Finite Group Databasebeta

← #7653838

Subgroups — #7653838

Order 512.

7515 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42799C216yesmaximal, complemented
4#42798C216yesmaximal, complemented
5#39726C213yesmaximal, complemented
6#39598C213yesmaximal, complemented
7#39359C216yesmaximal, complemented
8#39137C213yesmaximal, complemented
9#39126C213yesmaximal, complemented
10#38950C216yesmaximal, complemented
11#37620C213yesmaximal, complemented
12#36576C212yesmaximal, complemented
13#36576C211yesmaximal, characteristic, complemented
14Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
15#36456C211yesmaximal, characteristic, complemented
16#36455C211yesmaximal, characteristic, complemented
17#36434C212yesmaximal, complemented
18#35831C212yesmaximal, complemented
19#35816C212yesmaximal, complemented
20#35273C213yesmaximal, complemented
21#35238C213yesmaximal, complemented
22#34964C213yesmaximal, complemented
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24#3522—216no—
25#3482—216no—
26C2×#559C2213yes—
27C2×Q82C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#554C2213yes—
31C2×#552C2213yes—
32C2×#552C2213yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2212yes—
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2212yes—
40C2×#547C2216yes—
41C2×#547C2213yes—
42C2×#542C2216yes—
43C2×#537C2216yes—
44C2×#533C2213yes—
45C2×#532C2213yes—
46C2×#529C2213yes—
47C2×#529C2213yes—
48C2×#529C2213yes—
49C2×#520C2212yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2213yes—
52C22×C4×Q8C2211yescharacteristic
53C22×C4×Q8C2212yes—
54C22×C4×Q8C2211yescharacteristic
55#2857C2213yes—
56#2857C2213yes—
57#2856C2213yes—
58#2856C2216yes—
59#2856C2213yes—
60#2850C2216yes—
61#2823C22112yes—
62#2707C22112yes—
63#2705C22112yes—
64#2704C22112yes—
65#2702C22112yes—
66#2683C22112yes—
67#2682C22112yes—
68#2681C22112yes—
69#2681C22112yes—
70#2662C22112yes—
71#2629C2216yes—
72#2629C2216yes—
73#2620C2216yes—
74#2620C2216yes—
75#2620C2216yes—
76#2620C2216yes—
77#2618C22112yes—
78#2601C2216yes—
79#2601C2216yes—
80#2592C2213yes—
81#2584C2213yes—
82#2582C2213yes—
83#2567C2213yes—
84#2566C2216yes—
85#2563C2213yes—
86#2562C2213yes—
87#2548C2213yes—
88#2548C2216yes—
89#2545C2216yes—
90#2544C2216yes—
91#2541C2213yes—
92#2540C2213yes—
93#2538C2216yes—
94#2538C2216yes—
95#2538C2216yes—
96#2538C2213yes—
97#2538C2213yes—
98#2537C2216yes—
99#2537C2213yes—
100#2537C2216yes—
101#2536C2216yes—
102#2498C2216yes—
103#2454C2216yes—
104#2452C2216yes—
105#2452C2216yes—
106#2451C2216yes—
107#2442C2216yes—
108#2440C2216yes—
109#2440C2216yes—
110#2439C2216yes—
111#2430C22112yes—
112#2430C2216yes—
113#2429C2216yes—
114#2428C2216yes—
115#2428C2216yes—
116#2427C2216yes—
117#2426C2216yes—
118#2426C2216yes—
119#2426C2216yes—
120#2426C2216yes—
121#2417C2216yes—
122#2417C2216yes—
123#2417C2211yescharacteristic
124#2417C2213yes—
125#2416C2216yes—
126#2416C2216yes—
127#2416C2216yes—
128#2416C2213yes—
129#2416C2213yes—
130#2416C2216yes—
131#2416C2216yes—
132#2416C2216yes—
133#2414C2216yes—
134#2396C2216yes—
135#2392C2216yes—
136#2351C2212yes—
137Q8×C4⋊C4C2213yes—
138Q8×C4⋊C4C2216yes—
139Q8×C4⋊C4C2211yescharacteristic
