Finite Group Databasebeta

← #7712781

Subgroups — #7712781

Order 512.

5608 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60035C214yesmaximal, complemented
2#59193C214yesmaximal, complemented
3#45742C214yesmaximal, complemented
4#45728C214yesmaximal, complemented
5#39561C214yesmaximal, complemented
6#39435C214yesmaximal, complemented
7#38800C214yesmaximal, complemented
8#38782C214yesmaximal, complemented
9#38464C214yesmaximal, complemented
10#38446C214yesmaximal, complemented
11#37519C212yesmaximal, complemented
12#37386C211yesmaximal, characteristic, complemented
13#37324C212yesmaximal, complemented
14#37307C211yesmaximal, characteristic, complemented
15#36625C212yesmaximal, complemented
16#36207C214yesmaximal, complemented
17#36130C214yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35305C212yesmaximal
20#34412C212yesmaximal, complemented
21C2×#2297C211yesmaximal, characteristic
22C23×#41C2211yescharacteristic
23C2×#541C2212yescomplemented
24C2×#536C2212yes—
25C2×#536C2212yes—
26C2×#533C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yescomplemented
32#2857C2212yescomplemented
33#2857C2212yescomplemented
34#2857C2212yescomplemented
35#2855C2214yes—
36#2855C2214yes—
37#2851C2212yes—
38#2851C2214yescomplemented
39#2851C2214yescomplemented
40#2848C2214yes—
41#2848C2214yes—
42#2848C2214yes—
43#2827C2218yescomplemented
44#2808C2214yescomplemented
45#2806C2214yescomplemented
46#2806C2214yescomplemented
47#2805C2214yescomplemented
48#2796C2218yescomplemented
49#2755C2218yescomplemented
50#2748C2214yescomplemented
51#2741C2218yescomplemented
52#2734C2214yescomplemented
53#2732C2214yescomplemented
54#2728C2218yescomplemented
55#2727C2214yescomplemented
56#2724C2214yescomplemented
57#2723C2218yescomplemented
58#2717C2214yescomplemented
59#2717C2214yescomplemented
60#2715C2218yescomplemented
61#2713C2218yescomplemented
62#2702C2218yescomplemented
63#2695C2218yescomplemented
64#2694C2218yescomplemented
65#2683C2214yescomplemented
66#2666C2218yescomplemented
67#2651C2218yescomplemented
68#2629C2212yescomplemented
69#2625C2214yescomplemented
70#2621C2212yescomplemented
71#2616C2214yes—
72#2616C2214yes—
73#2605C2218yescomplemented
74#2578C2218yescomplemented
75#2575C2218yescomplemented
76#2560C2218yescomplemented
77#2558C2218yescomplemented
78#2556C2218yescomplemented
79#2553C2218yescomplemented
80#2550C2218yescomplemented
81#2549C2218yes—
82#2531C2218yescomplemented
83#2521C2218yescomplemented
84#2518C2218yescomplemented
85#2517C2218yescomplemented
86#2515C2218yescomplemented
87#2505C2218yes—
88#2499C2214yescomplemented
89#2496C2214yescomplemented
90#2495C2214yescomplemented
91#2492C2214yescomplemented
92#2489C2214yescomplemented
93#2482C2218yes—
94#2480C2218yes—
95#2480C2218yes—
96#2478C2218yescomplemented
97#2475C2218yescomplemented
98#2473C2218yes—
99#2473C2218yescomplemented
100#2465C2218yescomplemented
101#2441C2214yescomplemented
102#2440C2214yescomplemented
103#2438C2218yes—
104#2437C2218yes—
105#2435C2214yes—
106#2434C2214yes—
107#2434C2214yescomplemented
108#2432C2214yes—
109#2432C2214yes—
110#2429C2214yescomplemented
111#2429C2214yescomplemented
112#2423C2214yescomplemented
113#2423C2214yescomplemented
114#2406C2214yes—
115#2406C2214yes—
116#2405C2214yes—
117#2405C2214yes—
118#2379C2214yescomplemented
119#2376C2214yescomplemented
120#2374C2214yescomplemented
121#2373C2218yescomplemented
122#2372C2214yescomplemented
123#2362C2214yescomplemented
124#2360C2214yescomplemented
125#2360C2218yescomplemented
126#2346C2214yescomplemented
127#2343C2218yes—
128#2342C2218yes—
129Q8×C22⋊C4C2214yescomplemented
130#2335C2218yescomplemented
131#2331C2218yescomplemented
132#2323C2214yescomplemented
133#2314C2212yescomplemented
134#2311C2212yes—
135#2311C2212yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yescomplemented
138C4×C22⋊Q8C2214yescomplemented
139C4×C22⋊Q8C2214yescomplemented
140C4×C22⋊Q8C2214yescomplemented
141#2297C2211yescharacteristic
142#2297C2214yes—
143#2297C2211yescharacteristic
144#2297C2212yes—
