Finite Group Databasebeta

← #8701612

Subgroups — #8701612

Order 512.

5085 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59861C212yesmaximal, complemented
2#59201C212yesmaximal, complemented
3#59026C214yesmaximal, complemented
4#57956C214yesmaximal, complemented
5#55320C218yesmaximal, complemented
6#52301C211yesmaximal, characteristic, complemented
7#50867C214yesmaximal, complemented
8#49883C218yesmaximal, complemented
9#46147C211yesmaximal, characteristic, complemented
10#46015C212yesmaximal, complemented
11#45408C212yesmaximal, complemented
12#45006C214yesmaximal, complemented
13#42681C212yesmaximal, complemented
14#42515C214yesmaximal, complemented
15#39909C214yesmaximal, complemented
16#39338C212yesmaximal, complemented
17#37156C214yesmaximal, complemented
18#37129C212yesmaximal, complemented
19#36464C212yesmaximal, complemented
20#36289C211yesmaximal, characteristic, complemented
21C2×#563C2212yes—
22C2×#555C2212yes—
23C2×#554C2211yescharacteristic, complemented
24C2×D42C2211yescharacteristic
25C2×#534C2214yes—
26C22×#121C2212yescomplemented
27#2859C2212yescomplemented
28#2858C2211yescharacteristic, complemented
29#2854C2214yescomplemented
30#2850C2212yescomplemented
31#2847C2212yescomplemented
32#2837C2218yescomplemented
33#2822C2212yescomplemented
34#2819C2214yescomplemented
35#2816C2214yescomplemented
36#2808C2214yescomplemented
37#2804C2211yescharacteristic
38#2804C2212yescomplemented
39#2782C2212yescomplemented
40#2782C2214yescomplemented
41#2756C2218yescomplemented
42#2752C2218yescomplemented
43#2750C2218yescomplemented
44#2749C2218yescomplemented
45#2743C2218yescomplemented
46#2742C2218yescomplemented
47#2738C2218yescomplemented
48#2736C2214yescomplemented
49#2734C2212yescomplemented
50#2733C2214yescomplemented
51#2724C2212yes—
52#2711C2218yescomplemented
53#2710C2218yescomplemented
54#2701C2218yescomplemented
55#2700C2218yescomplemented
56#2699C2214yescomplemented
57#2699C2218yescomplemented
58#2698C2218yescomplemented
59#2697C2214yes—
60#2696C2218yescomplemented
61#2686C2218yescomplemented
62#2685C2218yescomplemented
63#2685C2218yescomplemented
64#2684C2212yes—
65#2684C2214yescomplemented
66#2682C2214yescomplemented
67#2679C2211yescharacteristic
68#2678C2218yescomplemented
69#2674C2218yescomplemented
70#2672C2218yescomplemented
71#2671C2218yescomplemented
72#2668C2218yes—
73#2663C2218yescomplemented
74#2660C2212yescomplemented
75#2648C2218yescomplemented
76#2632C2218yescomplemented
77#2625C2214yescomplemented
78#2618C2214yescomplemented
79#2613C2214yescomplemented
80#2597C2218yescomplemented
81#2593C2214yescomplemented
82#2580C2214yescomplemented
83#2578C2218yescomplemented
84#2572C2218yescomplemented
85#2572C2214yescomplemented
86#2563C2211yescharacteristic
87#2562C2212yescomplemented
88#2561C2218yescomplemented
89#2559C2218yescomplemented
90#2558C2218yescomplemented
91#2555C2218yescomplemented
92#2548C2211yescharacteristic, complemented
93#2546C2212yescomplemented
94#2538C2212yescomplemented
95#2537C2214yes—
96#2537C2212yes—
97#2523C2214yescomplemented
98#2518C2218yescomplemented
99#2515C2218yescomplemented
100#2504C2212yescomplemented
101#2501C2212yescomplemented
102#2500C2214yescomplemented
103#2497C2214yescomplemented
104#2496C2214yescomplemented
105#2495C2214yescomplemented
106#2495C2214yescomplemented
107#2491C2214yescomplemented
108#2491C2218yescomplemented
109#2490C2214yescomplemented
110#2486C2212yes—
111#2485C2214yescomplemented
112#2484C2214yescomplemented
