Finite Group Databasebeta

← #16963527

Subgroups — #16963527

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×#11762697C211yesmaximal, characteristic
2#14527050C211yesmaximal, characteristic, complemented
3#14527044C211yesmaximal, characteristic, complemented
4#14527044C211yesmaximal, characteristic, complemented
5#14527042C211yesmaximal, characteristic, complemented
6#14527031C211yesmaximal, characteristic
7#14527027C211yesmaximal, characteristic
8#14527017C211yesmaximal, characteristic, complemented
9#14527017C211yesmaximal, characteristic, complemented
10#14527009C211yesmaximal, characteristic, complemented
11#14527009C211yesmaximal, characteristic, complemented
12#14527006C211yesmaximal, characteristic
13#14527006C211yesmaximal, characteristic
14#14527006C211yesmaximal, characteristic
15C17×#1437C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23#11762697C418yescomplemented
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2211yescharacteristic
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×C22⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C42×C17C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C25×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×Dic17—22no—
60C23×Dic17—22no—
61C23×Dic17—22no—
62C23×Dic17—41no—
63C23×Dic17—41no—
64C23×Dic17—41no—
65C23×Dic17—41no—
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C2×C22⋊C4×C17—22no—
75C2×C22⋊C4×C17—22no—
76C2×C22⋊C4×C17—22no—
77C2×C22⋊C4×C17—22no—
78C2×C22⋊C4×C17—41no—
79C2×C22⋊C4×C17—41no—
80C2×C22⋊C4×C17—41no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17C2×C414yes—
83C2×C42×C17—41no—
84C2×C42×C17—41no—
85C2×C42×C17—41no—
86C2×C22⋊Dic17—22no—
87C2×C22⋊Dic17—22no—
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17—41no—
90C2×C22⋊Dic17—41no—
91C2×C22⋊Dic17—41no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17C2×C414yes—
94C2×C22⋊Dic17C2×C414yes—
95C2×#63225—22no—
96C2×#63225—41no—
97C2×#63225—41no—
98C2×#63225—41no—
99C2×#63225—41no—
100C2×#63225C2×C414yescomplemented
101C2×C4×Dic17—41no—
102C2×C4×Dic17—41no—
103C2×C4×Dic17C2×C414yescomplemented
104C17×#95—22no—
105C17×#95—22no—
106C17×#95—41no—
107#10587502—22no—
108#10587502—22no—
109#10587502—22no—
110#10587502—22no—
111#10587502—22no—
112#10587502—41no—
113#10587502—41no—
114#10587502—41no—
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×C17—21no—
129C24×C17—21no—
130C24×C17—21no—
131C24×C17—21no—
132C24×C17—21no—
133C24×C17—21no—
134C24×C17—21no—
135C24×C17—21no—
136C24×C17—21no—
137C24×C17—21no—
138C24×C17—21no—
139C24×C17—21no—
140C24×C17C22×C412yes—
141C24×C17#4112yes—
142C24×C17#4112yes—
143C24×C17C2411yescharacteristic
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×C17C22×C412yes—
183C22×C4×C17C22×C412yes—
184C22×C4×C17#4112yes—
185C22×C4×C17#4112yes—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—21no—
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—44no—
237C22×Dic17—44no—
238C22×Dic17—44no—
239C22×Dic17—44no—
240C22×Dic17—44no—
241C22×Dic17—44no—
242C22×Dic17—44no—
243C22×Dic17C22×C412yes—
244C22×Dic17C22×C412yes—
245C22×Dic17C22×C412yes—
246C22×Dic17C22×C412yes—
247C22×Dic17#4112yes—
248C22×Dic17#4112yes—
249C22⋊C4×C17—44no—
250C22⋊C4×C17—44no—
251C22⋊C4×C17—44no—
252C42×C17—44no—
253C22⋊Dic17—28no—
254C22⋊Dic17—44no—
255C22⋊Dic17—44no—
256#63225—44no—
257#63225—44no—
258C4×Dic17—44no—
259#14509—171nomaximal, Sylow
260C23×C17—22no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—22no—
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—41no—
279C23×C17—41no—
280C23×C17—41no—
281C23×C17—41no—
282C23×C17—41no—
283C23×C17—41no—
284C23×C17—41no—
285C23×C17—41no—
286C23×C17—41no—
287C23×C17—41no—
288C23×C17—41no—
289C23×C17—41no—
290C23×C17—41no—
291C23×C17—41no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17#11714yes—
295C23×C17C23×C411yescharacteristic
296C23×C17C2×#4111yescharacteristic
297C23×C17C2×#4111yescharacteristic
298C23×C17C2×#4111yescharacteristic
299C23×C17C2×#4111yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17C2×#4111yescharacteristic
302C23×C17H(5,𝔽2)11yescharacteristic
303C23×C17H(5,𝔽2)11yescharacteristic
304C23×C17H(5,𝔽2)11yescharacteristic
305C23×C17H(5,𝔽2)11yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C172−1+411yescharacteristic
309C23×C172−1+411yescharacteristic
