Finite Group Databasebeta

← #7643462

Subgroups — #7643462

Order 512.

5644 conjugacy classes of subgroups.

The subgroup lattice has 1039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39985C214yesmaximal, complemented
2#39984C214yesmaximal, complemented
3#39179C214yesmaximal, complemented
4#38962C214yesmaximal, complemented
5#38448C218yesmaximal, complemented
6#38096C218yesmaximal, complemented
7#37426C212yesmaximal, complemented
8#37425C212yesmaximal, complemented
9#37310C214yesmaximal, complemented
10#36625C211yesmaximal, characteristic, complemented
11C2×#2851C211yesmaximal, characteristic, complemented
12#35639C212yesmaximal, complemented
13#35620C212yesmaximal, complemented
14#35575C212yesmaximal, complemented
15#35519C212yesmaximal, complemented
16#35253C212yesmaximal, complemented
17#35079C214yesmaximal, complemented
18#35033C212yesmaximal, complemented
19#35020C212yesmaximal, complemented
20#34175C212yesmaximal
21C2×#2297C211yesmaximal, characteristic
22C23×#41C2211yescharacteristic
23C2×#544C2212yescomplemented
24C2×#533C2211yescharacteristic, complemented
25C22×#125C2211yescharacteristic, complemented
26C2×#520C2212yes—
27C2×#520C2212yes—
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857C2212yes—
31#2857C2214yes—
32#2857C2212yescomplemented
33#2855C2214yescomplemented
34#2851C2212yes—
35#2851C2214yes—
36#2851C2214yes—
37#2851C2212yes—
38#2851C2211yescharacteristic
39#2851C2211yescharacteristic
40#2851C2214yescomplemented
41#2851C2212yescomplemented
42#2851C2212yescomplemented
43#2851C2211yescharacteristic, complemented
44#2851C2211yescharacteristic, complemented
45#2848C2214yes—
46#2809C2218yescomplemented
47#2806C2218yescomplemented
48#2804C2218yescomplemented
49#2799C2218yescomplemented
50#2799C2218yescomplemented
51#2784C2218yescomplemented
52#2784C2218yescomplemented
53#2780C2218yescomplemented
54#2780C2218yescomplemented
55#2780C2218yescomplemented
56#2780C2218yescomplemented
57#2748C2218yescomplemented
58#2748C2218yescomplemented
59#2732C2218yescomplemented
60#2692C2218yescomplemented
61#2692C2218yescomplemented
62#2667C2218yescomplemented
63#2665C2218yescomplemented
64#2646C2218yes—
65#2629C2214yescomplemented
66#2628C2214yescomplemented
67#2626C2218yes—
68#2608C2218yescomplemented
69#2607C2218yescomplemented
70#2582C2214yescomplemented
71#2581C2214yescomplemented
72#2580C2214yescomplemented
73#2579C2218yescomplemented
74#2569C2218yes—
75#2569C2218yescomplemented
76#2569C2218yescomplemented
77#2568C2214yescomplemented
78#2566C2214yescomplemented
79#2565C2214yescomplemented
80#2564C2218yescomplemented
81#2563C2214yescomplemented
82#2549C2218yes—
83#2538C2214yescomplemented
84#2487C2218yescomplemented
85#2454C2214yescomplemented
86#2454C2214yescomplemented
87#2454C2214yescomplemented
88#2453C2214yescomplemented
89#2453C2214yescomplemented
90#2453C2214yescomplemented
91#2452C2214yescomplemented
92#2451C2214yescomplemented
93#2450C2218yescomplemented
94#2450C2218yescomplemented
95#2450C2218yescomplemented
96#2449C2218yescomplemented
97#2442C2214yes—
98#2442C2214yescomplemented
99#2442C2214yescomplemented
100#2442C2214yescomplemented
101#2442C2214yescomplemented
102#2442C2214yescomplemented
103#2442C2214yescomplemented
104#2441C2214yescomplemented
105#2441C2214yescomplemented
106#2441C2214yescomplemented
107#2441C2214yescomplemented
108#2441C2214yescomplemented
109#2440C2214yes—
110#2440C2214yescomplemented
111#2440C2214yescomplemented
112#2439C2214yescomplemented
113#2439C2214yescomplemented
114#2439C2214yescomplemented
115#2439C2214yescomplemented
116#2439C2214yescomplemented
117#2438C2218yescomplemented
118#2437C2218yes—
119#2437C2218yes—
120#2437C2218yes—
121#2417C2218yescomplemented
122#2341C2214yes—
123Q8×C22⋊C4C2214yes—
124#2339C2218yes—
125#2339C2214yes—
126D4×C22⋊C4C2214yes—
127D4×C22⋊C4C2218yes—
128#2329C2218yes—
129#2329C2218yescomplemented
130#2329C2218yescomplemented
131#2317C2212yescomplemented
