Finite Group Databasebeta

← #7646187

Subgroups — #7646187

Order 512.

4948 conjugacy classes of subgroups.

The subgroup lattice has 1049 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42751C214yesmaximal, complemented
2#42725C214yesmaximal, complemented
3#42607C214yesmaximal, complemented
4#42542C214yesmaximal, complemented
5#40222C214yesmaximal, complemented
6#40117C214yesmaximal, complemented
7#39792C214yesmaximal, complemented
8#39221C214yesmaximal, complemented
9#37462C214yesmaximal, complemented
10#36766C214yesmaximal, complemented
11#36730C214yesmaximal, complemented
12#35629C212yesmaximal, complemented
13#35556C212yesmaximal, complemented
14#35254C212yesmaximal, complemented
15#35174C211yesmaximal, characteristic, complemented
16#35173C211yesmaximal, characteristic, complemented
17#35168C211yesmaximal, characteristic
18#35158C211yesmaximal, characteristic, complemented
19#35080C214yesmaximal, complemented
20#34745C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22C2×#2357C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#535C2212yes—
27C2×#533C2212yes—
28C2×C4×#41C2212yes—
29C22×C4×D4C2211yescharacteristic
30#2857C2214yes—
31#2854C2214yes—
32#2854C2214yes—
33#2850C2214yes—
34#2848C2214yes—
35#2847C2214yes—
36#2838C2218yescomplemented
37#2829C2218yescomplemented
38#2801C2218yescomplemented
39#2795C2218yescomplemented
40#2773C2218yescomplemented
41#2759C2218yescomplemented
42#2757C2218yescomplemented
43#2746C2218yescomplemented
44#2745C2218yescomplemented
45#2738C2218yescomplemented
46#2737C2218yescomplemented
47#2730C2218yescomplemented
48#2710C2218yescomplemented
49#2701C2218yescomplemented
50#2700C2218yescomplemented
51#2687C2218yescomplemented
52#2686C2218yescomplemented
53#2674C2218yescomplemented
54#2663C2218yescomplemented
55#2659C2214yes—
56#2653C2218yescomplemented
57#2653C2218yescomplemented
58#2651C2218yescomplemented
59#2649C2218yescomplemented
60#2639C2214yes—
61#2632C2218yescomplemented
62#2626C2214yes—
63#2624C2214yes—
64#2624C2214yes—
65#2617C2214yes—
66#2592C2214yes—
67#2592C2214yes—
68#2584C2214yescomplemented
69#2584C2214yescomplemented
70#2567C2214yescomplemented
71#2548C2214yes—
72#2548C2214yes—
73#2546C2214yescomplemented
74#2525C2218yescomplemented
75#2514C2214yescomplemented
76#2514C2214yescomplemented
77#2513C2214yescomplemented
78#2513C2214yescomplemented
79#2510C2218yes—
80#2510C2218yes—
81#2495C2214yescomplemented
82#2495C2214yescomplemented
83#2495C2214yescomplemented
84#2494C2214yescomplemented
85#2494C2214yescomplemented
86#2494C2214yescomplemented
87#2492C2214yescomplemented
88#2492C2214yescomplemented
89#2491C2214yes—
90#2491C2214yes—
91#2491C2214yescomplemented
92#2491C2214yescomplemented
93#2490C2214yes—
94#2490C2214yes—
95#2490C2214yescomplemented
96#2489C2214yescomplemented
97#2472C2218yes—
98#2472C2218yes—
99#2461C2218yescomplemented
100#2454C2214yes—
101#2454C2214yes—
102#2454C2212yescomplemented
103#2454C2212yescomplemented
104#2453C2212yescomplemented
105#2453C2212yescomplemented
106#2452C2214yes—
107#2452C2214yes—
108#2452C2212yescomplemented
109#2452C2212yescomplemented
110#2451C2212yescomplemented
111#2451C2212yescomplemented
112#2450C2214yes—
113#2450C2214yes—
114#2449C2214yes—
115#2449C2214yes—
116#2448C2214yes—
117#2448C2214yes—
118#2445C2214yes—
119#2445C2214yes—
120#2428C2214yes—
121#2428C2214yes—
122#2427C2214yes—
123#2427C2214yes—
124#2427C2214yescomplemented
125#2426C2214yescomplemented
126#2423C2214yescomplemented
127#2422C2214yescomplemented
128#2418C2218yes—
129#2418C2218yes—
130#2396C2214yescomplemented
131#2396C2214yescomplemented
132#2370C2214yescomplemented
133#2370C2214yescomplemented
134#2369C2214yescomplemented
135#2365C2214yescomplemented
136#2357C2214yes—
137#2357C2214yes—
138#2357C2214yes—
139#2357C2214yes—
140#2337C2218yescomplemented
141#2335C2218yescomplemented
142#2329C2214yes—
143#2325C2214yes—
144#2324C2214yescomplemented
145#2323C2214yescomplemented
146#2316C2211yescharacteristic
147#2316C2212yes—
148#2316C2211yescharacteristic
149#2311C2212yes—
150#2311C2212yes—
151#2309C2212yes—
152C4×C22⋊Q8C2214yes—
153C4×C22⋊Q8C2214yescomplemented
154C4×C22⋊Q8C2214yescomplemented
155C4×C22⋊Q8C2214yescomplemented
156C4×#121C2214yes—
157C4×#121C2214yescomplemented
158#2297C2212yes—
159#2297C2212yes—
160#2296C2212yes—
161#2296C2212yes—
162C2×#390C2211yescharacteristic
163C2×#390C2211yescharacteristic
164C2×#388C2212yes—
165C2×#388C2212yes—
166C2×#382C2211yescharacteristic
167C2×#381C2212yes—
168#2274C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#537—28no—
