Finite Group Databasebeta

← #7646957

Subgroups — #7646957

Order 512.

8130 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C22×#548C211yesmaximal, characteristic, complemented
3#42890C214yesmaximal, complemented
4#42887C214yesmaximal, complemented
5#42815C214yesmaximal, complemented
6#42810C214yesmaximal, complemented
7#39954C218yesmaximal, complemented
8#39950C218yesmaximal, complemented
9#37606C214yesmaximal, complemented
10#37185C214yesmaximal, complemented
11#37118C214yesmaximal, complemented
12#35633C212yesmaximal, complemented
13#35563C212yesmaximal, complemented
14#35338C211yesmaximal, characteristic, complemented
15#35329C211yesmaximal, characteristic, complemented
16#35242C212yesmaximal, complemented
17#35232C214yesmaximal, complemented
18#35149C212yesmaximal, complemented
19#34946C211yesmaximal, characteristic, complemented
20#34936C211yesmaximal, characteristic, complemented
21#34059C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C24×Q8C2211yescharacteristic
24#3507—216no—
25C2×#559C2212yescomplemented
26C2×#557C2212yescomplemented
27C2×#556C2214yescomplemented
28C2×#556C2212yescomplemented
29C2×#554C2212yescomplemented
30C2×#552C2214yescomplemented
31C2×#548—216no—
32C2×#548C2214yes—
33C2×#548C2214yes—
34C2×#548C2214yes—
35C2×#548C2214yes—
36C2×#539C2214yes—
37C2×#536C2212yes—
38C2×#536C2212yes—
39C2×#535C2212yes—
40C2×#533C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#529C2214yes—
43C22×#124C2211yescharacteristic
44C22×#124C2212yes—
45C2×#525C2212yes—
46C2×#525C2212yes—
47C22×C22⋊Q8C2211yescharacteristic
48C22×C22⋊Q8C2212yes—
49C22×#121C2212yes—
50C22×#121C2211yescharacteristic
51C2×#520C2212yes—
52C22×C4×Q8C2211yescharacteristic
53C22×C4×D4C2211yescharacteristic
54C22×C4×D4C2212yes—
55#2861C2214yescomplemented
56#2858C2214yescomplemented
57#2849C2218yes—
58#2849C2218yes—
59#2820C2218yescomplemented
60#2819C2218yescomplemented
61#2723C22116yescomplemented
62#2720C22116yescomplemented
63#2714C22116yescomplemented
64#2711C22116yescomplemented
65#2696C22116yescomplemented
66#2692C22116yescomplemented
67#2676C22116yescomplemented
68#2673C22116yescomplemented
69#2662C22116yescomplemented
70#2658C2212yescomplemented
71#2657C2212yescomplemented
72#2640C2212yescomplemented
73#2640C2212yescomplemented
74#2633C2218yescomplemented
75#2632C2218yescomplemented
76#2631C2218yescomplemented
77#2631C2218yescomplemented
78#2614C2218yes—
79#2613C2218yes—
80#2610C22116yescomplemented
81#2603C22116yescomplemented
82#2592C2214yescomplemented
83#2592C2214yescomplemented
84#2580C2218yescomplemented
85#2563C2212yescomplemented
86#2562C2214yescomplemented
87#2561C2214yes—
88#2561C2214yes—
89#2561C2212yes—
90#2561C2212yes—
91#2547C2212yescomplemented
92#2542C2212yescomplemented
93#2541C2212yescomplemented
94#2540C2214yescomplemented
95#2540C2214yescomplemented
96#2540C2214yescomplemented
97#2539C2214yes—
98#2539C2214yes—
99#2539C2212yes—
100#2539C2212yes—
101#2535C2218yescomplemented
102#2534C2218yes—
103#2534C2218yes—
104#2503C2212yes—
105#2501C2212yes—
106#2486C2218yes—
107#2436C2218yescomplemented
108#2435C2212yes—
109#2434C2218yescomplemented
110#2433C2212yes—
111#2432C2218yescomplemented
112#2431C2218yescomplemented
113#2429C2218yescomplemented
114#2428C2218yescomplemented
115#2427C2218yescomplemented
116#2426C2218yescomplemented
117#2417C2218yescomplemented
118#2416C2218yescomplemented
119#2415C2218yescomplemented
120#2414C2218yescomplemented
121#2409C2218yescomplemented
122#2409C2218yescomplemented
123#2408C2218yes—
124#2407C2218yescomplemented
125#2407C2218yescomplemented
126#2398C2214yescomplemented
127#2397C2214yescomplemented
128#2324C22116yescomplemented
129#2320C2214yescomplemented
130#2320C2214yescomplemented
131#2316C2212yes—
132#2313C2214yes—
133#2310C2212yes—
