Finite Group Databasebeta

← C22×#63066 #72301081

Subgroups — C22×#63066 #72301081

Order 1024.

477689 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63066C21192yesmaximal, direct product factor
2C22×#3549C213yesmaximal, complemented
3C22×#3543C2112yesmaximal, complemented
4C22×#3551C216yesmaximal, complemented
5C22×#3558C216yesmaximal, complemented
6C22×#3537C216yesmaximal, complemented
7C22×#3542C2112yesmaximal, complemented
8C22×#3529C213yesmaximal, complemented
9C22×#3500C211yesmaximal, characteristic, complemented
10C22×#3498C212yesmaximal, complemented
11C22×#3488C214yesmaximal, complemented
12C22×#3524C214yesmaximal, complemented
13C22×#3517C212yesmaximal, complemented
14C22×#3487C212yesmaximal, complemented
15C23×2−1+4C2211yescharacteristic, complemented
16C23×H(5,𝔽2)C2212yescomplemented
17C23×H(5,𝔽2)C2211yescharacteristic, complemented
18C24×#41C2212yescomplemented
19#63066C2214096yesdirect product factor
20C2×#3500C22196yescomplemented
21C2×#3498C221192yescomplemented
22C2×#3488C221384yescomplemented
23C2×#3524C221384yescomplemented
24C2×#3517C221192yescomplemented
25C2×#3487C221192yescomplemented
26C2×#3549C221288yescomplemented
27C2×#3543C2211152yescomplemented
28C2×#3551C221576yescomplemented
29C2×#3558C221576yescomplemented
30C2×#3537C221576yescomplemented
31C2×#3542C2211152yescomplemented
32C22×#559C22112yescomplemented
33C22×#557C2212yescomplemented
34C22×#555C22112yescomplemented
35C22×#555C2216yescomplemented
36C22×#553C22112yescomplemented
37C22×#553C22112yescomplemented
38C22×#552C22112yescomplemented
39C22×#551C22112yescomplemented
40C22×#550C22112yescomplemented
41C22×#550C2216yescomplemented
42C22×#550C2214yescomplemented
43C22×#550C2212yescomplemented
44C22×#550C2214yescomplemented
45C22×#547C2216yescomplemented
46C22×#548C22112yescomplemented
47C22×#548C2214yescomplemented
48C22×#548C2214yescomplemented
49C22×#546C22124yescomplemented
50C22×#546C22112yescomplemented
51C22×#546C22112yescomplemented
52C22×#546C22112yescomplemented
53C22×D42C22112yescomplemented
54C22×D42C2216yescomplemented
55C22×D42C22112yescomplemented
56C22×D42C22112yescomplemented
57C22×D42C22112yescomplemented
58C22×D42C22112yescomplemented
59C2×#3529C221288yescomplemented
60C22×#563C2211yescharacteristic, complemented
61C22×#563C2216yescomplemented
62C22×#562C22112yescomplemented
63C22×#562C2216yescomplemented
64C22×H(3,𝔽4)C2213yescomplemented
65C22×H(3,𝔽4)C2216yescomplemented
66C22×#560C2216yescomplemented
67C22×#560C22112yescomplemented
68C22×#560C22112yescomplemented
69C22×#560C22112yescomplemented
70C22×#536C2213yescomplemented
71C22×#542C22112yescomplemented
72C22×#540C22124yescomplemented
73C22×#540C22112yescomplemented
74C22×#540C22112yescomplemented
75C22×#537C22112yescomplemented
76C22×#535C2216yescomplemented
77C22×#535C22124yescomplemented
78C22×#535C2213yescomplemented
79C22×#535C2216yescomplemented
80C22×#535C22112yescomplemented
81C22×#535C2216yescomplemented
82C22×#535C2216yescomplemented
83C22×#538C22112yescomplemented
84C22×#538C22124yescomplemented
85C22×#534C22124yescomplemented
86C22×#534C22112yescomplemented
87C22×#532C2216yescomplemented
88C22×#532C2213yescomplemented
89C22×#532C2216yescomplemented
90C23×#127C2216yescomplemented
91C22×#529C2216yescomplemented
92C22×#529C22112yescomplemented
93C22×#529C22112yescomplemented
94C23×#124C2213yescomplemented
95C22×#525C22112yescomplemented
96C22×#525C2216yescomplemented
97C22×#525C2216yescomplemented
98C23×#121C22112yescomplemented
99C22×#520C2214yescomplemented
100C22×#519C2212yescomplemented
101C22×C4×#41C2211yescharacteristic, complemented
102C22×C4×#41C2212yescomplemented
103C22×2−1+4—416no—
104C22×2−1+4C23148yescomplemented
105C22×H(5,𝔽2)—432no—
106C22×H(5,𝔽2)—416no—
107C22×H(5,𝔽2)C23196yescomplemented
108C22×H(5,𝔽2)C23148yescomplemented
109C23×#41—432no—
110C23×#41C2314yes—
111C23×#41C2312yes—
112C23×#41C2311yescharacteristic
113C23×#41C23112yes—
114C23×#41C2316yes—
115C23×#41C2313yes—
116C23×#41C2313yes—
117C23×#41C2316yes—
118C23×#41C23112yes—
119C23×#41C23196yescomplemented
120C24×Q8C2312yes—
121C24×Q8C2313yes—
122C24×D4C2316yes—
123C24×D4C23112yes—
124C24×D4C2313yes—
125C24×D4C2316yes—
126C24×D4C2316yes—
127C24×D4C23124yes—
128C24×D4C23124yes—
129C25×C4C2316yes—
130#3558C2316144yescomplemented
