Finite Group Databasebeta

← #7646831

Subgroups — #7646831

Order 512.

5068 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42637C214yesmaximal, complemented
2#42625C214yesmaximal, complemented
3#42583C214yesmaximal, complemented
4#42568C214yesmaximal, complemented
5#40166C214yesmaximal, complemented
6#40058C214yesmaximal, complemented
7#39398C214yesmaximal, complemented
8#39026C214yesmaximal, complemented
9#37464C214yesmaximal, complemented
10#36764C214yesmaximal, complemented
11#36730C214yesmaximal, complemented
12#35519C212yesmaximal, complemented
13#35516C212yesmaximal, complemented
14#35267C212yesmaximal, complemented
15#35260C214yesmaximal, complemented
16#35224C211yesmaximal, characteristic, complemented
17#35223C211yesmaximal, characteristic
18#35173C211yesmaximal, characteristic, complemented
19#35158C211yesmaximal, characteristic, complemented
20#34813C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2344C211yesmaximal, characteristic, complemented
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#542C2214yes—
26C2×#537C2211yescharacteristic
27C2×#533C2212yes—
28C2×#525C2212yes—
29C2×#520C2212yes—
30C22×#117C2212yes—
31C23×C4⋊C4C2211yescharacteristic
32#2863C2214yescomplemented
33#2860C2214yescomplemented
34#2857C2214yes—
35#2850C2214yes—
36#2848C2214yes—
37#2847C2214yes—
38#2839C2218yescomplemented
39#2830C2218yescomplemented
40#2796C2218yescomplemented
41#2793C2218yescomplemented
42#2777C2218yescomplemented
43#2765C2218yescomplemented
44#2762C2218yescomplemented
45#2755C2218yescomplemented
46#2746C2218yes—
47#2745C2218yes—
48#2738C2218yes—
49#2737C2218yes—
50#2729C2218yescomplemented
51#2701C2218yes—
52#2700C2218yes—
53#2700C2218yescomplemented
54#2687C2218yes—
55#2686C2218yes—
56#2665C2218yescomplemented
57#2659C2214yes—
58#2652C2218yescomplemented
59#2650C2218yescomplemented
60#2645C2214yescomplemented
61#2644C2214yescomplemented
62#2639C2214yes—
63#2637C2218yescomplemented
64#2628C2214yes—
65#2627C2214yes—
66#2625C2214yes—
67#2624C2214yes—
68#2620C2214yes—
69#2618C2214yes—
70#2584C2214yescomplemented
71#2584C2214yescomplemented
72#2582C2214yescomplemented
73#2581C2214yescomplemented
74#2580C2214yescomplemented
75#2567C2214yescomplemented
76#2546C2214yescomplemented
77#2538C2214yescomplemented
78#2520C2218yescomplemented
79#2510C2218yes—
80#2497C2214yescomplemented
81#2496C2214yescomplemented
82#2495C2214yescomplemented
83#2494C2214yescomplemented
84#2492C2212yes—
85#2492C2212yes—
86#2492C2214yescomplemented
87#2491C2212yes—
88#2491C2212yes—
89#2491C2214yescomplemented
90#2490C2212yes—
91#2490C2212yes—
92#2490C2214yescomplemented
93#2489C2212yes—
94#2489C2212yes—
95#2489C2214yescomplemented
96#2488C2214yes—
97#2488C2214yes—
98#2487C2214yes—
99#2486C2214yes—
100#2485C2214yes—
101#2485C2214yes—
102#2481C2218yes—
103#2479C2218yes—
104#2477C2218yes—
105#2474C2218yes—
106#2472C2214yes—
107#2472C2214yes—
108#2470C2218yes—
109#2468C2218yescomplemented
110#2450C2218yes—
111#2449C2218yes—
112#2442C2214yes—
113#2442C2214yes—
114#2442C2214yescomplemented
115#2441C2214yescomplemented
116#2440C2214yes—
117#2440C2214yes—
118#2440C2214yescomplemented
119#2439C2214yescomplemented
120#2423C2214yes—
121#2422C2214yes—
122#2421C2214yes—
123#2420C2214yes—
124#2419C2218yes—
125#2418C2218yes—
126#2417C2214yes—
127#2417C2214yes—
128#2416C2214yes—
129#2416C2214yes—
130#2398C2214yes—
131#2398C2214yes—
132#2363C2214yescomplemented
133#2362C2214yescomplemented
134#2361C2214yescomplemented
135#2360C2214yescomplemented
136#2344C2214yes—
137#2344C2214yes—
138#2344C2214yes—
139#2344C2214yes—
140#2331C2214yescomplemented
141#2330C2214yescomplemented
142#2329C2214yes—
143#2325C2214yes—
144#2324C2214yes—
145#2323C2214yes—
146#2317C2212yes—
147#2317C2212yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2212yes—
151#2314C2214yes—
152#2311C2212yes—
153#2311C2212yes—
154C4×C4⋊Q8C2214yescomplemented
155C4×#125C2214yescomplemented
156C4×#124C2214yes—
157C4×#124C2214yes—
158C4×C22⋊Q8C2214yes—
159C4×#121C2214yes—
160#2297C2212yes—
161#2297C2212yes—
162C2×#389C2211yescharacteristic
163C2×#389C2211yescharacteristic
164C2×#387C2212yes—
165C2×#387C2212yes—
166#2280C2212yes—
167C2×#381C2212yes—
168C2×#380C2211yescharacteristic
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#542—416no—
178#537—28no—
179#533—48no—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2312yes—
184C2×#126C2318yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#125C2312yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2314yes—
191#525—48no—
192C2×#123C2314yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2318yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#120C2314yes—
210#520—48no—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×#117—48no—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C22×C4⋊C4—28no—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246C22×C42C2312yes—
247#401C2318yes—
248#400C2318yes—
249#400C2314yes—
