Finite Group Databasebeta

← #7731081

Subgroups — #7731081

Order 512.

4690 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48798C214yesmaximal, complemented
2#48796C214yesmaximal, complemented
3#47195C212yesmaximal, complemented
4#46837C212yesmaximal, complemented
5#46386C212yesmaximal, complemented
6#46385C212yesmaximal, complemented
7#43522C218yesmaximal, complemented
8#39042C214yesmaximal, complemented
9#38074C214yesmaximal, complemented
10#37938C214yesmaximal, complemented
11#37921C218yesmaximal, complemented
12#37480C211yesmaximal, characteristic, complemented
13#37330C214yesmaximal, complemented
14#36203C214yesmaximal, complemented
15#35590C214yesmaximal, complemented
16#35262C211yesmaximal, characteristic, complemented
17#35076C211yesmaximal, characteristic
18#34809C211yesmaximal, characteristic, complemented
19#34363C211yesmaximal, characteristic, complemented
20#34179C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic, complemented
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2857C2214yescomplemented
26#2854C2212yes—
27#2854C2214yescomplemented
28#2854C2214yescomplemented
29#2847C2212yes—
30#2842C2212yes—
31#2840C2212yes—
32#2798C2218yescomplemented
33#2771C2218yescomplemented
34#2764C2218yescomplemented
35#2758C2218yescomplemented
36#2751C2218yescomplemented
37#2750C2218yescomplemented
38#2749C2218yescomplemented
39#2743C2218yes—
40#2738C2218yescomplemented
41#2737C2218yescomplemented
42#2735C2218yescomplemented
43#2732C2218yescomplemented
44#2707C2218yescomplemented
45#2707C2218yescomplemented
46#2696C2218yescomplemented
47#2694C2218yescomplemented
48#2693C2218yescomplemented
49#2687C2218yescomplemented
50#2687C2218yescomplemented
51#2684C2218yes—
52#2665C2214yescomplemented
53#2665C2214yescomplemented
54#2647C2214yescomplemented
55#2644C2214yescomplemented
56#2635C2214yes—
57#2628C2214yescomplemented
58#2624C2214yes—
59#2611C2218yescomplemented
60#2607C2214yescomplemented
61#2597C2218yescomplemented
62#2597C2218yescomplemented
63#2591C2212yes—
64#2577C2218yescomplemented
65#2572C2218yescomplemented
66#2572C2218yescomplemented
67#2561C2218yescomplemented
68#2557C2218yescomplemented
69#2556C2218yescomplemented
70#2539C2212yes—
71#2534C2218yescomplemented
72#2533C2218yescomplemented
73#2532C2218yescomplemented
74#2532C2218yescomplemented
75#2529C2218yescomplemented
76#2526C2218yescomplemented
77#2526C2218yescomplemented
78#2518C2218yescomplemented
79#2515C2218yescomplemented
80#2513C2214yescomplemented
81#2509C2214yescomplemented
82#2506C2214yescomplemented
83#2504C2212yescomplemented
84#2501C2212yescomplemented
85#2500C2214yes—
86#2497C2214yescomplemented
87#2495C2214yescomplemented
88#2491C2214yescomplemented
89#2489C2218yescomplemented
90#2488C2218yescomplemented
91#2487C2212yes—
92#2487C2212yescomplemented
93#2486C2212yescomplemented
94#2485C2214yes—
95#2484C2212yescomplemented
96#2483C2212yes—
97#2482C2214yescomplemented
98#2482C2212yescomplemented
99#2477C2218yes—
100#2472C2218yescomplemented
101#2461C2218yescomplemented
102#2457C2218yescomplemented
103#2452C2214yescomplemented
104#2447C2218yescomplemented
105#2439C2214yescomplemented
106#2439C2214yescomplemented
107#2420C2214yescomplemented
108#2418C2218yes—
109#2414C2214yes—
110#2408C2212yes—
111#2405C2212yes—
112#2405C2212yes—
113#2405C2212yes—
114#2405C2212yes—
115#2403C2212yes—
116#2395C2214yes—
117#2377C2214yes—
118#2372C2218yescomplemented
119#2363C2214yes—
120#2353C2218yescomplemented
121#2347C2214yescomplemented
122#2347C2214yescomplemented
123#2346C2214yescomplemented
124#2346C2214yescomplemented
125#2344C2212yescomplemented
126#2342C2214yescomplemented
127D4×C22⋊C4C2212yescomplemented
128#2333C2214yescomplemented
129#2331C2214yescomplemented
130#2324C2214yescomplemented
131#2321C2214yes—
132#2319C2214yescomplemented
133#2318C2214yes—
134#2318C2214yescomplemented
135#2317C2212yescomplemented
136#2316C2212yescomplemented
137#2315C2212yescomplemented
138#2313C2212yescomplemented
