Finite Group Databasebeta

← #7626926

Subgroups — #7626926

Order 512.

6818 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3516C211yesmaximal, characteristic
2#34499C213yesmaximal, complemented
3#34484C213yesmaximal, complemented
4#34483C213yesmaximal, complemented
5#34482C213yesmaximal, complemented
6#34466C213yesmaximal, complemented
7#34464C213yesmaximal, complemented
8#34430C213yesmaximal, complemented
9#34429C213yesmaximal, complemented
10#34422C213yesmaximal, complemented
11#34420C213yesmaximal, complemented
12#34397C213yesmaximal, complemented
13#34385C213yesmaximal, complemented
14#34336C211yesmaximal, characteristic, complemented
15#34322C213yesmaximal, complemented
16#34314C213yesmaximal, complemented
17#34312C211yesmaximal, characteristic, complemented
18#34312C211yesmaximal, characteristic, complemented
19#34311C211yesmaximal, characteristic, complemented
20#34293C211yesmaximal, characteristic, complemented
21#34291C211yesmaximal, characteristic, complemented
22#34263C211yesmaximal, characteristic, complemented
23#34262C211yesmaximal, characteristic, complemented
24#34250C211yesmaximal, characteristic, complemented
25#34249C211yesmaximal, characteristic, complemented
26#34242C213yesmaximal, complemented
27#34182C211yesmaximal, characteristic, complemented
28C4×#557C211yesmaximal, characteristic, complemented
29C4×#548C211yesmaximal, characteristic, complemented
30#34128C211yesmaximal, characteristic, complemented
31#34084C213yesmaximal, complemented
32#3516C4132yescomplemented
33C2×#557C2211yescharacteristic
34C2×#556C2213yes—
35C2×#554C2213yes—
36C2×#553C2213yes—
37C2×#552C2213yes—
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#542C2213yes—
42C2×#541C2213yes—
43C2×#529C2213yes—
44C2×#529C2213yes—
45C2×#520C2211yescharacteristic
46C2×#520C2211yescharacteristic
47C2×#519C2211yescharacteristic
48C2×#519C2211yescharacteristic
49C2×#519C2211yescharacteristic
50C2×#519C2211yescharacteristic
51C2×C4×#41C2211yescharacteristic
52C22×C4×Q8C2211yescharacteristic
53C22×C4×Q8C2211yescharacteristic
54#2383C2216yes—
55#2383C2216yes—
56#2383C2216yes—
57#2382C2216yes—
58#2378C2216yes—
59#2378C2216yes—
60#2377C2216yes—
61#2376C2216yes—
62#2373C2216yes—
63#2373C2216yes—
64#2373C2216yes—
65#2373C2216yes—
66#2373C2216yes—
67#2370C2213yes—
68#2370C2216yes—
69#2370C2213yes—
70#2370C2213yes—
71#2370C2213yes—
72#2369C2213yes—
73#2367C2213yes—
74#2367C2213yes—
75#2367C2213yes—
76#2367C2213yes—
77#2365C2213yes—
78#2365C2213yes—
79#2365C2213yes—
80#2363C2213yes—
81#2363C2213yes—
82#2363C2213yes—
83#2362C2213yes—
84#2362C2213yes—
85#2362C2213yes—
86#2362C2213yes—
87#2362C2213yes—
88#2361C2213yes—
89#2360C2213yes—
90#2360C2213yes—
91#2360C2216yes—
92#2360C2213yes—
93#2359C2216yes—
94#2357C2213yes—
95#2356C2213yes—
96#2356C2213yes—
97#2356C2213yes—
98#2355C2213yes—
99#2355C2213yes—
100#2355C2213yes—
101#2354C2213yes—
102#2354C2213yes—
103#2354C2213yes—
104#2354C2216yes—
105#2352C2213yes—
106#2352C2213yes—
107#2352C2213yes—
108#2352C2213yes—
109#2352C2216yes—
110#2351C2211yescharacteristic
111#2351C2211yescharacteristic
112#2351C2213yes—
113#2351C2213yes—
114#2351C2213yes—
115#2351C2211yescharacteristic
116#2351C2211yescharacteristic
117#2351C2211yescharacteristic
118#2351C2213yes—
119#2351C2211yescharacteristic
120Q8×C4⋊C4C2211yescharacteristic
121Q8×C4⋊C4C2213yes—
122Q8×C4⋊C4C2213yes—
123Q8×C4⋊C4C2213yes—
124Q8×C4⋊C4C2211yescharacteristic
