Finite Group Databasebeta

← #7673906

Subgroups — #7673906

Order 512.

5164 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45262C214yesmaximal, complemented
2#45257C214yesmaximal, complemented
3#44926C214yesmaximal, complemented
4#44912C214yesmaximal, complemented
5#39553C214yesmaximal, complemented
6#39552C214yesmaximal, complemented
7#39279C218yesmaximal, complemented
8#39277C218yesmaximal, complemented
9#37899C214yesmaximal, complemented
10#37892C214yesmaximal, complemented
11#35518C212yesmaximal, complemented
12#35516C212yesmaximal, complemented
13#35339C211yesmaximal, characteristic, complemented
14#35328C211yesmaximal, characteristic, complemented
15#35160C212yesmaximal, complemented
16#34633C211yesmaximal, characteristic, complemented
17#34274C212yesmaximal, complemented
18#34207C211yesmaximal, characteristic, complemented
19#34183C211yesmaximal, characteristic, complemented
20#34065C211yesmaximal, characteristic, complemented
21C2×#2314C211yesmaximal, characteristic, complemented
22C2×#537C2212yes—
23C2×#532C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C2×#525C2212yes—
26C2×#520C2212yes—
27C2×#520C2212yes—
28C2×C4×#41C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2864C2214yescomplemented
31#2852C2218yes—
32#2850C2214yescomplemented
33#2803C2218yes—
34#2802C2218yescomplemented
35#2800C2218yescomplemented
36#2797C2218yescomplemented
37#2796C2218yes—
38#2795C2218yes—
39#2793C2218yescomplemented
40#2790C2218yescomplemented
41#2787C2218yescomplemented
42#2786C2218yescomplemented
43#2778C2218yes—
44#2777C2218yes—
45#2756C2218yes—
46#2750C2218yescomplemented
47#2718C2218yes—
48#2714C2218yes—
49#2647C2212yescomplemented
50#2647C2212yescomplemented
51#2643C2218yes—
52#2621C2212yes—
53#2621C2212yescomplemented
54#2620C2212yes—
55#2620C2212yes—
56#2619C2212yes—
57#2619C2212yescomplemented
58#2618C2214yes—
59#2617C2214yes—
60#2602C2218yes—
61#2600C2218yescomplemented
62#2597C2218yes—
63#2595C2218yes—
64#2594C2218yes—
65#2594C2218yescomplemented
66#2593C2218yes—
67#2591C2218yes—
68#2590C2218yescomplemented
69#2579C2218yescomplemented
70#2577C2218yescomplemented
71#2573C2218yescomplemented
72#2570C2214yescomplemented
73#2570C2214yescomplemented
74#2569C2218yes—
75#2543C2218yes—
76#2538C2214yes—
77#2537C2214yes—
78#2536C2214yes—
79#2536C2214yescomplemented
80#2535C2214yes—
81#2535C2214yescomplemented
82#2514C2214yescomplemented
83#2513C2214yescomplemented
84#2512C2214yescomplemented
85#2511C2214yescomplemented
86#2497C2214yescomplemented
87#2496C2214yescomplemented
88#2495C2214yescomplemented
89#2494C2214yescomplemented
90#2487C2214yes—
91#2486C2214yes—
92#2485C2214yes—
93#2485C2214yes—
94#2481C2218yescomplemented
95#2466C2218yescomplemented
96#2456C2218yes—
97#2443C2218yes—
98#2425C2218yes—
99#2424C2218yes—
100#2423C2214yes—
101#2422C2214yes—
102#2421C2214yes—
103#2420C2214yes—
104#2419C2218yes—
105#2418C2218yes—
106#2417C2214yes—
107#2416C2214yes—
108#2415C2214yes—
109#2414C2214yes—
110#2392C2214yes—
111#2392C2214yes—
112#2363C2214yescomplemented
113#2363C2214yescomplemented
114#2362C2214yescomplemented
115#2362C2214yescomplemented
116#2361C2218yes—
117#2361C2214yescomplemented
118#2361C2214yescomplemented
119#2360C2214yescomplemented
120#2360C2214yescomplemented
121#2354C2214yescomplemented
122Q8×C4⋊C4C2214yescomplemented
123D4×C4⋊C4C2218yes—
124D4×C4⋊C4C2214yescomplemented
125D4×C4⋊C4C2214yescomplemented
126#2326C2214yescomplemented
127#2325C2218yes—
128#2324C2212yes—
129#2324C2212yes—
130#2323C2212yes—
131#2323C2212yes—
132#2322C2214yes—
133#2321C2214yes—
134#2317C2212yes—
135#2317C2212yes—
136#2317C2214yescomplemented
137#2316C2212yes—
138#2314C2214yes—
139#2314C2214yes—
140#2314C2214yes—
