Finite Group Databasebeta

← #8095528

Subgroups — #8095528

Order 512.

4390 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C214yesmaximal, complemented
2#53114C214yesmaximal, complemented
3#53113C214yesmaximal, complemented
4#52994C214yesmaximal, complemented
5#52511C214yesmaximal, complemented
6#52396C214yesmaximal, complemented
7#46347C214yesmaximal, complemented
8#46343C214yesmaximal, complemented
9#46341C214yesmaximal, complemented
10#46332C214yesmaximal, complemented
11#46168C218yesmaximal, complemented
12#35679C211yesmaximal, characteristic
13#35662C212yesmaximal, complemented
14#35626C211yesmaximal, characteristic
15#35515C212yesmaximal
16#35313C212yesmaximal, complemented
17#35266C212yesmaximal
18#35159C212yesmaximal, complemented
19#34953C212yesmaximal, complemented
20C2×#2592C211yesmaximal, characteristic
21C2×#533C2212yes—
22C22×#124C2211yescharacteristic
23C2×#519C2211yescharacteristic
24C2×#518C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26#2863C2214yescomplemented
27#2863C2214yescomplemented
28#2860C2214yes—
29#2860C2214yes—
30#2851C2218yes—
31#2841C2214yescomplemented
32#2838C2218yescomplemented
33#2838C2218yescomplemented
34#2838C2218yescomplemented
35#2836C2218yescomplemented
36#2836C2218yescomplemented
37#2835C2214yescomplemented
38#2834C2214yescomplemented
39#2831C2218yescomplemented
40#2831C2218yescomplemented
41#2821C2218yescomplemented
42#2817C2214yescomplemented
43#2793C2218yescomplemented
44#2787C2218yescomplemented
45#2777C2218yescomplemented
46#2775C2218yescomplemented
47#2773C2218yescomplemented
48#2771C2214yescomplemented
49#2770C2218yescomplemented
50#2765C2218yescomplemented
51#2764C2214yescomplemented
52#2759C2218yescomplemented
53#2745C2218yescomplemented
54#2738C2218yescomplemented
55#2729C2218yescomplemented
56#2725C2218yescomplemented
57#2722C2214yescomplemented
58#2721C2218yescomplemented
59#2720C2218yescomplemented
60#2716C2218yescomplemented
61#2698C2218yescomplemented
62#2690C2218yescomplemented
63#2689C2218yescomplemented
64#2677C2214yescomplemented
65#2646C2218yes—
66#2645C2214yescomplemented
67#2645C2214yescomplemented
68#2644C2214yes—
69#2644C2214yes—
70#2592C2214yes—
71#2592C2214yes—
72#2592C2214yes—
73#2592C2214yes—
74#2584C2212yescomplemented
75#2584C2212yescomplemented
76#2584C2212yescomplemented
77#2584C2212yescomplemented
78#2583C2214yes—
79#2583C2214yes—
80#2582C2214yescomplemented
81#2582C2214yescomplemented
82#2581C2214yescomplemented
83#2581C2214yescomplemented
84#2580C2214yes—
85#2580C2214yes—
86#2567C2212yescomplemented
87#2567C2212yescomplemented
88#2546C2212yescomplemented
89#2546C2212yescomplemented
90#2538C2214yes—
91#2538C2214yes—
92#2514C2214yescomplemented
93#2514C2214yescomplemented
94#2513C2214yes—
95#2513C2214yes—
96#2512C2214yes—
97#2512C2214yes—
98#2511C2214yescomplemented
99#2511C2214yescomplemented
100#2509C2214yescomplemented
101#2509C2214yescomplemented
102#2508C2214yescomplemented
103#2508C2214yescomplemented
104#2507C2214yescomplemented
105#2507C2214yescomplemented
106#2506C2214yescomplemented
107#2506C2214yescomplemented
108#2502C2214yes—
109#2493C2218yes—
110#2493C2218yes—
111#2483C2214yes—
112#2483C2214yes—
113#2482C2214yes—
114#2482C2214yes—
115#2480C2218yes—
116#2480C2218yes—
117#2454C2214yes—
118#2454C2214yes—
119#2453C2214yescomplemented
120#2453C2214yescomplemented
121#2452C2214yes—
122#2452C2214yes—
123#2451C2214yescomplemented
124#2451C2214yescomplemented
125#2448C2214yes—
126#2448C2214yes—
127#2448C2214yes—
128#2448C2214yes—
129#2447C2214yes—
130#2447C2214yes—
131#2447C2214yes—
132#2447C2214yes—
133#2438C2218yes—
134#2438C2218yes—
135#2437C2218yes—
136#2437C2218yes—
137#2434C2214yes—
138#2399C2214yescomplemented
139#2399C2214yescomplemented
140C2×#397C2212yes—
141C2×#393C2212yes—
142#2383C2218yescomplemented
143#2378C2218yescomplemented
144#2317C2212yes—
145#2317C2212yes—
146#2316C2212yes—
147#2316C2212yes—
148#2310C2212yes—
149#2310C2211yescharacteristic
150#2309C2211yescharacteristic
151#2309C2212yes—
152C4×C4⋊Q8C2214yescomplemented
153C4×C4⋊Q8C2214yescomplemented
154#2296C2212yes—
155#2296C2212yes—
156#2296C2212yes—
157#2296C2212yes—
158C2×#391C2212yes—
159C2×#390C2212yes—
160C2×#388C2214yes—
161C4×#117C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C23×Q8C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165C23×D4C2311yescharacteristic
166#533—48no—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2312yes—
