Finite Group Databasebeta

← #7689402

Subgroups — #7689402

Order 512.

8136 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3497C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#59421C213yesmaximal, complemented
4#59104C216yesmaximal, complemented
5#59049C213yesmaximal, complemented
6#59042C213yesmaximal, complemented
7#45265C216yesmaximal, complemented
8#45236C216yesmaximal, complemented
9#39471C213yesmaximal, complemented
10#38956C213yesmaximal, complemented
11#37785C216yesmaximal, complemented
12#36583C211yesmaximal, characteristic, complemented
13#36578C212yesmaximal, complemented
14#36577C211yesmaximal, characteristic, complemented
15#36455C211yesmaximal, characteristic, complemented
16#36410C213yesmaximal, complemented
17#36150C213yesmaximal, complemented
18#36018C212yesmaximal, complemented
19#35757C212yesmaximal, complemented
20#34715C213yesmaximal, complemented
21#34311C211yesmaximal, characteristic, complemented
22#34257C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3497—216no—
26#3482—216no—
27C2×#557C2211yescharacteristic
28C2×#556C2213yes—
29C2×#552C2216yes—
30C2×#550C2213yes—
31C2×#550C2211yescharacteristic
32C2×#550C2212yes—
33C2×D4×Q8C2213yes—
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#548C2216yes—
37C2×#548C2211yescharacteristic
38C2×#548C2212yes—
39C2×#547C2213yes—
40C2×#537C2216yes—
41C2×#533C2213yes—
42C2×#532C2213yes—
43C2×#532C2213yes—
44C2×#529C2216yes—
45C2×#519C2212yes—
46C2×C4×#41C2213yes—
47C2×C4×#41C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2212yes—
50#2858C2213yes—
51#2857C2213yes—
52#2856C2213yes—
53#2854C2216yes—
54#2714C22112yes—
55#2710C22112yes—
56#2703C22112yes—
57#2703C22112yes—
58#2703C22112yes—
59#2702C22112yes—
60#2690C22112yes—
61#2619C2216yes—
62#2615C2216yes—
63#2582C2213yes—
64#2568C2213yes—
65#2560C22112yes—
66#2548C2213yes—
67#2548C2216yes—
68#2547C2213yes—
69#2541C2213yes—
70#2540C2216yes—
71#2537C2213yes—
72#2536C2216yes—
73#2504C2216yes—
74#2492C2216yes—
75#2490C2216yes—
76#2490C2216yes—
77#2490C2216yes—
78#2487C2216yes—
79#2477C22112yes—
80#2476C22112yes—
81#2476C2216yes—
82#2474C2216yes—
83#2467C22112yes—
84#2464C22112yes—
85#2459C2216yes—
86#2456C2216yes—
87#2454C2216yes—
88#2453C2216yes—
89#2451C2213yes—
90#2448C2216yes—
91#2448C2216yes—
92#2445C2213yes—
93#2442C2216yes—
94#2439C2213yes—
95#2436C2216yes—
96#2431C2213yes—
97#2431C2216yes—
98#2431C2216yes—
99#2431C2216yes—
100#2428C2216yes—
101#2427C2216yes—
102#2427C2216yes—
103#2426C2216yes—
104#2426C2213yes—
105#2426C2216yes—
106#2421C2216yes—
107#2421C2216yes—
108#2420C2211yescharacteristic
109#2414C2216yes—
110#2414C2216yes—
111#2414C2216yes—
112#2414C2216yes—
113#2414C2213yes—
114#2409C2216yes—
115#2407C2213yes—
116#2407C2216yes—
117#2407C2216yes—
118#2392C2216yes—
119#2388C2216yes—
120#2367C2216yes—
121#2367C2213yes—
122#2365C2213yes—
123#2363C2216yes—
124#2363C2216yes—
125#2362C2216yes—
126#2362C2213yes—
127#2361C2213yes—
128#2354C2213yes—
129#2352C2213yes—
130#2351C2211yescharacteristic
131#2351C2212yes—
132Q8×C4⋊C4C2211yescharacteristic
133#2341C2216yes—
134#2341C2212yes—
135#2341C2211yescharacteristic
136#2341C2216yes—
137#2341C2212yes—
138#2341C2212yes—
139Q8×C22⋊C4C2212yes—
140Q8×C22⋊C4C2216yes—
141Q8×C22⋊C4C2211yescharacteristic
142Q8×C22⋊C4C2216yes—
143Q8×C22⋊C4C2212yes—
144#2323C2216yes—
145#2311C2216yes—
146#2311C2216yes—
147C4×C4⋊Q8C2213yes—
148C4×#124C2213yes—
149C4×#124C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×#123C2216yes—
153C4×#121C2213yes—
154C4×#121C2213yes—
155#2297C2216yes—
156#2297C2216yes—
157#2293C2213yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C2×2−1+4—216no—