140Q8×C4⋊C4C2211yescharacteristic
141Q8×C4⋊C4C2213yes—
142Q8×C4⋊C4C2212yes—
143Q8×C4⋊C4C2212yes—
144#2341C2212yes—
145#2341C2212yes—
146#2341C2212yes—
147Q8×C22⋊C4C2212yes—
148#2324C2216yes—
149#2324C2216yes—
150#2311C2216yes—
151C4×C22⋊Q8C2213yes—
152C4×C22⋊Q8C2213yes—
153C4×#121C2216yes—
154C4×#121C2216yes—
155C4×#121C2213yes—
156C4×#121C2213yes—
157C2×#389C2216yes—
158C2×#384C2213yes—
159C2×C4×C4⋊C4C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2312yes—
162C22×#41C2313yes—
163C22×#41C2316yes—
164C23×Q8C2311yescharacteristic
165C23×Q8C2311yescharacteristic
166#559—224no—
167Q82—28no—
168#557—28no—
169#556—224no—
170#554—224no—
171#552—224no—
172#552—224no—
173#550—28no—
174#550—48no—
175D4×Q8—28no—
176#548—28no—
177#548—216no—
178#548—28no—
179#548—48no—
180#547—224no—
181#547—248no—
182#542—248no—
183#537—424no—
184#533—224no—
185#532—224no—
186C2×C4⋊Q8C2313yes—
187C2×C4⋊Q8C2313yes—
188C2×C4⋊Q8C2313yes—
189C2×C4⋊Q8C2316yes—
190C2×#127C2313yes—
191C2×#127C2316yes—
192#529—224no—
193#529—224no—
194#529—224no—
195C2×#126C2316yes—
196C2×#126C2316yes—
197C2×#126C2316yes—
198C2×#125C2313yes—
199C2×#125C2313yes—
200C2×#125C2313yes—
201C2×#125C2316yes—
202C2×#124C2313yes—
203C2×#124C2316yes—
204C2×#124C2313yes—
205C2×#124C2313yes—
206C2×#124C2316yes—
207C2×#124C2316yes—
208C2×#123C2316yes—
209C2×#123C2316yes—
210C2×#123C2316yes—
211C2×#123C23112yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2313yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C2313yes—
219C2×C22⋊Q8C23112yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2316yes—
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2316yes—
225C2×C22⋊Q8C23112yes—
226C2×#121C2313yes—
227C2×#121C2316yes—
228C2×#121C2313yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2313yes—
232C2×#121C2316yes—
233C2×#121C2316yes—
234C2×#121C2316yes—
235C2×#121C2313yes—
236C2×#121C23112yes—
237C2×#121C2316yes—
238C2×#121C2316yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#121C2316yes—
242C2×#121C23112yes—
243#520—216no—
244C4×#41—28no—
245C4×#41—224no—
246C2×C4×Q8—28no—
247C2×C4×Q8—48no—
248C2×C4×Q8D4116yescomplemented
249C2×C4×Q8C2313yes—
250C2×C4×Q8C2313yes—
251C2×C4×Q8C2313yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2313yes—
258C2×C4×Q8C2313yes—
259C2×C4×Q8C2316yes—
260C2×C4×Q8C2316yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2313yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2316yes—
276C2×C4×D4C2316yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×#117C2313yes—
281C2×#117C2316yes—
282C2×#117C2313yes—
283C2×#117C2313yes—
284C2×#117C2316yes—
285C2×#117C2313yes—
286C22×C4⋊C4C2313yes—
287C22×C4⋊C4C2316yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2316yes—
290C22×C4⋊C4C2316yes—
291C22×C4⋊C4C2313yes—
292C22×C4⋊C4C2313yes—
293C22×C42C2313yes—
294C22×C42C2313yes—
295C22×C42C2316yes—
296C22×C42C2313yes—
297#400C2316yes—
298#399C2316yes—
299#398C2316yes—
300#398C23112yes—
301#398C23112yes—
302#398C2316yes—
303#398C2312yes—
304#398C23112yes—
305#397C2316yes—
306#396C2316yes—
307#396C23112yes—
308#396C2316yes—
309#396C23112yes—
310#396C23112yes—
311#396C23112yes—
312#396C23112yes—
