Finite Group Databasebeta

← #7715677

Subgroups — #7715677

Order 512.

5254 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50237C214yesmaximal, complemented
2#50200C214yesmaximal, complemented
3#48997C214yesmaximal, complemented
4#48949C214yesmaximal, complemented
5#47660C214yesmaximal, complemented
6#47657C214yesmaximal, complemented
7#47180C214yesmaximal, complemented
8#47173C214yesmaximal, complemented
9#37973C214yesmaximal, complemented
10#37859C214yesmaximal, complemented
11#37783C214yesmaximal, complemented
12#37663C214yesmaximal, complemented
13#37514C212yesmaximal, complemented
14#37426C211yesmaximal, characteristic, complemented
15#37393C212yesmaximal, complemented
16#37386C211yesmaximal, characteristic, complemented
17#35325C212yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35305C212yesmaximal
20#34412C212yesmaximal, complemented
21#34044C211yesmaximal, characteristic
22C23×#41C2211yescharacteristic
23C2×#541C2212yes—
24C2×#536C2212yes—
25C2×#536C2212yes—
26C2×#533C2212yescomplemented
27C22×C22⋊Q8C2212yes—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2857C2212yescomplemented
31#2855C2214yescomplemented
32#2851C2212yescomplemented
33#2848C2214yes—
34#2848C2214yes—
35#2833C2214yescomplemented
36#2830C2214yescomplemented
37#2804C2214yescomplemented
38#2800C2218yescomplemented
39#2799C2214yescomplemented
40#2784C2214yescomplemented
41#2781C2218yescomplemented
42#2779C2218yescomplemented
43#2774C2218yescomplemented
44#2762C2218yescomplemented
45#2761C2218yescomplemented
46#2757C2218yescomplemented
47#2750C2218yescomplemented
48#2748C2214yescomplemented
49#2745C2218yescomplemented
50#2739C2218yescomplemented
51#2736C2218yes—
52#2735C2218yes—
53#2734C2214yescomplemented
54#2724C2214yescomplemented
55#2717C2214yescomplemented
56#2717C2214yescomplemented
57#2713C2218yescomplemented
58#2707C2218yescomplemented
59#2704C2218yescomplemented
60#2700C2218yescomplemented
61#2698C2218yes—
62#2690C2218yescomplemented
63#2689C2218yes—
64#2687C2218yescomplemented
65#2653C2218yescomplemented
66#2649C2218yescomplemented
67#2629C2212yescomplemented
68#2628C2212yes—
69#2628C2212yescomplemented
70#2625C2214yes—
71#2621C2212yes—
72#2621C2212yescomplemented
73#2621C2212yescomplemented
74#2616C2214yes—
75#2616C2214yes—
76#2612C2218yescomplemented
77#2611C2214yes—
78#2611C2214yescomplemented
79#2599C2214yes—
80#2599C2214yescomplemented
81#2593C2214yescomplemented
82#2586C2214yescomplemented
83#2583C2214yescomplemented
84#2576C2218yescomplemented
85#2575C2218yes—
86#2574C2218yescomplemented
87#2561C2214yes—
88#2531C2218yescomplemented
89#2530C2218yescomplemented
90#2527C2218yes—
91#2526C2218yescomplemented
92#2499C2214yescomplemented
93#2497C2214yescomplemented
94#2494C2214yescomplemented
95#2492C2214yescomplemented
96#2489C2214yescomplemented
97#2484C2214yescomplemented
98#2482C2214yes—
99#2480C2218yes—
100#2480C2218yes—
101#2480C2218yes—
102#2478C2218yes—
103#2475C2218yescomplemented
104#2474C2218yescomplemented
105#2473C2218yescomplemented
106#2473C2218yescomplemented
107#2470C2218yescomplemented
108#2458C2218yescomplemented
109#2451C2218yescomplemented
110#2442C2218yescomplemented
111#2442C2214yescomplemented
112#2439C2214yescomplemented
113#2435C2214yes—
114#2434C2214yes—
115#2434C2214yescomplemented
116#2432C2214yes—
117#2432C2214yes—
118#2429C2214yescomplemented
119#2429C2214yescomplemented
120#2421C2214yescomplemented
121#2421C2214yescomplemented
122#2406C2214yes—
123#2406C2214yes—
124#2405C2214yes—
125#2405C2214yes—
126#2379C2214yescomplemented
127#2376C2214yescomplemented
128#2374C2214yescomplemented
129#2372C2214yescomplemented
130#2362C2214yescomplemented
131#2360C2214yescomplemented
132#2346C2214yescomplemented
133Q8×C22⋊C4C2214yescomplemented