161C2×2−1+4—216no—
162C2×2−1+4—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C2316yes—
167C22×#41C2316yes—
168C22×#41C2313yes—
169C23×Q8C2316yes—
170C23×Q8C2312yes—
171C23×Q8C2311yescharacteristic
172#557—28no—
173#556—224no—
174#552—248no—
175#550—28no—
176#550—224no—
177#550—48no—
178D4×Q8—224no—
179D4×Q8D4116yescomplemented
180#548—216no—
181#548—216no—
182#548—28no—
183#548—248no—
184#547—224no—
185#537—248no—
186#533—224no—
187#532—224no—
188#532—224no—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×#127C2313yes—
193C2×#127C2313yes—
194C2×#127C2316yes—
195#529—248no—
196C2×#126C23112yes—
197C2×#125C2316yes—
198C2×#125C2316yes—
199C2×#124C2313yes—
200C2×#124C2316yes—
201C2×#124C2316yes—
202C2×#124C2316yes—
203C2×#124C2313yes—
204C2×#124C2316yes—
205C2×#123C23112yes—
206C2×#123C2316yes—
207C2×C22⋊Q8C23112yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2316yes—
214C2×#121C2316yes—
215C2×#121C2313yes—
216C2×#121C2316yes—
217C2×#121C2311yescharacteristic
218C2×#121C2313yes—
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C2316yes—
222C2×#121C23112yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C2313yes—
228#519—48no—
229C4×#41—28no—
230C4×#41—224no—
231C2×C4×Q8—216no—
232C2×C4×Q8—28no—
233C2×C4×Q8C2313yes—
234C2×C4×Q8C2313yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2316yes—
241C2×C4×Q8C2316yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2313yes—
244C2×C4×Q8C2313yes—
245C2×C4×Q8C2316yes—
246C2×C4×Q8C2316yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2316yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×#117C2313yes—
263C2×#117C2313yes—
264C2×#117C2316yes—
265C2×#117C2316yes—
266C2×#117C2316yes—
267C2×#117C2316yes—
268C22×C4⋊C4C2316yes—
269C22×C4⋊C4C2313yes—
270C22×C42C2316yes—
271C22×C42C2313yes—
272C22×C42C2313yes—
273#400C23112yes—
274#400C23112yes—
275#399C23112yes—
276#398C23112yes—
277#398C2316yes—
278#397C23112yes—
279#397C2312yes—
280#397C23112yes—
281#397C23112yes—
282#396C2316yes—
283#396C2316yes—
284#395C2316yes—
285#394C23112yes—
286#394C23112yes—
287#394C23112yes—
288#394C2312yes—
289#394C2316yes—
290#394C2316yes—
291#394C2316yes—
292#394C2316yes—
293#394C2316yes—
294#394C23112yes—
295#393C2316yes—
296#393C23112yes—
297#392C2316yes—
298#392C23112yes—
299#392C23112yes—
300#392C2316yes—
301#392C23112yes—
302#392C2316yes—
303#392C2316yes—
304#392C23112yes—
305#391C23112yes—
306#391C2316yes—
307#391C2313yes—
308#391C2316yes—
309#391C2313yes—
310#391C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C2313yes—
314#391C2316yes—
315#391C2316yes—
316#391C2313yes—
317#390C23112yes—
318#390C2316yes—
319#390C2316yes—
320#390C23112yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2313yes—
329#390C2313yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2313yes—
334#390C2313yes—
335#390C23112yes—
336#390C2311yescharacteristic
337#389C2313yes—
338#389C2316yes—
339#389C2316yes—
340#389C2313yes—
341#389C2316yes—
342#389C2313yes—
343#389C2316yes—
344#389C2316yes—
345#389C2313yes—
346#389C2313yes—
347#389C2311yescharacteristic
348#388C2316yes—
349#388C2316yes—
350#388C23112yes—
351#388C2316yes—
352#388C23112yes—
353#388C23112yes—
354#388C23112yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C23112yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#387C2316yes—
364#387C23112yes—
365#387C2316yes—
366#387C2316yes—
367#387C2316yes—
368#386C23112yes—
369#386C2316yes—
370#386C2316yes—
371#386C23112yes—
372#386C23112yes—
373#386C2316yes—
374#386C23112yes—
375#386C23112yes—
376#386C2312yes—
377#386C2316yes—
378#386C2316yes—
379#386C2316yes—
380#385C2316yes—
381#385C23112yes—
382#385C2316yes—
383#385C2316yes—
