Finite Group Databasebeta

← #17962996

Subgroups — #17962996

Order 4352.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763759C211yesmaximal, characteristic
2C2×C22⋊C4×#595C211yesmaximal, characteristic
3#14543965C211yesmaximal, characteristic
4#14543965C211yesmaximal, characteristic
5#14543964C211yesmaximal, characteristic, complemented
6#14543963C211yesmaximal, characteristic, complemented
7#14543961C211yesmaximal, characteristic, complemented
8#14543960C211yesmaximal, characteristic, complemented
9#14543959C211yesmaximal, characteristic, complemented
10#14543959C211yesmaximal, characteristic, complemented
11#14543957C211yesmaximal, characteristic
12#14543957C211yesmaximal, characteristic
13C4×(C2×#595)⋊C4C211yesmaximal, characteristic, complemented
14#95×#595C211yesmaximal, characteristic, complemented
15D17×#388C211yesmaximal, characteristic
16C24×#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C22⋊#595C2211yescharacteristic
19C22×C22⋊#595C2211yescharacteristic
20C22×C22⋊#595C2211yescharacteristic
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26#11763759C418yescomplemented
27C22⋊C4×#595C418yescomplemented
28C2×(C2×#595)⋊C4C2211yescharacteristic
29C2×(C2×#595)⋊C4C2211yescharacteristic
30C2×(C2×#595)⋊C4C2211yescharacteristic
31C2×(C2×#595)⋊C4C2211yescharacteristic
32C2×(C2×#595)⋊C4C2211yescharacteristic
33C2×(C2×#595)⋊C4C2211yescharacteristic
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2211yescharacteristic
37C2×(C2×#595)⋊C4C2211yescharacteristic
38C2×(C2×#595)⋊C4C2211yescharacteristic
39C2×(C2×#595)⋊C4C2211yescharacteristic
40C2×(C2×#595)⋊C4C2211yescharacteristic
41C2×(C2×#595)⋊C4C2211yescharacteristic
42C2×(C2×#595)⋊C4C2211yescharacteristic
43C2×(C2×#595)⋊C4C2211yescharacteristic
44C2×(C2×#595)⋊C4C2211yescharacteristic
45C2×(C2×#595)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D17C2211yescharacteristic
47C2×C22⋊C4×D17C2211yescharacteristic
48C2×C22⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2211yescharacteristic
50C2×C42×D17C2211yescharacteristic
51#11762703C411yescharacteristic, complemented
52#11762702C411yescharacteristic, complemented
53#11762701C411yescharacteristic, complemented
54#11762700C411yescharacteristic, complemented
55#11762699C411yescharacteristic, complemented
56#11762698C411yescharacteristic, complemented
57#11762697C411yescharacteristic, complemented
58#95×D17C2211yescharacteristic
59#95×D17C2211yescharacteristic
60C17×#388C411yescharacteristic, complemented
61C24×D17C2311yescharacteristic
62C23×#595—22no—
63C23×#595—22no—
64C23×#595—41no—
65C23×#595—41no—
66C23×#595—41no—
67C23×#595—41no—
68C23×#595C2×C414yes—
69C23×#595C2311yescharacteristic
70C23×#595C2311yescharacteristic
71C23×#595C2311yescharacteristic
72C23×#595C2311yescharacteristic
73C23×#595C2311yescharacteristic
74C23×#595C2311yescharacteristic
