Finite Group Databasebeta

← #7731026

Subgroups — #7731026

Order 512.

4660 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50188C214yesmaximal, complemented
2#50182C214yesmaximal, complemented
3#46997C212yesmaximal, complemented
4#46390C212yesmaximal, complemented
5#46389C212yesmaximal, complemented
6#46388C212yesmaximal, complemented
7#44472C218yesmaximal, complemented
8#39546C214yesmaximal, complemented
9#38202C214yesmaximal, complemented
10#37922C218yesmaximal, complemented
11#37857C214yesmaximal, complemented
12#37481C211yesmaximal, characteristic, complemented
13#37335C214yesmaximal, complemented
14#36391C214yesmaximal, complemented
15#35614C214yesmaximal, complemented
16#35262C211yesmaximal, characteristic, complemented
17#35076C211yesmaximal, characteristic
18#34809C211yesmaximal, characteristic, complemented
19#34363C211yesmaximal, characteristic, complemented
20#34179C211yesmaximal, characteristic, complemented
21#34058C211yesmaximal, characteristic, complemented
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2860C2214yescomplemented
26#2859C2214yescomplemented
27#2854C2212yes—
28#2854C2214yescomplemented
29#2847C2212yes—
30#2842C2212yes—
31#2842C2212yes—
32#2807C2218yescomplemented
33#2777C2218yescomplemented
34#2773C2218yescomplemented
35#2766C2218yescomplemented
36#2765C2218yescomplemented
37#2761C2218yes—
38#2757C2218yescomplemented
39#2756C2218yescomplemented
40#2746C2218yescomplemented
41#2740C2218yescomplemented
42#2735C2218yescomplemented
43#2727C2218yescomplemented
44#2706C2218yescomplemented
45#2705C2218yescomplemented
46#2697C2218yescomplemented
47#2695C2218yescomplemented
48#2694C2218yescomplemented
49#2694C2218yescomplemented
50#2685C2218yes—
51#2685C2218yescomplemented
52#2667C2214yescomplemented
53#2667C2214yescomplemented
54#2635C2214yes—
55#2629C2214yescomplemented
56#2629C2214yescomplemented
57#2624C2214yes—
58#2624C2214yescomplemented
59#2609C2218yescomplemented
60#2608C2214yescomplemented
61#2601C2218yes—
62#2597C2218yescomplemented
63#2594C2218yescomplemented
64#2591C2212yes—
65#2590C2218yescomplemented
66#2576C2218yescomplemented
67#2576C2218yescomplemented
68#2558C2218yescomplemented
69#2554C2218yescomplemented
70#2554C2218yescomplemented
71#2553C2218yescomplemented
72#2553C2218yescomplemented
73#2539C2212yes—
74#2531C2218yescomplemented
75#2529C2218yescomplemented
76#2526C2218yescomplemented
77#2519C2218yescomplemented
78#2519C2218yescomplemented
79#2516C2218yescomplemented
80#2513C2218yescomplemented
81#2512C2214yescomplemented
82#2508C2214yescomplemented
83#2507C2214yescomplemented
84#2504C2212yescomplemented
85#2501C2212yescomplemented
86#2500C2214yes—
87#2496C2214yescomplemented
88#2494C2214yescomplemented
89#2490C2214yescomplemented
90#2487C2212yes—
91#2487C2212yescomplemented
92#2486C2212yescomplemented
93#2485C2214yes—
94#2484C2212yescomplemented
95#2483C2212yes—
96#2482C2212yescomplemented
97#2482C2214yescomplemented
98#2480C2218yescomplemented
99#2479C2218yescomplemented
100#2479C2218yescomplemented
101#2478C2218yescomplemented
102#2475C2218yescomplemented
103#2471C2218yescomplemented
104#2454C2214yescomplemented
105#2441C2214yescomplemented
106#2441C2214yescomplemented
107#2422C2214yescomplemented
108#2414C2214yes—
109#2411C2218yes—
110#2408C2212yes—
111#2405C2212yes—
112#2405C2212yes—
113#2405C2212yes—
114#2405C2212yes—
115#2403C2212yes—
116#2395C2214yes—
117#2377C2214yes—
118#2373C2218yescomplemented
119#2363C2214yes—
120#2347C2214yescomplemented
121#2347C2214yescomplemented
122#2346C2218yescomplemented
123#2346C2214yescomplemented
124#2346C2214yescomplemented
125#2344C2212yescomplemented
126#2342C2214yescomplemented
127D4×C22⋊C4C2212yescomplemented
128#2333C2214yescomplemented
129#2324C2214yescomplemented
130#2324C2214yescomplemented
131#2321C2214yes—
132#2319C2214yes—
133#2319C2214yescomplemented
