Finite Group Databasebeta

← #8093535

Subgroups — #8093535

Order 512.

5434 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53151C214yesmaximal, complemented
2#53136C214yesmaximal, complemented
3#53128C214yesmaximal, complemented
4#53095C214yesmaximal, complemented
5#53060C214yesmaximal, complemented
6#53051C214yesmaximal, complemented
7#53011C214yesmaximal, complemented
8#52962C214yesmaximal, complemented
9#52799C214yesmaximal, complemented
10#52549C214yesmaximal, complemented
11#52369C218yesmaximal, complemented
12#35660C212yesmaximal, complemented
13#35659C211yesmaximal, characteristic, complemented
14#35634C211yesmaximal, characteristic, complemented
15#35619C212yesmaximal, complemented
16#35564C212yesmaximal, complemented
17#35545C212yesmaximal, complemented
18#35518C212yesmaximal, complemented
19#34633C212yesmaximal, complemented
20C2×#2625C211yesmaximal, characteristic, complemented
21C22×2−1+4C2211yescharacteristic
22C2×#537C2211yescharacteristic
23C2×#537C2212yes—
24C2×#536C2212yes—
25C2×#532C2212yes—
26C2×#525C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C2×#520C2212yes—
30C22×#117C2211yescharacteristic
31#2843C2214yescomplemented
32#2841C2218yescomplemented
33#2838C2218yes—
34#2838C2218yescomplemented
35#2830C2218yes—
36#2830C2214yescomplemented
37#2829C2218yes—
38#2829C2218yescomplemented
39#2828C2218yes—
40#2828C2214yescomplemented
41#2827C2218yes—
42#2827C2218yescomplemented
43#2827C2218yescomplemented
44#2826C2218yescomplemented
45#2825C2218yes—
46#2824C2218yes—
47#2823C2214yescomplemented
48#2815C2218yes—
49#2797C2218yes—
50#2797C2218yes—
51#2796C2218yes—
52#2795C2214yescomplemented
53#2792C2214yescomplemented
54#2790C2218yescomplemented
55#2790C2218yescomplemented
56#2784C2214yescomplemented
57#2780C2218yescomplemented
58#2749C2218yes—
59#2749C2218yescomplemented
60#2746C2218yescomplemented
61#2737C2218yes—
62#2714C2218yes—
63#2699C2214yescomplemented
64#2691C2218yes—
65#2691C2218yescomplemented
66#2688C2218yes—
67#2625C2214yes—
68#2625C2214yes—
69#2625C2214yes—
70#2625C2214yes—
71#2621C2212yes—
72#2621C2212yes—
73#2620C2212yes—
74#2620C2212yes—
75#2620C2212yes—
76#2620C2212yes—
77#2619C2212yes—
78#2619C2212yes—
79#2618C2214yes—
80#2618C2214yes—
81#2617C2214yes—
82#2617C2214yes—
83#2543C2218yes—
84#2542C2214yes—
85#2542C2214yes—
86#2540C2214yes—
87#2540C2214yes—
88#2539C2214yes—
89#2538C2214yes—
90#2537C2214yes—
91#2536C2214yes—
92#2535C2214yes—
93#2514C2214yescomplemented
94#2513C2214yescomplemented
95#2512C2214yescomplemented
96#2511C2214yescomplemented
97#2510C2218yes—
98#2503C2214yescomplemented
99#2502C2214yescomplemented
100#2501C2214yes—
101#2499C2214yescomplemented
102#2499C2214yescomplemented
103#2497C2214yescomplemented
104#2496C2214yescomplemented
105#2495C2214yescomplemented
106#2494C2214yescomplemented
107#2481C2218yes—
108#2447C2214yescomplemented
109#2447C2214yescomplemented
110#2446C2214yescomplemented
111#2446C2214yescomplemented
112#2436C2214yescomplemented
113#2434C2214yescomplemented
114#2432C2214yescomplemented
115#2431C2214yescomplemented
116#2430C2218yes—
117#2430C2218yes—
118#2429C2214yescomplemented
119#2428C2214yescomplemented
120#2427C2214yescomplemented
121#2426C2214yescomplemented
122#2425C2218yes—
123#2424C2218yes—
124#2419C2218yes—
125#2419C2218yes—
126#2417C2214yes—
127#2417C2214yescomplemented
