Finite Group Databasebeta

← #7674542

Subgroups — #7674542

Order 512.

4668 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43934C218yesmaximal, complemented
2#43052C218yesmaximal, complemented
3#39547C214yesmaximal, complemented
4#39546C214yesmaximal, complemented
5#37987C214yesmaximal, complemented
6#37986C214yesmaximal, complemented
7#37983C214yesmaximal, complemented
8#37982C214yesmaximal, complemented
9#37937C214yesmaximal, complemented
10#37936C214yesmaximal, complemented
11#35585C212yesmaximal, complemented
12#35545C212yesmaximal, complemented
13#35333C211yesmaximal, characteristic, complemented
14#35286C211yesmaximal, characteristic, complemented
15#35263C212yesmaximal
16C2×#2629C211yesmaximal, characteristic, complemented
17#34217C211yesmaximal, characteristic, complemented
18#34188C211yesmaximal, characteristic, complemented
19#34180C212yesmaximal, complemented
20#34065C211yesmaximal, characteristic
21#34052C211yesmaximal, characteristic, complemented
22C22×#125C2211yescharacteristic
23C2×#525C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2212yes—
27#2859C2214yescomplemented
28#2855C2214yes—
29#2854C2214yes—
30#2851C2212yescomplemented
31#2851C2212yescomplemented
32#2777C2218yescomplemented
33#2772C2218yescomplemented
34#2770C2218yescomplemented
35#2769C2218yescomplemented
36#2768C2218yescomplemented
37#2767C2218yescomplemented
38#2766C2218yescomplemented
39#2765C2218yes—
40#2765C2218yes—
41#2761C2218yes—
42#2750C2218yes—
43#2744C2218yes—
44#2739C2218yes—
45#2719C2218yescomplemented
46#2707C2218yes—
47#2695C2218yes—
48#2647C2212yescomplemented
49#2647C2212yescomplemented
50#2629C2214yes—
51#2629C2214yes—
52#2629C2214yes—
53#2629C2214yes—
54#2629C2214yescomplemented
55#2625C2214yes—
56#2624C2214yes—
57#2611C2218yescomplemented
58#2609C2218yes—
59#2606C2218yescomplemented
60#2601C2218yes—
61#2590C2218yescomplemented
62#2585C2218yescomplemented
63#2579C2218yes—
64#2573C2218yes—
65#2571C2214yescomplemented
66#2569C2218yes—
67#2566C2214yescomplemented
68#2565C2214yescomplemented
69#2558C2218yes—
70#2552C2214yescomplemented
71#2529C2218yescomplemented
72#2528C2218yescomplemented
73#2519C2218yescomplemented
74#2515C2218yes—
75#2514C2214yescomplemented
76#2513C2214yescomplemented
77#2512C2214yescomplemented
78#2511C2214yescomplemented
79#2510C2218yes—
80#2509C2214yescomplemented
81#2509C2214yescomplemented
82#2508C2214yescomplemented
83#2508C2214yescomplemented
84#2507C2214yescomplemented
85#2507C2214yescomplemented
86#2506C2214yescomplemented
87#2506C2214yescomplemented
88#2498C2218yes—
89#2497C2214yescomplemented
90#2496C2214yescomplemented
91#2495C2214yescomplemented
92#2494C2214yescomplemented
93#2487C2214yes—
94#2486C2214yes—
95#2485C2214yes—
96#2485C2214yes—
97#2481C2218yes—
98#2478C2218yescomplemented
99#2475C2218yes—
100#2475C2218yes—
101#2470C2218yes—
102#2442C2218yes—
103#2442C2218yes—
104#2412C2218yes—
105C2×#398C2214yes—
106C2×#396C2214yes—
107#2370C2214yescomplemented
108#2370C2214yescomplemented
109#2355C2214yescomplemented
110#2354C2214yescomplemented
111#2352C2218yes—
112#2347C2214yes—
113#2346C2214yes—
114#2345C2218yes—
115#2345C2214yes—
116#2344C2214yes—
117#2343C2218yes—
118#2342C2218yes—
119#2330C2214yescomplemented
120#2324C2212yes—
121#2324C2212yes—
122#2323C2212yes—
123#2323C2212yes—
124#2322C2214yes—
125#2321C2214yes—
126#2317C2212yes—
127#2317C2212yes—
128#2317C2212yes—
129#2317C2212yes—
130#2317C2212yes—
131#2317C2212yes—
132#2316C2212yes—
133#2316C2212yes—
134#2316C2214yes—
135#2315C2214yes—
