Finite Group Databasebeta

← #7715678

Subgroups — #7715678

Order 512.

4486 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50329C214yesmaximal, complemented
2#50293C214yesmaximal, complemented
3#49077C214yesmaximal, complemented
4#49032C214yesmaximal, complemented
5#47668C218yesmaximal, complemented
6#47188C218yesmaximal, complemented
7#38217C214yesmaximal, complemented
8#38203C214yesmaximal, complemented
9#37897C212yesmaximal, complemented
10#37889C212yesmaximal, complemented
11#37705C212yesmaximal, complemented
12#37695C212yesmaximal, complemented
13#37522C212yesmaximal, complemented
14#37380C212yesmaximal, complemented
15#37374C212yesmaximal
16#35333C211yesmaximal, characteristic, complemented
17#35323C212yesmaximal, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35310C212yesmaximal, complemented
20#34412C212yesmaximal, complemented
21#34065C211yesmaximal, characteristic
22C2×#541C2212yes—
23C2×#536C2212yes—
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#125C2211yescharacteristic, complemented
26C2×#525C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2863C2214yescomplemented
30#2857C2212yes—
31#2857C2212yescomplemented
32#2851C2212yes—
33#2851C2212yescomplemented
34#2848C2214yes—
35#2839C2218yescomplemented
36#2793C2218yes—
37#2787C2218yes—
38#2787C2218yescomplemented
39#2787C2218yescomplemented
40#2779C2218yes—
41#2768C2218yes—
42#2766C2218yescomplemented
43#2765C2218yes—
44#2757C2218yes—
45#2755C2218yescomplemented
46#2754C2218yes—
47#2747C2218yescomplemented
48#2741C2218yes—
49#2740C2218yes—
50#2739C2218yescomplemented
51#2735C2218yes—
52#2729C2218yes—
53#2725C2218yes—
54#2724C2214yes—
55#2719C2218yescomplemented
56#2717C2214yes—
57#2716C2218yes—
58#2713C2218yescomplemented
59#2708C2218yes—
60#2697C2214yes—
61#2684C2214yes—
62#2652C2218yes—
63#2652C2218yes—
64#2647C2212yescomplemented
65#2642C2212yescomplemented
66#2629C2212yes—
67#2629C2212yes—
68#2629C2212yescomplemented
69#2625C2214yes—
70#2625C2214yes—
71#2621C2212yes—
72#2621C2212yes—
73#2621C2212yescomplemented
74#2612C2218yescomplemented
75#2596C2218yes—
76#2595C2218yes—
77#2590C2218yescomplemented
78#2585C2218yescomplemented
79#2585C2218yescomplemented
80#2579C2214yes—
81#2579C2214yescomplemented
82#2577C2218yes—
83#2566C2214yes—
84#2565C2214yescomplemented
85#2547C2214yes—
86#2546C2214yescomplemented
87#2533C2218yescomplemented
88#2532C2218yes—
89#2530C2218yes—
90#2530C2218yescomplemented
91#2529C2218yes—
92#2529C2218yes—
93#2528C2218yescomplemented
94#2526C2218yes—
95#2515C2218yescomplemented
96#2511C2214yescomplemented
97#2509C2214yescomplemented
98#2507C2218yescomplemented
99#2494C2214yes—
100#2489C2214yes—
101#2486C2214yes—
102#2486C2214yescomplemented
103#2485C2214yes—
104#2481C2218yes—
105#2481C2218yes—
106#2480C2218yes—
107#2478C2218yes—
108#2475C2218yes—
109#2473C2218yes—
110#2473C2218yescomplemented
111#2453C2214yescomplemented
112#2446C2214yescomplemented
113#2442C2218yescomplemented
114#2429C2214yes—
115#2423C2214yes—
116#2417C2214yes—
117#2415C2214yes—
118#2409C2214yes—
119#2379C2214yes—
120#2376C2214yes—
121#2374C2214yes—
122#2372C2214yes—
123#2362C2214yescomplemented
124#2360C2214yescomplemented
125#2346C2214yescomplemented
126Q8×C22⋊C4C2214yescomplemented
127#2335C2218yescomplemented
128#2331C2218yescomplemented
129#2330C2212yescomplemented
130#2327C2212yescomplemented
131#2324C2214yes—
132#2323C2214yes—
133#2323C2214yes—
134#2323C2214yes—
135#2322C2212yes—
136#2322C2212yes—
137#2321C2212yes—
