Finite Group Databasebeta

← C22×#62916 #72299722

Subgroups — C22×#62916 #72299722

Order 1024.

508917 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#62916C21192yesmaximal, direct product factor
2C22×#3546C2112yesmaximal, complemented
3C22×#3543C2112yesmaximal, complemented
4C22×#3537C2112yesmaximal, complemented
5C22×#3498C216yesmaximal, complemented
6C22×#3498C214yesmaximal, complemented
7C22×#3488C214yesmaximal, complemented
8C22×#3517C214yesmaximal, complemented
9C22×#3496C213yesmaximal, complemented
10C22×#3480C212yesmaximal, complemented
11C23×#550C211yesmaximal, characteristic, complemented
12C22×#3460C213yesmaximal, complemented
13C23×H(5,𝔽2)C2216yescomplemented
14C23×H(5,𝔽2)C2214yescomplemented
15C24×#41C2212yescomplemented
16#62916C2214096yesdirect product factor
17C2×#3498C221576yescomplemented
18C2×#3498C221384yescomplemented
19C2×#3488C221384yescomplemented
20C2×#3517C221384yescomplemented
21C2×#3496C221288yescomplemented
22C2×#3546C2211152yescomplemented
23C2×#3543C2211152yescomplemented
24C2×#3537C2211152yescomplemented
25C2×#3480C221192yescomplemented
26C22×#559C2216yescomplemented
27C22×#557C2212yescomplemented
28C22×#556C2216yescomplemented
29C22×#553C22112yescomplemented
30C22×#553C22124yescomplemented
31C22×#550C22112yescomplemented
32C22×#550C22112yescomplemented
33C22×#550C22112yescomplemented
34C22×#550C2214yescomplemented
35C22×#550C2212yescomplemented
36C22×#550C2218yescomplemented
37C22×#550C22196yescomplemented
38C22×#547C22112yescomplemented
39C22×#548C2214yescomplemented
40C22×#546C22124yescomplemented
41C22×#546C22124yescomplemented
42C22×D42C22124yescomplemented
43C22×D42C22124yescomplemented
44C22×D42C22124yescomplemented
45C22×D42C22112yescomplemented
46C22×D42C22112yescomplemented
47C22×D42C22112yescomplemented
48C22×#560C22148yescomplemented
49C2×#3460C221288yescomplemented
50C22×#542C22112yescomplemented
51C22×#540C22124yescomplemented
52C22×#540C22112yescomplemented
53C22×#544C2211yescharacteristic, complemented
54C22×#537C22112yescomplemented
55C22×#537C2213yescomplemented
56C22×#535C22124yescomplemented
57C22×#535C22112yescomplemented
58C22×#535C22124yescomplemented
59C22×#535C2216yescomplemented
60C22×#538C22112yescomplemented
61C22×#538C22124yescomplemented
62C22×#534C22112yescomplemented
63C22×#534C22124yescomplemented
64C22×#532C22112yescomplemented
65C22×#532C22112yescomplemented
66C22×#532C2216yescomplemented
67C23×#127C22112yescomplemented
68C23×#127C2213yescomplemented
69C22×#529C22112yescomplemented
70C22×#529C22112yescomplemented
71C22×#525C22112yescomplemented
72C23×#121C2216yescomplemented
73C23×#121C22112yescomplemented
74C22×#520C2214yescomplemented
75C22×C4×#41C2216yescomplemented
76C22×C4×#41C2214yescomplemented
77C23×C4×Q8C2211yescharacteristic, complemented
78C23×C4×D4C2213yescomplemented
79C22×H(5,𝔽2)—496no—
80C22×H(5,𝔽2)—464no—
81C22×H(5,𝔽2)C231288yescomplemented
82C22×H(5,𝔽2)C231192yescomplemented
83C23×#41—432no—
84C23×#41C2314yes—
85C23×#41C2316yes—
86C23×#41C2314yes—
87C23×#41C23112yes—
88C23×#41C23112yes—
89C23×#41C23124yes—
90C23×#41C23196yescomplemented
91C24×Q8C2311yescharacteristic
92C24×D4C2313yes—
93C24×D4C2316yes—
94C24×D4C23124yes—
95C24×D4C23112yes—
96C24×D4C23124yes—
97C24×D4C23124yes—
98C24×D4C2316yes—