131#3551C2316144yescomplemented
132#3549C2313072yescomplemented
133#3543C23112288yescomplemented
134#3542C23112288yescomplemented
135#3537C2316144yescomplemented
136#3529C2313072yescomplemented
137C2×#563C231288yescomplemented
138C2×#563C23148yescomplemented
139C2×#562C231288yescomplemented
140C2×#562C231576yescomplemented
141C2×H(3,𝔽4)C231288yescomplemented
142C2×H(3,𝔽4)C231144yescomplemented
143C2×#560C231288yescomplemented
144C2×#560C231576yescomplemented
145C2×#560C231576yescomplemented
146C2×#560C231576yescomplemented
147#3524C2314096yescomplemented
148#3517C2312048yescomplemented
149#3500C2311024yescomplemented
150#3498C2312048yescomplemented
151#3488C2314096yescomplemented
152#3487C2312048yescomplemented
153C2×#559C231576yescomplemented
154C2×#557C23196yescomplemented
155C2×#555C231288yescomplemented
156C2×#555C231576yescomplemented
157C2×#553C231576yescomplemented
158C2×#553C231576yescomplemented
159C2×#552C231576yescomplemented
160C2×#551C231576yescomplemented
161C2×#550C231288yescomplemented
162C2×#550C231576yescomplemented
163C2×#550C231192yescomplemented
164C2×#550C23196yescomplemented
165C2×#550C231192yescomplemented
166C2×#548C231576yescomplemented
167C2×#548C231192yescomplemented
168C2×#548C231192yescomplemented
169C2×#547C231288yescomplemented
170C2×#546C2311152yescomplemented
171C2×#546C231576yescomplemented
172C2×#546C231576yescomplemented
173C2×#546C231576yescomplemented
174C2×D42C231288yescomplemented
175C2×D42C231576yescomplemented
176C2×D42C231576yescomplemented
177C2×D42C231576yescomplemented
178C2×D42C231576yescomplemented
179C2×D42C231576yescomplemented
180C2×#542C231576yescomplemented
181C2×#540C231576yescomplemented
182C2×#540C2311152yescomplemented
183C2×#540C231576yescomplemented
184C2×#538C2311152yescomplemented
185C2×#538C231576yescomplemented
186C2×#537C231576yescomplemented
187C2×#536C231144yescomplemented
188C2×#535C231144yescomplemented
189C2×#535C231288yescomplemented
190C2×#535C231576yescomplemented
191C2×#535C231288yescomplemented
192C2×#535C231288yescomplemented
193C2×#535C2311152yescomplemented
194C2×#535C231288yescomplemented
195C2×#534C2311152yescomplemented
196C2×#534C231576yescomplemented
197C2×#532C231288yescomplemented
198C2×#532C231288yescomplemented
199C2×#532C231144yescomplemented
200C22×C4⋊Q8C2312yes—
201C22×C4⋊Q8C2316yes—
202C22×C4⋊Q8C2313yes—
203C22×#127C2316yes—
204C22×#127C23112yes—
205C22×#127C23112yes—
206C22×#127C23112yes—
207C22×#127C2313yes—
208C22×#127C2316yes—
209C22×#127C23112yes—
210C22×#127C231288yescomplemented
211C2×#529C231288yescomplemented
212C2×#529C231576yescomplemented
213C2×#529C231576yescomplemented
214C22×#126C2314yes—
215C22×#126C23112yes—
216C22×#126C23112yes—
217C22×#126C23124yes—
218C22×#125C2312yes—
219C22×#125C23112yes—
220C22×#125C23112yes—
221C22×#124C2313yes—
222C22×#124C2316yes—
223C22×#124C23112yes—
224C22×#124C2316yes—
225C22×#124C23112yes—
226C22×#124C23112yes—
227C22×#124C2311yescharacteristic
228C22×#124C2316yes—
229C22×#124C2316yes—
230C22×#124C23112yes—
231C22×#124C23124yes—
232C22×#124C231144yescomplemented
233C2×#525C231288yescomplemented
234C2×#525C231288yescomplemented
235C2×#525C231576yescomplemented
236C22×#123C2312yes—
237C22×#123C2316yes—
238C22×#123C23112yes—
239C22×#123C23112yes—
240C22×#123C23124yes—
241C22×#123C23112yes—
242C22×#123C23112yes—
243C22×#123C23112yes—
244C22×#123C23124yes—
245C22×#123C23124yes—
246C22×#123C23112yes—
247C22×C22⋊Q8C2314yes—
248C22×C22⋊Q8C23112yes—
249C22×C22⋊Q8C23112yes—
250C22×C22⋊Q8C23112yes—
251C22×C22⋊Q8C2316yes—
252C22×C22⋊Q8C23112yes—
253C22×C22⋊Q8C23112yes—
254C22×#121C23112yes—
255C22×#121C23124yes—
256C22×#121C23112yes—
257C22×#121C23112yes—
258C22×#121C23112yes—
259C22×#121C23112yes—
260C22×#121C23112yes—
261C22×#121C23112yes—
262C22×#121C23112yes—
263C22×#121C2316yes—
264C22×#121C23112yes—
265C22×#121C23112yes—
266C22×#121C23112yes—
267C22×#121C23112yes—
268C22×#121C23112yes—
269C22×#121C23112yes—
270C22×#121C23112yes—
271C22×#121C23124yes—
272C22×#121C23124yes—
273C22×#121C23124yes—
274C22×#121C23124yes—
275C22×#121C23124yes—
276C22×#121C231576yescomplemented
277C22×#120C23112yes—
278C22×#120C23112yes—
279C22×#120C2316yes—
280C22×#120C2316yes—
281C22×#120C23112yes—
282C22×#120C23112yes—
283C22×#120C23124yes—
