Finite Group Databasebeta

← #17963000

Subgroups — #17963000

Order 4352.

1826 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×C4×C4⋊#595C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×#595C211yesmaximal, characteristic
5#14543965C211yesmaximal, characteristic
6#14543965C211yesmaximal, characteristic
7#14543964C211yesmaximal, characteristic, complemented
8#14543964C211yesmaximal, characteristic, complemented
9#14543964C211yesmaximal, characteristic, complemented
10#14543963C211yesmaximal, characteristic, complemented
11#14543961C211yesmaximal, characteristic, complemented
12#14543960C211yesmaximal, characteristic, complemented
13#14543957C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic, complemented
15D17×#388C211yesmaximal, characteristic
16C24×#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C22⋊#595C2211yescharacteristic
21C22×C22⋊#595C2211yescharacteristic
22C22×C22⋊#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26C22×C4×#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28#11763759C418yescomplemented
29#11763756C418yescomplemented
30C4×C4⋊#595—24no—
31C22⋊C4×#595—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—41no—
67C23×#595—41no—
68C23×#595—41no—
69C23×#595—41no—
70C23×#595C2×C414yes—
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—41no—
88C2×C22⋊#595—41no—
89C2×C22⋊#595—41no—
90C2×C22⋊#595—41no—
91C2×C22⋊#595C2×C414yes—
92C2×C22⋊#595C2×C414yes—
93C2×C22⋊#595C2×C414yes—
94C2×C4⋊#595—22no—
95C2×C4⋊#595—22no—
96C2×C4⋊#595—22no—
97C2×C4⋊#595—22no—
98C2×C4⋊#595—41no—
99C2×C4⋊#595—41no—
100C2×C4⋊#595C2×C414yes—
101C2×C4⋊#595C2×C414yes—
102C2×C4⋊#595C2×C414yescomplemented
103C2×C4×#595—22no—
104C2×C4×#595—22no—
105C2×C4×#595—22no—
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—41no—
116C2×C4×#595C2×C414yescomplemented
117C2×C4×#595D414yes—
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×D17C2×C414yes—
145C22⋊C4×D17C2×C414yes—
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—41no—
155(C2×#595)⋊C4—41no—
156(C2×#595)⋊C4—41no—
157(C2×#595)⋊C4—41no—
158(C2×#595)⋊C4—41no—
159(C2×#595)⋊C4—41no—
160(C2×#595)⋊C4C2×C414yes—
161(C2×#595)⋊C4C2×C414yes—
162(C2×#595)⋊C4C2×C414yescomplemented
163(C2×#595)⋊C4C2×C414yescomplemented
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×D17C22×C412yes—
187C23×D17C22×C412yes—
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—28no—
234C22×#595—44no—
235C22×#595—44no—
236C22×#595—44no—
237C22×#595—44no—
238C22×#595—44no—
239C22×#595—44no—
240C22×#595C22×C412yes—
241C22×#595C22×C412yes—
242C22×#595C22×C412yes—
243C22×#595C22×C412yes—
244C22×#595C22×C412yes—
245C22×#595C22×C412yes—
246C22×#595C22×C412yes—
247C22×#595C22×C412yes—
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×D17C22×C412yes—
295C2×C4×D17C22×C412yes—
296C2×C4×D17C22×C412yes—
297C2×C4×D17C22×C412yes—
298C2×C4×D17C2×D412yes—
299C2×C4×D17#4112yes—
300C22⋊#595—28no—
301C22⋊#595—44no—
302C22⋊#595—44no—
303C4⋊#595—28no—
304C4⋊#595—28no—
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×C17C4214yescomplemented
315C42×C17—22no—
316C22⋊Dic17—22no—
317C22⋊Dic17—41no—
318C22⋊Dic17C4214yescomplemented
319#63227—22no—
320#63227—22no—
321#63227—41no—
322#63227—41no—
323#63227C4214yescomplemented
324#63227C4214yescomplemented
325C4⋊Dic17—41no—
326#63225—41no—
327#63225—41no—
328C4×Dic17—22no—
329C4×Dic17—22no—
330C4×Dic17—22no—
331#13789—171nomaximal, Sylow
332C23×C17—21no—
333C23×C17—21no—
334C23×C17—21no—
335C23×C17—21no—
336C23×C17—21no—
337C23×C17—21no—
338C23×C17C2×C4212yes—
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×C4212yes—
375C22×D17C23×C411yescharacteristic
376C22×D17C23×C411yescharacteristic
377C22×D17C22×D411yescharacteristic
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—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—22no—
412C2×#595—22no—
413C2×#595—22no—
414C2×#595—22no—
415C2×#595—22no—
416C2×#595—22no—
417C2×#595—22no—
418C2×#595—22no—
419C2×#595—416no—
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×#595C4×D414yes—
445C2×#595C4×D414yes—