138#2321C2212yes—
139#2317C2212yescomplemented
140#2314C2212yes—
141#2311C2212yes—
142#2310C2212yescomplemented
143C4×C22⋊Q8C2214yes—
144#2297C2211yescharacteristic
145#2296C2211yescharacteristic
146#2295C2214yescomplemented
147#2293C2212yes—
148#2293C2212yes—
149#2290C2212yes—
150#2290C2212yes—
151#2285C2211yescharacteristic, complemented
152#2285C2211yescharacteristic, complemented
153#2280C2211yescharacteristic
154C4×#117C2211yescharacteristic
155C22×#41C2311yescharacteristic
156C23×Q8C2312yes—
157C24×C4C2311yescharacteristic
158#541—48no—
159#536—216no—
160C2×C4⋊Q8—44no—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2314yes—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2314yes—
165C2×#126C2318yes—
166C2×#125—44no—
167C2×#125C2312yes—
168C2×#125C2314yes—
169C2×#125C2312yes—
170C2×#125C2318yes—
171C2×#124C2314yes—
172#525—28no—
173C2×#123C2311yescharacteristic
174C2×#123C2311yescharacteristic
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×#121C2312yes—
183C2×#120C2311yescharacteristic
184C2×#120C2311yescharacteristic
185C4×#41—44no—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2312yes—
194C2×#117—44no—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2311yescharacteristic
198C2×#117C2311yescharacteristic
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2314yes—
204C2×#117C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2314yes—
208C22×C4⋊C4C2314yes—
209C22×C22⋊C4C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214#401C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#399C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#395C2318yes—
259#394C2318yes—
260#394C2318yes—
261#393C2318yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#391C2312yes—
268#391C2314yes—
269#391C2314yes—
270#391C2318yes—
271#391C2318yes—
272#391C2314yes—
273#391C2314yes—
274#390C2314yes—
275#390C2314yes—
276#390C2314yes—
277#390C2312yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2318yes—
286#389C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2314yes—
292#389C2318yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#388C2318yes—
298#388C2314yes—
299#388C2314yes—
300#388C2314yes—
301#388C2314yes—
302#388C2318yes—
303#388C2318yes—
304#388C2314yes—
305#388C2314yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2314yes—
326#387C2314yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
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#386C2314yes—
346#386C2314yes—
347#386C2312yes—
348#386C2312yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2314yes—
357#385C2312yes—
358#385C2312yes—
359#385C2314yes—
360#385C2314yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#384C2314yes—
368#384C2312yes—
369#384C2312yes—
370#383C2318yes—
371#382C2314yes—
372#382C2312yes—
373#382C2318yes—
374#382C2318yes—
375#382C2312yes—
376#381C2314yes—
377#381C2314yes—
378#381C2312yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2318yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2318yes—
387#380C2318yes—
388#380C2318yes—
389#380C2314yes—
390#379C2312yes—
391#379C2318yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2312yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2312yes—
407C4×C22⋊C4C2312yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2312yes—
411#376C2312yes—
412#376C2318yes—
413#376C2318yes—
414C43C2312yes—
415C25C2411yescharacteristic
416C2×#41—42no—
417C2×#41—42no—
418C2×#41#4118yes—
419C22×Q8—28no—
420C22×Q8—44no—
421C22×Q8—44no—
422C22×Q8C2414yes—
