Finite Group Databasebeta

← #7634884

Subgroups — #7634884

Order 512.

5794 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52280C214yesmaximal, complemented
2#52278C214yesmaximal, complemented
3#52277C218yesmaximal, complemented
4#37431C214yesmaximal, complemented
5#37393C212yesmaximal, complemented
6#37325C214yesmaximal, complemented
7#37324C212yesmaximal, complemented
8#37317C212yesmaximal, complemented
9#37316C212yesmaximal, complemented
10#37198C214yesmaximal, complemented
11#37140C214yesmaximal, complemented
12#36758C218yesmaximal, complemented
13#36625C211yesmaximal, characteristic, complemented
14#36624C211yesmaximal, characteristic, complemented
15#34814C212yesmaximal, complemented
16#34813C212yesmaximal, complemented
17#34743C212yesmaximal, complemented
18#34742C212yesmaximal, complemented
19#34632C212yesmaximal, complemented
20#34065C212yesmaximal, complemented
21C2×#2297C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C2×#533C2211yescharacteristic
24C2×#532C2211yescharacteristic
25C2×#525C2212yes—
26C2×#525C2212yes—
27C2×#525C2212yes—
28C2×C4×#41C2212yes—
29C22×#117C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2857C2211yescharacteristic, complemented
32#2857C2211yescharacteristic, complemented
33#2857C2212yescomplemented
34#2857C2212yescomplemented
35#2856C2211yescharacteristic, complemented
36#2856C2211yescharacteristic, complemented
37#2855C2214yes—
38#2854C2214yes—
39#2851C2212yescomplemented
40#2851C2212yescomplemented
41#2850C2212yescomplemented
42#2850C2212yescomplemented
43#2848C2214yes—
44#2847C2214yes—
45#2808C2214yescomplemented
46#2808C2214yescomplemented
47#2806C2214yescomplemented
48#2805C2214yescomplemented
49#2804C2214yescomplemented
50#2803C2218yescomplemented
51#2803C2218yescomplemented
52#2800C2218yescomplemented
53#2797C2218yescomplemented
54#2797C2218yescomplemented
55#2788C2218yescomplemented
56#2781C2218yescomplemented
57#2779C2218yescomplemented
58#2778C2218yescomplemented
59#2778C2218yescomplemented
60#2775C2218yescomplemented
61#2774C2218yescomplemented
62#2759C2218yescomplemented
63#2756C2218yescomplemented
64#2753C2218yescomplemented
65#2751C2218yescomplemented
66#2749C2218yescomplemented
67#2745C2218yescomplemented
68#2741C2218yescomplemented
69#2733C2214yescomplemented
70#2730C2218yescomplemented
71#2727C2214yescomplemented
72#2714C2218yescomplemented
73#2714C2218yescomplemented
74#2710C2218yescomplemented
75#2703C2218yescomplemented
76#2702C2218yescomplemented
77#2696C2218yescomplemented
78#2688C2218yescomplemented
79#2682C2214yescomplemented
80#2676C2218yescomplemented
81#2616C2214yes—
82#2616C2214yes—
83#2615C2214yes—
84#2615C2214yes—
85#2614C2214yes—
86#2613C2214yes—
87#2613C2214yes—
88#2613C2214yes—
89#2497C2214yescomplemented
90#2496C2214yescomplemented
91#2495C2214yescomplemented
92#2494C2214yescomplemented
93#2493C2218yes—
94#2492C2214yescomplemented
95#2491C2214yescomplemented
96#2490C2214yescomplemented
97#2489C2214yescomplemented
98#2488C2218yes—
99#2480C2218yes—
100#2472C2218yes—
101#2429C2214yescomplemented
102#2428C2214yescomplemented
103#2427C2214yescomplemented
104#2426C2214yescomplemented
105#2425C2218yes—
106#2424C2218yes—
107#2423C2214yescomplemented
108#2422C2214yescomplemented
109#2421C2214yescomplemented
110#2420C2214yescomplemented
111#2419C2218yes—
112#2418C2218yes—
113#2401C2218yescomplemented
114#2398C2218yescomplemented
115#2395C2218yescomplemented
116#2392C2218yescomplemented
117#2388C2218yes—
118#2388C2218yes—
119#2324C2214yescomplemented
120#2324C2214yescomplemented
121#2323C2214yescomplemented
122#2323C2214yescomplemented
123#2322C2218yes—
124#2321C2218yes—
125C4×#126C2218yescomplemented
126C4×#124C2218yescomplemented
127C4×C22⋊Q8C2214yescomplemented
128C4×C22⋊Q8C2214yescomplemented
129C4×#123C2218yescomplemented
130C4×#121C2214yescomplemented
131C4×#121C2214yescomplemented
