×#4111yescharacteristic
263C23×C17C2×#4111yescharacteristic
264C23×C17C2×#4111yescharacteristic
265C23×C17C2×#4111yescharacteristic
266C23×C17C2×#4111yescharacteristic
267C23×C17H(5,𝔽2)11yescharacteristic
268C23×C17H(5,𝔽2)11yescharacteristic
269C23×C17H(5,𝔽2)11yescharacteristic
270C23×C17H(5,𝔽2)11yescharacteristic
271C23×C17H(5,𝔽2)11yescharacteristic
272C23×C17H(5,𝔽2)11yescharacteristic
273C23×C172−1+411yescharacteristic
274C23×C172−1+411yescharacteristic
275C22×D17—22no—
276C22×D17—22no—
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—22no—
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—41no—
294C22×D17—41no—
295C22×D17—41no—
296C22×D17—41no—
297C22×D17—41no—
298C22×D17—41no—
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#11714yes—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
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—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17—41no—
329C2×C4×C17—41no—
330C2×C4×C17—41no—
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×Dic17—22no—
360C2×Dic17—22no—
361C2×Dic17—22no—
362C2×Dic17—22no—
363C2×Dic17—22no—
364C2×Dic17—22no—
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—41no—
375C2×Dic17—41no—
376C2×Dic17—41no—
377C2×Dic17—41no—
378C2×Dic17—41no—
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—
408C4×D17—416no—
409C2×#388—171no—
410#1445—171no—
411#1443—171no—
412#1442—171no—
413#1442—171no—
414#1440—171no—
415#1439—171no—
416#1437—171no—
417#1436—171no—
418#1434—171no—
419#1434—171no—
420#1434D1711yescharacteristic, complemented
421C22⋊#95—171no—
422C22⋊#95—171no—
423C22⋊#95—171no—
424C22×C17C2×#11711yescharacteristic
425C22×C17C4×#4111yescharacteristic
426C22×C17C4×#4111yescharacteristic
427C22×C17#51811yescharacteristic
428C22×C17#51811yescharacteristic
429C22×C17#52011yescharacteristic
430C22×C17#52011yescharacteristic
431C22×C17#53811yescharacteristic
432C22×C17#53811yescharacteristic
433C22×C17#53811yescharacteristic
434C22×C17#53811yescharacteristic
435C22×C17#53811yescharacteristic
436C22×C17#53911yescharacteristic
437C22×C17#53911yescharacteristic
438C22×C17#53911yescharacteristic
439C22×C17#54011yescharacteristic
440C22×C17#54011yescharacteristic
441C22×C17#54011yescharacteristic
442C22×C17#54211yescharacteristic
443C22×C17#55111yescharacteristic
444C22×C17#55111yescharacteristic
445C22×C17#55111yescharacteristic
446C22×C17#55111yescharacteristic
447C22×C17#55111yescharacteristic
448C22×C17#55211yescharacteristic
449C22×C17#55211yescharacteristic
450C22×C17#55211yescharacteristic
451C22×C17#55311yescharacteristic
452C22×C17#55311yescharacteristic
453C22×C17#55311yescharacteristic
454C22×C17#55611yescharacteristic
455C22×C17H(3,𝔽4)11yescharacteristic
456C22×C17#56211yescharacteristic
457C22×C17#56211yescharacteristic
458C22×C17#56311yescharacteristic
459C2×D17—24no—
460C2×D17—24no—
461C2×D17—24no—
462C2×D17—42no—
463C2×D17—42no—
464C2×D17—42no—
465C2×D17—42no—
466C2×D17—42no—
467C2×D17—42no—
468C2×D17—42no—
469C2×D17—42no—
470C2×D17—42no—
471C2×D17—42no—
472C2×D17—42no—
473C2×D17—42no—
474C4×C17—42no—
475C4×C17—42no—
476C4×C17—42no—
477C4×C17—42no—
478C4×C17—42no—
479C4×C17—81no—
480C4×C17—81no—
481Dic17—42no—
482Dic17—42no—
483Dic17—42no—
484Dic17—42no—
485Dic17—42no—
486Dic17—81no—
487Dic17—81no—
488C24×C4—171no—
489C22×C4⋊C4—171no—
490C22×C4⋊C4—171no—
491C22×C22⋊C4—171no—
492C22×C22⋊C4—171no—
493C22×C22⋊C4—171no—
494C22×C22⋊C4—171no—
495C22×C22⋊C4—171no—
496C22×C22⋊C4—171no—
497C22×C42—171no—
498C22×C42C2×D1711yescharacteristic
499#388—178no—
500C2×#95—171no—
501C2×#95—171no—
502C2×#95—171no—
503C2×#95—171no—
504C2×#95—171no—
505C2×#95—171no—
506C2×#95—171no—
507C2×#95—171no—
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×#95C2×D1711yescharacteristic
519C2×#95C2×D1711yescharacteristic
520C2×#95C2×D1711yescharacteristic