141#2314C2214yes—
142#2311C2212yes—
143#2311C2212yes—
144C4×C4⋊Q8C2212yescomplemented
145C4×#127C2212yescomplemented
146C4×#121C2218yes—
147#2297C2211yescharacteristic
148#2297C2212yes—
149#2296C2211yescharacteristic
150#2293C2214yes—
151#2290C2214yes—
152C2×#388C2214yes—
153C2×#387C2214yes—
154#2285C2211yescharacteristic
155#2285C2212yescomplemented
156C2×#384C2211yescharacteristic
157C2×#384C2212yescomplemented
158C2×#382C2211yescharacteristic
159#2280C2211yescharacteristic
160C2×#380C2212yes—
161C4×#117C2211yescharacteristic
162C2×C4×C4⋊C4C2212yes—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C24×C4C2311yescharacteristic
166#537—216no—
167#532—28no—
168C2×C4⋊Q8C2311yescharacteristic
169C2×#127C2311yescharacteristic
170C2×#126C2318yes—
171C2×#124C2312yes—
172#525—28no—
173#525—48no—
174C2×#123C2312yes—
175C2×#123C2314yes—
176C2×#123C2318yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2312yes—
182C2×#121C2312yes—
183C2×#121C2318yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2312yes—
188C2×#121C2312yes—
189C2×#121C2318yes—
190C2×#120C2312yes—
191C2×#120C2314yes—
192#520—48no—
193#520—48no—
194C4×#41—28no—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2318yes—
210C2×#117—28no—
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2314yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2318yes—
228C22×C4⋊C4C2314yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2314yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2314yes—
234C22×C42C2311yescharacteristic
235#401C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#399C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2314yes—
246#398C2318yes—
247#398C2314yes—
248#398C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2314yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2314yes—
258#397C2318yes—
259#397C2318yes—
260#396C2314yes—
261#396C2314yes—
262#396C2318yes—
263#396C2318yes—
264#396C2314yes—
265#396C2314yes—
266#396C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2314yes—
270#394C2318yes—
271#394C2314yes—
272#394C2318yes—
273#394C2314yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2314yes—
278#394C2314yes—
279#392C2318yes—
280#392C2314yes—
281#392C2314yes—
282#392C2318yes—
283#391C2314yes—
284#391C2314yes—
285#391C2311yescharacteristic
286#391C2311yescharacteristic
287#391C2312yes—
288#391C2312yes—
289#390C2314yes—
290#390C2318yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2311yescharacteristic
295#390C2311yescharacteristic
296#390C2318yes—
297#390C2312yes—
298#390C2312yes—
299#390C2318yes—
300#389C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2312yes—
315#389C2312yes—
316#389C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2318yes—
329#388C2314yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2314yes—
362#386C2314yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2314yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2314yes—
379#385C2314yes—
380#385C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#384C2312yes—
386#384C2312yes—
387#384C2314yes—
388#384C2314yes—
389#384C2314yes—
390#384C2318yes—
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#383C2318yes—
394#382C2314yes—
395#382C2312yes—
396#382C2312yes—
397#382C2314yes—
398#382C2314yes—
399#382C2312yes—
400#381C2318yes—
401#381C2312yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2318yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2312yes—
414#380C2312yes—
415#380C2318yes—
416#379C2312yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435#376C2312yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C43C2312yes—
440C25C2411yescharacteristic
441C2×#41—24no—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—24no—