284C22×#120C23124yes—
285C22×#120C23124yes—
286C22×#120C23112yes—
287C22×#120C23112yes—
288C2×#520C231192yescomplemented
289C2×#519C23196yescomplemented
290C2×C4×#41C23148yescomplemented
291C2×C4×#41C23196yescomplemented
292C22×C4×Q8C2314yes—
293C22×C4×Q8C2312yes—
294C22×C4×Q8C23112yes—
295C22×C4×Q8C2316yes—
296C22×C4×D4C2316yes—
297C22×C4×D4C23112yes—
298C22×C4×D4C23112yes—
299C22×C4×D4C23112yes—
300C22×C4×D4C23112yes—
301C22×C4×D4C2316yes—
302C22×C4×D4C23112yes—
303C22×C4×D4C23112yes—
304C22×C4×D4C23112yes—
305C22×C4×D4C23124yes—
306C22×C4×D4C23124yes—
307C22×C4×D4C23112yes—
308C22×#117C2316yes—
309C22×#117C2313yes—
310C22×#117C2316yes—
311C22×#117C2316yes—
312C22×#117C23112yes—
313C22×#117C23124yes—
314C23×C4⋊C4C23112yes—
315C23×C22⋊C4C23124yes—
316C23×C22⋊C4C23112yes—
317C23×C42C2313yes—
318C23×C42C2316yes—
319C26C2416yes—
320C26C2416yes—
321C26C24112yes—
322C2×2−1+4—4384no—
323C2×2−1+4C241256yescomplemented
324C2×H(5,𝔽2)—4768no—
325C2×H(5,𝔽2)—4384no—
326C2×H(5,𝔽2)C241512yescomplemented
327C2×H(5,𝔽2)C241256yescomplemented
328C22×#41—264no—
329C22×#41—232no—
330C22×#41—216no—
331C22×#41—448no—
332C22×#41—424no—
333C22×#41—424no—
334C22×#41—496no—
335C22×#41—448no—
336C22×#41—4768no—
337C22×#41—848no—
338C22×#41C24196yes—
339C22×#41C24148yes—
340C22×#41C24124yes—
341C22×#41C241288yes—
342C22×#41C241144yes—
343C22×#41C24172yes—
344C22×#41C24172yes—
345C22×#41C241144yes—
346C22×#41C241288yes—
347C22×#41C241512yescomplemented
348C23×Q8—232no—
349C23×Q8—424no—
350C23×Q8C2416yes—
351C23×Q8C24148yes—
352C23×Q8C2413yes—
353C23×Q8C24172yes—
354C23×Q8C2412yes—
355C23×Q8C2411yescharacteristic
356C23×Q8C2416yes—
357C23×Q8C2411yescharacteristic
358C23×D4—448no—
359C23×D4—496no—
360C23×D4—448no—
361C23×D4—448no—
362C23×D4—424no—
363C23×D4—896no—
364C23×D4—896no—
365C23×D4C2416yes—
366C23×D4C24112yes—
367C23×D4C2413yes—
368C23×D4C2413yes—
369C23×D4C24112yes—
370C23×D4C2416yes—
371C23×D4C2416yes—
372C23×D4C24112yes—
373C23×D4C24124yes—
374C23×D4C24112yes—
375C23×D4C24112yes—
376C23×D4C24112yes—
377C23×D4C24112yes—
378C23×D4C24112yes—
379C23×D4C24124yes—
380C23×D4C241144yes—
381C23×D4C241288yes—
382C23×D4C24172yes—
383C23×D4C241144yes—
384C23×D4C241144yes—
385C23×D4C2411yescharacteristic
386C23×D4C2416yes—
387C23×D4C2416yes—
388C23×D4C241576yes—
389C23×D4C241576yes—
390C24×C4—448no—
391C24×C4C2416yes—
392C24×C4C24112yes—
393C24×C4C2416yes—
394C24×C4C2413yes—
395C24×C4C2412yes—
396C24×C4C24112yes—
397C24×C4C241144yes—
398C24×C4C24112yes—
399C24×C4C24124yes—
400C24×C4C2416yes—
401C24×C4C2416yes—
402#563C241256yescomplemented
403#563C2411536yescomplemented
404#562C2413072yescomplemented
405#562C2411536yescomplemented
406H(3,𝔽4)C241768yescomplemented
407H(3,𝔽4)C2411536yescomplemented
408#560C2411536yescomplemented
409#560C2413072yescomplemented
410#560C2413072yescomplemented
411#560C2413072yescomplemented
412#559C2413072yescomplemented
413#557C241512yescomplemented
414#555C2413072yescomplemented
415#555C2411536yescomplemented
416#553C2413072yescomplemented
417#553C2413072yescomplemented
418#552C2413072yescomplemented
419#551C2413072yescomplemented
420#550C2411024yescomplemented
421#550C2413072yescomplemented
422#550C241512yescomplemented
423#550C2411024yescomplemented
424#550C2411536yescomplemented
425#548C2411024yescomplemented
426#548C2413072yescomplemented
427#548C2411024yescomplemented
428#547C2411536yescomplemented
429#546C2413072yescomplemented
430#546C2413072yescomplemented
431#546C2413072yescomplemented
432#546C2416144yescomplemented
433D42C2413072yescomplemented
434D42C2413072yescomplemented
435D42C2413072yescomplemented
436D42C2413072yescomplemented
437D42C2411536yescomplemented
438D42C2413072yescomplemented
439#542C2413072yescomplemented
440#540C2413072yescomplemented
441#540C2413072yescomplemented
442#540C2416144yescomplemented
443#538C2416144yescomplemented
444#538C2413072yescomplemented
445#537C2413072yescomplemented
446#536C241768yescomplemented
447#535C2411536yescomplemented
448#535C2411536yescomplemented
449#535C2413072yescomplemented
450#535C2411536yescomplemented
451#535C2411536yescomplemented
452#535C241768yescomplemented
453#535C2416144yescomplemented
454#534C2416144yescomplemented
455#534C2413072yescomplemented
456#532C2411536yescomplemented
457#532C241768yescomplemented
