Finite Group Databasebeta

← #7642635

Subgroups — #7642635

Order 512.

5334 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39806C214yesmaximal, complemented
2#39414C214yesmaximal, complemented
3#39076C214yesmaximal, complemented
4#39066C214yesmaximal, complemented
5#38260C214yesmaximal, complemented
6#38250C214yesmaximal, complemented
7#37771C214yesmaximal, complemented
8#37746C214yesmaximal, complemented
9#37016C214yesmaximal, complemented
10#37010C214yesmaximal, complemented
11#36631C212yesmaximal, complemented
12#35505C214yesmaximal, complemented
13#35474C214yesmaximal, complemented
14#35271C212yesmaximal, complemented
15#35262C212yesmaximal, complemented
16#35082C212yesmaximal, complemented
17#35033C211yesmaximal, characteristic, complemented
18#35006C212yesmaximal, complemented
19#35001C211yesmaximal, characteristic
20#34246C212yesmaximal, complemented
21C2×#2298C211yesmaximal, characteristic, complemented
22C2×#539C2214yescomplemented
23C2×#534C2214yes—
24C2×#529C2214yescomplemented
25C22×#121C2212yes—
26C22×#117C2211yescharacteristic
27#2861C2214yescomplemented
28#2860C2214yescomplemented
29#2860C2214yescomplemented
30#2859C2212yescomplemented
31#2858C2212yescomplemented
32#2857C2212yescomplemented
33#2856C2212yes—
34#2856C2212yes—
35#2854C2214yescomplemented
36#2854C2214yescomplemented
37#2854C2214yescomplemented
38#2851C2212yescomplemented
39#2850C2214yescomplemented
40#2797C2218yescomplemented
41#2773C2218yescomplemented
42#2754C2218yescomplemented
43#2752C2218yescomplemented
44#2730C2218yescomplemented
45#2721C2218yescomplemented
46#2721C2218yescomplemented
47#2707C2218yescomplemented
48#2705C2218yescomplemented
49#2697C2218yescomplemented
50#2695C2218yescomplemented
51#2694C2218yescomplemented
52#2687C2218yescomplemented
53#2685C2218yescomplemented
54#2685C2218yescomplemented
55#2684C2218yescomplemented
56#2656C2214yes—
57#2651C2218yescomplemented
58#2647C2212yescomplemented
59#2644C2214yescomplemented
60#2641C2212yescomplemented
61#2639C2214yescomplemented
62#2626C2214yes—
63#2624C2214yes—
64#2624C2214yes—
65#2618C2214yescomplemented
66#2608C2214yescomplemented
67#2607C2214yescomplemented
68#2602C2218yescomplemented
69#2575C2218yescomplemented
70#2560C2218yescomplemented
71#2558C2218yescomplemented
72#2558C2218yescomplemented
73#2557C2218yescomplemented
74#2553C2218yescomplemented
75#2539C2214yes—
76#2539C2214yes—
77#2534C2218yescomplemented
78#2531C2218yescomplemented
79#2526C2218yescomplemented
80#2517C2218yescomplemented
81#2513C2214yescomplemented
82#2512C2214yescomplemented
83#2507C2214yescomplemented
84#2506C2214yescomplemented
85#2504C2214yescomplemented
86#2501C2214yes—
87#2501C2214yescomplemented
88#2500C2214yes—
89#2500C2214yes—
90#2482C2214yescomplemented
91#2482C2214yescomplemented
92#2472C2218yescomplemented
93#2471C2218yescomplemented
94#2470C2218yescomplemented
95#2467C2218yescomplemented
96#2458C2218yescomplemented
97#2454C2214yescomplemented
98#2452C2214yescomplemented
99#2445C2214yescomplemented
100#2445C2214yescomplemented
101#2444C2218yescomplemented
102#2443C2218yescomplemented
103#2441C2218yescomplemented
104#2441C2214yescomplemented
105#2439C2214yescomplemented
106#2433C2214yes—
107#2425C2218yescomplemented
108#2425C2218yescomplemented
109#2423C2218yescomplemented
110#2418C2218yescomplemented
111#2411C2218yescomplemented
112#2405C2214yes—
113#2405C2214yes—
114#2364C2218yescomplemented
115#2363C2214yes—
116#2363C2214yes—
117#2345C2214yescomplemented
118D4×C22⋊C4C2218yes—
119D4×C22⋊C4C2214yescomplemented
120#2335C2218yescomplemented
121#2333C2214yes—
122#2333C2214yes—
123#2330C2212yescomplemented
124#2329C2214yescomplemented
125#2328C2212yescomplemented
126#2325C2214yescomplemented
127#2319C2214yescomplemented
128#2317C2212yescomplemented
129#2317C2212yescomplemented
130#2312C2214yescomplemented
131#2309C2212yescomplemented
132#2309C2212yescomplemented
133C4×C4⋊Q8C2212yescomplemented
134C4×#127C2212yescomplemented
135C4×#124C2214yescomplemented
136C4×#121C2214yescomplemented