313#396C2312yes—
314#396C2316yes—
315#396C23112yes—
316#396C23112yes—
317#396C23112yes—
318#396C23112yes—
319#395C23112yes—
320#395C2316yes—
321#394C2316yes—
322#394C23112yes—
323#394C23112yes—
324#394C23112yes—
325#394C2316yes—
326#394C2316yes—
327#394C23112yes—
328#394C23112yes—
329#394C23112yes—
330#394C23112yes—
331#393C23112yes—
332#393C2316yes—
333#392C2316yes—
334#392C23112yes—
335#391C2316yes—
336#391C2316yes—
337#391C2316yes—
338#391C2313yes—
339#391C2316yes—
340#391C2311yescharacteristic
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C2316yes—
346#390C2313yes—
347#390C2316yes—
348#390C23112yes—
349#390C23112yes—
350#390C2313yes—
351#390C2316yes—
352#390C2316yes—
353#390C2316yes—
354#390C2316yes—
355#390C2316yes—
356#389C2313yes—
357#389C2316yes—
358#389C2316yes—
359#389C2311yescharacteristic
360#389C2316yes—
361#389C2316yes—
362#389C2313yes—
363#389C2313yes—
364#389C2316yes—
365#389C2316yes—
366#389C2316yes—
367#389C2316yes—
368#389C2316yes—
369#389C2316yes—
370#389C23112yes—
371#389C23112yes—
372#389C2316yes—
373#388C2316yes—
374#388C2316yes—
375#388C23112yes—
376#388C23112yes—
377#388C2316yes—
378#388C2316yes—
379#388C2316yes—
380#388C2316yes—
381#387C2316yes—
382#387C2316yes—
383#386C2316yes—
384#386C23112yes—
385#386C23112yes—
386#386C23112yes—
387#386C2316yes—
388#386C2316yes—
389#386C2316yes—
390#386C2316yes—
391#386C2312yes—
392#385C23112yes—
393#385C23112yes—
394#385C2316yes—
395#385C2316yes—
396#384C2316yes—
397#384C2316yes—
398#384C2313yes—
399#384C2313yes—
400#384C2316yes—
401#384C2316yes—
402#382C2316yes—
403#380C2311yescharacteristic
404#380C2313yes—
405#380C2313yes—
406#380C2313yes—
407#380C2316yes—
408#380C23112yes—
409#380C23112yes—
410#380C2316yes—
411#380C2316yes—
412#380C2316yes—
413#380C2316yes—
414#380C2316yes—
415#380C2312yes—
416C4×C4⋊C4C2313yes—
417C4×C4⋊C4C2313yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2313yes—
420C4×C4⋊C4C2313yes—
421C4×C4⋊C4C2316yes—
422C4×C4⋊C4C2316yes—
423C4×C4⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C2×#95C2316yes—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—224no—
438C2×#41—46no—
439C2×#41—412no—
440C2×#41—412no—
441C22×Q8—24no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—24no—
445C22×Q8—24no—
446C22×Q8C2×D418yes—
447C22×Q8C2411yescharacteristic
448C22×Q8C2413yes—
449C22×Q8C2413yes—
450C22×Q8C2413yes—
451C22×Q8C2416yes—
452C22×Q8C2411yescharacteristic
453C22×D4C2413yes—
454C22×D4C2413yes—
455C22×D4C2413yes—
456C22×D4C2416yes—
457C22×D4C2416yes—
458C22×D4C2413yes—
459C22×D4C2411yescharacteristic
460C22×D4C2416yes—
461C22×D4C2416yes—
462C22×D4C2416yes—
463C22×D4C24112yes—
464C23×C4C2416yes—
465C23×C4C2413yes—
466C23×C4C2413yes—
467C23×C4C2413yes—
468C23×C4C2411yescharacteristic
469C23×C4C2413yes—
470C23×C4C2412yes—
471C23×C4C2413yes—
472C23×C4C2413yes—
473C23×C4C2411yescharacteristic
474C23×C4C2413yes—
475C23×C4C2416yes—
476C23×C4C24112yes—
477C4⋊Q8—212no—
478C4⋊Q8—212no—
479C4⋊Q8—224no—
480C4⋊Q8—212no—
481#127—212no—
482#127—412no—
483#126—224no—
484#126—224no—
485#126—224no—
486#125—212no—
487#125—224no—
488#125—212no—
489#125—212no—
490#124—212no—
491#124—224no—
492#124—212no—
