Finite Group Databasebeta

← #7656821

Subgroups — #7656821

Order 512.

5388 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42989C214yesmaximal, complemented
2#42946C214yesmaximal, complemented
3#42338C218yesmaximal, complemented
4#42060C218yesmaximal, complemented
5#39631C212yesmaximal, complemented
6#39420C214yesmaximal, complemented
7#39375C212yesmaximal, complemented
8#37940C214yesmaximal, complemented
9#37462C214yesmaximal, complemented
10#37439C212yesmaximal, complemented
11#36586C212yesmaximal, complemented
12#36160C212yesmaximal, complemented
13#36087C214yesmaximal, complemented
14#36000C214yesmaximal, complemented
15#35003C212yesmaximal, complemented
16#35002C211yesmaximal, characteristic, complemented
17#34578C212yesmaximal, complemented
18#34575C211yesmaximal, characteristic, complemented
19#34202C212yesmaximal, complemented
20C2×#2363C211yesmaximal, characteristic, complemented
21C2×#555C2212yescomplemented
22C2×#543C2212yes—
23C2×#538C2214yes—
24C2×#525C2212yes—
25C22×#121C2211yescharacteristic
26C2×#520C2212yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2850C2214yes—
32#2847C2214yes—
33#2838C2218yescomplemented
34#2829C2218yescomplemented
35#2813C2218yes—
36#2807C2218yescomplemented
37#2805C2214yescomplemented
38#2778C2218yescomplemented
39#2746C2218yescomplemented
40#2732C2214yescomplemented
41#2730C2218yescomplemented
42#2727C2214yescomplemented
43#2723C2218yescomplemented
44#2710C2218yescomplemented
45#2708C2218yescomplemented
46#2688C2218yescomplemented
47#2682C2214yescomplemented
48#2681C2218yescomplemented
49#2676C2218yescomplemented
50#2667C2218yescomplemented
51#2665C2218yescomplemented
52#2663C2214yescomplemented
53#2663C2218yescomplemented
54#2661C2214yescomplemented
55#2659C2211yescharacteristic
56#2659C2212yes—
57#2659C2212yes—
58#2656C2211yescharacteristic
59#2656C2214yes—
60#2653C2218yescomplemented
61#2651C2218yescomplemented
62#2646C2214yes—
63#2639C2212yes—
64#2639C2214yes—
65#2632C2218yescomplemented
66#2626C2214yes—
67#2626C2214yes—
68#2624C2214yes—
69#2617C2212yes—
70#2617C2212yes—
71#2617C2214yes—
72#2615C2214yes—
73#2598C2218yescomplemented
74#2596C2218yescomplemented
75#2578C2218yescomplemented
76#2571C2212yescomplemented
77#2563C2212yescomplemented
78#2560C2218yescomplemented
79#2555C2218yescomplemented
80#2553C2218yescomplemented
81#2549C2218yescomplemented
82#2547C2212yescomplemented
83#2540C2218yescomplemented
84#2537C2212yescomplemented
85#2525C2218yescomplemented
86#2521C2218yescomplemented
87#2514C2214yescomplemented
88#2512C2214yescomplemented
89#2510C2218yes—
90#2507C2214yescomplemented
91#2501C2214yescomplemented
92#2497C2214yescomplemented
93#2494C2214yescomplemented
94#2491C2214yescomplemented
95#2487C2214yes—
96#2487C2214yescomplemented
97#2485C2214yescomplemented
98#2476C2218yescomplemented
99#2472C2218yes—
100#2464C2218yescomplemented
101#2464C2218yescomplemented
102#2461C2218yescomplemented
103#2461C2218yescomplemented
104#2459C2218yescomplemented
105#2449C2218yes—
106#2448C2214yescomplemented
107#2440C2214yescomplemented
108#2440C2214yescomplemented
109#2440C2214yescomplemented
110#2426C2218yescomplemented
111#2420C2214yescomplemented
112#2418C2218yes—
113#2416C2214yes—
114#2416C2214yes—
115#2416C2214yescomplemented
116#2414C2214yescomplemented
117#2410C2218yes—
118#2408C2214yes—
119#2396C2218yescomplemented
120#2396C2218yescomplemented
121#2395C2214yescomplemented
122#2388C2214yescomplemented
123#2365C2212yescomplemented
124#2363C2218yes—
125#2363C2214yes—
126#2363C2214yes—
127#2363C2214yescomplemented
128#2359C2218yescomplemented
129#2358C2218yes—
130#2354C2212yescomplemented
131#2354C2214yescomplemented
132#2354C2212yescomplemented
133#2352C2214yes—
134#2352C2214yescomplemented
135D4×C4⋊C4C2214yes—
136#2347C2214yescomplemented
137#2325C2214yes—
138#2324C2214yescomplemented
139#2323C2214yescomplemented
140#2317C2212yescomplemented
141#2315C2212yes—
142#2311C2212yescomplemented
143C4×C22⋊Q8C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×#121C2212yes—