134#2310C2212yes—
135#2309C2212yes—
136C4×#127C2214yescomplemented
137C4×#124C2214yescomplemented
138#2295C2214yescomplemented
139#2295C2214yescomplemented
140#2283C2214yes—
141#2280C2212yes—
142#2280C2212yes—
143C4×#117C2211yescharacteristic
144C4×#117C2211yescharacteristic
145C22×#41—28no—
146C22×#41—48no—
147C22×#41C2312yes—
148C22×#41C2314yes—
149C22×#41C2314yes—
150C23×Q8—28no—
151C23×Q8—48no—
152C23×Q8C2311yescharacteristic
153C23×Q8C2311yescharacteristic
154C23×Q8C2312yes—
155C23×Q8C2314yes—
156C23×Q8C2314yes—
157C23×D4C2311yescharacteristic
158C23×D4C2312yes—
159C23×D4C2312yes—
160C23×D4C2311yescharacteristic
161C24×C4C2311yescharacteristic
162C24×C4C2311yescharacteristic
163C24×C4C2312yes—
164C24×C4C2312yes—
165#559—216no—
166#557—216no—
167#556—216no—
168#556—232no—
169#554—216no—
170#552—232no—
171#548—232no—
172#548—232no—
173#548—232no—
174#548—232no—
175#539—232no—
176#536—216no—
177#536—48no—
178#535—48no—
179#533—28no—
180#532—28no—
181C2×C4⋊Q8C2311yescharacteristic
182C2×C4⋊Q8C2311yescharacteristic
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186C2×#127C2311yescharacteristic
187C2×#127C2314yes—
188C2×#127C2314yes—
189#529—232no—
190C2×#126C2318yes—
191C2×#126C2318yes—
192C2×#125C2312yes—
193C2×#125C2314yes—
194C2×#125C2318yes—
195C2×#124—216no—
196C2×#124—28no—
197C2×#124C2314yes—
198C2×#124C2318yes—
199C2×#124C2312yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2312yes—
203C2×#124C2318yes—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209#525—48no—
210#525—48no—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×#123C2314yes—
216C2×C22⋊Q8—28no—
217C2×C22⋊Q8—216no—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×#121—28no—
231C2×#121—216no—
232C2×#121C2314yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C23116yes—
239C2×#121C2318yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#120C2314yes—
243C2×#120C2318yes—
244C2×#120C2314yes—
245#520—216no—
246C2×C4×Q8D4116yescomplemented
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×D4—216no—
256C2×C4×D4—28no—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2318yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2318yes—
269C2×C4×D4C2318yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2318yes—
274C2×#117C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C42C2312yes—
287C22×C42C2311yescharacteristic
288#400C2318yes—
289#399C2314yes—
290#399C2318yes—
291#399C2314yes—
292#399C2318yes—
293#399C2318yes—
294#398C23116yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C23116yes—
300#396C23116yes—
301#396C23116yes—
302#395C23116yes—
303#395C23116yes—
304#394C2318yes—
305#394C23116yes—
306#394C23116yes—
307#394C23116yes—
308#394C23116yes—
309#394C23116yes—
310#393C2314yes—
311#393C2314yes—
312#393C2318yes—
313#393C2318yes—
314#393C23116yes—
315#393C23116yes—
316#392C2314yes—
317#392C23116yes—
318#392C2318yes—
319#392C23116yes—
320#392C23116yes—
321#392C2314yes—
322#392C2318yes—
323#392C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#390C2318yes—
331#390C2318yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#390C2314yes—
338#390C23116yes—
339#390C23116yes—
340#390C23116yes—
341#389C2318yes—
342#389C2318yes—
343#389C23116yes—
344#388C2318yes—
345#388C2318yes—
346#388C23116yes—
347#388C23116yes—
348#388C23116yes—
349#388C23116yes—
350#387C23116yes—
351#387C23116yes—
352#386C23116yes—
353#386C23116yes—
354#386C23116yes—
355#386C23116yes—
356#386C23116yes—
357#386C23116yes—
358#385C23116yes—
359#385C23116yes—
360#385C23116yes—
361#385C23116yes—
362#384C2314yes—
363#383C2318yes—
364#382C2314yes—
365#382C2318yes—
366#381C2318yes—
367#381C2314yes—
368#381C2314yes—
369#381C2318yes—
370#380C2314yes—
371#380C2314yes—
372#380C2314yes—
373#380C2314yes—
374#380C2318yes—