125Q8×C4⋊C4C2211yescharacteristic
126Q8×C4⋊C4C2211yescharacteristic
127Q8×C4⋊C4C2213yes—
128#2349C2213yes—
129#2349C2213yes—
130D4×C4⋊C4C2213yes—
131D4×C4⋊C4C2213yes—
132#2347C2213yes—
133#2346C2216yes—
134#2346C2213yes—
135#2345C2213yes—
136#2344C2213yes—
137#2344C2213yes—
138#2344C2213yes—
139#2343C2216yes—
140#2341C2211yescharacteristic
141#2341C2211yescharacteristic
142Q8×C22⋊C4C2211yescharacteristic
143Q8×C22⋊C4C2211yescharacteristic
144Q8×C22⋊C4C2211yescharacteristic
145Q8×C22⋊C4C2211yescharacteristic
146#2337C2216yes—
147#2336C2216yes—
148#2336C2216yes—
149#2335C2211yescharacteristic
150#2335C2213yes—
151#2335C2213yes—
152#2335C2213yes—
153#2335C2216yes—
154#2335C2216yes—
155#2334C2213yes—
156#2334C2213yes—
157#2334C2216yes—
158#2334C2213yes—
159#2334C2213yes—
160#2334C2216yes—
161#2331C2213yes—
162#2330C2213yes—
163#2330C2213yes—
164#2330C2213yes—
165#2330C2216yes—
166#2329C2216yes—
167#2327C2213yes—
168#2326C2213yes—
169#2326C2213yes—
170#2326C2213yes—
171#2324C2213yes—
172#2324C2213yes—
173#2324C2213yes—
174#2324C2213yes—
175#2324C2213yes—
176#2323C2213yes—
177#2323C2213yes—
178#2323C2213yes—
179#2323C2213yes—
180#2323C2216yes—
181#2323C2213yes—
182#2323C2213yes—
183#2323C2213yes—
184#2322C2216yes—
185#2320C2213yes—
186#2319C2216yes—
187#2319C2213yes—
188#2318C2216yes—
189#2317C2213yes—
190#2317C2213yes—
191#2317C2213yes—
192#2316C2213yes—
193#2316C2213yes—
194#2316C2213yes—
195#2314C2213yes—
196#2314C2213yes—
197#2314C2216yes—
198C4×C4⋊Q8C2213yes—
199C4×C4⋊Q8C2213yes—
200C4×#125C2213yes—
201C4×#125C2213yes—
202C4×#125C2213yes—
203C4×#124C2213yes—
204C4×#124C2213yes—
205C4×#124C2213yes—
206C4×C22⋊Q8C2213yes—
207C4×C22⋊Q8C2213yes—
208C4×C22⋊Q8C2213yes—
209C4×#121C2213yes—
210#2298C2213yes—
211#2298C2213yes—
212#2296C2213yes—
213#2296C2213yes—
214#2296C2213yes—
215#2295C2213yes—
216#2295C2213yes—
217#2295C2213yes—
218#2295C2213yes—
219#2293C2213yes—
220#2293C2213yes—
221#2293C2213yes—
222#2293C2213yes—
223C2×#389C2213yes—
224#2290C2213yes—
225#2290C2213yes—
226#2285C2213yes—
227#2285C2213yes—
228#2283C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2274C2216yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C4×#117C2213yes—
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#557C2×C4116yescomplemented
243#556C2×C4148yescomplemented
244#554C2×C4148yescomplemented
245#553C2×C4148yescomplemented
246#552C2×C4148yescomplemented
247D4×Q8C2×C4116yescomplemented
248#548C2×C4116yes—
249#548C2×C4116yescomplemented
250#542C2×C4148yescomplemented
251#541C2×C4148yescomplemented
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254#529C2×C4148yescomplemented
255#529C2×C4148yescomplemented
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#126C2316yes—
259C2×#126C2316yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2316yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#123C2316yes—
268C2×#123C2311yescharacteristic
269C2×#123C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2316yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279#520—44no—
280#520C2×C4116yescomplemented
281#519—44no—
282#519—44no—
283#519—44no—
284#519C2×C4116yescomplemented
285C4×#41—44no—
286C2×C4×Q8—44no—
287C2×C4×Q8C2×C4116yescomplemented
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2313yes—
314C2×C4×Q8C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2316yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×#117C2313yes—