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×C4212yes—
462C2×C4×C17C2×C4212yes—
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×C4212yes—
480C2×Dic17C2×C4212yes—
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×C4×C4⋊C4—171no—
510C2×C4×C22⋊C4—171no—
511#1437—171no—
512#1437—171no—
513#1436—171no—
514#1436—171no—
515#1436—171no—
516#1436—171no—
517C4⋊#95—171no—
518#1434—171no—
519C22⋊#95—171no—
520C4×#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×C4211yescharacteristic
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×D17C2×C4×D411yescharacteristic
551C2×D17C2×C4×D411yescharacteristic
552C2×D17C4×#4111yescharacteristic
553C2×D17C4×#4111yescharacteristic
554C2×D17#51811yescharacteristic
555C2×D17#51811yescharacteristic
556C2×D17#51811yescharacteristic
557C2×D17#51911yescharacteristic
558C2×D17#52011yescharacteristic
559C2×D17#52011yescharacteristic
560C2×D17#52011yescharacteristic
561C2×D17#52011yescharacteristic
562C2×D17#53411yescharacteristic
563C2×D17#53511yescharacteristic
564C2×D17#53611yescharacteristic
565C2×D17#53711yescharacteristic
566C2×D17#53811yescharacteristic
567C2×D17#53811yescharacteristic
568C2×D17#53811yescharacteristic
569C2×D17#53911yescharacteristic
570C2×D17#53911yescharacteristic
571C2×D17#53911yescharacteristic
572C2×D17#54011yescharacteristic
573C2×D17#54111yescharacteristic
574C2×D17#54211yescharacteristic
575C2×D17#54211yescharacteristic
576C2×D17#54211yescharacteristic
577C2×D17#54211yescharacteristic
578#595—24no—
579#595—24no—
580#595—42no—
581#595—42no—
582#595—42no—
583#595—42no—
584#595—42no—
585#595—42no—
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×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C22⋊C4—171no—
607C22×C22⋊C4—171no—
608C22×C22⋊C4—171no—
609C22×C42—171no—
610C22×C42—171no—
611C22×C42—171no—
612C22×C42—171no—
613C22×C42—171no—
614C22×C42—171no—
615#388—178no—
616#388—171no—
617#388—171no—
618#388—171no—
619#388—171no—
620#388—171no—
621#388—171no—
622#388—171no—
623#388#59511yescharacteristic, complemented
624#385—178no—
625C4×C4⋊C4—344no—
626C4×C22⋊C4—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×C17C42×D411yescharacteristic
647C2×C17#227411yescharacteristic
648C2×C17#227511yescharacteristic
649C2×C17#232211yescharacteristic
650C2×C17#232411yescharacteristic
651C2×C17#233411yescharacteristic
652C2×C17#233711yescharacteristic
653D17—42no—
654D17#232111yescharacteristic
655D17#232311yescharacteristic
656D17#232511yescharacteristic
657D17#232611yescharacteristic
658D17#233211yescharacteristic
659D17#233411yescharacteristic
660D17#233511yescharacteristic
661D17#233511yescharacteristic
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—174no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—681no—
681C23×C4—681no—
682C23×C4—681no—
683C23×C4—681no—
684C2×C4⋊C4—174no—
685C2×C4⋊C4—174no—
686C2×C4⋊C4—174no—
687C2×C4⋊C4—171no—
688C2×C4⋊C4—171no—
689C2×C4⋊C4—171no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—681no—
695C2×C4⋊C4—681no—
696C2×C4⋊C4—681no—
697C2×C4⋊C4—681no—
698C2×C4⋊C4C2×#59511yescharacteristic, complemented
699C2×C22⋊C4—171no—
700C2×C22⋊C4—171no—
701C2×C22⋊C4—171no—
702C2×C22⋊C4—174no—
703C2×C22⋊C4—174no—
704C2×C22⋊C4—174no—
705C2×C22⋊C4—171no—
706C2×C22⋊C4—171no—
707C2×C22⋊C4—171no—
708C2×C22⋊C4—174no—
709C2×C22⋊C4—174no—
710C2×C22⋊C4—171no—
711C2×C22⋊C4—171no—
712C2×C22⋊C4—171no—
713C2×C22⋊C4—342no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—342no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4—681no—
720C2×C22⋊C4—681no—
721C2×C22⋊C4—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4C2×#59511yescharacteristic
724C2×C22⋊C4C2×#59511yescharacteristic
725C2×C22⋊C4C2×#59511yescharacteristic
726C2×C42—171no—
727C2×C42—171no—
728C2×C42—171no—
729C2×C42—174no—
730C2×C42—174no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—342no—
734C2×C42—342no—
735C2×C42—342no—
736C2×C42—681no—
737C2×C42—681no—
738C2×C42—681no—
739C2×C42—681no—
740C2×C42—681no—
741C2×C42—681no—
742C2×C42—681no—
743C2×C42—681no—
744C2×C42—681no—