145#2297C2212yes—
146#2297C2211yescharacteristic
147#2297C2212yes—
148#2297C2212yes—
149#2297C2211yescharacteristic
150#2296C2214yes—
151C2×#391C2212yes—
152C2×#390C2212yes—
153C2×#386C2212yes—
154C2×#386C2212yes—
155#2285C2212yes—
156#2280C2214yes—
157#2280C2212yes—
158C2×C4×C22⋊C4C2214yes—
159C22×#41—28no—
160C22×#41—44no—
161C22×#41—44no—
162C22×#41C2312yes—
163C22×#41C2311yescharacteristic
164C22×#41C2311yescharacteristic
165C22×#41C2312yes—
166C22×#41C2311yescharacteristic
167C22×#41C2311yescharacteristic
168C23×Q8C2311yescharacteristic
169C23×Q8C2312yes—
170C23×D4C2311yescharacteristic
171C23×D4C2312yes—
172C24×C4C2311yescharacteristic
173C24×C4C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176#541—48no—
177#536—216no—
178#536—48no—
179#533—48no—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#125C2312yes—
188C2×#125C2314yes—
189C2×#125C2318yes—
190C2×#124C2314yes—
191C2×#124C2314yes—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×C22⋊Q8—48no—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×#117—44no—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2314yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2314yes—
219C2×#117C2311yescharacteristic
220C2×#117C2312yes—
221C2×#117C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2314yes—
229C22×C42—44no—
230C22×C42C2312yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#399C2318yes—
245#399C2318yes—
246#399C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#393C2318yes—
279#391C2314yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2312yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2318yes—
291#391C2314yes—
292#391C2312yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#390C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2312yes—
300#390C2312yes—
301#390C2314yes—
302#390C2312yes—
303#390C2312yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2314yes—
319#389C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#386C2314yes—
351#386C2314yes—
352#386C2314yes—
353#386C2314yes—
354#386C2312yes—
355#386C2314yes—
356#386C2312yes—
357#386C2312yes—
358#386C2312yes—
359#386C2314yes—
360#386C2312yes—
361#386C2314yes—
362#386C2312yes—
363#386C2312yes—
364#386C2312yes—
365#386C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#384C2312yes—
382#384C2312yes—
383#384C2312yes—
384#383C2318yes—
385#382C2312yes—
386#382C2314yes—
387#382C2318yes—
388#382C2318yes—
389#381C2314yes—
390#381C2318yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2318yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#380C2314yes—
406#379C2318yes—
407#379C2318yes—
408#379C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431#376C2318yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C25C2411yescharacteristic
435C25C2412yes—
436C2×#41—24no—
437C2×#41—28no—
438C2×#41—24no—
439C2×#41—28no—
440C2×#41—24no—
441C2×#41—28no—
442C2×#41—42no—
443C2×#41—44no—
444C2×#41—42no—
445C2×#41—44no—
446C2×#41—42no—
447C2×#41—42no—
448C2×#41—42no—
449C2×#41—42no—
450C2×#41—42no—
451C2×#41—42no—
452C2×#41—44no—
453C2×#41—464no—
454C2×#41#4118yes—
455C22×Q8—24no—
456C22×Q8—28no—
457C22×Q8—42no—
458C22×Q8—42no—
459C22×Q8—44no—
460C22×Q8—44no—
461C22×Q8C2414yes—
462C22×Q8C2412yes—
463C22×Q8C2414yes—
464C22×Q8C2414yes—
465C22×Q8C2411yescharacteristic
466C22×Q8C2411yescharacteristic
467C22×D4—24no—
468C22×D4—28no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2412yes—
476C22×D4C2412yes—
477C22×D4C2411yescharacteristic
478C22×D4C2411yescharacteristic
479C22×D4C2412yes—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—28no—
484C23×C4—28no—
485C23×C4—28no—
486C23×C4—44no—
487C23×C4—44no—
488C23×C4—42no—
489C23×C4—42no—
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2412yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2414yes—
508C23×C4C2414yes—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2411yescharacteristic
512C4⋊Q8—216no—
513C4⋊Q8—44no—
514C4⋊Q8—44no—
515C4⋊Q8—44no—
516C4⋊Q8—48no—
517#126—416no—
518#126—416no—
519#125—48no—
520#125—44no—