458#532C2411536yescomplemented
459C2×C4⋊Q8C24148yes—
460C2×C4⋊Q8C24172yes—
461C2×C4⋊Q8C241144yes—
462C2×#127C241144yes—
463C2×#127C241288yes—
464C2×#127C241288yes—
465C2×#127C241288yes—
466C2×#127C241144yes—
467C2×#127C24172yes—
468C2×#127C241288yes—
469C2×#127C2411536yescomplemented
470#529C2411536yescomplemented
471#529C2413072yescomplemented
472#529C2413072yescomplemented
473C2×#126C24196yes—
474C2×#126C241288yes—
475C2×#126C241288yes—
476C2×#126C241576yes—
477C2×#125C24148yes—
478C2×#125C241288yes—
479C2×#125C241288yes—
480C2×#124C24172yes—
481C2×#124C241144yes—
482C2×#124C241288yes—
483C2×#124C241144yes—
484C2×#124C241288yes—
485C2×#124C241288yes—
486C2×#124C24124yes—
487C2×#124C241144yes—
488C2×#124C241144yes—
489C2×#124C241288yes—
490C2×#124C241576yes—
491C2×#124C241768yescomplemented
492#525C2411536yescomplemented
493#525C2411536yescomplemented
494#525C2413072yescomplemented
495C2×#123C24148yes—
496C2×#123C241144yes—
497C2×#123C241288yes—
498C2×#123C241288yes—
499C2×#123C241576yes—
500C2×#123C241288yes—
501C2×#123C241288yes—
502C2×#123C241288yes—
503C2×#123C241576yes—
504C2×#123C241576yes—
505C2×#123C241288yes—
506C2×C22⋊Q8C24196yes—
507C2×C22⋊Q8C241288yes—
508C2×C22⋊Q8C241288yes—
509C2×C22⋊Q8C241288yes—
510C2×C22⋊Q8C241288yes—
511C2×C22⋊Q8C241144yes—
512C2×C22⋊Q8C241288yes—
513C2×#121C241288yes—
514C2×#121C241576yes—
515C2×#121C241288yes—
516C2×#121C241288yes—
517C2×#121C241288yes—
518C2×#121C241288yes—
519C2×#121C241288yes—
520C2×#121C241288yes—
521C2×#121C241288yes—
522C2×#121C241144yes—
523C2×#121C241288yes—
524C2×#121C241288yes—
525C2×#121C241288yes—
526C2×#121C241288yes—
527C2×#121C241288yes—
528C2×#121C241288yes—
529C2×#121C241288yes—
530C2×#121C241576yes—
531C2×#121C241576yes—
532C2×#121C241576yes—
533C2×#121C241576yes—
534C2×#121C241576yes—
535C2×#121C2413072yescomplemented
536C2×#120C241288yes—
537C2×#120C241288yes—
538C2×#120C241144yes—
539C2×#120C241144yes—
540C2×#120C241288yes—
541C2×#120C241288yes—
542C2×#120C241576yes—
543C2×#120C241576yes—
544C2×#120C241576yes—
545C2×#120C241288yes—
546C2×#120C241288yes—
547#520C2411024yescomplemented
548#519C241512yescomplemented
549C4×#41C241512yescomplemented
550C4×#41C241256yescomplemented
551C2×C4×Q8C24196yes—
552C2×C4×Q8C24148yes—
553C2×C4×Q8C241288yes—
554C2×C4×Q8C241144yes—
555C2×C4×D4C241144yes—
556C2×C4×D4C241288yes—
557C2×C4×D4C241288yes—
558C2×C4×D4C241288yes—
559C2×C4×D4C241288yes—
560C2×C4×D4C241144yes—
561C2×C4×D4C241288yes—
562C2×C4×D4C241288yes—
563C2×C4×D4C241288yes—
564C2×C4×D4C241576yes—
565C2×C4×D4C241576yes—
566C2×C4×D4C241288yes—
567C2×#117C241144yes—
568C2×#117C24172yes—
569C2×#117C241144yes—
570C2×#117C241144yes—
571C2×#117C241288yes—
572C2×#117C241576yes—
573C22×C4⋊C4C2416yes—
574C22×C4⋊C4C24112yes—
575C22×C4⋊C4C24112yes—
576C22×C4⋊C4C241288yes—
577C22×C4⋊C4C2414yes—
578C22×C4⋊C4C24112yes—
579C22×C4⋊C4C24112yes—
580C22×C4⋊C4C24112yes—
581C22×C4⋊C4C2414yes—
582C22×C4⋊C4C2414yes—
583C22×C4⋊C4C24112yes—
584C22×C4⋊C4C2412yes—
585C22×C4⋊C4C24112yes—
586C22×C4⋊C4C2412yes—
587C22×C22⋊C4C24112yes—
588C22×C22⋊C4C24124yes—
589C22×C22⋊C4C24112yes—
590C22×C22⋊C4C24112yes—
591C22×C22⋊C4C24124yes—
592C22×C22⋊C4C241576yes—
593C22×C22⋊C4C241288yes—
594C22×C22⋊C4C2412yes—
595C22×C22⋊C4C2416yes—
596C22×C22⋊C4C24112yes—
597C22×C22⋊C4C24112yes—
598C22×C22⋊C4C24112yes—
599C22×C22⋊C4C24112yes—
600C22×C22⋊C4C2416yes—
601C22×C22⋊C4C2414yes—
602C22×C22⋊C4C24112yes—
603C22×C22⋊C4C2414yes—
604C22×C22⋊C4C24112yes—
605C22×C22⋊C4C24112yes—
606C22×C42C2411yescharacteristic
607C22×C42C2412yes—
608C22×C42C2416yes—
609C22×C42C2416yes—
610C22×C42C24112yes—
611C22×C42C2413yes—
612C22×C42C24172yes—
613C22×C42C241144yes—
614C22×C42C24112yes—
615C25—424no—
616C25—448no—
617C25—424no—
618C25—448no—
619C25—496no—
620C25—448no—
621C25C2516yes—
622C25C2512yes—
623C25C25112yes—
624C25C2513yes—
625C25C25172yes—
626C25C251144yes—
627C25C25172yes—
6282−1+4—41024no—
629H(5,𝔽2)—42048no—
630H(5,𝔽2)—41024no—
631C2×#41—2768no—
632C2×#41—2384no—
633C2×#41—2192no—
634C2×#41—4576no—
635C2×#41—4288no—
636C2×#41—4288no—
637C2×#41—41152no—
638C2×#41—4576no—
639C2×#41—42048no—
640C2×#41—8576no—
641C2×#41C251128yes—
642C2×#41C25164yes—
643C2×#41C251256yes—
644C2×#41C251192yes—
645C2×#41C251384yes—
646C2×#41C251384yes—