178#535—48no—
179#533—48no—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2314yes—
184C2×#127C2314yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#125C2312yes—
188C2×#124C2314yes—
189C2×#124C2318yes—
190C2×#124C2314yes—
191C2×#124C2318yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#120C2318yes—
209C4×#41—48no—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2314yes—
215C2×C4×D4—28no—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2314yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243#401C2318yes—
244#401C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2314yes—
248#400C2318yes—
249#400C2314yes—
250#399C2314yes—
251#399C2318yes—
252#399C2318yes—
253#399C2318yes—
254#399C2314yes—
255#398C2318yes—
256#398C2314yes—
257#398C2318yes—
258#398C2314yes—
259#398C2314yes—
260#398C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#396C2314yes—
272#396C2318yes—
273#396C2318yes—
274#396C2314yes—
275#396C2314yes—
276#396C2314yes—
277#395C2318yes—
278#395C2318yes—
279#395C2314yes—
280#395C2314yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#393C2314yes—
297#393C2314yes—
298#392C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2318yes—
302#391C2318yes—
303#391C2312yes—
304#391C2312yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2318yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2314yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#385C2318yes—
395#385C2314yes—
396#385C2318yes—
397#385C2314yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#384C2314yes—
406#383C2318yes—
407#383C2318yes—
408#382C2314yes—
409#382C2314yes—
410#382C2314yes—
411#381C2318yes—
412#381C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2318yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#379C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
460C2×#95C2312yes—
461C2×#95C2312yes—
462C25C2412yes—
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—28no—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×Q8C2414yes—
469C22×Q8C2414yes—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2414yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C23×C4—28no—
480C23×C4—82no—
481C23×C4—82no—
482C23×C4C2414yes—
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2411yescharacteristic
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—216no—
498C4⋊Q8—44no—
499C4⋊Q8—44no—
500C4⋊Q8—84no—
501#127—48no—
502#125—216no—
503#125—44no—
504#125—44no—
505#124—48no—
506#124—416no—
507#124—84no—
508#124—88no—
509#123—416no—
510#123—88no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—48no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516C22⋊Q8—48no—
517C22⋊Q8—84no—
518C22⋊Q8—84no—
519#121—216no—
520#121—216no—
521#121—48no—
522#121—48no—
523#121—84no—
524#121—84no—
525#120—416no—
526C4×Q8—48no—
527C4×Q8—48no—
528C4×Q8—44no—
529C4×Q8—44no—
530C4×Q8—84no—
531C4×D4—216no—
532C4×D4—216no—
533C4×D4—44no—
534C4×D4—44no—
535C4×D4—48no—
536C4×D4—48no—
537C4×D4—84no—
538#117—28no—
539#117—28no—
540#117—28no—
541#117—48no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—42no—
545C2×C4⋊C4—42no—
546C2×C4⋊C4#4118yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C22⋊C4—28no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—44no—
588C2×C22⋊C4—82no—
589C2×C22⋊C4—82no—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C42—24no—
622C2×C42—24no—
623C2×C42—24no—
624C2×C42—48no—
625C2×C42—82no—
626C2×C42—82no—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2418yes—
643C2×C42C2414yes—
644#95C2411yescharacteristic
645#95C2411yescharacteristic
646#95C2411yescharacteristic
647#95C2411yescharacteristic
648#95C2414yes—
649#95C2414yes—
650#95C2412yes—
651#95C2412yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2418yes—
660#95C2418yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2414yes—
673#95C2418yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681C24—24no—
682C24—24no—
683C24—24no—
684C24—42no—
685C24—42no—
686C24—42no—
687C24—42no—
688C24C2514yes—
689C24C2514yes—
690C24C2511yescharacteristic
691#41—432no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—28no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—416no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—816no—
765C22×C4C2×#4118yes—
766C22×C4C2×#4114yes—
767C22×C4H(5,𝔽2)14yes—
768C22×C42−1+414yes—
769C22×C4C2514yes—
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2512yes—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—216no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—42no—