128#2416C2218yes—
129#2416C2214yes—
130#2416C2214yescomplemented
131#2415C2214yes—
132#2415C2214yescomplemented
133#2414C2214yes—
134#2414C2214yescomplemented
135#2409C2214yes—
136#2409C2214yes—
137#2409C2214yescomplemented
138#2409C2214yescomplemented
139#2407C2214yes—
140#2407C2214yes—
141#2407C2214yescomplemented
142#2407C2214yescomplemented
143#2406C2214yes—
144#2404C2214yes—
145C2×#400C2212yes—
146#2392C2214yes—
147#2392C2214yes—
148#2392C2214yes—
149#2392C2214yes—
150C2×#398C2212yes—
151C2×#397C2214yes—
152#2317C2212yes—
153#2311C2212yes—
154#2311C2212yes—
155#2310C2211yescharacteristic
156#2297C2212yes—
157#2297C2212yes—
158C2×#391C2212yes—
159C2×#389C2212yes—
160#2285C2212yes—
161C2×#380C2211yescharacteristic
162#2274C2211yescharacteristic
163C2×2−1+4—44no—
164C2×2−1+4—48no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2314yes—
168C22×#41C2314yes—
169C23×Q8C2311yescharacteristic
170C23×Q8C2314yes—
171C24×C4C2311yescharacteristic
172#537—48no—
173#537—44no—
174#536—48no—
175#532—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×#127C2312yes—
179C2×#126C2318yes—
180C2×#124C2312yes—
181C2×#124C2312yes—
182C2×#124C2314yes—
183#525—48no—
184#525—48no—
185C2×#123C2314yes—
186C2×#123C2314yes—
187C2×#123C2318yes—
188C2×C22⋊Q8—44no—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#120C2314yes—
214C2×#120C2314yes—
215#520—48no—
216C2×C4×Q8C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×#117—44no—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2314yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2314yes—
239C22×C4⋊C4C2314yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C42C2312yes—
244#401C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2314yes—
250#400C2318yes—
251#400C2318yes—
252#400C2314yes—
253#399C2318yes—
254#399C2318yes—
255#399C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2314yes—
260#398C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2314yes—
283#397C2318yes—
284#396C2314yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2314yes—
289#396C2318yes—
290#396C2314yes—
291#396C2314yes—
292#396C2318yes—
293#396C2314yes—
294#396C2314yes—
295#396C2314yes—
296#396C2314yes—
297#395C2318yes—
298#395C2314yes—
299#395C2318yes—
300#395C2314yes—
301#394C2314yes—
302#394C2318yes—
303#394C2314yes—
304#394C2314yes—
305#394C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2314yes—
309#394C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2314yes—
317#394C2314yes—
318#394C2314yes—
319#394C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#393C2318yes—
324#393C2318yes—
325#393C2318yes—
326#392C2318yes—
327#392C2314yes—
328#392C2318yes—
329#392C2318yes—
330#392C2318yes—
331#392C2314yes—
332#392C2318yes—
333#392C2318yes—
334#392C2314yes—
335#392C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2318yes—
351#390C2314yes—
352#390C2318yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#384C2314yes—
408#384C2314yes—
409#384C2314yes—
410#384C2312yes—
411#384C2312yes—
412#383C2318yes—
413#382C2314yes—
414#382C2312yes—
415#382C2312yes—
416#381C2314yes—
417#381C2318yes—
418#381C2318yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2318yes—
424#380C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2312yes—
442C25C2411yescharacteristic
4432−1+4—464no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—48no—