423C22×Q8C2414yes—
424C22×Q8C2411yescharacteristic
425C22×D4C2412yes—
426C22×D4C2412yes—
427C22×D4C2411yescharacteristic
428C22×D4C2411yescharacteristic
429C22×D4C2411yescharacteristic
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2414yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2414yes—
445C4⋊Q8—216no—
446C4⋊Q8—28no—
447C4⋊Q8—48no—
448C4⋊Q8—44no—
449#126—416no—
450#125—28no—
451#125—44no—
452#125—48no—
453#125—416no—
454#124—216no—
455#123—24no—
456#123—24no—
457#123—216no—
458#123—216no—
459C22⋊Q8—28no—
460C22⋊Q8—216no—
461C22⋊Q8—216no—
462C22⋊Q8—48no—
463C22⋊Q8—48no—
464#121—28no—
465#120—24no—
466#120—24no—
467C4×Q8—44no—
468C4×Q8—48no—
469C4×Q8—48no—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—44no—
473C4×D4—44no—
474C4×D4—44no—
475#117—24no—
476#117—28no—
477#117—28no—
478#117—44no—
479#117—42no—
480#117—42no—
481#117—42no—
482#117—42no—
483#117—48no—
484#117—44no—
485C2×C4⋊C4—44no—
486C2×C4⋊C4—44no—
487C2×C4⋊C4—48no—
488C2×C4⋊C4—48no—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C22⋊C4—44no—
523C2×C22⋊C4C2414yes—
524C2×C22⋊C4C2411yescharacteristic
525C2×C22⋊C4C2411yescharacteristic
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2412yes—
528C2×C22⋊C4C2412yes—
529C2×C22⋊C4C2412yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—42no—
553C2×C42C2411yescharacteristic
554C2×C42C2412yes—
555C2×C42C2412yes—
556C2×C42C2411yescharacteristic
557C2×C42C2411yescharacteristic
558C2×C42C2412yes—
559C2×C42C2412yes—
560C2×C42C2414yes—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2414yes—
565C2×C42C2418yes—
566C2×C42C2418yes—
567C2×C42C2414yes—
568C2×C42C2414yes—
569C2×C42C2418yes—
570C2×C42C2418yes—
571C2×C42C2411yescharacteristic
572#95C2414yes—
573#95C2418yes—
574#95C2414yes—
575#95C2414yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2414yes—
596#95C2414yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606C24—22no—
607C24—41no—
608C24—41no—
609C24—44no—
610C24C2512yes—
611C24C2511yescharacteristic
612C24C2511yescharacteristic
613C24C2511yescharacteristic
614#41—416no—
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—41no—
620C2×Q8—41no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—816no—
624C2×Q8C2×#4114yes—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4C2×#4114yes—
636C2×D4C2×#4114yes—
637C2×D4C2×#4114yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—41no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—41no—
657C22×C4—44no—
658C22×C4—42no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—48no—
665C22×C4—44no—
666C22×C4—416no—
667C22×C4C2×#4114yes—
668C22×C4C2×#4114yes—
669C22×C4C2×#4114yes—
670C22×C4C2512yes—
671C22×C4C2512yes—
672C22×C4C2514yes—
673C22×C4C2518yes—
674C22×C4C2518yes—
675C22×C4C2512yes—
676C22×C4C2514yes—
677C22×C4C2512yes—
678C22×C4C2512yes—
679C22×C4C2518yes—
680C22×C4C2518yes—
681C22×C4C2512yes—
682C22×C4C2511yescharacteristic
683C22×C4C2511yescharacteristic
684C22×C4C2511yescharacteristic
685C22×C4C2512yes—
686C22×C4C2511yescharacteristic
687C4⋊C4—24no—
688C4⋊C4—28no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—216no—
692C4⋊C4—216no—
693C4⋊C4—28no—
694C4⋊C4—28no—
695C4⋊C4—216no—
696C4⋊C4—216no—
697C4⋊C4—28no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—42no—
713C4⋊C4—42no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—28no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—216no—
726C22⋊C4—216no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—28no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—48no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—42no—