647C2×#41C251192yes—
648C2×#41C251768yes—
649C2×#41C251768yes—
650C22×Q8—2384no—
651C22×Q8—248no—
652C22×Q8—412no—
653C22×Q8—48no—
654C22×Q8—44no—
655C22×Q8—424no—
656C22×Q8—4288no—
657C22×Q8H(5,𝔽2)116yes—
658C22×Q8C25172yes—
659C22×Q8C251128yes—
660C22×Q8C25172yes—
661C22×Q8C25124yes—
662C22×Q8C25136yes—
663C22×Q8C25112yes—
664C22×Q8C251192yes—
665C22×Q8C25112yes—
666C22×D4—248no—
667C22×D4—296no—
668C22×D4—224no—
669C22×D4—4576no—
670C22×D4—41152no—
671C22×D4—4576no—
672C22×D4—4576no—
673C22×D4—4288no—
674C22×D4—448no—
675C22×D4—424no—
676C22×D4—424no—
677C22×D4—412no—
678C22×D4—448no—
679C22×D4—448no—
680C22×D4—448no—
681C22×D4—448no—
682C22×D4—448no—
683C22×D4—496no—
684C22×D4—448no—
685C22×D4—496no—
686C22×D4—44no—
687C22×D4—424no—
688C22×D4—424no—
689C22×D4—81152no—
690C22×D4—81152no—
691C22×D4C25172yes—
692C22×D4C251144yes—
693C22×D4C25136yes—
694C22×D4C25172yes—
695C22×D4C251144yes—
696C22×D4C251288yes—
697C22×D4C251288yes—
698C22×D4C251144yes—
699C22×D4C251144yes—
700C22×D4C251144yes—
701C22×D4C251144yes—
702C22×D4C25112yes—
703C22×D4C25172yes—
704C22×D4C251144yes—
705C22×D4C25136yes—
706C22×D4C251144yes—
707C22×D4C25172yes—
708C22×D4C25172yes—
709C22×D4C251768yes—
710C22×D4C251192yes—
711C22×D4C251384yes—
712C22×D4C251384yes—
713C22×D4C251384yes—
714C22×D4C2511536yes—
715C22×D4C2511536yes—
716C23×C4—248no—
717C23×C4—296no—
718C23×C4—248no—
719C23×C4—224no—
720C23×C4—4576no—
721C23×C4—48no—
722C23×C4—448no—
723C23×C4—448no—
724C23×C4—496no—
725C23×C4—424no—
726C23×C4—424no—
727C23×C4C251144yes—
728C23×C4C25172yes—
729C23×C4C25136yes—
730C23×C4C25172yes—
731C23×C4C2512yes—
732C23×C4C2516yes—
733C23×C4C2511yescharacteristic
734C23×C4C2514yes—
735C23×C4C2516yes—
736C23×C4C25112yes—
737C23×C4C2514yes—
738C23×C4C2512yes—
739C23×C4C25172yes—
740C23×C4C25172yes—
741C23×C4C251144yes—
742C23×C4C251288yes—
743C23×C4C251144yes—
744C23×C4C25124yes—
745C23×C4C251384yes—
746C23×C4C2513yes—
747C4⋊Q8C251128yes—
748C4⋊Q8C251192yes—
749C4⋊Q8C251384yes—
750#127C251384yes—
751#127C251768yes—
752#127C251768yes—
753#127C251768yes—
754#127C251384yes—
755#127C251192yes—
756#127C251768yes—
757#126C251256yes—
758#126C251768yes—
759#126C251768yes—
760#126C2511536yes—
761#125C251128yes—
762#125C251768yes—
763#125C251768yes—
764#124C251192yes—
765#124C251384yes—
766#124C251768yes—
767#124C251384yes—
768#124C251768yes—
769#124C251768yes—
770#124C25164yes—
771#124C251384yes—
772#124C251384yes—
773#124C251768yes—
774#124C2511536yes—
775#123C251128yes—
776#123C251384yes—
777#123C251768yes—
778#123C251768yes—
779#123C2511536yes—
780#123C251768yes—
781#123C251768yes—
782#123C251768yes—
783#123C2511536yes—
784#123C2511536yes—
785#123C251768yes—
786C22⋊Q8C251256yes—
787C22⋊Q8C251768yes—
788C22⋊Q8C251768yes—
789C22⋊Q8C251768yes—
790C22⋊Q8C251768yes—
791C22⋊Q8C251384yes—
792C22⋊Q8C251768yes—
793#121C251768yes—
794#121C2511536yes—
795#121C251768yes—
796#121C251768yes—
797#121C251768yes—
798#121C251768yes—
799#121C251768yes—
800#121C251768yes—
801#121C251768yes—
802#121C251384yes—
803#121C251768yes—
804#121C251768yes—
805#121C251768yes—
806#121C251768yes—
807#121C251768yes—
808#121C251768yes—
809#121C251768yes—
810#121C2511536yes—
811#121C2511536yes—
812#121C2511536yes—
813#121C2511536yes—
814#121C2511536yes—
815#120C251768yes—
816#120C251768yes—
817#120C251384yes—
818#120C251384yes—
819#120C251768yes—
820#120C251768yes—
821#120C2511536yes—
822#120C2511536yes—
823#120C2511536yes—
824#120C251768yes—
825#120C251768yes—
826C4×Q8C251256yes—
827C4×Q8C251128yes—
828C4×Q8C251768yes—
829C4×Q8C251384yes—
830C4×D4C251384yes—
831C4×D4C251768yes—
832C4×D4C251768yes—
833C4×D4C251768yes—
834C4×D4C251768yes—
835C4×D4C251384yes—
836C4×D4C251768yes—
837C4×D4C251768yes—
838C4×D4C251768yes—
839C4×D4C2511536yes—
840C4×D4C2511536yes—
841C4×D4C251768yes—
842#117C251384yes—
843#117C251192yes—
844#117C251384yes—
845#117C251384yes—
846#117C251768yes—
847#117C2511536yes—
848C2×C4⋊C4C25172yes—
849C2×C4⋊C4C251144yes—
850C2×C4⋊C4C251144yes—
851C2×C4⋊C4C251768yes—
852C2×C4⋊C4C25148yes—
853C2×C4⋊C4C251144yes—
854C2×C4⋊C4C251144yes—
855C2×C4⋊C4C251144yes—
856C2×C4⋊C4C25148yes—
857C2×C4⋊C4C25148yes—
858C2×C4⋊C4C251144yes—
859C2×C4⋊C4C25124yes—
860C2×C4⋊C4C251144yes—
861C2×C4⋊C4C25124yes—
862C2×C22⋊C4C251144yes—
863C2×C22⋊C4C251288yes—