75C23×#595C2311yescharacteristic
76C23×#595C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C22×C4×D17C2311yescharacteristic
79C22×C4×D17C2311yescharacteristic
80C22×C4×D17C2311yescharacteristic
81C22×C4×D17C2311yescharacteristic
82C22×C4×D17C2311yescharacteristic
83C2×C22⋊#595—22no—
84C2×C22⋊#595—22no—
85C2×C22⋊#595—41no—
86C2×C22⋊#595—41no—
87C2×C22⋊#595—41no—
88C2×C22⋊#595—41no—
89C2×C22⋊#595C2×C414yes—
90C2×C22⋊#595C2×C414yes—
91C2×C22⋊#595C2×C414yes—
92C2×C4⋊#595—41no—
93C2×C4⋊#595—41no—
94C2×C4⋊#595C2×C414yescomplemented
95C2×C4×#595—22no—
96C2×C4×#595—22no—
97C2×C4×#595—41no—
98C2×C4×#595—41no—
99C2×C4×#595—41no—
100C2×C4×#595—41no—
101C2×C4×#595—41no—
102C2×C4×#595—41no—
103C2×C4×#595—41no—
104C2×C4×#595—41no—
105C2×C4×#595—41no—
106C2×C4×#595—41no—
107C2×C4×#595C2×C414yes—
108C2×C4×#595C2×C414yes—
109C2×C4×#595C2×C414yescomplemented
110C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
111C2×C22⋊C4×C17C2×C411yescharacteristic
112C2×C22⋊C4×C17C2×C411yescharacteristic
113C2×C22⋊C4×C17C2×C411yescharacteristic
114C2×C42×C17C2×C411yescharacteristic, complemented
115C2×C22⋊Dic17C2×C411yescharacteristic
116C2×C22⋊Dic17C2×C411yescharacteristic
117C2×C22⋊Dic17C2×C411yescharacteristic
118C2×#63227C2×C411yescharacteristic
119C2×#63227C2×C411yescharacteristic
120C2×#63227C2×C411yescharacteristic
121C2×#63227C2×C411yescharacteristic
122C2×#63227C2×C411yescharacteristic
123C2×#63227C2×C411yescharacteristic
124C2×C4⋊Dic17C2×C411yescharacteristic, complemented
125C2×#63225C2×C411yescharacteristic, complemented
126C2×#63225C2×C411yescharacteristic, complemented
127C2×C4×Dic17C2×C411yescharacteristic, complemented
128C2×C4×Dic17C2×C411yescharacteristic, complemented
129C2×C4×Dic17C2×C411yescharacteristic, complemented
130C4⋊C4×D17—41no—
131C4⋊C4×D17—41no—
132C22⋊C4×D17—41no—
133C22⋊C4×D17—41no—
134C22⋊C4×D17—41no—
135C22⋊C4×D17—41no—
136C22⋊C4×D17C2×C414yes—
137C22⋊C4×D17C2×C414yes—
138C42×D17—41no—
139C42×D17—41no—
140(C2×#595)⋊C4—22no—
141(C2×#595)⋊C4—22no—
142(C2×#595)⋊C4—22no—
143(C2×#595)⋊C4—22no—
144(C2×#595)⋊C4—22no—
145(C2×#595)⋊C4—22no—
146(C2×#595)⋊C4—41no—
147(C2×#595)⋊C4—41no—
148(C2×#595)⋊C4—41no—
149(C2×#595)⋊C4—41no—
150(C2×#595)⋊C4—41no—
151(C2×#595)⋊C4—41no—
152(C2×#595)⋊C4—41no—
153(C2×#595)⋊C4—41no—
154(C2×#595)⋊C4C2×C414yes—
155(C2×#595)⋊C4C2×C414yes—
156(C2×#595)⋊C4C2×C414yescomplemented
157(C2×#595)⋊C4C2×C414yescomplemented
158C17×#95C2×C411yescharacteristic, complemented
159C17×#95C2×C411yescharacteristic, complemented
160#10587502C2×C411yescharacteristic, complemented
161#10587502C2×C411yescharacteristic, complemented
162#10587502C2×C411yescharacteristic, complemented
163#10587502C2×C411yescharacteristic, complemented
164#10587502C2×C411yescharacteristic, complemented
165#10587502C2×C411yescharacteristic, complemented
166C24×C17C22×C411yescharacteristic