113#2480C2218yescomplemented
114#2476C2218yescomplemented
115#2472C2218yescomplemented
116#2472C2218yescomplemented
117#2458C2218yescomplemented
118#2441C2214yescomplemented
119#2440C2214yescomplemented
120#2439C2214yescomplemented
121#2435C2212yes—
122#2435C2218yescomplemented
123#2428C2214yescomplemented
124#2426C2214yescomplemented
125#2422C2214yescomplemented
126#2422C2214yescomplemented
127#2420C2214yescomplemented
128#2414C2214yescomplemented
129#2414C2214yescomplemented
130#2412C2218yescomplemented
131#2412C2214yescomplemented
132#2410C2218yescomplemented
133#2408C2214yes—
134#2405C2214yes—
135#2398C2214yescomplemented
136#2398C2212yescomplemented
137#2379C2214yescomplemented
138#2374C2214yes—
139#2363C2214yescomplemented
140#2363C2214yescomplemented
141#2354C2212yescomplemented
142#2352C2214yescomplemented
143Q8×C4⋊C4C2212yescomplemented
144#2347C2214yescomplemented
145#2342C2218yescomplemented
146D4×C22⋊C4C2214yescomplemented
147D4×C22⋊C4C2212yescomplemented
148#2335C2218yescomplemented
149#2319C2214yescomplemented
150#2319C2212yescomplemented
151C4×#124C2211yescharacteristic
152C4×#124C2212yescomplemented
153C4×C22⋊Q8C2214yescomplemented
154C4×#120C2212yes—
155C4×#120C2214yescomplemented
156C2×#390C2212yes—
157#2280C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C23×D4C2312yes—
160C23×D4C2312yes—
161C23×D4C2314yes—
162C24×C4C2312yes—
163#563—48no—
164#555—48no—
165#554—44no—
166D42—44no—
167#534—416no—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×#127C2311yescharacteristic
172C2×#126C2318yes—
173C2×#125C2312yes—
174C2×#125C2314yes—
175C2×#124C2311yescharacteristic
176C2×#124C2312yes—
177C2×#124C2314yes—
178C2×#124C2318yes—
179C2×#124C2312yes—
180C2×#124C2318yes—
181C2×#123C2314yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×#123C2314yes—
185C2×#123C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2318yes—
190C2×#121—48no—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2312yes—
195C2×#121C2312yes—
196C2×#121C2318yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2314yes—
201C2×#120C2312yes—
202C2×#120C2314yes—
203C2×#120C2314yes—
204C2×#120C2318yes—
205C2×#120C2314yes—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2311yescharacteristic
211C2×C4×D4C2312yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2314yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C22⋊C4C2318yes—
223C22×C22⋊C4C2314yes—
224C22×C22⋊C4C2314yes—
225C22×C42C2312yes—
226#400C2314yes—
227#400C2318yes—
228#400C2312yes—
229#400C2318yes—
230#400C2314yes—
231#400C2312yes—
232#400C2314yes—
233#400C2318yes—
234#399C2318yes—
235#399C2318yes—
236#399C2318yes—
237#398C2314yes—
238#398C2314yes—
239#398C2318yes—
240#398C2314yes—
241#398C2314yes—
242#398C2314yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2314yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2314yes—
251#397C2314yes—
252#397C2318yes—
253#397C2314yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#395C2318yes—
259#395C2318yes—
260#394C2312yes—
261#394C2314yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2312yes—
274#394C2318yes—
275#394C2314yes—
276#394C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#393C2318yes—
282#393C2314yes—
283#393C2318yes—
284#393C2314yes—
285#393C2318yes—
286#393C2314yes—
287#393C2314yes—
288#392C2318yes—
289#392C2318yes—
290#392C2318yes—
291#392C2318yes—
292#391C2318yes—
293#391C2314yes—
294#391C2311yescharacteristic
295#391C2312yes—