137C4×#121C2214yescomplemented
138C4×#121C2214yescomplemented
139#2298C2214yescomplemented
140#2298C2212yescomplemented
141#2298C2212yescomplemented
142#2298C2212yescomplemented
143#2298C2214yescomplemented
144#2298C2212yescomplemented
145#2293C2214yescomplemented
146#2293C2214yescomplemented
147C2×#388C2212yes—
148C2×#388C2212yes—
149C2×#387C2212yescomplemented
150C2×#387C2212yescomplemented
151#2280C2212yes—
152#2273C2214yescomplemented
153C2×C4×C4⋊C4C2211yescharacteristic, complemented
154C2×C4×C4⋊C4C2211yescharacteristic, complemented
155C2×C4×C22⋊C4C2211yescharacteristic
156C2×C4×C22⋊C4C2211yescharacteristic
157C2×#376C2211yescharacteristic, complemented
158C2×C43C2211yescharacteristic, complemented
159C23×D4C2312yes—
160C23×D4C2314yes—
161C24×C4C2311yescharacteristic
162#539—416no—
163#534—416no—
164C2×C4⋊Q8C2312yes—
165C2×#127C2312yes—
166C2×#127C2312yes—
167#529—416no—
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125C2312yes—
171C2×#125C2314yes—
172C2×#125C2318yes—
173C2×#124C2314yes—
174C2×#124C2314yes—
175C2×#123C2318yes—
176C2×#123C2318yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×#121—216no—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2318yes—
191C2×#120C2318yes—
192C2×#120C2318yes—
193C2×C4×Q8C2314yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C2318yes—
200C2×#117—28no—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2318yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2312yes—
213C22×C22⋊C4C2314yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2318yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#399C2318yes—
231#399C2318yes—
232#399C2318yes—
233#399C2318yes—
234#399C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#397C2318yes—
240#397C2318yes—
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#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#393C2318yes—
264#393C2318yes—
265#392C2318yes—
266#392C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2318yes—
270#390C2314yes—
271#390C2314yes—
272#390C2314yes—
273#390C2314yes—
274#390C2314yes—
275#390C2314yes—
276#390C2314yes—
277#390C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2318yes—
283#390C2318yes—
284#390C2318yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
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#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#387C2318yes—
333#387C2314yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#384C2312yes—
368#384C2312yes—
369#384C2314yes—
370#384C2314yes—
371#384C2312yes—
372#382C2314yes—
373#382C2314yes—
374#382C2312yes—
375#382C2314yes—
376#381C2318yes—
377#381C2314yes—
378#380C2318yes—
379#380C2318yes—
380#380C2314yes—
381#380C2318yes—
382#380C2314yes—
383#380C2314yes—
384#379C2314yes—
385#379C2314yes—
386#379C2314yes—
387#379C2314yes—
388#379C2318yes—
389#379C2314yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2312yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2318yes—
403C4×C22⋊C4C2314yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2318yes—
407C4×C22⋊C4C2314yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2318yes—
413#376C2312yes—
414#376C2312yes—
415#376C2312yes—
416#376C2312yes—
417C2×#95C2312yes—
418C2×#95C2312yes—
419C2×#95C2312yes—
420C2×#95C2312yes—
421C2×#95C2312yes—
422C2×#95C2312yes—
423C43C2312yes—
424C43C2312yes—
425C43C2311yescharacteristic
426C43C2311yescharacteristic
427C43C2311yescharacteristic
428C43C2311yescharacteristic
429C25C2411yescharacteristic
430C25C2414yes—
431C22×Q8C2414yes—
432C22×D4—216no—
433C22×D4—28no—
434C22×D4—44no—
435C22×D4—44no—
436C22×D4—416no—
437C22×D4C2418yes—
438C22×D4C2414yes—
439C22×D4C2414yes—
440C22×D4C2414yes—
441C22×D4C2418yes—
442C22×D4C2414yes—
443C22×D4C2418yes—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4#4118yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2411yescharacteristic
457C23×C4C2418yes—
458C23×C4C2418yes—
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C23×C4C2412yes—
462C4⋊Q8—44no—
463#127—44no—
464#127—44no—
465#126—416no—
