Finite Group Databasebeta

← #7642468

Subgroups — #7642468

Order 512.

5616 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39676C214yesmaximal, complemented
2#39563C214yesmaximal, complemented
3#39540C214yesmaximal, complemented
4#39435C214yesmaximal, complemented
5#37971C214yesmaximal, complemented
6#37957C214yesmaximal, complemented
7#37932C214yesmaximal, complemented
8#37783C214yesmaximal, complemented
9#36819C214yesmaximal, complemented
10#36813C214yesmaximal, complemented
11#36625C212yesmaximal, complemented
12#35440C214yesmaximal, complemented
13#35435C214yesmaximal, complemented
14#35310C212yesmaximal, complemented
15#35305C212yesmaximal
16#35086C212yesmaximal, complemented
17#35033C211yesmaximal, characteristic, complemented
18#35014C212yesmaximal, complemented
19#35011C211yesmaximal, characteristic, complemented
20#34245C212yesmaximal, complemented
21C2×#2297C211yesmaximal, characteristic
22C23×#41C2211yescharacteristic
23C2×#541C2212yescomplemented
24C2×#536C2212yes—
25C2×#536C2212yes—
26C2×#533C2212yescomplemented
27C22×C22⋊Q8C2212yes—
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2857C2212yes—
33#2857C2212yescomplemented
34#2857C2212yescomplemented
35#2855C2214yescomplemented
36#2855C2214yescomplemented
37#2851C2212yes—
38#2851C2214yes—
39#2851C2214yescomplemented
40#2848C2214yes—
41#2848C2214yes—
42#2848C2214yes—
43#2799C2218yescomplemented
44#2786C2218yescomplemented
45#2761C2218yescomplemented
46#2755C2218yescomplemented
47#2751C2218yescomplemented
48#2750C2218yescomplemented
49#2743C2218yescomplemented
50#2740C2218yescomplemented
51#2715C2218yescomplemented
52#2713C2218yescomplemented
53#2713C2218yescomplemented
54#2707C2218yescomplemented
55#2700C2218yescomplemented
56#2695C2218yescomplemented
57#2694C2218yescomplemented
58#2687C2218yescomplemented
59#2659C2214yes—
60#2652C2218yescomplemented
61#2646C2214yes—
62#2629C2212yescomplemented
63#2626C2214yes—
64#2626C2214yes—
65#2625C2214yescomplemented
66#2621C2212yescomplemented
67#2616C2214yes—
68#2616C2214yes—
69#2609C2218yescomplemented
70#2608C2214yescomplemented
71#2607C2214yescomplemented
72#2601C2218yescomplemented
73#2601C2218yescomplemented
74#2589C2218yescomplemented
75#2588C2218yescomplemented
76#2587C2218yescomplemented
77#2583C2214yescomplemented
78#2583C2214yescomplemented
79#2560C2218yescomplemented
80#2558C2218yescomplemented
81#2553C2218yescomplemented
82#2550C2218yescomplemented
83#2521C2218yescomplemented
84#2520C2218yescomplemented
85#2505C2218yes—
86#2502C2214yescomplemented
87#2497C2214yescomplemented
88#2496C2214yescomplemented
89#2492C2214yescomplemented
90#2489C2214yescomplemented
91#2480C2218yes—
92#2480C2218yes—
93#2479C2218yescomplemented
94#2478C2218yescomplemented
95#2477C2218yescomplemented
96#2475C2218yescomplemented
97#2474C2218yescomplemented
98#2473C2218yes—
99#2470C2218yescomplemented
100#2458C2218yescomplemented
101#2451C2218yescomplemented
102#2441C2214yescomplemented
103#2439C2214yescomplemented
104#2435C2214yes—
105#2434C2214yes—
106#2434C2214yescomplemented
107#2432C2214yes—
108#2432C2214yes—
109#2429C2214yescomplemented
110#2429C2214yescomplemented
111#2423C2214yescomplemented
112#2421C2214yescomplemented
113#2406C2214yes—
114#2406C2214yes—
115#2405C2214yes—
116#2405C2214yes—
117#2368C2218yes—
118#2362C2214yescomplemented
119#2362C2214yescomplemented
120#2344C2214yescomplemented
121#2342C2218yes—
122Q8×C22⋊C4C2214yescomplemented
123#2334C2218yescomplemented
124#2332C2214yescomplemented
125#2332C2214yescomplemented
126#2329C2214yes—
127#2329C2214yes—
128#2323C2214yescomplemented
129#2315C2214yes—
130#2314C2212yescomplemented
131#2313C2214yescomplemented
132#2312C2214yes—
133#2311C2212yes—
134#2311C2212yes—
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2214yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yescomplemented
