Finite Group Databasebeta

← #7674380

Subgroups — #7674380

Order 512.

5102 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#45228C214yesmaximal, complemented
2#45208C214yesmaximal, complemented
3#45078C214yesmaximal, complemented
4#45052C214yesmaximal, complemented
5#39505C214yesmaximal, complemented
6#39502C214yesmaximal, complemented
7#38283C218yesmaximal, complemented
8#38281C218yesmaximal, complemented
9#37955C214yesmaximal, complemented
10#37954C214yesmaximal, complemented
11#35542C212yesmaximal, complemented
12#35518C212yesmaximal, complemented
13#35275C211yesmaximal, characteristic, complemented
14#35273C211yesmaximal, characteristic, complemented
15#35158C212yesmaximal, complemented
16#34633C211yesmaximal, characteristic, complemented
17#34252C212yesmaximal, complemented
18#34208C211yesmaximal, characteristic, complemented
19#34189C211yesmaximal, characteristic, complemented
20#34065C211yesmaximal, characteristic, complemented
21C2×#2314C211yesmaximal, characteristic, complemented
22C2×#544C2212yes—
23C2×#537C2212yes—
24C2×#532C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C2×#525C2212yes—
27C2×#520C2212yes—
28C2×C4×#41C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2868C2212yescomplemented
31#2859C2212yescomplemented
32#2857C2212yescomplemented
33#2856C2212yescomplemented
34#2850C2218yes—
35#2803C2218yes—
36#2803C2218yes—
37#2795C2218yes—
38#2795C2218yescomplemented
39#2783C2218yescomplemented
40#2783C2218yescomplemented
41#2775C2218yes—
42#2769C2218yescomplemented
43#2756C2218yes—
44#2744C2218yescomplemented
45#2737C2218yes—
46#2737C2218yescomplemented
47#2731C2218yes—
48#2731C2218yescomplemented
49#2699C2218yes—
50#2686C2218yescomplemented
51#2660C2214yescomplemented
52#2639C2218yes—
53#2621C2212yes—
54#2620C2212yes—
55#2620C2212yes—
56#2620C2214yescomplemented
57#2619C2212yes—
58#2618C2214yes—
59#2617C2214yes—
60#2612C2218yescomplemented
61#2610C2218yes—
62#2574C2218yescomplemented
63#2563C2214yes—
64#2562C2214yes—
65#2562C2214yes—
66#2555C2218yes—
67#2552C2214yescomplemented
68#2551C2214yescomplemented
69#2547C2214yes—
70#2538C2214yes—
71#2538C2214yescomplemented
72#2537C2214yes—
73#2537C2214yescomplemented
74#2536C2214yes—
75#2535C2214yes—
76#2531C2218yes—
77#2531C2218yescomplemented
78#2529C2218yes—
79#2526C2218yes—
80#2526C2218yescomplemented
81#2518C2218yes—
82#2518C2218yescomplemented
83#2500C2218yes—
84#2497C2218yescomplemented
85#2492C2214yes—
86#2492C2214yescomplemented
87#2492C2214yescomplemented
88#2491C2214yes—
89#2491C2218yes—
90#2491C2214yescomplemented
91#2491C2214yescomplemented
92#2490C2214yes—
93#2490C2214yescomplemented
94#2490C2214yescomplemented
95#2489C2214yes—
96#2489C2214yescomplemented
97#2489C2214yescomplemented
98#2488C2218yes—
99#2476C2218yescomplemented
100#2472C2218yes—
101#2440C2218yes—
102#2439C2218yescomplemented
103#2425C2218yes—
104#2424C2218yes—
105#2417C2214yes—
106#2416C2218yes—
107#2416C2214yes—
108#2415C2214yes—
109#2414C2214yes—
110#2392C2214yes—
111#2392C2214yes—
112#2364C2218yes—
113#2357C2214yescomplemented
114#2357C2214yescomplemented
115#2356C2214yescomplemented
116#2356C2214yescomplemented
117#2355C2214yescomplemented
118#2354C2214yescomplemented
119#2353C2218yes—
120#2352C2214yescomplemented
121#2352C2214yescomplemented
122#2347C2214yescomplemented
123#2346C2214yescomplemented
124#2345C2214yescomplemented
125#2344C2214yescomplemented
126#2328C2212yescomplemented
127#2327C2212yescomplemented
128#2324C2212yes—
129#2324C2212yes—
130#2323C2212yes—
131#2323C2212yes—
132#2322C2214yes—
133#2321C2214yes—
134#2318C2218yes—
135#2317C2212yes—
136#2314C2214yes—
137#2314C2214yes—
138#2314C2214yes—
