Finite Group Databasebeta

← #7642158

Subgroups — #7642158

Order 512.

4200 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37413C214yesmaximal, complemented
2#37367C214yesmaximal, complemented
3#37353C214yesmaximal, complemented
4#37344C214yesmaximal, complemented
5#37328C214yesmaximal, complemented
6#37328C214yesmaximal, complemented
7#37295C214yesmaximal, complemented
8#37291C214yesmaximal, complemented
9#36825C218yesmaximal, complemented
10#36782C218yesmaximal, complemented
11#35335C211yesmaximal, characteristic, complemented
12#35333C211yesmaximal, characteristic
13#35286C211yesmaximal, characteristic, complemented
14#35280C211yesmaximal, characteristic
15#35267C212yesmaximal
16#35265C212yesmaximal, complemented
17#35160C212yesmaximal
18#35159C212yesmaximal, complemented
19#34074C211yesmaximal, characteristic, complemented
20C2×#2330C211yesmaximal, characteristic, complemented
21#34056C211yesmaximal, characteristic
22C2×#533C2211yescharacteristic
23C22×#125C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25#2864C2214yes—
26#2863C2214yes—
27#2860C2214yes—
28#2859C2212yes—
29#2859C2212yes—
30#2859C2214yes—
31#2859C2214yes—
32#2857C2214yes—
33#2852C2218yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2218yes—
37#2802C2218yes—
38#2802C2218yes—
39#2783C2218yes—
40#2783C2218yes—
41#2776C2218yes—
42#2776C2218yes—
43#2776C2218yes—
44#2772C2218yes—
45#2772C2218yes—
46#2769C2218yes—
47#2766C2218yes—
48#2766C2218yes—
49#2766C2218yes—
50#2762C2218yes—
51#2762C2218yes—
52#2758C2218yes—
53#2755C2218yes—
54#2747C2218yes—
55#2744C2218yes—
56#2739C2218yes—
57#2725C2218yes—
58#2725C2218yes—
59#2725C2218yes—
60#2725C2218yes—
61#2722C2218yes—
62#2719C2218yes—
63#2719C2218yes—
64#2719C2218yes—
65#2704C2218yes—
66#2698C2218yes—
67#2690C2218yes—
68#2689C2218yes—
69#2660C2214yes—
70#2647C2214yes—
71#2647C2212yes—
72#2647C2212yes—
73#2647C2214yes—
74#2646C2218yes—
75#2645C2214yes—
76#2644C2214yes—
77#2643C2218yes—
78#2629C2214yes—
79#2629C2212yes—
80#2629C2212yes—
81#2584C2214yes—
82#2584C2214yes—
83#2583C2218yes—
84#2582C2214yes—
85#2579C2218yes—
86#2571C2214yes—
87#2566C2214yes—
88#2565C2214yes—
89#2552C2214yes—
90#2538C2214yes—
91#2514C2214yes—
92#2513C2214yes—
93#2512C2214yes—
94#2511C2214yes—
95#2510C2218yes—
96#2509C2214yes—
97#2509C2214yes—
98#2509C2214yes—
99#2508C2214yes—
100#2508C2214yes—
101#2508C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2507C2214yes—
105#2506C2214yes—
106#2506C2214yes—
107#2506C2214yes—
108#2505C2218yes—
109#2497C2214yes—
110#2497C2214yes—
111#2496C2214yes—
112#2496C2214yes—
113#2495C2214yes—
114#2495C2214yes—
115#2494C2214yes—
116#2494C2214yes—
117#2481C2218yes—
118#2473C2218yes—
119#2442C2218yes—
120#2417C2218yes—
121#2331C2212yes—
122#2331C2212yes—
123#2330C2214yes—
124#2330C2214yes—
125#2330C2214yes—
126#2330C2214yes—
127#2330C2212yes—
128#2330C2212yes—
129#2329C2214yes—
130#2329C2214yes—
131#2320C2212yes—
132#2320C2212yes—
133#2319C2212yes—
134#2319C2212yes—
135#2318C2214yes—
136#2318C2214yes—
137#2317C2212yes—
138#2317C2212yes—
139#2317C2212yes—
140#2317C2212yes—
141#2316C2212yes—
142#2316C2212yes—
143#2311C2212yes—
144#2311C2212yes—
145#2298C2214yes—
146#2297C2211yescharacteristic
147#2297C2211yescharacteristic
148#2296C2211yescharacteristic
149#2296C2211yescharacteristic
150#2296C2212yes—
151#2295C2214yes—
152#2295C2214yes—
153C2×#389C2212yes—
154C2×#389C2214yes—
155C2×#387C2214yes—
156#2285C2211yescharacteristic
157C2×#384C2211yescharacteristic
158#2283C2214yes—
159C4×#117C2211yescharacteristic
160C4×#117C2212yes—
161C2×C4×C4⋊C4C2212yes—
162C2×#376C2211yescharacteristic
163C22×#41C2311yescharacteristic
164#533—28no—
165C2×C4⋊Q8C2312yes—
166C2×#126C2318yes—
167C2×#126C2318yes—
168C2×#125—28no—
169C2×#125C2314yes—
170C2×#125C2312yes—
171C2×#125C2312yes—
172C2×#125C2311yescharacteristic
173C2×#125C2311yescharacteristic
174C2×#125C2318yes—
175C2×#125C2318yes—
176C2×#125C2318yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2318yes—