99C24×D4C23124yes—
100C25×C4C2316yes—
101#3546C23112288yescomplemented
102#3543C23112288yescomplemented
103#3537C23112288yescomplemented
104C2×#560C2312304yescomplemented
105#3517C2314096yescomplemented
106#3498C2316144yescomplemented
107#3498C2314096yescomplemented
108#3496C2313072yescomplemented
109#3488C2314096yescomplemented
110#3480C2312048yescomplemented
111C2×#559C231288yescomplemented
112C2×#557C23196yescomplemented
113C2×#556C231288yescomplemented
114C2×#553C231576yescomplemented
115C2×#553C2311152yescomplemented
116C2×#550C231576yescomplemented
117C2×#550C231576yescomplemented
118C2×#550C231576yescomplemented
119C2×#550C231384yescomplemented
120C2×#550C231192yescomplemented
121C2×#550C23196yescomplemented
122C2×#550C2311024yescomplemented
123C2×#548C231192yescomplemented
124C2×#547C231576yescomplemented
125C2×#546C2311152yescomplemented
126C2×#546C2311152yescomplemented
127C2×D42C2311152yescomplemented
128C2×D42C2311152yescomplemented
129C2×D42C2311152yescomplemented
130C2×D42C231576yescomplemented
131C2×D42C231576yescomplemented
132C2×D42C231576yescomplemented
133#3460C2313072yescomplemented
134C2×#544C23148yescomplemented
135C2×#542C231576yescomplemented
136C2×#540C2311152yescomplemented
137C2×#540C231576yescomplemented
138C2×#538C231576yescomplemented
139C2×#538C2311152yescomplemented
140C2×#537C231576yescomplemented
141C2×#537C231144yescomplemented
142C2×#535C2311152yescomplemented
143C2×#535C231576yescomplemented
144C2×#535C2311152yescomplemented
145C2×#535C231288yescomplemented
146C2×#534C231576yescomplemented
147C2×#534C2311152yescomplemented
148C2×#532C231576yescomplemented
149C2×#532C231576yescomplemented
150C2×#532C231288yescomplemented
151C22×C4⋊Q8C2314yes—
152C22×C4⋊Q8C2316yes—
153C22×#127C23112yes—
154C22×#127C2316yes—
155C22×#127C23112yes—
156C22×#127C23124yes—
157C22×#127C23112yes—
158C22×#127C23124yes—
159C22×#127C231576yescomplemented
160C22×#127C231144yescomplemented
161C2×#529C231576yescomplemented
162C2×#529C231576yescomplemented
163C22×#126C23124yes—
164C22×#126C23124yes—
165C22×#125C2314yes—
166C22×#125C23112yes—
167C22×#124C23112yes—
168C22×#124C23112yes—
169C22×#124C23124yes—
170C22×#124C23112yes—
171C2×#525C231576yescomplemented
172C22×#123C23124yes—
173C22×#123C23124yes—
174C22×#123C23124yes—
175C22×#123C23148yes—
176C22×C22⋊Q8C2314yes—
177C22×C22⋊Q8C23112yes—
178C22×C22⋊Q8C23112yes—
179C22×C22⋊Q8C23112yes—
180C22×#121C23112yes—
181C22×#121C23112yes—
182C22×#121C23124yes—
183C22×#121C23124yes—
184C22×#121C23124yes—
185C22×#121C23124yes—
186C22×#121C23112yes—
187C22×#121C23112yes—
188C22×#121C23112yes—
189C22×#121C23112yes—
190C22×#121C23124yes—
191C22×#121C23124yes—
192C22×#121C23112yes—
193C22×#121C23112yes—
194C22×#121C23124yes—
195C22×#121C23148yes—
196C22×#121C23148yes—
197C22×#121C231288yescomplemented
198C22×#121C231576yescomplemented
199C22×#120C23124yes—
200C22×#120C23148yes—
201C22×#120C23148yes—
202C22×#120C23148yes—
203C2×#520C231192yescomplemented
204C2×C4×#41C231192yescomplemented
205C2×C4×#41C231288yescomplemented
206C22×C4×Q8C2312yes—
207C22×C4×Q8C2316yes—
208C22×C4×Q8C2314yes—
209C22×C4×Q8C2316yes—
210C22×C4×Q8C2316yes—
211C22×C4×Q8C23148yescomplemented
212C22×C4×D4C23112yes—
213C22×C4×D4C23112yes—
214C22×C4×D4C23112yes—
215C22×C4×D4C23112yes—