136#2314C2214yes—
137#2314C2214yes—
138#2314C2212yescomplemented
139#2314C2212yescomplemented
140#2311C2212yes—
141#2311C2212yes—
142C4×#125C2212yescomplemented
143C4×#125C2212yescomplemented
144#2297C2211yescharacteristic
145#2296C2211yescharacteristic
146#2296C2214yes—
147#2296C2214yes—
148#2293C2214yes—
149C2×#389C2212yes—
150#2290C2214yes—
151#2285C2212yes—
152#2285C2211yescharacteristic
153#2285C2211yescharacteristic
154#2285C2214yes—
155#2285C2214yescomplemented
156C2×#384C2211yescharacteristic
157#2283C2214yes—
158#2280C2211yescharacteristic
159C2×#380C2212yes—
160#2274C2212yes—
161#2274C2212yes—
162C4×#117C2211yescharacteristic
163C22×#41C2311yescharacteristic
164C24×C4C2311yescharacteristic
165C2×#126C2318yes—
166C2×#125—28no—
167C2×#125C2312yes—
168C2×#125C2314yes—
169C2×#125C2312yes—
170C2×#125C2318yes—
171C2×#125C2318yes—
172#525—28no—
173C2×#123C2312yes—
174C2×#123C2318yes—
175C2×C22⋊Q8C2312yes—
176C2×#121C2312yes—
177C2×#120C2312yes—
178C4×#41—28no—
179C2×C4×Q8C2312yes—
180C2×C4×D4C2312yes—
181C2×C4×D4C2314yes—
182C2×C4×D4C2314yes—
183C2×#117—216no—
184C2×#117—28no—
185C2×#117C2312yes—
186C2×#117C2312yes—
187C2×#117C2314yes—
188C2×#117C2312yes—
189C2×#117C2311yescharacteristic
190C2×#117C2314yes—
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2311yescharacteristic
196C2×#117C2311yescharacteristic
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2318yes—
200C2×#117C2318yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2314yes—
208C22×C4⋊C4C2314yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2314yes—
212C22×C42C2312yes—
213C22×C42C2314yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216#401C2318yes—
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#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#394C2318yes—
255#394C2318yes—
256#391C2314yes—
257#391C2314yes—
258#391C2311yescharacteristic
259#391C2311yescharacteristic
260#390C2314yes—
261#390C2314yes—
262#390C2314yes—
263#390C2314yes—
264#390C2311yescharacteristic
265#390C2311yescharacteristic
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2318yes—
271#389C2314yes—
272#389C2314yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#389C2312yes—
291#389C2312yes—
292#389C2318yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2314yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2314yes—
311#388C2314yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2314yes—
333#387C2314yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2314yes—
343#386C2314yes—
344#386C2314yes—
345#386C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2314yes—
349#385C2318yes—
350#385C2314yes—
351#385C2314yes—
352#385C2314yes—
353#385C2314yes—
354#385C2314yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2318yes—
359#385C2314yes—
360#385C2314yes—
361#385C2318yes—
362#384C2314yes—
363#384C2314yes—
364#384C2312yes—
365#384C2314yes—
366#384C2312yes—
367#384C2312yes—
368#384C2312yes—
369#384C2312yes—
370#384C2312yes—
371#383C2318yes—
372#383C2318yes—
373#382C2311yescharacteristic
374#382C2311yescharacteristic
375#382C2314yes—
376#382C2314yes—
377#382C2318yes—
378#382C2311yescharacteristic
379#382C2311yescharacteristic
380#382C2312yes—
381#382C2312yes—
382#382C2318yes—
383#382C2318yes—
384#382C2318yes—
385#381C2318yes—
386#381C2312yes—
387#381C2318yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2318yes—
394#380C2318yes—
395#380C2312yes—
396#380C2312yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#380C2314yes—
406#379C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432#376C2312yes—