384#384C2313yes—
385#382C2316yes—
386#382C2313yes—
387#382C2311yescharacteristic
388#381C2312yes—
389#380C2313yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C23112yes—
394#380C23112yes—
395#380C2316yes—
396#380C2313yes—
397#380C2316yes—
398#380C2316yes—
399#380C2313yes—
400#380C2311yescharacteristic
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C23112yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2313yes—
425C43C2313yes—
4262−1+4—4128no—
427C2×#41—24no—
428C2×#41—224no—
429C2×#41—28no—
430C2×#41—24no—
431C2×#41—224no—
432C2×#41—28no—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—224no—
439C2×#41—224no—
440C2×#41—412no—
441C2×#41—46no—
442C2×#41—46no—
443C2×#41—412no—
444C2×#41—412no—
445C22×Q8—24no—
446C22×Q8—28no—
447C22×Q8—28no—
448C22×Q8—24no—
449C22×Q8—224no—
450C22×Q8—224no—
451C22×Q8—412no—
452C22×Q8C2×D4116yes—
453C22×Q8#4118yescomplemented
454C22×Q8C2413yes—
455C22×Q8C2416yes—
456C22×Q8C2416yes—
457C22×Q8C2413yes—
458C22×Q8C2411yescharacteristic
459C22×D4C2413yes—
460C22×D4C2413yes—
461C22×D4C2416yes—
462C22×D4C2412yes—
463C22×D4C2416yes—
464C22×D4C2416yes—
465C22×D4C2411yescharacteristic
466C22×D4C2413yes—
467C22×D4C2416yes—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2416yes—
471C22×D4C24112yes—
472C23×C4C2413yes—
473C23×C4C2413yes—
474C23×C4C2411yescharacteristic
475C23×C4C2416yes—
476C23×C4C2413yes—
477C23×C4C2412yes—
478C23×C4C24112yes—
479C23×C4C2416yes—
480C23×C4C2413yes—
481C23×C4C2416yes—
482C23×C4C2413yes—
483C4⋊Q8—212no—
484C4⋊Q8—212no—
485C4⋊Q8C2×D4124yes—
486#127—212no—
487#127—212no—
488#127—412no—
489#126—248no—
490#125—224no—
491#125—224no—
492#124—224no—
493#124—224no—
494#124—212no—
495#124—224no—
496#124—412no—
497#124—46no—
498#123—248no—
499#123—412no—
500C22⋊Q8—224no—
501C22⋊Q8—224no—
502C22⋊Q8—212no—
503C22⋊Q8—224no—
504C22⋊Q8—248no—
505C22⋊Q8—46no—
506C22⋊Q8C2×D4148yes—
507#121—24no—
508#121—224no—
509#121—224no—
510#121—212no—
511#121—212no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—248no—
516#121—412no—
517#121—46no—
518#121—412no—
519#121—412no—
520#121—412no—
521C4×Q8—24no—
522C4×Q8—224no—
523C4×Q8—24no—
524C4×Q8—28no—
525C4×Q8—224no—
526C4×Q8—24no—
527C4×Q8—24no—
528C4×Q8—28no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8—212no—
532C4×Q8—212no—
533C4×Q8—412no—
534C4×Q8—412no—
535C4×Q8C2×D418yes—
536C4×D4—24no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—224no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—46no—
547C4×D4—412no—
548C4×D4—46no—
549C4×D4C2×D4124yes—
550#117—212no—
551#117—212no—
552#117—224no—
553#117—224no—
554#117—412no—
555#117—412no—
556C2×C4⋊C4—224no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C24112yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2416yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C24112yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2411yescharacteristic
593C2×C22⋊C4C2411yescharacteristic
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C24112yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C24112yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C24112yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C42—224no—
621C2×C42—212no—
622C2×C42—212no—
623C2×C42C2413yes—
624C2×C42C2416yes—
625C2×C42C2413yes—
626C2×C42C2416yes—
627C2×C42C2416yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2416yes—
632C2×C42C2413yes—
633C2×C42C2411yescharacteristic
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2411yescharacteristic
637C2×C42C24112yes—
638C2×C42C2413yes—
639C2×C42C2413yes—
640C2×C42C2413yes—
641#95C2413yes—
642#95C2411yescharacteristic
643#95C2411yescharacteristic