521#125—416no—
522#124—216no—
523#124—48no—
524#123—216no—
525#123—216no—
526#123—48no—
527#123—48no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—48no—
533C22⋊Q8—48no—
534C22⋊Q8—416no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537C22⋊Q8—48no—
538C22⋊Q8—48no—
539C22⋊Q8—48no—
540C4×Q8—48no—
541C4×Q8—48no—
542C4×Q8—48no—
543#117—28no—
544#117—28no—
545#117—216no—
546#117—42no—
547#117—42no—
548#117—44no—
549#117—48no—
550#117—44no—
551#117—44no—
552C2×C4⋊C4—44no—
553C2×C4⋊C4—48no—
554C2×C4⋊C4—44no—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C22⋊C4—216no—
585C2×C22⋊C4—48no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—48no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C42—28no—
614C2×C42—44no—
615C2×C42—42no—
616C2×C42—42no—
617C2×C42—44no—
618C2×C42—44no—
619C2×C42—42no—
620C2×C42—42no—
621C2×C42—44no—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2414yes—
625C2×C42C2418yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2414yes—
631C2×C42C2418yes—
632C2×C42C2414yes—
633C2×C42C2418yes—
634C2×C42C2418yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2412yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
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—22no—
671C24—24no—
672C24—24no—
673C24—24no—
674C24—28no—
675C24—42no—
676C24—44no—
677C24—42no—
678C24C2512yes—
679C24C2511yescharacteristic
680C24C2512yes—
681C24C2511yescharacteristic
682C24C2511yescharacteristic
683#41—416no—
684#41—432no—
685#41—416no—
686#41—432no—
687#41—416no—
688#41—416no—
689C2×Q8—28no—
690C2×Q8—24no—
691C2×Q8—22no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—24no—
696C2×Q8—28no—
697C2×Q8—41no—
698C2×Q8—42no—
699C2×Q8—41no—
700C2×Q8—41no—
701C2×Q8—41no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—44no—
706C2×Q8—416no—
707C2×Q8—816no—
708C2×Q8C2×#4114yes—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—41no—
718C2×D4—42no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—416no—
729C2×D4—432no—
730C2×D4C2×#4114yes—
731C2×D4C2×#4118yes—
732C22×C4—232no—
733C22×C4—22no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—24no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—41no—
772C22×C4—42no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—42no—
776C22×C4—41no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—416no—
784C22×C4—432no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—44no—
791C22×C4—416no—
792C22×C4C2×#4118yes—
793C22×C4C2×#4114yes—
794C22×C4H(5,𝔽2)14yes—
795C22×C4H(5,𝔽2)14yes—
796C22×C42−1+418yes—
797C22×C4C2512yes—
798C22×C4C2518yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2518yes—
803C22×C4C2518yes—
804C22×C4C2518yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C4⋊C4—28no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—28no—
817C4⋊C4—216no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—216no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—216no—
847C22⋊C4—216no—
848C22⋊C4—216no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C42—28no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—216no—
875C42—42no—
876C42—42no—
877C42—42no—
878C42—42no—
879C42—44no—
880C42—48no—
881C42—44no—
882C42—48no—
883C42—48no—
884C23—21no—
885C23—21no—
886C23—22no—
887C23—28no—
888C23—21no—
889C23—21no—
890C23—22no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—24no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—48no—
906C23—48no—
907C23—48no—
908C23—416no—
909C23—44no—
910C23—44no—
911C23—48no—
912C23—84no—
913C23—88no—
914C23C22×#4112yes—
915C23C22×#4114yes—
916C23C2×H(5,𝔽2)12yes—
917C23C2×H(5,𝔽2)12yes—
918C23C2×2−1+414yes—
919C23C2611yescharacteristic
920Q8—44no—
921Q8—48no—
922Q8—44no—
923Q8—416no—
924Q8—88no—
925Q8—88no—
926D4—44no—
927D4—48no—
928D4—48no—
929D4—48no—
930D4—44no—
931D4—48no—
932D4—48no—
933C2×C4—28no—
934C2×C4—28no—
935C2×C4—28no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—216no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—216no—
955C2×C4—28no—