375#380C23116yes—
376#379C2318yes—
377#379C2314yes—
378#379C2314yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2312yes—
381C4×C4⋊C4C2312yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2312yes—
384C4×C22⋊C4C2312yes—
385C4×C22⋊C4C2312yes—
386C4×C22⋊C4C2312yes—
387C4×C22⋊C4C2312yes—
388C4×C22⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390#376C2312yes—
391#376C2312yes—
392#376C2318yes—
393C43C2312yes—
394C43C2312yes—
395C25C2411yescharacteristic
396C25C2411yescharacteristic
397C25C2412yes—
398C2×#41—216no—
399C2×#41—216no—
400C2×#41—28no—
401C2×#41—28no—
402C2×#41—28no—
403C2×#41—416no—
404C2×#41—416no—
405C2×#41—464no—
406C22×Q8—216no—
407C22×Q8—216no—
408C22×Q8—28no—
409C22×Q8—24no—
410C22×Q8—28no—
411C22×Q8—28no—
412C22×Q8—48no—
413C22×Q8—416no—
414C22×Q8—416no—
415C22×Q8—464no—
416C22×Q8C2×D418yes—
417C22×Q8C2412yes—
418C22×Q8C2412yes—
419C22×Q8C2412yes—
420C22×Q8C2412yes—
421C22×Q8C2412yes—
422C22×Q8C2412yes—
423C22×Q8C2412yes—
424C22×Q8C2418yes—
425C22×D4—28no—
426C22×D4—24no—
427C22×D4—28no—
428C22×D4—24no—
429C22×D4—28no—
430C22×D4—48no—
431C22×D4—48no—
432C22×D4—44no—
433C22×D4C2414yes—
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2418yes—
438C22×D4C2412yes—
439C22×D4C2412yes—
440C22×D4C2412yes—
441C22×D4C2418yes—
442C22×D4C2412yes—
443C22×D4C2418yes—
444C22×D4C2418yes—
445C22×D4C24116yes—
446C23×C4—28no—
447C23×C4—24no—
448C23×C4—28no—
449C23×C4—24no—
450C23×C4—28no—
451C23×C4—28no—
452C23×C4—48no—
453C23×C4—48no—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2418yes—
464C23×C4C2418yes—
465C23×C4C2418yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C4⋊Q8—216no—
471C4⋊Q8—24no—
472C4⋊Q8—24no—
473C4⋊Q8—24no—
474C4⋊Q8—48no—
475#127—24no—
476#127—48no—
477#127—48no—
478#126—232no—
479#126—232no—
480#125—232no—
481#125—216no—
482#125—28no—
483#124—216no—
484#124—232no—
485#124—28no—
486#124—28no—
487#124—232no—
488#124—28no—
489#124—28no—
490#124—216no—
491#124—28no—
492#124—48no—
493#124—48no—
494#124—48no—
495#123—232no—
496#123—232no—
497#123—48no—
498#123—48no—
499#123—416no—
500C22⋊Q8—216no—
501C22⋊Q8—216no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8—216no—
505C22⋊Q8—216no—
506C22⋊Q8—232no—
507C22⋊Q8—232no—
508C22⋊Q8—232no—
509C22⋊Q8—48no—
510C22⋊Q8—48no—
511C22⋊Q8—416no—
512#121—28no—
513#121—28no—
514#121—216no—
515#121—216no—
516#121—232no—
517#121—232no—
518#121—432no—
519#121—48no—
520#121—48no—
521#121—416no—
522#120—48no—
523#120—48no—
524#120—416no—
525C4×Q8—216no—
526C4×Q8—216no—
527C4×Q8—28no—
528C4×Q8—28no—
529C4×Q8C2×D4116yes—
530C4×Q8C2×D4116yes—
531C4×Q8C2×D4116yes—
532C4×Q8C2×D4116yes—
533C4×D4—232no—
534C4×D4—216no—
535C4×D4—232no—
536C4×D4—28no—
537C4×D4—28no—
538C4×D4—232no—
539C4×D4—28no—
540C4×D4—28no—
541C4×D4—216no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—416no—
545C4×D4—416no—
546#117—28no—
547#117—28no—
548#117—28no—
549#117—216no—
550#117—232no—
551C2×C4⋊C4—28no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—216no—
554C2×C4⋊C4C2×D418yes—
555C2×C4⋊C4C2×D4116yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C24116yes—
575C2×C4⋊C4C24116yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—28no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—28no—
584C2×C22⋊C4—28no—
585C2×C22⋊C4—28no—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C24116yes—
610C2×C22⋊C4C24116yes—
611C2×C22⋊C4C24116yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C24116yes—
616C2×C42C2×D4116yes—
617C2×C42C2×D418yes—
618C2×C42C2418yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2414yes—
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2414yes—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C24116yes—
637#95C24116yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C24116yes—
643#95C24116yes—