296#390C2312yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2318yes—
302#390C2312yes—
303#390C2312yes—
304#390C2318yes—
305#390C2312yes—
306#390C2314yes—
307#390C2312yes—
308#390C2318yes—
309#390C2318yes—
310#390C2318yes—
311#390C2311yescharacteristic
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2318yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2314yes—
343#388C2314yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2314yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2312yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2312yes—
373#385C2314yes—
374#385C2314yes—
375#384C2312yes—
376#384C2312yes—
377#384C2314yes—
378#383C2318yes—
379#383C2318yes—
380#382C2312yes—
381#382C2314yes—
382#382C2311yescharacteristic
383#382C2314yes—
384#382C2312yes—
385#381C2314yes—
386#381C2318yes—
387#381C2314yes—
388#381C2318yes—
389#381C2318yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2318yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#379C2314yes—
402#379C2318yes—
403#379C2318yes—
404#379C2312yes—
405#379C2318yes—
406#379C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2312yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2312yes—
425#376C2312yes—
426C43C2311yescharacteristic
427C25C2414yes—
428C25C2412yes—
429C22×Q8C2412yes—
430C22×Q8C2411yescharacteristic
431C22×Q8C2414yes—
432C22×Q8C2412yes—
433C22×D4—28no—
434C22×D4—28no—
435C22×D4—48no—
436C22×D4—48no—
437C22×D4—44no—
438C22×D4—48no—
439C22×D4—82no—
440C22×D4—84no—
441C22×D4C2412yes—
442C22×D4C2411yescharacteristic
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2414yes—
446C22×D4C2418yes—
447C22×D4C2414yes—
448C22×D4C2412yes—
449C22×D4C2412yes—
450C22×D4C2418yes—
451C22×D4C2412yes—
452C22×D4C2418yes—
453C22×D4C2411yescharacteristic
454C23×C4—44no—
455C23×C4—48no—
456C23×C4C2412yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2418yes—
464C23×C4C2414yes—
465C4⋊Q8—42no—
466C4⋊Q8—44no—
467C4⋊Q8—48no—
468#127—42no—
469#126—416no—
470#125—44no—
471#125—48no—
472#124—24no—
473#124—48no—
474#124—44no—
475#124—416no—
476#124—82no—
477#124—88no—
478#123—216no—
479#123—416no—
480#123—416no—
481#123—48no—
482#123—84no—
483C22⋊Q8—48no—
484C22⋊Q8—44no—
485C22⋊Q8—416no—
486C22⋊Q8—48no—
487#121—216no—
488#121—416no—
489#121—416no—
490#121—416no—
491#121—48no—
492#121—48no—
493#121—44no—
494#121—44no—
495#121—48no—
496#121—84no—
497#120—28no—
498#120—48no—
499#120—48no—
500#120—416no—
501#120—48no—
502C4×Q8—44no—
503C4×Q8—42no—
504C4×Q8—84no—
505C4×D4—24no—
506C4×D4—28no—
507C4×D4—44no—
508C4×D4—48no—
509C4×D4—48no—
510C4×D4—44no—
511C4×D4—42no—
512C4×D4—44no—
513#117—48no—
514#117—48no—
515#117—48no—
516C2×C4⋊C4—44no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2411yescharacteristic
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C22⋊C4—416no—
548C2×C22⋊C4—48no—
549C2×C22⋊C4—48no—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C42—82no—
590C2×C42C2412yes—
591C2×C42C2411yescharacteristic
592C2×C42C2412yes—
593C2×C42C2414yes—
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2418yes—
597C2×C42C2418yes—
598C2×C42C2418yes—
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2411yescharacteristic
603#95C2412yes—
604#95C2414yes—
605#95C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2418yes—
609#95C2412yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—28no—
633C24—28no—
634C24—24no—
635C24—42no—
636C24—42no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—48no—
641C24—48no—
642C24C2514yes—
643C24C2514yes—