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17C22×C411yescharacteristic
180C23×D17C22×C412yes—
181C23×D17C22×C412yes—
182C23×D17C2411yescharacteristic
183C22×#595—21no—
184C22×#595—21no—
185C22×#595—21no—
186C22×#595—21no—
187C22×#595—21no—
188C22×#595—21no—
189C22×#595—21no—
190C22×#595—21no—
191C22×#595—21no—
192C22×#595—21no—
193C22×#595—21no—
194C22×#595—21no—
195C22×#595—21no—
196C22×#595—21no—
197C22×#595—21no—
198C22×#595—21no—
199C22×#595—21no—
200C22×#595—21no—
201C22×#595—21no—
202C22×#595—21no—
203C22×#595—21no—
204C22×#595—21no—
205C22×#595—21no—
206C22×#595—21no—
207C22×#595—21no—
208C22×#595—21no—
209C22×#595—21no—
210C22×#595—21no—
211C22×#595—21no—
212C22×#595—21no—
213C22×#595—21no—
214C22×#595—21no—
215C22×#595—21no—
216C22×#595—21no—
217C22×#595—21no—
218C22×#595—21no—
219C22×#595—21no—
220C22×#595—21no—
221C22×#595—21no—
222C22×#595—21no—
223C22×#595—21no—
224C22×#595—21no—
225C22×#595—21no—
226C22×#595—21no—
227C22×#595—28no—
228C22×#595—44no—
229C22×#595—44no—
230C22×#595—44no—
231C22×#595—44no—
232C22×#595—44no—
233C22×#595—44no—
234C22×#595C22×C412yes—
235C22×#595C22×C412yes—
236C22×#595C22×C412yes—
237C22×#595C22×C412yes—
238C22×#595C22×C412yes—
239C22×#595C22×C412yes—
240C22×#595C22×C412yes—
241C22×#595C22×C412yes—
242C22×#595#4112yes—
243C22×#595#4112yes—
244C22×#595#4112yes—
245C22×#595#4112yes—
246C22×C4×C17C22×C411yescharacteristic
247C22×C4×C17C22×C411yescharacteristic
248C22×C4×C17C22×C411yescharacteristic
249C22×C4×C17C22×C411yescharacteristic
250C22×C4×C17C22×C411yescharacteristic
251C22×C4×C17C22×C411yescharacteristic
252C22×Dic17C22×C411yescharacteristic
253C22×Dic17C22×C411yescharacteristic
254C22×Dic17C22×C411yescharacteristic
255C22×Dic17C22×C411yescharacteristic
256C22×Dic17C22×C411yescharacteristic
257C22×Dic17C22×C411yescharacteristic
258C2×C4×D17—21no—
259C2×C4×D17—21no—
260C2×C4×D17—21no—
261C2×C4×D17—21no—
262C2×C4×D17—21no—
263C2×C4×D17—21no—
264C2×C4×D17—21no—
265C2×C4×D17—21no—
266C2×C4×D17—21no—
267C2×C4×D17—21no—
268C2×C4×D17—21no—
269C2×C4×D17—21no—
270C2×C4×D17—21no—
271C2×C4×D17—21no—
272C2×C4×D17—21no—
273C2×C4×D17—21no—
274C2×C4×D17—21no—
275C2×C4×D17—21no—
276C2×C4×D17—21no—
277C2×C4×D17—21no—
278C2×C4×D17—21no—
279C2×C4×D17—21no—
280C2×C4×D17—21no—
281C2×C4×D17—21no—
282C2×C4×D17—21no—
283C2×C4×D17—21no—
284C2×C4×D17—21no—
285C2×C4×D17—21no—
286C2×C4×D17—21no—
287C2×C4×D17—21no—
288C2×C4×D17—21no—
289C2×C4×D17—21no—
290C2×C4×D17C22×C412yes—
291C2×C4×D17C22×C412yes—
292C2×C4×D17C22×C412yes—
293C2×C4×D17C22×C412yes—
294C22⋊#595—28no—
295C22⋊#595—44no—
296C22⋊#595—44no—
297C4⋊#595—44no—
298C4×#595—44no—
299C4×#595—44no—
300C4×#595—44no—
301C4×#595—44no—
302C4×#595—44no—
303C4⋊C4×C17—41no—
304C22⋊C4×C17—41no—
305C22⋊C4×C17—41no—
306C22⋊C4×C17C4214yescomplemented
307C42×C17—41no—
308C22⋊Dic17—41no—
309C22⋊Dic17—41no—