466#126—416no—
467#125—44no—
468#125—48no—
469#125—416no—
470#124—48no—
471#124—48no—
472#123—416no—
473#123—416no—
474#123—416no—
475#123—416no—
476#123—416no—
477#123—416no—
478C22⋊Q8—216no—
479C22⋊Q8—416no—
480#121—216no—
481#121—216no—
482#121—216no—
483#121—216no—
484#121—216no—
485#121—216no—
486#121—416no—
487#120—416no—
488#120—416no—
489C4×Q8—48no—
490C4×D4—48no—
491C4×D4—48no—
492C4×D4—48no—
493C4×D4—48no—
494C4×D4—416no—
495C4×D4—416no—
496#117—28no—
497#117—28no—
498#117—28no—
499#117—28no—
500#117—416no—
501#117—44no—
502#117—44no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—28no—
507C2×C4⋊C4—44no—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—216no—
538C2×C22⋊C4—28no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4—416no—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2412yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—28no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—44no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42C2412yes—
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C2×C42C2411yescharacteristic
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2418yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2418yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
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#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634C24—24no—
635C24—28no—
636C24—42no—
637C24—41no—
638C24—41no—
639C24—48no—
640C24—48no—
641C24—44no—
642C24—44no—
643C24C2×#4114yes—
644C24C2518yes—
645C24C2512yes—
646C24C2511yescharacteristic
647C2×Q8—28no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×D4—216no—
651C2×D4—216no—
652C2×D4—216no—
653C2×D4—216no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—44no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—816no—
672C2×D4—832no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—216no—
689C22×C4—416no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4C2×#4114yes—
710C22×C4C2×#4118yes—
711C22×C4C2×#4118yes—
712C22×C4C2×#4114yes—
713C22×C4H(5,𝔽2)18yes—
714C22×C4C2511yescharacteristic
715C22×C4C2511yescharacteristic
716C22×C4C2514yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2518yes—
720C22×C4C2512yes—
721C22×C4C2518yes—
722C22×C4C2518yes—
723C22×C4C2511yescharacteristic
724C22×C4C2511yescharacteristic
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2511yescharacteristic
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—216no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—216no—
772C22⋊C4—44no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C42—22no—
792C42—22no—
793C42—24no—
794C42—22no—
795C42—22no—
796C42—24no—
797C42—24no—
798C42—24no—
799C42—24no—
800C42—24no—
801C42—24no—
802C42—24no—
803C42—24no—
804C42—24no—
805C42—24no—
806C42—24no—
807C42—41no—
808C42—42no—
809C42—41no—
810C42—41no—
811C42—42no—
812C42—41no—
813C42—42no—
814C42—42no—
815C42—44no—
816C42—44no—
817C42—48no—
818C42—48no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—28no—
832C23—28no—
833C23—28no—
834C23—44no—
835C23—44no—
836C23—416no—
837C23—84no—
838C23—84no—
839C23—88no—
840C23—88no—
841C23—168no—
842C23—168no—
843C23C22×#4114yes—
844C23C22×#4112yes—
845C23C2×H(5,𝔽2)14yes—
846C23C2611yescharacteristic
847Q8—88no—
848D4—432no—
849D4—416no—
850D4—88no—
851D4—88no—
852D4—88no—
853D4—816no—
854D4—168no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—28no—
896C2×C4—24no—
897C2×C4—48no—
898C2×C4—44no—
899C2×C4—48no—
900C2×C4—48no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—816no—
906C2×C4—84no—
907C2×C4—84no—
908C2×C4—88no—
909C2×C4—168no—
910C2×C4C22×#4112yes—
911C2×C4C22×#4114yes—
912C2×C4C22×#4112yes—
913C2×C4C2×H(5,𝔽2)14yes—
914C2×C4C2×H(5,𝔽2)14yes—
915C2×C4#58514yes—
916C2×C4#58512yes—
917C2×C4#58512yes—
918C22—22no—
919C22—24no—
920C22—24no—
921C22—22no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—44no—
926C22—44no—
927C22—48no—
928C22—48no—
929C22—48no—
930C22—48no—
931C22—48no—
932C22—48no—
933C22—48no—
934C22—88no—