134#2335C2218yescomplemented
135#2331C2218yescomplemented
136#2323C2214yes—
137#2323C2214yescomplemented
138#2323C2214yescomplemented
139#2314C2212yes—
140#2311C2212yes—
141#2311C2212yes—
142#2311C2212yes—
143#2311C2212yes—
144#2311C2212yes—
145#2311C2212yes—
146#2310C2212yes—
147#2309C2212yes—
148#2308C2212yes—
149#2308C2212yes—
150C4×C22⋊Q8C2214yescomplemented
151#2297C2211yescharacteristic
152#2297C2211yescharacteristic
153#2297C2214yes—
154#2297C2211yescharacteristic
155#2297C2211yescharacteristic
156#2283C2212yescomplemented
157#2280C2214yes—
158#2280C2212yes—
159C22×#41—28no—
160C22×#41—44no—
161C22×#41—44no—
162C22×#41C2312yes—
163C22×#41C2311yescharacteristic
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C22×#41C2311yescharacteristic
167C22×#41C2311yescharacteristic
168C23×Q8C2311yescharacteristic
169C23×Q8C2312yes—
170C23×D4C2312yes—
171C23×D4C2311yescharacteristic
172C24×C4C2311yescharacteristic
173C24×C4C2312yes—
174#541—48no—
175#536—216no—
176#536—48no—
177#533—48no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×#126C2318yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×#123C2314yes—
193C2×C22⋊Q8—48no—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×#117—44no—
207C2×#117—44no—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2311yescharacteristic
220C2×#117C2314yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2314yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2314yes—
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#401C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#400C2314yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#399C2314yes—
243#399C2314yes—
244#398C2318yes—
245#398C2314yes—
246#398C2314yes—
247#398C2318yes—
248#398C2314yes—
249#398C2314yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#397C2314yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2314yes—
261#397C2314yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2314yes—
273#395C2314yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#393C2314yes—
285#393C2314yes—
286#393C2318yes—
287#393C2318yes—
288#391C2312yes—
289#391C2312yes—
290#391C2314yes—
291#391C2314yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2318yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2318yes—
301#391C2318yes—
302#391C2318yes—
303#391C2314yes—
304#390C2312yes—
305#390C2312yes—
306#390C2314yes—
307#390C2314yes—
308#390C2312yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#389C2318yes—
313#389C2314yes—
314#389C2318yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
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#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#386C2314yes—
360#386C2312yes—
361#386C2312yes—
362#386C2312yes—
363#386C2312yes—
364#386C2314yes—
365#386C2312yes—
366#386C2312yes—
367#386C2314yes—
368#386C2314yes—
369#386C2312yes—
370#386C2312yes—
371#386C2314yes—
372#386C2314yes—
373#386C2314yes—
374#386C2314yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#384C2312yes—
389#383C2314yes—
390#382C2312yes—
391#382C2318yes—
392#382C2318yes—
393#382C2312yes—
394#382C2312yes—
395#381C2318yes—
396#381C2314yes—
397#381C2314yes—
398#381C2314yes—
399#381C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2318yes—
410#380C2318yes—
411#380C2314yes—
412#380C2318yes—
413#379C2318yes—
414#379C2314yes—
415#379C2314yes—
416#379C2318yes—
417#379C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432#376C2318yes—
433#376C2314yes—
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—42no—
444C2×#41—44no—
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×Q8C2411yescharacteristic
465C22×Q8C2414yes—
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—44no—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C4⋊Q8—216no—
