Finite Group Databasebeta

← #7628154

Subgroups — #7628154

Order 512.

6396 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34978C211yesmaximal, characteristic, complemented
2#34977C212yesmaximal, complemented
3#34976C211yesmaximal, characteristic, complemented
4#34974C214yesmaximal, complemented
5#34970C214yesmaximal, complemented
6#34962C214yesmaximal, complemented
7#34954C211yesmaximal, characteristic, complemented
8#34950C211yesmaximal, characteristic, complemented
9#34943C211yesmaximal, characteristic, complemented
10#34941C212yesmaximal, complemented
11#34934C212yesmaximal, complemented
12#34925C211yesmaximal, characteristic, complemented
13#34874C214yesmaximal, complemented
14#34871C214yesmaximal, complemented
15#34800C214yesmaximal, complemented
16#34797C214yesmaximal, complemented
17#34727C214yesmaximal, complemented
18#34715C214yesmaximal, complemented
19#34547C214yesmaximal, complemented
20C4×#532C211yesmaximal, characteristic, complemented
21C4×#532C214yesmaximal, complemented
22C4×#529C214yesmaximal, complemented
23C42×#41C212yesmaximal, complemented
24C2×#532C2214yes—
25C2×#532C2211yescharacteristic
26C2×#529C2214yes—
27C2×C4×#41C2212yes—
28C2×C4×#41C2212yes—
29C2×C4×#41C2212yes—
30C2×C4×#41C2212yes—
31C2×C4×#41C2214yes—
32#2612C2214yes—
33#2610C2218yes—
34#2609C2214yes—
35#2593C2214yes—
36#2586C2214yes—
37#2582C2211yescharacteristic
38#2574C2218yes—
39#2572C2214yes—
40#2571C2211yescharacteristic
41#2567C2212yes—
42#2563C2212yes—
43#2555C2214yes—
44#2554C2218yes—
45#2552C2212yes—
46#2551C2211yescharacteristic
47#2548C2212yes—
48#2541C2212yes—
49#2538C2212yes—
50#2537C2211yescharacteristic
51#2532C2218yes—
52#2531C2218yes—
53#2529C2218yes—
54#2526C2218yes—
55#2518C2218yes—
56#2513C2214yes—
57#2512C2214yes—
58#2508C2214yes—
59#2507C2214yes—
60#2500C2214yes—
61#2497C2214yes—
62#2495C2214yes—
63#2491C2214yes—
64#2490C2214yes—
65#2485C2214yes—
66#2479C2218yes—
67#2476C2218yes—
68#2474C2218yes—
69#2471C2218yes—
70#2467C2218yes—
71#2459C2218yes—
72#2456C2218yes—
73#2454C2214yes—
74#2451C2214yes—
75#2448C2214yes—
76#2445C2214yes—
77#2441C2214yes—
78#2439C2214yes—
79#2431C2214yes—
80#2428C2214yes—
81#2426C2214yes—
82#2423C2214yes—
83#2420C2214yes—
84#2414C2214yes—
85#2414C2214yes—
86#2407C2214yes—
87#2399C2214yes—
88#2398C2214yes—
89#2398C2214yes—
90#2397C2214yes—
91#2396C2218yes—
92#2396C2214yes—
93#2396C2214yes—
94#2395C2214yes—
95#2395C2218yes—
96#2395C2214yes—
97#2392C2218yes—
98#2392C2214yes—
99#2392C2214yes—
100#2392C2218yes—
101#2392C2218yes—
102#2388C2214yes—
103#2388C2218yes—
104#2388C2214yes—
105C4×C4⋊Q8C2211yescharacteristic
106C4×C4⋊Q8C2211yescharacteristic
107C4×C4⋊Q8C2214yes—
108C4×C4⋊Q8C2214yes—
109C4×#127C2211yescharacteristic
110C4×#127C2211yescharacteristic
111C4×#127C2214yes—
112C4×#127C2214yes—
113C4×#125C2214yes—
114C4×#125C2214yes—
115C4×#126C2218yes—
116C4×#126C2218yes—
117C4×#124C2212yes—
118C4×#124C2212yes—
119C4×#124C2218yes—
120C4×#124C2214yes—
121C4×#124C2218yes—
122C4×#124C2214yes—
123C4×C22⋊Q8C2214yes—
124C4×C22⋊Q8C2214yes—
125C4×#123C2218yes—
126C4×#123C2218yes—
127C4×#121C2218yes—
128C4×#121C2214yes—
129C4×#121C2214yes—
130C4×#121C2214yes—
131C4×#121C2218yes—
132C4×#121C2214yes—
133C4×#121C2214yes—
134C4×#121C2214yes—
135C4×#121C2214yes—
136C4×#121C2214yes—
137#2298C2218yes—
138#2297C2218yes—
139#2297C2212yes—
140#2295C2214yes—
141#2293C2218yes—
142#2293C2214yes—
143#2293C2214yes—
144#2293C2214yes—
145#2293C2214yes—