644#95C24116yes—
645C24—22no—
646C24—24no—
647C24—24no—
648C24—22no—
649C24—24no—
650C24—24no—
651C24—28no—
652C24—42no—
653C24—42no—
654C24—44no—
655C24—42no—
656C24—44no—
657C24C2512yes—
658C24C2514yes—
659C24C2514yes—
660C24C2512yes—
661C24C2511yescharacteristic
662#41—464no—
663#41—464no—
664#41—432no—
665C2×Q8—232no—
666C2×Q8—24no—
667C2×Q8—24no—
668C2×Q8—216no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—24no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—416no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—432no—
682C2×Q8—464no—
683C2×Q8—464no—
684C2×Q8—416no—
685C2×Q8C22×D418yes—
686C2×Q8C22×D418yes—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—216no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—216no—
694C2×D4—24no—
695C2×D4—216no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—216no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—48no—
710C2×D4—416no—
711C2×D4—44no—
712C2×D4—432no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—44no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—416no—
720C2×D4—416no—
721C2×D4—416no—
722C2×D4—432no—
723C2×D4—416no—
724C2×D4—416no—
725C22×C4—28no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—216no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—216no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—216no—
746C22×C4—416no—
747C22×C4—416no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—416no—
752C22×C4—432no—
753C22×C4—432no—
754C22×C4—416no—
755C22×C4—416no—
756C22×C4C22×D418yes—
757C22×C4C22×D414yes—
758C22×C4C22×D418yes—
759C22×C4C22×D414yes—
760C22×C4C22×D414yes—
761C22×C4H(5,𝔽2)18yes—
762C22×C4C2518yes—
763C22×C4C2518yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2512yes—
769C22×C4C2514yes—
770C22×C4C2511yescharacteristic
771C22×C4C2514yes—
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C22×C4C2514yes—
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C4⋊C4—24no—
779C4⋊C4—216no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—216no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—216no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—216no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—416no—
797C4⋊C4—416no—
798C4⋊C4C22×D418yes—
799C4⋊C4C22×D418yes—
800C4⋊C4C22×D4116yes—
801C4⋊C4C22×D4116yes—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—216no—
806C22⋊C4—24no—
807C22⋊C4—24no—
808C22⋊C4—24no—
809C22⋊C4—28no—
810C22⋊C4—24no—
811C22⋊C4—28no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—28no—
820C22⋊C4—216no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—416no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—416no—
829C22⋊C4—416no—
830C22⋊C4—416no—
831C22⋊C4—48no—
832C42—216no—
833C42—28no—
834C42—28no—
835C42—28no—
836C42—44no—
837C42—44no—
838C42—44no—
839C42—44no—
840C42C22×D4116yes—
841C42C22×D414yes—
842C42C22×D414yes—
843C42C22×D4116yes—
844C42C22×D414yes—
845C42C22×D414yes—
846C23—22no—
847C23—22no—
848C23—28no—
849C23—22no—
850C23—24no—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—22no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—28no—
860C23—22no—
861C23—28no—
862C23—28no—
863C23—22no—
864C23—24no—
865C23—28no—
866C23—28no—
867C23—416no—
868C23—44no—
869C23—44no—
870C23—48no—
871C23—44no—
872C23—48no—
873C23—44no—
874C23—48no—
875C23—44no—
876C23—88no—
877C23—816no—
878C23C23×D412yes—
879C23C2×H(5,𝔽2)14yes—
880C23#58514yes—
881C23C2611yescharacteristic
882Q8—216no—
883Q8—216no—
884Q8—48no—
885Q8—432no—
886Q8—48no—
887Q8—48no—
888Q8—48no—
889Q8—84no—
890D4—432no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—432no—
895D4—416no—
896D4—48no—
897D4—48no—
898D4—48no—
899D4—84no—
900D4—816no—
901D4—816no—
902D4—1616no—