433#376C2318yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C43C2312yes—
437C25C2411yescharacteristic
438C2×#41—24no—
439C2×#41—24no—
440C2×#41—24no—
441C22×Q8C2411yescharacteristic
442C22×D4C2412yes—
443C22×D4C2411yescharacteristic
444C22×D4C2414yes—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4#4118yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2414yes—
453C23×C4C2414yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460#126—88no—
461#125—28no—
462#125—28no—
463#125—216no—
464#125—88no—
465#125—88no—
466#123—28no—
467#123—88no—
468C22⋊Q8—28no—
469#121—28no—
470#120—28no—
471C4×Q8—28no—
472C4×D4—216no—
473C4×D4—216no—
474C4×D4—28no—
475#117—216no—
476#117—28no—
477#117—28no—
478#117—216no—
479#117—28no—
480#117—28no—
481#117—24no—
482#117—24no—
483#117—24no—
484#117—28no—
485#117—28no—
486#117—28no—
487#117—28no—
488#117—28no—
489#117—88no—
490#117—88no—
491C2×C4⋊C4—28no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—28no—
494C2×C4⋊C4—216no—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—84no—
498C2×C4⋊C4—84no—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C22⋊C4—216no—
544C2×C22⋊C4—28no—
545C2×C22⋊C4—84no—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C42—216no—
571C2×C42—24no—
572C2×C42—28no—
573C2×C42#4118yes—
574C2×C42C2414yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2411yescharacteristic
580C2×C42C2411yescharacteristic
581C2×C42C2414yes—
582C2×C42C2412yes—
583C2×C42C2412yes—
584C2×C42C2414yes—
585C2×C42C2418yes—
586C2×C42C2418yes—
587C2×C42C2418yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2418yes—
591C2×C42C2411yescharacteristic
592C2×C42C2412yes—
593C2×C42C2411yescharacteristic
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2414yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2418yes—
624#95C2414yes—
625#95C2414yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630C24—22no—
631C24—22no—
632C24—42no—
633C24—42no—
634C24C2×#4114yes—
635C24C2512yes—
636C24C2512yes—
637C24C2511yescharacteristic
638#41—416no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—28no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—44no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—232no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—28no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—42no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—42no—
681C22×C4C2×#4118yes—
682C22×C4C2×#4118yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4118yes—
685C22×C4C2×#4114yes—
686C22×C4C2×#4114yes—
687C22×C42−1+414yes—
688C22×C4C2512yes—
689C22×C4C2512yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2512yes—
695C22×C4C2514yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2518yes—
700C22×C4C2512yes—
701C22×C4C2512yes—
702C22×C4C2512yes—
703C22×C4C2512yes—
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—216no—
717C4⋊C4—216no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—24no—
721C4⋊C4—28no—
722C4⋊C4—24no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—44no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—28no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—48no—
769C22⋊C4—44no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—44no—
774C42—28no—
775C42—28no—
776C42—28no—
777C42—28no—
778C42—24no—
779C42—24no—
780C42—22no—
781C42—22no—
782C42—28no—
783C42—24no—
784C42—24no—
785C42—44no—
786C42—48no—
787C42—48no—
788C42—48no—
789C42—48no—
790C42—44no—
791C42C2×#4114yes—
792C42C2×#4114yes—