139#2314C2214yes—
140#2314C2212yescomplemented
141#2314C2212yescomplemented
142#2311C2212yes—
143#2311C2212yes—
144#2311C2212yes—
145C4×#124C2214yescomplemented
146#2297C2211yescharacteristic
147#2297C2212yes—
148#2296C2211yescharacteristic
149#2293C2214yes—
150#2290C2214yes—
151#2290C2218yes—
152C2×#388C2214yes—
153C2×#387C2214yes—
154#2285C2211yescharacteristic
155C2×#384C2211yescharacteristic
156#2283C2214yescomplemented
157C2×#382C2211yescharacteristic
158#2280C2211yescharacteristic
159C2×#380C2212yes—
160#2274C2212yes—
161C4×#117C2211yescharacteristic
162C2×C4×C4⋊C4C2212yes—
163C22×#41C2311yescharacteristic
164C22×#41C2312yes—
165C24×C4C2311yescharacteristic
166#544—48no—
167#537—48no—
168#532—28no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2318yes—
173C2×#127C2311yescharacteristic
174C2×#125C2314yes—
175C2×#125C2314yes—
176C2×#124C2312yes—
177C2×#124C2318yes—
178C2×#124C2318yes—
179#525—28no—
180#525—48no—
181C2×#123C2312yes—
182C2×#123C2314yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2314yes—
189C2×#121C2312yes—
190C2×#121C2314yes—
191C2×#121C2318yes—
192C2×#121C2314yes—
193C2×#121C2312yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2318yes—
197C2×#121C2318yes—
198C2×#120C2312yes—
199C2×#120C2314yes—
200#520—216no—
201C4×#41—28no—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×#117—28no—
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2314yes—
222C2×#117C2318yes—
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2314yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2314yes—
234C22×C42C2311yescharacteristic
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#398C2314yes—
240#398C2314yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#397C2314yes—
245#397C2314yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#396C2318yes—
252#396C2314yes—
253#396C2314yes—
254#396C2314yes—
255#396C2314yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#395C2318yes—
260#395C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2314yes—
265#394C2314yes—
266#394C2314yes—
267#394C2314yes—
268#394C2314yes—
269#394C2314yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#393C2318yes—
277#393C2318yes—
278#393C2318yes—
279#393C2318yes—
280#392C2314yes—
281#392C2314yes—
282#392C2318yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2318yes—
287#391C2311yescharacteristic
288#391C2311yescharacteristic
289#391C2318yes—
290#391C2312yes—
291#391C2312yes—
292#390C2318yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2311yescharacteristic
299#390C2311yescharacteristic
300#390C2318yes—
301#390C2318yes—
302#390C2312yes—
303#390C2312yes—
304#390C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2312yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2314yes—
353#387C2314yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2314yes—
361#386C2314yes—
362#386C2314yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2318yes—
369#385C2318yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#384C2312yes—
374#384C2312yes—
375#384C2314yes—
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#384C2314yes—
379#384C2318yes—
380#383C2318yes—
381#383C2318yes—
382#382C2318yes—
383#382C2312yes—
384#382C2312yes—
385#382C2314yes—
386#382C2314yes—
387#382C2318yes—
388#382C2318yes—
389#382C2312yes—
390#381C2318yes—
391#381C2312yes—
392#381C2318yes—
393#380C2312yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2318yes—
406#380C2318yes—
407#380C2314yes—
408#380C2318yes—
409#379C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433#376C2312yes—
434#376C2318yes—
435#376C2318yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C43C2312yes—
440C25C2411yescharacteristic