146C4×#121C2212yes—
147C4×#121C2214yes—
148C2×#390C2211yescharacteristic
149C2×#390C2212yes—
150C2×#389C2211yescharacteristic
151C2×#388C2212yes—
152C2×#386C2212yes—
153#2280C2214yes—
154C2×#380C2212yes—
155#2274C2212yescomplemented
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C22⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2212yes—
159C22×#41C2312yes—
160C23×D4C2311yescharacteristic
161C23×D4C2312yes—
162C24×C4C2312yes—
163C24×C4C2311yescharacteristic
164#555—48no—
165#543—48no—
166#538—416no—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×#126C2318yes—
170C2×#124C2318yes—
171C2×#124C2318yes—
172C2×#124C2314yes—
173#525—216no—
174C2×#123C2314yes—
175C2×#123C2318yes—
176C2×#123C2318yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×#121—28no—
185C2×#121C2312yes—
186C2×#121C2312yes—
187C2×#121C2312yes—
188C2×#121C2314yes—
189C2×#121C2312yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2318yes—
195C2×#121C2314yes—
196C2×#121C2318yes—
197C2×#121C2318yes—
198C2×#120C2314yes—
199C2×#120C2318yes—
200#520—48no—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×D4—44no—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×#117—44no—
215C2×#117C2312yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2312yes—
241#401C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2314yes—
245#400C2318yes—
246#400C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#399C2318yes—
252#399C2314yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#397C2314yes—
260#397C2318yes—
261#397C2318yes—
262#397C2314yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2314yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2314yes—
275#395C2318yes—
276#394C2318yes—
277#394C2314yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2314yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#394C2318yes—
289#394C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2314yes—
294#392C2318yes—
295#392C2318yes—
296#392C2318yes—
297#392C2314yes—
298#392C2314yes—
299#392C2314yes—
300#392C2318yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#390C2318yes—
307#390C2314yes—
308#390C2314yes—
309#390C2318yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2318yes—
316#390C2312yes—
317#390C2312yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2312yes—
331#389C2312yes—
332#389C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2314yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2314yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2314yes—
369#386C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#384C2312yes—
379#384C2314yes—
380#384C2312yes—
381#383C2318yes—
382#382C2314yes—
383#382C2314yes—
384#381C2318yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2312yes—
398#380C2314yes—
399#380C2312yes—
400#380C2314yes—
401#379C2318yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C2×#95C2312yes—
425C2×#95C2314yes—
426C2×#95C2311yescharacteristic
427C2×#95C2311yescharacteristic
428C2×#95C2312yes—
429C25C2412yes—
430C25C2411yescharacteristic
431C2×#41—28no—
432C2×#41—44no—
433C2×#41—44no—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2414yes—
437C22×D4—28no—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4—82no—
442C22×D4—82no—
443C22×D4C2414yes—
444C22×D4C2412yes—
445C22×D4C2414yes—
446C22×D4C2412yes—
447C22×D4C2412yes—
448C22×D4C2414yes—
449C22×D4C2412yes—
450C22×D4C2412yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2418yes—
454C23×C4—28no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—44no—
458C23×C4—82no—
459C23×C4#4118yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2418yes—
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C4⋊Q8—44no—
478C4⋊Q8—44no—
479#126—416no—
480#124—416no—
481#124—416no—
482#124—84no—
483#123—216no—
484#123—416no—
485#123—88no—
486C22⋊Q8—28no—
487C22⋊Q8—28no—
488C22⋊Q8—216no—
489C22⋊Q8—48no—
490C22⋊Q8—416no—
491C22⋊Q8—416no—
492C22⋊Q8—88no—
493#121—216no—
494#121—216no—
495#121—28no—
496#121—28no—
497#121—28no—
498#121—28no—