310C22⋊Dic17C4214yescomplemented
311#63227—41no—
312#63227—41no—
313#63227—41no—
314#63227—41no—
315#63227C4214yescomplemented
316#63227C4214yescomplemented
317C4⋊Dic17—41no—
318#63225—41no—
319#63225—41no—
320C4×Dic17—41no—
321C4×Dic17—41no—
322C4×Dic17—41no—
323#13788—171nomaximal, Sylow
324C23×C17—21no—
325C23×C17—21no—
326C23×C17—21no—
327C23×C17—21no—
328C23×C17—21no—
329C23×C17—21no—
330C23×C17C2×C4212yes—
331C23×C17C23×C411yescharacteristic
332C22×D17—21no—
333C22×D17—21no—
334C22×D17—21no—
335C22×D17—21no—
336C22×D17—21no—
337C22×D17—21no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17C2×C4212yes—
367C22×D17C23×C411yescharacteristic
368C22×D17C23×C411yescharacteristic
369C22×D17C2×#4111yescharacteristic
370C22×D17C2×#4111yescharacteristic
371C22×D17C2×#4111yescharacteristic
372C22×D17C2×#4111yescharacteristic
373C22×D17H(5,𝔽2)11yescharacteristic
374C22×D17H(5,𝔽2)11yescharacteristic
375C22×D17H(5,𝔽2)11yescharacteristic
376C22×D17H(5,𝔽2)11yescharacteristic
377C22×D17H(5,𝔽2)11yescharacteristic
378C22×D17H(5,𝔽2)11yescharacteristic
379C22×D172−1+411yescharacteristic
380C22×D172−1+411yescharacteristic
381C2×#595—22no—
382C2×#595—22no—
383C2×#595—22no—
384C2×#595—22no—
385C2×#595—22no—
386C2×#595—22no—
387C2×#595—22no—
388C2×#595—22no—
389C2×#595—22no—
390C2×#595—22no—
391C2×#595—22no—
392C2×#595—22no—
393C2×#595—22no—
394C2×#595—22no—
395C2×#595—22no—
396C2×#595—22no—
397C2×#595—22no—
398C2×#595—22no—
399C2×#595—22no—
400C2×#595—22no—
401C2×#595—22no—
402C2×#595—22no—
403C2×#595—22no—
404C2×#595—22no—
405C2×#595—22no—
406C2×#595—22no—
407C2×#595—22no—
408C2×#595—22no—
409C2×#595—22no—
410C2×#595—22no—
411C2×#595—416no—
412C2×#595—41no—
413C2×#595—41no—
414C2×#595—41no—
415C2×#595—41no—
416C2×#595—41no—
417C2×#595—41no—
418C2×#595—41no—
419C2×#595—41no—
420C2×#595—41no—
421C2×#595—41no—
422C2×#595—41no—
423C2×#595—41no—
424C2×#595—41no—
425C2×#595—41no—
426C2×#595—41no—
427C2×#595—41no—
428C2×#595—41no—
429C2×#595—41no—
430C2×#595—41no—
431C2×#595—41no—
432C2×#595—41no—
433C2×#595—41no—
434C2×#595—41no—
435C2×#595—41no—
436C2×#595#11714yes—
437C2×#595#11714yes—
438C2×C4×C17—21no—
439C2×C4×C17—21no—
440C2×C4×C17—21no—
441C2×C4×C17—21no—
442C2×C4×C17—21no—
443C2×C4×C17—21no—
444C2×C4×C17—21no—
445C2×C4×C17—21no—
446C2×C4×C17—21no—
447C2×C4×C17—21no—
448C2×C4×C17—21no—
449C2×C4×C17—21no—
450C2×C4×C17—21no—
451C2×C4×C17—21no—
452C2×C4×C17—21no—
453C2×C4×C17—21no—
454C2×C4×C17C2×C4212yes—
455C2×C4×C17C2×C4212yes—
456C2×Dic17—21no—
457C2×Dic17—21no—
458C2×Dic17—21no—
459C2×Dic17—21no—
460C2×Dic17—21no—
461C2×Dic17—21no—
462C2×Dic17—21no—
463C2×Dic17—21no—
464C2×Dic17—21no—
465C2×Dic17—21no—
466C2×Dic17—21no—
467C2×Dic17—21no—
468C2×Dic17—21no—
469C2×Dic17—21no—
470C2×Dic17—21no—
471C2×Dic17—21no—
472C2×Dic17C2×C4212yes—
473C2×Dic17C2×C4212yes—
474C4×D17—22no—
475C4×D17—22no—