171C2×#126C2318yes—
172C2×#126C2318yes—
173C2×#125C2312yes—
174C2×#125C2312yes—
175C2×#125C2318yes—
176C2×#124—44no—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183#519—44no—
184#518—44no—
185C2×C4×Q8—44no—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2314yes—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2312yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2314yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2314yes—
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2312yes—
212#401C2318yes—
213#401C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#399C2314yes—
227#399C2318yes—
228#399C2318yes—
229#399C2314yes—
230#399C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2314yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2314yes—
238#398C2314yes—
239#398C2314yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2314yes—
244#398C2314yes—
245#398C2314yes—
246#398C2314yes—
247#397C2314yes—
248#397C2314yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2314yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#395C2314yes—
270#395C2318yes—
271#395C2314yes—
272#395C2318yes—
273#395C2314yes—
274#395C2314yes—
275#395C2314yes—
276#395C2314yes—
277#395C2314yes—
278#395C2314yes—
279#393C2318yes—
280#393C2318yes—
281#393C2318yes—
282#393C2314yes—
283#393C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2318yes—
295#391C2314yes—
296#391C2314yes—
297#391C2318yes—
298#391C2314yes—
299#391C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2314yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#385C2314yes—
388#385C2314yes—
389#385C2314yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2318yes—
395#384C2314yes—
396#384C2314yes—
397#384C2314yes—
398#384C2314yes—
399#383C2318yes—
400#383C2318yes—
401#382C2314yes—
402#382C2314yes—
403#382C2318yes—
404#381C2314yes—
405#381C2318yes—
406#381C2314yes—
407#381C2314yes—
408#381C2318yes—
409#380C2318yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#379C2318yes—
414#379C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431#376C2314yes—
432C2×#95C2312yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C43C2314yes—
436C25C2412yes—
437C22×Q8—24no—
438C22×Q8—28no—
439C22×Q8—42no—
440C22×Q8—44no—
441C22×Q8C2414yes—
442C22×Q8C2411yescharacteristic
443C22×Q8C2412yes—
444C22×Q8C2414yes—
445C22×Q8C2411yescharacteristic
446C22×Q8C2414yes—
447C22×D4—24no—
448C22×D4—28no—
449C22×D4C2414yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2411yescharacteristic
459C4⋊Q8—44no—
460C4⋊Q8—44no—
461C4⋊Q8—48no—
462C4⋊Q8—48no—
463#126—416no—
464#126—88no—
465#125—44no—
466#125—44no—
467#125—88no—
468#124—48no—
469#124—48no—
470C22⋊Q8—48no—
471C22⋊Q8—48no—
472C22⋊Q8—416no—
473C22⋊Q8—88no—
474C4×Q8—44no—
475C4×Q8—44no—
476C4×Q8—44no—
477C4×Q8—44no—
478C4×Q8—48no—
479C4×Q8—48no—
480C4×Q8—48no—
481C4×Q8—48no—
482C4×D4—48no—
483C4×D4—48no—
484#117—28no—
485#117—28no—
486#117—28no—
487#117—28no—
488#117—48no—
489C2×C4⋊C4—28no—
490C2×C4⋊C4—44no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C22⋊C4—48no—
542C2×C22⋊C4—48no—
543C2×C22⋊C4—44no—
544C2×C22⋊C4—44no—
545C2×C22⋊C4—84no—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C42—24no—
566C2×C42—28no—
567C2×C42—82no—
568C2×C42C2414yes—
569C2×C42C2414yes—
570C2×C42C2414yes—
571C2×C42C2414yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2418yes—
580C2×C42C2418yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2418yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625C24—24no—
626C24—28no—
627C24—44no—
628C24—42no—
629C24—42no—
630C24C2514yes—
631C24C2511yescharacteristic
632C2×Q8—28no—
633C2×Q8—28no—
634C2×Q8—28no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—28no—
638C2×Q8—41no—
639C2×Q8—42no—
640C2×Q8—41no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8—44no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—416no—
649C2×Q8—416no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—416no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—28no—
659C22×C4—24no—
660C22×C4—28no—
661C22×C4—24no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—48no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4H(5,𝔽2)14yes—
676C22×C42−1+418yes—
677C22×C4C2514yes—
678C22×C4C2514yes—
679C22×C4C2514yes—
680C22×C4C2518yes—
681C22×C4C2514yes—
682C22×C4C2514yes—
683C22×C4C2511yescharacteristic
684C22×C4C2511yescharacteristic