521C2×#95C2×D1711yescharacteristic
522C2×#95C2×D1711yescharacteristic
523C2×#95C2×D1711yescharacteristic
524C2×C17#231811yescharacteristic
525C2×C17#233311yescharacteristic
526C2×C17#233511yescharacteristic
527C2×C17#234311yescharacteristic
528C2×C17#235311yescharacteristic
529C2×C17#237311yescharacteristic
530C2×C17#237911yescharacteristic
531C2×C17#273611yescharacteristic
532C2×C17#273811yescharacteristic
533C2×C17#274011yescharacteristic
534C2×C17#274111yescharacteristic
535C2×C17#275011yescharacteristic
536C2×C17#275011yescharacteristic
537C2×C17#275311yescharacteristic
538C2×C17#278711yescharacteristic
539D17—44no—
540C25—171no—
541C23×C4—171no—
542C23×C4—171no—
543C23×C4—171no—
544C23×C4—171no—
545C23×C4—171no—
546C23×C4—171no—
547C23×C4—171no—
548C23×C4—342no—
549C23×C4—342no—
550C23×C4—342no—
551C23×C4—681no—
552C23×C4—681no—
553C23×C4—681no—
554C23×C4—681no—
555C23×C4C22×D1711yescharacteristic
556C23×C4C22×D1711yescharacteristic
557C23×C4C22×D1711yescharacteristic
558C23×C4C22×D1711yescharacteristic
559C23×C4C22×D1711yescharacteristic
560C23×C4C22×D1711yescharacteristic
561C23×C4C22×D1711yescharacteristic
562C2×C4⋊C4—174no—
563C2×C4⋊C4—681no—
564C2×C4⋊C4—681no—
565C2×C4⋊C4—681no—
566C2×C4⋊C4—681no—
567C2×C4⋊C4—681no—
568C2×C22⋊C4—174no—
569C2×C22⋊C4—174no—
570C2×C22⋊C4—174no—
571C2×C22⋊C4—342no—
572C2×C22⋊C4—342no—
573C2×C22⋊C4—342no—
574C2×C22⋊C4—342no—
575C2×C22⋊C4—342no—
576C2×C22⋊C4—342no—
577C2×C22⋊C4—342no—
578C2×C22⋊C4—681no—
579C2×C22⋊C4—681no—
580C2×C22⋊C4—681no—
581C2×C22⋊C4—681no—
582C2×C22⋊C4—681no—
583C2×C22⋊C4—681no—
584C2×C22⋊C4—681no—
585C2×C22⋊C4—681no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—342no—
589C2×C42—681no—
590C2×C42—681no—
591C2×C42C4×D1714yescomplemented
592#95—22no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—174no—
599#95—174no—
600#95—342no—
601#95—342no—
602#95—342no—
603#95—342no—
604#95—342no—
605#95—681no—
606#95—681no—
607#95—681no—
608#95—681no—
609#95—681no—
610#95—681no—
611#95—681no—
612#95—681no—
613#95—681no—
614#95—681no—
615#95—681no—
616C17#1448111yescharacteristic, complemented, Sylow
617C24—172no—
618C24—172no—
619C24—172no—
620C24—341no—
621C24—341no—
622C24—341no—
623C24—341no—
624C24—341no—
625C24—341no—
626C24—341no—
627C24—341no—
628C24—341no—
629C24—341no—
630C24—341no—
631C24—341no—
632C24C23×D1711yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
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—172no—
678C22×C4—172no—
679C22×C4—172no—
680C22×C4—172no—
681C22×C4—172no—
682C22×C4—341no—
683C22×C4—341no—
684C22×C4—341no—
685C22×C4—341no—
686C22×C4—341no—
687C22×C4—341no—
688C22×C4—341no—
689C22×C4—341no—
690C22×C4—341no—
691C22×C4—341no—
692C22×C4—341no—
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—684no—
727C22×C4—684no—
728C22×C4—684no—
729C22×C4—684no—
730C22×C4—684no—
731C22×C4—684no—
732C22×C4—684no—
733C22×C4C2×C4×D1712yes—
734C22×C4C2×C4×D1712yes—
735C22×C4C2×C4×D1712yes—
736C22×C4#6325212yes—
737C22×C4#6325212yes—
738C4⋊C4—684no—
739C4⋊C4—684no—
740C22⋊C4—348no—
741C22⋊C4—684no—
742C22⋊C4—684no—
743C22⋊C4—684no—
744C22⋊C4—684no—
745C22⋊C4—684no—
746C42—44no—
747C42—684no—
748C23—174no—
749C23—342no—
750C23—342no—
751C23—342no—
752C23—342no—
753C23—342no—
754C23—342no—
755C23—342no—
756C23—342no—
757C23—342no—
758C23—342no—
759C23—342no—
760C23—342no—
761C23—342no—
762C23—342no—
763C23—342no—
764C23—342no—
765C23—342no—
766C23—342no—
767C23—681no—
768C23—681no—
769C23—681no—
770C23—681no—
771C23—681no—
772C23—681no—
773C23—681no—
774C23—681no—
775C23—681no—
776C23—681no—
777C23—681no—
778C23—681no—
779C23—681no—
780C23—681no—
781C23—681no—
782C23—681no—
783C23C22×C4×D1711yescharacteristic
784C23C2×#6325211yescharacteristic
785C23C2×#6325211yescharacteristic
786C23#1058769111yescharacteristic