476C4×D17—22no—
477C4×D17—22no—
478C4×D17—22no—
479C4×D17—22no—
480C4×D17—22no—
481C4×D17—22no—
482C4×D17—41no—
483C4×D17—41no—
484C4×D17—41no—
485C4×D17—41no—
486C4×D17—41no—
487C4×D17—41no—
488C4×D17—41no—
489C4×D17—41no—
490C4×D17—41no—
491C4×D17—41no—
492C4×D17—41no—
493C4×D17—41no—
494C4×D17—41no—
495C4×D17—41no—
496C4×D17—41no—
497C4×D17—41no—
498C2×#388—171no—
499C2×#388—171no—
500C2×C4×C22⋊C4—171no—
501#1437—171no—
502#1437—171no—
503#1436—171no—
504#1436—171no—
505C4⋊#95—171no—
506#1434—171no—
507#1434—171no—
508#1434—171no—
509C22⋊#95—171no—
510C22⋊#95—171no—
511C4×#95—171no—
512C4×#95—171no—
513C22×C17—22no—
514C22×C17—22no—
515C22×C17—22no—
516C22×C17—41no—
517C22×C17—41no—
518C22×C17—41no—
519C22×C17—41no—
520C22×C17C22×C4211yescharacteristic
521C22×C17C4×#4111yescharacteristic
522C22×C17C4×#4111yescharacteristic
523C22×C17#51811yescharacteristic
524C22×C17#51811yescharacteristic
525C22×C17#52011yescharacteristic
526C22×C17#52011yescharacteristic
527C2×D17—22no—
528C2×D17—22no—
529C2×D17—22no—
530C2×D17—41no—
531C2×D17—41no—
532C2×D17—41no—
533C2×D17—41no—
534C2×D17—42no—
535C2×D17—42no—
536C2×D17—42no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17C2×#11711yescharacteristic
543C2×D17C2×#11711yescharacteristic
544C2×D17C4×#4111yescharacteristic
545C2×D17C4×#4111yescharacteristic
546C2×D17#51811yescharacteristic
547C2×D17#51811yescharacteristic
548C2×D17#51811yescharacteristic
549C2×D17#51811yescharacteristic
550C2×D17#52011yescharacteristic
551C2×D17#52011yescharacteristic
552C2×D17#52011yescharacteristic
553C2×D17#52011yescharacteristic
554C2×D17#53811yescharacteristic
555C2×D17#53811yescharacteristic
556C2×D17#53811yescharacteristic
557C2×D17#53811yescharacteristic
558C2×D17#53811yescharacteristic
559C2×D17#53811yescharacteristic
560C2×D17#53911yescharacteristic
561C2×D17#53911yescharacteristic
562C2×D17#54011yescharacteristic
563C2×D17#54011yescharacteristic
564C2×D17#54011yescharacteristic
565C2×D17#54111yescharacteristic
566C2×D17#54211yescharacteristic
567C2×D17#54211yescharacteristic
568C2×D17#54211yescharacteristic
569C2×D17#54211yescharacteristic
570#595—24no—
571#595—24no—
572#595—42no—
573#595—42no—
574#595—42no—
575#595—42no—
576#595—42no—
577#595—42no—
578C4×C17—22no—
579C4×C17—22no—
580C4×C17—41no—
581C4×C17—41no—
582C4×C17—41no—
583C4×C17—41no—
584Dic17—22no—
585Dic17—22no—
586Dic17—41no—
587Dic17—41no—
588Dic17—41no—
589Dic17—41no—
590C24×C4—171no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C42—171no—
600C22×C42—171no—
601C22×C42—171no—
602C22×C42—171no—
603C22×C42—171no—
604C22×C42—171no—
605#388—178no—
606#388—171no—
607#388—171no—
608#388—171no—
609#388—171no—
610#388—171no—
611#388—171no—
612#388—171no—
613#388#59511yescharacteristic, complemented
614C4×C22⋊C4—178no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—171no—
634C2×#95—171no—