644#95C2416yes—
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2416yes—
649#95C2413yes—
650#95C2413yes—
651#95C2413yes—
652#95C2416yes—
653#95C2416yes—
654#95C24112yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2412yes—
661#95C2416yes—
662#95C24112yes—
663#95C2416yes—
664#95C2416yes—
665#95C24112yes—
666C24C2513yes—
667C24C2516yes—
668C24C2512yes—
669C24C2511yescharacteristic
670#41—496no—
671#41—496no—
672#41—496no—
673#41—448no—
674#41—416no—
675#41—432no—
676C2×Q8—264no—
677C2×Q8—232no—
678C2×Q8—26no—
679C2×Q8—26no—
680C2×Q8—212no—
681C2×Q8—212no—
682C2×Q8—212no—
683C2×Q8—212no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—26no—
687C2×Q8—46no—
688C2×Q8—496no—
689C2×Q8C22×D4124yes—
690C2×Q8C22×D414yes—
691C2×Q8C2×#41112yes—
692C2×Q8C2×#4114yes—
693C2×Q8H(5,𝔽2)14yes—
694C2×D4—212no—
695C2×D4—24no—
696C2×D4—212no—
697C2×D4—26no—
698C2×D4—212no—
699C2×D4—24no—
700C2×D4—212no—
701C2×D4—26no—
702C2×D4—26no—
703C2×D4—212no—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—26no—
707C2×D4—212no—
708C2×D4—212no—
709C2×D4—26no—
710C2×D4—212no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—26no—
714C2×D4—26no—
715C2×D4—43no—
716C2×D4—43no—
717C2×D4—46no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—42no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—412no—
730C2×D4—412no—
731C2×D4—412no—
732C2×D4C22×D414yes—
733C22×C4—26no—
734C22×C4—212no—
735C22×C4—212no—
736C22×C4—26no—
737C22×C4—24no—
738C22×C4—212no—
739C22×C4—22no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—224no—
744C22×C4—212no—
745C22×C4—26no—
746C22×C4—224no—
747C22×C4—212no—
748C22×C4—26no—
749C22×C4—212no—
750C22×C4—22no—
751C22×C4—26no—
752C22×C4—26no—
753C22×C4—26no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—26no—
757C22×C4—43no—
758C22×C4—42no—
759C22×C4—412no—
760C22×C4—46no—
761C22×C4—46no—
762C22×C4—43no—
763C22×C4—43no—
764C22×C4C22×D4124yes—
765C22×C4C2×#41112yes—
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C22×C4C2513yes—
769C22×C4C2512yes—
770C22×C4C2516yes—
771C22×C4C2513yes—
772C22×C4C2513yes—
773C22×C4C2513yes—
774C22×C4C2516yes—
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2513yes—
780C22×C4C2516yes—
781C22×C4C2513yes—
782C22×C4C2511yescharacteristic
783C22×C4C2513yes—
784C22×C4C2511yescharacteristic
785C4⋊C4—26no—
786C4⋊C4—212no—
787C4⋊C4—26no—
788C4⋊C4—212no—
789C4⋊C4—224no—
790C4⋊C4—22no—
791C4⋊C4—212no—
792C4⋊C4—212no—
793C4⋊C4—212no—
794C4⋊C4—22no—
795C4⋊C4—212no—
796C4⋊C4—26no—
797C4⋊C4—26no—
798C4⋊C4—26no—
799C4⋊C4—212no—
800C4⋊C4—26no—
801C4⋊C4—22no—
802C4⋊C4—26no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—43no—
806C4⋊C4—42no—
807C4⋊C4—46no—
808C4⋊C4—46no—
809C4⋊C4—46no—
810C4⋊C4C22×D4112yes—
811C4⋊C4C22×D4112yes—
812C4⋊C4C22×D4124yes—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—22no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—224no—
819C22⋊C4—212no—
820C22⋊C4—224no—
821C22⋊C4—212no—
822C22⋊C4—26no—
823C22⋊C4—212no—
824C22⋊C4—22no—
825C22⋊C4—212no—
826C22⋊C4—42no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—46no—
832C22⋊C4—43no—
833C22⋊C4—43no—
834C22⋊C4—43no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—412no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C22⋊C4—412no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—412no—
846C22⋊C4C22×D4124yes—
847C42—26no—
848C42—22no—
849C42—26no—
850C42—212no—
851C42—212no—
852C42—26no—
853C42—26no—
854C42—26no—
855C42—212no—
856C42—26no—
857C42—26no—
858C42—212no—
859C42—26no—
860C42—22no—
861C42—43no—
862C42—412no—
863C42—43no—
864C42C22×D4112yes—
865C23—21no—
866C23—22no—
867C23—22no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—22no—