132C4×#121C2218yescomplemented
133#2297C2212yes—
134#2297C2212yes—
135#2297C2212yes—
136#2297C2214yes—
137#2297C2212yes—
138#2297C2212yes—
139#2297C2212yes—
140#2297C2212yes—
141#2297C2212yes—
142#2296C2212yes—
143#2296C2212yes—
144C2×#391C2212yes—
145#2293C2214yescomplemented
146#2293C2214yescomplemented
147C2×#390C2212yes—
148#2290C2214yescomplemented
149#2290C2214yescomplemented
150C2×#386C2214yes—
151#2285C2211yescharacteristic
152#2285C2211yescharacteristic
153#2280C2212yes—
154#2280C2212yes—
155#2280C2212yes—
156C4×#117C2212yes—
157C2×C4×C22⋊C4C2212yes—
158C2×C4×C22⋊C4C2212yes—
159C22×#41—28no—
160C22×#41—44no—
161C22×#41—44no—
162C22×#41C2312yes—
163C22×#41C2312yes—
164C22×#41C2312yes—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C23×Q8C2311yescharacteristic
168C23×D4C2312yes—
169C23×D4C2311yescharacteristic
170C24×C4C2312yes—
171C24×C4C2311yescharacteristic
172C24×C4C2312yes—
173#533—44no—
174#532—44no—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2312yes—
177C2×#127C2311yescharacteristic
178C2×#126C2318yes—
179C2×#125C2312yes—
180C2×#124C2312yes—
181C2×#124C2318yes—
182#525—216no—
183#525—48no—
184#525—48no—
185C2×#123C2314yes—
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2318yes—
204C2×#120C2314yes—
205C2×#120C2314yes—
206C2×#120C2314yes—
207C4×#41—48no—
208C2×C4×Q8C2314yes—
209C2×C4×Q8C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2314yes—
217C2×#117—44no—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C2×#117C2311yescharacteristic
225C2×#117C2312yes—
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2314yes—
231C22×C42—44no—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2312yes—
241C22×C42C2312yes—
242C22×C42C2314yes—
243#401C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#398C2318yes—
252#398C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#395C2318yes—
266#395C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#393C2318yes—
281#393C2318yes—
282#393C2318yes—
283#393C2318yes—
284#392C2318yes—
285#392C2318yes—
286#392C2318yes—
287#392C2318yes—
288#392C2318yes—
289#392C2318yes—
290#392C2318yes—
291#391C2314yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2318yes—
297#391C2312yes—
298#391C2314yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#390C2318yes—
304#390C2318yes—
305#390C2314yes—
306#390C2312yes—
307#390C2312yes—
308#390C2314yes—
309#390C2314yes—
310#390C2318yes—
311#390C2312yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#389C2318yes—
319#389C2318yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#388C2318yes—
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#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2314yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2314yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2312yes—
384#383C2318yes—
385#382C2312yes—
386#382C2312yes—
387#382C2318yes—
388#381C2314yes—
389#381C2314yes—
390#381C2314yes—
391#381C2318yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#379C2314yes—
406#379C2314yes—
407#379C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431#376C2314yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C43C2314yes—
435C25C2412yes—
436C25C2411yescharacteristic
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—44no—
445C2×#41—44no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41—44no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—464no—
453C22×Q8—24no—
454C22×Q8—42no—
455C22×Q8—42no—
456C22×Q8C2412yes—
457C22×Q8C2414yes—
458C22×Q8C2412yes—
459C22×Q8C2412yes—
460C22×D4—28no—
461C22×D4—24no—
462C22×D4—42no—
463C22×D4—42no—
464C22×D4—44no—
465C22×D4—44no—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2418yes—
476C22×D4C2418yes—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—28no—
480C23×C4—28no—
481C23×C4—28no—
482C23×C4—44no—
483C23×C4—44no—
484C23×C4—44no—