499#121—48no—
500#121—416no—
501#121—48no—
502#121—48no—
503#121—88no—
504#121—88no—
505#121—84no—
506#120—216no—
507#120—416no—
508C4×Q8—48no—
509C4×Q8—84no—
510C4×D4—216no—
511C4×D4—216no—
512C4×D4—28no—
513C4×D4—48no—
514C4×D4—416no—
515C4×D4—44no—
516C4×D4—44no—
517C4×D4—44no—
518C4×D4—48no—
519C4×D4—416no—
520#117—28no—
521#117—28no—
522#117—216no—
523#117—48no—
524#117—48no—
525#117—44no—
526#117—84no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—44no—
530C2×C4⋊C4—42no—
531C2×C4⋊C4—48no—
532C2×C4⋊C4—44no—
533C2×C4⋊C4—82no—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2411yescharacteristic
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C22⋊C4—28no—
570C2×C22⋊C4—28no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—44no—
574C2×C22⋊C4—44no—
575C2×C22⋊C4—48no—
576C2×C22⋊C4—82no—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C42—44no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42—82no—
614C2×C42C2418yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2414yes—
620C2×C42C2418yes—
621C2×C42C2412yes—
622C2×C42C2418yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C2418yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2414yes—
634#95C2418yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651C24—22no—
652C24—22no—
653C24—24no—
654C24—24no—
655C24—24no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—41no—
660C24—42no—
661C24—42no—
662C24—41no—
663C24—41no—
664C24C2×#4114yes—
665C24C2514yes—
666C24C2514yes—
667C24C2512yes—
668C24C2511yescharacteristic
669#41—432no—
670C2×Q8—24no—
671C2×Q8—28no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—216no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—44no—
698C2×D4—416no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—42no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—816no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—22no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—416no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—44no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—42no—
748C22×C4—41no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—48no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—48no—
760C22×C4—816no—
761C22×C4C2×#4114yes—
762C22×C4C2×#4118yes—
763C22×C4C2×#4114yes—
764C22×C4C2×#4118yes—
765C22×C4H(5,𝔽2)14yes—
766C22×C42−1+414yes—
767C22×C4C2512yes—
768C22×C4C2512yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2518yes—
773C22×C4C2514yes—
774C22×C4C2518yes—
775C22×C4C2514yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2511yescharacteristic
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—24no—
790C4⋊C4—22no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—216no—
795C4⋊C4—28no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—44no—
799C4⋊C4—42no—
800C4⋊C4—44no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—42no—
804C4⋊C4—44no—
805C4⋊C4—42no—
806C4⋊C4—44no—
807C4⋊C4—42no—
808C4⋊C4—48no—
809C4⋊C4—42no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4H(5,𝔽2)14yes—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—216no—
822C22⋊C4—216no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—216no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—48no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C42—28no—
852C42—28no—
853C42—24no—
854C42—216no—
855C42—24no—
856C42—42no—
857C42—44no—
858C42—42no—
859C42—44no—
860C42—44no—
861C42—48no—
862C42—48no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—28no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—44no—
889C23—44no—
890C23—48no—
891C23—48no—
892C23—48no—
893C23—84no—
894C23—82no—
895C23—82no—
896C23—84no—
897C23—82no—
898C23—84no—
899C23—82no—
900C23—84no—
901C23C22×#4114yes—
902C23C22×#4112yes—
903C23C2×H(5,𝔽2)12yes—
904C23C2×2−1+412yes—
905C23C2611yescharacteristic
906Q8—48no—
907Q8—88no—
908Q8—164no—
909D4—48no—
910D4—48no—
911D4—416no—
912D4—416no—
913D4—48no—
914D4—84no—
915D4—84no—
916D4—88no—
917D4—816no—
918D4—168no—
919D4—168no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—28no—
