Finite Group Databasebeta

← #7633120

Subgroups — #7633120

Order 512.

6174 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36476C212yesmaximal, complemented
2#36463C212yesmaximal, complemented
3#36147C214yesmaximal, complemented
4#36144C214yesmaximal, complemented
5#36128C212yesmaximal, complemented
6#36115C212yesmaximal, complemented
7#35992C214yesmaximal, complemented
8#35813C214yesmaximal, complemented
9#35741C214yesmaximal, complemented
10#35684C214yesmaximal, complemented
11#35562C214yesmaximal, complemented
12#35438C214yesmaximal, complemented
13#35422C214yesmaximal, complemented
14#35293C211yesmaximal, characteristic, complemented
15#35237C211yesmaximal, characteristic, complemented
16#35109C214yesmaximal, complemented
17#34936C211yesmaximal, characteristic, complemented
18#34912C211yesmaximal, characteristic, complemented
19#34889C214yesmaximal, complemented
20#34330C214yesmaximal, complemented
21#34232C211yesmaximal, characteristic, complemented
22#34155C211yesmaximal, characteristic, complemented
23C4×#518C211yesmaximal, characteristic, complemented
24C2×#550C2214yes—
25C2×#532C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×#532C2214yescomplemented
28C2×#529C2214yescomplemented
29C2×#525C2214yes—
30C2×#518C2212yes—
31C22×C4×D4C2211yescharacteristic
32#2867C2211yescharacteristic, complemented
33#2862C2211yescharacteristic, complemented
34#2858C2211yescharacteristic, complemented
35#2858C2211yescharacteristic, complemented
36#2856C2214yescomplemented
37#2855C2214yescomplemented
38#2854C2214yescomplemented
39#2850C2214yescomplemented
40#2847C2212yes—
41#2847C2212yes—
42#2651C2218yescomplemented
43#2635C2218yes—
44#2631C2214yes—
45#2619C2214yes—
46#2608C2212yes—
47#2607C2212yes—
48#2607C2218yescomplemented
49#2606C2212yescomplemented
50#2605C2212yescomplemented
51#2589C2218yescomplemented
52#2580C2214yes—
53#2570C2212yescomplemented
54#2570C2214yescomplemented
55#2563C2212yes—
56#2559C2218yescomplemented
57#2557C2218yes—
58#2557C2218yescomplemented
59#2557C2218yescomplemented
60#2554C2218yes—
61#2550C2212yescomplemented
62#2548C2214yescomplemented
63#2544C2214yescomplemented
64#2544C2212yescomplemented
65#2544C2212yescomplemented
66#2542C2212yes—
67#2541C2212yes—
68#2541C2212yes—
69#2541C2214yes—
70#2540C2212yes—
71#2540C2212yes—
72#2539C2218yes—
73#2539C2214yes—
74#2535C2214yes—
75#2521C2218yescomplemented
76#2516C2218yescomplemented
77#2513C2214yescomplemented
78#2512C2214yescomplemented
79#2504C2212yes—
80#2501C2212yes—
81#2492C2214yescomplemented
82#2490C2214yescomplemented
83#2476C2218yescomplemented
84#2471C2218yes—
85#2471C2218yescomplemented
86#2471C2218yescomplemented
87#2467C2218yescomplemented
88#2467C2218yescomplemented
89#2464C2218yes—
90#2464C2218yes—
91#2459C2218yescomplemented
92#2459C2218yescomplemented
93#2457C2218yes—
94#2445C2214yes—
95#2445C2214yes—
96#2444C2218yescomplemented
97#2441C2212yes—
98#2439C2212yes—
99#2433C2212yes—
100#2433C2212yes—
101#2431C2214yes—
102#2431C2212yes—
103#2431C2212yes—
104#2431C2218yescomplemented
105#2428C2214yescomplemented
106#2428C2214yescomplemented
107#2428C2218yescomplemented
108#2427C2214yescomplemented
109#2426C2214yescomplemented
110#2425C2218yescomplemented
111#2424C2218yes—
112#2424C2218yes—
113#2423C2214yescomplemented
114#2420C2214yescomplemented
115#2404C2218yes—
116#2404C2214yes—
117#2397C2214yes—
118#2396C2214yes—
119#2395C2218yescomplemented
120#2388C2218yes—
121#2372C2214yescomplemented
122#2369C2212yescomplemented
123#2366C2214yes—
124#2366C2214yes—
125#2366C2212yescomplemented
126#2366C2214yescomplemented
127#2366C2212yescomplemented
128#2365C2212yescomplemented
129#2364C2218yescomplemented
130#2364C2218yescomplemented
131#2363C2214yes—
132#2363C2214yes—
133#2363C2214yes—
134#2363C2218yescomplemented
135#2357C2214yes—
136#2357C2214yescomplemented
137#2355C2214yescomplemented
138#2354C2214yescomplemented
139#2353C2214yescomplemented
140#2341C2212yes—
141#2339C2212yes—
142#2339C2218yescomplemented
143#2333C2214yes—
144#2333C2218yescomplemented
145#2333C2218yescomplemented
146#2328C2214yes—
147#2328C2214yescomplemented
148#2319C2212yescomplemented