485C23×C4#4118yes—
486C23×C4C2414yes—
487C23×C4C2412yes—
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2414yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2418yes—
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C4⋊Q8—44no—
505C4⋊Q8—42no—
506#127—42no—
507#126—416no—
508#125—44no—
509#124—44no—
510#124—416no—
511#123—216no—
512#123—416no—
513#123—48no—
514#123—48no—
515C22⋊Q8—28no—
516C22⋊Q8—28no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C22⋊Q8—48no—
520C22⋊Q8—48no—
521C22⋊Q8—48no—
522#121—28no—
523#121—28no—
524#121—48no—
525#121—416no—
526#121—48no—
527#121—48no—
528#121—48no—
529#121—48no—
530#120—216no—
531#120—48no—
532#120—48no—
533C4×Q8—48no—
534C4×Q8—48no—
535C4×D4—216no—
536C4×D4—216no—
537C4×D4—48no—
538C4×D4—416no—
539C4×D4—416no—
540C4×D4—48no—
541C4×D4—416no—
542#117—28no—
543#117—28no—
544#117—28no—
545#117—42no—
546#117—44no—
547#117—42no—
548#117—44no—
549#117—44no—
550#117—48no—
551C2×C4⋊C4—44no—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C22⋊C4—48no—
576C2×C22⋊C4—48no—
577C2×C22⋊C4—44no—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C42—28no—
613C2×C42—24no—
614C2×C42—24no—
615C2×C42—48no—
616C2×C42—44no—
617C2×C42—44no—
618C2×C42—42no—
619C2×C42—42no—
620C2×C42—42no—
621C2×C42—42no—
622C2×C42—44no—
623C2×C42C2414yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2418yes—
636C2×C42C2418yes—
637C2×C42C2418yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668C24—22no—
669C24—22no—
670C24—24no—
671C24—24no—
672C24—24no—
673C24—42no—
674C24—42no—
675C24—44no—
676C24—44no—
677C24C2×#4114yes—
678C24C2514yes—
679C24C2514yes—
680C24C2511yescharacteristic
681C24C2511yescharacteristic
682C24C2511yescharacteristic
683#41—432no—
684#41—432no—
685#41—432no—
686#41—432no—
687#41—432no—
688C2×Q8—24no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—24no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—42no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—42no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—416no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—28no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—416no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—432no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—232no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—48no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—432no—
782C22×C4—432no—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C22×C4H(5,𝔽2)14yes—
790C22×C4H(5,𝔽2)14yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2518yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—42no—
817C4⋊C4—44no—
818C4⋊C4—42no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—216no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—42no—
847C22⋊C4—44no—
848C22⋊C4—42no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C42—28no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—22no—
869C42—22no—
870C42—22no—
871C42—22no—
872C42—24no—
873C42—28no—
874C42—28no—
875C42—28no—
876C42—42no—
877C42—42no—
878C42—42no—
879C42—42no—
880C42—48no—
881C42—48no—
882C42—48no—
883C23—22no—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—28no—
894C23—24no—
895C23—24no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—28no—
904C23—24no—
905C23—28no—
906C23—44no—
907C23—44no—
908C23—48no—
909C23—48no—
910C23—48no—
911C23—48no—
912C23—48no—
913C23—88no—
914C23—88no—
915C23C22×#4112yes—
916C23C22×#4112yes—
917C23C22×#4112yes—
918C23C2×H(5,𝔽2)12yes—
919C23C2×H(5,𝔽2)12yes—
920C23C2611yescharacteristic
921Q8—48no—
922Q8—48no—
923Q8—48no—
924Q8—88no—
925D4—48no—
926D4—48no—
927D4—416no—
928D4—416no—
929D4—416no—
930D4—48no—
931D4—88no—
932D4—88no—
933D4—88no—
934D4—816no—
935D4—816no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—28no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—48no—
978C2×C4—48no—
979C2×C4—48no—