445C2×#41—28no—
446C2×#41#4118yes—
447C22×Q8C2412yes—
448C22×Q8C2411yescharacteristic
449C22×D4C2414yes—
450C22×D4C2412yes—
451C22×D4C2412yes—
452C22×D4C2411yescharacteristic
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—24no—
461C23×C4C2411yescharacteristic
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2418yes—
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C4⋊Q8—24no—
475#127—24no—
476#126—88no—
477#124—28no—
478#123—28no—
479#123—48no—
480#123—88no—
481C22⋊Q8—28no—
482C22⋊Q8—216no—
483C22⋊Q8—216no—
484C22⋊Q8—44no—
485C22⋊Q8—44no—
486#121—28no—
487#121—216no—
488#121—232no—
489#121—216no—
490#121—216no—
491#121—44no—
492#121—44no—
493#121—88no—
494#120—28no—
495#120—48no—
496C4×Q8—28no—
497C4×Q8—48no—
498C4×Q8—48no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—28no—
502C4×D4—216no—
503C4×D4—48no—
504C4×D4—48no—
505C4×D4—48no—
506C4×D4—48no—
507C4×D4—416no—
508C4×D4—416no—
509C4×D4—88no—
510C4×D4—88no—
511#117—24no—
512#117—24no—
513#117—24no—
514#117—28no—
515#117—28no—
516#117—28no—
517#117—28no—
518#117—28no—
519#117—28no—
520#117—48no—
521#117—48no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—48no—
526C2×C4⋊C4—48no—
527C2×C4⋊C4—84no—
528C2×C4⋊C4—88no—
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—84no—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C42—24no—
601C2×C42—28no—
602C2×C42—84no—
603C2×C42#4118yes—
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2418yes—
613C2×C42C2418yes—
614C2×C42C2414yes—
615C2×C42C2418yes—
616C2×C42C2418yes—
617C2×C42C2414yes—
618C2×C42C2411yescharacteristic
619C2×C42C2412yes—
620C2×C42C2411yescharacteristic
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—42no—
655C24—42no—
656C24C2512yes—
657C24C2514yes—
658C24C2512yes—
659C24C2511yescharacteristic
660#41—232no—
661#41—432no—
662C2×Q8—22no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—22no—
666C2×Q8—24no—
667C2×Q8C2×#4114yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—216no—
675C2×D4—22no—
676C2×D4—28no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—24no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4C2×#4118yes—
694C2×D4C2×#4114yes—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—28no—
708C22×C4—24no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—44no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—42no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—416no—
730C22×C4C2×#4118yes—
731C22×C4C2×#4118yes—
732C22×C4C2×#4114yes—
733C22×C4C2×#4114yes—
734C22×C4H(5,𝔽2)14yes—
735C22×C4C2518yes—
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2518yes—
746C22×C4C2514yes—
747C22×C4C2512yes—
748C22×C4C2512yes—
749C22×C4C2512yes—
750C22×C4C2511yescharacteristic
751C22×C4C2511yescharacteristic
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—216no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—22no—
767C4⋊C4—24no—
768C4⋊C4—22no—
769C4⋊C4—24no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C4⋊C4—48no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—44no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—28no—
789C22⋊C4—216no—
790C22⋊C4—24no—
791C22⋊C4—28no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—216no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—24no—
822C42—24no—
823C42—22no—
824C42—22no—
825C42—28no—
826C42—24no—
827C42—28no—
828C42—24no—
829C42—48no—
830C42—48no—
831C42—44no—
832C42—48no—
833C42—48no—
834C42—44no—
835C42C2×#4114yes—
836C42C2×#4114yes—
837C42C2×#4118yes—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—22no—
845C23—22no—
846C23—24no—
847C23—24no—
848C23—22no—
849C23—24no—
850C23—22no—
851C23—24no—
852C23—22no—
853C23—24no—
854C23—24no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—48no—