149C4×C4⋊Q8C2212yescomplemented
150C4×#127C2214yes—
151C4×#125C2212yescomplemented
152C4×#124C2214yescomplemented
153C4×C22⋊Q8C2214yescomplemented
154C4×#121C2218yescomplemented
155C4×#121C2214yescomplemented
156#2297C2214yes—
157#2297C2218yescomplemented
158#2295C2214yescomplemented
159#2293C2212yescomplemented
160#2293C2212yescomplemented
161#2283C2211yescharacteristic
162#2275C2212yes—
163#2275C2212yes—
164#2275C2212yes—
165#2275C2212yes—
166#2275C2212yescomplemented
167#2274C2212yes—
168#2273C2212yes—
169#2273C2212yes—
170C42×D4C2212yes—
171C42×D4C2212yes—
172C42×D4C2214yes—
173C42×D4C2212yescomplemented
174C42×D4C2212yescomplemented
175C4×#117C2211yescharacteristic
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C2×C4×C22⋊C4C2214yes—
179C22×#41C2312yes—
180C22×#41C2318yes—
181C22×#41C2312yes—
182C23×D4C2311yescharacteristic
183C24×C4C2312yes—
184#550—232no—
185#532—28no—
186#532—28no—
187#532—416no—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2311yescharacteristic
191C2×#127C2314yes—
192C2×#127C2314yes—
193C2×#127C2314yes—
194C2×#127C2311yescharacteristic
195C2×#127C2311yescharacteristic
196C2×#127C2314yes—
197C2×#127C2312yes—
198C2×#127C2312yes—
199#529—416no—
200C2×#126C2318yes—
201C2×#125C2312yes—
202C2×#124C2312yes—
203C2×#124C2312yes—
204C2×#124C2314yes—
205C2×#124C2318yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208#525—416no—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×#121C2312yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2318yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#120C2318yes—
228C2×#120C2314yes—
229C2×#120C2314yes—
230#518—216no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×D4—28no—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2318yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2318yes—
261C2×#117C2314yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2314yes—
266C22×C42C2314yes—
267C22×C42C2314yes—
268C22×C42C2314yes—
269C22×C42C2311yescharacteristic
270#400C2318yes—
271#400C2314yes—
272#399C2318yes—
273#399C2318yes—
274#399C2314yes—
275#399C2314yes—
276#399C2314yes—
277#398C2318yes—
278#398C2314yes—
279#398C2314yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#396C2314yes—
285#396C2314yes—
286#396C2318yes—
287#395C2314yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#393C2318yes—
297#393C2318yes—
298#393C2314yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2314yes—
304#392C2318yes—
305#392C2314yes—
306#392C2318yes—
307#392C2318yes—
308#391C2314yes—
309#391C2312yes—
310#391C2318yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#390C2314yes—
318#390C2318yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2318yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2318yes—
333#390C2312yes—
334#390C2312yes—
335#390C2318yes—
336#390C2314yes—
337#390C2318yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2314yes—
371#387C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2314yes—
387#386C2314yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#385C2318yes—
395#385C2318yes—
396#384C2314yes—
397#384C2312yes—
398#383C2312yes—
399#382C2312yes—
400#382C2314yes—
401#382C2314yes—
402#382C2312yes—
403#381C2314yes—
404#381C2312yes—
405#381C2318yes—
406#381C2318yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2318yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2318yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2318yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2312yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2312yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467#376C2312yes—
468#376C2312yes—
469#376C2312yes—
470#376C2312yes—
471C2×#95C2314yes—
472C2×#95C2314yes—
473C2×#95C2314yes—
474C43C2311yescharacteristic
475C43C2312yes—
476C43C2311yescharacteristic
477C43C2312yes—
478C25C2412yes—
479C2×#41—28no—
480C2×#41—28no—
481C2×#41—232no—
482C2×#41—48no—
483C2×#41—416no—
484C2×#41—82no—
485C2×#41—88no—
486C2×#41—82no—
487C22×Q8C2412yes—
488C22×Q8C2414yes—
489C22×Q8C2412yes—
490C22×D4—28no—
491C22×D4—24no—
492C22×D4C2412yes—
493C22×D4C2412yes—
494C22×D4C2412yes—
495C22×D4C2412yes—
496C22×D4C2412yes—
497C22×D4C2418yes—