134#2317C2212yescomplemented
135#2316C2212yescomplemented
136#2316C2212yescomplemented
137#2314C2214yescomplemented
138#2312C2211yescharacteristic
139#2312C2211yescharacteristic
140#2312C2212yes—
141#2312C2212yes—
142#2312C2212yescomplemented
143#2309C2211yescharacteristic
144#2309C2211yescharacteristic
145#2309C2212yes—
146#2309C2212yescomplemented
147#2308C2212yes—
148C4×#125C2214yescomplemented
149C4×#123C2214yescomplemented
150#2296C2212yescomplemented
151#2293C2214yes—
152#2293C2214yescomplemented
153#2293C2214yescomplemented
154#2283C2214yescomplemented
155#2280C2211yescharacteristic
156#2280C2211yescharacteristic
157#2280C2211yescharacteristic
158#2280C2211yescharacteristic
159#2280C2212yescomplemented
160#2280C2212yescomplemented
161#2274C2212yescomplemented
162C4×#117C2212yescomplemented
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#126C2318yes—
171C2×#125C2314yes—
172C2×#125C2318yes—
173C2×#123C2314yes—
174C2×#123C2314yes—
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×#123C2318yes—
178C2×#121—28no—
179C2×#121C2312yes—
180C2×#121C2312yes—
181C2×#121C2312yes—
182C2×#121C2312yes—
183C2×#121C2314yes—
184C2×#120C2314yes—
185C2×#120C2314yes—
186C2×C4×D4—28no—
187C2×C4×D4C2312yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2314yes—
192C2×#117—28no—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2314yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2318yes—
204C2×#117C2312yes—
205C2×#117C2314yes—
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2314yes—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217#401C2318yes—
218#400C2314yes—
219#400C2318yes—
220#400C2314yes—
221#400C2318yes—
222#399C2318yes—
223#399C2318yes—
224#399C2318yes—
225#399C2318yes—
226#399C2314yes—
227#399C2314yes—
228#399C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2314yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2314yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2314yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#392C2318yes—
264#392C2314yes—
265#390C2314yes—
266#390C2314yes—
267#390C2314yes—
268#390C2314yes—
269#390C2318yes—
270#390C2318yes—
271#390C2314yes—
272#390C2318yes—
273#390C2314yes—
274#390C2318yes—
275#390C2314yes—
276#390C2318yes—
277#390C2314yes—
278#390C2318yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2314yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2314yes—
295#389C2318yes—
296#389C2318yes—
297#389C2314yes—
298#388C2314yes—
299#388C2314yes—
300#388C2314yes—
301#388C2314yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2314yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2314yes—
343#386C2318yes—
344#386C2318yes—
345#386C2314yes—
346#386C2318yes—
347#386C2314yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#385C2314yes—
352#385C2314yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2318yes—
357#385C2314yes—
358#385C2318yes—
359#385C2314yes—
360#385C2314yes—
361#384C2314yes—
362#384C2314yes—
363#383C2318yes—
364#382C2314yes—
365#382C2318yes—
366#382C2318yes—
367#382C2318yes—
368#381C2314yes—
369#381C2312yes—
370#381C2314yes—
371#381C2312yes—
372#381C2314yes—
373#381C2312yes—
374#381C2312yes—
375#381C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2312yes—
379#380C2312yes—
380#380C2312yes—
381#380C2312yes—
382#380C2314yes—
383#380C2314yes—
384#380C2312yes—
385#380C2314yes—
386#380C2312yes—
387#380C2312yes—
388#380C2312yes—
389#380C2312yes—
390#380C2318yes—
391#380C2312yes—
392#380C2314yes—
393#379C2311yescharacteristic
394#379C2312yes—
395#379C2311yescharacteristic
396#379C2311yescharacteristic
397#379C2311yescharacteristic
398#379C2312yes—
399#379C2312yes—
400#379C2314yes—
401#379C2314yes—
402#379C2314yes—
403#379C2312yes—
404#379C2314yes—
405#379C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432#376C2314yes—
433#376C2318yes—
