Finite Group Databasebeta

← #7642461

Subgroups — #7642461

Order 512.

5718 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39818C214yesmaximal, complemented
2#39805C214yesmaximal, complemented
3#39690C214yesmaximal, complemented
4#39413C214yesmaximal, complemented
5#37980C214yesmaximal, complemented
6#37792C214yesmaximal, complemented
7#37768C214yesmaximal, complemented
8#37745C214yesmaximal, complemented
9#36833C214yesmaximal, complemented
10#36828C214yesmaximal, complemented
11#36624C212yesmaximal, complemented
12#35436C214yesmaximal, complemented
13#35419C214yesmaximal, complemented
14#35301C212yesmaximal, complemented
15#35261C212yesmaximal, complemented
16#35166C211yesmaximal, characteristic, complemented
17#35104C211yesmaximal, characteristic, complemented
18#35082C212yesmaximal, complemented
19#35006C212yesmaximal, complemented
20#34236C212yesmaximal, complemented
21C2×#2296C211yesmaximal, characteristic, complemented
22C2×#540C2212yes—
23C2×#539C2214yes—
24C2×#537C2214yes—
25C2×#532C2212yes—
26C2×#532C2212yes—
27C2×#525C2214yes—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2857C2212yes—
32#2857C2212yes—
33#2856C2212yes—
34#2856C2212yes—
35#2856C2212yes—
36#2854C2214yes—
37#2854C2214yes—
38#2854C2214yes—
39#2851C2212yes—
40#2850C2214yes—
41#2850C2214yes—
42#2847C2214yes—
43#2847C2214yes—
44#2807C2218yescomplemented
45#2803C2218yescomplemented
46#2773C2218yescomplemented
47#2732C2218yes—
48#2714C2218yes—
49#2710C2218yescomplemented
50#2704C2218yescomplemented
51#2701C2218yescomplemented
52#2698C2218yescomplemented
53#2694C2218yes—
54#2692C2218yes—
55#2688C2218yes—
56#2687C2218yes—
57#2682C2218yes—
58#2672C2218yescomplemented
59#2671C2218yes—
60#2656C2214yes—
61#2651C2218yescomplemented
62#2639C2214yes—
63#2629C2212yes—
64#2628C2212yes—
65#2628C2212yes—
66#2627C2214yes—
67#2624C2214yes—
68#2619C2212yes—
69#2619C2212yes—
70#2619C2212yes—
71#2618C2214yes—
72#2610C2214yes—
73#2610C2214yes—
74#2606C2214yescomplemented
75#2605C2214yescomplemented
76#2602C2218yescomplemented
77#2598C2214yes—
78#2598C2214yes—
79#2596C2218yescomplemented
80#2591C2214yes—
81#2589C2218yescomplemented
82#2570C2214yescomplemented
83#2560C2218yescomplemented
84#2559C2218yescomplemented
85#2558C2218yescomplemented
86#2556C2218yescomplemented
87#2550C2214yescomplemented
88#2549C2218yescomplemented
89#2542C2214yescomplemented
90#2541C2214yescomplemented
91#2540C2214yescomplemented
92#2540C2214yescomplemented
93#2539C2214yes—
94#2513C2214yescomplemented
95#2512C2214yescomplemented
96#2507C2214yescomplemented
97#2506C2214yescomplemented
98#2479C2218yes—
99#2477C2218yes—
100#2476C2218yes—
101#2471C2218yes—
102#2464C2218yes—
103#2456C2218yes—
104#2455C2218yescomplemented
105#2454C2218yes—
106#2454C2214yescomplemented
107#2452C2214yescomplemented
108#2450C2218yes—
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2443C2218yes—
112#2443C2218yes—
113#2430C2218yes—
114#2425C2218yes—
115#2425C2218yescomplemented
116#2424C2218yes—
117#2407C2218yes—
118#2406C2214yes—
119#2404C2214yes—
120#2369C2214yescomplemented
121#2366C2214yescomplemented
122#2361C2218yes—
123#2357C2214yescomplemented
124#2349C2214yescomplemented
125#2339C2218yes—
126#2337C2214yescomplemented
127#2337C2214yescomplemented
128#2335C2218yescomplemented
129#2329C2214yes—
130#2325C2214yes—
131#2324C2214yes—
132#2324C2214yes—
133#2324C2214yes—
134#2319C2214yescomplemented
135#2314C2212yes—