146#2290C2218yes—
147#2285C2214yes—
148#2285C2211yescharacteristic
149#2283C2214yes—
150C42×Q8C2212yes—
151C42×Q8C2212yes—
152C42×Q8C2212yes—
153C42×Q8C2212yes—
154C42×D4C2212yes—
155C42×D4C2212yes—
156C42×D4C2214yes—
157C42×D4C2212yes—
158C42×D4C2214yes—
159C42×D4C2214yes—
160C42×D4C2214yes—
161C42×D4C2212yes—
162C42×D4C2218yes—
163C42×D4C2214yes—
164C4×#117C2214yes—
165C4×#117C2214yes—
166C4×#117C2214yes—
167C4×#117C2212yes—
168C4×#117C2212yes—
169C4×#117C2212yes—
170C4×#117C2214yes—
171C2×C43C2211yescharacteristic
172C2×C43C2214yes—
173C22×#41C2312yes—
174C22×#41C2314yes—
175C22×#41C2312yes—
176#532—232no—
177#532—28no—
178C2×C4⋊Q8C2311yescharacteristic
179C2×C4⋊Q8C2314yes—
180C2×#127C2314yes—
181C2×#127C2311yescharacteristic
182#529—232no—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#124C2312yes—
186C2×#124C2314yes—
187C2×#124C2318yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2318yes—
195C4×#41—216no—
196C4×#41—216no—
197C4×#41—216no—
198C4×#41—48no—
199C4×#41—416no—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2318yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×#117C2314yes—
237C2×#117C2318yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2314yes—
241C2×#117C2314yes—
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2318yes—
246C2×#117C2314yes—
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2314yes—
250C22×C42C2314yes—
251C22×C42C2314yes—
252C22×C42C2314yes—
253C22×C42C2314yes—
254C22×C42C2311yescharacteristic
255C22×C42C2314yes—
256C22×C42C2314yes—
257C22×C42C2311yescharacteristic
258C22×C42C2314yes—
259C22×C42C2311yescharacteristic
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#399C2318yes—
264#399C2314yes—
265#399C2314yes—
266#398C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2314yes—
270#398C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#395C2318yes—
281#395C2314yes—
282#395C2314yes—
283#394C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#393C2318yes—
293#393C2314yes—
294#393C2314yes—
295#392C2318yes—
296#392C2318yes—
297#392C2314yes—
298#392C2318yes—
299#392C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2318yes—
303#391C2318yes—
304#391C2314yes—
305#391C2314yes—
306#390C2314yes—
307#390C2312yes—
308#390C2318yes—
309#390C2318yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2318yes—
314#390C2314yes—
315#390C2318yes—
316#390C2314yes—
317#390C2312yes—
318#390C2314yes—
319#390C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#385C2318yes—
366#385C2318yes—
367#384C2314yes—
368#384C2311yescharacteristic
369#384C2314yes—
370#384C2311yescharacteristic
371#383C2318yes—
372#382C2314yes—
373#382C2314yes—
374#382C2318yes—
375#382C2312yes—
376#381C2318yes—
377#380C2314yes—
378#380C2314yes—
379#380C2318yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2312yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2318yes—
446#376C2314yes—
447#376C2314yes—
448#376C2314yes—
449#376C2314yes—
450#376C2314yes—
451C43C2314yes—
452C43C2314yes—
453C43C2314yes—
454C43C2314yes—
455C43C2311yescharacteristic
456C43C2311yescharacteristic
457C43C2314yes—
458C43C2311yescharacteristic
459C43C2311yescharacteristic
460C43C2312yes—
461C43C2314yes—
462C43C2312yes—
463C43C2314yes—
464C2×#41—28no—
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—232no—
468C2×#41—28no—
469C2×#41—48no—
470C2×#41—44no—
471C2×#41—44no—
472C22×Q8C2414yes—
473C22×Q8C2412yes—