635C2×C17—42no—
636C2×C17C4×#11711yescharacteristic
637C2×C17#227511yescharacteristic
638C2×C17#227511yescharacteristic
639C2×C17#233311yescharacteristic
640C2×C17#233411yescharacteristic
641C2×C17#233511yescharacteristic
642C2×C17#233711yescharacteristic
643D17—42no—
644D17#231211yescharacteristic
645D17#231411yescharacteristic
646D17#231811yescharacteristic
647D17#231911yescharacteristic
648D17#233311yescharacteristic
649D17#233411yescharacteristic
650D17#233511yescharacteristic
651D17#233711yescharacteristic
652C25—171no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—174no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—342no—
669C23×C4—342no—
670C23×C4—681no—
671C23×C4—681no—
672C23×C4—681no—
673C23×C4—681no—
674C2×C4⋊C4—174no—
675C2×C4⋊C4—171no—
676C2×C4⋊C4—171no—
677C2×C4⋊C4—171no—
678C2×C4⋊C4—681no—
679C2×C4⋊C4—681no—
680C2×C4⋊C4—681no—
681C2×C4⋊C4—681no—
682C2×C4⋊C4C2×#59511yescharacteristic, complemented
683C2×C22⋊C4—171no—
684C2×C22⋊C4—171no—
685C2×C22⋊C4—171no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—174no—
690C2×C22⋊C4—174no—
691C2×C22⋊C4—171no—
692C2×C22⋊C4—171no—
693C2×C22⋊C4—171no—
694C2×C22⋊C4—171no—
695C2×C22⋊C4—171no—
696C2×C22⋊C4—171no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4—681no—
702C2×C22⋊C4—681no—
703C2×C22⋊C4—681no—
704C2×C22⋊C4—681no—
705C2×C22⋊C4—681no—
706C2×C22⋊C4—681no—
707C2×C22⋊C4C2×#59511yescharacteristic
708C2×C22⋊C4C2×#59511yescharacteristic
709C2×C22⋊C4C2×#59511yescharacteristic
710C2×C42—174no—
711C2×C42—174no—
712C2×C42—174no—
713C2×C42—171no—
714C2×C42—171no—
715C2×C42—171no—
716C2×C42—342no—
717C2×C42—342no—
718C2×C42—681no—
719C2×C42—681no—
720C2×C42—681no—
721C2×C42—681no—
722C2×C42—681no—
723C2×C42—681no—
724C2×C42—681no—
725C2×C42—681no—
726C2×C42—681no—
727C2×C42—681no—
728C2×C42—681no—
729C2×C42—681no—
730C2×C42C2×#59511yescharacteristic, complemented
731#95—174no—
732#95—174no—
733#95—174no—
734#95—174no—
735#95—171no—
736#95—171no—
737#95—171no—
738#95—171no—
739#95—171no—
740#95—171no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—681no—
748#95—681no—
749#95—681no—
750#95—681no—
751#95—681no—
752#95—681no—
753#95—681no—
754#95—681no—
755#95C2×#59511yescharacteristic, complemented
756#95C2×#59511yescharacteristic, complemented
757C17#1378811yescharacteristic, complemented, Sylow
758C24—171no—
759C24—172no—
760C24—172no—
761C24—171no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24C22×#59511yescharacteristic
775C22×C4—172no—
776C22×C4—172no—
777C22×C4—172no—
778C22×C4—172no—
779C22×C4—172no—
780C22×C4—172no—
781C22×C4—171no—
782C22×C4—171no—
783C22×C4—172no—
784C22×C4—172no—
785C22×C4—172no—
786C22×C4—172no—
787C22×C4—172no—
788C22×C4—172no—
789C22×C4—172no—
790C22×C4—172no—
791C22×C4—172no—
792C22×C4—172no—
793C22×C4—171no—
794C22×C4—171no—
795C22×C4—171no—
796C22×C4—171no—