179C4×#41—28no—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2314yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2314yes—
184C2×#117C2312yes—
185C2×#117C2312yes—
186C2×#117C2311yescharacteristic
187C2×#117C2311yescharacteristic
188C2×#117C2311yescharacteristic
189C2×#117C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2314yes—
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2314yes—
195C22×C42C2312yes—
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2314yes—
199C22×C42C2311yescharacteristic
200#401C2318yes—
201#401C2318yes—
202#400C2318yes—
203#400C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#395C2318yes—
247#395C2318yes—
248#391C2314yes—
249#391C2314yes—
250#391C2312yes—
251#391C2311yescharacteristic
252#391C2311yescharacteristic
253#391C2318yes—
254#391C2314yes—
255#391C2314yes—
256#391C2314yes—
257#391C2314yes—
258#390C2314yes—
259#390C2314yes—
260#390C2312yes—
261#390C2311yescharacteristic
262#390C2311yescharacteristic
263#389C2314yes—
264#389C2314yes—
265#389C2318yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2318yes—
285#389C2318yes—
286#389C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2314yes—
301#389C2312yes—
302#389C2312yes—
303#389C2312yes—
304#389C2312yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#388C2314yes—
311#388C2314yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2314yes—
323#387C2314yes—
324#387C2314yes—
325#387C2314yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2314yes—
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#387C2318yes—
351#387C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2314yes—
355#386C2312yes—
356#386C2312yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2312yes—
365#385C2312yes—
366#385C2314yes—
367#385C2314yes—
368#384C2314yes—
369#384C2314yes—
370#384C2314yes—
371#384C2314yes—
372#384C2314yes—
373#384C2312yes—
374#384C2312yes—
375#384C2312yes—
376#383C2314yes—
377#383C2314yes—
378#383C2318yes—
379#383C2318yes—
380#382C2314yes—
381#382C2314yes—
382#382C2318yes—
383#382C2314yes—
384#382C2314yes—
385#382C2314yes—
386#382C2314yes—
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2318yes—
390#382C2318yes—
391#381C2314yes—
392#381C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2318yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423#376C2312yes—
424#376C2312yes—
425#376C2312yes—
426#376C2312yes—
427#376C2314yes—
428#376C2312yes—
429C2×#95C2312yes—
430C2×#95C2312yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C43C2312yes—
434C43C2314yes—
435C2×#41—24no—
436C2×#41—24no—
437C2×#41—24no—
438C22×Q8C2411yescharacteristic
439C22×Q8C2414yes—
440C22×D4C2412yes—
441C22×D4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2414yes—
445C23×C4C2414yes—
446C23×C4C2414yes—
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C4⋊Q8—28no—
452#126—88no—
453#126—88no—
454#125—28no—
455#125—28no—
456#125—216no—
457#125—24no—
458#125—24no—
459#125—88no—
460#125—88no—
461#125—88no—
462C22⋊Q8—216no—
463C22⋊Q8—88no—
464C4×Q8—28no—
465C4×Q8—216no—
466C4×D4—216no—
467C4×D4—28no—
468#117—24no—
469#117—28no—
470#117—24no—
471#117—28no—
472#117—24no—
473#117—28no—
474C2×C4⋊C4—216no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4—28no—
477C2×C4⋊C4—84no—
478C2×C4⋊C4—84no—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2411yescharacteristic
492C2×C4⋊C4C2411yescharacteristic
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
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×C22⋊C4C2412yes—
524C2×C22⋊C4C2414yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2412yes—
528C2×C22⋊C4C2412yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2418yes—
537C2×C42—24no—
538C2×C42—24no—
539C2×C42—28no—
540C2×C42—84no—
541C2×C42#4118yes—
542C2×C42C2412yes—
543C2×C42C2414yes—
544C2×C42C2412yes—
545C2×C42C2412yes—
546C2×C42C2414yes—
547C2×C42C2414yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553C2×C42C2414yes—
