Finite Group Databasebeta

← #7643417

Subgroups — #7643417

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40479C218yesmaximal, complemented
2#39709C214yesmaximal, complemented
3#39583C214yesmaximal, complemented
4#38803C214yesmaximal, complemented
5#38783C214yesmaximal, complemented
6#38015C218yesmaximal, complemented
7#37387C211yesmaximal, characteristic, complemented
8#37380C212yesmaximal, complemented
9#37375C212yesmaximal
10#37324C212yesmaximal, complemented
11#37309C211yesmaximal, characteristic, complemented
12#36625C212yesmaximal, complemented
13#35637C214yesmaximal, complemented
14#35609C214yesmaximal, complemented
15#35309C212yesmaximal, complemented
16#35176C214yesmaximal, complemented
17#35110C214yesmaximal, complemented
18#34281C212yesmaximal, complemented
19C4×#525C211yesmaximal, characteristic
20C2×#541C2212yes—
21C2×#541C2212yescomplemented
22C2×#533C2212yes—
23C2×#525C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2857C2212yes—
27#2857C2212yes—
28#2857C2212yes—
29#2857C2212yes—
30#2857C2212yescomplemented
31#2855C2214yes—
32#2855C2214yes—
33#2855C2214yescomplemented
34#2851C2214yes—
35#2851C2214yes—
36#2851C2212yescomplemented
37#2848C2214yes—
38#2848C2214yes—
39#2808C2214yescomplemented
40#2806C2214yescomplemented
41#2806C2214yescomplemented
42#2805C2214yescomplemented
43#2787C2218yes—
44#2768C2218yes—
45#2765C2218yes—
46#2741C2218yes—
47#2735C2218yes—
48#2727C2214yescomplemented
49#2726C2214yescomplemented
50#2726C2214yescomplemented
51#2726C2214yescomplemented
52#2722C2218yes—
53#2720C2218yes—
54#2718C2218yes—
55#2711C2218yes—
56#2704C2218yes—
57#2702C2218yes—
58#2685C2218yes—
59#2667C2218yes—
60#2667C2218yescomplemented
61#2655C2218yescomplemented
62#2638C2218yes—
63#2629C2212yes—
64#2621C2212yes—
65#2616C2214yes—
66#2611C2218yes—
67#2604C2218yescomplemented
68#2601C2218yes—
69#2594C2218yescomplemented
70#2590C2218yescomplemented
71#2565C2214yescomplemented
72#2565C2218yescomplemented
73#2562C2214yes—
74#2560C2218yes—
75#2556C2218yes—
76#2552C2214yescomplemented
77#2550C2214yescomplemented
78#2546C2214yescomplemented
79#2542C2214yes—
80#2538C2214yes—
81#2536C2214yes—
82#2531C2218yes—
83#2530C2218yes—
84#2528C2218yescomplemented
85#2527C2218yescomplemented
86#2522C2218yes—
87#2522C2218yes—
88#2522C2218yescomplemented
89#2520C2218yescomplemented
90#2519C2218yescomplemented
91#2519C2218yescomplemented
92#2507C2218yescomplemented
93#2506C2218yescomplemented
94#2496C2214yescomplemented
95#2494C2214yes—
96#2492C2214yescomplemented
97#2489C2214yes—
98#2479C2218yes—
99#2475C2218yes—
100#2468C2218yes—
101#2468C2218yescomplemented
102#2466C2218yes—
103#2462C2218yescomplemented
104#2460C2218yes—
105#2454C2218yes—
106#2429C2214yes—
107#2429C2214yescomplemented
108#2423C2214yes—
109#2423C2214yescomplemented
110#2373C2218yes—
111#2373C2218yes—
112#2371C2218yescomplemented
113#2370C2218yescomplemented
114#2334C2218yescomplemented
115#2332C2218yes—
116#2330C2212yescomplemented
117#2330C2218yescomplemented
118#2327C2212yescomplemented
119#2323C2214yes—
120#2323C2214yescomplemented
121#2319C2218yes—
122#2314C2212yes—
123#2314C2212yescomplemented
124C4×C4⋊Q8C2212yescomplemented
125C4×#125C2212yescomplemented
126C4×C22⋊Q8C2214yes—
127C4×C22⋊Q8C2214yes—
128C4×C22⋊Q8C2214yes—
129C4×C22⋊Q8C2214yes—
130C4×C22⋊Q8C2212yes—
131C4×C22⋊Q8C2212yes—
132C4×#123C2214yes—
133C4×#121C2212yes—
134C4×#121C2212yes—
135C4×#120C2214yes—
136#2297C2211yescharacteristic
137#2296C2211yescharacteristic
138#2296C2214yes—
139#2295C2214yescomplemented
140#2290C2214yes—
141#2285C2212yes—
142#2280C2211yescharacteristic