136C4×#121C2214yes—
137C4×#121C2214yes—
138C4×#121C2214yes—
139C4×#121C2214yes—
140C4×#121C2214yes—
141#2297C2214yes—
142#2296C2214yes—
143#2296C2212yes—
144#2296C2214yes—
145#2296C2212yes—
146#2296C2212yes—
147#2296C2212yes—
148C2×#389C2212yes—
149C2×#389C2212yes—
150C2×#385C2212yes—
151C2×#385C2212yes—
152#2285C2212yes—
153#2283C2212yes—
154#2275C2214yescomplemented
155C2×C4×C4⋊C4C2211yescharacteristic
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C4⋊C4C2211yescharacteristic
159C22×#41C2314yes—
160C22×#41C2314yes—
161C24×C4C2311yescharacteristic
162C24×C4C2312yes—
163#540—48no—
164#539—416no—
165#537—416no—
166#532—216no—
167#532—48no—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×#127C2312yes—
171C2×#127C2312yes—
172C2×#127C2312yes—
173C2×#126C2318yes—
174C2×#125C2312yes—
175C2×#125C2318yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178#525—416no—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#121C2318yes—
202C2×#120C2318yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×#117—28no—
213C2×#117—44no—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C42—44no—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#400C2318yes—
251#399C2318yes—
252#399C2318yes—
253#399C2314yes—
254#399C2314yes—
255#399C2318yes—
256#399C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#395C2318yes—
272#395C2314yes—
273#395C2314yes—
274#394C2318yes—
275#394C2314yes—
276#394C2314yes—
277#394C2318yes—
278#394C2314yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#393C2318yes—
286#393C2314yes—
287#393C2314yes—
288#392C2314yes—
289#392C2314yes—
290#392C2318yes—
291#392C2314yes—
292#392C2314yes—
293#392C2318yes—
294#392C2318yes—
295#391C2314yes—
296#391C2318yes—
297#391C2314yes—
298#391C2318yes—
299#391C2318yes—
300#390C2314yes—
301#390C2318yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2318yes—
306#390C2318yes—
307#390C2318yes—
308#390C2318yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2314yes—
381#385C2314yes—
382#385C2314yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#384C2312yes—
388#384C2312yes—
389#384C2312yes—
390#383C2314yes—
391#382C2312yes—
392#382C2312yes—
393#382C2314yes—
394#382C2312yes—
395#381C2318yes—
396#381C2314yes—
397#380C2314yes—
398#380C2318yes—
399#380C2314yes—
400#380C2314yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427#376C2314yes—
428C2×#95C2312yes—
429C2×#95C2312yes—
430C2×#95C2312yes—
431C2×#95C2318yes—
432C2×#95C2312yes—
433C25C2411yescharacteristic
434C2×#41—216no—
435C2×#41—48no—
436C2×#41—48no—
437C2×#41—416no—
438C2×#41—48no—
439C22×Q8C2414yes—
440C22×Q8C2414yes—
441C22×D4C2414yes—
442C22×D4C2418yes—
443C22×D4C2414yes—
444C22×D4C2418yes—
445C22×D4C2414yes—
446C22×D4C2418yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C22×D4C2418yes—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—28no—
454C23×C4—44no—
455C23×C4—44no—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2418yes—
472C23×C4C2418yes—
473C23×C4C2412yes—
474C23×C4C2418yes—
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C4⋊Q8—28no—
478C4⋊Q8—44no—
479#127—28no—
480#127—44no—
481#127—44no—
482#126—416no—
483#125—44no—
484#125—416no—
485#124—216no—
486#124—48no—
487#123—416no—
488#123—416no—
489#123—416no—
490#123—416no—
491#123—416no—
492C22⋊Q8—216no—
493C22⋊Q8—416no—
494C22⋊Q8—416no—
495C22⋊Q8—416no—
496C22⋊Q8—48no—
497#121—216no—
498#121—216no—
499#121—216no—
500#121—216no—
501#121—216no—