132#2317C2212yescomplemented
133#2316C2212yescomplemented
134#2315C2218yes—
135#2311C2212yes—
136#2311C2214yes—
137#2311C2214yes—
138#2311C2212yes—
139C4×C22⋊Q8C2214yes—
140C4×C22⋊Q8C2214yescomplemented
141#2297C2212yes—
142#2297C2214yes—
143#2297C2212yes—
144#2297C2212yes—
145#2297C2212yes—
146#2297C2212yes—
147#2297C2212yes—
148#2296C2212yescomplemented
149C2×#391C2212yes—
150C2×#390C2212yes—
151C2×#389C2212yescomplemented
152C2×#387C2214yescomplemented
153C2×#386C2214yes—
154C2×#385C2214yes—
155#2285C2211yescharacteristic, complemented
156C2×#382C2211yescharacteristic, complemented
157#2280C2214yes—
158#2280C2212yes—
159C2×#380C2214yes—
160C2×#380C2212yes—
161C2×C4×C22⋊C4C2212yes—
162C2×C4×C22⋊C4C2212yes—
163C22×#41—44no—
164C22×#41—44no—
165C22×#41Q8116yescomplemented
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2312yes—
172C23×D4C2311yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2312yes—
175C24×C4C2312yes—
176#544—48no—
177#533—44no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2314yes—
181C2×#125—44no—
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2311yescharacteristic
187C2×#125C2311yescharacteristic
188C2×#125C2314yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196#520—48no—
197#520—48no—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×#117—44no—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2314yes—
222C22×C22⋊C4C2318yes—
223C22×C22⋊C4C2314yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C42—44no—
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2312yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#399C2318yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#393C2318yes—
274#393C2318yes—
275#393C2318yes—
276#393C2318yes—
277#393C2318yes—
278#391C2312yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2318yes—
283#391C2312yes—
284#391C2318yes—
285#391C2318yes—
286#391C2312yes—
287#391C2312yes—
288#391C2318yes—
289#391C2318yes—
290#391C2314yes—
291#391C2318yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#390C2312yes—
296#390C2314yes—
297#390C2312yes—
298#390C2318yes—
299#390C2314yes—
300#390C2318yes—
301#390C2312yes—
302#390C2314yes—
303#390C2312yes—
304#390C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#389C2318yes—
317#389C2314yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2314yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#386C2314yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2314yes—
355#386C2314yes—
356#386C2314yes—
357#386C2314yes—
358#386C2314yes—
359#386C2314yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#385C2318yes—
381#385C2318yes—
382#384C2314yes—
383#384C2314yes—
384#384C2312yes—
385#382C2314yes—
386#382C2314yes—
387#382C2314yes—
388#382C2311yescharacteristic
389#382C2312yes—
390#382C2312yes—
391#382C2311yescharacteristic
392#381C2314yes—
393#381C2318yes—
394#380C2318yes—
395#380C2318yes—
396#380C2314yes—
397#380C2318yes—
398#380C2314yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2318yes—
407#380C2318yes—
408#380C2318yes—
409#380C2318yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2312yes—
418#380C2312yes—
419#379C2314yes—
420#379C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2318yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C25C2411yescharacteristic
443C25C2412yes—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41—44no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—464no—
453C2×#41C2×Q8116yes—
454C2×#41C2×Q8116yes—
455C2×#41C2×Q8116yes—
456C2×#41C2×Q8116yes—
457C22×Q8—42no—
458C22×Q8—42no—
459C22×Q8C2×Q818yes—
460C22×Q8C2412yes—
461C22×Q8C2414yes—
462C22×Q8C2418yes—
463C22×Q8C2412yes—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—44no—
467C22×D4—44no—
468C22×D4C2×Q818yes—
469C22×D4C2×Q8116yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—44no—
477C23×C4—44no—
478C23×C4—44no—
479C23×C4—44no—
480C23×C4—44no—
481C23×C4C2×Q818yes—
482C23×C4C2×Q8116yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2418yes—
