Finite Group Databasebeta

← #7637138

Subgroups — #7637138

Order 512.

5402 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52225C218yesmaximal, complemented
2#39149C212yesmaximal, complemented
3#39148C212yesmaximal, complemented
4#39147C212yesmaximal, complemented
5#39146C212yesmaximal, complemented
6#39145C214yesmaximal, complemented
7#39144C214yesmaximal, complemented
8#39143C214yesmaximal, complemented
9#39142C214yesmaximal, complemented
10#39141C214yesmaximal, complemented
11#39140C214yesmaximal, complemented
12#36624C211yesmaximal, characteristic, complemented
13#34948C211yesmaximal, characteristic, complemented
14#34937C211yesmaximal, characteristic, complemented
15#34917C214yesmaximal, complemented
16#34788C214yesmaximal, complemented
17#34743C212yesmaximal, complemented
18#34742C212yesmaximal, complemented
19#34639C212yesmaximal, complemented
20#34141C211yesmaximal, characteristic, complemented
21C4⋊C4×#41C211yesmaximal, characteristic, complemented
22#34070C212yesmaximal, complemented
23C4×#525C211yesmaximal, characteristic, complemented
24C2×#2283C211yesmaximal, characteristic, complemented
25C2×#532C2211yescharacteristic
26C2×#532C2212yes—
27C2×#525C2211yescharacteristic
28C2×#525C2212yes—
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2212yes—
31C2×C4×#41C2212yes—
32C23×C42C2211yescharacteristic
33#2857C2212yes—
34#2856C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2850C2214yes—
38#2847C2212yes—
39#2847C2212yes—
40#2783C2218yescomplemented
41#2782C2218yescomplemented
42#2781C2218yescomplemented
43#2780C2218yes—
44#2779C2218yes—
45#2778C2218yes—
46#2776C2218yescomplemented
47#2770C2218yescomplemented
48#2765C2218yescomplemented
49#2757C2218yescomplemented
50#2749C2218yescomplemented
51#2746C2218yes—
52#2739C2218yes—
53#2708C2218yes—
54#2701C2218yes—
55#2688C2218yes—
56#2645C2214yescomplemented
57#2645C2214yescomplemented
58#2644C2214yescomplemented
59#2644C2214yescomplemented
60#2643C2218yes—
61#2643C2218yes—
62#2578C2218yescomplemented
63#2576C2218yes—
64#2571C2212yescomplemented
65#2570C2214yescomplemented
66#2570C2214yescomplemented
67#2569C2214yes—
68#2566C2214yescomplemented
69#2562C2214yes—
70#2552C2212yescomplemented
71#2548C2211yescharacteristic, complemented
72#2547C2211yescharacteristic, complemented
73#2546C2211yescharacteristic, complemented
74#2545C2212yescomplemented
75#2544C2212yescomplemented
76#2543C2214yes—
77#2541C2211yescharacteristic, complemented
78#2535C2214yes—
79#2525C2218yescomplemented
80#2516C2218yes—
81#2515C2218yescomplemented
82#2513C2214yescomplemented
83#2510C2218yescomplemented
84#2509C2214yescomplemented
85#2504C2214yescomplemented
86#2497C2214yes—
87#2494C2214yes—
88#2494C2214yescomplemented
89#2490C2214yes—
90#2487C2214yes—
91#2457C2218yes—
92#2444C2218yes—
93#2442C2214yes—
94#2442C2214yescomplemented
95#2429C2214yes—
96#2428C2214yes—
97#2427C2214yes—
98#2426C2214yes—
99#2425C2218yes—
100#2424C2218yes—
101#2423C2214yes—
102#2422C2214yes—
103#2422C2214yes—
104#2421C2214yes—
105#2420C2214yes—
106#2420C2214yescomplemented
107#2419C2218yes—
108#2418C2218yes—
109#2416C2214yes—
110#2416C2214yes—
111#2402C2214yescomplemented
112#2401C2218yescomplemented
113#2401C2218yescomplemented
114#2395C2218yes—
115#2392C2218yes—
116#2392C2214yescomplemented
117#2367C2214yescomplemented
118#2366C2212yescomplemented
119#2365C2212yescomplemented
120#2364C2214yes—
121#2361C2214yes—
122#2351C2212yescomplemented
123Q8×C4⋊C4C2212yescomplemented
124#2349C2214yes—
125#2349C2212yescomplemented
126D4×C4⋊C4C2214yes—
127D4×C4⋊C4C2212yescomplemented
128#2328C2214yescomplemented
129#2327C2214yescomplemented
130#2326C2214yescomplemented
131#2326C2214yescomplemented
132#2325C2218yes—
133#2325C2218yes—
134C4×#125C2214yescomplemented
135C4×C22⋊Q8C2212yes—
136C4×C22⋊Q8C2212yes—
137C4×#123C2218yes—
138C4×#123C2212yes—
139C4×#123C2212yes—
140C4×#121C2214yes—