498C22×D4C2412yes—
499C22×D4C2418yes—
500C22×D4C2418yes—
501C22×D4C2418yes—
502C22×D4C2412yes—
503C22×D4C2414yes—
504C22×D4C2414yes—
505C22×D4C2418yes—
506C22×D4C2418yes—
507C22×D4C2412yes—
508C23×C4—28no—
509C23×C4—48no—
510C23×C4C2414yes—
511C23×C4C2418yes—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2414yes—
517C23×C4C2414yes—
518C23×C4C2414yes—
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2418yes—
522C23×C4C2411yescharacteristic
523C23×C4C2414yes—
524C4⋊Q8—28no—
525C4⋊Q8—24no—
526C4⋊Q8—24no—
527#127—216no—
528#127—216no—
529#127—24no—
530#127—24no—
531#127—216no—
532#127—48no—
533#127—82no—
534#127—82no—
535#126—416no—
536#125—28no—
537#124—28no—
538#124—28no—
539#124—48no—
540#124—416no—
541#124—82no—
542#124—82no—
543#123—416no—
544#123—416no—
545#123—88no—
546C22⋊Q8—216no—
547C22⋊Q8—48no—
548#121—28no—
549#121—28no—
550#121—28no—
551#121—28no—
552#121—232no—
553#121—216no—
554#121—232no—
555#121—232no—
556#121—416no—
557#121—48no—
558#121—48no—
559#121—48no—
560#121—88no—
561#120—416no—
562#120—84no—
563#120—84no—
564C4×Q8—216no—
565C4×Q8—48no—
566C4×D4—28no—
567C4×D4—216no—
568C4×D4—28no—
569C4×D4—216no—
570C4×D4—216no—
571C4×D4—216no—
572C4×D4—216no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—416no—
583C4×D4—416no—
584C4×D4—48no—
585C4×D4—416no—
586C4×D4—416no—
587C4×D4—88no—
588C4×D4#41116yescomplemented
589#117—28no—
590#117—28no—
591#117—28no—
592#117—416no—
593#117—84no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C22⋊C4—28no—
623C2×C22⋊C4—216no—
624C2×C22⋊C4—216no—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C42—48no—
660C2×C42—48no—
661C2×C42—84no—
662C2×C42#4118yescomplemented
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2418yes—
675C2×C42C2414yes—
676C2×C42C2418yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2412yes—
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2414yes—
706#95C2414yes—
707#95C2412yes—
708#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723C24—28no—
724C24—24no—
725C24—44no—
726C24—42no—
727C24—42no—
728C24C2514yes—
729C24C2514yes—
730C24C2511yescharacteristic
731C24C2514yes—
732#41—816no—
733#41—816no—
734#41—864no—
735C2×Q8—28no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8—28no—
740C2×Q8—44no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×D4—232no—
744C2×D4—28no—
745C2×D4—216no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—216no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—216no—
762C2×D4—216no—
763C2×D4—24no—
764C2×D4—28no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—48no—
785C2×D4C2×#4118yes—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—216no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—216no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—216no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—44no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—44no—
816C22×C4—48no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—816no—
821C22×C4C2×#4114yes—
822C22×C4C2×#4114yes—
823C22×C4C2×#4114yes—
824C22×C4C2×#41116yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4C2×#4118yes—
870C4⋊C4H(5,𝔽2)18yes—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4C2×#41116yes—
905C42—28no—
906C42—24no—
907C42—28no—
908C42—28no—
909C42—28no—
910C42—24no—
911C42—24no—
912C42—28no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—44no—
917C42—42no—
918C42—42no—
919C42—48no—
920C42—48no—
921C42—42no—
922C42—42no—
923C42—41no—
924C42—41no—
925C42—41no—
926C42—41no—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C42C2×#4114yes—
931C42C2×#4118yes—
932C23—216no—
933C23—22no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—21no—
942C23—21no—
943C23—24no—
944C23—24no—
945C23—28no—
946C23—28no—
947C23—28no—
948C23—28no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—84no—
954C23—88no—
955C23—88no—
956C23—84no—
957C23C22×#4118yes—
958C23C22×#4112yes—
959C23C2611yescharacteristic
960Q8—416no—
961Q8—48no—
962Q8—84no—
963D4—216no—
964D4—216no—
965D4—432no—
966D4—48no—
967D4—48no—
968D4—48no—
969D4—48no—
970D4—816no—
971D4—84no—
972D4—816no—
973D4—84no—
974D4—816no—
975D4—816no—
976D4—816no—