872C23—21no—
873C23—22no—
874C23—22no—
875C23—21no—
876C23—22no—
877C23—23no—
878C23—26no—
879C23—23no—
880C23—26no—
881C23—23no—
882C23—26no—
883C23—26no—
884C23—26no—
885C23—26no—
886C23—23no—
887C23—23no—
888C23—23no—
889C23—23no—
890C23—26no—
891C23C23×D414yes—
892C23C22×#4112yes—
893C23C2611yescharacteristic
894Q8—224no—
895Q8—248no—
896Q8—424no—
897Q8—412no—
898Q8#546116yes—
899D4—28no—
900D4—424no—
901D4—424no—
902D4—48no—
903D4—412no—
904D4—424no—
905D4—412no—
906D4—424no—
907D4—412no—
908D4—812no—
909D4—812no—
910D4—812no—
911D4—1612no—
912C2×C4—21no—
913C2×C4—23no—
914C2×C4—26no—
915C2×C4—26no—
916C2×C4—23no—
917C2×C4—23no—
918C2×C4—23no—
919C2×C4—21no—
920C2×C4—248no—
921C2×C4—224no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—23no—
925C2×C4—21no—
926C2×C4—23no—
927C2×C4—26no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—23no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—23no—
936C2×C4—26no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—23no—
942C2×C4—23no—
943C2×C4—21no—
944C2×C4—23no—
945C2×C4—26no—
946C2×C4—23no—
947C2×C4—26no—
948C2×C4—26no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—26no—
954C2×C4—23no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—22no—
959C2×C4—23no—
960C2×C4—22no—
961C2×C4—412no—
962C2×C4—448no—
963C2×C4—48no—
964C2×C4—424no—
965C2×C4—424no—
966C2×C4—412no—
967C2×C4—44no—
968C2×C4—412no—
969C2×C4—86no—
970C2×C4C23×D416yes—
971C2×C4C23×D4112yes—
972C2×C4C23×D416yes—
973C2×C4C23×D412yes—
974C2×C4C22×#4116yes—
975C2×C4C22×#4116yes—
976C2×C4C2×H(5,𝔽2)16yes—
977C2×C4#58512yes—
978C2×C4#58512yes—
979C2×C4#58512yes—
980C22—24no—
981C22—22no—
982C22—24no—
983C22—22no—
984C22—22no—
985C22—24no—
986C22—41no—
987C22—42no—
988C22—42no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—43no—
995C22—46no—
996C22—43no—
997C22—46no—
998C22—43no—
999C22—46no—
1000C22—43no—
1001C22—46no—
1002C22—43no—
1003C22—46no—
1004C22—43no—
1005C22—46no—
1006C22—46no—
1007C22—43no—
1008C22C24×D411yescharacteristic
1009C22C23×#4111yescharacteristic
1010C22C22×H(5,𝔽2)11yescharacteristic
1011C22C2×#58511yescharacteristic
1012C22C2×#58511yescharacteristic
1013C22C2×#58511yescharacteristic
1014C222−1+611yescharacteristic
1015C4—22no—
1016C4—26no—
1017C4—26no—
1018C4—212no—
1019C4—42no—
1020C4—43no—
1021C4—41no—
1022C4—41no—
1023C4—46no—
1024C4—41no—
1025C4—43no—
1026C4—46no—
1027C4—43no—
1028C4—43no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4C2×#546112yes—
1033C4#348714yes—
1034C2—44no—
1035C2—42no—
1036C2—83no—
1037C2—86no—
1038C2C22×#54611yescharacteristic
1039C2C2×#348711yescharacteristic
1040C2#6279311yescharacteristic
1041C2#6292211yescharacteristic
1042C2#6300211yescharacteristic
1043C2#6300711yescharacteristic
1044C2#6303511yescharacteristic
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×#3497C2semidirect
2. C2×#3482C2semidirect
3. #59421C2semidirect
4. #59104C2semidirect
5. #59049C2semidirect
6. #59042C2semidirect
7. #45265C2semidirect
8. #45236C2semidirect
9. #39471C2semidirect
10. #38956C2semidirect
11. #37785C2semidirect
12. #36583C2semidirect
13. #36578C2semidirect
14. #36577C2semidirect
15. #36455C2semidirect
16. #36410C2semidirect
17. #36150C2semidirect
18. #36018C2semidirect
19. #35757C2semidirect
20. #34715C2semidirect
21. #34311C2semidirect
22. #34257C2semidirect
23. C4×#548C2semidirect
179. D4×Q8D4semidirect
453. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34972
C2×#34822
#594212
#591042
#590492
#590422
#452652
#452362
#394712
#389562
#377852
#365832
#365782
#365772
#364552
#364102
#361502
#360182
#357572
#347152
#343112
#342572
C4×#5482