141C4×#121C2218yes—
142C4×#121C2214yes—
143C4×#121C2212yes—
144C4×#121C2212yes—
145C4×#121C2214yescomplemented
146C4×#120C2212yes—
147C4×#120C2212yes—
148#2297C2212yes—
149#2297C2211yescharacteristic
150#2297C2212yes—
151#2297C2212yes—
152#2296C2212yes—
153#2296C2211yescharacteristic
154#2296C2212yes—
155#2296C2214yescomplemented
156#2293C2212yescomplemented
157#2290C2214yes—
158#2290C2214yescomplemented
159#2290C2218yescomplemented
160#2290C2218yescomplemented
161#2285C2211yescharacteristic
162#2285C2212yes—
163#2285C2212yescomplemented
164#2283C2214yes—
165#2283C2212yes—
166#2283C2212yes—
167#2283C2214yes—
168#2283C2212yes—
169#2283C2212yes—
170C2×#383C2212yes—
171C2×#382C2212yes—
172#2280C2211yescharacteristic
173C2×#381C2212yes—
174C2×#380C2212yes—
175C42×D4C2214yes—
176C42×D4C2212yescomplemented
177C4×#117C2211yescharacteristic
178C2×C4×C4⋊C4C2211yescharacteristic
179C2×C4×C4⋊C4C2211yescharacteristic
180C2×C4×C4⋊C4C2212yescomplemented
181C2×C4×C22⋊C4C2212yes—
182C2×#376C2212yes—
183C22×#41C2312yes—
184C22×#41C2311yescharacteristic
185C24×C4C2311yescharacteristic
186C24×C4C2311yescharacteristic
187C24×C4C2311yescharacteristic
188#532—216no—
189#532—28no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×#127C2312yes—
193C2×#127C2311yescharacteristic
194C2×#125C2314yes—
195C2×#124C2312yes—
196C2×#124C2312yes—
197C2×#124C2312yes—
198#525—28no—
199#525—48no—
200C2×#123C2312yes—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×#121C2318yes—
206C2×#121C2312yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2318yes—
214C2×#120C2312yes—
215C2×#120C2314yes—
216C4×#41—28no—
217C4×#41—48no—
218C4×#41—48no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2314yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2314yes—
245C2×#117C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2312yes—
249C22×C22⋊C4C2314yes—
250C22×C42—28no—
251C22×C42C2312yes—
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2312yes—
257C22×C42C2312yes—
258C22×C42C2312yes—
259C22×C42C2312yes—
260C22×C42C2312yes—
261C22×C42C2314yes—
262C22×C42C2314yes—
263C22×C42C2311yescharacteristic
264#401C2318yes—
265#401C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#399C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2314yes—
302#394C2318yes—
303#394C2318yes—
304#392C2318yes—
305#392C2314yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2312yes—
319#390C2312yes—
320#390C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2314yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C2312yes—
334#389C2312yes—
335#389C2318yes—
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#388C2314yes—
350#388C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2314yes—
361#387C2314yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2312yes—
367#386C2312yes—
368#386C2314yes—
369#386C2314yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2314yes—
380#386C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2312yes—
392#385C2312yes—
393#385C2314yes—
394#385C2314yes—
395#384C2314yes—
396#384C2314yes—
397#384C2312yes—
398#383C2314yes—
399#383C2314yes—
400#383C2314yes—
401#383C2314yes—
402#382C2314yes—
403#382C2312yes—
404#382C2312yes—
405#382C2312yes—
406#382C2314yes—
407#382C2314yes—
408#382C2312yes—
409#382C2312yes—
410#382C2314yes—
411#382C2314yes—
412#381C2314yes—
413#381C2312yes—
414#381C2318yes—
415#381C2314yes—
416#381C2314yes—
417#381C2314yes—
418#380C2312yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2312yes—
423#380C2318yes—
424#380C2314yes—
425#380C2312yes—
426#380C2314yes—
427#380C2312yes—
428#380C2312yes—
429#380C2312yes—
430#380C2318yes—
431#380C2314yes—
432#380C2312yes—
433#380C2312yes—
434#380C2314yes—
435#379C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2318yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477#376C2314yes—
478#376C2314yes—
479#376C2314yes—
480#376C2314yes—