434C43C2314yes—
435C25C2412yes—
436C25C2411yescharacteristic
437C25C2411yescharacteristic
438C22×D4—24no—
439C22×D4—28no—
440C22×D4—24no—
441C22×D4—44no—
442C22×D4—44no—
443C22×D4—84no—
444C22×D4C2412yes—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C22×D4C2412yes—
450C22×D4C2418yes—
451C23×C4—24no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4#4118yes—
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2412yes—
466C23×C4C2418yes—
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470#126—416no—
471#126—88no—
472#126—88no—
473#125—48no—
474#125—88no—
475#123—48no—
476#123—84no—
477#123—84no—
478#123—88no—
479#123—84no—
480#121—28no—
481#121—28no—
482#121—28no—
483#121—28no—
484#121—48no—
485#120—48no—
486#120—84no—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—28no—
491C4×D4—48no—
492#117—28no—
493#117—28no—
494#117—28no—
495#117—28no—
496#117—44no—
497#117—44no—
498#117—48no—
499#117—44no—
500#117—416no—
501#117—44no—
502#117—44no—
503#117—44no—
504#117—84no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C22⋊C4—28no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—28no—
543C2×C22⋊C4—84no—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C42—28no—
588C2×C42—24no—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2418yes—
597C2×C42C2414yes—
598C2×C42C2418yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—22no—
633C24—24no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—44no—
639C24—42no—
640C24—42no—
641C24—44no—
642C24—44no—
643C24C2×#4114yes—
644C24C2512yes—
645C24C2514yes—
646C24C2511yescharacteristic
647C24C2511yescharacteristic
648C24C2511yescharacteristic
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—416no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—88no—
670C2×D4—816no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—416no—
685C22×C4—44no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—48no—
692C22×C4—44no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—88no—
698C22×C4C2×#4114yes—
699C22×C4C2×#4114yes—
700C22×C4C2×#4114yes—
701C22×C4C2×#4114yes—
702C22×C4C2×#4114yes—
703C22×C4C2×#4114yes—
704C22×C4C2512yes—
705C22×C4C2514yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2518yes—
709C22×C4C2518yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2511yescharacteristic
716C22×C4C2511yescharacteristic
717C22×C4C2511yescharacteristic
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—216no—
731C4⋊C4—28no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—48no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—216no—
759C22⋊C4—42no—
760C22⋊C4—44no—
761C22⋊C4—48no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—44no—
765C22⋊C4—42no—
766C22⋊C4—48no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—44no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—42no—
776C22⋊C4—48no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—44no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—44no—
793C42—28no—
794C42—28no—
795C42—24no—
796C42—24no—
797C42—28no—
798C42—28no—
799C42—28no—
800C42—44no—
801C42—44no—
802C42—44no—
803C42—48no—
804C42—48no—
805C42—44no—
806C42—48no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—28no—
820C23—22no—
821C23—24no—
822C23—28no—
823C23—22no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—48no—
832C23—82no—
833C23—82no—
834C23—84no—
835C23—84no—
836C23—88no—
837C23—88no—
838C23—168no—
839C23C22×#4112yes—
840C23C22×#4112yes—
841C23C22×#4112yes—
842C23C2611yescharacteristic
843D4—48no—
844D4—48no—
845D4—48no—
846D4—84no—
847D4—88no—
848D4—88no—
849D4—168no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—24no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—48no—
892C2×C4—48no—
893C2×C4—84no—
894C2×C4—84no—
895C2×C4—84no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—816no—
899C2×C4C22×#4112yes—