935C22—1616no—
936C22#350814yes—
937C22C23×#4111yescharacteristic
938C22C22×H(5,𝔽2)12yes—
939C22C2×#58511yescharacteristic
940C22C2×#58511yescharacteristic
941C22C2×#58512yes—
942C4—22no—
943C4—24no—
944C4—24no—
945C4—24no—
946C4—24no—
947C4—41no—
948C4—41no—
949C4—42no—
950C4—48no—
951C4—44no—
952C4—48no—
953C4—42no—
954C4—48no—
955C4—44no—
956C4—41no—
957C4—41no—
958C4—42no—
959C4#349114yes—
960C2—24no—
961C2—44no—
962C2—88no—
963C2#6268611yescharacteristic
964C2C2×#349111yescharacteristic
965C2C2×#350811yescharacteristic
966C2#6282212yes—
967C2#6283012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35001C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39806C2semidirect
2. #39414C2semidirect
3. #39076C2semidirect
4. #39066C2semidirect
5. #38260C2semidirect
6. #38250C2semidirect
7. #37771C2semidirect
8. #37746C2semidirect
9. #37016C2semidirect
10. #37010C2semidirect
11. #36631C2semidirect
12. #35505C2semidirect
13. #35474C2semidirect
14. #35271C2semidirect
15. #35262C2semidirect
16. #35082C2semidirect
17. #35033C2semidirect
18. #35006C2semidirect
20. #34246C2semidirect
21. C2×#2298C2semidirect
22. C2×#539C22semidirect
24. C2×#529C22semidirect
27. #2861C22semidirect
28. #2860C22semidirect
29. #2860C22semidirect
30. #2859C22semidirect
31. #2858C22semidirect
32. #2857C22semidirect
35. #2854C22semidirect
36. #2854C22semidirect
37. #2854C22semidirect
38. #2851C22semidirect
39. #2850C22semidirect
40. #2797C22semidirect
41. #2773C22semidirect
42. #2754C22semidirect
43. #2752C22semidirect
44. #2730C22semidirect
45. #2721C22semidirect
46. #2721C22semidirect
47. #2707C22semidirect
48. #2705C22semidirect
49. #2697C22semidirect
50. #2695C22semidirect
51. #2694C22semidirect
52. #2687C22semidirect
53. #2685C22semidirect
54. #2685C22semidirect
55. #2684C22semidirect
57. #2651C22semidirect
58. #2647C22semidirect
59. #2644C22semidirect
60. #2641C22semidirect
61. #2639C22semidirect
65. #2618C22semidirect
66. #2608C22semidirect
67. #2607C22semidirect
68. #2602C22semidirect
69. #2575C22semidirect
70. #2560C22semidirect
71. #2558C22semidirect
72. #2558C22semidirect
73. #2557C22semidirect
74. #2553C22semidirect
77. #2534C22semidirect
78. #2531C22semidirect
79. #2526C22semidirect
80. #2517C22semidirect
81. #2513C22semidirect
82. #2512C22semidirect
83. #2507C22semidirect
84. #2506C22semidirect
85. #2504C22semidirect
87. #2501C22semidirect
90. #2482C22semidirect
91. #2482C22semidirect
92. #2472C22semidirect
93. #2471C22semidirect
94. #2470C22semidirect
95. #2467C22semidirect
96. #2458C22semidirect
97. #2454C22semidirect
98. #2452C22semidirect
99. #2445C22semidirect
100. #2445C22semidirect
101. #2444C22semidirect
102. #2443C22semidirect
103. #2441C22semidirect
104. #2441C22semidirect
105. #2439C22semidirect
107. #2425C22semidirect
108. #2425C22semidirect
109. #2423C22semidirect
110. #2418C22semidirect
111. #2411C22semidirect
114. #2364C22semidirect
117. #2345C22semidirect
119. D4×C22⋊C4C22semidirect
120. #2335C22semidirect
123. #2330C22semidirect
124. #2329C22semidirect
125. #2328C22semidirect
126. #2325C22semidirect
127. #2319C22semidirect
128. #2317C22semidirect
129. #2317C22semidirect
130. #2312C22semidirect
131. #2309C22semidirect
132. #2309C22semidirect
133. C4×C4⋊Q8C22semidirect
134. C4×#127C22semidirect
135. C4×#124C22semidirect
136. C4×#121C22semidirect
137. C4×#121C22semidirect
138. C4×#121C22semidirect
139. #2298C22semidirect
140. #2298C22semidirect
141. #2298C22semidirect
142. #2298C22semidirect
143. #2298C22semidirect
144. #2298C22semidirect
145. #2293C22semidirect
146. #2293C22semidirect
149. C2×#387C22semidirect
150. C2×#387C22semidirect
152. #2273C22semidirect
153. C2×C4×C4⋊C4C22semidirect
154. C2×C4×C4⋊C4C22semidirect
157. C2×#376C22semidirect
158. C2×C43C22semidirect

Maximal subgroups

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

subgroupindex
#398062
#394142
#390762
#390662
#382602
#382502
#377712
#377462
#370162
#370102
#366312
#355052
#354742
#352712
#352622
#350822
#350332
#350062
#350012
#342462
C2×#22982