481#376C2312yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C2×#95C2312yes—
486C2×#95C2314yes—
487C2×#95C2314yes—
488C43C2312yes—
489C25C2411yescharacteristic
490C2×#41—24no—
491C2×#41—28no—
492C2×#41—28no—
493C2×#41—24no—
494C2×#41—28no—
495C2×#41#4118yes—
496C22×Q8C2412yes—
497C22×Q8C2411yescharacteristic
498C22×D4C2412yes—
499C22×D4C2414yes—
500C22×D4C2412yes—
501C22×D4C2414yes—
502C22×D4C2412yes—
503C22×D4C2411yescharacteristic
504C22×D4C2418yes—
505C22×D4C2418yes—
506C22×D4C2412yes—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—44no—
513C23×C4—44no—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2411yescharacteristic
518C23×C4C2414yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2412yes—
530C23×C4C2418yes—
531C23×C4C2418yes—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536#127—28no—
537#127—24no—
538#125—48no—
539#124—28no—
540#124—28no—
541#124—28no—
542#123—28no—
543#123—416no—
544#123—48no—
545C22⋊Q8—28no—
546C22⋊Q8—48no—
547#121—28no—
548#121—232no—
549#121—28no—
550#121—28no—
551#121—416no—
552#121—48no—
553#121—48no—
554#121—48no—
555#121—48no—
556#120—28no—
557#120—48no—
558C4×Q8—24no—
559C4×Q8—24no—
560C4×Q8—48no—
561C4×Q8—48no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—232no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—48no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—416no—
575C4×D4—48no—
576C4×D4—416no—
577C4×D4—416no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—28no—
582#117—28no—
583#117—48no—
584#117—48no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—48no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C22⋊C4—48no—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
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×C42—28no—
650C2×C42—24no—
651C2×C42—24no—
652C2×C42—24no—
653C2×C42—28no—
654C2×C42—28no—
655C2×C42—28no—
656C2×C42—28no—
657C2×C42—28no—
658C2×C42—28no—
659C2×C42—48no—
660C2×C42—48no—
661C2×C42#4118yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#95C2412yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2412yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2412yes—
706#95C2412yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728C24—22no—
729C24—24no—
730C24—22no—
731C24—22no—
732C24—42no—
733C24C2514yes—
734C24C2512yes—
735C24C2512yes—
736C24C2511yescharacteristic
737#41—232no—
738#41—432no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8C2×#4114yes—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—216no—
753C2×D4—216no—
754C2×D4—22no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—22no—
760C2×D4—24no—
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4C2×#4118yes—
769C2×D4C2×#4114yes—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—24no—
793C22×C4—28no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—416no—
819C22×C4—416no—
820C22×C4—416no—
821C22×C4C2×#4114yes—
822C22×C4C2×#4118yes—
823C22×C4C2×#4114yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4114yes—
826C22×C4H(5,𝔽2)14yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2518yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—216no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—28no—
880C22⋊C4—216no—
881C22⋊C4—24no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—28no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—24no—
924C42—28no—
925C42—28no—
926C42—48no—
927C42—48no—
928C42—44no—
929C42C2×#4114yes—
930C42C2×#4114yes—
931C42C2×#4114yes—
932C42C2×#4114yes—
933C23—22no—
934C23—22no—
935C23—28no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—28no—
950C23—28no—
951C23—48no—
952C23—48no—
953C23—44no—
954C23—44no—
955C23C22×#4114yes—
956C23C22×#4112yes—
957C23C22×#4112yes—
958C23C2×H(5,𝔽2)12yes—
959C23#58514yes—
960C23C2611yescharacteristic
961Q8—28no—
962Q8—48no—
963D4—216no—
964D4—28no—
965D4—416no—
966D4—416no—
967D4—48no—
968D4—48no—