797C22×C4—341no—
798C22×C4—341no—
799C22×C4—341no—
800C22×C4—341no—
801C22×C4—341no—
802C22×C4—341no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—348no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—684no—
875C22×C4—684no—
876C22×C4—684no—
877C22×C4—684no—
878C22×C4—684no—
879C22×C4—684no—
880C22×C4C22×#59511yescharacteristic
881C22×C4C22×#59511yescharacteristic
882C22×C4C22×#59511yescharacteristic
883C22×C4C22×#59511yescharacteristic
884C22×C4C22×#59511yescharacteristic
885C22×C4C22×#59511yescharacteristic
886C4⋊C4—41no—
887C4⋊C4—681no—
888C4⋊C4—681no—
889C4⋊C4—681no—
890C4⋊C4—684no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—174no—
894C22⋊C4—174no—
895C22⋊C4—174no—
896C22⋊C4—348no—
897C22⋊C4—681no—
898C22⋊C4—681no—
899C22⋊C4—681no—
900C22⋊C4—681no—
901C22⋊C4—681no—
902C22⋊C4—681no—
903C22⋊C4—684no—
904C22⋊C4—684no—
905C22⋊C4C4×#59514yescomplemented
906C42—41no—
907C42—681no—
908C42—681no—
909C42—681no—
910C42—684no—
911C42—684no—
912C42—684no—
913C42—684no—
914C42—684no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—171no—
922C23—171no—
923C23—171no—
924C23—171no—
925C23—171no—
926C23—171no—
927C23—171no—
928C23—171no—
929C23—171no—
930C23—171no—
931C23—171no—
932C23—171no—
933C23—171no—
934C23—171no—
935C23—172no—
936C23—342no—
937C23—342no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—341no—
949C23—341no—
950C23—341no—
951C23—341no—
952C23—341no—
953C23—341no—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23C2×C4×#59512yes—
971C23C23×#59511yescharacteristic
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—174no—
989C2×C4—174no—
990C2×C4—172no—
991C2×C4—172no—
992C2×C4—342no—
993C2×C4—342no—
994C2×C4—342no—
995C2×C4—342no—
996C2×C4—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—342no—
1000C2×C4—342no—
1001C2×C4—342no—
1002C2×C4—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—341no—
1013C2×C4—341no—
1014C2×C4—341no—
1015C2×C4—341no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
1034C2×C4—341no—
1035C2×C4—341no—
1036C2×C4—341no—
1037C2×C4—341no—
1038C2×C4—341no—
1039C2×C4—341no—
1040C2×C4—341no—
1041C2×C4—341no—
1042C2×C4—341no—
1043C2×C4—341no—
1044C2×C4—341no—
1045C2×C4—341no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—6816no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4C2×C4×#59512yes—
1088C2×C4C2×C4×#59512yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—171no—
1097C22—171no—
1098C22—171no—
1099C22—171no—
1100C22—171no—
1101C22—171no—
1102C22—171no—
1103C22—171no—
1104C22—171no—
1105C22—171no—
1106C22—171no—
1107C22—171no—
1108C22—171no—
1109C22—171no—
1110C22—171no—
1111C22—171no—
1112C22—171no—
1113C22—171no—
1114C22—171no—
1115C22—171no—
1116C22—171no—
1117C22—171no—
1118C22—171no—
1119C22—171no—
1120C22—171no—
1121C22—171no—
1122C22—171no—
1123C22—171no—
1124C22—342no—
1125C22—342no—