493#124—212no—
494#124—224no—
495#124—412no—
496#123—224no—
497#123—224no—
498#123—224no—
499#123—248no—
500C22⋊Q8—212no—
501C22⋊Q8—212no—
502C22⋊Q8—224no—
503C22⋊Q8—24no—
504C22⋊Q8—212no—
505C22⋊Q8—224no—
506C22⋊Q8—212no—
507C22⋊Q8—248no—
508C22⋊Q8—24no—
509C22⋊Q8—412no—
510C22⋊Q8—424no—
511C22⋊Q8—412no—
512C22⋊Q8—46no—
513C22⋊Q8—412no—
514#121—224no—
515#121—212no—
516#121—212no—
517#121—224no—
518#121—212no—
519#121—224no—
520#121—212no—
521#121—412no—
522#121—424no—
523#121—412no—
524#121—46no—
525#121—412no—
526#121—412no—
527#121—412no—
528#121—412no—
529#121—412no—
530#121—424no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—28no—
536C4×Q8—212no—
537C4×Q8—212no—
538C4×Q8—212no—
539C4×Q8—212no—
540C4×Q8—212no—
541C4×Q8—412no—
542C4×Q8—412no—
543C4×Q8C2×D418yes—
544C4×Q8C2×D418yes—
545C4×Q8C2×D4124yes—
546C4×Q8C2×D4124yes—
547C4×D4—24no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—212no—
551C4×D4—224no—
552C4×D4—212no—
553C4×D4—224no—
554C4×D4—212no—
555C4×D4—212no—
556C4×D4—212no—
557C4×D4—224no—
558C4×D4—212no—
559C4×D4—224no—
560C4×D4—412no—
561C4×D4—412no—
562#117—212no—
563#117—212no—
564#117—212no—
565#117—212no—
566#117—224no—
567#117—224no—
568C2×C4⋊C4—212no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—46no—
572C2×C4⋊C4—412no—
573C2×C4⋊C4—412no—
574C2×C4⋊C4C2×D4124yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2413yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C24112yes—
602C2×C4⋊C4C24112yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2416yes—
608C2×C4⋊C4C24112yes—
609C2×C4⋊C4C2416yes—
610C2×C4⋊C4C2416yes—
611C2×C4⋊C4C2413yes—
612C2×C4⋊C4C2413yes—
613C2×C4⋊C4C2416yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C22⋊C4C2411yescharacteristic
616C2×C22⋊C4C2411yescharacteristic
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C24112yes—
639C2×C22⋊C4C24112yes—
640C2×C22⋊C4C24112yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C24112yes—
645C2×C22⋊C4C2416yes—
646C2×C42—212no—
647C2×C42—212no—
648C2×C42—412no—
649C2×C42C2×D4124yes—
650C2×C42C2413yes—
651C2×C42C2413yes—
652C2×C42C2413yes—
653C2×C42C2416yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2411yescharacteristic
657C2×C42C2416yes—
658C2×C42C2416yes—
659C2×C42C2416yes—
660C2×C42C2416yes—
661C2×C42C2413yes—
662C2×C42C2413yes—
663C2×C42C2413yes—
664C2×C42C2413yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2412yes—
670#95C2412yes—
671#95C2412yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2412yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C24112yes—
682#95C24112yes—
683C24C2513yes—
684C24C2516yes—
685C24C2511yescharacteristic
686C24C2511yescharacteristic
687#41—448no—
688#41—416no—
689#41—432no—
690#41—848no—
691C2×Q8—232no—
692C2×Q8—22no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—212no—
696C2×Q8—26no—
697C2×Q8—26no—
698C2×Q8—26no—
699C2×Q8—26no—
700C2×Q8—22no—
701C2×Q8—26no—
702C2×Q8—22no—
703C2×Q8—43no—
704C2×Q8—46no—
705C2×Q8—46no—
706C2×Q8—416no—
707C2×Q8C22×D4112yes—
708C2×Q8C22×D414yes—
709C2×Q8H(5,𝔽2)14yes—
710C2×Q82−1+414yes—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—212no—
716C2×D4—26no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—212no—