216C22×C4×D4C2316yes—
217C22×C4×D4C23112yes—
218C22×C4×D4C23112yes—
219C22×C4×D4C2316yes—
220C22×C4×D4C23124yes—
221C22×C4×D4C23124yes—
222C22×C4×D4C23112yes—
223C22×C4×D4C23124yes—
224C22×C4×D4C231144yescomplemented
225C22×#117C2312yes—
226C22×#117C23112yes—
227C22×#117C23112yes—
228C22×#117C23112yes—
229C23×C4⋊C4C2311yescharacteristic
230C23×C4⋊C4C2313yes—
231C23×C4⋊C4C23112yes—
232C23×C22⋊C4C2316yes—
233C23×C22⋊C4C23124yes—
234C23×C42C2313yes—
235C23×C42C23112yes—
236C26C2416yes—
237C26C24124yes—
238C2×H(5,𝔽2)—42304no—
239C2×H(5,𝔽2)—41536no—
240C2×H(5,𝔽2)C2411024yescomplemented
241C2×H(5,𝔽2)C2411536yescomplemented
242C22×#41—264no—
243C22×#41—264no—
244C22×#41—296no—
245C22×#41—496no—
246C22×#41—496no—
247C22×#41—4192no—
248C22×#41—4768no—
249C22×#41C24196yes—
250C22×#41C241144yes—
251C22×#41C24196yes—
252C22×#41C241288yes—
253C22×#41C241288yes—
254C22×#41C241576yes—
255C22×#41C241512yescomplemented
256C23×Q8—216no—
257C23×Q8C2413yes—
258C23×Q8C24124yes—
259C23×Q8C2416yes—
260C23×Q8C2414yes—
261C23×Q8C2411yescharacteristic
262C23×D4—248no—
263C23×D4—448no—
264C23×D4—496no—
265C23×D4—4192no—
266C23×D4—4192no—
267C23×D4—4192no—
268C23×D4—824no—
269C23×D4—896no—
270C23×D4C24112yes—
271C23×D4C24112yes—
272C23×D4C2416yes—
273C23×D4C24112yes—
274C23×D4C24112yes—
275C23×D4C24172yes—
276C23×D4C24112yes—
277C23×D4C24148yes—
278C23×D4C24124yes—
279C23×D4C24112yes—
280C23×D4C24124yes—
281C23×D4C24124yes—
282C23×D4C24112yes—
283C23×D4C241144yes—
284C23×D4C241576yes—
285C23×D4C241288yes—
286C23×D4C241576yes—
287C23×D4C241576yes—
288C23×D4C241144yes—
289C23×D4C241576yes—
290C24×C4—448no—
291C24×C4C2413yes—
292C24×C4C24112yes—
293C24×C4C24112yes—
294C24×C4C24112yes—
295C24×C4C2412yes—
296C24×C4C24112yes—
297C24×C4C241144yes—
298C24×C4C2413yes—
299C24×C4C24112yes—
300C24×C4C24124yes—
301C24×C4C2411yescharacteristic
302#560C24112288yescomplemented
303#559C2411536yescomplemented
304#557C241512yescomplemented
305#556C2411536yescomplemented
306#553C2413072yescomplemented
307#553C2416144yescomplemented
308#550C2411024yescomplemented
309#550C2413072yescomplemented
310#550C241512yescomplemented
311#550C2412048yescomplemented
312#550C2413072yescomplemented
313#550C2413072yescomplemented
314#548C2411024yescomplemented
315#547C2413072yescomplemented
316#546C2416144yescomplemented
317#546C2416144yescomplemented
318D42C2416144yescomplemented
319D42C2413072yescomplemented
320D42C2413072yescomplemented
321D42C2416144yescomplemented
322D42C2416144yescomplemented
323D42C2413072yescomplemented
324#544C241256yescomplemented
325#542C2413072yescomplemented
326#540C2413072yescomplemented
327#540C2416144yescomplemented
328#538C2413072yescomplemented
329#538C2416144yescomplemented
330#537C241768yescomplemented
331#537C2413072yescomplemented
332#535C2411536yescomplemented
333#535C2413072yescomplemented
334#535C2416144yescomplemented
335#535C2416144yescomplemented
336#534C2413072yescomplemented
337#534C2416144yescomplemented
338#532C2413072yescomplemented
339#532C2411536yescomplemented
340#532C2413072yescomplemented
341C2×C4⋊Q8C24196yes—
342C2×C4⋊Q8C241144yes—
343C2×#127C241288yes—
344C2×#127C241144yes—
345C2×#127C241288yes—
346C2×#127C241288yes—
347C2×#127C241576yes—
348C2×#127C241576yes—
349C2×#127C241768yescomplemented