554C2×C42C2414yes—
555C2×C42C2418yes—
556C2×C42C2414yes—
557C2×C42C2418yes—
558C2×C42C2414yes—
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2411yescharacteristic
562C2×C42C2412yes—
563C2×C42C2411yescharacteristic
564#95C2412yes—
565#95C2412yes—
566#95C2412yes—
567#95C2412yes—
568#95C2412yes—
569#95C2412yes—
570#95C2412yes—
571#95C2412yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2414yes—
580#95C2414yes—
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2414yes—
587#95C2414yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612C24C2512yes—
613C24C2511yescharacteristic
614#41—416no—
615C2×Q8—22no—
616C2×Q8—28no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C22×C4—28no—
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—28no—
636C22×C4—42no—
637C22×C4—44no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—42no—
648C22×C4C2×#4118yes—
649C22×C4C2×#4114yes—
650C22×C42−1+414yes—
651C22×C42−1+414yes—
652C22×C4C2512yes—
653C22×C4C2512yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C22×C4C2512yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2514yes—
660C22×C4C2512yes—
661C22×C4C2514yes—
662C22×C4C2514yes—
663C22×C4C2514yes—
664C22×C4C2518yes—
665C22×C4C2518yes—
666C22×C4C2512yes—
667C22×C4C2512yes—
668C22×C4C2512yes—
669C22×C4C2511yescharacteristic
670C22×C4C2511yescharacteristic
671C4⋊C4—216no—
672C4⋊C4—216no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—24no—
676C4⋊C4—28no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—44no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—44no—
715C22⋊C4—24no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—28no—
721C22⋊C4—44no—
722C22⋊C4—48no—
723C22⋊C4—44no—
724C22⋊C4—48no—
725C22⋊C4—48no—
726C22⋊C4—44no—
727C22⋊C4—44no—
728C22⋊C4—48no—
729C42—24no—
730C42—28no—
731C42—28no—
732C42—22no—
733C42—22no—
734C42—24no—
735C42—24no—
736C42—24no—
737C42—28no—
738C42—24no—
739C42—24no—
740C42—48no—
741C42—48no—
742C42—44no—
743C42—44no—
744C42—44no—
745C42—44no—
746C42—44no—
747C42—44no—
748C42C2×#4114yes—
749C42C2×#4114yes—
750C42C2×#4118yes—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—24no—
757C23—24no—
758C23C22×#4112yes—
759C23C2×2−1+412yes—
760C23C2×2−1+412yes—
761C23C2611yescharacteristic
762Q8—44no—
763Q8—88no—
764D4—48no—
765D4—44no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—28no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—416no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—88no—
818C2×C4—82no—
819C2×C4—88no—
820C2×C4—82no—
821C2×C4#541116yes—
822C2×C4C22×#4114yes—
823C2×C4C22×#4114yes—
824C2×C4C22×#4112yes—
825C2×C4C22×#4112yes—
826C2×C4C2×2−1+412yes—
827C2×C4C2×2−1+412yes—
828C2×C4C2×2−1+412yes—
829C2×C4C2×2−1+412yes—
830C22—24no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22C2×#54114yes—
840C22C23×#4111yescharacteristic
841C22C22×2−1+411yescharacteristic
842C22C22×2−1+411yescharacteristic
843C22H(7,𝔽2)12yes—
844C222−1+612yes—
845C4—24no—
846C4—24no—
847C4—48no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—44no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—48no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4C2×#54114yes—
863C4C2×#54114yes—
864C2—24no—
865C2—82no—
866C2C22×#54111yescharacteristic
867C2#6285612yes—
868C2#6287712yes—
869C2#6288111yescharacteristic
870C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37413C2semidirect
2. #37367C2semidirect
3. #37353C2semidirect
4. #37344C2semidirect
5. #37328C2semidirect
6. #37328C2semidirect
7. #37295C2semidirect
8. #37291C2semidirect
9. #36825C2semidirect
10. #36782C2semidirect
11. #35335C2semidirect
13. #35286C2semidirect
16. #35265C2semidirect
18. #35159C2semidirect
19. #34074C2semidirect
20. C2×#2330C2semidirect

Maximal subgroups

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

subgroupindex
#374132
#373672
#373532
#373442
#373282
#372952
#372912
#368252
#367822
#353352
#353332
#352862
#352802
#352672
#352652
#351602
#351592
#340742
C2×#23302
#340562