502#121—216no—
503#121—48no—
504#121—416no—
505#121—416no—
506#121—416no—
507#121—48no—
508#121—48no—
509#121—416no—
510#120—416no—
511C4×D4—216no—
512C4×D4—216no—
513C4×D4—48no—
514C4×D4—48no—
515C4×D4—48no—
516C4×D4—416no—
517C4×D4—416no—
518C4×D4—416no—
519C4×D4—416no—
520#117—28no—
521#117—28no—
522#117—28no—
523#117—28no—
524#117—28no—
525#117—44no—
526#117—44no—
527#117—44no—
528#117—48no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—28no—
532C2×C4⋊C4—28no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—44no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—44no—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C42—24no—
598C2×C42—28no—
599C2×C42—42no—
600C2×C42—42no—
601C2×C42—42no—
602C2×C42—42no—
603C2×C42—44no—
604C2×C42—44no—
605C2×C42—42no—
606C2×C42—42no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42#4118yescomplemented
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2418yes—
621C2×C42C2418yes—
622C2×C42C2418yes—
623C2×C42C2411yescharacteristic
624C2×C42C2412yes—
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—24no—
660C24—42no—
661C24C2518yes—
662C24C2511yescharacteristic
663C24C2511yescharacteristic
664C24C2511yescharacteristic
665#41—832no—
666#41—832no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—48no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—216no—
676C2×D4—216no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—44no—
690C2×D4—48no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C22×C4—232no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—24no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—24no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—216no—
730C22×C4—216no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—432no—
752C22×C4C2×#4114yes—
753C22×C4C2×#4114yes—
754C22×C4C2×#4114yes—
755C22×C4H(5,𝔽2)14yes—
756C22×C4H(5,𝔽2)18yes—
757C22×C42−1+414yes—
758C22×C4C2518yes—
759C22×C4C2512yes—
760C22×C4C2518yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2518yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C22×C4C2512yes—
769C22×C4C2511yescharacteristic
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2511yescharacteristic
773C22×C4C2512yes—
774C22×C4C2511yescharacteristic
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—216no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—44no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C22⋊C4—28no—
807C22⋊C4—216no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—24no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—216no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—44no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C42—24no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—24no—
838C42—24no—
839C42—24no—
840C42—24no—
841C42—41no—
842C42—42no—
843C42—41no—
844C42—42no—
845C42—41no—
846C42—41no—
847C42—42no—
848C42—42no—
849C42—48no—
850C42—48no—
851C42—48no—
852C42C2×#4118yes—
853C42C2×#4118yes—
854C23—21no—
855C23—21no—
856C23—22no—
857C23—28no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—22no—
862C23—22no—
863C23—21no—
864C23—22no—
865C23—22no—
866C23—28no—
867C23—28no—
868C23—28no—
869C23—28no—
870C23—28no—
871C23—28no—
872C23—28no—
873C23—48no—
874C23—48no—
875C23—44no—
876C23—44no—
877C23C22×#4112yes—
878C23C2×H(5,𝔽2)12yes—
879C23C2×H(5,𝔽2)14yes—
880C23C2×2−1+412yes—
881C23C2611yescharacteristic
882Q8—88no—
883Q8—88no—
884D4—416no—
