Finite Group Databasebeta

← #17963654

Subgroups — #17963654

Order 4352.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763759C211yesmaximal, characteristic
2C2×#11763756C211yesmaximal, characteristic
3C2×#11763756C211yesmaximal, characteristic
4C2×#11763753C211yesmaximal, characteristic, complemented
5#14543972C211yesmaximal, characteristic, complemented
6#14543972C211yesmaximal, characteristic, complemented
7#14543970C211yesmaximal, characteristic, complemented
8#14543969C211yesmaximal, characteristic, complemented
9#14543967C211yesmaximal, characteristic
10#14543967C211yesmaximal, characteristic
11#14543964C211yesmaximal, characteristic, complemented
12#14543962C211yesmaximal, characteristic, complemented
13#14543961C211yesmaximal, characteristic, complemented
14#14543957C211yesmaximal, characteristic
15D17×#388C211yesmaximal, characteristic
16C24×#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C4⋊#595C2211yescharacteristic
21C22×C4⋊#595C2211yescharacteristic
22C22×C4⋊#595C2211yescharacteristic
23C22×C4⋊#595C2211yescharacteristic
24C22×C22⋊#595C2211yescharacteristic
25C22×C22⋊#595C2211yescharacteristic
26C22×C22⋊#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28#11763759—24no—
29#11763756—24no—
30#11763756—24no—
31#11763753—24no—
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×(C2×#595)⋊C4C2211yescharacteristic
47C2×(C2×#595)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2211yescharacteristic
50C2×C22⋊C4×D17C2211yescharacteristic
51C2×C22⋊C4×D17C2211yescharacteristic
52C2×C42×D17C2211yescharacteristic
53#11762703C411yescharacteristic, complemented
54#11762702C411yescharacteristic, complemented
55#11762701C411yescharacteristic, complemented
56#11762700C411yescharacteristic, complemented
57#11762699C411yescharacteristic, complemented
58#11762698C411yescharacteristic, complemented
59#11762697C411yescharacteristic, complemented
60#95×D17C2211yescharacteristic
61#95×D17C2211yescharacteristic
62C17×#388C411yescharacteristic, complemented
63C24×D17C2311yescharacteristic
64C23×#595—22no—
65C23×#595—22no—
66C23×#595—22no—
67C23×#595—41no—
68C23×#595—41no—
69C23×#595—41no—
70C23×#595—41no—
71C23×#595C2311yescharacteristic
72C23×#595C2311yescharacteristic
73C23×#595C2311yescharacteristic
74C23×#595C2311yescharacteristic
75C23×#595C2311yescharacteristic
76C23×#595C2311yescharacteristic
77C23×#595C2311yescharacteristic
78C23×#595C2311yescharacteristic
79C22×C4×D17C2311yescharacteristic
80C22×C4×D17C2311yescharacteristic
81C22×C4×D17C2311yescharacteristic
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×C4×D17C2311yescharacteristic
85C2×C22⋊#595—22no—
86C2×C22⋊#595—22no—
87C2×C22⋊#595—22no—
88C2×C22⋊#595—22no—
89C2×C22⋊#595—22no—
90C2×C22⋊#595—41no—
91C2×C22⋊#595—41no—
92C2×C22⋊#595—41no—
93C2×C22⋊#595—41no—
94C2×C4⋊#595—22no—
95C2×C4⋊#595—22no—
96C2×C4⋊#595—22no—
97C2×C4⋊#595—22no—
98C2×C4⋊#595—22no—
99C2×C4⋊#595—22no—
100C2×C4⋊#595—22no—