441C2×#41—24no—
442C2×#41—28no—
443C2×#41—24no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—24no—
447C22×Q8C2411yescharacteristic
448C22×Q8C2412yes—
449C22×Q8C2418yes—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2411yescharacteristic
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2418yes—
459C23×C4—24no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4C2411yescharacteristic
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C4⋊Q8—24no—
475C4⋊Q8—48no—
476C4⋊Q8—48no—
477C4⋊Q8—88no—
478#127—24no—
479#125—48no—
480#125—48no—
481#124—28no—
482#124—88no—
483#124—88no—
484#123—28no—
485#123—48no—
486C22⋊Q8—28no—
487C22⋊Q8—416no—
488C22⋊Q8—44no—
489C22⋊Q8—44no—
490C22⋊Q8—48no—
491C22⋊Q8—48no—
492#121—216no—
493#121—28no—
494#121—44no—
495#121—44no—
496#121—48no—
497#121—48no—
498#121—416no—
499#121—88no—
500#121—88no—
501#120—28no—
502#120—48no—
503C4×Q8—28no—
504C4×Q8—216no—
505C4×D4—216no—
506C4×D4—232no—
507C4×D4—28no—
508C4×D4—216no—
509C4×D4—216no—
510C4×D4—216no—
511C4×D4—48no—
512C4×D4—48no—
513#117—24no—
514#117—28no—
515#117—24no—
516#117—216no—
517#117—28no—
518#117—28no—
519#117—28no—
520#117—28no—
521#117—28no—
522#117—88no—
523#117#4118yes—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—216no—
528C2×C4⋊C4—84no—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2411yescharacteristic
543C2×C4⋊C4C2411yescharacteristic
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2412yes—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—84no—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2412yes—
599C2×C42—24no—
600C2×C42—28no—
601C2×C42—84no—
602C2×C42#4118yes—
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2414yes—
608C2×C42C2418yes—
609C2×C42C2412yes—
610C2×C42C2414yes—
611C2×C42C2418yes—
612C2×C42C2418yes—
613C2×C42C2418yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2418yes—
617C2×C42C2411yescharacteristic
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2412yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—42no—
655C24—42no—
656C24C2512yes—
657C24C2514yes—
658C24C2512yes—
659C24C2511yescharacteristic
660#41—416no—
661#41—432no—
662C2×Q8—22no—
663C2×Q8—24no—
664C2×Q8—22no—
665C2×Q8—24no—
666C2×Q8—22no—
667C2×Q8—24no—
668C2×Q8—48no—
669C2×Q8—48no—
670C2×Q8—48no—
671C2×D4—24no—
672C2×D4—28no—
673C2×D4—24no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—24no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—24no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—22no—
684C2×D4—24no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C22×C4—24no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—28no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—216no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—48no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—416no—
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×C4C2512yes—
742C22×C4C2512yes—
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2514yes—
746C22×C4C2518yes—
747C22×C4C2512yes—
748C22×C4C2514yes—
749C22×C4C2512yes—
750C22×C4C2511yescharacteristic
751C22×C4C2511yescharacteristic
752C4⋊C4—28no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—216no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—44no—
783C4⋊C4C2×#4118yes—
784C22⋊C4—24no—
785C22⋊C4—28no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—44no—
803C22⋊C4—48no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4C2×#4118yes—
820C42—24no—
821C42—24no—
822C42—22no—
823C42—22no—
824C42—28no—
825C42—216no—
826C42—28no—
827C42—24no—
828C42—48no—
829C42—48no—
830C42—44no—
831C42—48no—
832C42—48no—
833C42—44no—
834C42C2×#4114yes—
835C42C2×#4114yes—