328C2×#117C2313yes—
329C2×#117C2313yes—
330C2×#117C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C2×#117C2313yes—
334C2×#117C2313yes—
335C2×#117C2313yes—
336C2×#117C2313yes—
337C2×#117C2316yes—
338C2×#117C2313yes—
339C2×#117C2313yes—
340C2×#117C2316yes—
341C2×#117C2313yes—
342C22×C4⋊C4C2313yes—
343C22×C4⋊C4C2313yes—
344C22×C4⋊C4C2316yes—
345C22×C4⋊C4C2313yes—
346C22×C4⋊C4C2313yes—
347C22×C42C2313yes—
348C22×C42C2313yes—
349C22×C42C2313yes—
350#391C2316yes—
351#391C2313yes—
352#391C2313yes—
353#391C2313yes—
354#391C2313yes—
355#391C2313yes—
356#391C2313yes—
357#391C2313yes—
358#391C2313yes—
359#391C2316yes—
360#391C2313yes—
361#391C2313yes—
362#390C2313yes—
363#390C2316yes—
364#390C2313yes—
365#390C2313yes—
366#390C2313yes—
367#390C2311yescharacteristic
368#390C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2313yes—
372#390C2313yes—
373#389C2313yes—
374#389C2313yes—
375#389C2313yes—
376#389C2313yes—
377#389C2313yes—
378#389C2313yes—
379#389C2313yes—
380#389C2313yes—
381#389C2313yes—
382#389C2316yes—
383#389C2316yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2316yes—
389#389C2313yes—
390#389C2313yes—
391#389C2316yes—
392#389C2316yes—
393#389C2316yes—
394#389C2313yes—
395#389C2313yes—
396#389C2316yes—
397#389C2313yes—
398#389C2316yes—
399#389C2316yes—
400#389C2313yes—
401#389C2316yes—
402#389C2313yes—
403#389C2313yes—
404#389C2316yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2311yescharacteristic
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#388C2313yes—
421#388C2313yes—
422#388C2316yes—
423#388C2316yes—
424#388C2316yes—
425#388C2316yes—
426#388C2316yes—
427#388C2316yes—
428#388C2313yes—
429#388C2316yes—
430#388C2313yes—
431#388C2313yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2311yescharacteristic
437#388C2311yescharacteristic
438#388C2313yes—
439#388C2313yes—
440#388C2316yes—
441#388C2316yes—
442#388C2316yes—
443#388C2316yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#388C2311yescharacteristic
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2311yescharacteristic
458#388C2313yes—
459#388C2313yes—
460#387C2313yes—
461#387C2316yes—
462#387C2316yes—
463#387C2316yes—
464#387C2316yes—
465#387C2316yes—
466#387C2313yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2316yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2313yes—
479#387C2316yes—
480#387C2313yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2311yescharacteristic
487#387C2313yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2311yescharacteristic
496#387C2313yes—
497#387C2313yes—
498#386C2313yes—
499#386C2316yes—
500#386C2316yes—
501#386C2311yescharacteristic
502#386C2313yes—
503#386C2313yes—
504#386C2316yes—
505#385C2313yes—
506#385C2313yes—
507#385C2316yes—
508#385C2316yes—
509#385C2316yes—
510#385C2316yes—
511#385C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2316yes—
515#385C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2313yes—
519#385C2311yescharacteristic
520#385C2313yes—
521#385C2313yes—
522#385C2313yes—
523#385C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2316yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#383C2316yes—
532#383C2316yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#382C2316yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#381C2316yes—
544#381C2316yes—
545#380C2316yes—
546#380C2316yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2316yes—