139C4×C22⋊Q8C2214yescomplemented
140#2297C2214yes—
141#2297C2214yes—
142#2297C2212yes—
143#2297C2212yes—
144#2297C2212yes—
145#2297C2212yes—
146#2296C2214yescomplemented
147C2×#391C2212yes—
148C2×#390C2212yes—
149C2×#386C2212yes—
150C2×#386C2212yes—
151#2285C2212yescomplemented
152#2280C2214yes—
153#2280C2212yes—
154#2274C2214yescomplemented
155C2×C4×C22⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×C4×C22⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2211yescharacteristic
159C22×#41—28no—
160C22×#41—44no—
161C22×#41—44no—
162C22×#41C2312yes—
163C22×#41C2312yes—
164C22×#41C2312yes—
165C22×#41C2312yes—
166C23×Q8C2311yescharacteristic
167C23×Q8C2312yes—
168C23×D4C2311yescharacteristic
169C23×D4C2311yescharacteristic
170C23×D4C2311yescharacteristic
171C24×C4C2311yescharacteristic
172C24×C4C2311yescharacteristic
173C24×C4C2312yes—
174C24×C4C2311yescharacteristic
175#541—48no—
176#536—48no—
177#536—48no—
178#533—48no—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#126C2318yes—
185C2×#126C2318yes—
186C2×#125C2314yes—
187C2×#125C2312yes—
188C2×#125C2318yes—
189C2×#124C2314yes—
190C2×#124C2314yes—
191C2×#123C2314yes—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×C22⋊Q8—216no—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2314yes—
209C2×C4×Q8C2314yes—
210C2×#117—44no—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2318yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C42—44no—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#399C2318yes—
248#399C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#393C2318yes—
280#393C2318yes—
281#391C2318yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2318yes—
286#391C2318yes—
287#391C2318yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#388C2318yes—
319#388C2318yes—
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#387C2318yes—
333#387C2318yes—
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#386C2314yes—
355#386C2314yes—
356#386C2314yes—
357#386C2314yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#384C2312yes—
378#384C2312yes—
379#384C2312yes—
380#382C2312yes—
381#382C2318yes—
382#382C2314yes—
383#381C2318yes—
384#381C2314yes—
385#381C2318yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2318yes—
393#380C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#379C2318yes—
402#379C2318yes—
403#379C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2314yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C2×#95C2312yes—
431C2×#95C2312yes—
432C2×#95C2312yes—
433C2×#95C2312yes—
434C25C2411yescharacteristic
435C25C2411yescharacteristic
436C25C2411yescharacteristic
437C2×#41—28no—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—44no—
444C2×#41—44no—
445C2×#41—44no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—44no—
449C2×#41—464no—
450C22×Q8—24no—
451C22×Q8—28no—
452C22×Q8—42no—
453C22×Q8—42no—
454C22×Q8—44no—
455C22×Q8—44no—
456C22×Q8C2414yes—
457C22×Q8C2412yes—
458C22×Q8C2412yes—
459C22×Q8C2414yes—
460C22×Q8C2414yes—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C2412yes—
471C22×D4C2412yes—
472C22×D4C2412yes—
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2412yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—28no—
481C23×C4—44no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4—42no—
485C23×C4—42no—
486C23×C4—44no—
487C23×C4#4118yes—
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2411yescharacteristic
505C23×C4C2412yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2412yes—
510C4⋊Q8—44no—
511C4⋊Q8—44no—
512C4⋊Q8—44no—
513C4⋊Q8—48no—
514C4⋊Q8—48no—
515#126—416no—
516#126—416no—
517#125—48no—
518#125—44no—
519#125—416no—
520#124—48no—
521#124—48no—
522#123—48no—
523#123—48no—
524#123—48no—
525#123—48no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—216no—
533C22⋊Q8—48no—