139#2312C2211yescharacteristic
140#2312C2211yescharacteristic
141#2312C2212yes—
142#2312C2212yes—
143#2309C2212yes—
144#2309C2212yescomplemented
145#2308C2211yescharacteristic
146#2308C2211yescharacteristic
147#2308C2212yes—
148C4×#123C2214yescomplemented
149C4×#121C2214yescomplemented
150#2296C2212yescomplemented
151#2290C2214yes—
152#2290C2214yescomplemented
153#2283C2214yescomplemented
154#2283C2212yescomplemented
155#2283C2214yescomplemented
156#2280C2211yescharacteristic
157#2280C2211yescharacteristic
158#2280C2211yescharacteristic
159#2280C2211yescharacteristic
160#2280C2212yescomplemented
161#2274C2212yescomplemented
162C2×C4×C22⋊C4C2212yescomplemented
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C2×C4⋊Q8C2314yes—
169C2×#125C2318yes—
170C2×#124C2318yes—
171C2×#123C2314yes—
172C2×#123C2314yes—
173C2×#123C2314yes—
174C2×#123C2314yes—
175C2×#123C2318yes—
176C2×C22⋊Q8C2318yes—
177C2×C22⋊Q8C2318yes—
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×C4×D4C2318yes—
193C2×#117—28no—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2314yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2314yes—
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2314yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2314yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2314yes—
225#400C2318yes—
226#400C2318yes—
227#399C2318yes—
228#399C2318yes—
229#399C2314yes—
230#399C2314yes—
231#398C2314yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2314yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#395C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2314yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#393C2318yes—
259#393C2318yes—
260#393C2318yes—
261#393C2318yes—
262#393C2318yes—
263#392C2318yes—
264#392C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#390C2318yes—
271#390C2318yes—
272#390C2314yes—
273#390C2318yes—
274#390C2314yes—
275#390C2314yes—
276#390C2318yes—
277#390C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2318yes—
281#389C2318yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#388C2314yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2314yes—
295#388C2318yes—
296#388C2314yes—
297#388C2314yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#387C2314yes—
316#387C2314yes—
317#387C2314yes—
318#387C2314yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#386C2318yes—
329#386C2318yes—
330#386C2314yes—
331#386C2314yes—
332#386C2314yes—
333#386C2314yes—
334#386C2314yes—
335#386C2314yes—
336#386C2318yes—
337#386C2314yes—
338#386C2318yes—
339#386C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2314yes—
343#386C2318yes—
344#386C2314yes—
345#385C2314yes—
346#385C2314yes—
347#385C2314yes—
348#385C2314yes—
349#385C2314yes—
350#385C2314yes—
351#385C2314yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#385C2314yes—
356#385C2314yes—
357#384C2314yes—
358#383C2318yes—
359#383C2318yes—
360#383C2314yes—
361#383C2318yes—
362#382C2314yes—
363#382C2314yes—
364#382C2318yes—
365#382C2314yes—
366#381C2318yes—
367#381C2318yes—
368#381C2312yes—
369#381C2312yes—
370#381C2314yes—
371#381C2314yes—
372#381C2314yes—
373#381C2312yes—
374#381C2312yes—
375#381C2312yes—
376#381C2312yes—
377#381C2318yes—
378#380C2312yes—
379#380C2312yes—
380#380C2314yes—
381#380C2314yes—
382#380C2312yes—
383#380C2312yes—
384#380C2312yes—
385#380C2312yes—
386#380C2318yes—
387#380C2312yes—
388#380C2312yes—
389#380C2314yes—
390#380C2312yes—
391#380C2314yes—
392#380C2318yes—
393#380C2312yes—
394#380C2314yes—
395#379C2314yes—
396#379C2314yes—
397#379C2311yescharacteristic
398#379C2311yescharacteristic
399#379C2312yes—
400#379C2311yescharacteristic
401#379C2311yescharacteristic
402#379C2314yes—
403#379C2314yes—
404#379C2312yes—
405#379C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2312yes—
431#376C2314yes—
432#376C2318yes—
433#376C2318yes—
434C2×#95C2314yes—
435C25C2411yescharacteristic
436C25C2412yes—
437C25C2411yescharacteristic
438C22×Q8C2418yes—
439C22×D4—24no—
440C22×D4—28no—