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—41no—
323C2×C4×C17—41no—
324C2×C4×C17—41no—
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×Dic17—22no—
353C2×Dic17—22no—
354C2×Dic17—22no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—22no—
358C2×Dic17—22no—
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—416no—
371C2×Dic17—41no—
372C2×Dic17—41no—
373C2×Dic17—41no—
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—
408C2×Dic17—41no—
409C2×#388—171no—
410#1445—171no—
411#1443—171no—
412#1443—171no—
413#1442—171no—
414#1440—171no—
415#1439—171no—
416#1437D1711yescharacteristic
417#1436—171no—
418#1436—171no—
419#1434—171no—
420#1434—171no—
421C22⋊#95—171no—
422C22⋊#95—171no—
423C22⋊#95—171no—
424C22×C17—24no—
425C22×C17—24no—
426C22×C17—24no—
427C22×C17—42no—
428C22×C17—42no—
429C22×C17—42no—
430C22×C17—42no—
431C22×C17—42no—
432C22×C17—42no—
433C22×C17—42no—
434C22×C17—42no—
435C22×C17—42no—
436C22×C17—42no—
437C22×C17—42no—
438C22×C17—42no—
439C22×C17C2×#11711yescharacteristic
440C22×C17C4×#4111yescharacteristic
441C22×C17C4×#4111yescharacteristic
442C22×C17#51811yescharacteristic
443C22×C17#51811yescharacteristic
444C22×C17#52011yescharacteristic
445C22×C17#52011yescharacteristic
446C22×C17#53811yescharacteristic
447C22×C17#53811yescharacteristic
448C22×C17#53811yescharacteristic
449C22×C17#53811yescharacteristic
450C22×C17#53811yescharacteristic
451C22×C17#53911yescharacteristic
452C22×C17#53911yescharacteristic
453C22×C17#53911yescharacteristic
454C22×C17#54111yescharacteristic
455C22×C17#54211yescharacteristic
456C22×C17#54211yescharacteristic
457C22×C17#54211yescharacteristic
458C22×C17#55111yescharacteristic
459C22×C17#55111yescharacteristic
460C22×C17#55111yescharacteristic
461C22×C17#55111yescharacteristic
462C22×C17#55111yescharacteristic
463C22×C17#55211yescharacteristic
464C22×C17#55211yescharacteristic
465C22×C17#55311yescharacteristic
466C22×C17#55311yescharacteristic
467C22×C17#55311yescharacteristic
468C22×C17#55311yescharacteristic
469C22×C17#55911yescharacteristic
470C22×C17#56011yescharacteristic
471C22×C17#56011yescharacteristic
472C22×C17#56211yescharacteristic
473C22×C17#56211yescharacteristic
474C4×C17—42no—
475C4×C17—42no—
476C4×C17—42no—
477C4×C17—42no—
478C4×C17—81no—
479C4×C17—81no—
480Dic17—42no—
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⋊C4C2×D1711yescharacteristic
495C22×C22⋊C4C2×D1711yescharacteristic
496C22×C22⋊C4C2×D1711yescharacteristic
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×#95—171no—
519C2×#95—171no—
520C2×#95—171no—
521C2×#95C2×D1711yescharacteristic
522C2×#95C2×D1711yescharacteristic
523C2×#95C2×D1711yescharacteristic
524C2×C17—44no—
525C2×C17#231811yescharacteristic
526C2×C17#233411yescharacteristic
527C2×C17#233711yescharacteristic
528C2×C17#234311yescharacteristic
529C2×C17#235311yescharacteristic
530C2×C17#237411yescharacteristic
531C2×C17#237711yescharacteristic
532C2×C17#273511yescharacteristic
533C2×C17#273911yescharacteristic
534C2×C17#274611yescharacteristic
535C2×C17#274711yescharacteristic
536C2×C17#275111yescharacteristic
537C2×C17#277811yescharacteristic
538C2×C17#277911yescharacteristic
539C2×C17#279611yescharacteristic
540C25C22×D1711yescharacteristic
541C23×C4—171no—
542C23×C4—171no—
543C23×C4—171no—
544C23×C4—171no—
545C23×C4—171no—
546C23×C4—171no—
547C23×C4—171no—
548C23×C4—171no—
549C23×C4—342no—
550C23×C4—342no—
551C23×C4—342no—
552C23×C4—681no—
553C23×C4—681no—
554C23×C4—681no—
555C23×C4—681no—
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—342no—
564C2×C4⋊C4—681no—
565C2×C4⋊C4—681no—
566C2×C4⋊C4—681no—
567C2×C4⋊C4—681no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—174no—
577C2×C22⋊C4—174no—
578C2×C22⋊C4—342no—
579C2×C22⋊C4—342no—
580C2×C22⋊C4—342no—
581C2×C22⋊C4—681no—
582C2×C22⋊C4—681no—
583C2×C22⋊C4—681no—
584C2×C22⋊C4—681no—
585C2×C22⋊C4C4×D1714yes—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—174no—
590C2×C42—681no—
591C2×C42—681no—
592#95—22no—
593#95—22no—
594#95—41no—
595#95—174no—
596#95—174no—
597#95—342no—
598#95—342no—
599#95—342no—
600#95—342no—
601#95—342no—
602#95—681no—
603#95—681no—
604#95—681no—
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#1450911yescharacteristic, complemented, Sylow
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24C2×C4×D1712yes—
630C24#6325212yes—