101C2×C4⋊#595—22no—
102C2×C4⋊#595—22no—
103C2×C4⋊#595—22no—
104C2×C4⋊#595—22no—
105C2×C4⋊#595—41no—
106C2×C4⋊#595—41no—
107C2×C4⋊#595—41no—
108C2×C4⋊#595—41no—
109C2×C4⋊#595—41no—
110C2×C4⋊#595—41no—
111C2×C4⋊#595—41no—
112C2×C4⋊#595—41no—
113C2×C4⋊#595—41no—
114C2×C4⋊#595—41no—
115C2×C4×#595—22no—
116C2×C4×#595—22no—
117C2×C4×#595—41no—
118C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
119C2×C22⋊C4×C17C2×C411yescharacteristic
120C2×C22⋊C4×C17C2×C411yescharacteristic
121C2×C22⋊C4×C17C2×C411yescharacteristic
122C2×C42×C17C2×C411yescharacteristic, complemented
123C2×C22⋊Dic17C2×C411yescharacteristic
124C2×C22⋊Dic17C2×C411yescharacteristic
125C2×C22⋊Dic17C2×C411yescharacteristic
126C2×#63227C2×C411yescharacteristic
127C2×#63227C2×C411yescharacteristic
128C2×#63227C2×C411yescharacteristic
129C2×#63227C2×C411yescharacteristic
130C2×#63227C2×C411yescharacteristic
131C2×#63227C2×C411yescharacteristic
132C2×C4⋊Dic17C2×C411yescharacteristic, complemented
133C2×#63225C2×C411yescharacteristic, complemented
134C2×#63225C2×C411yescharacteristic, complemented
135C2×C4×Dic17C2×C411yescharacteristic, complemented
136C2×C4×Dic17C2×C411yescharacteristic, complemented
137C2×C4×Dic17C2×C411yescharacteristic, complemented
138C4⋊C4×D17—41no—
139C4⋊C4×D17—41no—
140C22⋊C4×D17—22no—
141C22⋊C4×D17—22no—
142C22⋊C4×D17—41no—
143C22⋊C4×D17—41no—
144C22⋊C4×D17D414yes—
145C22⋊C4×D17Q814yes—
146C42×D17—22no—
147C42×D17—22no—
148(C2×#595)⋊C4—22no—
149(C2×#595)⋊C4—22no—
150(C2×#595)⋊C4—22no—
151(C2×#595)⋊C4—22no—
152(C2×#595)⋊C4—22no—
153(C2×#595)⋊C4—22no—
154(C2×#595)⋊C4—22no—
155(C2×#595)⋊C4—22no—
156(C2×#595)⋊C4—41no—
157(C2×#595)⋊C4—41no—
158(C2×#595)⋊C4—41no—
159(C2×#595)⋊C4—41no—
160(C2×#595)⋊C4—41no—
161(C2×#595)⋊C4—41no—
162(C2×#595)⋊C4—41no—
163(C2×#595)⋊C4D414yes—
164C17×#95C2×C411yescharacteristic, complemented
165C17×#95C2×C411yescharacteristic, complemented
166#10587502C2×C411yescharacteristic, complemented
167#10587502C2×C411yescharacteristic, complemented
168#10587502C2×C411yescharacteristic, complemented
169#10587502C2×C411yescharacteristic, complemented
170#10587502C2×C411yescharacteristic, complemented
171#10587502C2×C411yescharacteristic, complemented
172C24×C17C22×C411yescharacteristic
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17C22×C411yescharacteristic
186C23×D17C2×D412yes—
187C23×D17C2×Q812yes—
188C23×D17C2411yescharacteristic
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—21no—
228C22×#595—21no—
229C22×#595—21no—
230C22×#595—21no—
231C22×#595—21no—
232C22×#595—21no—
233C22×#595—21no—
234C22×#595—21no—
235C22×#595—21no—
236C22×#595—21no—
237C22×#595—21no—
238C22×#595—21no—
239C22×#595—21no—
240C22×#595—21no—
241C22×#595—44no—
242C22×#595—44no—
243C22×#595—44no—
244C22×#595—44no—
245C22×#595—44no—
246C22×#595—44no—
247C22×#595—44no—
248C22×#595C2×D412yes—
249C22×#595C2×D412yes—
250C22×#595#4112yes—
251C22×#595#4112yes—
252C22×C4×C17C22×C411yescharacteristic