836C42C2×#4118yes—
837C42C2×#4118yes—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—24no—
845C23—22no—
846C23—22no—
847C23—24no—
848C23—22no—
849C23—22no—
850C23—24no—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—48no—
860C23—44no—
861C23—84no—
862C23—82no—
863C23—82no—
864C23C22×#4112yes—
865C23C22×#4112yes—
866C23C2×H(5,𝔽2)12yes—
867C23C2611yescharacteristic
868Q8—44no—
869Q8—48no—
870Q8—168no—
871D4—48no—
872D4—416no—
873D4—44no—
874D4—48no—
875D4—88no—
876D4—88no—
877D4—88no—
878D4—88no—
879D4—168no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—28no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—24no—
908C2×C4—28no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—48no—
921C2×C4—48no—
922C2×C4—44no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—416no—
926C2×C4—48no—
927C2×C4—88no—
928C2×C4—816no—
929C2×C4—88no—
930C2×C4—88no—
931C2×C4#555116yes—
932C2×C4C22×#4114yes—
933C2×C4C22×#4118yes—
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—44no—
946C22—44no—
947C22—44no—
948C22—42no—
949C22—42no—
950C22—44no—
951C22—42no—
952C22—44no—
953C22—44no—
954C22—42no—
955C22—42no—
956C22—44no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—44no—
964C22—88no—
965C22C2×#55514yes—
966C22C23×#4111yescharacteristic
967C22C23×#4111yescharacteristic
968C22C22×H(5,𝔽2)11yescharacteristic
969C22H(7,𝔽2)12yes—
970C222−1+612yes—
971C4—24no—
972C4—24no—
973C4—28no—
974C4—42no—
975C4—42no—
976C4—44no—
977C4—48no—
978C4—48no—
979C4—44no—
980C4—42no—
981C4—42no—
982C4—44no—
983C4—42no—
984C4—42no—
985C4—44no—
986C4C2×#55514yes—
987C4C2×#55514yes—
988C2—24no—
989C2—82no—
990C2—84no—
991C2—82no—
992C2C22×#55511yescharacteristic
993C2#6285612yes—
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. #45228C2semidirect
2. #45208C2semidirect
3. #45078C2semidirect
4. #45052C2semidirect
5. #39505C2semidirect
6. #39502C2semidirect
7. #38283C2semidirect
8. #38281C2semidirect
9. #37955C2semidirect
10. #37954C2semidirect
11. #35542C2semidirect
12. #35518C2semidirect
13. #35275C2semidirect
14. #35273C2semidirect
15. #35158C2semidirect
16. #34633C2semidirect
17. #34252C2semidirect
18. #34208C2semidirect
19. #34189C2semidirect
20. #34065C2semidirect
21. C2×#2314C2semidirect
30. #2868C22semidirect
31. #2859C22semidirect
32. #2857C22semidirect
33. #2856C22semidirect
38. #2795C22semidirect
39. #2783C22semidirect
40. #2783C22semidirect
42. #2769C22semidirect
44. #2744C22semidirect
46. #2737C22semidirect
48. #2731C22semidirect
50. #2686C22semidirect
51. #2660C22semidirect
56. #2620C22semidirect
60. #2612C22semidirect
62. #2574C22semidirect
67. #2552C22semidirect
68. #2551C22semidirect
71. #2538C22semidirect
73. #2537C22semidirect
77. #2531C22semidirect
80. #2526C22semidirect
82. #2518C22semidirect
84. #2497C22semidirect
86. #2492C22semidirect
87. #2492C22semidirect
90. #2491C22semidirect
91. #2491C22semidirect
93. #2490C22semidirect
94. #2490C22semidirect
96. #2489C22semidirect
97. #2489C22semidirect
99. #2476C22semidirect
102. #2439C22semidirect
113. #2357C22semidirect
114. #2357C22semidirect
115. #2356C22semidirect
116. #2356C22semidirect
117. #2355C22semidirect
118. #2354C22semidirect
120. #2352C22semidirect
121. #2352C22semidirect
122. #2347C22semidirect
123. #2346C22semidirect
124. #2345C22semidirect
125. #2344C22semidirect
126. #2328C22semidirect
127. #2327C22semidirect
140. #2314C22semidirect
141. #2314C22semidirect
145. C4×#124C22semidirect
156. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#452282
#452082
#450782
#450522
#395052
#395022
#382832
#382812
#379552
#379542
#355422
#355182
#352752
#352732
#351582
#346332
#342522
#342082
#341892
#340652
C2×#23142