441C22×D4—24no—
442C22×D4—44no—
443C22×D4—44no—
444C22×D4—84no—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2412yes—
448C22×D4C2418yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2412yes—
452C23×C4—24no—
453C23×C4—44no—
454C23×C4—44no—
455C23×C4#4118yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2414yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2418yes—
469C23×C4C2414yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C4⋊Q8—48no—
474#125—88no—
475#124—416no—
476#123—48no—
477#123—88no—
478#123—84no—
479#123—84no—
480#123—84no—
481C22⋊Q8—88no—
482C22⋊Q8—88no—
483#121—28no—
484#121—28no—
485#121—28no—
486#121—28no—
487#121—48no—
488#120—48no—
489#120—84no—
490C4×D4—28no—
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—28no—
494C4×D4—48no—
495C4×D4—416no—
496#117—28no—
497#117—28no—
498#117—28no—
499#117—28no—
500#117—44no—
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⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C22⋊C4—28no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—28no—
538C2×C22⋊C4—44no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4—84no—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C42—28no—
583C2×C42—24no—
584C2×C42—48no—
585C2×C42C2414yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2418yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2418yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2418yes—
604#95C2414yes—
605#95C2418yes—
606#95C2414yes—
607#95C2418yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—22no—
633C24—24no—
634C24—24no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—44no—
639C24—42no—
640C24—42no—
641C24—44no—
642C24—44no—
643C24C2×#4114yes—
644C24C2514yes—
645C24C2511yescharacteristic
646C24C2511yescharacteristic
647C24C2511yescharacteristic
648C24C2512yes—
649C2×Q8—48no—
650C2×Q8—48no—
651C2×Q8—48no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—216no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—28no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—48no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—416no—
672C2×D4—88no—
673C2×D4—816no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—28no—
684C22×C4—24no—
685C22×C4—28no—
686C22×C4—24no—
687C22×C4—416no—
688C22×C4—44no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—42no—
701C22×C4—44no—
702C22×C4—42no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—88no—
707C22×C4C2×#4114yes—
708C22×C4C2×#4114yes—
709C22×C4C2×#4114yes—
710C22×C4C2×#4114yes—
711C22×C4C2×#4114yes—
712C22×C4C2×#4114yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2518yes—
719C22×C4C2518yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2514yes—
723C22×C4C2512yes—
724C22×C4C2514yes—
725C22×C4C2511yescharacteristic
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—28no—
759C22⋊C4—216no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—44no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—44no—
771C22⋊C4—48no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—42no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—44no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—42no—
791C22⋊C4—48no—
792C22⋊C4—42no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C42—28no—
796C42—28no—
797C42—24no—
798C42—24no—
799C42—28no—
800C42—28no—
801C42—44no—
802C42—44no—
803C42—44no—
804C42—44no—
805C42—48no—
806C42—48no—
807C42—48no—
808C23—28no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—24no—
818C23—24no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—24no—
823C23—28no—
824C23—28no—
825C23—24no—
826C23—24no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—48no—
831C23—82no—
832C23—82no—
833C23—88no—
834C23—84no—
835C23—84no—
836C23—88no—
837C23—168no—
838C23C22×#4112yes—
839C23C22×#4112yes—
840C23C22×#4112yes—
841C23#58514yes—
842C23C2611yescharacteristic
843Q8—168no—
844D4—48no—
845D4—48no—
846D4—48no—
847D4—84no—
848D4—816no—
849D4—88no—
850D4—88no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—48no—