864C2×C22⋊C4C251144yes—
865C2×C22⋊C4C251144yes—
866C2×C22⋊C4C251288yes—
867C2×C22⋊C4C2511536yes—
868C2×C22⋊C4C251768yes—
869C2×C22⋊C4C25124yes—
870C2×C22⋊C4C25172yes—
871C2×C22⋊C4C251144yes—
872C2×C22⋊C4C251144yes—
873C2×C22⋊C4C251144yes—
874C2×C22⋊C4C251144yes—
875C2×C22⋊C4C25172yes—
876C2×C22⋊C4C25148yes—
877C2×C22⋊C4C251144yes—
878C2×C22⋊C4C25148yes—
879C2×C22⋊C4C251144yes—
880C2×C22⋊C4C251144yes—
881C2×C42C25172yes—
882C2×C42C251144yes—
883C2×C42C25172yes—
884C2×C42C251144yes—
885C2×C42C25136yes—
886C2×C42C251192yes—
887C2×C42C251384yes—
888C2×C42C25112yes—
889C2×C42C25124yes—
890C24—28no—
891C24—212no—
892C24—248no—
893C24—224no—
894C24—248no—
895C24—224no—
896C24—248no—
897C24—216no—
898C24—248no—
899C24—4144no—
900C24—4288no—
901C24—4144no—
902C24—4288no—
903C24—4576no—
904C24—4288no—
905C24—8192no—
906C24—16192no—
907C24—1696no—
908C24C26136yes—
909C24C26112yes—
910C24C26172yes—
911C24C26118yes—
912C24C26196yes—
913C24C261192yes—
914C24C26196yes—
915C24C2611yescharacteristic
916#41—21024no—
917#41—2512no—
918#41—2256no—
919#41—4768no—
920#41—4384no—
921#41—4384no—
922#41—41536no—
923#41—4768no—
924#41—8768no—
925C2×Q8—2512no—
926C2×Q8—2288no—
927C2×Q8—472no—
928C2×Q8—448no—
929C2×Q8—424no—
930C2×Q8—4144no—
931C2×Q8—4384no—
932C2×Q8C2×H(5,𝔽2)196yes—
933C2×Q8C26196yes—
934C2×Q8C26196yes—
935C2×Q8C26132yes—
936C2×Q8C26148yes—
937C2×Q8C26116yes—
938C2×Q8C26116yes—
939C2×D4—2288no—
940C2×D4—2576no—
941C2×D4—2144no—
942C2×D4—4768no—
943C2×D4—41536no—
944C2×D4—4768no—
945C2×D4—4768no—
946C2×D4—4384no—
947C2×D4—4288no—
948C2×D4—4144no—
949C2×D4—4144no—
950C2×D4—472no—
951C2×D4—4288no—
952C2×D4—4288no—
953C2×D4—4288no—
954C2×D4—4288no—
955C2×D4—4288no—
956C2×D4—4576no—
957C2×D4—4288no—
958C2×D4—4576no—
959C2×D4—424no—
960C2×D4—4144no—
961C2×D4—4144no—
962C2×D4—81536no—
963C2×D4—81536no—
964C2×D4C26196yes—
965C2×D4C261192yes—
966C2×D4C26148yes—
967C2×D4C26196yes—
968C2×D4C261192yes—
969C2×D4C261384yes—
970C2×D4C261384yes—
971C2×D4C261192yes—
972C2×D4C261192yes—
973C2×D4C261192yes—
974C2×D4C261192yes—
975C2×D4C26116yes—
976C2×D4C26196yes—
977C2×D4C261192yes—
978C2×D4C26148yes—
979C2×D4C261192yes—
980C2×D4C26196yes—
981C2×D4C26196yes—
982C22×C4—216no—
983C22×C4—28no—
984C22×C4—24no—
985C22×C4—224no—
986C22×C4—224no—
987C22×C4—216no—
988C22×C4—248no—
989C22×C4—28no—
990C22×C4—2288no—
991C22×C4—2576no—
992C22×C4—2288no—
993C22×C4—2144no—
994C22×C4—4768no—
995C22×C4—448no—
996C22×C4—4288no—
997C22×C4—4288no—
998C22×C4—4576no—
999C22×C4—4144no—
1000C22×C4—4144no—
1001C22×C4C2×H(5,𝔽2)124yes—
1002C22×C4C26112yes—
1003C22×C4C2616yes—
1004C22×C4C26172yes—
1005C22×C4C26124yes—
1006C22×C4C26112yes—
1007C22×C4C26136yes—
1008C22×C4C26136yes—
1009C22×C4C26148yes—
1010C22×C4C26196yes—
1011C22×C4C26124yes—
1012C22×C4C261192yes—
1013C22×C4C26196yes—
1014C22×C4C26196yes—
1015C22×C4C261192yes—
1016C22×C4C26196yes—
1017C22×C4C261192yes—
1018C22×C4C261384yes—
1019C22×C4C26132yes—
1020C22×C4C26118yes—
1021C4⋊C4C26196yes—
1022C4⋊C4C261192yes—
1023C4⋊C4C261192yes—
1024C4⋊C4C26164yes—
1025C4⋊C4C261192yes—
1026C4⋊C4C261192yes—
1027C4⋊C4C261192yes—
1028C4⋊C4C26164yes—
1029C4⋊C4C26164yes—
1030C4⋊C4C261192yes—
1031C4⋊C4C26132yes—
1032C4⋊C4C261192yes—
1033C4⋊C4C26132yes—
1034C22⋊C4C261192yes—
1035C22⋊C4C261384yes—
1036C22⋊C4C261192yes—
1037C22⋊C4C261192yes—
1038C22⋊C4C261384yes—
1039C22⋊C4C26132yes—
1040C22⋊C4C26196yes—
1041C22⋊C4C261192yes—
1042C22⋊C4C261192yes—
1043C22⋊C4C261192yes—
1044C22⋊C4C261192yes—
1045C22⋊C4C26196yes—
1046C22⋊C4C26164yes—
1047C22⋊C4C261192yes—
1048C22⋊C4C26164yes—
1049C22⋊C4C261192yes—
1050C22⋊C4C261192yes—
1051C42C26116yes—
1052C42C26132yes—
1053C42C26196yes—
1054C42C26196yes—
1055C42C261192yes—
1056C42C26148yes—
1057C42C261192yes—
1058C23—224no—
1059C23—236no—
1060C23—2144no—
1061C23—272no—
1062C23—2144no—
1063C23—272no—
1064C23—2144no—
1065C23—248no—
1066C23—2144no—
1067C23—496no—
1068C23—4192no—
1069C23—496no—
1070C23—4192no—
1071C23—4384no—
1072C23—4192no—
1073C23—432no—
1074C23—4192no—
1075C23—448no—
1076C23—496no—
1077C23—8576no—
1078C23—16576no—
1079C23—16288no—
1080C23C22×H(5,𝔽2)14yes—
1081C23H(7,𝔽2)18yes—
1082C23C27124yes—
1083C23C2718yes—
1084C23C27148yes—
1085C23C27112yes—
1086C23C2713yes—
1087Q8—2192no—
1088Q8—448no—
1089Q8—432no—
1090Q8—416no—
1091Q8—496no—