504C4⋊Q8—44no—
505C4⋊Q8—44no—
506C4⋊Q8—44no—
507C4⋊Q8—48no—
508#126—416no—
509#125—48no—
510#125—44no—
511#125—416no—
512#124—216no—
513#124—48no—
514#123—216no—
515#123—216no—
516#123—48no—
517#123—48no—
518C22⋊Q8—216no—
519C22⋊Q8—216no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—48no—
523C22⋊Q8—48no—
524C22⋊Q8—48no—
525C22⋊Q8—48no—
526C22⋊Q8—48no—
527C4×Q8—48no—
528C4×Q8—48no—
529C4×Q8—48no—
530#117—28no—
531#117—28no—
532#117—42no—
533#117—42no—
534#117—44no—
535#117—44no—
536#117—42no—
537#117—42no—
538#117—44no—
539#117—44no—
540#117—48no—
541#117—44no—
542#117—44no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4—44no—
545C2×C4⋊C4—48no—
546C2×C4⋊C4—44no—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C22⋊C4—44no—
576C2×C22⋊C4—48no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2411yescharacteristic
588C2×C22⋊C4C2411yescharacteristic
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2411yescharacteristic
591C2×C22⋊C4C2411yescharacteristic
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C42—28no—
610C2×C42—42no—
611C2×C42—42no—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2412yes—
620C2×C42C2412yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2418yes—
624C2×C42C2418yes—
625C2×C42C2418yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—24no—
663C24—24no—
664C24—42no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24C2512yes—
669C24C2511yescharacteristic
670C24C2512yes—
671C24C2511yescharacteristic
672C24C2511yescharacteristic
673#41—416no—
674#41—432no—
675#41—416no—
676#41—432no—
677#41—416no—
678#41—416no—
679C2×Q8—28no—
680C2×Q8—24no—
681C2×Q8—22no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—24no—
686C2×Q8—41no—
687C2×Q8—41no—
688C2×Q8—41no—
689C2×Q8—42no—
690C2×Q8—41no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—48no—
695C2×Q8—416no—
696C2×Q8—816no—
697C2×Q8C2×#4114yes—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—24no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—41no—
710C2×D4—42no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—416no—
718C2×D4—432no—
719C2×D4C2×#4114yes—
720C2×D4C2×#4118yes—
721C22×C4—232no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—432no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—48no—
764C22×C4—44no—
765C22×C4C2×#4118yes—
766C22×C4C2×#4114yes—
767C22×C4H(5,𝔽2)14yes—
768C22×C4H(5,𝔽2)14yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2518yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2518yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2518yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C4⋊C4—28no—
786C4⋊C4—216no—
787C4⋊C4—216no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—216no—
791C4⋊C4—28no—
792C4⋊C4—216no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—42no—
796C4⋊C4—42no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—216no—
816C22⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—41no—
820C22⋊C4—42no—
821C22⋊C4—41no—
822C22⋊C4—41no—
823C22⋊C4—42no—
824C22⋊C4—41no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C42—28no—
844C42—24no—
845C42—24no—
846C42—24no—
847C42—24no—
848C42—24no—
849C42—24no—
850C42—42no—
851C42—42no—
852C42—48no—
853C42—48no—
854C42—48no—
855C42—44no—
856C42—48no—
857C23—28no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—21no—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—24no—
875C23—24no—
876C23—48no—
877C23—48no—
878C23—84no—
879C23—88no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—88no—
884C23C22×#4112yes—
885C23C22×#4114yes—
886C23C2×H(5,𝔽2)12yes—
887C23C2×H(5,𝔽2)12yes—
888C23C2611yescharacteristic
889Q8—44no—
890Q8—48no—
891Q8—44no—
892Q8—416no—
893Q8—88no—
894Q8—88no—
895D4—44no—
896D4—48no—
897D4—48no—
898D4—48no—
899D4—44no—