451C2×#41—416no—
452C2×#41—48no—
453C2×#41—48no—
454C2×#41—48no—
455C22×Q8—24no—
456C22×Q8—28no—
457C22×Q8—48no—
458C22×Q8—48no—
459C22×Q8—48no—
460C22×Q8C2412yes—
461C22×Q8C2414yes—
462C22×Q8C2412yes—
463C22×Q8C2414yes—
464C22×D4C2414yes—
465C22×D4C2412yes—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2418yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C23×C4—24no—
478C23×C4—28no—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2414yes—
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2414yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2412yes—
489C23×C4C2418yes—
490C23×C4C2418yes—
491C23×C4C2411yescharacteristic
492C4⋊Q8—44no—
493C4⋊Q8—48no—
494#127—44no—
495#126—88no—
496#124—44no—
497#124—44no—
498#124—48no—
499#123—48no—
500#123—48no—
501#123—416no—
502C22⋊Q8—48no—
503C22⋊Q8—48no—
504C22⋊Q8—44no—
505C22⋊Q8—44no—
506C22⋊Q8—44no—
507C22⋊Q8—44no—
508C22⋊Q8—48no—
509C22⋊Q8—48no—
510C22⋊Q8—48no—
511C22⋊Q8—48no—
512C22⋊Q8—48no—
513#121—44no—
514#121—44no—
515#121—44no—
516#121—44no—
517#121—48no—
518#121—48no—
519#121—48no—
520#121—48no—
521#121—48no—
522#121—48no—
523#121—416no—
524#121—88no—
525#121—88no—
526#120—48no—
527#120—48no—
528C4×Q8—48no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—416no—
537#117—28no—
538#117—28no—
539#117—44no—
540#117—44no—
541#117—44no—
542#117—44no—
543#117—48no—
544C2×C4⋊C4—28no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—42no—
548C2×C4⋊C4—42no—
549C2×C4⋊C4—44no—
550C2×C4⋊C4—84no—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C22⋊C4—44no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—82no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C42—28no—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2418yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2414yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666C24—22no—
667C24—24no—
668C24—41no—
669C24—41no—
670C24—42no—
671C24C2512yes—
672C24C2514yes—
673C24C2514yes—
674C24C2511yescharacteristic
675#41—464no—
676#41—464no—
677#41—432no—
678#41—432no—
679C2×Q8—24no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—24no—
685C2×Q8—24no—
686C2×Q8—28no—
687C2×Q8—24no—
688C2×Q8—44no—
689C2×Q8—48no—
690C2×Q8—464no—
691C2×Q8—416no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C22×C4—24no—
731C22×C4—22no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—48no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—416no—
765C22×C4H(5,𝔽2)14yes—
766C22×C4H(5,𝔽2)18yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2518yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—41no—
791C4⋊C4—41no—
792C4⋊C4—42no—
793C4⋊C4—42no—
794C4⋊C4—41no—
795C4⋊C4—41no—
796C4⋊C4—48no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—48no—
816C4⋊C4—44no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—48no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—44no—
855C42—24no—
856C42—24no—
857C42—24no—
858C42—24no—
859C42—28no—
860C42—28no—
861C42—44no—
862C42—48no—
863C42—44no—
864C23—21no—
865C23—21no—
866C23—22no—
867C23—22no—
868C23—24no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—22no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—44no—
889C23—44no—
890C23—44no—
891C23—84no—
892C23—84no—
893C23C2×H(5,𝔽2)14yes—
894C23C2×H(5,𝔽2)12yes—
895C23C2611yescharacteristic
896Q8—416no—
897Q8—416no—