534C22⋊Q8—48no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537C4×Q8—48no—
538C4×Q8—48no—
539C4×Q8—48no—
540#117—28no—
541#117—44no—
542#117—48no—
543#117—416no—
544#117—44no—
545#117—48no—
546#117—44no—
547#117—44no—
548#117—44no—
549C2×C4⋊C4—28no—
550C2×C4⋊C4—216no—
551C2×C4⋊C4—44no—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C22⋊C4—216no—
581C2×C22⋊C4—28no—
582C2×C22⋊C4—28no—
583C2×C22⋊C4—44no—
584C2×C22⋊C4—44no—
585C2×C22⋊C4—44no—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C42—28no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42—42no—
614C2×C42—42no—
615C2×C42—44no—
616C2×C42—44no—
617C2×C42—42no—
618C2×C42—42no—
619C2×C42—42no—
620C2×C42—42no—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2418yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2418yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2418yes—
634C2×C42C2418yes—
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2412yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
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—
668#95C2418yes—
669#95C2418yes—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—24no—
674C24—22no—
675C24—24no—
676C24—24no—
677C24—42no—
678C24—42no—
679C24—42no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24C2×#4114yes—
685C24C2512yes—
686C24C2512yes—
687C24C2511yescharacteristic
688C24C2511yescharacteristic
689C24C2511yescharacteristic
690#41—432no—
691#41—432no—
692#41—432no—
693#41—432no—
694C2×Q8—28no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—28no—
699C2×Q8—28no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—28no—
703C2×Q8—42no—
704C2×Q8—42no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—416no—
710C2×Q8—816no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—416no—
730C2×D4—416no—
731C2×D4—416no—
732C22×C4—232no—
733C22×C4—22no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
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—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—28no—
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—416no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—48no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—432no—
793C22×C4—416no—
794C22×C4C2×#4118yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4118yes—
797C22×C4C2×#4114yes—
798C22×C4H(5,𝔽2)14yes—
799C22×C4H(5,𝔽2)14yes—
800C22×C42−1+418yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2518yes—
805C22×C4C2518yes—
806C22×C4C2514yes—
807C22×C4C2518yes—
808C22×C4C2518yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—216no—
820C4⋊C4—216no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—216no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—28no—
848C22⋊C4—216no—
849C22⋊C4—216no—
850C22⋊C4—216no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—216no—
876C42—41no—
877C42—42no—
878C42—41no—
879C42—41no—
880C42—42no—
881C42—41no—
882C42—42no—
883C42—42no—
884C42—48no—
885C42—48no—
886C42—44no—
887C42—44no—
888C42—48no—
889C23—21no—
890C23—21no—
891C23—22no—
892C23—28no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—21no—
899C23—24no—
900C23—22no—
901C23—22no—
902C23—24no—
903C23—22no—
904C23—22no—
905C23—28no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—24no—
910C23—24no—
911C23—44no—
912C23—44no—
913C23—48no—
914C23—48no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—84no—
921C23—84no—
922C23—84no—
923C23—84no—
924C23C22×#4114yes—
925C23C22×#4112yes—
926C23C2×H(5,𝔽2)12yes—
927C23C2×H(5,𝔽2)12yes—
928C23C2×2−1+414yes—
929C23C2611yescharacteristic
930Q8—48no—
931Q8—48no—
932Q8—416no—
933Q8—88no—
934Q8—88no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—48no—
939D4—48no—
940D4—48no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—216no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—216no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—28no—