685C22×C4C2512yes—
686C22×C4C2512yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2512yes—
690C22×C4C2512yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2512yes—
694C22×C4C2512yes—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—28no—
706C4⋊C4—28no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—41no—
712C4⋊C4—42no—
713C4⋊C4—41no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C4⋊C4—44no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—44no—
732C4⋊C4—44no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—28no—
748C22⋊C4—216no—
749C22⋊C4—48no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C22⋊C4—44no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—44no—
763C42—24no—
764C42—24no—
765C42—24no—
766C42—24no—
767C42—24no—
768C42—24no—
769C42—28no—
770C42—28no—
771C42—28no—
772C42—28no—
773C42—28no—
774C42—48no—
775C42—44no—
776C42—48no—
777C42—44no—
778C42—44no—
779C23—22no—
780C23—21no—
781C23—21no—
782C23—24no—
783C23—28no—
784C23—28no—
785C23—24no—
786C23—24no—
787C23—48no—
788C23—84no—
789C23—84no—
790C23—88no—
791C23—88no—
792C23C2×H(5,𝔽2)12yes—
793C23C2×2−1+414yes—
794C23C2611yescharacteristic
795Q8—44no—
796Q8—48no—
797Q8—44no—
798Q8—416no—
799Q8—88no—
800Q8—88no—
801D4—416no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—48no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—48no—
853C2×C4—84no—
854C2×C4—88no—
855C2×C4—164no—
856C2×C4—164no—
857C2×C4#563116yes—
858C2×C4C2×H(5,𝔽2)14yes—
859C2×C4C2×2−1+414yes—
860C2×C4C2×2−1+414yes—
861C2×C4#58514yes—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—44no—
867C22—44no—
868C22—48no—
869C22—44no—
870C22—48no—
871C22—168no—
872C22C2×#56314yes—
873C22C22×H(5,𝔽2)11yescharacteristic
874C22C22×2−1+412yes—
875C22C2×#58512yes—
876C22H(7,𝔽2)11yescharacteristic
877C222−1+611yescharacteristic
878C4—24no—
879C4—41no—
880C4—41no—
881C4—42no—
882C4—44no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—48no—
895C4C2×#56318yes—
896C2—24no—
897C2—84no—
898C2C22×#56311yescharacteristic
899C2#6282111yescharacteristic
900C2#6287511yescharacteristic
901C2#6293212yes—
902C2#6296212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53153C2semidirect
2. #53114C2semidirect
3. #53113C2semidirect
4. #52994C2semidirect
5. #52511C2semidirect
6. #52396C2semidirect
7. #46347C2semidirect
8. #46343C2semidirect
9. #46341C2semidirect
10. #46332C2semidirect
11. #46168C2semidirect
13. #35662C2semidirect
16. #35313C2semidirect
18. #35159C2semidirect
19. #34953C2semidirect
26. #2863C22semidirect
27. #2863C22semidirect
31. #2841C22semidirect
32. #2838C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2836C22semidirect
36. #2836C22semidirect
37. #2835C22semidirect
38. #2834C22semidirect
39. #2831C22semidirect
40. #2831C22semidirect
41. #2821C22semidirect
42. #2817C22semidirect
43. #2793C22semidirect
44. #2787C22semidirect
45. #2777C22semidirect
46. #2775C22semidirect
47. #2773C22semidirect
48. #2771C22semidirect
49. #2770C22semidirect
50. #2765C22semidirect
51. #2764C22semidirect
52. #2759C22semidirect
53. #2745C22semidirect
54. #2738C22semidirect
55. #2729C22semidirect
56. #2725C22semidirect
57. #2722C22semidirect
58. #2721C22semidirect
59. #2720C22semidirect
60. #2716C22semidirect
61. #2698C22semidirect
62. #2690C22semidirect
63. #2689C22semidirect
64. #2677C22semidirect
66. #2645C22semidirect
67. #2645C22semidirect
74. #2584C22semidirect
75. #2584C22semidirect
76. #2584C22semidirect
77. #2584C22semidirect
80. #2582C22semidirect
81. #2582C22semidirect
82. #2581C22semidirect
83. #2581C22semidirect
86. #2567C22semidirect
87. #2567C22semidirect
88. #2546C22semidirect
89. #2546C22semidirect
92. #2514C22semidirect
93. #2514C22semidirect
98. #2511C22semidirect
99. #2511C22semidirect
100. #2509C22semidirect
101. #2509C22semidirect
102. #2508C22semidirect
103. #2508C22semidirect
104. #2507C22semidirect
105. #2507C22semidirect
106. #2506C22semidirect
107. #2506C22semidirect
119. #2453C22semidirect
120. #2453C22semidirect
123. #2451C22semidirect
124. #2451C22semidirect
138. #2399C22semidirect
139. #2399C22semidirect
142. #2383C22semidirect
143. #2378C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×C4⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#531532
#531142
#531132
#529942
#525112
#523962
#463472
#463432
#463412
#463322
#461682
#356792
#356622
#356262
#355152
#353132
#352662
#351592
#349532
C2×#25922