Finite Group Databasebeta

← #7642125

Subgroups — #7642125

Order 512.

4782 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37407C214yesmaximal, complemented
2#37403C214yesmaximal, complemented
3#37360C214yesmaximal, complemented
4#37355C214yesmaximal, complemented
5#37350C214yesmaximal, complemented
6#37347C214yesmaximal, complemented
7#37342C214yesmaximal, complemented
8#37339C214yesmaximal, complemented
9#37236C214yesmaximal, complemented
10#37124C214yesmaximal, complemented
11#36757C218yesmaximal, complemented
12#35267C212yesmaximal, complemented
13#35265C212yesmaximal, complemented
14#35257C212yesmaximal, complemented
15#35255C212yesmaximal, complemented
16#35224C211yesmaximal, characteristic, complemented
17#35223C211yesmaximal, characteristic
18#35157C212yesmaximal, complemented
19#34065C212yesmaximal, complemented
20C2×#2317C211yesmaximal, characteristic, complemented
21C2×#544C2211yescharacteristic
22C2×#537C2211yescharacteristic
23C2×#525C2212yes—
24C2×C4×#41C2212yes—
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2864C2214yescomplemented
29#2863C2214yescomplemented
30#2860C2214yescomplemented
31#2859C2214yescomplemented
32#2857C2214yescomplemented
33#2855C2214yescomplemented
34#2854C2214yescomplemented
35#2853C2218yes—
36#2851C2214yescomplemented
37#2848C2214yes—
38#2847C2214yes—
39#2796C2218yes—
40#2795C2214yescomplemented
41#2794C2214yescomplemented
42#2793C2218yescomplemented
43#2792C2214yescomplemented
44#2791C2218yescomplemented
45#2790C2218yescomplemented
46#2789C2214yescomplemented
47#2787C2218yes—
48#2786C2218yes—
49#2785C2214yescomplemented
50#2783C2218yescomplemented
51#2782C2218yes—
52#2782C2214yescomplemented
53#2781C2218yescomplemented
54#2775C2218yescomplemented
55#2770C2218yes—
56#2769C2214yescomplemented
57#2767C2218yescomplemented
58#2765C2218yescomplemented
59#2757C2218yes—
60#2750C2218yes—
61#2747C2218yes—
62#2746C2218yes—
63#2744C2218yescomplemented
64#2728C2218yes—
65#2723C2218yes—
66#2721C2218yescomplemented
67#2720C2218yescomplemented
68#2718C2218yescomplemented
69#2711C2218yes—
70#2708C2218yes—
71#2691C2218yes—
72#2690C2218yes—
73#2681C2218yes—
74#2680C2214yescomplemented
75#2647C2214yescomplemented
76#2647C2214yescomplemented
77#2645C2214yescomplemented
78#2644C2214yescomplemented
79#2629C2214yescomplemented
80#2628C2214yescomplemented
81#2627C2214yes—
82#2625C2214yescomplemented
83#2624C2214yescomplemented
84#2622C2218yes—
85#2618C2214yes—
86#2510C2218yes—
87#2509C2214yescomplemented
88#2508C2214yescomplemented
89#2507C2214yescomplemented
90#2506C2214yescomplemented
91#2505C2218yes—
92#2500C2214yes—
93#2500C2214yes—
94#2499C2214yes—
95#2499C2214yes—
96#2497C2214yescomplemented
97#2496C2214yescomplemented
98#2495C2214yescomplemented
99#2494C2214yescomplemented
100#2485C2214yes—
101#2485C2214yes—
102#2485C2214yes—
103#2485C2214yes—
104#2481C2218yes—
105#2473C2218yes—
106#2454C2214yescomplemented
107#2453C2214yescomplemented
108#2452C2214yescomplemented
109#2451C2214yescomplemented
110#2450C2218yes—
111#2449C2218yes—
112#2444C2218yes—
113#2443C2218yes—
114#2442C2214yes—
115#2442C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2423C2214yescomplemented
119#2422C2214yescomplemented
120#2421C2214yescomplemented
121#2420C2214yescomplemented
122#2417C2214yes—
123#2417C2214yes—
124#2416C2214yes—
125#2416C2214yes—
126#2324C2212yes—
127#2324C2212yes—
128#2324C2212yes—
129#2324C2212yes—
130#2323C2212yes—
131#2323C2212yes—
132#2323C2212yes—
133#2323C2212yes—
134#2322C2214yes—
135#2322C2214yes—
136#2321C2214yes—
137#2321C2214yes—
138#2317C2214yes—
139#2317C2214yes—
140#2317C2214yes—
141#2317C2214yes—
142#2317C2212yes—
143#2317C2212yes—
144#2317C2212yes—
145#2316C2211yescharacteristic
146#2316C2211yescharacteristic
147#2311C2212yes—
148#2311C2212yes—
149#2311C2212yes—
150#2297C2212yes—
151#2296C2212yes—
152#2293C2214yes—
153#2293C2214yes—
154C2×#389C2212yes—
155C2×#389C2212yes—
156#2290C2214yes—
157#2290C2214yes—
158C2×#385C2214yes—
159C2×#384C2212yes—
160C2×#382C2212yes—
161#2280C2212yes—
162C4×#117C2212yes—
163C22×#41C2312yes—
164C24×C4C2311yescharacteristic
165C24×C4C2312yes—
166#544—44no—
167#537—44no—
168C2×C4⋊Q8C2314yes—
169C2×#126C2318yes—
170C2×#125C2314yes—