885D4—432no—
886D4—416no—
887D4—88no—
888D4—88no—
889D4—88no—
890D4—816no—
891D4—816no—
892D4—168no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—216no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—28no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—28no—
931C2×C4—28no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—48no—
938C2×C4—44no—
939C2×C4—48no—
940C2×C4—48no—
941C2×C4—48no—
942C2×C4—48no—
943C2×C4—44no—
944C2×C4—44no—
945C2×C4—816no—
946C2×C4—816no—
947C2×C4—84no—
948C2×C4—84no—
949C2×C4—168no—
950C2×C4C22×#4112yes—
951C2×C4C22×#4114yes—
952C2×C4C22×#4114yes—
953C2×C4C22×#4112yes—
954C2×C4C2×H(5,𝔽2)12yes—
955C2×C4C2×H(5,𝔽2)14yes—
956C2×C4C2×H(5,𝔽2)14yes—
957C2×C4C2×H(5,𝔽2)12yes—
958C2×C4C2×2−1+412yes—
959C2×C4C2×2−1+412yes—
960C2×C4#58514yes—
961C22—22no—
962C22—24no—
963C22—24no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—24no—
968C22—24no—
969C22—416no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—48no—
977C22—48no—
978C22—48no—
979C22—48no—
980C22—48no—
981C22—48no—
982C22—48no—
983C22#350814yes—
984C22C23×#4111yescharacteristic
985C22C22×H(5,𝔽2)11yescharacteristic
986C22C22×H(5,𝔽2)12yes—
987C22C22×2−1+411yescharacteristic
988C22C2×#58512yes—
989C4—22no—
990C4—22no—
991C4—22no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—24no—
996C4—24no—
997C4—42no—
998C4—48no—
999C4—42no—
1000C4—44no—
1001C4—48no—
1002C4—44no—
1003C4—48no—
1004C4—42no—
1005C4#349214yes—
1006C2—24no—
1007C2—42no—
1008C2—42no—
1009C2—88no—
1010C2#6268611yescharacteristic
1011C2C2×#349211yescharacteristic
1012C2C2×#350811yescharacteristic
1013C2#6281812yes—
1014C2#6283512yes—
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. #39818C2semidirect
2. #39805C2semidirect
3. #39690C2semidirect
4. #39413C2semidirect
5. #37980C2semidirect
6. #37792C2semidirect
7. #37768C2semidirect
8. #37745C2semidirect
9. #36833C2semidirect
10. #36828C2semidirect
11. #36624C2semidirect
12. #35436C2semidirect
13. #35419C2semidirect
14. #35301C2semidirect
15. #35261C2semidirect
16. #35166C2semidirect
17. #35104C2semidirect
18. #35082C2semidirect
19. #35006C2semidirect
20. #34236C2semidirect
21. C2×#2296C2semidirect
44. #2807C22semidirect
45. #2803C22semidirect
46. #2773C22semidirect
49. #2710C22semidirect
50. #2704C22semidirect
51. #2701C22semidirect
52. #2698C22semidirect
58. #2672C22semidirect
61. #2651C22semidirect
74. #2606C22semidirect
75. #2605C22semidirect
76. #2602C22semidirect
79. #2596C22semidirect
81. #2589C22semidirect
82. #2570C22semidirect
83. #2560C22semidirect
84. #2559C22semidirect
85. #2558C22semidirect
86. #2556C22semidirect
87. #2550C22semidirect
88. #2549C22semidirect
89. #2542C22semidirect
90. #2541C22semidirect
91. #2540C22semidirect
92. #2540C22semidirect
94. #2513C22semidirect
95. #2512C22semidirect
96. #2507C22semidirect
97. #2506C22semidirect
104. #2455C22semidirect
106. #2454C22semidirect
107. #2452C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
115. #2425C22semidirect
120. #2369C22semidirect
121. #2366C22semidirect
123. #2357C22semidirect
124. #2349C22semidirect
126. #2337C22semidirect
127. #2337C22semidirect
128. #2335C22semidirect
134. #2319C22semidirect
154. #2275C22semidirect
609. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#398182
#398052
#396902
#394132
#379802
#377922
#377682
#377452
#368332
#368282
#366242
#354362
#354192
#353012
#352612
#351662
#351042
#350822
#350062
#342362
C2×#22962