956C2×C4—28no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—28no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—28no—
978C2×C4—22no—
979C2×C4—44no—
980C2×C4—48no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—48no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—88no—
991C2×C4—88no—
992C2×C4—88no—
993C2×C4C22×#4114yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×H(5,𝔽2)12yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4#58514yes—
1003C22—22no—
1004C22—22no—
1005C22—24no—
1006C22—24no—
1007C22—22no—
1008C22—22no—
1009C22—24no—
1010C22—24no—
1011C22—28no—
1012C22—24no—
1013C22—416no—
1014C22—41no—
1015C22—41no—
1016C22—42no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—44no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—44no—
1027C22—44no—
1028C22—816no—
1029C22#353814yes—
1030C22C23×#4111yescharacteristic
1031C22C22×H(5,𝔽2)11yescharacteristic
1032C22C22×H(5,𝔽2)11yescharacteristic
1033C22C22×2−1+412yes—
1034C22C2×#58512yes—
1035C4—24no—
1036C4—24no—
1037C4—24no—
1038C4—22no—
1039C4—22no—
1040C4—22no—
1041C4—24no—
1042C4—42no—
1043C4—48no—
1044C4—42no—
1045C4—48no—
1046C4—48no—
1047C4—48no—
1048C4—44no—
1049C4—44no—
1050C4#349014yes—
1051C2—24no—
1052C2—42no—
1053C2—42no—
1054C2—44no—
1055C2—82no—
1056C2C2×#353811yescharacteristic
1057C2#6272911yescharacteristic
1058C2C2×#349011yescharacteristic
1059C2#6280512yes—
1060C2#6283512yes—
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. #60035C2semidirect
2. #59193C2semidirect
3. #45742C2semidirect
4. #45728C2semidirect
5. #39561C2semidirect
6. #39435C2semidirect
7. #38800C2semidirect
8. #38782C2semidirect
9. #38464C2semidirect
10. #38446C2semidirect
11. #37519C2semidirect
12. #37386C2semidirect
13. #37324C2semidirect
14. #37307C2semidirect
15. #36625C2semidirect
16. #36207C2semidirect
17. #36130C2semidirect
18. #35310C2semidirect
20. #34412C2semidirect
23. C2×#541C22semidirect
31. #2857C22semidirect
32. #2857C22semidirect
33. #2857C22semidirect
34. #2857C22semidirect
38. #2851C22semidirect
39. #2851C22semidirect
43. #2827C22semidirect
44. #2808C22semidirect
45. #2806C22semidirect
46. #2806C22semidirect
47. #2805C22semidirect
48. #2796C22semidirect
49. #2755C22semidirect
50. #2748C22semidirect
51. #2741C22semidirect
52. #2734C22semidirect
53. #2732C22semidirect
54. #2728C22semidirect
55. #2727C22semidirect
56. #2724C22semidirect
57. #2723C22semidirect
58. #2717C22semidirect
59. #2717C22semidirect
60. #2715C22semidirect
61. #2713C22semidirect
62. #2702C22semidirect
63. #2695C22semidirect
64. #2694C22semidirect
65. #2683C22semidirect
66. #2666C22semidirect
67. #2651C22semidirect
68. #2629C22semidirect
69. #2625C22semidirect
70. #2621C22semidirect
73. #2605C22semidirect
74. #2578C22semidirect
75. #2575C22semidirect
76. #2560C22semidirect
77. #2558C22semidirect
78. #2556C22semidirect
79. #2553C22semidirect
80. #2550C22semidirect
82. #2531C22semidirect
83. #2521C22semidirect
84. #2518C22semidirect
85. #2517C22semidirect
86. #2515C22semidirect
88. #2499C22semidirect
89. #2496C22semidirect
90. #2495C22semidirect
91. #2492C22semidirect
92. #2489C22semidirect
96. #2478C22semidirect
97. #2475C22semidirect
99. #2473C22semidirect
100. #2465C22semidirect
101. #2441C22semidirect
102. #2440C22semidirect
107. #2434C22semidirect
110. #2429C22semidirect
111. #2429C22semidirect
112. #2423C22semidirect
113. #2423C22semidirect
118. #2379C22semidirect
119. #2376C22semidirect
120. #2374C22semidirect
121. #2373C22semidirect
122. #2372C22semidirect
123. #2362C22semidirect
124. #2360C22semidirect
125. #2360C22semidirect
126. #2346C22semidirect
129. Q8×C22⋊C4C22semidirect
130. #2335C22semidirect
131. #2331C22semidirect
132. #2323C22semidirect
133. #2314C22semidirect
137. C4×C22⋊Q8C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×C22⋊Q8C22semidirect
140. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#600352
#591932
#457422
#457282
#395612
#394352
#388002
#387822
#384642
#384462
#375192
#373862
#373242
#373072
#366252
#362072
#361302
#353102
#353052
#344122
C2×#22972