720C2×D4—212no—
721C2×D4—26no—
722C2×D4—26no—
723C2×D4—26no—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—26no—
733C2×D4—43no—
734C2×D4—46no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—412no—
741C2×D4—412no—
742C2×D4—412no—
743C2×D4H(5,𝔽2)14yes—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—22no—
748C22×C4—26no—
749C22×C4—22no—
750C22×C4—26no—
751C22×C4—24no—
752C22×C4—212no—
753C22×C4—22no—
754C22×C4—26no—
755C22×C4—26no—
756C22×C4—26no—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—212no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—212no—
763C22×C4—26no—
764C22×C4—24no—
765C22×C4—26no—
766C22×C4—22no—
767C22×C4—26no—
768C22×C4—212no—
769C22×C4—26no—
770C22×C4—22no—
771C22×C4—26no—
772C22×C4—224no—
773C22×C4—42no—
774C22×C4—43no—
775C22×C4—43no—
776C22×C4—46no—
777C22×C4—46no—
778C22×C4—412no—
779C22×C4—412no—
780C22×C4C22×D414yes—
781C22×C4C22×D4112yes—
782C22×C4C22×D4112yes—
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C22×C4C2513yes—
788C22×C4C2513yes—
789C22×C4C2516yes—
790C22×C4C2516yes—
791C22×C4C2512yes—
792C22×C4C2516yes—
793C22×C4C2513yes—
794C22×C4C2513yes—
795C22×C4C2513yes—
796C22×C4C2511yescharacteristic
797C22×C4C2513yes—
798C22×C4C2511yescharacteristic
799C22×C4C2512yes—
800C22×C4C2513yes—
801C22×C4C2511yescharacteristic
802C4⋊C4—212no—
803C4⋊C4—212no—
804C4⋊C4—26no—
805C4⋊C4—212no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—26no—
809C4⋊C4—26no—
810C4⋊C4—26no—
811C4⋊C4—26no—
812C4⋊C4—26no—
813C4⋊C4—26no—
814C4⋊C4—212no—
815C4⋊C4—212no—
816C4⋊C4—22no—
817C4⋊C4—26no—
818C4⋊C4—212no—
819C4⋊C4—212no—
820C4⋊C4—212no—
821C4⋊C4—212no—
822C4⋊C4—212no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—24no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—46no—
829C4⋊C4—412no—
830C4⋊C4—46no—
831C4⋊C4—46no—
832C4⋊C4—412no—
833C4⋊C4—42no—
834C4⋊C4—46no—
835C4⋊C4—46no—
836C4⋊C4—412no—
837C4⋊C4—46no—
838C4⋊C4C22×D4112yes—
839C4⋊C4C22×D4112yes—
840C4⋊C4C22×D4124yes—
841C4⋊C42−1+414yes—
842C22⋊C4—22no—
843C22⋊C4—26no—
844C22⋊C4—24no—
845C22⋊C4—212no—
846C22⋊C4—22no—
847C22⋊C4—212no—
848C22⋊C4—26no—
849C22⋊C4—212no—
850C22⋊C4—212no—
851C22⋊C4—26no—
852C22⋊C4—26no—
853C22⋊C4—212no—
854C22⋊C4—212no—
855C22⋊C4—212no—
856C22⋊C4—224no—
857C22⋊C4—212no—
858C22⋊C4—212no—
859C22⋊C4—212no—
860C22⋊C4—24no—
861C22⋊C4—42no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—412no—
869C22⋊C4—412no—
870C22⋊C4—412no—
871C22⋊C4—412no—
872C22⋊C4—46no—
873C42—22no—
874C42—26no—
875C42—26no—
876C42—26no—
877C42—26no—
878C42—26no—
879C42—212no—
880C42—212no—
881C42—212no—
882C42—46no—
883C42—46no—
884C42C22×D4112yes—
885C42C22×D4112yes—
886C42C22×D4112yes—
887C42C22×D4112yes—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—23no—
899C23—26no—
900C23—26no—
901C23—26no—
902C23—23no—
903C23—23no—
904C23—26no—
905C23—23no—
906C23—26no—
907C23—23no—
908C23—26no—
909C23—23no—
910C23—23no—
911C23—26no—
912C23C23×D412yes—
913C23C2×H(5,𝔽2)12yes—
914C23C2×H(5,𝔽2)12yes—
915C23#58512yes—
916C23C2611yescharacteristic
917Q8—224no—
918Q8—412no—
919Q8—412no—
920Q8—44no—
921Q8—812no—
922Q8#537116yescomplemented