474C22×Q8C2412yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2418yes—
478C22×D4C2414yes—
479C22×D4C2418yes—
480C22×D4C2412yes—
481C22×D4C2414yes—
482C22×D4C2412yes—
483C23×C4C2414yes—
484C23×C4C2414yes—
485C23×C4C2414yes—
486C23×C4C2414yes—
487C23×C4C2414yes—
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2414yes—
497C23×C4C2411yescharacteristic
498C4⋊Q8—216no—
499C4⋊Q8—24no—
500#127—216no—
501#127—24no—
502#126—232no—
503#125—216no—
504#124—216no—
505#124—232no—
506#124—28no—
507#123—232no—
508C22⋊Q8—216no—
509#121—216no—
510#121—216no—
511#121—216no—
512#121—216no—
513#121—232no—
514C4×Q8—28no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—28no—
518C4×Q8—28no—
519C4×Q8—44no—
520C4×Q8—48no—
521C4×Q8—48no—
522C4×Q8—44no—
523C4×Q8#41116yescomplemented
524C4×D4—28no—
525C4×D4—216no—
526C4×D4—216no—
527C4×D4—216no—
528C4×D4—232no—
529C4×D4—28no—
530C4×D4—216no—
531C4×D4—216no—
532C4×D4—28no—
533C4×D4—28no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—216no—
537C4×D4—232no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—416no—
541C4×D4—48no—
542C4×D4—48no—
543C4×D4—44no—
544C4×D4—416no—
545C4×D4—44no—
546C4×D4—416no—
547C4×D4—48no—
548C4×D4—48no—
549C4×D4#41116yescomplemented
550#117—28no—
551#117—28no—
552#117—216no—
553#117—28no—
554#117—216no—
555#117—216no—
556#117—232no—
557#117—48no—
558#117—416no—
559#117—48no—
560#117—44no—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C42—216no—
616C2×C42—28no—
617C2×C42—28no—
618C2×C42—216no—
619C2×C42—216no—
620C2×C42—216no—
621C2×C42—216no—
622C2×C42—24no—
623C2×C42—216no—
624C2×C42—216no—
625C2×C42—42no—
626C2×C42—48no—
627C2×C42#4118yescomplemented
628C2×C42C2414yes—
629C2×C42C2411yescharacteristic
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2411yescharacteristic
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697C24C2514yes—
698C24C2511yescharacteristic
699C24C2514yes—
700#41—264no—
701#41—464no—
702#41—432no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—216no—
706C2×Q8—24no—
707C2×Q8—44no—
708C2×Q8—42no—
709C2×Q8—42no—
710C2×Q8C2×#4118yes—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—216no—
715C2×D4—28no—
716C2×D4—216no—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—216no—
725C2×D4—24no—
726C2×D4—48no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—48no—
731C2×D4—42no—
732C2×D4—44no—
733C2×D4C2×#4118yes—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—28no—
740C22×C4—22no—
741C22×C4—28no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—28no—
759C22×C4—216no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—42no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C2×#41116yes—
773C22×C4C2×#4118yes—
774C22×C4C2×#4114yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—216no—
805C4⋊C4—216no—
806C4⋊C4—216no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—216no—
811C4⋊C4—48no—
812C4⋊C4—42no—
813C4⋊C4—48no—
814C4⋊C4—42no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4C2×#4118yes—
821C4⋊C4C2×#41116yes—
822C4⋊C4C2×#4118yes—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—216no—
833C22⋊C4—216no—
834C22⋊C4—216no—
835C22⋊C4—216no—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—216no—
839C22⋊C4—216no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—48no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4C2×#41116yes—
849C42—24no—
850C42—24no—
851C42—24no—
852C42—24no—
853C42—28no—
854C42—28no—
855C42—28no—
856C42—28no—
857C42—28no—