900D4—48no—
901D4—48no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—216no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—48no—
950C2×C4—48no—
951C2×C4—84no—
952C2×C4—88no—
953C2×C4—84no—
954C2×C4—84no—
955C2×C4—88no—
956C2×C4C22×#4114yes—
957C2×C4C22×#4112yes—
958C2×C4C22×#4112yes—
959C2×C4C2×H(5,𝔽2)12yes—
960C2×C4C2×H(5,𝔽2)12yes—
961C2×C4C2×H(5,𝔽2)12yes—
962C2×C4C2×H(5,𝔽2)12yes—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—24no—
967C22—28no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—42no—
980C22—42no—
981C22—44no—
982C22—42no—
983C22—42no—
984C22—44no—
985C22—88no—
986C22—816no—
987C22C23×#4111yescharacteristic
988C22C22×H(5,𝔽2)11yescharacteristic
989C22C22×H(5,𝔽2)11yescharacteristic
990C222−1+614yes—
991C4—22no—
992C4—22no—
993C4—22no—
994C4—24no—
995C4—42no—
996C4—48no—
997C4—48no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—44no—
1002C4—44no—
1003C4—48no—
1004C4—42no—
1005C4—48no—
1006C4#349014yes—
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—42no—
1011C2—82no—
1012C2C2×#349011yescharacteristic
1013C2#6286112yes—
1014C2#6288612yes—
1015C2#6288612yes—
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. #50237C2semidirect
2. #50200C2semidirect
3. #48997C2semidirect
4. #48949C2semidirect
5. #47660C2semidirect
6. #47657C2semidirect
7. #47180C2semidirect
8. #47173C2semidirect
9. #37973C2semidirect
10. #37859C2semidirect
11. #37783C2semidirect
12. #37663C2semidirect
13. #37514C2semidirect
14. #37426C2semidirect
15. #37393C2semidirect
16. #37386C2semidirect
17. #35325C2semidirect
18. #35310C2semidirect
20. #34412C2semidirect
26. C2×#533C22semidirect
30. #2857C22semidirect
31. #2855C22semidirect
32. #2851C22semidirect
35. #2833C22semidirect
36. #2830C22semidirect
37. #2804C22semidirect
38. #2800C22semidirect
39. #2799C22semidirect
40. #2784C22semidirect
41. #2781C22semidirect
42. #2779C22semidirect
43. #2774C22semidirect
44. #2762C22semidirect
45. #2761C22semidirect
46. #2757C22semidirect
47. #2750C22semidirect
48. #2748C22semidirect
49. #2745C22semidirect
50. #2739C22semidirect
53. #2734C22semidirect
54. #2724C22semidirect
55. #2717C22semidirect
56. #2717C22semidirect
57. #2713C22semidirect
58. #2707C22semidirect
59. #2704C22semidirect
60. #2700C22semidirect
62. #2690C22semidirect
64. #2687C22semidirect
65. #2653C22semidirect
66. #2649C22semidirect
67. #2629C22semidirect
69. #2628C22semidirect
72. #2621C22semidirect
73. #2621C22semidirect
76. #2612C22semidirect
78. #2611C22semidirect
80. #2599C22semidirect
81. #2593C22semidirect
82. #2586C22semidirect
83. #2583C22semidirect
84. #2576C22semidirect
86. #2574C22semidirect
88. #2531C22semidirect
89. #2530C22semidirect
91. #2526C22semidirect
92. #2499C22semidirect
93. #2497C22semidirect
94. #2494C22semidirect
95. #2492C22semidirect
96. #2489C22semidirect
97. #2484C22semidirect
103. #2475C22semidirect
104. #2474C22semidirect
105. #2473C22semidirect
106. #2473C22semidirect
107. #2470C22semidirect
108. #2458C22semidirect
109. #2451C22semidirect
110. #2442C22semidirect
111. #2442C22semidirect
112. #2439C22semidirect
115. #2434C22semidirect
118. #2429C22semidirect
119. #2429C22semidirect
120. #2421C22semidirect
121. #2421C22semidirect
126. #2379C22semidirect
127. #2376C22semidirect
128. #2374C22semidirect
129. #2372C22semidirect
130. #2362C22semidirect
131. #2360C22semidirect
132. #2346C22semidirect
133. Q8×C22⋊C4C22semidirect
134. #2335C22semidirect
135. #2331C22semidirect
137. #2323C22semidirect
138. #2323C22semidirect
150. C4×C22⋊Q8C22semidirect
156. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#502372
#502002
#489972
#489492
#476602
#476572
#471802
#471732
#379732
#378592
#377832
#376632
#375142
#374262
#373932
#373862
#353252
#353102
#353052
#344122
#340442