253C22×C4×C17C22×C411yescharacteristic
254C22×C4×C17C22×C411yescharacteristic
255C22×C4×C17C22×C411yescharacteristic
256C22×C4×C17C22×C411yescharacteristic
257C22×C4×C17C22×C411yescharacteristic
258C22×Dic17C22×C411yescharacteristic
259C22×Dic17C22×C411yescharacteristic
260C22×Dic17C22×C411yescharacteristic
261C22×Dic17C22×C411yescharacteristic
262C22×Dic17C22×C411yescharacteristic
263C22×Dic17C22×C411yescharacteristic
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×D17—21no—
291C2×C4×D17—21no—
292C2×C4×D17—21no—
293C2×C4×D17—21no—
294C2×C4×D17C2×D412yes—
295C2×C4×D17C2×D412yes—
296C2×C4×D17C2×D412yes—
297C2×C4×D17C2×Q812yes—
298C2×C4×D17C2×Q812yes—
299C2×C4×D17#4112yes—
300C22⋊#595—44no—
301C22⋊#595—44no—
302C22⋊#595—44no—
303C4⋊#595—44no—
304C4⋊#595—44no—
305C4⋊#595—44no—
306C4⋊#595—44no—
307C4⋊#595—44no—
308C4⋊#595—44no—
309C4⋊#595—44no—
310C4×#595—44no—
311C4⋊C4×C17—41no—
312C22⋊C4×C17—22no—
313C22⋊C4×C17—41no—
314C22⋊C4×C17C4⋊C414yescomplemented
315C42×C17—22no—
316C22⋊Dic17—22no—
317C22⋊Dic17—41no—
318C22⋊Dic17C4⋊C414yescomplemented
319#63227—22no—
320#63227—22no—
321#63227—41no—
322#63227—41no—
323#63227C4⋊C414yescomplemented
324#63227C4⋊C414yescomplemented
325C4⋊Dic17—41no—
326#63225—41no—
327#63225—41no—
328C4×Dic17—22no—
329C4×Dic17—22no—
330C4×Dic17—22no—
331#14403—171nomaximal, Sylow
332C23×C17—21no—
333C23×C17—21no—
334C23×C17—21no—
335C23×C17—21no—
336C23×C17—21no—
337C23×C17—21no—
338C23×C17C2×C4⋊C412yes—
339C23×C17C23×C411yescharacteristic
340C22×D17—21no—
341C22×D17—21no—
342C22×D17—21no—
343C22×D17—21no—
344C22×D17—21no—
345C22×D17—21no—
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
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×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17C2×C4⋊C412yes—
375C22×D17C22×D411yescharacteristic
376C22×D17C22×D411yescharacteristic
377C22×D17C22×Q811yescharacteristic
378C22×D17C2×#4111yescharacteristic
379C22×D17C2×#4111yescharacteristic
380C22×D17C2×#4111yescharacteristic
381C22×D17H(5,𝔽2)11yescharacteristic
382C22×D17H(5,𝔽2)11yescharacteristic
383C22×D17H(5,𝔽2)11yescharacteristic
384C22×D17H(5,𝔽2)11yescharacteristic
385C22×D17H(5,𝔽2)11yescharacteristic
386C22×D172−1+411yescharacteristic
387C22×D172−1+411yescharacteristic
388C22×D172−1+411yescharacteristic
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—416no—
402C2×#595—41no—
403C2×#595—41no—
404C2×#595—41no—
405C2×#595—41no—
406C2×#595—41no—
407C2×#595—41no—
408C2×#595—41no—
409C2×#595—41no—
410C2×#595—41no—
411C2×#595—41no—
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—41no—
437C2×#595—41no—
438C2×#595—41no—
439C2×#595—41no—
440C2×#595—41no—
441C2×#595—41no—
442C2×#595—41no—
443C2×#595—41no—
444C2×#595—41no—
445C2×#595—41no—
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×C17—21no—
455C2×C4×C17—21no—
456C2×C4×C17—21no—
457C2×C4×C17—21no—
458C2×C4×C17—21no—
459C2×C4×C17—21no—
460C2×C4×C17—21no—
461C2×C4×C17C2×C4⋊C412yes—