804C4⋊C4—42no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4C2×#41116yes—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—216no—
831C22⋊C4—216no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C42—24no—
859C42—24no—
860C42—28no—
861C42—24no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—28no—
866C42—28no—
867C42—44no—
868C42—44no—
869C42—44no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—48no—
874C42—48no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—48no—
894C23—48no—
895C23—48no—
896C23—84no—
897C23—84no—
898C23—84no—
899C23—84no—
900C23C22×#4112yes—
901C23C2×H(5,𝔽2)12yes—
902C23C2×2−1+412yes—
903C23C2611yescharacteristic
904Q8—48no—
905Q8—88no—
906Q8—88no—
907Q8—88no—
908D4—416no—
909D4—416no—
910D4—48no—
911D4—88no—
912D4—168no—
913D4—168no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—24no—
954C2×C4—21no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—48no—
969C2×C4—44no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—416no—
974C2×C4—88no—
975C2×C4—88no—
976C2×C4—88no—
977C2×C4—82no—
978C2×C4—82no—
979C2×C4—84no—
980C2×C4—84no—
981C2×C4—88no—
982C2×C4#542116yes—
983C2×C4C22×#4118yes—
984C2×C4C22×#4114yes—
985C2×C4C2×H(5,𝔽2)14yes—
986C2×C4C2×2−1+414yes—
987C2×C4#58512yes—
988C2×C4#58512yes—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—816no—
1010C22C2×#54214yes—
1011C22C23×#4111yescharacteristic
1012C22C22×H(5,𝔽2)11yescharacteristic
1013C22C22×2−1+411yescharacteristic
1014C22C2×#58511yescharacteristic
1015C22C2×#58511yescharacteristic
1016C22H(7,𝔽2)11yescharacteristic
1017C22H(7,𝔽2)11yescharacteristic
1018C4—28no—
1019C4—22no—
1020C4—22no—
1021C4—44no—
1022C4—42no—
1023C4—41no—
1024C4—41no—
1025C4—44no—
1026C4—44no—
1027C4—41no—
1028C4—41no—
1029C4—42no—
1030C4—44no—
1031C4—44no—
1032C4—42no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4C2×#54218yes—
1038C2—24no—
1039C2—84no—
1040C2—84no—
1041C2C22×#54211yescharacteristic
1042C2#6279311yescharacteristic
1043C2#6284611yescharacteristic
1044C2#6295711yescharacteristic
1045C2#6295711yescharacteristic
1046C2#6296211yescharacteristic
1047C2#6296211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42751C2semidirect
2. #42725C2semidirect
3. #42607C2semidirect
4. #42542C2semidirect
5. #40222C2semidirect
6. #40117C2semidirect
7. #39792C2semidirect
8. #39221C2semidirect
9. #37462C2semidirect
10. #36766C2semidirect
11. #36730C2semidirect
12. #35629C2semidirect
13. #35556C2semidirect
14. #35254C2semidirect
15. #35174C2semidirect
16. #35173C2semidirect
18. #35158C2semidirect
19. #35080C2semidirect
20. #34745C2semidirect
21. #34271C2semidirect
22. C2×#2357C2semidirect
23. C4×#537C2semidirect
36. #2838C22semidirect
37. #2829C22semidirect
38. #2801C22semidirect
39. #2795C22semidirect
40. #2773C22semidirect
41. #2759C22semidirect
42. #2757C22semidirect
43. #2746C22semidirect
44. #2745C22semidirect
45. #2738C22semidirect
46. #2737C22semidirect
47. #2730C22semidirect
48. #2710C22semidirect
49. #2701C22semidirect
50. #2700C22semidirect
51. #2687C22semidirect
52. #2686C22semidirect
53. #2674C22semidirect
54. #2663C22semidirect
56. #2653C22semidirect
57. #2653C22semidirect
58. #2651C22semidirect
59. #2649C22semidirect
61. #2632C22semidirect
68. #2584C22semidirect
69. #2584C22semidirect
70. #2567C22semidirect
73. #2546C22semidirect
74. #2525C22semidirect
75. #2514C22semidirect
76. #2514C22semidirect
77. #2513C22semidirect
78. #2513C22semidirect
81. #2495C22semidirect
82. #2495C22semidirect
83. #2495C22semidirect
84. #2494C22semidirect
85. #2494C22semidirect
86. #2494C22semidirect
87. #2492C22semidirect
88. #2492C22semidirect
91. #2491C22semidirect
92. #2491C22semidirect
95. #2490C22semidirect
96. #2489C22semidirect
99. #2461C22semidirect
102. #2454C22semidirect
103. #2454C22semidirect
104. #2453C22semidirect
105. #2453C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
110. #2451C22semidirect
111. #2451C22semidirect
124. #2427C22semidirect
125. #2426C22semidirect
126. #2423C22semidirect
127. #2422C22semidirect
130. #2396C22semidirect
131. #2396C22semidirect
132. #2370C22semidirect
133. #2370C22semidirect
134. #2369C22semidirect
135. #2365C22semidirect
140. #2337C22semidirect
141. #2335C22semidirect
144. #2324C22semidirect
145. #2323C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×C22⋊Q8C22semidirect
155. C4×C22⋊Q8C22semidirect
157. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#427512
#427252
#426072
#425422
#402222
#401172
#397922
#392212
#374622
#367662
#367302
#356292
#355562
#352542
#351742
#351732
#351682
#351582
#350802
#347452
#342712
C2×#23572
C4×#5372