350C2×#127C2413072yescomplemented
351#529C2413072yescomplemented
352#529C2413072yescomplemented
353C2×#126C241576yes—
354C2×#126C241576yes—
355C2×#125C24196yes—
356C2×#125C241288yes—
357C2×#124C241288yes—
358C2×#124C241288yes—
359C2×#124C241576yes—
360C2×#124C241288yes—
361#525C2413072yescomplemented
362C2×#123C241576yes—
363C2×#123C241576yes—
364C2×#123C241576yes—
365C2×#123C2411152yes—
366C2×C22⋊Q8C24196yes—
367C2×C22⋊Q8C241288yes—
368C2×C22⋊Q8C241288yes—
369C2×C22⋊Q8C241288yes—
370C2×#121C241288yes—
371C2×#121C241288yes—
372C2×#121C241576yes—
373C2×#121C241576yes—
374C2×#121C241576yes—
375C2×#121C241576yes—
376C2×#121C241288yes—
377C2×#121C241288yes—
378C2×#121C241288yes—
379C2×#121C241288yes—
380C2×#121C241576yes—
381C2×#121C241288yes—
382C2×#121C241288yes—
383C2×#121C241576yes—
384C2×#121C241576yes—
385C2×#121C2411152yes—
386C2×#121C2411152yes—
387C2×#121C2411536yescomplemented
388C2×#121C2413072yescomplemented
389C2×#120C241576yes—
390C2×#120C2411152yes—
391C2×#120C2411152yes—
392C2×#120C2411152yes—
393#520C2411024yescomplemented
394C4×#41C2411536yescomplemented
395C4×#41C2411024yescomplemented
396C2×C4×Q8C24148yes—
397C2×C4×Q8C241144yes—
398C2×C4×Q8C24196yes—
399C2×C4×Q8C241144yes—
400C2×C4×Q8C241144yes—
401C2×C4×Q8C241256yescomplemented
402C2×C4×D4C241288yes—
403C2×C4×D4C241288yes—
404C2×C4×D4C241288yes—
405C2×C4×D4C241288yes—
406C2×C4×D4C241144yes—
407C2×C4×D4C241288yes—
408C2×C4×D4C241288yes—
409C2×C4×D4C241144yes—
410C2×C4×D4C241576yes—
411C2×C4×D4C241576yes—
412C2×C4×D4C241288yes—
413C2×C4×D4C241576yes—
414C2×C4×D4C241768yescomplemented
415C2×#117C24148yes—
416C2×#117C241288yes—
417C2×#117C241288yes—
418C2×#117C241288yes—
419C22×C4⋊C4C24112yes—
420C22×C4⋊C4C24112yes—
421C22×C4⋊C4C2416yes—
422C22×C4⋊C4C2414yes—
423C22×C4⋊C4C24124yes—
424C22×C4⋊C4C2416yes—
425C22×C4⋊C4C24172yes—
426C22×C4⋊C4C241288yes—
427C22×C4⋊C4C2414yes—
428C22×C4⋊C4C2412yes—
429C22×C4⋊C4C2412yes—
430C22×C4⋊C4C24112yes—
431C22×C4⋊C4C24112yes—
432C22×C4⋊C4C2418yes—
433C22×C4⋊C4C24112yes—
434C22×C22⋊C4C24124yes—
435C22×C22⋊C4C24124yes—
436C22×C22⋊C4C24124yes—
437C22×C22⋊C4C241144yes—
438C22×C22⋊C4C241576yes—
439C22×C22⋊C4C2414yes—
440C22×C22⋊C4C24112yes—
441C22×C22⋊C4C24124yes—
442C22×C22⋊C4C24112yes—
443C22×C22⋊C4C24124yes—
444C22×C22⋊C4C24124yes—
445C22×C42C2414yes—
446C22×C42C2416yes—
447C22×C42C24112yes—
448C22×C42C2416yes—
449C22×C42C24112yes—
450C22×C42C24172yes—
451C22×C42C241288yes—
452C25—248no—
453C25—424no—
454C25—424no—
455C25—496no—
456C25—496no—
457C25—496no—
458C25C25112yes—
459C25C25112yes—
460C25C2511yescharacteristic
461C25C25172yes—
462C25C251288yes—
463H(5,𝔽2)—46144no—
464H(5,𝔽2)—44096no—
465C2×#41—2768no—
466C2×#41—2768no—
467C2×#41—21152no—
468C2×#41—41152no—
469C2×#41—41152no—
470C2×#41—42304no—
471C2×#41—42048no—
472C2×#41C251384yes—
473C2×#41C251256yes—
474C2×#41C251256yes—
475C2×#41C251768yes—
476C2×#41C2511536yes—
477C2×#41C251768yes—
478C22×Q8—2192no—
479C22×Q8—224no—
480C22×Q8—248no—
481C22×Q8—416no—
482C22×Q8H(5,𝔽2)116yescomplemented
483C22×Q8C25136yes—
484C22×Q8C25172yes—
485C22×Q8C25164yes—
486C22×Q8C25148yes—
487C22×Q8C25112yes—
488C22×D4—296no—
489C22×D4—296no—
490C22×D4—296no—
491C22×D4—248no—
492C22×D4—296no—
493C22×D4—2576no—
494C22×D4—4576no—
495C22×D4—41152no—
496C22×D4—42304no—