462C2×C4×C17C2×C4⋊C412yes—
463C2×C4×C17C4×D412yes—
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×Dic17—21no—
473C2×Dic17—21no—
474C2×Dic17—21no—
475C2×Dic17—21no—
476C2×Dic17—21no—
477C2×Dic17—21no—
478C2×Dic17—21no—
479C2×Dic17C2×C4⋊C412yes—
480C2×Dic17C2×C4⋊C412yes—
481C2×Dic17C4×D412yes—
482C4×D17—22no—
483C4×D17—22no—
484C4×D17—22no—
485C4×D17—22no—
486C4×D17—22no—
487C4×D17—22no—
488C4×D17—22no—
489C4×D17—22no—
490C4×D17—22no—
491C4×D17—22no—
492C4×D17—22no—
493C4×D17—22no—
494C4×D17—41no—
495C4×D17—41no—
496C4×D17—41no—
497C4×D17—41no—
498C4×D17—41no—
499C4×D17—41no—
500C4×D17—41no—
501C4×D17—41no—
502C4×D17—41no—
503C4×D17—41no—
504C4×D17—41no—
505C4×D17—41no—
506C2×#388—171no—
507C2×#388—171no—
508C2×#385—171no—
509C2×#385—171no—
510C2×#382—171no—
511#1444—171no—
512#1444—171no—
513#1442—171no—
514#1441—171no—
515#1439—171no—
516#1439—171no—
517#1436—171no—
518C4⋊#95—171no—
519C4⋊#95—171no—
520C22⋊#95—171no—
521C22×C17—22no—
522C22×C17—22no—
523C22×C17—22no—
524C22×C17—41no—
525C22×C17—41no—
526C22×C17—41no—
527C22×C17—41no—
528C22×C17C22×C4⋊C411yescharacteristic
529C22×C17C2×C4×D411yescharacteristic
530C22×C17C4×#4111yescharacteristic
531C22×C17#51811yescharacteristic
532C22×C17#52011yescharacteristic
533C22×C17#52011yescharacteristic
534C22×C17#52011yescharacteristic
535C2×D17—22no—
536C2×D17—22no—
537C2×D17—22no—
538C2×D17—41no—
539C2×D17—41no—
540C2×D17—41no—
541C2×D17—41no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17#53511yescharacteristic
551C2×D17#53511yescharacteristic
552C2×D17#53611yescharacteristic
553C2×D17#53711yescharacteristic
554C2×D17#53811yescharacteristic
555C2×D17#53911yescharacteristic
556C2×D17#54011yescharacteristic
557C2×D17#54111yescharacteristic
558C2×D17#54211yescharacteristic
559C2×D17#54211yescharacteristic
560C2×D17#54411yescharacteristic
561C2×D17#54411yescharacteristic
562C2×D17D4211yescharacteristic
563C2×D17#54611yescharacteristic
564C2×D17#54611yescharacteristic
565C2×D17#54611yescharacteristic
566C2×D17#54711yescharacteristic
567C2×D17#54711yescharacteristic
568C2×D17D4×Q811yescharacteristic
569C2×D17#55111yescharacteristic
570C2×D17#55211yescharacteristic
571C2×D17#55411yescharacteristic
572C2×D17#55411yescharacteristic
573C2×D17#55411yescharacteristic
574C2×D17H(3,𝔽4)11yescharacteristic
575C2×D17#56211yescharacteristic
576C2×D17#56211yescharacteristic
577C2×D17#56311yescharacteristic
578#595—42no—
579#595—42no—
580#595—42no—
581#595—42no—
582#595—81no—
583#595—81no—
584#595—81no—
585#595—81no—
586C4×C17—22no—
587C4×C17—22no—
588C4×C17—22no—
589C4×C17—41no—
590C4×C17—41no—
591C4×C17—41no—
592Dic17—22no—
593Dic17—22no—
594Dic17—22no—
595Dic17—41no—
596Dic17—41no—
597Dic17—41no—
598C24×C4—171no—
599C22×C4⋊C4—171no—
600C22×C4⋊C4—171no—
601C22×C4⋊C4—171no—
602C22×C4⋊C4—171no—
603C22×C4⋊C4—171no—
604C22×C4⋊C4—171no—
605C22×C4⋊C4—171no—
606C22×C4⋊C4—171no—
607C22×C22⋊C4—171no—
608C22×C22⋊C4—171no—
609C22×C22⋊C4—171no—