1092Q8C22×H(5,𝔽2)164yes—
1093D4—2192no—
1094D4—2384no—
1095D4—296no—
1096D4—4192no—
1097D4—496no—
1098D4—496no—
1099D4—448no—
1100D4—4192no—
1101D4—4192no—
1102D4—4192no—
1103D4—4192no—
1104D4—4192no—
1105D4—4384no—
1106D4—4192no—
1107D4—4384no—
1108D4—416no—
1109D4—496no—
1110D4—496no—
1111C2×C4—248no—
1112C2×C4—224no—
1113C2×C4—212no—
1114C2×C4—272no—
1115C2×C4—272no—
1116C2×C4—248no—
1117C2×C4—2144no—
1118C2×C4—224no—
1119C2×C4—2192no—
1120C2×C4—2384no—
1121C2×C4—2192no—
1122C2×C4—296no—
1123C2×C4—432no—
1124C2×C4—4192no—
1125C2×C4—4192no—
1126C2×C4—4384no—
1127C2×C4—496no—
1128C2×C4—496no—
1129C2×C4C22×H(5,𝔽2)172yes—
1130C2×C4C2718yes—
1131C2×C4C2714yes—
1132C2×C4C27148yes—
1133C2×C4C27116yes—
1134C2×C4C2718yes—
1135C2×C4C27124yes—
1136C2×C4C27124yes—
1137C2×C4C27116yes—
1138C2×C4C27112yes—
1139C22—28no—
1140C22—212no—
1141C22—248no—
1142C22—224no—
1143C22—248no—
1144C22—224no—
1145C22—248no—
1146C22—216no—
1147C22—248no—
1148C22—448no—
1149C22—4288no—
1150C22—472no—
1151C22—4144no—
1152C22—8192no—
1153C22—16192no—
1154C22—1696no—
1155C22#63066116yesdirect product factor
1156C22C23×H(5,𝔽2)16yes—
1157C22C2×H(7,𝔽2)112yes—
1158C22C2811yescharacteristic
1159C4—216no—
1160C4—28no—
1161C4—24no—
1162C4—224no—
1163C4—224no—
1164C4—216no—
1165C4—248no—
1166C4—28no—
1167C4C23×H(5,𝔽2)124yes—
1168C2—48no—
1169C2—448no—
1170C2—412no—
1171C2—424no—
1172C2C2×#63066112yesdirect product factor
1173C2C24×H(5,𝔽2)11yescharacteristic
1174C2C22×H(7,𝔽2)12yes—
subgroupG/H
center, socleC24C26
commutator, Frattini, cosocleC22C28
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#63066C2direct (N × H)
2. C22×#3549C2semidirect
3. C22×#3543C2semidirect
4. C22×#3551C2semidirect
5. C22×#3558C2semidirect
6. C22×#3537C2semidirect
7. C22×#3542C2semidirect
8. C22×#3529C2semidirect
9. C22×#3500C2semidirect
10. C22×#3498C2semidirect
11. C22×#3488C2semidirect
12. C22×#3524C2semidirect
13. C22×#3517C2semidirect
14. C22×#3487C2semidirect
15. C23×2−1+4C22semidirect
16. C23×H(5,𝔽2)C22semidirect
17. C23×H(5,𝔽2)C22semidirect
18. C24×#41C22semidirect
19. #63066C22direct (N × H)
20. C2×#3500C22semidirect
21. C2×#3498C22semidirect
22. C2×#3488C22semidirect
23. C2×#3524C22semidirect
24. C2×#3517C22semidirect
25. C2×#3487C22semidirect
26. C2×#3549C22semidirect
27. C2×#3543C22semidirect
28. C2×#3551C22semidirect
29. C2×#3558C22semidirect
30. C2×#3537C22semidirect
31. C2×#3542C22semidirect
32. C22×#559C22semidirect
33. C22×#557C22semidirect
34. C22×#555C22semidirect
35. C22×#555C22semidirect
36. C22×#553C22semidirect
37. C22×#553C22semidirect
38. C22×#552C22semidirect
39. C22×#551C22semidirect
40. C22×#550C22semidirect
41. C22×#550C22semidirect
42. C22×#550C22semidirect
43. C22×#550C22semidirect
44. C22×#550C22semidirect
45. C22×#547C22semidirect
46. C22×#548C22semidirect
47. C22×#548C22semidirect
48. C22×#548C22semidirect
49. C22×#546C22semidirect
50. C22×#546C22semidirect
51. C22×#546C22semidirect
52. C22×#546C22semidirect
53. C22×D42C22semidirect
54. C22×D42C22semidirect
55. C22×D42C22semidirect
56. C22×D42C22semidirect
57. C22×D42C22semidirect
58. C22×D42C22semidirect
59. C2×#3529C22semidirect
60. C22×#563C22semidirect
61. C22×#563C22semidirect
62. C22×#562C22semidirect
63. C22×#562C22semidirect
64. C22×H(3,𝔽4)C22semidirect
65. C22×H(3,𝔽4)C22semidirect
66. C22×#560C22semidirect
67. C22×#560C22semidirect
68. C22×#560C22semidirect
69. C22×#560C22semidirect
70. C22×#536C22semidirect
71. C22×#542C22semidirect
72. C22×#540C22semidirect
73. C22×#540C22semidirect
74. C22×#540C22semidirect
75. C22×#537C22semidirect
76. C22×#535C22semidirect
77. C22×#535C22semidirect
78. C22×#535C22semidirect
79. C22×#535C22semidirect
80. C22×#535C22semidirect
81. C22×#535C22semidirect
82. C22×#535C22semidirect
83. C22×#538C22semidirect
84. C22×#538C22semidirect
85. C22×#534C22semidirect
86. C22×#534C22semidirect
87. C22×#532C22semidirect
88. C22×#532C22semidirect
89. C22×#532C22semidirect
90. C23×#127C22semidirect
91. C22×#529C22semidirect
92. C22×#529C22semidirect
93. C22×#529C22semidirect
94. C23×#124C22semidirect
95. C22×#525C22semidirect
96. C22×#525C22semidirect
97. C22×#525C22semidirect
98. C23×#121C22semidirect
99. C22×#520C22semidirect
100. C22×#519C22semidirect
101. C22×C4×#41C22semidirect
102. C22×C4×#41C22semidirect