497C22×D4—42304no—
498C22×D4—448no—
499C22×D4—496no—
500C22×D4—4192no—
501C22×D4—448no—
502C22×D4—448no—
503C22×D4—496no—
504C22×D4—496no—
505C22×D4—42304no—
506C22×D4—8288no—
507C22×D4—81152no—
508C22×D4C251144yes—
509C22×D4C251144yes—
510C22×D4C251144yes—
511C22×D4C25172yes—
512C22×D4C251144yes—
513C22×D4C251192yes—
514C22×D4C251144yes—
515C22×D4C251288yes—
516C22×D4C251288yes—
517C22×D4C251144yes—
518C22×D4C251144yes—
519C22×D4C251576yes—
520C22×D4C251288yes—
521C22×D4C251384yes—
522C22×D4C2511536yes—
523C22×D4C251768yes—
524C22×D4C2511536yes—
525C22×D4C2511536yes—
526C22×D4C251384yes—
527C22×D4C2511536yes—
528C23×C4—224no—
529C23×C4—296no—
530C23×C4—296no—
531C23×C4—296no—
532C23×C4—4576no—
533C23×C4—48no—
534C23×C4—448no—
535C23×C4—496no—
536C23×C4—412no—
537C23×C4—448no—
538C23×C4H(5,𝔽2)116yescomplemented
539C23×C4C251144yes—
540C23×C4C25136yes—
541C23×C4C251144yes—
542C23×C4C251144yes—
543C23×C4C2514yes—
544C23×C4C2513yes—
545C23×C4C25112yes—
546C23×C4C2516yes—
547C23×C4C2514yes—
548C23×C4C2514yes—
549C23×C4C25124yes—
550C23×C4C25136yes—
551C23×C4C251144yes—
552C23×C4C251288yes—
553C23×C4C251144yes—
554C23×C4C251384yes—
555C23×C4C2513yes—
556C23×C4C2512yes—
557C23×C4C25112yes—
558C4⋊Q8C251256yes—
559C4⋊Q8C251384yes—
560#127C251768yes—
561#127C251384yes—
562#127C251768yes—
563#127C251768yes—
564#127C2511536yes—
565#127C2511536yes—
566#126C2511536yes—
567#126C2511536yes—
568#125C251256yes—
569#125C251768yes—
570#124C251768yes—
571#124C251768yes—
572#124C2511536yes—
573#124C251768yes—
574#123C2511536yes—
575#123C2511536yes—
576#123C2511536yes—
577#123C2513072yes—
578C22⋊Q8C251256yes—
579C22⋊Q8C251768yes—
580C22⋊Q8C251768yes—
581C22⋊Q8C251768yes—
582#121C251768yes—
583#121C251768yes—
584#121C2511536yes—
585#121C2511536yes—
586#121C2511536yes—
587#121C2511536yes—
588#121C251768yes—
589#121C251768yes—
590#121C251768yes—
591#121C251768yes—
592#121C2511536yes—
593#121C251768yes—
594#121C251768yes—
595#121C2511536yes—
596#121C2511536yes—
597#121C2513072yes—
598#121C2513072yes—
599#120C2511536yes—
600#120C2513072yes—
601#120C2513072yes—
602#120C2513072yes—
603C4×Q8C251128yes—
604C4×Q8C251384yes—
605C4×Q8C251256yes—
606C4×Q8C251384yes—
607C4×Q8C251384yes—
608C4×D4C251768yes—
609C4×D4C251768yes—
610C4×D4C251768yes—
611C4×D4C251768yes—
612C4×D4C251384yes—
613C4×D4C251768yes—
614C4×D4C251768yes—
615C4×D4C251384yes—
616C4×D4C2511536yes—
617C4×D4C2511536yes—
618C4×D4C251768yes—
619C4×D4C2511536yes—
620#117C251128yes—
621#117C251768yes—
622#117C251768yes—
623#117C251768yes—
624C2×C4⋊C4C251144yes—
625C2×C4⋊C4C251144yes—
626C2×C4⋊C4C25172yes—
627C2×C4⋊C4C25148yes—
628C2×C4⋊C4C25164yes—
629C2×C4⋊C4C25172yes—
630C2×C4⋊C4C251192yes—
631C2×C4⋊C4C251768yes—
632C2×C4⋊C4C25148yes—
633C2×C4⋊C4C25124yes—
634C2×C4⋊C4C25124yes—
635C2×C4⋊C4C251144yes—
636C2×C4⋊C4C251144yes—
637C2×C4⋊C4C25196yes—
638C2×C4⋊C4C251144yes—
639C2×C22⋊C4C251288yes—
640C2×C22⋊C4C251288yes—
641C2×C22⋊C4C251288yes—
642C2×C22⋊C4C251384yes—
643C2×C22⋊C4C2511536yes—
644C2×C22⋊C4C25148yes—
645C2×C22⋊C4C251144yes—
646C2×C22⋊C4C251288yes—
647C2×C22⋊C4C251144yes—
648C2×C22⋊C4C251288yes—
649C2×C22⋊C4C251288yes—
650C2×C42C25148yes—
651C2×C42C251144yes—
652C2×C42C25172yes—
653C2×C42C251144yes—
654C2×C42C25172yes—
655C2×C42C251192yes—
656C2×C42C251768yes—