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C42—171no—
614C22×C42—171no—
615#388—171no—
616#388—171no—
617#388—171no—
618#388—171no—
619#388—171no—
620#388—171no—
621#388—171no—
622#388—344no—
623#388#59511yescharacteristic, complemented
624#385—344no—
625#385—344no—
626#382—344no—
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×#95—171no—
636C2×#95—171no—
637C2×#95—171no—
638C2×#95—171no—
639C2×#95—171no—
640C2×#95—171no—
641C2×#95—171no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×C17—42no—
646C2×C17#231711yescharacteristic
647C2×C17#232411yescharacteristic
648C2×C17#233411yescharacteristic
649C2×C17D4×C4⋊C411yescharacteristic
650C2×C17#234911yescharacteristic
651C2×C17#235911yescharacteristic
652C2×C17#237911yescharacteristic
653D17—42no—
654D17#267011yescharacteristic
655D17#267211yescharacteristic
656D17#269811yescharacteristic
657D17#270411yescharacteristic
658D17#270611yescharacteristic
659D17#272011yescharacteristic
660D17#276311yescharacteristic
661D17#276811yescharacteristic
662C25—171no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—171no—
670C23×C4—171no—
671C23×C4—171no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—342no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—681no—
681C23×C4—681no—
682C23×C4—681no—
683C23×C4—681no—
684C2×C4⋊C4—171no—
685C2×C4⋊C4—171no—
686C2×C4⋊C4—171no—
687C2×C4⋊C4—342no—
688C2×C4⋊C4—342no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—342no—
696C2×C4⋊C4—342no—
697C2×C4⋊C4—342no—
698C2×C4⋊C4—681no—
699C2×C4⋊C4—681no—
700C2×C4⋊C4—681no—
701C2×C4⋊C4—681no—
702C2×C4⋊C4—681no—
703C2×C4⋊C4—681no—
704C2×C4⋊C4—681no—
705C2×C4⋊C4—681no—
706C2×C4⋊C4—681no—
707C2×C4⋊C4—681no—
708C2×C4⋊C4—681no—
709C2×C4⋊C4—681no—
710C2×C4⋊C4C2×#59511yescharacteristic, complemented
711C2×C22⋊C4—171no—
712C2×C22⋊C4—171no—
713C2×C22⋊C4—171no—
714C2×C22⋊C4—174no—
715C2×C22⋊C4—174no—
716C2×C22⋊C4—171no—
717C2×C22⋊C4—171no—
718C2×C22⋊C4—171no—
719C2×C22⋊C4—171no—
720C2×C22⋊C4—171no—
721C2×C22⋊C4—171no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—342no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—342no—
727C2×C22⋊C4—342no—
728C2×C22⋊C4—342no—
729C2×C22⋊C4—681no—
730C2×C22⋊C4—681no—
731C2×C22⋊C4—681no—
732C2×C22⋊C4—681no—
733C2×C22⋊C4—681no—
734C2×C22⋊C4—681no—
735C2×C22⋊C4C2×#59511yescharacteristic
736C2×C22⋊C4C2×#59511yescharacteristic
737C2×C22⋊C4C2×#59511yescharacteristic
738C2×C42—171no—
739C2×C42—171no—
740C2×C42—171no—
741C2×C42—342no—
742C2×C42—342no—
743C2×C42—342no—
744C2×C42—342no—
745C2×C42—681no—
746C2×C42C2×#59511yescharacteristic, complemented
747#95—174no—
748#95—171no—
749#95—171no—
750#95—171no—
751#95—171no—
752#95—171no—
753#95—171no—
754#95—342no—
755#95—342no—
756#95—342no—
757#95—342no—
758#95—342no—
759#95—342no—
760#95—342no—
761#95—342no—
762#95—681no—
763#95—681no—
764#95—681no—
765#95—681no—
766#95—681no—
767#95—681no—
768#95—681no—
769#95C2×#59511yescharacteristic, complemented