898Q8—48no—
899Q8—48no—
900D4—416no—
901D4—416no—
902D4—416no—
903D4—48no—
904D4—48no—
905D4—88no—
906D4—88no—
907D4—88no—
908D4—88no—
909D4—88no—
910D4—88no—
911D4—164no—
912D4—168no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—432no—
956C2×C4—44no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—416no—
961C2×C4—416no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—88no—
965C2×C4—84no—
966C2×C4—168no—
967C2×C4#560116yes—
968C2×C4C2×H(5,𝔽2)14yes—
969C2×C4C2×H(5,𝔽2)14yes—
970C2×C4C2×H(5,𝔽2)14yes—
971C22—22no—
972C22—24no—
973C22—22no—
974C22—24no—
975C22—44no—
976C22—44no—
977C22—42no—
978C22—44no—
979C22—42no—
980C22—42no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—44no—
993C22—44no—
994C22—42no—
995C22—44no—
996C22—88no—
997C22C2×#56014yes—
998C22C22×H(5,𝔽2)11yescharacteristic
999C22C22×H(5,𝔽2)12yes—
1000C22H(7,𝔽2)11yescharacteristic
1001C222−1+611yescharacteristic
1002C222−1+612yes—
1003C4—42no—
1004C4—42no—
1005C4—44no—
1006C4—48no—
1007C4—44no—
1008C4—44no—
1009C4—42no—
1010C4—42no—
1011C4—44no—
1012C4—44no—
1013C4—41no—
1014C4—41no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4C2×#56018yes—
1019C2—24no—
1020C2—84no—
1021C2—84no—
1022C2—82no—
1023C2C22×#56011yescharacteristic
1024C2#6287511yescharacteristic
1025C2#6287812yes—
1026C2#6288611yescharacteristic
1027C2#6288812yes—
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. #53151C2semidirect
2. #53136C2semidirect
3. #53128C2semidirect
4. #53095C2semidirect
5. #53060C2semidirect
6. #53051C2semidirect
7. #53011C2semidirect
8. #52962C2semidirect
9. #52799C2semidirect
10. #52549C2semidirect
11. #52369C2semidirect
12. #35660C2semidirect
13. #35659C2semidirect
14. #35634C2semidirect
15. #35619C2semidirect
16. #35564C2semidirect
17. #35545C2semidirect
18. #35518C2semidirect
19. #34633C2semidirect
20. C2×#2625C2semidirect
31. #2843C22semidirect
32. #2841C22semidirect
34. #2838C22semidirect
36. #2830C22semidirect
38. #2829C22semidirect
40. #2828C22semidirect
42. #2827C22semidirect
43. #2827C22semidirect
44. #2826C22semidirect
47. #2823C22semidirect
52. #2795C22semidirect
53. #2792C22semidirect
54. #2790C22semidirect
55. #2790C22semidirect
56. #2784C22semidirect
57. #2780C22semidirect
59. #2749C22semidirect
60. #2746C22semidirect
63. #2699C22semidirect
65. #2691C22semidirect
93. #2514C22semidirect
94. #2513C22semidirect
95. #2512C22semidirect
96. #2511C22semidirect
98. #2503C22semidirect
99. #2502C22semidirect
101. #2499C22semidirect
102. #2499C22semidirect
103. #2497C22semidirect
104. #2496C22semidirect
105. #2495C22semidirect
106. #2494C22semidirect
108. #2447C22semidirect
109. #2447C22semidirect
110. #2446C22semidirect
111. #2446C22semidirect
112. #2436C22semidirect
113. #2434C22semidirect
114. #2432C22semidirect
115. #2431C22semidirect
118. #2429C22semidirect
119. #2428C22semidirect
120. #2427C22semidirect
121. #2426C22semidirect
127. #2417C22semidirect
130. #2416C22semidirect
132. #2415C22semidirect
134. #2414C22semidirect
137. #2409C22semidirect
138. #2409C22semidirect
141. #2407C22semidirect
142. #2407C22semidirect

Maximal subgroups

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

subgroupindex
#531512
#531362
#531282
#530952
#530602
#530512
#530112
#529622
#527992
#525492
#523692
#356602
#356592
#356342
#356192
#355642
#355452
#355182
#346332
C2×#26252