657C24—24no—
658C24—24no—
659C24—248no—
660C24—248no—
661C24—248no—
662C24—248no—
663C24—248no—
664C24—248no—
665C24—2288no—
666C24—4144no—
667C24—4144no—
668C24—4576no—
669C24—4576no—
670C24—4576no—
671C24—8192no—
672C24—16384no—
673C24C2×H(5,𝔽2)18yes—
674C24C26172yes—
675C24C26172yes—
676C24C2616yes—
677C24C26196yes—
678C24C261384yes—
679C24C2611yescharacteristic
680#41—21024no—
681#41—21024no—
682#41—21536no—
683#41—41536no—
684#41—41536no—
685#41—43072no—
686C2×Q8—2256no—
687C2×Q8—2144no—
688C2×Q8—2288no—
689C2×Q8—496no—
690C2×Q8C2×H(5,𝔽2)196yescomplemented
691C2×Q8C26148yes—
692C2×Q8C26196yes—
693C2×Q8C26164yes—
694C2×Q8C26116yes—
695C2×D4—2576no—
696C2×D4—2576no—
697C2×D4—2576no—
698C2×D4—2288no—
699C2×D4—2576no—
700C2×D4—2768no—
701C2×D4—4768no—
702C2×D4—41536no—
703C2×D4—43072no—
704C2×D4—43072no—
705C2×D4—4288no—
706C2×D4—4576no—
707C2×D4—41152no—
708C2×D4—4288no—
709C2×D4—4288no—
710C2×D4—4576no—
711C2×D4—4576no—
712C2×D4—43072no—
713C2×D4—8384no—
714C2×D4—81536no—
715C2×D4C261192yes—
716C2×D4C261192yes—
717C2×D4C261192yes—
718C2×D4C26196yes—
719C2×D4C261192yes—
720C2×D4C261192yes—
721C2×D4C261384yes—
722C2×D4C261384yes—
723C2×D4C261192yes—
724C2×D4C261192yes—
725C2×D4C261768yes—
726C2×D4C261384yes—
727C22×C4—216no—
728C22×C4—216no—
729C22×C4—248no—
730C22×C4—212no—
731C22×C4—224no—
732C22×C4—216no—
733C22×C4—2144no—
734C22×C4—2576no—
735C22×C4—2576no—
736C22×C4—2576no—
737C22×C4—4768no—
738C22×C4—448no—
739C22×C4—4288no—
740C22×C4—4576no—
741C22×C4—472no—
742C22×C4—4288no—
743C22×C4C2×H(5,𝔽2)124yes—
744C22×C4C2×H(5,𝔽2)116yes—
745C22×C4C2×H(5,𝔽2)196yescomplemented
746C22×C4C26124yes—
747C22×C4C26136yes—
748C22×C4C26124yes—
749C22×C4C26118yes—
750C22×C4C26172yes—
751C22×C4C26148yes—
752C22×C4C261192yes—
753C22×C4C261192yes—
754C22×C4C26124yes—
755C22×C4C261192yes—
756C22×C4C26148yes—
757C22×C4C261192yes—
758C22×C4C26132yes—
759C22×C4C261192yes—
760C22×C4C261384yes—
761C22×C4C26112yes—
762C22×C4C26118yes—
763C22×C4C26116yes—
764C4⋊C4C261192yes—
765C4⋊C4C261192yes—
766C4⋊C4C26196yes—
767C4⋊C4C26164yes—
768C4⋊C4C26196yes—
769C4⋊C4C26164yes—
770C4⋊C4C26132yes—
771C4⋊C4C26132yes—
772C4⋊C4C261192yes—
773C4⋊C4C261192yes—
774C4⋊C4C261128yes—
775C4⋊C4C261192yes—
776C22⋊C4C261384yes—
777C22⋊C4C261384yes—
778C22⋊C4C261384yes—
779C22⋊C4C26164yes—
780C22⋊C4C261192yes—
781C22⋊C4C261384yes—
782C22⋊C4C261192yes—
783C22⋊C4C261384yes—
784C22⋊C4C261384yes—
785C42C26164yes—
786C42C26196yes—
787C42C261192yes—
788C42C26196yes—
789C42C261192yes—
790C23—212no—
791C23—212no—
792C23—232no—
793C23—2144no—
794C23—2144no—
795C23—2144no—
796C23—2144no—
797C23—2144no—
798C23—2144no—
799C23—2192no—
800C23—496no—
801C23—496no—
802C23—4384no—
803C23—4384no—
804C23—4384no—
805C23—4192no—
806C23—4192no—
807C23—8576no—
808C23—161152no—
809C23C22×H(5,𝔽2)124yes—
810C23C22×H(5,𝔽2)14yes—
811C23C22×H(5,𝔽2)14yes—
812C23H(7,𝔽2)14yes—
813C23C27148yes—
814C23C27148yes—
815C23C2714yes—
816C23C2713yes—
817Q8—296no—
818Q8—2192no—
819Q8—464no—
820Q8C22×H(5,𝔽2)164yescomplemented
821D4—2384no—
822D4—2384no—
823D4—2384no—
824D4—2192no—
825D4—2384no—
826D4—4192no—
827D4—4384no—
828D4—4768no—
829D4—4192no—
830D4—4192no—
831D4—4384no—
832D4—4384no—
833C2×C4—248no—
834C2×C4—248no—
835C2×C4—2144no—
836C2×C4—236no—
837C2×C4—272no—