143#2280C2214yes—
144#2276C2214yescomplemented
145C42×D4C2214yes—
146C4×#117C2211yescharacteristic
147C22×#41C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150#541—216no—
151#541—48no—
152#533—48no—
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2312yes—
155C2×C4⋊Q8C2312yes—
156C2×C4⋊Q8C2312yes—
157C2×#126C2318yes—
158C2×#126C2318yes—
159C2×#126C2318yes—
160C2×#125C2312yes—
161C2×#125C2318yes—
162C2×#125C2318yes—
163C2×#125C2318yes—
164C2×#125C2314yes—
165C2×#125C2312yes—
166#525—28no—
167C2×#123C2312yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2312yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×#121C2312yes—
178C2×#120C2312yes—
179C4×#41—44no—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2312yes—
185C2×C4×D4C2314yes—
186C2×C4×D4C2314yes—
187C2×C4×D4C2314yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2314yes—
190C2×#117C2312yes—
191C2×#117C2311yescharacteristic
192C2×#117C2314yes—
193C2×#117C2311yescharacteristic
194C2×#117C2314yes—
195C2×#117C2311yescharacteristic
196C22×C42—44no—
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2311yescharacteristic
205#401C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#399C2318yes—
211#399C2318yes—
212#399C2318yes—
213#399C2318yes—
214#398C2318yes—
215#398C2318yes—
216#398C2318yes—
217#398C2318yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#396C2318yes—
233#396C2318yes—
234#396C2318yes—
235#396C2318yes—
236#396C2318yes—
237#395C2318yes—
238#395C2318yes—
239#394C2318yes—
240#394C2318yes—
241#394C2318yes—
242#394C2318yes—
243#394C2318yes—
244#393C2318yes—
245#391C2318yes—
246#391C2314yes—
247#391C2314yes—
248#391C2318yes—
249#391C2314yes—
250#391C2314yes—
251#391C2314yes—
252#391C2314yes—
253#391C2311yescharacteristic
254#391C2311yescharacteristic
255#390C2318yes—
256#390C2318yes—
257#390C2311yescharacteristic
258#390C2311yescharacteristic
259#389C2314yes—
260#389C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2314yes—
264#389C2318yes—
265#389C2318yes—
266#389C2314yes—
267#389C2314yes—
268#389C2318yes—
269#389C2318yes—
270#389C2318yes—
271#389C2318yes—
272#389C2318yes—
273#389C2318yes—
274#389C2314yes—
275#389C2318yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2312yes—
282#389C2312yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2314yes—
301#388C2314yes—
302#387C2318yes—
303#387C2318yes—
304#387C2314yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#386C2314yes—
328#386C2314yes—
329#386C2314yes—
330#385C2318yes—
331#385C2318yes—
332#385C2318yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#385C2318yes—
337#385C2318yes—
338#385C2314yes—
339#385C2314yes—
340#385C2314yes—
341#384C2312yes—
342#384C2312yes—
343#384C2318yes—
344#384C2312yes—
345#384C2312yes—
346#382C2312yes—
347#382C2312yes—
348#382C2318yes—
349#382C2314yes—
350#381C2318yes—
351#381C2318yes—
352#381C2312yes—
353#380C2314yes—
354#380C2314yes—
355#380C2314yes—
356#380C2314yes—
357#380C2314yes—
358#380C2314yes—
359#380C2318yes—
360#380C2314yes—
361#380C2314yes—
362#380C2314yes—
363#380C2314yes—
364#380C2314yes—
365#380C2314yes—
366#380C2312yes—
367#380C2312yes—
368#379C2318yes—
369#379C2312yes—
370C4×C4⋊C4C2318yes—
371C4×C4⋊C4C2314yes—
372C4×C4⋊C4C2318yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2318yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C22⋊C4C2318yes—
388C4×C22⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C2314yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2314yes—
396#376C2318yes—
397#376C2312yes—
398#376C2318yes—
399C43C2312yes—
400C25C2411yescharacteristic