793C42C2×#4118yes—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—28no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—24no—
807C23—24no—
808C23—48no—
809C23—84no—
810C23—82no—
811C23—82no—
812C23C22×#4114yes—
813C23C22×#4112yes—
814C23C22×#4112yes—
815C23C2×2−1+412yes—
816C23C2611yescharacteristic
817Q8—44no—
818D4—48no—
819D4—44no—
820D4—88no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—216no—
829C2×C4—216no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—28no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—48no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—48no—
871C2×C4—84no—
872C2×C4—88no—
873C2×C4—88no—
874C2×C4—88no—
875C2×C4#552116yes—
876C2×C4C22×#4114yes—
877C2×C4C22×#4114yes—
878C2×C4C22×#4114yes—
879C2×C4C22×#4112yes—
880C2×C4C22×#4112yes—
881C2×C4C22×#4112yes—
882C2×C4C22×#4112yes—
883C2×C4C2×2−1+412yes—
884C2×C4C2×2−1+412yes—
885C22—24no—
886C22—24no—
887C22—22no—
888C22—22no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—44no—
897C22—44no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—88no—
902C22C2×#55214yes—
903C22C23×#4111yescharacteristic
904C22C23×#4111yescharacteristic
905C22C22×2−1+411yescharacteristic
906C22H(7,𝔽2)12yes—
907C222−1+612yes—
908C4—24no—
909C4—24no—
910C4—24no—
911C4—44no—
912C4—44no—
913C4—44no—
914C4—42no—
915C4—42no—
916C4—48no—
917C4—44no—
918C4—44no—
919C4—44no—
920C4—42no—
921C4—48no—
922C4—42no—
923C4—42no—
924C4C2×#55214yes—
925C4C2×#55214yes—
926C2—24no—
927C2—44no—
928C2—82no—
929C2C22×#55211yescharacteristic
930C2#6285612yes—
931C2#6285612yes—
932C2#6288111yescharacteristic
933C2#6288911yescharacteristic
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. #43934C2semidirect
2. #43052C2semidirect
3. #39547C2semidirect
4. #39546C2semidirect
5. #37987C2semidirect
6. #37986C2semidirect
7. #37983C2semidirect
8. #37982C2semidirect
9. #37937C2semidirect
10. #37936C2semidirect
11. #35585C2semidirect
12. #35545C2semidirect
13. #35333C2semidirect
14. #35286C2semidirect
16. C2×#2629C2semidirect
17. #34217C2semidirect
18. #34188C2semidirect
19. #34180C2semidirect
21. #34052C2semidirect
27. #2859C22semidirect
30. #2851C22semidirect
31. #2851C22semidirect
32. #2777C22semidirect
33. #2772C22semidirect
34. #2770C22semidirect
35. #2769C22semidirect
36. #2768C22semidirect
37. #2767C22semidirect
38. #2766C22semidirect
45. #2719C22semidirect
48. #2647C22semidirect
49. #2647C22semidirect
54. #2629C22semidirect
57. #2611C22semidirect
59. #2606C22semidirect
61. #2590C22semidirect
62. #2585C22semidirect
65. #2571C22semidirect
67. #2566C22semidirect
68. #2565C22semidirect
70. #2552C22semidirect
71. #2529C22semidirect
72. #2528C22semidirect
73. #2519C22semidirect
75. #2514C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2511C22semidirect
80. #2509C22semidirect
81. #2509C22semidirect
82. #2508C22semidirect
83. #2508C22semidirect
84. #2507C22semidirect
85. #2507C22semidirect
86. #2506C22semidirect
87. #2506C22semidirect
89. #2497C22semidirect
90. #2496C22semidirect
91. #2495C22semidirect
92. #2494C22semidirect
98. #2478C22semidirect
107. #2370C22semidirect
108. #2370C22semidirect
109. #2355C22semidirect
110. #2354C22semidirect
119. #2330C22semidirect
138. #2314C22semidirect
139. #2314C22semidirect
142. C4×#125C22semidirect
143. C4×#125C22semidirect
155. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#439342
#430522
#395472
#395462
#379872
#379862
#379832
#379822
#379372
#379362
#355852
#355452
#353332
#352862
#352632
C2×#26292
#342172
#341882
#341802
#340652
#340522