838C2×C4—248no—
839C2×C4—296no—
840C2×C4—2384no—
841C2×C4—2384no—
842C2×C4—2384no—
843C2×C4—432no—
844C2×C4—4192no—
845C2×C4—4384no—
846C2×C4—448no—
847C2×C4—4192no—
848C2×C4C22×H(5,𝔽2)172yes—
849C2×C4C22×H(5,𝔽2)148yes—
850C2×C4C22×H(5,𝔽2)164yescomplemented
851C2×C4C27116yes—
852C2×C4C27124yes—
853C2×C4C27116yes—
854C2×C4C27112yes—
855C2×C4C27148yes—
856C2×C4C27116yes—
857C2×C4C2718yes—
858C2×C4C27112yes—
859C22—24no—
860C22—24no—
861C22—248no—
862C22—248no—
863C22—248no—
864C22—248no—
865C22—248no—
866C22—248no—
867C22—248no—
868C22—4288no—
869C22—4288no—
870C22—8192no—
871C22—16384no—
872C22#62916116yesdirect product factor
873C22C23×H(5,𝔽2)18yes—
874C22C23×H(5,𝔽2)16yes—
875C22C23×H(5,𝔽2)16yes—
876C22C2×H(7,𝔽2)16yes—
877C22C2811yescharacteristic
878C4—216no—
879C4—216no—
880C4—248no—
881C4—212no—
882C4—224no—
883C4—216no—
884C4C23×H(5,𝔽2)124yes—
885C4C23×H(5,𝔽2)116yes—
886C2—28no—
887C2—448no—
888C2—448no—
889C2C2×#62916112yesdirect product factor
890C2C24×H(5,𝔽2)11yescharacteristic
891C2C24×H(5,𝔽2)11yescharacteristic
892C2C22×H(7,𝔽2)11yescharacteristic
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×#62916C2direct (N × H)
2. C22×#3546C2semidirect
3. C22×#3543C2semidirect
4. C22×#3537C2semidirect
5. C22×#3498C2semidirect
6. C22×#3498C2semidirect
7. C22×#3488C2semidirect
8. C22×#3517C2semidirect
9. C22×#3496C2semidirect
10. C22×#3480C2semidirect
11. C23×#550C2semidirect
12. C22×#3460C2semidirect
13. C23×H(5,𝔽2)C22semidirect
14. C23×H(5,𝔽2)C22semidirect
15. C24×#41C22semidirect
16. #62916C22direct (N × H)
17. C2×#3498C22semidirect
18. C2×#3498C22semidirect
19. C2×#3488C22semidirect
20. C2×#3517C22semidirect
21. C2×#3496C22semidirect
22. C2×#3546C22semidirect
23. C2×#3543C22semidirect
24. C2×#3537C22semidirect
25. C2×#3480C22semidirect
26. C22×#559C22semidirect
27. C22×#557C22semidirect
28. C22×#556C22semidirect
29. C22×#553C22semidirect
30. C22×#553C22semidirect
31. C22×#550C22semidirect
32. C22×#550C22semidirect
33. C22×#550C22semidirect
34. C22×#550C22semidirect
35. C22×#550C22semidirect
36. C22×#550C22semidirect
37. C22×#550C22semidirect
38. C22×#547C22semidirect
39. C22×#548C22semidirect
40. C22×#546C22semidirect
41. C22×#546C22semidirect
42. C22×D42C22semidirect
43. C22×D42C22semidirect
44. C22×D42C22semidirect
45. C22×D42C22semidirect
46. C22×D42C22semidirect
47. C22×D42C22semidirect
48. C22×#560C22semidirect
49. C2×#3460C22semidirect
50. C22×#542C22semidirect
51. C22×#540C22semidirect
52. C22×#540C22semidirect
53. C22×#544C22semidirect
54. C22×#537C22semidirect
55. C22×#537C22semidirect
56. C22×#535C22semidirect
57. C22×#535C22semidirect
58. C22×#535C22semidirect
59. C22×#535C22semidirect
60. C22×#538C22semidirect
61. C22×#538C22semidirect
62. C22×#534C22semidirect
63. C22×#534C22semidirect
64. C22×#532C22semidirect
65. C22×#532C22semidirect
66. C22×#532C22semidirect
67. C23×#127C22semidirect
68. C23×#127C22semidirect
69. C22×#529C22semidirect
70. C22×#529C22semidirect
71. C22×#525C22semidirect
72. C23×#121C22semidirect
73. C23×#121C22semidirect
74. C22×#520C22semidirect
75. C22×C4×#41C22semidirect
76. C22×C4×#41C22semidirect
77. C23×C4×Q8C22semidirect
78. C23×C4×D4C22semidirect
81. C22×H(5,𝔽2)C23semidirect
82. C22×H(5,𝔽2)C23semidirect
90. C23×#41C23semidirect
101. #3546C23semidirect