104. C22×2−1+4C23semidirect
107. C22×H(5,𝔽2)C23semidirect
108. C22×H(5,𝔽2)C23semidirect
119. C23×#41C23semidirect
130. #3558C23semidirect
131. #3551C23semidirect
132. #3549C23semidirect
133. #3543C23semidirect
134. #3542C23semidirect
135. #3537C23semidirect
136. #3529C23semidirect
137. C2×#563C23semidirect
138. C2×#563C23semidirect
139. C2×#562C23semidirect
140. C2×#562C23semidirect
141. C2×H(3,𝔽4)C23semidirect
142. C2×H(3,𝔽4)C23semidirect
143. C2×#560C23semidirect
144. C2×#560C23semidirect
145. C2×#560C23semidirect
146. C2×#560C23semidirect
147. #3524C23semidirect
148. #3517C23semidirect
149. #3500C23semidirect
150. #3498C23semidirect
151. #3488C23semidirect
152. #3487C23semidirect
153. C2×#559C23semidirect
154. C2×#557C23semidirect
155. C2×#555C23semidirect
156. C2×#555C23semidirect
157. C2×#553C23semidirect
158. C2×#553C23semidirect
159. C2×#552C23semidirect
160. C2×#551C23semidirect
161. C2×#550C23semidirect
162. C2×#550C23semidirect
163. C2×#550C23semidirect
164. C2×#550C23semidirect
165. C2×#550C23semidirect
166. C2×#548C23semidirect
167. C2×#548C23semidirect
168. C2×#548C23semidirect
169. C2×#547C23semidirect
170. C2×#546C23semidirect
171. C2×#546C23semidirect
172. C2×#546C23semidirect
173. C2×#546C23semidirect
174. C2×D42C23semidirect
175. C2×D42C23semidirect
176. C2×D42C23semidirect
177. C2×D42C23semidirect
178. C2×D42C23semidirect
179. C2×D42C23semidirect
180. C2×#542C23semidirect
181. C2×#540C23semidirect
182. C2×#540C23semidirect
183. C2×#540C23semidirect
184. C2×#538C23semidirect
185. C2×#538C23semidirect
186. C2×#537C23semidirect
187. C2×#536C23semidirect
188. C2×#535C23semidirect
189. C2×#535C23semidirect
190. C2×#535C23semidirect
191. C2×#535C23semidirect
192. C2×#535C23semidirect
193. C2×#535C23semidirect
194. C2×#535C23semidirect
195. C2×#534C23semidirect
196. C2×#534C23semidirect
197. C2×#532C23semidirect
198. C2×#532C23semidirect
199. C2×#532C23semidirect
210. C22×#127C23semidirect
211. C2×#529C23semidirect
212. C2×#529C23semidirect
213. C2×#529C23semidirect
232. C22×#124C23semidirect
233. C2×#525C23semidirect
234. C2×#525C23semidirect
235. C2×#525C23semidirect
276. C22×#121C23semidirect
288. C2×#520C23semidirect
289. C2×#519C23semidirect
290. C2×C4×#41C23semidirect
291. C2×C4×#41C23semidirect
323. C2×2−1+4C24semidirect
326. C2×H(5,𝔽2)C24semidirect
327. C2×H(5,𝔽2)C24semidirect
347. C22×#41C24semidirect
402. #563C24semidirect
403. #563C24semidirect
404. #562C24semidirect
405. #562C24semidirect
406. H(3,𝔽4)C24semidirect
407. H(3,𝔽4)C24semidirect
408. #560C24semidirect
409. #560C24semidirect
410. #560C24semidirect
411. #560C24semidirect
412. #559C24semidirect
413. #557C24semidirect
414. #555C24semidirect
415. #555C24semidirect
416. #553C24semidirect
417. #553C24semidirect
418. #552C24semidirect
419. #551C24semidirect
420. #550C24semidirect
421. #550C24semidirect
422. #550C24semidirect
423. #550C24semidirect
424. #550C24semidirect
425. #548C24semidirect
426. #548C24semidirect
427. #548C24semidirect
428. #547C24semidirect
429. #546C24semidirect
430. #546C24semidirect
431. #546C24semidirect
432. #546C24semidirect
433. D42C24semidirect
434. D42C24semidirect
435. D42C24semidirect
436. D42C24semidirect
437. D42C24semidirect
438. D42C24semidirect
439. #542C24semidirect
440. #540C24semidirect
441. #540C24semidirect
442. #540C24semidirect
443. #538C24semidirect
444. #538C24semidirect
445. #537C24semidirect
446. #536C24semidirect
447. #535C24semidirect
448. #535C24semidirect
449. #535C24semidirect
450. #535C24semidirect
451. #535C24semidirect
452. #535C24semidirect
453. #535C24semidirect
454. #534C24semidirect
455. #534C24semidirect
456. #532C24semidirect
457. #532C24semidirect
458. #532C24semidirect
469. C2×#127C24semidirect
470. #529C24semidirect
471. #529C24semidirect
472. #529C24semidirect
491. C2×#124C24semidirect
492. #525C24semidirect
493. #525C24semidirect
494. #525C24semidirect
535. C2×#121C24semidirect
547. #520C24semidirect
548. #519C24semidirect
549. C4×#41C24semidirect
550. C4×#41C24semidirect
1155. C22#63066direct (N × H)
1172. C2C2×#63066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#630662
C22×#35492
C22×#35432
C22×#35512
C22×#35582
C22×#35372
C22×#35422
C22×#35292
C22×#35002
C22×#34982
C22×#34882
C22×#35242
C22×#35172
C22×#34872