554#380C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2311yescharacteristic
558#380C2313yes—
559C4×C4⋊C4C2316yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2316yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2311yescharacteristic
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2316yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2311yescharacteristic
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2311yescharacteristic
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2316yes—
629#376C2313yes—
630#376C2316yes—
631#376C2313yes—
632#376C2313yes—
633#376C2313yes—
634#376C2316yes—
635C2×#95C2316yes—
636C43C2313yes—
637C43C2313yes—
638C43C2313yes—
639C43C2313yes—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41C22×C418yes—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8C22×C418yes—
648C22×Q8C22×C418yes—
649C22×Q8C2413yes—
650C22×Q8C2413yes—
651C22×Q8C2413yes—
652C22×Q8C2411yescharacteristic
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2411yescharacteristic
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2411yescharacteristic
662C23×C4C2416yes—
663C23×C4C2413yes—
664C23×C4C2413yes—
665C23×C4C2416yes—
666C23×C4C2413yes—
667C23×C4C2411yescharacteristic
668C4⋊Q8C22×C4124yes—
669C4⋊Q8C22×C4124yes—
670#126C22×C4148yes—
671#126C22×C4124yes—
672#126C22×C4124yes—
673#126C22×C4148yes—
674#125C22×C4124yes—
675#125C22×C4124yes—
676#125C22×C4148yes—
677#125C22×C4124yes—
678#124C22×C4124yes—
679#124C22×C4124yes—
680#124C22×C4124yes—
681#123C22×C418yes—
682#123C22×C4124yes—
683#123C22×C4148yes—
684C22⋊Q8C22×C4124yes—
685C22⋊Q8C22×C4124yes—
686C22⋊Q8C22×C4124yes—
687C22⋊Q8C22×C4124yes—
688C22⋊Q8C22×C4124yes—
689C22⋊Q8C22×C4148yes—
690#121C22×C4124yes—
691#121C22×C4124yes—
692#121C22×C4124yes—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—46no—
702C4×Q8—46no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8—46no—
706C4×Q8—46no—
707C4×Q8—46no—
708C4×Q8—46no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8C22×C418yes—
712C4×Q8C22×C4124yes—
713C4×Q8C22×C418yes—
714C4×Q8C22×C4124yes—
715C4×Q8C22×C4124yes—
716C4×Q8C22×C418yes—
717C4×Q8C22×C4124yes—
718C4×Q8C22×C418yes—
719C4×Q8C22×C4124yes—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4C22×C4124yes—
727C4×D4C22×C4124yes—
728C4×D4C22×C4124yes—
729C4×D4C22×C4124yes—
730C4×D4C22×C4124yes—
731C4×D4C22×C4148yes—
732#117—46no—
733#117—46no—
734#117—46no—
735#117—46no—
736#117—412no—
737#117—46no—
738#117—46no—
739#117—46no—
740#117—46no—
741#117—46no—
742#117—46no—
743#117C22×C4124yes—
744#117C22×C4124yes—
745#117C22×C4124yes—
746#117C22×C4148yes—
747C2×C4⋊C4—412no—
748C2×C4⋊C4—46no—
749C2×C4⋊C4—46no—
750C2×C4⋊C4C22×C4124yes—
751C2×C4⋊C4C22×C4124yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2416yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2416yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C42—46no—
846C2×C42—46no—
847C2×C42C22×C4124yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2411yescharacteristic
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2416yes—
862C2×C42C2416yes—
863C2×C42C2416yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2416yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2416yes—
880C2×C42C2411yescharacteristic
881C2×C42C2413yes—
882C2×C42C2416yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2416yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2416yes—