770#95C2×#59511yescharacteristic, complemented
771C17#1440311yescharacteristic, complemented, Sylow
772C24—171no—
773C24—172no—
774C24—172no—
775C24—171no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24C22×#59511yescharacteristic
789C22×C4—171no—
790C22×C4—171no—
791C22×C4—171no—
792C22×C4—172no—
793C22×C4—172no—
794C22×C4—172no—
795C22×C4—172no—
796C22×C4—172no—
797C22×C4—172no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—172no—
802C22×C4—171no—
803C22×C4—171no—
804C22×C4—171no—
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—341no—
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—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4—684no—
890C22×C4—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4—684no—
894C22×C4C22×#59511yescharacteristic
895C22×C4C22×#59511yescharacteristic
896C22×C4C22×#59511yescharacteristic
897C22×C4C22×#59511yescharacteristic
898C22×C4C22×#59511yescharacteristic
899C22×C4C22×#59511yescharacteristic
900C4⋊C4—41no—
901C4⋊C4—681no—
902C4⋊C4—681no—
903C4⋊C4—681no—
904C4⋊C4—684no—
905C4⋊C4—684no—
906C4⋊C4—684no—
907C4⋊C4—684no—
908C4⋊C4—684no—
909C4⋊C4—684no—
910C4⋊C4—684no—
911C22⋊C4—22no—
912C22⋊C4—41no—
913C22⋊C4—174no—
914C22⋊C4—174no—
915C22⋊C4—174no—
916C22⋊C4—342no—
917C22⋊C4—342no—
918C22⋊C4—342no—
919C22⋊C4—681no—
920C22⋊C4—681no—
921C22⋊C4—681no—
922C22⋊C4—684no—
923C22⋊C4—684no—
924C22⋊C4—684no—
925C22⋊C4C4⋊#59514yescomplemented
926C42—22no—
927C42—342no—
928C42—342no—
929C42—342no—
930C42—684no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—171no—
938C23—171no—
939C23—171no—
940C23—171no—
941C23—171no—
942C23—171no—
943C23—171no—
944C23—171no—
945C23—171no—
946C23—171no—
947C23—171no—
948C23—171no—
949C23—171no—
950C23—171no—
951C23—172no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
964C23—341no—
965C23—341no—
966C23—341no—
967C23—341no—
968C23—341no—
969C23—341no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23—681no—
976C23—681no—
977C23—681no—
978C23—681no—
979C23—681no—
980C23—681no—
981C23—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23C2×C4⋊#59512yes—
987C23C23×#59511yescharacteristic
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—172no—
1004C2×C4—172no—
1005C2×C4—172no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—341no—
1019C2×C4—341no—
1020C2×C4—341no—
1021C2×C4—341no—
1022C2×C4—341no—
1023C2×C4—341no—
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—342no—
1035C2×C4—342no—
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—681no—
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—681no—
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—6816no—
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×C4—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4—681no—
1098C2×C4—681no—
1099C2×C4—681no—
1100C2×C4—681no—
1101C2×C4—681no—
1102C2×C4C2×C4⋊#59512yes—
1103C2×C4C2×C4⋊#59512yes—
1104C2×C4D4×#59512yes—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