740C22⋊C4—44no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C42—24no—
747C42—28no—
748C42—22no—
749C42—24no—
750C42—22no—
751C42—22no—
752C42—24no—
753C42—24no—
754C42—24no—
755C42—24no—
756C42—42no—
757C42—44no—
758C42—48no—
759C42—48no—
760C42—44no—
761C42—44no—
762C42—48no—
763C42—48no—
764C42H(5,𝔽2)14yes—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—44no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23C22×#4112yes—
784C23C22×#4112yes—
785C23C22×#4112yes—
786C23C2611yescharacteristic
787Q8—44no—
788Q8—416no—
789Q8—88no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—84no—
794D4—84no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—28no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—44no—
839C2×C4—48no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—88no—
843C2×C4—88no—
844C2×C4—84no—
845C2×C4C22×#4112yes—
846C2×C4C22×#4112yes—
847C2×C4C22×#4112yes—
848C2×C4C22×#4112yes—
849C2×C4C2×H(5,𝔽2)14yes—
850C2×C4C2×H(5,𝔽2)12yes—
851C2×C4#58512yes—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—44no—
868C22—44no—
869C22—88no—
870C22C23×#4111yescharacteristic
871C22C22×H(5,𝔽2)11yescharacteristic
872C22C2×#58511yescharacteristic
873C222−1+614yes—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—24no—
878C4—42no—
879C4—48no—
880C4—48no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—48no—
888C4—44no—
889C4—48no—
890C4#350514yes—
891C2—42no—
892C2—42no—
893C2—42no—
894C2—82no—
895C2C2×#350511yescharacteristic
896C2#6286112yes—
897C2#6288612yes—
898C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50329C2semidirect
2. #50293C2semidirect
3. #49077C2semidirect
4. #49032C2semidirect
5. #47668C2semidirect
6. #47188C2semidirect
7. #38217C2semidirect
8. #38203C2semidirect
9. #37897C2semidirect
10. #37889C2semidirect
11. #37705C2semidirect
12. #37695C2semidirect
13. #37522C2semidirect
14. #37380C2semidirect
16. #35333C2semidirect
17. #35323C2semidirect
18. #35316C2semidirect
19. #35310C2semidirect
20. #34412C2semidirect
24. C22×C4⋊Q8C22semidirect
25. C22×#125C22semidirect
29. #2863C22semidirect
31. #2857C22semidirect
33. #2851C22semidirect
35. #2839C22semidirect
38. #2787C22semidirect
39. #2787C22semidirect
42. #2766C22semidirect
45. #2755C22semidirect
47. #2747C22semidirect
50. #2739C22semidirect
55. #2719C22semidirect
58. #2713C22semidirect
64. #2647C22semidirect
65. #2642C22semidirect
68. #2629C22semidirect
73. #2621C22semidirect
74. #2612C22semidirect
77. #2590C22semidirect
78. #2585C22semidirect
79. #2585C22semidirect
81. #2579C22semidirect
84. #2565C22semidirect
86. #2546C22semidirect
87. #2533C22semidirect
90. #2530C22semidirect
93. #2528C22semidirect
95. #2515C22semidirect
96. #2511C22semidirect
97. #2509C22semidirect
98. #2507C22semidirect
102. #2486C22semidirect
110. #2473C22semidirect
111. #2453C22semidirect
112. #2446C22semidirect
113. #2442C22semidirect
123. #2362C22semidirect
124. #2360C22semidirect
125. #2346C22semidirect
126. Q8×C22⋊C4C22semidirect
127. #2335C22semidirect
128. #2331C22semidirect
129. #2330C22semidirect
130. #2327C22semidirect
139. #2317C22semidirect
142. #2310C22semidirect
146. #2295C22semidirect
151. #2285C22semidirect
152. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#503292
#502932
#490772
#490322
#476682
#471882
#382172
#382032
#378972
#378892
#377052
#376952
#375222
#373802
#373742
#353332
#353232
#353162
#353102
#344122
#340652