1126C22—342no—
1127C22—682no—
1128C22—682no—
1129C22—682no—
1130C22—682no—
1131C22—682no—
1132C22—682no—
1133C22—682no—
1134C22—682no—
1135C22—681no—
1136C22—681no—
1137C22—681no—
1138C22—681no—
1139C22C22×C4×#59511yescharacteristic
1140C22#41×#59511yescharacteristic
1141C22#41×#59511yescharacteristic
1142C22#1176387611yescharacteristic
1143C22#1176387611yescharacteristic
1144C22#1176387811yescharacteristic
1145C22#1176387811yescharacteristic
1146C4—22no—
1147C4—22no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—344no—
1153C4—344no—
1154C4—342no—
1155C4—342no—
1156C4—682no—
1157C4—682no—
1158C4—682no—
1159C4—682no—
1160C4—682no—
1161C4—682no—
1162C4—681no—
1163C4—681no—
1164C4—681no—
1165C4—681no—
1166C2—42no—
1167C2—171no—
1168C2—171no—
1169C2—171no—
1170C2—171no—
1171C2—171no—
1172C2—171no—
1173C2—171no—
1174C2—171no—
1175C2—682no—
1176C2#117×#59511yescharacteristic
1177C2#1454522311yescharacteristic
1178C2#1454522311yescharacteristic
1179C2#1454528111yescharacteristic
1180C2#1454528211yescharacteristic
1181C2#1454528311yescharacteristic
1182C2#1454528511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#388C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenter#388#595
hypocenterC17#13788
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #14543964C2semidirect
6. #14543963C2semidirect
7. #14543961C2semidirect
8. #14543960C2semidirect
9. #14543959C2semidirect
10. #14543959C2semidirect
13. C4×(C2×#595)⋊C4C2semidirect
14. #95×#595C2semidirect
26. #11763759C4semidirect
27. C22⋊C4×#595C4semidirect
51. #11762703C4semidirect
52. #11762702C4semidirect
53. #11762701C4semidirect
54. #11762700C4semidirect
55. #11762699C4semidirect
56. #11762698C4semidirect
57. #11762697C4semidirect
60. C17×#388C4semidirect
94. C2×C4⋊#595C2×C4semidirect
109. C2×C4×#595C2×C4semidirect
110. C2×C4⋊C4×C17C2×C4semidirect
114. C2×C42×C17C2×C4semidirect
124. C2×C4⋊Dic17C2×C4semidirect
125. C2×#63225C2×C4semidirect
126. C2×#63225C2×C4semidirect
127. C2×C4×Dic17C2×C4semidirect
128. C2×C4×Dic17C2×C4semidirect
129. C2×C4×Dic17C2×C4semidirect
156. (C2×#595)⋊C4C2×C4semidirect
157. (C2×#595)⋊C4C2×C4semidirect
158. C17×#95C2×C4semidirect
159. C17×#95C2×C4semidirect
160. #10587502C2×C4semidirect
161. #10587502C2×C4semidirect
162. #10587502C2×C4semidirect
163. #10587502C2×C4semidirect
164. #10587502C2×C4semidirect
165. #10587502C2×C4semidirect
306. C22⋊C4×C17C42semidirect
310. C22⋊Dic17C42semidirect
315. #63227C42semidirect
316. #63227C42semidirect
613. #388#595semidirect
682. C2×C4⋊C4C2×#595semidirect
730. C2×C42C2×#595semidirect
755. #95C2×#595semidirect
756. #95C2×#595semidirect
757. C17#13788semidirect
905. C22⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637592
C2×C22⋊C4×#5952
#145439652
#145439642
#145439632
#145439612
#145439602
#145439592
#145439572
C4×(C2×#595)⋊C42
#95×#5952
D17×#3882
#1378817