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—171no—
1125C22—171no—
1126C22—171no—
1127C22—171no—
1128C22—171no—
1129C22—171no—
1130C22—171no—
1131C22—171no—
1132C22—171no—
1133C22—171no—
1134C22—171no—
1135C22—171no—
1136C22—171no—
1137C22—171no—
1138C22—171no—
1139C22—171no—
1140C22—342no—
1141C22—342no—
1142C22—342no—
1143C22—682no—
1144C22—682no—
1145C22—682no—
1146C22—682no—
1147C22—682no—
1148C22—682no—
1149C22—682no—
1150C22—682no—
1151C22—681no—
1152C22—681no—
1153C22—681no—
1154C22—681no—
1155C22C22×C4⋊#59511yescharacteristic
1156C22C2×D4×#59511yescharacteristic
1157C22#41×#59511yescharacteristic
1158C22#1176387611yescharacteristic
1159C22#1176387811yescharacteristic
1160C22#1176387811yescharacteristic
1161C22#1176387811yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—342no—
1169C4—342no—
1170C4—342no—
1171C4—682no—
1172C4—682no—
1173C4—682no—
1174C4—682no—
1175C4—681no—
1176C4—681no—
1177C4—681no—
1178C4—1361no—
1179C4—1361no—
1180C4—1361no—
1181C4—1361no—
1182C2—42no—
1183C2—171no—
1184C2—171no—
1185C2—171no—
1186C2—171no—
1187C2—171no—
1188C2—171no—
1189C2—171no—
1190C2—171no—
1191C2—682no—
1192C2#1454526511yescharacteristic
1193C2#1454527211yescharacteristic
1194C2#1454528211yescharacteristic
1195C2D4×C4⋊#59511yescharacteristic
1196C2#1454529711yescharacteristic
1197C2#1454530711yescharacteristic
1198C2#1454532711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#388C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenter#388#595
hypocenterC17#14403
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. C2×#11763753C2semidirect
5. #14543972C2semidirect
6. #14543972C2semidirect
7. #14543970C2semidirect
8. #14543969C2semidirect
11. #14543964C2semidirect
12. #14543962C2semidirect
13. #14543961C2semidirect
53. #11762703C4semidirect
54. #11762702C4semidirect
55. #11762701C4semidirect
56. #11762700C4semidirect
57. #11762699C4semidirect
58. #11762698C4semidirect
59. #11762697C4semidirect
62. C17×#388C4semidirect
118. C2×C4⋊C4×C17C2×C4semidirect
122. C2×C42×C17C2×C4semidirect
132. C2×C4⋊Dic17C2×C4semidirect
133. C2×#63225C2×C4semidirect
134. C2×#63225C2×C4semidirect
135. C2×C4×Dic17C2×C4semidirect
136. C2×C4×Dic17C2×C4semidirect
137. C2×C4×Dic17C2×C4semidirect
164. C17×#95C2×C4semidirect
165. C17×#95C2×C4semidirect
166. #10587502C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502C2×C4semidirect
169. #10587502C2×C4semidirect
170. #10587502C2×C4semidirect
171. #10587502C2×C4semidirect
314. C22⋊C4×C17C4⋊C4semidirect
318. C22⋊Dic17C4⋊C4semidirect
323. #63227C4⋊C4semidirect
324. #63227C4⋊C4semidirect
623. #388#595semidirect
710. C2×C4⋊C4C2×#595semidirect
746. C2×C42C2×#595semidirect
769. #95C2×#595semidirect
770. #95C2×#595semidirect
771. C17#14403semidirect
925. 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×#117637562
C2×#117637532
#145439722
#145439702
#145439692
#145439672
#145439642
#145439622
#145439612
#145439572
D17×#3882
#1440317