903#95C2416yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2413yes—
917#95C2411yescharacteristic
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930#95C2416yes—
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2413yes—
934#95C2413yes—
935#95C2416yes—
936#95C2416yes—
937#95C2416yes—
938#95C2413yes—
939#95C2413yes—
940#95C2416yes—
941#95C2411yescharacteristic
942C24C2511yescharacteristic
943C24C2511yescharacteristic
944C24C2513yes—
945#41—232no—
946C2×Q8—232no—
947C2×Q8—232no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—43no—
953C2×Q8—43no—
954C2×Q8C23×C4112yes—
955C2×Q8C23×C4112yes—
956C2×Q8C23×C4112yes—
957C2×Q8C23×C414yes—
958C2×Q8H(5,𝔽2)14yes—
959C2×Q82−1+414yes—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—43no—
968C2×D4C23×C4112yes—
969C2×D4C23×C4112yes—
970C2×D4C23×C414yes—
971C2×D4C23×C4112yes—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—22no—
979C22×C4—26no—
980C22×C4—41no—
981C22×C4—46no—
982C22×C4—46no—
983C22×C4—43no—
984C22×C4—43no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—43no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—46no—
997C22×C4—46no—
998C22×C4—46no—
999C22×C4C23×C4112yes—
1000C22×C4C23×C4112yes—
1001C22×C4C23×C4112yes—
1002C22×C4C23×C414yes—
1003C22×C4C23×C4112yes—
1004C22×C4C23×C4124yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2513yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2513yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2513yes—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—22no—
1045C4⋊C4—43no—
1046C4⋊C4—46no—
1047C4⋊C4—46no—
1048C4⋊C4—46no—
1049C4⋊C4—41no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—46no—
1053C4⋊C4—43no—
1054C4⋊C4—41no—
1055C4⋊C4—43no—
1056C4⋊C4—41no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—41no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4C23×C4112yes—
1075C4⋊C4C23×C4112yes—
1076C4⋊C4C23×C4112yes—
1077C4⋊C4C23×C4112yes—
1078C4⋊C4C23×C4124yes—
1079C4⋊C4C23×C414yes—
1080C4⋊C4C23×C4112yes—
1081C4⋊C4C23×C4112yes—
1082C4⋊C4C23×C4112yes—
1083C4⋊C4C23×C4112yes—
1084C4⋊C4C23×C4124yes—
1085C4⋊C4C23×C4112yes—
1086C4⋊C4C23×C4112yes—
1087C4⋊C4C23×C4124yes—
1088C4⋊C4C23×C4112yes—
1089C4⋊C4C23×C414yes—
1090C4⋊C4C23×C4112yes—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—26no—
1094C22⋊C4—22no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—41no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—46no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4C23×C4112yes—
1115C22⋊C4C23×C414yes—
1116C22⋊C4C23×C4112yes—
1117C22⋊C4C23×C4112yes—
1118C22⋊C4C23×C4112yes—
1119C22⋊C4C23×C4124yes—
1120C22⋊C4C23×C414yes—
1121C22⋊C4C23×C4112yes—
1122C22⋊C4C23×C414yes—
1123C22⋊C4C23×C4124yes—
1124C22⋊C4C23×C4112yes—
1125C22⋊C4C23×C4112yes—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—22no—
1138C42—41no—
1139C42—43no—
1140C42—43no—
1141C42—43no—
1142C42—41no—
1143C42—43no—
1144C42—41no—
1145C42—43no—
1146C42—43no—
1147C42—41no—
1148C42—46no—
1149C42—43no—
1150C42—43no—
1151C42—46no—
1152C42—43no—
1153C42—43no—
1154C42—46no—
1155C42—46no—
1156C42—46no—
1157C42—43no—
1158C42—43no—
1159C42C23×C4112yes—
1160C42C23×C4112yes—
1161C42C23×C4112yes—
1162C42C23×C4112yes—
1163C42C23×C4124yes—
1164C42C23×C4112yes—
1165C42C23×C4112yes—
1166C23—21no—
1167C23—21no—
1168C23—23no—
1169C23—21no—
1170C23—21no—
1171C23—23no—
1172C23—21no—
1173C23—21no—
1174C23—23no—
1175C23—21no—
1176C23—21no—
1177C23—23no—
1178C23—21no—
1179C23—23no—