401C2×#41—24no—
402C2×#41—42no—
403C2×#41—42no—
404C22×Q8C2414yes—
405C22×Q8C2411yescharacteristic
406C22×Q8C2414yes—
407C22×D4C2414yes—
408C22×D4C2412yes—
409C22×D4C2411yescharacteristic
410C23×C4—24no—
411C23×C4—28no—
412C23×C4—44no—
413C23×C4—42no—
414C23×C4—44no—
415C23×C4—42no—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2414yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C4⋊Q8—28no—
429C4⋊Q8—44no—
430C4⋊Q8—44no—
431C4⋊Q8—44no—
432#126—232no—
433#126—416no—
434#126—416no—
435#125—232no—
436#125—28no—
437#125—48no—
438#125—44no—
439#125—416no—
440#125—416no—
441#123—28no—
442C22⋊Q8—216no—
443C22⋊Q8—216no—
444C22⋊Q8—28no—
445C22⋊Q8—48no—
446C22⋊Q8—48no—
447C22⋊Q8—48no—
448C22⋊Q8—48no—
449C22⋊Q8—48no—
450C22⋊Q8—48no—
451#121—28no—
452#120—28no—
453C4×Q8—216no—
454C4×Q8—216no—
455C4×Q8—48no—
456C4×Q8—44no—
457C4×Q8—48no—
458C4×D4—216no—
459C4×D4—216no—
460C4×D4—44no—
461C4×D4—48no—
462C4×D4—48no—
463#117—28no—
464#117—42no—
465#117—42no—
466#117—48no—
467#117—48no—
468#117#4118yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2412yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2411yescharacteristic
490C2×C4⋊C4C2411yescharacteristic
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2412yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2412yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2412yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2412yes—
525C2×C42—24no—
526C2×C42—28no—
527C2×C42—44no—
528C2×C42—44no—
529C2×C42—44no—
530C2×C42—44no—
531C2×C42—44no—
532C2×C42—42no—
533C2×C42C2412yes—
534C2×C42C2418yes—
535C2×C42C2412yes—
536C2×C42C2412yes—
537C2×C42C2414yes—
538C2×C42C2412yes—
539C2×C42C2418yes—
540C2×C42C2412yes—
541C2×C42C2412yes—
542C2×C42C2411yescharacteristic
543C2×C42C2418yes—
544C2×C42C2414yes—
545C2×C42C2414yes—
546C2×C42C2418yes—
547C2×C42C2418yes—
548C2×C42C2418yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553C2×C42C2412yes—
554C2×C42C2411yescharacteristic
555#95C2414yes—
556#95C2414yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2414yes—
565#95C2414yes—
566#95C2414yes—
567#95C2414yes—
568#95C2414yes—
569#95C2414yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585C24—22no—
586C24—24no—
587C24—41no—
588C24—42no—
589C24—41no—
590C24C2512yes—
591C24C2511yescharacteristic
592C24C2512yes—
593#41—416no—
594C2×Q8—28no—
595C2×Q8—22no—
596C2×Q8—28no—
597C2×Q8—28no—
598C2×Q8—28no—
599C2×Q8—41no—
600C2×Q8—41no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×D4—24no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—22no—
607C2×D4—41no—
608C2×D4—42no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—28no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—41no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—432no—
647C22×C4—416no—
648C22×C4C2×#4114yes—
649C22×C42−1+418yes—
650C22×C4C2512yes—
651C22×C4C2518yes—
652C22×C4C2512yes—
653C22×C4C2518yes—
654C22×C4C2514yes—
655C22×C4C2512yes—
656C22×C4C2512yes—
657C22×C4C2518yes—
658C22×C4C2518yes—
659C22×C4C2514yes—
660C22×C4C2511yescharacteristic
661C22×C4C2512yes—
662C22×C4C2512yes—
663C22×C4C2512yes—
664C22×C4C2512yes—
665C22×C4C2511yescharacteristic
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—216no—
669C4⋊C4—216no—
670C4⋊C4—216no—
671C4⋊C4—216no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—216no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—216no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—42no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4C2×#4118yes—
702C22⋊C4—216no—
703C22⋊C4—28no—
704C22⋊C4—216no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—42no—