644C24C2512yes—
645C24C2512yes—
646C2×Q8—22no—
647C2×Q8—24no—
648C2×Q8—42no—
649C2×Q8—42no—
650C2×Q8—41no—
651C2×Q8—41no—
652C2×Q8—42no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—216no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—48no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—42no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—44no—
689C2×D4—816no—
690C2×D4—816no—
691C2×D4—832no—
692C2×D4H(5,𝔽2)14yes—
693C2×D4H(5,𝔽2)14yes—
694C22×C4—24no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—28no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—42no—
705C22×C4—44no—
706C22×C4—42no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—816no—
719C22×C4C2512yes—
720C22×C4C2511yescharacteristic
721C22×C4C2514yes—
722C22×C4C2512yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2518yes—
728C22×C4C2518yes—
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C22×C4C2512yes—
734C22×C4C2511yescharacteristic
735C4⋊C4—28no—
736C4⋊C4—24no—
737C4⋊C4—22no—
738C4⋊C4—216no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—41no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—44no—
748C4⋊C4—42no—
749C4⋊C4—44no—
750C4⋊C4—41no—
751C4⋊C4—42no—
752C4⋊C4—44no—
753C4⋊C4—42no—
754C4⋊C4—44no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—44no—
764C22⋊C4—24no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—24no—
768C22⋊C4—28no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—216no—
774C22⋊C4—28no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—42no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—42no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—44no—
803C42—24no—
804C42—22no—
805C42—22no—
806C42—24no—
807C42—28no—
808C42—24no—
809C42—41no—
810C42—44no—
811C42—42no—
812C42—48no—
813C42—48no—
814C42—48no—
815C42—44no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—22no—
823C23—22no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—28no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—28no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—416no—
837C23—48no—
838C23—88no—
839C23—88no—
840C23—88no—
841C23—816no—
842C23—84no—
843C23—84no—
844C23—88no—
845C23—168no—
846C23C2×H(5,𝔽2)14yes—
847C23C2×H(5,𝔽2)14yes—
848C23C2611yescharacteristic
849Q8—48no—
850Q8—82no—
851Q8—162no—
852Q8—164no—
853D4—28no—
854D4—44no—
855D4—48no—
856D4—84no—
857D4—84no—
858D4—88no—
859D4—88no—
860D4—88no—
861D4—816no—
862D4—84no—
863D4—816no—
864D4—162no—
865D4—168no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—28no—
904C2×C4—22no—
905C2×C4—48no—
906C2×C4—416no—
907C2×C4—48no—
908C2×C4—88no—
909C2×C4—88no—
910C2×C4—88no—
911C2×C4—84no—
912C2×C4—88no—
913C2×C4—168no—
914C2×C4C2×H(5,𝔽2)12yes—
915C2×C4C2×H(5,𝔽2)12yes—
916C2×C4#58514yes—
917C2×C4#58514yes—
918C22—24no—
919C22—24no—
920C22—28no—
921C22—24no—
922C22—24no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—48no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—48no—
940C22—816no—
941C22—1616no—
942C22C22×H(5,𝔽2)11yescharacteristic
943C22C22×H(5,𝔽2)11yescharacteristic
944C22C2×#58512yes—
945C22C2×#58512yes—
946C22H(7,𝔽2)11yescharacteristic
947C4—22no—
948C4—24no—
949C4—44no—
950C4—42no—
951C4—42no—
952C4—44no—
953C4—41no—
954C4—42no—
955C4—44no—
956C4—48no—
957C4—42no—
958C4—48no—
959C4—42no—
960C4—44no—
961C4—44no—
962C4#354514yes—
963C2—44no—
964C2—44no—
965C2—84no—
966C2—84no—
967C2C2×#354511yescharacteristic
968C2#6289211yescharacteristic
969C2#6290812yes—
970C2#6302111yescharacteristic