900C2×C4C22×#4112yes—
901C2×C4C22×#4112yes—
902C2×C4C22×#4112yes—
903C2×C4#58514yes—
904C2×C4#58514yes—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—42no—
918C22—44no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—42no—
923C22—48no—
924C22—44no—
925C22—44no—
926C22—48no—
927C22—88no—
928C22—88no—
929C22—168no—
930C22C23×#4111yescharacteristic
931C22C2×#58512yes—
932C22C2×#58512yes—
933C22H(7,𝔽2)12yes—
934C4—22no—
935C4—22no—
936C4—22no—
937C4—24no—
938C4—42no—
939C4—44no—
940C4—44no—
941C4—42no—
942C4—44no—
943C4—44no—
944C4—44no—
945C4—44no—
946C4—48no—
947C4—44no—
948C4—48no—
949C4#349114yes—
950C2—42no—
951C2—42no—
952C2—42no—
953C2—82no—
954C2—84no—
955C2C2×#349111yescharacteristic
956C2#6281411yescharacteristic
957C2#6285511yescharacteristic
958C2#6293714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35076C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50188C2semidirect
2. #50182C2semidirect
3. #46997C2semidirect
4. #46390C2semidirect
5. #46389C2semidirect
6. #46388C2semidirect
7. #44472C2semidirect
8. #39546C2semidirect
9. #38202C2semidirect
10. #37922C2semidirect
11. #37857C2semidirect
12. #37481C2semidirect
13. #37335C2semidirect
14. #36391C2semidirect
15. #35614C2semidirect
16. #35262C2semidirect
18. #34809C2semidirect
19. #34363C2semidirect
20. #34179C2semidirect
21. #34058C2semidirect
25. #2860C22semidirect
26. #2859C22semidirect
28. #2854C22semidirect
32. #2807C22semidirect
33. #2777C22semidirect
34. #2773C22semidirect
35. #2766C22semidirect
36. #2765C22semidirect
38. #2757C22semidirect
39. #2756C22semidirect
40. #2746C22semidirect
41. #2740C22semidirect
42. #2735C22semidirect
43. #2727C22semidirect
44. #2706C22semidirect
45. #2705C22semidirect
46. #2697C22semidirect
47. #2695C22semidirect
48. #2694C22semidirect
49. #2694C22semidirect
51. #2685C22semidirect
52. #2667C22semidirect
53. #2667C22semidirect
55. #2629C22semidirect
56. #2629C22semidirect
58. #2624C22semidirect
59. #2609C22semidirect
60. #2608C22semidirect
62. #2597C22semidirect
63. #2594C22semidirect
65. #2590C22semidirect
66. #2576C22semidirect
67. #2576C22semidirect
68. #2558C22semidirect
69. #2554C22semidirect
70. #2554C22semidirect
71. #2553C22semidirect
72. #2553C22semidirect
74. #2531C22semidirect
75. #2529C22semidirect
76. #2526C22semidirect
77. #2519C22semidirect
78. #2519C22semidirect
79. #2516C22semidirect
80. #2513C22semidirect
81. #2512C22semidirect
82. #2508C22semidirect
83. #2507C22semidirect
84. #2504C22semidirect
85. #2501C22semidirect
87. #2496C22semidirect
88. #2494C22semidirect
89. #2490C22semidirect
91. #2487C22semidirect
92. #2486C22semidirect
94. #2484C22semidirect
96. #2482C22semidirect
97. #2482C22semidirect
98. #2480C22semidirect
99. #2479C22semidirect
100. #2479C22semidirect
101. #2478C22semidirect
102. #2475C22semidirect
103. #2471C22semidirect
104. #2454C22semidirect
105. #2441C22semidirect
106. #2441C22semidirect
107. #2422C22semidirect
118. #2373C22semidirect
120. #2347C22semidirect
121. #2347C22semidirect
122. #2346C22semidirect
123. #2346C22semidirect
124. #2346C22semidirect
125. #2344C22semidirect
126. #2342C22semidirect
127. D4×C22⋊C4C22semidirect
128. #2333C22semidirect
129. #2324C22semidirect
130. #2324C22semidirect
133. #2319C22semidirect
134. #2317C22semidirect
135. #2316C22semidirect
136. #2316C22semidirect
137. #2314C22semidirect
142. #2312C22semidirect
146. #2309C22semidirect
148. C4×#125C22semidirect
149. C4×#123C22semidirect
150. #2296C22semidirect
152. #2293C22semidirect
153. #2293C22semidirect
154. #2283C22semidirect
159. #2280C22semidirect
160. #2280C22semidirect
161. #2274C22semidirect
162. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#501882
#501822
#469972
#463902
#463892
#463882
#444722
#395462
#382022
#379222
#378572
#374812
#373352
#363912
#356142
#352622
#350762
#348092
#343632
#341792
#340582