987C2×C4—44no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4—48no—
995C2×C4—416no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—84no—
999C2×C4—84no—
1000C2×C4—88no—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4114yes—
1003C2×C4C22×#4112yes—
1004C2×C4C2×H(5,𝔽2)12yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×2−1+414yes—
1009C2×C4C2×2−1+414yes—
1010C2×C4#58514yes—
1011C22—22no—
1012C22—24no—
1013C22—24no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—416no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—44no—
1027C22—42no—
1028C22—44no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—44no—
1034C22—44no—
1035C22—42no—
1036C22—88no—
1037C22—88no—
1038C22#350914yes—
1039C22C23×#4111yescharacteristic
1040C22C22×H(5,𝔽2)11yescharacteristic
1041C22C22×H(5,𝔽2)11yescharacteristic
1042C22C22×2−1+412yes—
1043C22C2×#58512yes—
1044C4—22no—
1045C4—22no—
1046C4—22no—
1047C4—24no—
1048C4—24no—
1049C4—24no—
1050C4—24no—
1051C4—42no—
1052C4—48no—
1053C4—42no—
1054C4—48no—
1055C4—48no—
1056C4—44no—
1057C4—44no—
1058C4—48no—
1059C4#349014yes—
1060C2—24no—
1061C2—42no—
1062C2—42no—
1063C2—44no—
1064C2—82no—
1065C2#6268611yescharacteristic
1066C2C2×#349011yescharacteristic
1067C2C2×#350911yescharacteristic
1068C2#6281912yes—
1069C2#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. #39676C2semidirect
2. #39563C2semidirect
3. #39540C2semidirect
4. #39435C2semidirect
5. #37971C2semidirect
6. #37957C2semidirect
7. #37932C2semidirect
8. #37783C2semidirect
9. #36819C2semidirect
10. #36813C2semidirect
11. #36625C2semidirect
12. #35440C2semidirect
13. #35435C2semidirect
14. #35310C2semidirect
16. #35086C2semidirect
17. #35033C2semidirect
18. #35014C2semidirect
19. #35011C2semidirect
20. #34245C2semidirect
23. C2×#541C22semidirect
26. C2×#533C22semidirect
33. #2857C22semidirect
34. #2857C22semidirect
35. #2855C22semidirect
36. #2855C22semidirect
39. #2851C22semidirect
43. #2799C22semidirect
44. #2786C22semidirect
45. #2761C22semidirect
46. #2755C22semidirect
47. #2751C22semidirect
48. #2750C22semidirect
49. #2743C22semidirect
50. #2740C22semidirect
51. #2715C22semidirect
52. #2713C22semidirect
53. #2713C22semidirect
54. #2707C22semidirect
55. #2700C22semidirect
56. #2695C22semidirect
57. #2694C22semidirect
58. #2687C22semidirect
60. #2652C22semidirect
62. #2629C22semidirect
65. #2625C22semidirect
66. #2621C22semidirect
69. #2609C22semidirect
70. #2608C22semidirect
71. #2607C22semidirect
72. #2601C22semidirect
73. #2601C22semidirect
74. #2589C22semidirect
75. #2588C22semidirect
76. #2587C22semidirect
77. #2583C22semidirect
78. #2583C22semidirect
79. #2560C22semidirect
80. #2558C22semidirect
81. #2553C22semidirect
82. #2550C22semidirect
83. #2521C22semidirect
84. #2520C22semidirect
86. #2502C22semidirect
87. #2497C22semidirect
88. #2496C22semidirect
89. #2492C22semidirect
90. #2489C22semidirect
93. #2479C22semidirect
94. #2478C22semidirect
95. #2477C22semidirect
96. #2475C22semidirect
97. #2474C22semidirect
99. #2470C22semidirect
100. #2458C22semidirect
101. #2451C22semidirect
102. #2441C22semidirect
103. #2439C22semidirect
106. #2434C22semidirect
109. #2429C22semidirect
110. #2429C22semidirect
111. #2423C22semidirect
112. #2421C22semidirect
118. #2362C22semidirect
119. #2362C22semidirect
120. #2344C22semidirect
122. Q8×C22⋊C4C22semidirect
123. #2334C22semidirect
124. #2332C22semidirect
125. #2332C22semidirect
128. #2323C22semidirect
130. #2314C22semidirect
131. #2313C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×C22⋊Q8C22semidirect
146. #2296C22semidirect
151. #2285C22semidirect
154. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#396762
#395632
#395402
#394352
#379712
#379572
#379322
#377832
#368192
#368132
#366252
#354402
#354352
#353102
#353052
#350862
#350332
#350142
#350112
#342452
C2×#22972