971C2#6302412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59861C2semidirect
2. #59201C2semidirect
3. #59026C2semidirect
4. #57956C2semidirect
5. #55320C2semidirect
6. #52301C2semidirect
7. #50867C2semidirect
8. #49883C2semidirect
9. #46147C2semidirect
10. #46015C2semidirect
11. #45408C2semidirect
12. #45006C2semidirect
13. #42681C2semidirect
14. #42515C2semidirect
15. #39909C2semidirect
16. #39338C2semidirect
17. #37156C2semidirect
18. #37129C2semidirect
19. #36464C2semidirect
20. #36289C2semidirect
23. C2×#554C22semidirect
26. C22×#121C22semidirect
27. #2859C22semidirect
28. #2858C22semidirect
29. #2854C22semidirect
30. #2850C22semidirect
31. #2847C22semidirect
32. #2837C22semidirect
33. #2822C22semidirect
34. #2819C22semidirect
35. #2816C22semidirect
36. #2808C22semidirect
38. #2804C22semidirect
39. #2782C22semidirect
40. #2782C22semidirect
41. #2756C22semidirect
42. #2752C22semidirect
43. #2750C22semidirect
44. #2749C22semidirect
45. #2743C22semidirect
46. #2742C22semidirect
47. #2738C22semidirect
48. #2736C22semidirect
49. #2734C22semidirect
50. #2733C22semidirect
52. #2711C22semidirect
53. #2710C22semidirect
54. #2701C22semidirect
55. #2700C22semidirect
56. #2699C22semidirect
57. #2699C22semidirect
58. #2698C22semidirect
60. #2696C22semidirect
61. #2686C22semidirect
62. #2685C22semidirect
63. #2685C22semidirect
65. #2684C22semidirect
66. #2682C22semidirect
68. #2678C22semidirect
69. #2674C22semidirect
70. #2672C22semidirect
71. #2671C22semidirect
73. #2663C22semidirect
74. #2660C22semidirect
75. #2648C22semidirect
76. #2632C22semidirect
77. #2625C22semidirect
78. #2618C22semidirect
79. #2613C22semidirect
80. #2597C22semidirect
81. #2593C22semidirect
82. #2580C22semidirect
83. #2578C22semidirect
84. #2572C22semidirect
85. #2572C22semidirect
87. #2562C22semidirect
88. #2561C22semidirect
89. #2559C22semidirect
90. #2558C22semidirect
91. #2555C22semidirect
92. #2548C22semidirect
93. #2546C22semidirect
94. #2538C22semidirect
97. #2523C22semidirect
98. #2518C22semidirect
99. #2515C22semidirect
100. #2504C22semidirect
101. #2501C22semidirect
102. #2500C22semidirect
103. #2497C22semidirect
104. #2496C22semidirect
105. #2495C22semidirect
106. #2495C22semidirect
107. #2491C22semidirect
108. #2491C22semidirect
109. #2490C22semidirect
111. #2485C22semidirect
112. #2484C22semidirect
113. #2480C22semidirect
114. #2476C22semidirect
115. #2472C22semidirect
116. #2472C22semidirect
117. #2458C22semidirect
118. #2441C22semidirect
119. #2440C22semidirect
120. #2439C22semidirect
122. #2435C22semidirect
123. #2428C22semidirect
124. #2426C22semidirect
125. #2422C22semidirect
126. #2422C22semidirect
127. #2420C22semidirect
128. #2414C22semidirect
129. #2414C22semidirect
130. #2412C22semidirect
131. #2412C22semidirect
132. #2410C22semidirect
135. #2398C22semidirect
136. #2398C22semidirect
137. #2379C22semidirect
139. #2363C22semidirect
140. #2363C22semidirect
141. #2354C22semidirect
142. #2352C22semidirect
143. Q8×C4⋊C4C22semidirect
144. #2347C22semidirect
145. #2342C22semidirect
146. D4×C22⋊C4C22semidirect
147. D4×C22⋊C4C22semidirect
148. #2335C22semidirect
149. #2319C22semidirect
150. #2319C22semidirect
152. C4×#124C22semidirect
153. C4×C22⋊Q8C22semidirect
155. C4×#120C22semidirect
157. #2280C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598612
#592012
#590262
#579562
#553202
#523012
#508672
#498832
#461472
#460152
#454082
#450062
#426812
#425152
#399092
#393382
#371562
#371292
#364642
#362892