980C2×C4—48no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—416no—
985C2×C4—416no—
986C2×C4—416no—
987C2×C4—88no—
988C2×C4—816no—
989C2×C4#538116yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C2×H(5,𝔽2)12yes—
995C2×C4C2×H(5,𝔽2)12yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×H(5,𝔽2)12yes—
998C2×C4#58514yes—
999C2×C4#58514yes—
1000C22—24no—
1001C22—24no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—416no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—48no—
1016C22—44no—
1017C22—44no—
1018C22—48no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—816no—
1028C22C2×#53814yes—
1029C22C23×#4111yescharacteristic
1030C22C22×H(5,𝔽2)11yescharacteristic
1031C22C22×H(5,𝔽2)11yescharacteristic
1032C22C2×#58512yes—
1033C22C2×#58512yes—
1034C4—24no—
1035C4—24no—
1036C4—22no—
1037C4—22no—
1038C4—42no—
1039C4—42no—
1040C4—48no—
1041C4—44no—
1042C4—44no—
1043C4—48no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4C2×#53814yes—
1049C4C2×#53814yes—
1050C2—24no—
1051C2—42no—
1052C2—42no—
1053C2—84no—
1054C2—84no—
1055C2C22×#53811yescharacteristic
1056C2#6272912yes—
1057C2#6275912yes—
1058C2#6281511yescharacteristic
1059C2#6281511yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52280C2semidirect
2. #52278C2semidirect
3. #52277C2semidirect
4. #37431C2semidirect
5. #37393C2semidirect
6. #37325C2semidirect
7. #37324C2semidirect
8. #37317C2semidirect
9. #37316C2semidirect
10. #37198C2semidirect
11. #37140C2semidirect
12. #36758C2semidirect
13. #36625C2semidirect
14. #36624C2semidirect
15. #34814C2semidirect
16. #34813C2semidirect
17. #34743C2semidirect
18. #34742C2semidirect
19. #34632C2semidirect
20. #34065C2semidirect
21. C2×#2297C2semidirect
31. #2857C22semidirect
32. #2857C22semidirect
33. #2857C22semidirect
34. #2857C22semidirect
35. #2856C22semidirect
36. #2856C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
41. #2850C22semidirect
42. #2850C22semidirect
45. #2808C22semidirect
46. #2808C22semidirect
47. #2806C22semidirect
48. #2805C22semidirect
49. #2804C22semidirect
50. #2803C22semidirect
51. #2803C22semidirect
52. #2800C22semidirect
53. #2797C22semidirect
54. #2797C22semidirect
55. #2788C22semidirect
56. #2781C22semidirect
57. #2779C22semidirect
58. #2778C22semidirect
59. #2778C22semidirect
60. #2775C22semidirect
61. #2774C22semidirect
62. #2759C22semidirect
63. #2756C22semidirect
64. #2753C22semidirect
65. #2751C22semidirect
66. #2749C22semidirect
67. #2745C22semidirect
68. #2741C22semidirect
69. #2733C22semidirect
70. #2730C22semidirect
71. #2727C22semidirect
72. #2714C22semidirect
73. #2714C22semidirect
74. #2710C22semidirect
75. #2703C22semidirect
76. #2702C22semidirect
77. #2696C22semidirect
78. #2688C22semidirect
79. #2682C22semidirect
80. #2676C22semidirect
89. #2497C22semidirect
90. #2496C22semidirect
91. #2495C22semidirect
92. #2494C22semidirect
94. #2492C22semidirect
95. #2491C22semidirect
96. #2490C22semidirect
97. #2489C22semidirect
101. #2429C22semidirect
102. #2428C22semidirect
103. #2427C22semidirect
104. #2426C22semidirect
107. #2423C22semidirect
108. #2422C22semidirect
109. #2421C22semidirect
110. #2420C22semidirect
113. #2401C22semidirect
114. #2398C22semidirect
115. #2395C22semidirect
116. #2392C22semidirect
119. #2324C22semidirect
120. #2324C22semidirect
121. #2323C22semidirect
122. #2323C22semidirect
125. C4×#126C22semidirect
126. C4×#124C22semidirect
127. C4×C22⋊Q8C22semidirect
128. C4×C22⋊Q8C22semidirect
129. C4×#123C22semidirect
130. C4×#121C22semidirect
131. C4×#121C22semidirect
132. C4×#121C22semidirect
145. #2293C22semidirect
146. #2293C22semidirect
148. #2290C22semidirect
149. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#522802
#522782
#522772
#374312
#373932
#373252
#373242
#373172
#373162
#371982
#371402
#367582
#366252
#366242
#348142
#348132
#347432
#347422
#346322
#340652
C2×#22972