787C23#1058769111yescharacteristic
788C23#1058769111yescharacteristic
789C23#1058769411yescharacteristic
790C23#41×D1711yescharacteristic
791C23#41×D1711yescharacteristic
792C23#41×D1711yescharacteristic
793C23#41×D1711yescharacteristic
794C23#1058769611yescharacteristic
795C23#1058769611yescharacteristic
796C23#1058769611yescharacteristic
797C23#1058769711yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
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—342no—
848C2×C4—342no—
849C2×C4—342no—
850C2×C4—342no—
851C2×C4—342no—
852C2×C4—342no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—342no—
856C2×C4—342no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—6816no—
863C2×C4—681no—
864C2×C4—681no—
865C2×C4—681no—
866C2×C4—681no—
867C2×C4—681no—
868C2×C4—681no—
869C2×C4—681no—
870C2×C4—681no—
871C2×C4—681no—
872C2×C4—681no—
873C2×C4—681no—
874C2×C4—681no—
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—
897C22—344no—
898C22—344no—
899C22—344no—
900C22—682no—
901C22—682no—
902C22—682no—
903C22—682no—
904C22—682no—
905C22—682no—
906C22—682no—
907C22—682no—
908C22—682no—
909C22—682no—
910C22—682no—
911C22—682no—
912C22#117×D1711yescharacteristic
913C22#1176327711yescharacteristic
914C22C4×#6325211yescharacteristic
915C22#1176328211yescharacteristic
916C22#1176328311yescharacteristic
917C22#1176328911yescharacteristic
918C22#1176329011yescharacteristic
919C22#1176339111yescharacteristic
920C22#1176339211yescharacteristic
921C22#1176339211yescharacteristic
922C22#1176339511yescharacteristic
923C22#1176339511yescharacteristic
924C22#1176340211yescharacteristic
925C22#1176340211yescharacteristic
926C22#1176340511yescharacteristic
927C22#1176340911yescharacteristic
928C22#1176341011yescharacteristic
929C22#1176341011yescharacteristic
930C22#1176342911yescharacteristic
931C22#1176348311yescharacteristic
932C22#1176348411yescharacteristic
933C22#1176348411yescharacteristic
934C22#1176348811yescharacteristic
935C22#1176348811yescharacteristic
936C22#1176349211yescharacteristic
937C22#1176350011yescharacteristic
938C22#1176350011yescharacteristic
939C22#1176350311yescharacteristic
940C22#1176351011yescharacteristic
941C22#1176351011yescharacteristic
942C22#1176352711yescharacteristic
943C22#1176355111yescharacteristic
944C22#1176355311yescharacteristic
945C22#1176355711yescharacteristic
946C22#1176356311yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—682no—
955C4—682no—
956C4—682no—
957C4—682no—
958C4—682no—
959C4—1361no—
960C4—1361no—
961C2—684no—
962C2#1453141311yescharacteristic
963C2#1453154911yescharacteristic
964C2#1453157011yescharacteristic
965C2#1453164711yescharacteristic
966C2#1453171711yescharacteristic
967C2#1453190411yescharacteristic
968C2#1453195511yescharacteristic
969C2#1453582911yescharacteristic
970C2#1453585111yescharacteristic
971C2#1453588711yescharacteristic
972C2#1453589411yescharacteristic
973C2#1453601911yescharacteristic
974C2#1453602011yescharacteristic
975C2#1453605911yescharacteristic
976C2#1453650911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1434D17
hypocenterC17#14481
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #14527050C2semidirect
3. #14527045C2semidirect
4. #14527042C2semidirect
5. #14527039C2semidirect
9. #14527015C2semidirect
10. #14527011C2semidirect
11. #14527008C2semidirect
15. C17×#1434C2semidirect
26. #11762700C4semidirect
76. C2×C42×C17C2×C4semidirect
100. C2×#63225C2×C4semidirect
126. #10587502C2×C4semidirect
127. #10587502C2×C4semidirect
420. #1434D17semidirect
591. C2×C42C4×D17semidirect
616. C17#14481semidirect

Maximal subgroups

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

subgroupindex
C2×#117627002
#145270502
#145270452
#145270422
#145270392
#145270322
#145270282
#145270202
#145270152
#145270112
#145270082
#145270052
C17×#14342
#1448117