903C2×C4—28no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—216no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—28no—
917C2×C4—28no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—44no—
930C2×C4—48no—
931C2×C4—44no—
932C2×C4—432no—
933C2×C4—432no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—48no—
937C2×C4—48no—
938C2×C4—48no—
939C2×C4—48no—
940C2×C4—48no—
941C2×C4—416no—
942C2×C4—816no—
943C2×C4#535116yes—
944C2×C4C23×D418yes—
945C2×C4C23×D412yes—
946C2×C4C23×D412yes—
947C2×C4C23×D412yes—
948C2×C4C23×D412yes—
949C2×C4C23×D418yes—
950C2×C4C23×D412yes—
951C2×C4C23×D412yes—
952C2×C4C2×H(5,𝔽2)14yes—
953C2×C4C2×H(5,𝔽2)14yes—
954C22—22no—
955C22—22no—
956C22—28no—
957C22—24no—
958C22—28no—
959C22—416no—
960C22—42no—
961C22—42no—
962C22—44no—
963C22—44no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—42no—
968C22—44no—
969C22—44no—
970C22—42no—
971C22—44no—
972C22—44no—
973C22—48no—
974C22—48no—
975C22—416no—
976C22—44no—
977C22—88no—
978C22—816no—
979C22C2×#53514yes—
980C22C24×D411yescharacteristic
981C22C22×H(5,𝔽2)12yes—
982C22C2×#58512yes—
983C222−1+612yes—
984C4—28no—
985C4—22no—
986C4—22no—
987C4—22no—
988C4—22no—
989C4—28no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—42no—
994C4—44no—
995C4—44no—
996C4—48no—
997C4—48no—
998C4C2×#53514yes—
999C4C2×#53514yes—
1000C2—24no—
1001C2—44no—
1002C2—84no—
1003C2—82no—
1004C2—84no—
1005C2C22×#53511yescharacteristic
1006C2#6281111yescharacteristic
1007C2#6284811yescharacteristic
1008C2#6295414yes—
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. C2×#3507C2semidirect
2. C22×#548C2semidirect
3. #42890C2semidirect
4. #42887C2semidirect
5. #42815C2semidirect
6. #42810C2semidirect
7. #39954C2semidirect
8. #39950C2semidirect
9. #37606C2semidirect
10. #37185C2semidirect
11. #37118C2semidirect
12. #35633C2semidirect
13. #35563C2semidirect
14. #35338C2semidirect
15. #35329C2semidirect
16. #35242C2semidirect
17. #35232C2semidirect
18. #35149C2semidirect
19. #34946C2semidirect
20. #34936C2semidirect
21. #34059C2semidirect
25. C2×#559C22semidirect
26. C2×#557C22semidirect
27. C2×#556C22semidirect
28. C2×#556C22semidirect
29. C2×#554C22semidirect
30. C2×#552C22semidirect
55. #2861C22semidirect
56. #2858C22semidirect
59. #2820C22semidirect
60. #2819C22semidirect
61. #2723C22semidirect
62. #2720C22semidirect
63. #2714C22semidirect
64. #2711C22semidirect
65. #2696C22semidirect
66. #2692C22semidirect
67. #2676C22semidirect
68. #2673C22semidirect
69. #2662C22semidirect
70. #2658C22semidirect
71. #2657C22semidirect
72. #2640C22semidirect
73. #2640C22semidirect
74. #2633C22semidirect
75. #2632C22semidirect
76. #2631C22semidirect
77. #2631C22semidirect
80. #2610C22semidirect
81. #2603C22semidirect
82. #2592C22semidirect
83. #2592C22semidirect
84. #2580C22semidirect
85. #2563C22semidirect
86. #2562C22semidirect
91. #2547C22semidirect
92. #2542C22semidirect
93. #2541C22semidirect
94. #2540C22semidirect
95. #2540C22semidirect
96. #2540C22semidirect
101. #2535C22semidirect
107. #2436C22semidirect
109. #2434C22semidirect
111. #2432C22semidirect
112. #2431C22semidirect
113. #2429C22semidirect
114. #2428C22semidirect
115. #2427C22semidirect
116. #2426C22semidirect
117. #2417C22semidirect
118. #2416C22semidirect
119. #2415C22semidirect
120. #2414C22semidirect
121. #2409C22semidirect
122. #2409C22semidirect
124. #2407C22semidirect
125. #2407C22semidirect
126. #2398C22semidirect
127. #2397C22semidirect
128. #2324C22semidirect
129. #2320C22semidirect
130. #2320C22semidirect
136. C4×#127C22semidirect
137. C4×#124C22semidirect
138. #2295C22semidirect
139. #2295C22semidirect
246. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C22×#5482
#428902
#428872
#428152
#428102
#399542
#399502
#376062
#371852
#371182
#356332
#355632
#353382
#353292
#352422
#352322
#351492
#349462
#349362
#340592