859C23—44no—
860C23—84no—
861C23—82no—
862C23—82no—
863C23C22×#4114yes—
864C23C22×#4112yes—
865C23C22×#4112yes—
866C23C2×H(5,𝔽2)12yes—
867C23C2611yescharacteristic
868Q8—28no—
869Q8—48no—
870D4—216no—
871D4—28no—
872D4—416no—
873D4—416no—
874D4—48no—
875D4—816no—
876D4—88no—
877D4—88no—
878D4—88no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—216no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—48no—
921C2×C4—416no—
922C2×C4—48no—
923C2×C4—44no—
924C2×C4—48no—
925C2×C4—48no—
926C2×C4—416no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4—168no—
930C2×C4—168no—
931C2×C4#553116yes—
932C2×C4C22×#4114yes—
933C2×C4C22×#4114yes—
934C2×C4C22×#4114yes—
935C2×C4C22×#4112yes—
936C2×C4C22×#4112yes—
937C2×C4C22×#4112yes—
938C2×C4C22×#4112yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4C2×H(5,𝔽2)12yes—
941C22—24no—
942C22—24no—
943C22—22no—
944C22—22no—
945C22—28no—
946C22—24no—
947C22—44no—
948C22—42no—
949C22—42no—
950C22—44no—
951C22—44no—
952C22—42no—
953C22—42no—
954C22—44no—
955C22—42no—
956C22—44no—
957C22—42no—
958C22—44no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22—42no—
963C22—44no—
964C22—88no—
965C22C2×#55314yes—
966C22C23×#4111yescharacteristic
967C22C23×#4111yescharacteristic
968C22C22×H(5,𝔽2)11yescharacteristic
969C22H(7,𝔽2)12yes—
970C222−1+612yes—
971C4—24no—
972C4—24no—
973C4—24no—
974C4—42no—
975C4—42no—
976C4—44no—
977C4—48no—
978C4—44no—
979C4—48no—
980C4—42no—
981C4—44no—
982C4—42no—
983C4—44no—
984C4—42no—
985C4—44no—
986C4C2×#55314yes—
987C4C2×#55314yes—
988C2—24no—
989C2—44no—
990C2—84no—
991C2—82no—
992C2C22×#55311yescharacteristic
993C2#6284512yes—
994C2#6285712yes—
995C2#6288011yescharacteristic
996C2#6288811yescharacteristic
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. #45262C2semidirect
2. #45257C2semidirect
3. #44926C2semidirect
4. #44912C2semidirect
5. #39553C2semidirect
6. #39552C2semidirect
7. #39279C2semidirect
8. #39277C2semidirect
9. #37899C2semidirect
10. #37892C2semidirect
11. #35518C2semidirect
12. #35516C2semidirect
13. #35339C2semidirect
14. #35328C2semidirect
15. #35160C2semidirect
16. #34633C2semidirect
17. #34274C2semidirect
18. #34207C2semidirect
19. #34183C2semidirect
20. #34065C2semidirect
21. C2×#2314C2semidirect
30. #2864C22semidirect
32. #2850C22semidirect
34. #2802C22semidirect
35. #2800C22semidirect
36. #2797C22semidirect
39. #2793C22semidirect
40. #2790C22semidirect
41. #2787C22semidirect
42. #2786C22semidirect
46. #2750C22semidirect
49. #2647C22semidirect
50. #2647C22semidirect
53. #2621C22semidirect
57. #2619C22semidirect
61. #2600C22semidirect
65. #2594C22semidirect
68. #2590C22semidirect
69. #2579C22semidirect
70. #2577C22semidirect
71. #2573C22semidirect
72. #2570C22semidirect
73. #2570C22semidirect
79. #2536C22semidirect
81. #2535C22semidirect
82. #2514C22semidirect
83. #2513C22semidirect
84. #2512C22semidirect
85. #2511C22semidirect
86. #2497C22semidirect
87. #2496C22semidirect
88. #2495C22semidirect
89. #2494C22semidirect
94. #2481C22semidirect
95. #2466C22semidirect
112. #2363C22semidirect
113. #2363C22semidirect
114. #2362C22semidirect
115. #2362C22semidirect
117. #2361C22semidirect
118. #2361C22semidirect
119. #2360C22semidirect
120. #2360C22semidirect
121. #2354C22semidirect
122. Q8×C4⋊C4C22semidirect
124. D4×C4⋊C4C22semidirect
125. D4×C4⋊C4C22semidirect
126. #2326C22semidirect
136. #2317C22semidirect
144. C4×C4⋊Q8C22semidirect
145. C4×#127C22semidirect
155. #2285C22semidirect
157. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#452622
#452572
#449262
#449122
#395532
#395522
#392792
#392772
#378992
#378922
#355182
#355162
#353392
#353282
#351602
#346332
#342742
#342072
#341832
#340652
C2×#23142