631C24#6325212yes—
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—172no—
672C22×C4—172no—
673C22×C4—172no—
674C22×C4—172no—
675C22×C4—172no—
676C22×C4—172no—
677C22×C4—341no—
678C22×C4—341no—
679C22×C4—341no—
680C22×C4—341no—
681C22×C4—341no—
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—341no—
727C22×C4—684no—
728C22×C4—684no—
729C22×C4—684no—
730C22×C4—684no—
731C22×C4—684no—
732C22×C4—684no—
733C22×C4—684no—
734C22×C4C2×C4×D1712yes—
735C22×C4C2×C4×D1712yes—
736C22×C4#6325412yes—
737C22×C4#6325412yes—
738C4⋊C4—684no—
739C4⋊C4—684no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—348no—
744C22⋊C4—684no—
745C22⋊C4—684no—
746C42—44no—
747C42—684no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#1058755814yes—
783C23C22×C4×D1711yescharacteristic
784C23C2×#6325211yescharacteristic
785C23C2×#6325211yescharacteristic
786C23C2×#6325411yescharacteristic
787C23C2×#6325411yescharacteristic
788C23#1058769111yescharacteristic
789C23#1058769111yescharacteristic
790C23#1058769111yescharacteristic
791C23#1058769111yescharacteristic
792C23#41×D1711yescharacteristic
793C23#41×D1711yescharacteristic
794C23#1058769611yescharacteristic
795C23#1058769611yescharacteristic
796C23#1058769711yescharacteristic
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—41no—
811C2×C4—41no—
812C2×C4—41no—
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—342no—
841C2×C4—342no—
842C2×C4—342no—
843C2×C4—342no—
844C2×C4—342no—
845C2×C4—342no—
846C2×C4—342no—
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—6816no—
859C2×C4—681no—
860C2×C4—681no—
861C2×C4—681no—
862C2×C4—681no—
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—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C2×#1058755811yescharacteristic
913C22C4×#6325411yescharacteristic
914C22C4×#6325411yescharacteristic
915C22#1176328111yescharacteristic
916C22#1176328211yescharacteristic
917C22#1176328811yescharacteristic
918C22#1176328911yescharacteristic
919C22#1176339211yescharacteristic
920C22#1176339211yescharacteristic
921C22#1176339511yescharacteristic
922C22#1176339611yescharacteristic
923C22#1176339811yescharacteristic
924C22#1176340111yescharacteristic
925C22#1176340111yescharacteristic
926C22#1176340411yescharacteristic
927C22#1176341611yescharacteristic
928C22#1176342711yescharacteristic
929C22#1176342811yescharacteristic
930C22#1176342811yescharacteristic
931C22#1176348311yescharacteristic
932C22#1176348511yescharacteristic
933C22#1176348511yescharacteristic
934C22#1176348811yescharacteristic
935C22#1176348911yescharacteristic
936C22#1176349211yescharacteristic
937C22#1176349911yescharacteristic
938C22#1176350211yescharacteristic
939C22#1176350211yescharacteristic
940C22#1176350511yescharacteristic
941C22#1176350811yescharacteristic
942C22#1176354511yescharacteristic
943C22#1176354711yescharacteristic
944C22#1176354811yescharacteristic
945C22#1176355411yescharacteristic
946C22#1176355611yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—682no—
954C4—682no—
955C4—682no—
956C4—682no—
957C4—682no—
958C4—682no—
959C4—1361no—
960C4—1361no—
961C2—44no—
962C2#1453141111yescharacteristic
963C2#1453155611yescharacteristic
964C2#1453159111yescharacteristic
965C2#1453163811yescharacteristic
966C2#1453171811yescharacteristic
967C2#1453191911yescharacteristic
968C2#1453193611yescharacteristic
969C2#1453582011yescharacteristic
970C2#1453586311yescharacteristic
971C2#1453596611yescharacteristic
972C2#1453598411yescharacteristic
973C2#1453603111yescharacteristic
974C2#1453640311yescharacteristic
975C2#1453641811yescharacteristic
976C2#1453662011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1437D17
hypocenterC17#14509
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #14527050C2semidirect
3. #14527044C2semidirect
4. #14527044C2semidirect
5. #14527042C2semidirect
8. #14527017C2semidirect
9. #14527017C2semidirect
10. #14527009C2semidirect
11. #14527009C2semidirect
23. #11762697C4semidirect
100. C2×#63225C2×C4semidirect
103. C2×C4×Dic17C2×C4semidirect
126. #10587502C2×C4semidirect
127. #10587502C2×C4semidirect
616. C17#14509semidirect

Maximal subgroups

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

subgroupindex
C2×#117626972
#145270502
#145270442
#145270422
#145270312
#145270272
#145270172
#145270092
#145270062
C17×#14372
#1450917