171C2×#125C2318yes—
172#525—216no—
173C2×#123C2314yes—
174C2×#123C2318yes—
175C2×C22⋊Q8C2312yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2318yes—
181C2×#121C2312yes—
182C2×#121C2312yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2318yes—
186C2×#120C2314yes—
187C4×#41—48no—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2312yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2312yes—
195C2×C4×D4C2312yes—
196C2×#117—28no—
197C2×#117—44no—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2314yes—
202C2×#117C2314yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2314yes—
208C22×C4⋊C4—44no—
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2314yes—
213C22×C4⋊C4C2314yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2314yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2314yes—
224#401C2318yes—
225#400C2318yes—
226#400C2314yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#399C2318yes—
237#399C2318yes—
238#398C2314yes—
239#398C2314yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2314yes—
265#395C2314yes—
266#395C2318yes—
267#394C2314yes—
268#394C2314yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#393C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2312yes—
280#391C2312yes—
281#391C2318yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2312yes—
290#390C2312yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
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#387C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2314yes—
364#386C2314yes—
365#386C2314yes—
366#386C2314yes—
367#386C2314yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2314yes—
381#385C2314yes—
382#385C2314yes—
383#385C2314yes—
384#385C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#384C2314yes—
391#384C2318yes—
392#384C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#383C2318yes—
397#382C2314yes—
398#382C2318yes—
399#382C2314yes—
400#382C2314yes—
401#382C2314yes—
402#382C2314yes—
403#382C2318yes—
404#381C2314yes—
405#381C2318yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2312yes—
415#380C2312yes—
416#380C2312yes—
417#380C2312yes—
418#380C2318yes—
419#380C2318yes—
420#380C2318yes—
421#379C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434#376C2314yes—
435C2×#95C2314yes—
436C2×#95C2314yes—
437C43C2314yes—
438C25C2411yescharacteristic
439C2×#41—28no—
440C2×#41—28no—
441C2×#41—28no—
442C22×Q8C2412yes—
443C22×Q8C2414yes—
444C22×D4C2414yes—
445C22×D4C2412yes—
446C22×D4C2414yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—44no—
452C23×C4—84no—
453C23×C4#4118yes—
454C23×C4C2414yes—
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2418yes—
464C23×C4C2414yes—
465C23×C4C2414yes—
466C23×C4C2411yescharacteristic
467C4⋊Q8—48no—
468#126—88no—
469#125—48no—
470#125—88no—
471#123—216no—
472#123—88no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—48no—
476C22⋊Q8—48no—
477C22⋊Q8—88no—
478C22⋊Q8—88no—
479#121—28no—
480#121—28no—
481#121—48no—
482#121—48no—
483#121—88no—
484#120—216no—
485C4×Q8—44no—
486C4×Q8—44no—
487C4×D4—216no—
488C4×D4—216no—
489C4×D4—44no—
490C4×D4—44no—
491C4×D4—48no—
492C4×D4—48no—
493#117—216no—
494#117—216no—
495#117—28no—
496#117—28no—
497#117—28no—
498#117—44no—
499#117—44no—
500#117—44no—
501#117—44no—
502#117—48no—
503C2×C4⋊C4—28no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—48no—
507C2×C4⋊C4—48no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—84no—
512C2×C4⋊C4—84no—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2411yescharacteristic
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C22⋊C4—28no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C42—28no—
586C2×C42—28no—
587C2×C42—48no—
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2414yes—
592C2×C42C2412yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2418yes—
633#95C2414yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639C24—22no—
640C24—22no—
641C24—42no—
642C24—42no—
643C24C2×#4114yes—
644C24C2514yes—
645C24C2512yes—
646C24C2511yescharacteristic
647#41—432no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—44no—
652C2×Q8—48no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—232no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—816no—