711C22⋊C4—48no—
712C22⋊C4—42no—
713C22⋊C4—48no—
714C22⋊C4—44no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4C2×#4118yes—
722C42—216no—
723C42—22no—
724C42—24no—
725C42—24no—
726C42—24no—
727C42—24no—
728C42—24no—
729C42—216no—
730C42—28no—
731C42—24no—
732C42—42no—
733C42—42no—
734C42—41no—
735C42—41no—
736C42—44no—
737C42—48no—
738C42—44no—
739C42—48no—
740C42—48no—
741C42—48no—
742C42C2×#4118yes—
743C42H(5,𝔽2)14yes—
744C23—22no—
745C23—22no—
746C23—21no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—21no—
754C23—22no—
755C23—22no—
756C23—24no—
757C23—24no—
758C23—22no—
759C23—48no—
760C23—44no—
761C23—48no—
762C23—44no—
763C23—44no—
764C23C22×#4112yes—
765C23C2×2−1+414yes—
766C23C2611yescharacteristic
767Q8—44no—
768Q8—416no—
769Q8—88no—
770D4—416no—
771D4—44no—
772D4—48no—
773C2×C4—216no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—44no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—88no—
822C2×C4C22×#4118yes—
823C2×C4C22×#4112yes—
824C2×C4C22×#4112yes—
825C2×C4C2×H(5,𝔽2)14yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C2×C4C2×2−1+414yes—
828C2×C4C2×2−1+414yes—
829C2×C4#58514yes—
830C2×C4#58512yes—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—22no—
836C22—416no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22C23×#4111yescharacteristic
850C22C22×H(5,𝔽2)11yescharacteristic
851C22C22×2−1+412yes—
852C22C2×#58512yes—
853C22C2×#58511yescharacteristic
854C4—28no—
855C4—24no—
856C4—24no—
857C4—24no—
858C4—24no—
859C4—22no—
860C4—48no—
861C4—44no—
862C4—48no—
863C4—42no—
864C4—42no—
865C4—48no—
866C4—42no—
867C4—42no—
868C4—48no—
869C4#346014yes—
870C2—44no—
871C2—42no—
872C2—82no—
873C2C2×#346011yescharacteristic
874C2#6280512yes—
875C2#6281912yes—
876C2#6283711yescharacteristic
877C2#6284011yescharacteristic
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. #40479C2semidirect
2. #39709C2semidirect
3. #39583C2semidirect
4. #38803C2semidirect
5. #38783C2semidirect
6. #38015C2semidirect
7. #37387C2semidirect
8. #37380C2semidirect
10. #37324C2semidirect
11. #37309C2semidirect
12. #36625C2semidirect
13. #35637C2semidirect
14. #35609C2semidirect
15. #35309C2semidirect
16. #35176C2semidirect
17. #35110C2semidirect
18. #34281C2semidirect
21. C2×#541C22semidirect
30. #2857C22semidirect
33. #2855C22semidirect
36. #2851C22semidirect
39. #2808C22semidirect
40. #2806C22semidirect
41. #2806C22semidirect
42. #2805C22semidirect
48. #2727C22semidirect
49. #2726C22semidirect
50. #2726C22semidirect
51. #2726C22semidirect
60. #2667C22semidirect
61. #2655C22semidirect
67. #2604C22semidirect
69. #2594C22semidirect
70. #2590C22semidirect
71. #2565C22semidirect
72. #2565C22semidirect
76. #2552C22semidirect
77. #2550C22semidirect
78. #2546C22semidirect
84. #2528C22semidirect
85. #2527C22semidirect
88. #2522C22semidirect
89. #2520C22semidirect
90. #2519C22semidirect
91. #2519C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
94. #2496C22semidirect
96. #2492C22semidirect
101. #2468C22semidirect
103. #2462C22semidirect
107. #2429C22semidirect
109. #2423C22semidirect
112. #2371C22semidirect
113. #2370C22semidirect
114. #2334C22semidirect
116. #2330C22semidirect
117. #2330C22semidirect
118. #2327C22semidirect
120. #2323C22semidirect
123. #2314C22semidirect
124. C4×C4⋊Q8C22semidirect
125. C4×#125C22semidirect
139. #2295C22semidirect
144. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#404792
#397092
#395832
#388032
#387832
#380152
#373872
#373802
#373752
#373242
#373092
#366252
#356372
#356092
#353092
#351762
#351102
#342812
C4×#5252