498C23×C4C2418yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2414yes—
502C23×C4C2411yescharacteristic
503C4⋊Q8—44no—
504C4⋊Q8—48no—
505C4⋊Q8—48no—
506#125—44no—
507#125—44no—
508#125—48no—
509#125—42no—
510#125—42no—
511#125—48no—
512#125—48no—
513C22⋊Q8—48no—
514C22⋊Q8—416no—
515C22⋊Q8—48no—
516C22⋊Q8—416no—
517C22⋊Q8—416no—
518C22⋊Q8—416no—
519C22⋊Q8—48no—
520C4×Q8—48no—
521C4×Q8—48no—
522C4×Q8—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—416no—
526C4×D4—416no—
527#117—28no—
528#117—28no—
529#117—28no—
530#117—44no—
531#117—44no—
532#117—42no—
533#117—42no—
534#117—48no—
535#117—48no—
536C2×C4⋊C4—28no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—48no—
539C2×C4⋊C4—44no—
540C2×C4⋊C4—48no—
541C2×C4⋊C4—48no—
542C2×C4⋊C4—48no—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—48no—
580C2×C22⋊C4—416no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4—48no—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C42—24no—
609C2×C42—24no—
610C2×C42—44no—
611C2×C42—44no—
612C2×C42—44no—
613C2×C42—42no—
614C2×C42—42no—
615C2×C42—42no—
616C2×C42—42no—
617C2×C42—44no—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2412yes—
626C2×C42C2411yescharacteristic
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2418yes—
630C2×C42C2418yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2418yes—
655#95C2418yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669C24—22no—
670C24—22no—
671C24—24no—
672C24—28no—
673C24—42no—
674C24—44no—
675C24—42no—
676C24—42no—
677C24C22×Q814yes—
678C24C22×Q818yes—
679C24C2511yescharacteristic
680C24C2514yes—
681C24C2511yescharacteristic
682C24C2511yescharacteristic
683#41—264no—
684#41—432no—
685#41—432no—
686#41—432no—
687C2×Q8—24no—
688C2×Q8—24no—
689C2×Q8—28no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—48no—
695C2×Q8—48no—
696C2×Q8—48no—
697C2×Q8—416no—
698C2×Q8C22×Q818yes—
699C2×Q8C22×Q818yes—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—416no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4—432no—
710C2×D4C22×Q8116yes—
711C2×D4C22×Q818yes—
712C2×D4C22×Q818yes—
713C2×D4C22×Q8116yes—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—232no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—432no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4—432no—
766C22×C4C22×Q814yes—
767C22×C4C22×Q814yes—
768C22×C4C22×Q814yes—
769C22×C4C22×Q814yes—
770C22×C4C22×Q814yes—
771C22×C4C22×Q8116yes—
772C22×C4C22×Q818yes—
773C22×C4C22×Q8116yes—
774C22×C4C22×Q814yes—
775C22×C4H(5,𝔽2)14yes—
776C22×C4H(5,𝔽2)14yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2518yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—216no—
805C4⋊C4—28no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—216no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C42—24no—
855C42—24no—
856C42—22no—
857C42—22no—
858C42—22no—
859C42—22no—
860C42—28no—
861C42—28no—
862C42—28no—
863C42—42no—
864C42—42no—
865C42—42no—
866C42—42no—
867C42—42no—
868C42—42no—
869C42—48no—
870C42—48no—
871C23—21no—
872C23—21no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—24no—
878C23—24no—
879C23—21no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—22no—
884C23—22no—
885C23—24no—
886C23—28no—
887C23—28no—
888C23—216no—
889C23—44no—
890C23—48no—
891C23—48no—
892C23—48no—
893C23—48no—
894C23—88no—
895C23—88no—
896C23C23×Q812yes—
897C23C23×Q818yes—
898C23C23×Q812yes—
899C23C23×Q812yes—
900C23C2×H(5,𝔽2)12yes—
901C23C2×H(5,𝔽2)12yes—
902C23#58514yes—
903C23C2611yescharacteristic
904Q8—216no—
905Q8—48no—
906Q8—88no—
907Q8—168no—
908D4—232no—
909D4—216no—
910D4—48no—
911D4—416no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—232no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—48no—
960C2×C4—416no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—48no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—48no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4—88no—