923D4—28no—
924D4—412no—
925D4—412no—
926D4—424no—
927D4—412no—
928D4—424no—
929D4—412no—
930D4—812no—
931D4—812no—
932D4—812no—
933D4—1612no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—23no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—21no—
940C2×C4—23no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—23no—
944C2×C4—23no—
945C2×C4—21no—
946C2×C4—224no—
947C2×C4—224no—
948C2×C4—28no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—23no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—26no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—21no—
963C2×C4—23no—
964C2×C4—26no—
965C2×C4—22no—
966C2×C4—23no—
967C2×C4—23no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—23no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—23no—
977C2×C4—22no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—23no—
981C2×C4—26no—
982C2×C4—412no—
983C2×C4—48no—
984C2×C4—412no—
985C2×C4—412no—
986C2×C4—412no—
987C2×C4—424no—
988C2×C4—44no—
989C2×C4—412no—
990C2×C4—824no—
991C2×C4—812no—
992C2×C4C23×D416yes—
993C2×C4C23×D412yes—
994C2×C4C23×D416yes—
995C2×C4C23×D416yes—
996C2×C4C23×D416yes—
997C2×C4C23×D412yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)16yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+416yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4#58512yes—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—46no—
1018C22—43no—
1019C22—43no—
1020C22—46no—
1021C22—46no—
1022C22—43no—
1023C22—46no—
1024C22—43no—
1025C22—43no—
1026C22—46no—
1027C22—43no—
1028C22—46no—
1029C22—43no—
1030C22—46no—
1031C22#348814yes—
1032C22C24×D411yescharacteristic
1033C22C22×H(5,𝔽2)11yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22C2×#58511yescharacteristic
1038C22C2×#58511yescharacteristic
1039C4—24no—
1040C4—22no—
1041C4—26no—
1042C4—26no—
1043C4—22no—
1044C4—26no—
1045C4—46no—
1046C4—46no—
1047C4—42no—
1048C4—41no—
1049C4—43no—
1050C4—42no—
1051C4—43no—
1052C4—46no—
1053C4—41no—
1054C4—42no—
1055C4—43no—
1056C4C2×#537112yes—
1057C4#349714yes—
1058C2—24no—
1059C2—42no—
1060C2—86no—
1061C2—83no—
1062C2C22×#53711yescharacteristic
1063C2C2×#349711yescharacteristic
1064C2C2×#348811yescharacteristic
1065C2#6301411yescharacteristic
1066C2#6301511yescharacteristic
1067C2#6303311yescharacteristic
1068C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3522C2semidirect
2. C2×#3482C2semidirect
3. #42799C2semidirect
4. #42798C2semidirect
5. #39726C2semidirect
6. #39598C2semidirect
7. #39359C2semidirect
8. #39137C2semidirect
9. #39126C2semidirect
10. #38950C2semidirect
11. #37620C2semidirect
12. #36576C2semidirect
13. #36576C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. #36456C2semidirect
16. #36455C2semidirect
17. #36434C2semidirect
18. #35831C2semidirect
19. #35816C2semidirect
20. #35273C2semidirect
21. #35238C2semidirect
22. #34964C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
248. C2×C4×Q8D4semidirect
922. Q8#537semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×#34822
#427992
#427982
#397262
#395982
#393592
#391372
#391262
#389502
#376202
#365762
Q8×C22⋊Q82
#364562
#364552
#364342
#358312
#358162
#352732
#352382
#349642
C2×Q8×C4⋊C42