700C22×C4C2×#4114yes—
701C22×C4C2×#4118yes—
702C22×C4C2×#4118yes—
703C22×C4C2×#4114yes—
704C22×C4H(5,𝔽2)14yes—
705C22×C42−1+414yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2514yes—
713C22×C4C2518yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2512yes—
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2512yes—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—41no—
742C4⋊C4—41no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—44no—
777C22⋊C4—48no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—48no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—48no—
792C22⋊C4—44no—
793C42—28no—
794C42—28no—
795C42—28no—
796C42—24no—
797C42—24no—
798C42—24no—
799C42—24no—
800C42—28no—
801C42—28no—
802C42—44no—
803C42—44no—
804C42—44no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—28no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—48no—
825C23—44no—
826C23—48no—
827C23—44no—
828C23C22×#4114yes—
829C23C22×#4112yes—
830C23C2×H(5,𝔽2)12yes—
831C23C2×2−1+412yes—
832C23C2611yescharacteristic
833Q8—48no—
834Q8—164no—
835D4—416no—
836D4—48no—
837D4—88no—
838D4—88no—
839D4—164no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—28no—
845C2×C4—216no—
846C2×C4—216no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—28no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—416no—
888C2×C4—416no—
889C2×C4—84no—
890C2×C4—84no—
891C2×C4—84no—
892C2×C4—84no—
893C2×C4—88no—
894C2×C4—88no—
895C2×C4—816no—
896C2×C4#539116yes—
897C2×C4C22×#4112yes—
898C2×C4C22×#4112yes—
899C2×C4C22×#4114yes—
900C2×C4C2×H(5,𝔽2)14yes—
901C2×C4C2×2−1+414yes—
902C22—24no—
903C22—22no—
904C22—24no—
905C22—22no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—416no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22C2×#53914yes—
922C22C23×#4111yescharacteristic
923C22C22×H(5,𝔽2)11yescharacteristic
924C22C22×2−1+411yescharacteristic
925C22H(7,𝔽2)12yes—
926C222−1+612yes—
927C4—22no—
928C4—22no—
929C4—48no—
930C4—44no—
931C4—44no—
932C4—42no—
933C4—42no—
934C4—44no—
935C4—44no—
936C4—44no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—44no—
941C4—42no—
942C4—44no—
943C4C2×#53918yes—
944C2—24no—
945C2—44no—
946C2—84no—
947C2C22×#53911yescharacteristic
948C2#6285612yes—
949C2#6287411yescharacteristic
950C2#6287712yes—
951C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37407C2semidirect
2. #37403C2semidirect
3. #37360C2semidirect
4. #37355C2semidirect
5. #37350C2semidirect
6. #37347C2semidirect
7. #37342C2semidirect
8. #37339C2semidirect
9. #37236C2semidirect
10. #37124C2semidirect
11. #36757C2semidirect
12. #35267C2semidirect
13. #35265C2semidirect
14. #35257C2semidirect
15. #35255C2semidirect
16. #35224C2semidirect
18. #35157C2semidirect
19. #34065C2semidirect
20. C2×#2317C2semidirect
28. #2864C22semidirect
29. #2863C22semidirect
30. #2860C22semidirect
31. #2859C22semidirect
32. #2857C22semidirect
33. #2855C22semidirect
34. #2854C22semidirect
36. #2851C22semidirect
40. #2795C22semidirect
41. #2794C22semidirect
42. #2793C22semidirect
43. #2792C22semidirect
44. #2791C22semidirect
45. #2790C22semidirect
46. #2789C22semidirect
49. #2785C22semidirect
50. #2783C22semidirect
52. #2782C22semidirect
53. #2781C22semidirect
54. #2775C22semidirect
56. #2769C22semidirect
57. #2767C22semidirect
58. #2765C22semidirect
63. #2744C22semidirect
66. #2721C22semidirect
67. #2720C22semidirect
68. #2718C22semidirect
74. #2680C22semidirect
75. #2647C22semidirect
76. #2647C22semidirect
77. #2645C22semidirect
78. #2644C22semidirect
79. #2629C22semidirect
80. #2628C22semidirect
82. #2625C22semidirect
83. #2624C22semidirect
87. #2509C22semidirect
88. #2508C22semidirect
89. #2507C22semidirect
90. #2506C22semidirect
96. #2497C22semidirect
97. #2496C22semidirect
98. #2495C22semidirect
99. #2494C22semidirect
106. #2454C22semidirect
107. #2453C22semidirect
108. #2452C22semidirect
109. #2451C22semidirect
118. #2423C22semidirect
119. #2422C22semidirect
120. #2421C22semidirect
121. #2420C22semidirect

Maximal subgroups

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

subgroupindex
#374072
#374032
#373602
#373552
#373502
#373472
#373422
#373392
#372362
#371242
#367572
#352672
#352652
#352572
#352552
#352242
#352232
#351572
#340652
C2×#23172