970C2×C4—168no—
971C2×C4—168no—
972C2×C4#543116yes—
973C2×C4C23×Q812yes—
974C2×C4C23×Q812yes—
975C2×C4C23×Q818yes—
976C2×C4C23×Q812yes—
977C2×C4C23×Q812yes—
978C2×C4C2×H(5,𝔽2)12yes—
979C2×C4C2×H(5,𝔽2)12yes—
980C2×C4C2×H(5,𝔽2)12yes—
981C2×C4C2×H(5,𝔽2)12yes—
982C2×C4#58514yes—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—22no—
991C22—22no—
992C22—28no—
993C22—22no—
994C22—28no—
995C22—22no—
996C22—28no—
997C22—416no—
998C22—42no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—816no—
1005C22C2×#54314yes—
1006C22#350414yes—
1007C22C24×Q811yescharacteristic
1008C22C22×H(5,𝔽2)11yescharacteristic
1009C22C22×H(5,𝔽2)11yescharacteristic
1010C22C2×#58512yes—
1011C22C2×#58512yes—
1012C4—24no—
1013C4—22no—
1014C4—22no—
1015C4—28no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—48no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—48no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4C2×#54314yes—
1028C4C2×#54314yes—
1029C2—24no—
1030C2—24no—
1031C2—42no—
1032C2—48no—
1033C2C22×#54311yescharacteristic
1034C2C2×#350411yescharacteristic
1035C2#6281311yescharacteristic
1036C2#6282112yes—
1037C2#6283012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39985C2semidirect
2. #39984C2semidirect
3. #39179C2semidirect
4. #38962C2semidirect
5. #38448C2semidirect
6. #38096C2semidirect
7. #37426C2semidirect
8. #37425C2semidirect
9. #37310C2semidirect
10. #36625C2semidirect
11. C2×#2851C2semidirect
12. #35639C2semidirect
13. #35620C2semidirect
14. #35575C2semidirect
15. #35519C2semidirect
16. #35253C2semidirect
17. #35079C2semidirect
18. #35033C2semidirect
19. #35020C2semidirect
23. C2×#544C22semidirect
24. C2×#533C22semidirect
25. C22×#125C22semidirect
32. #2857C22semidirect
33. #2855C22semidirect
40. #2851C22semidirect
41. #2851C22semidirect
42. #2851C22semidirect
43. #2851C22semidirect
44. #2851C22semidirect
46. #2809C22semidirect
47. #2806C22semidirect
48. #2804C22semidirect
49. #2799C22semidirect
50. #2799C22semidirect
51. #2784C22semidirect
52. #2784C22semidirect
53. #2780C22semidirect
54. #2780C22semidirect
55. #2780C22semidirect
56. #2780C22semidirect
57. #2748C22semidirect
58. #2748C22semidirect
59. #2732C22semidirect
60. #2692C22semidirect
61. #2692C22semidirect
62. #2667C22semidirect
63. #2665C22semidirect
65. #2629C22semidirect
66. #2628C22semidirect
68. #2608C22semidirect
69. #2607C22semidirect
70. #2582C22semidirect
71. #2581C22semidirect
72. #2580C22semidirect
73. #2579C22semidirect
75. #2569C22semidirect
76. #2569C22semidirect
77. #2568C22semidirect
78. #2566C22semidirect
79. #2565C22semidirect
80. #2564C22semidirect
81. #2563C22semidirect
83. #2538C22semidirect
84. #2487C22semidirect
85. #2454C22semidirect
86. #2454C22semidirect
87. #2454C22semidirect
88. #2453C22semidirect
89. #2453C22semidirect
90. #2453C22semidirect
91. #2452C22semidirect
92. #2451C22semidirect
93. #2450C22semidirect
94. #2450C22semidirect
95. #2450C22semidirect
96. #2449C22semidirect
98. #2442C22semidirect
99. #2442C22semidirect
100. #2442C22semidirect
101. #2442C22semidirect
102. #2442C22semidirect
103. #2442C22semidirect
104. #2441C22semidirect
105. #2441C22semidirect
106. #2441C22semidirect
107. #2441C22semidirect
108. #2441C22semidirect
110. #2440C22semidirect
111. #2440C22semidirect
112. #2439C22semidirect
113. #2439C22semidirect
114. #2439C22semidirect
115. #2439C22semidirect
116. #2439C22semidirect
117. #2438C22semidirect
121. #2417C22semidirect
129. #2329C22semidirect
130. #2329C22semidirect
131. #2317C22semidirect
132. #2317C22semidirect
133. #2316C22semidirect
140. C4×C22⋊Q8C22semidirect
148. #2296C22semidirect
151. C2×#389C22semidirect
152. C2×#387C22semidirect
155. #2285C22semidirect
156. C2×#382C22semidirect
165. C22×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#399852
#399842
#391792
#389622
#384482
#380962
#374262
#374252
#373102
#366252
C2×#28512
#356392
#356202
#355752
#355192
#352532
#350792
#350332
#350202
#341752
C2×#22972