858C42—28no—
859C42—28no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—28no—
864C42—28no—
865C42—28no—
866C42—28no—
867C42—28no—
868C42—28no—
869C42—22no—
870C42—28no—
871C42—28no—
872C42—28no—
873C42—28no—
874C42—22no—
875C42—22no—
876C42—28no—
877C42—28no—
878C42—24no—
879C42—28no—
880C42—41no—
881C42—41no—
882C42—44no—
883C42—44no—
884C42C2×#4118yes—
885C42C2×#4118yes—
886C42C2×#4118yes—
887C42C2×#41116yes—
888C42C2×#4114yes—
889C42C2×#4114yes—
890C42H(5,𝔽2)14yes—
891C23—24no—
892C23—22no—
893C23—24no—
894C23—22no—
895C23—24no—
896C23—24no—
897C23—21no—
898C23—24no—
899C23—24no—
900C23—21no—
901C23—28no—
902C23—24no—
903C23—28no—
904C23—24no—
905C23—24no—
906C23C22×#4112yes—
907C23C22×#4118yes—
908C23C2611yescharacteristic
909Q8—216no—
910Q8—416no—
911Q8—48no—
912D4—232no—
913D4—216no—
914D4—432no—
915D4—432no—
916D4—48no—
917D4—416no—
918D4—416no—
919D4—416no—
920C2×C4—232no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—21no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—21no—
935C2×C4—216no—
936C2×C4—28no—
937C2×C4—232no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—48no—
962C2×C4—416no—
963C2×C4—416no—
964C2×C4—416no—
965C2×C4—416no—
966C2×C4—416no—
967C2×C4—44no—
968C2×C4—416no—
969C2×C4—44no—
970C2×C4—416no—
971C2×C4—416no—
972C2×C4C22×#4114yes—
973C2×C4C22×#4114yes—
974C2×C4C22×#4114yes—
975C2×C4C22×#4118yes—
976C2×C4C22×#4118yes—
977C2×C4C22×#4118yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4114yes—
980C2×C4C22×#4114yes—
981C2×C4C22×#4114yes—
982C2×C4C22×#4112yes—
983C2×C4C22×#4114yes—
984C2×C4C22×#4114yes—
985C2×C4C2×H(5,𝔽2)12yes—
986C2×C4C2×H(5,𝔽2)12yes—
987C2×C4C2×H(5,𝔽2)12yes—
988C2×C4#58512yes—
989C22—28no—
990C22—24no—
991C22—22no—
992C22—28no—
993C22—28no—
994C22—44no—
995C22—44no—
996C22—41no—
997C22—41no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—48no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—48no—
1006C22C23×#4111yescharacteristic
1007C22C23×#4112yes—
1008C22C23×#4112yes—
1009C22C22×H(5,𝔽2)11yescharacteristic
1010C22C2×#58511yescharacteristic
1011C4—24no—
1012C4—28no—
1013C4—22no—
1014C4—28no—
1015C4—24no—
1016C4—24no—
1017C4—28no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—41no—
1022C4—44no—
1023C4—41no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4#344418yes—
1028C4#346014yes—
1029C4#348114yes—
1030C4#348314yes—
1031C2—42no—
1032C2—48no—
1033C2—84no—
1034C2C2×#344412yes—
1035C2C2×#346011yescharacteristic
1036C2C2×#348111yescharacteristic
1037C2C2×#348311yescharacteristic
1038C2#41212yes—
subgroupG/H
centerC2×C42C24
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34978C2semidirect
2. #34977C2semidirect
3. #34976C2semidirect
4. #34974C2semidirect
5. #34970C2semidirect
6. #34962C2semidirect
7. #34954C2semidirect
8. #34950C2semidirect
9. #34943C2semidirect
10. #34941C2semidirect
11. #34934C2semidirect
12. #34925C2semidirect
13. #34874C2semidirect
14. #34871C2semidirect
15. #34800C2semidirect
16. #34797C2semidirect
17. #34727C2semidirect
18. #34715C2semidirect
19. #34547C2semidirect
20. C4×#532C2semidirect
21. C4×#532C2semidirect
22. C4×#529C2semidirect
23. C42×#41C2semidirect
523. C4×Q8#41semidirect
549. C4×D4#41semidirect
627. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#349782
#349772
#349762
#349742
#349702
#349622
#349542
#349502
#349432
#349412
#349342
#349252
#348742
#348712
#348002
#347972
#347272
#347152
#345472
C4×#5322
C4×#5292
C42×#412