1180C23—23no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23C24×C412yes—
1185C23C24×C416yes—
1186C23C24×C412yes—
1187C23C2611yescharacteristic
1188Q8—224no—
1189Q8—224no—
1190Q8—412no—
1191Q8#520116yes—
1192D4—224no—
1193D4—412no—
1194D4—412no—
1195D4—44no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—224no—
1223C2×C4—224no—
1224C2×C4—224no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—424no—
1268C2×C4—412no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—86no—
1272C2×C4—86no—
1273C2×C4—86no—
1274C2×C4—166no—
1275C2×C4C24×C412yes—
1276C2×C4C24×C412yes—
1277C2×C4C24×C416yes—
1278C2×C4C24×C412yes—
1279C2×C4C24×C416yes—
1280C2×C4C24×C412yes—
1281C2×C4C24×C416yes—
1282C2×C4C24×C416yes—
1283C2×C4C24×C416yes—
1284C2×C4C24×C416yes—
1285C2×C4C24×C412yes—
1286C2×C4C24×C416yes—
1287C2×C4C2×H(5,𝔽2)16yes—
1288C2×C4C2×2−1+416yes—
1289C2×C4#58512yes—
1290C2×C4#58512yes—
1291C22—22no—
1292C22—22no—
1293C22—26no—
1294C22—22no—
1295C22—26no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—26no—
1300C22—41no—
1301C22—43no—
1302C22—41no—
1303C22—41no—
1304C22—43no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—43no—
1309C22—41no—
1310C22—41no—
1311C22—43no—
1312C22C25×C411yescharacteristic
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58511yescharacteristic
1317C222−1+611yescharacteristic
1318C222−1+611yescharacteristic
1319C4—22no—
1320C4—26no—
1321C4—26no—
1322C4—26no—
1323C4—26no—
1324C4—26no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—26no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—43no—
1335C4—43no—
1336C4—43no—
1337C4—41no—
1338C4—41no—
1339C4—43no—
1340C4—43no—
1341C4—43no—
1342C4—41no—
1343C4—43no—
1344C4—41no—
1345C4—43no—
1346C4C2×#520112yes—
1347C2—42no—
1348C2—42no—
1349C2—46no—
1350C2C22×#52011yescharacteristic
1351C2C4×#58511yescharacteristic
1352C2#6265311yescharacteristic
1353C2#6291911yescharacteristic
1354C2#6292211yescharacteristic
1355C2#6294911yescharacteristic
1356C2#6295311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3516C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34499C2semidirect
3. #34484C2semidirect
4. #34483C2semidirect
5. #34482C2semidirect
6. #34466C2semidirect
7. #34464C2semidirect
8. #34430C2semidirect
9. #34429C2semidirect
10. #34422C2semidirect
11. #34420C2semidirect
12. #34397C2semidirect
13. #34385C2semidirect
14. #34336C2semidirect
15. #34322C2semidirect
16. #34314C2semidirect
17. #34312C2semidirect
18. #34312C2semidirect
19. #34311C2semidirect
20. #34293C2semidirect
21. #34291C2semidirect
22. #34263C2semidirect
23. #34262C2semidirect
24. #34250C2semidirect
25. #34249C2semidirect
26. #34242C2semidirect
27. #34182C2semidirect
28. C4×#557C2semidirect
29. C4×#548C2semidirect
30. #34128C2semidirect
31. #34084C2semidirect
32. #3516C4semidirect
242. #557C2×C4semidirect
243. #556C2×C4semidirect
244. #554C2×C4semidirect
245. #553C2×C4semidirect
246. #552C2×C4semidirect
247. D4×Q8C2×C4semidirect
249. #548C2×C4semidirect
250. #542C2×C4semidirect
251. #541C2×C4semidirect
254. #529C2×C4semidirect
255. #529C2×C4semidirect
280. #520C2×C4semidirect
284. #519C2×C4semidirect
287. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35162
#344992
#344842
#344832
#344822
#344662
#344642
#344302
#344292
#344222
#344202
#343972
#343852
#343362
#343222
#343142
#343122
#343112
#342932
#342912
#342632
#342622
#342502
#342492
#342422
#341822
C4×#5572
C4×#5482
#341282
#340842