894C2×C4—48no—
895C2×C4—84no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4—82no—
899C2×C4—88no—
900C2×C4—82no—
901C2×C4—88no—
902C2×C4—168no—
903C2×C4C22×#4112yes—
904C2×C4C22×#4112yes—
905C2×C4C22×#4112yes—
906C2×C4C22×#4112yes—
907C2×C4#58514yes—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—24no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—28no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—48no—
929C22—48no—
930C22—88no—
931C22—88no—
932C22—168no—
933C22C23×#4111yescharacteristic
934C22C2×#58512yes—
935C22C2×#58512yes—
936C22H(7,𝔽2)12yes—
937C4—22no—
938C4—22no—
939C4—22no—
940C4—42no—
941C4—42no—
942C4—44no—
943C4—44no—
944C4—42no—
945C4—44no—
946C4—44no—
947C4—44no—
948C4—44no—
949C4—44no—
950C4—48no—
951C4—48no—
952C4#349114yes—
953C2—42no—
954C2—44no—
955C2—42no—
956C2—42no—
957C2—84no—
958C2C2×#349111yescharacteristic
959C2#6281411yescharacteristic
960C2#6285511yescharacteristic
961C2#6291014yes—
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. #48798C2semidirect
2. #48796C2semidirect
3. #47195C2semidirect
4. #46837C2semidirect
5. #46386C2semidirect
6. #46385C2semidirect
7. #43522C2semidirect
8. #39042C2semidirect
9. #38074C2semidirect
10. #37938C2semidirect
11. #37921C2semidirect
12. #37480C2semidirect
13. #37330C2semidirect
14. #36203C2semidirect
15. #35590C2semidirect
16. #35262C2semidirect
18. #34809C2semidirect
19. #34363C2semidirect
20. #34179C2semidirect
21. #34057C2semidirect
25. #2857C22semidirect
27. #2854C22semidirect
28. #2854C22semidirect
32. #2798C22semidirect
33. #2771C22semidirect
34. #2764C22semidirect
35. #2758C22semidirect
36. #2751C22semidirect
37. #2750C22semidirect
38. #2749C22semidirect
40. #2738C22semidirect
41. #2737C22semidirect
42. #2735C22semidirect
43. #2732C22semidirect
44. #2707C22semidirect
45. #2707C22semidirect
46. #2696C22semidirect
47. #2694C22semidirect
48. #2693C22semidirect
49. #2687C22semidirect
50. #2687C22semidirect
52. #2665C22semidirect
53. #2665C22semidirect
54. #2647C22semidirect
55. #2644C22semidirect
57. #2628C22semidirect
59. #2611C22semidirect
60. #2607C22semidirect
61. #2597C22semidirect
62. #2597C22semidirect
64. #2577C22semidirect
65. #2572C22semidirect
66. #2572C22semidirect
67. #2561C22semidirect
68. #2557C22semidirect
69. #2556C22semidirect
71. #2534C22semidirect
72. #2533C22semidirect
73. #2532C22semidirect
74. #2532C22semidirect
75. #2529C22semidirect
76. #2526C22semidirect
77. #2526C22semidirect
78. #2518C22semidirect
79. #2515C22semidirect
80. #2513C22semidirect
81. #2509C22semidirect
82. #2506C22semidirect
83. #2504C22semidirect
84. #2501C22semidirect
86. #2497C22semidirect
87. #2495C22semidirect
88. #2491C22semidirect
89. #2489C22semidirect
90. #2488C22semidirect
92. #2487C22semidirect
93. #2486C22semidirect
95. #2484C22semidirect
97. #2482C22semidirect
98. #2482C22semidirect
100. #2472C22semidirect
101. #2461C22semidirect
102. #2457C22semidirect
103. #2452C22semidirect
104. #2447C22semidirect
105. #2439C22semidirect
106. #2439C22semidirect
107. #2420C22semidirect
118. #2372C22semidirect
120. #2353C22semidirect
121. #2347C22semidirect
122. #2347C22semidirect
123. #2346C22semidirect
124. #2346C22semidirect
125. #2344C22semidirect
126. #2342C22semidirect
127. D4×C22⋊C4C22semidirect
128. #2333C22semidirect
129. #2331C22semidirect
130. #2324C22semidirect
132. #2319C22semidirect
134. #2318C22semidirect
135. #2317C22semidirect
136. #2316C22semidirect
137. #2315C22semidirect
138. #2313C22semidirect
144. #2309C22semidirect
148. C4×#123C22semidirect
149. C4×#121C22semidirect
150. #2296C22semidirect
152. #2290C22semidirect
153. #2283C22semidirect
154. #2283C22semidirect
155. #2283C22semidirect
160. #2280C22semidirect
161. #2274C22semidirect
162. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#487982
#487962
#471952
#468372
#463862
#463852
#435222
#390422
#380742
#379382
#379212
#374802
#373302
#362032
#355902
#352622
#350762
#348092
#343632
#341792
#340572