969D4—84no—
970D4—816no—
971D4—816no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—28no—
978C2×C4—216no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
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—22no—
1011C2×C4—22no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—44no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—48no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—416no—
1028C2×C4—84no—
1029C2×C4—88no—
1030C2×C4—88no—
1031C2×C4—816no—
1032C2×C4—816no—
1033C2×C4#553116yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4114yes—
1038C2×C4C22×#4112yes—
1039C2×C4C22×#4112yes—
1040C2×C4C22×#4112yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4112yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4#58514yes—
1046C22—24no—
1047C22—22no—
1048C22—24no—
1049C22—22no—
1050C22—24no—
1051C22—24no—
1052C22—24no—
1053C22—28no—
1054C22—24no—
1055C22—416no—
1056C22—44no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—48no—
1064C22—44no—
1065C22—48no—
1066C22—44no—
1067C22—44no—
1068C22C2×#55314yes—
1069C22C23×#4111yescharacteristic
1070C22C23×#4111yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C2×#58512yes—
1073C22C2×#58512yes—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—24no—
1078C4—44no—
1079C4—44no—
1080C4—44no—
1081C4—48no—
1082C4—42no—
1083C4—42no—
1084C4—44no—
1085C4—44no—
1086C4—44no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4#345514yes—
1092C4C2×#55314yes—
1093C4C2×#55314yes—
1094C2—24no—
1095C2—44no—
1096C2—44no—
1097C2—84no—
1098C2C2×#345511yescharacteristic
1099C2C22×#55311yescharacteristic
1100C2#6274812yes—
1101C2#6281411yescharacteristic
1102C2#6281612yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52225C2semidirect
2. #39149C2semidirect
3. #39148C2semidirect
4. #39147C2semidirect
5. #39146C2semidirect
6. #39145C2semidirect
7. #39144C2semidirect
8. #39143C2semidirect
9. #39142C2semidirect
10. #39141C2semidirect
11. #39140C2semidirect
12. #36624C2semidirect
13. #34948C2semidirect
14. #34937C2semidirect
15. #34917C2semidirect
16. #34788C2semidirect
17. #34743C2semidirect
18. #34742C2semidirect
19. #34639C2semidirect
20. #34141C2semidirect
21. C4⋊C4×#41C2semidirect
22. #34070C2semidirect
23. C4×#525C2semidirect
24. C2×#2283C2semidirect
40. #2783C22semidirect
41. #2782C22semidirect
42. #2781C22semidirect
46. #2776C22semidirect
47. #2770C22semidirect
48. #2765C22semidirect
49. #2757C22semidirect
50. #2749C22semidirect
56. #2645C22semidirect
57. #2645C22semidirect
58. #2644C22semidirect
59. #2644C22semidirect
62. #2578C22semidirect
64. #2571C22semidirect
65. #2570C22semidirect
66. #2570C22semidirect
68. #2566C22semidirect
70. #2552C22semidirect
71. #2548C22semidirect
72. #2547C22semidirect
73. #2546C22semidirect
74. #2545C22semidirect
75. #2544C22semidirect
77. #2541C22semidirect
79. #2525C22semidirect
81. #2515C22semidirect
82. #2513C22semidirect
83. #2510C22semidirect
84. #2509C22semidirect
85. #2504C22semidirect
88. #2494C22semidirect
94. #2442C22semidirect
106. #2420C22semidirect
111. #2402C22semidirect
112. #2401C22semidirect
113. #2401C22semidirect
116. #2392C22semidirect
117. #2367C22semidirect
118. #2366C22semidirect
119. #2365C22semidirect
122. #2351C22semidirect
123. Q8×C4⋊C4C22semidirect
125. #2349C22semidirect
127. D4×C4⋊C4C22semidirect
128. #2328C22semidirect
129. #2327C22semidirect
130. #2326C22semidirect
131. #2326C22semidirect
134. C4×#125C22semidirect
145. C4×#121C22semidirect
155. #2296C22semidirect
156. #2293C22semidirect
158. #2290C22semidirect
159. #2290C22semidirect
160. #2290C22semidirect
163. #2285C22semidirect
176. C42×D4C22semidirect
180. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#522252
#391492
#391482
#391472
#391462
#391452
#391442
#391432
#391422
#391412
#391402
#366242
#349482
#349372
#349172
#347882
#347432
#347422
#346392
#341412
C4⋊C4×#412
#340702
C4×#5252
C2×#22832