102. #3543C23semidirect
103. #3537C23semidirect
104. C2×#560C23semidirect
105. #3517C23semidirect
106. #3498C23semidirect
107. #3498C23semidirect
108. #3496C23semidirect
109. #3488C23semidirect
110. #3480C23semidirect
111. C2×#559C23semidirect
112. C2×#557C23semidirect
113. C2×#556C23semidirect
114. C2×#553C23semidirect
115. C2×#553C23semidirect
116. C2×#550C23semidirect
117. C2×#550C23semidirect
118. C2×#550C23semidirect
119. C2×#550C23semidirect
120. C2×#550C23semidirect
121. C2×#550C23semidirect
122. C2×#550C23semidirect
123. C2×#548C23semidirect
124. C2×#547C23semidirect
125. C2×#546C23semidirect
126. C2×#546C23semidirect
127. C2×D42C23semidirect
128. C2×D42C23semidirect
129. C2×D42C23semidirect
130. C2×D42C23semidirect
131. C2×D42C23semidirect
132. C2×D42C23semidirect
133. #3460C23semidirect
134. C2×#544C23semidirect
135. C2×#542C23semidirect
136. C2×#540C23semidirect
137. C2×#540C23semidirect
138. C2×#538C23semidirect
139. C2×#538C23semidirect
140. C2×#537C23semidirect
141. C2×#537C23semidirect
142. C2×#535C23semidirect
143. C2×#535C23semidirect
144. C2×#535C23semidirect
145. C2×#535C23semidirect
146. C2×#534C23semidirect
147. C2×#534C23semidirect
148. C2×#532C23semidirect
149. C2×#532C23semidirect
150. C2×#532C23semidirect
159. C22×#127C23semidirect
160. C22×#127C23semidirect
161. C2×#529C23semidirect
162. C2×#529C23semidirect
171. C2×#525C23semidirect
197. C22×#121C23semidirect
198. C22×#121C23semidirect
203. C2×#520C23semidirect
204. C2×C4×#41C23semidirect
205. C2×C4×#41C23semidirect
211. C22×C4×Q8C23semidirect
224. C22×C4×D4C23semidirect
240. C2×H(5,𝔽2)C24semidirect
241. C2×H(5,𝔽2)C24semidirect
255. C22×#41C24semidirect
302. #560C24semidirect
303. #559C24semidirect
304. #557C24semidirect
305. #556C24semidirect
306. #553C24semidirect
307. #553C24semidirect
308. #550C24semidirect
309. #550C24semidirect
310. #550C24semidirect
311. #550C24semidirect
312. #550C24semidirect
313. #550C24semidirect
314. #548C24semidirect
315. #547C24semidirect
316. #546C24semidirect
317. #546C24semidirect
318. D42C24semidirect
319. D42C24semidirect
320. D42C24semidirect
321. D42C24semidirect
322. D42C24semidirect
323. D42C24semidirect
324. #544C24semidirect
325. #542C24semidirect
326. #540C24semidirect
327. #540C24semidirect
328. #538C24semidirect
329. #538C24semidirect
330. #537C24semidirect
331. #537C24semidirect
332. #535C24semidirect
333. #535C24semidirect
334. #535C24semidirect
335. #535C24semidirect
336. #534C24semidirect
337. #534C24semidirect
338. #532C24semidirect
339. #532C24semidirect
340. #532C24semidirect
349. C2×#127C24semidirect
350. C2×#127C24semidirect
351. #529C24semidirect
352. #529C24semidirect
361. #525C24semidirect
387. C2×#121C24semidirect
388. C2×#121C24semidirect
393. #520C24semidirect
394. C4×#41C24semidirect
395. C4×#41C24semidirect
401. C2×C4×Q8C24semidirect
414. C2×C4×D4C24semidirect
482. C22×Q8H(5,𝔽2)semidirect
538. C23×C4H(5,𝔽2)semidirect
690. C2×Q8C2×H(5,𝔽2)semidirect
745. C22×C4C2×H(5,𝔽2)semidirect
820. Q8C22×H(5,𝔽2)semidirect
850. C2×C4C22×H(5,𝔽2)semidirect
872. C22#62916direct (N × H)
889. C2C2×#62916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#629162
C22×#35462
C22×#35432
C22×#35372
C22×#34982
C22×#34882
C22×#35172
C22×#34962
C22×#34802
C23×#5502
C22×#34602