745C2×C42—681no—
746C2×C42C2×#59511yescharacteristic, complemented
747#95—174no—
748#95—174no—
749#95—174no—
750#95—174no—
751#95—171no—
752#95—171no—
753#95—171no—
754#95—171no—
755#95—171no—
756#95—171no—
757#95—342no—
758#95—342no—
759#95—342no—
760#95—342no—
761#95—342no—
762#95—342no—
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#1378911yescharacteristic, 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—172no—
790C22×C4—172no—
791C22×C4—172no—
792C22×C4—172no—
793C22×C4—172no—
794C22×C4—172no—
795C22×C4—171no—
796C22×C4—171no—
797C22×C4—171no—
798C22×C4—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—172no—
802C22×C4—172no—
803C22×C4—172no—
804C22×C4—172no—
805C22×C4—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—172no—
809C22×C4—172no—
810C22×C4—171no—
811C22×C4—171no—
812C22×C4—171no—
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—348no—
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—341no—
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—348no—
902C4⋊C4—348no—
903C4⋊C4—681no—
904C4⋊C4—681no—
905C4⋊C4—681no—
906C4⋊C4—684no—
907C22⋊C4—22no—
908C22⋊C4—41no—
909C22⋊C4—174no—
910C22⋊C4—174no—
911C22⋊C4—174no—
912C22⋊C4—342no—
913C22⋊C4—342no—
914C22⋊C4—348no—
915C22⋊C4—342no—
916C22⋊C4—681no—
917C22⋊C4—681no—
918C22⋊C4—681no—
919C22⋊C4—684no—
920C22⋊C4—684no—
921C22⋊C4C4×#59514yescomplemented
922C42—22no—
923C42—342no—
924C42—342no—
925C42—342no—
926C42—684no—
927C42—684no—
928C42—684no—
929C42—684no—
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—174no—
1004C2×C4—174no—
1005C2×C4—172no—
1006C2×C4—172no—
1007C2×C4—172no—
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—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—341no—
1033C2×C4—341no—
1034C2×C4—341no—
1035C2×C4—341no—
1036C2×C4—341no—
1037C2×C4—341no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—342no—
1055C2×C4—342no—
1056C2×C4—341no—
1057C2×C4—341no—
1058C2×C4—341no—
1059C2×C4—341no—
1060C2×C4—341no—
1061C2×C4—341no—
1062C2×C4—341no—
1063C2×C4—341no—
1064C2×C4—341no—
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—6816no—
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—344no—
1169C4—344no—
1170C4—342no—
1171C4—342no—
1172C4—342no—
1173C4—682no—
1174C4—682no—
1175C4—682no—
1176C4—682no—
1177C4—682no—
1178C4—682no—
1179C4—681no—
1180C4—681no—
1181C4—681no—
1182C2—42no—
1183C2—171no—
1184C2—171no—
1185C2—171no—
1186C2—171no—
1187C2—171no—
1188C2—171no—
1189C2—171no—
1190C2—171no—
1191C2—682no—
1192C2C4×D4×#59511yescharacteristic
1193C2#1454522111yescharacteristic
1194C2#1454522311yescharacteristic
1195C2#1454527011yescharacteristic
1196C2#1454527211yescharacteristic
1197C2#1454528211yescharacteristic
1198C2#1454528511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#388C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenter#388#595
hypocenterC17#13789
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊#595C2semidirect
7. #14543964C2semidirect
8. #14543964C2semidirect
9. #14543964C2semidirect
10. #14543963C2semidirect
11. #14543961C2semidirect
12. #14543960C2semidirect
14. #95×#595C2semidirect
28. #11763759C4semidirect
29. #11763756C4semidirect
53. #11762703C4semidirect
54. #11762702C4semidirect
55. #11762701C4semidirect
56. #11762700C4semidirect
57. #11762699C4semidirect
58. #11762698C4semidirect
59. #11762697C4semidirect
62. C17×#388C4semidirect
102. C2×C4⋊#595C2×C4semidirect
116. C2×C4×#595C2×C4semidirect
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
162. (C2×#595)⋊C4C2×C4semidirect
163. (C2×#595)⋊C4C2×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×C17C42semidirect
318. C22⋊Dic17C42semidirect
323. #63227C42semidirect
324. #63227C42semidirect
623. #388#595semidirect
698. C2×C4⋊C4C2×#595semidirect
746. C2×C42C2×#595semidirect
769. #95C2×#595semidirect
770. #95C2×#595semidirect
771. C17#13789semidirect
921. 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×C4×C4⋊#5952
C2×C22⋊C4×#5952
#145439652
#145439642
#145439632
#145439612
#145439602
#145439572
#95×#5952
D17×#3882
#1378917