977D4—88no—
978D4—88no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—416no—
1022C2×C4—44no—
1023C2×C4—432no—
1024C2×C4—416no—
1025C2×C4—416no—
1026C2×C4—88no—
1027C2×C4—88no—
1028C2×C4—88no—
1029C2×C4—816no—
1030C2×C4—88no—
1031C2×C4—88no—
1032C2×C4—84no—
1033C2×C4C22×#4118yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4114yes—
1039C2×C4C22×#4114yes—
1040C2×C4C22×#4114yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4112yes—
1043C2×C4C2×H(5,𝔽2)18yes—
1044C2×C4C2×H(5,𝔽2)14yes—
1045C22—28no—
1046C22—28no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—28no—
1051C22—44no—
1052C22—42no—
1053C22—44no—
1054C22—42no—
1055C22—44no—
1056C22—44no—
1057C22—48no—
1058C22—48no—
1059C22—48no—
1060C22—48no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—816no—
1068C22C23×#4112yes—
1069C22C23×#4111yescharacteristic
1070C22C22×H(5,𝔽2)12yes—
1071C22H(7,𝔽2)11yescharacteristic
1072C22H(7,𝔽2)11yescharacteristic
1073C4—28no—
1074C4—24no—
1075C4—28no—
1076C4—24no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—42no—
1082C4—44no—
1083C4—44no—
1084C4—42no—
1085C4—44no—
1086C4—44no—
1087C4—44no—
1088C4—44no—
1089C4—44no—
1090C4#344414yes—
1091C4#350814yes—
1092C2—48no—
1093C2—42no—
1094C2—84no—
1095C2—84no—
1096C2C2×#344411yescharacteristic
1097C2C2×#350811yescharacteristic
1098C2#6285511yescharacteristic
1099C2#6298312yes—
1100C2#6298612yes—
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. #36476C2semidirect
2. #36463C2semidirect
3. #36147C2semidirect
4. #36144C2semidirect
5. #36128C2semidirect
6. #36115C2semidirect
7. #35992C2semidirect
8. #35813C2semidirect
9. #35741C2semidirect
10. #35684C2semidirect
11. #35562C2semidirect
12. #35438C2semidirect
13. #35422C2semidirect
14. #35293C2semidirect
15. #35237C2semidirect
16. #35109C2semidirect
17. #34936C2semidirect
18. #34912C2semidirect
19. #34889C2semidirect
20. #34330C2semidirect
21. #34232C2semidirect
22. #34155C2semidirect
23. C4×#518C2semidirect
27. C2×#532C22semidirect
28. C2×#529C22semidirect
32. #2867C22semidirect
33. #2862C22semidirect
34. #2858C22semidirect
35. #2858C22semidirect
36. #2856C22semidirect
37. #2855C22semidirect
38. #2854C22semidirect
39. #2850C22semidirect
42. #2651C22semidirect
48. #2607C22semidirect
49. #2606C22semidirect
50. #2605C22semidirect
51. #2589C22semidirect
53. #2570C22semidirect
54. #2570C22semidirect
56. #2559C22semidirect
58. #2557C22semidirect
59. #2557C22semidirect
61. #2550C22semidirect
62. #2548C22semidirect
63. #2544C22semidirect
64. #2544C22semidirect
65. #2544C22semidirect
75. #2521C22semidirect
76. #2516C22semidirect
77. #2513C22semidirect
78. #2512C22semidirect
81. #2492C22semidirect
82. #2490C22semidirect
83. #2476C22semidirect
85. #2471C22semidirect
86. #2471C22semidirect
87. #2467C22semidirect
88. #2467C22semidirect
91. #2459C22semidirect
92. #2459C22semidirect
96. #2444C22semidirect
104. #2431C22semidirect
105. #2428C22semidirect
106. #2428C22semidirect
107. #2428C22semidirect
108. #2427C22semidirect
109. #2426C22semidirect
110. #2425C22semidirect
113. #2423C22semidirect
114. #2420C22semidirect
119. #2395C22semidirect
121. #2372C22semidirect
122. #2369C22semidirect
125. #2366C22semidirect
126. #2366C22semidirect
127. #2366C22semidirect
128. #2365C22semidirect
129. #2364C22semidirect
130. #2364C22semidirect
134. #2363C22semidirect
136. #2357C22semidirect
137. #2355C22semidirect
138. #2354C22semidirect
139. #2353C22semidirect
142. #2339C22semidirect
144. #2333C22semidirect
145. #2333C22semidirect
147. #2328C22semidirect
148. #2319C22semidirect
149. C4×C4⋊Q8C22semidirect
151. C4×#125C22semidirect
152. C4×#124C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×#121C22semidirect
155. C4×#121C22semidirect
157. #2297C22semidirect
158. #2295C22semidirect
159. #2293C22semidirect
160. #2293C22semidirect
166. #2275C22semidirect
173. C42×D4C22semidirect
174. C42×D4C22semidirect
588. C4×D4#41semidirect
662. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#364762
#364632
#361472
#361442
#361282
#361152
#359922
#358132
#357412
#356842
#355622
#354382
#354222
#352932
#352372
#351092
#349362
#349122
#348892
#343302
#342322
#341552
C4×#5182