931C2×C4—216no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—22no—
945C2×C4—28no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—48no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—416no—
967C2×C4—48no—
968C2×C4—48no—
969C2×C4—416no—
970C2×C4—88no—
971C2×C4—84no—
972C2×C4—82no—
973C2×C4—82no—
974C2×C4—164no—
975C2×C4—168no—
976C2×C4—164no—
977C2×C4C22×#4114yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C2×H(5,𝔽2)14yes—
981C2×C4C2×H(5,𝔽2)14yes—
982C2×C4C2×H(5,𝔽2)12yes—
983C2×C4C2×2−1+414yes—
984C2×C4#58512yes—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—88no—
1013C22—816no—
1014C22#351114yes—
1015C22C23×#4111yescharacteristic
1016C22C22×H(5,𝔽2)11yescharacteristic
1017C22C22×H(5,𝔽2)11yescharacteristic
1018C22C22×2−1+411yescharacteristic
1019C22C2×#58511yescharacteristic
1020C22H(7,𝔽2)11yescharacteristic
1021C22H(7,𝔽2)11yescharacteristic
1022C4—24no—
1023C4—24no—
1024C4—24no—
1025C4—22no—
1026C4—24no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—42no—
1031C4—48no—
1032C4—44no—
1033C4—42no—
1034C4—48no—
1035C4—44no—
1036C4—42no—
1037C4#345914yes—
1038C2—24no—
1039C2—44no—
1040C2—84no—
1041C2—84no—
1042C2C2×#345911yescharacteristic
1043C2C2×#351111yescharacteristic
1044C2#6285511yescharacteristic
1045C2#6289411yescharacteristic
1046C2#6290511yescharacteristic
1047C2#6291611yescharacteristic
1048C2#6292911yescharacteristic
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. #42989C2semidirect
2. #42946C2semidirect
3. #42338C2semidirect
4. #42060C2semidirect
5. #39631C2semidirect
6. #39420C2semidirect
7. #39375C2semidirect
8. #37940C2semidirect
9. #37462C2semidirect
10. #37439C2semidirect
11. #36586C2semidirect
12. #36160C2semidirect
13. #36087C2semidirect
14. #36000C2semidirect
15. #35003C2semidirect
16. #35002C2semidirect
17. #34578C2semidirect
18. #34575C2semidirect
19. #34202C2semidirect
20. C2×#2363C2semidirect
21. C2×#555C22semidirect
26. C2×#520C22semidirect
33. #2838C22semidirect
34. #2829C22semidirect
36. #2807C22semidirect
37. #2805C22semidirect
38. #2778C22semidirect
39. #2746C22semidirect
40. #2732C22semidirect
41. #2730C22semidirect
42. #2727C22semidirect
43. #2723C22semidirect
44. #2710C22semidirect
45. #2708C22semidirect
46. #2688C22semidirect
47. #2682C22semidirect
48. #2681C22semidirect
49. #2676C22semidirect
50. #2667C22semidirect
51. #2665C22semidirect
52. #2663C22semidirect
53. #2663C22semidirect
54. #2661C22semidirect
60. #2653C22semidirect
61. #2651C22semidirect
65. #2632C22semidirect
73. #2598C22semidirect
74. #2596C22semidirect
75. #2578C22semidirect
76. #2571C22semidirect
77. #2563C22semidirect
78. #2560C22semidirect
79. #2555C22semidirect
80. #2553C22semidirect
81. #2549C22semidirect
82. #2547C22semidirect
83. #2540C22semidirect
84. #2537C22semidirect
85. #2525C22semidirect
86. #2521C22semidirect
87. #2514C22semidirect
88. #2512C22semidirect
90. #2507C22semidirect
91. #2501C22semidirect
92. #2497C22semidirect
93. #2494C22semidirect
94. #2491C22semidirect
96. #2487C22semidirect
97. #2485C22semidirect
98. #2476C22semidirect
100. #2464C22semidirect
101. #2464C22semidirect
102. #2461C22semidirect
103. #2461C22semidirect
104. #2459C22semidirect
106. #2448C22semidirect
107. #2440C22semidirect
108. #2440C22semidirect
109. #2440C22semidirect
110. #2426C22semidirect
111. #2420C22semidirect
115. #2416C22semidirect
116. #2414C22semidirect
119. #2396C22semidirect
120. #2396C22semidirect
121. #2395C22semidirect
122. #2388C22semidirect
123. #2365C22semidirect
127. #2363C22semidirect
128. #2359C22semidirect
130. #2354C22semidirect
131. #2354C22semidirect
132. #2354C22semidirect
134. #2352C22semidirect
136. #2347C22semidirect
138. #2324C22semidirect
139. #2323C22semidirect
140. #2317C22semidirect
142. #2311C22semidirect
155. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#429892
#429462
#423382
#420602
#396312
#394202
#393752
#379402
#374622
#374392
#365862
#361602
#360872
#360002
#350032
#350022
#345782
#345752
#342022
C2×#23632