250#400C2314yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2314yes—
259#399C2318yes—
260#399C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#397C2314yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2314yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2314yes—
279#397C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C2314yes—
296#394C2314yes—
297#393C2314yes—
298#393C2318yes—
299#393C2314yes—
300#393C2318yes—
301#393C2314yes—
302#393C2314yes—
303#391C2318yes—
304#391C2314yes—
305#391C2314yes—
306#391C2318yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2318yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#390C2314yes—
325#390C2312yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#388C2314yes—
350#388C2318yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2314yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2314yes—
389#386C2314yes—
390#386C2314yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#384C2314yes—
400#384C2314yes—
401#384C2314yes—
402#383C2318yes—
403#382C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2314yes—
407#382C2314yes—
408#381C2318yes—
409#381C2318yes—
410#381C2314yes—
411#381C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2318yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2312yes—
430#379C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2312yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455#376C2314yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2312yes—
459C2×#95C2312yes—
460C2×#95C2311yescharacteristic
461C2×#95C2311yescharacteristic
462C2×#95C2312yes—
463C43C2314yes—
464C25C2411yescharacteristic
465C2×#41—28no—
466C2×#41—28no—
467C2×#41—28no—
468C22×Q8C2412yes—
469C22×Q8C2414yes—
470C22×Q8C2414yes—
471C22×Q8C2414yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C23×C4—28no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—44no—
482C23×C4—44no—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2411yescharacteristic
486C23×C4C2414yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2412yes—
496C23×C4C2418yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C4⋊Q8—216no—
500C4⋊Q8—44no—
501C4⋊Q8—44no—
502C4⋊Q8—48no—
503#126—416no—
504#125—216no—
505#125—44no—
506#125—44no—
507#124—216no—
508#124—48no—
509#124—48no—
510#123—416no—
511#123—48no—
512C22⋊Q8—216no—
513C22⋊Q8—216no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516C22⋊Q8—48no—
517C22⋊Q8—48no—
518C22⋊Q8—416no—
519C22⋊Q8—44no—
520C22⋊Q8—44no—
521#121—216no—
522#121—216no—
523#121—44no—
524#121—44no—
525#121—48no—
526#121—48no—
527#120—48no—
528C4×Q8—48no—
529C4×Q8—48no—
530C4×Q8—48no—
531C4×Q8—48no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—416no—
537#117—28no—
538#117—28no—
539#117—28no—
540#117—216no—
541#117—48no—
542#117—48no—
543#117—48no—
544#117—48no—
545C2×C4⋊C4—28no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—216no—
550C2×C4⋊C4—216no—
551C2×C4⋊C4—44no—
552C2×C4⋊C4—44no—
553C2×C4⋊C4—48no—
554C2×C4⋊C4#4118yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—44no—
595C2×C22⋊C4C2411yescharacteristic
596C2×C22⋊C4C2411yescharacteristic
597C2×C22⋊C4C2411yescharacteristic
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2411yescharacteristic
628C2×C42—24no—
629C2×C42—24no—
630C2×C42—44no—
631C2×C42—44no—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2418yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—41no—
691C24—41no—
692C24C2514yes—
693C24C2511yescharacteristic
694C24C2511yescharacteristic
695C24C2511yescharacteristic
696#41—432no—
697C2×Q8—24no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—28no—
701C2×Q8—24no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—28no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—28no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—42no—
763C22×C4—41no—
764C22×C4—42no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—432no—
769C22×C4—416no—
770C22×C4C2×#4118yes—
771C22×C4C2×#4114yes—
772C22×C4H(5,𝔽2)14yes—
773C22×C42−1+414yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2511yescharacteristic
789C22×C4C2514yes—
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C4⋊C4—216no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4C2×#41116yes—
830C22⋊C4—28no—
831C22⋊C4—22no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—24no—
837C22⋊C4—28no—
838C22⋊C4—216no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—42no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4H(5,𝔽2)14yes—
863C42—28no—
864C42—24no—
865C42—24no—
866C42—28no—
867C42—28no—
868C42—28no—
869C42—28no—
870C42—28no—
871C42—24no—
872C42—24no—
873C42—44no—
874C42—44no—
875C42—44no—
876C42—44no—
877C42—48no—
878C42—44no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—28no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—44no—
904C23—44no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23C22×#4112yes—
910C23C2×H(5,𝔽2)12yes—
911C23C2×H(5,𝔽2)12yes—
912C23C2×2−1+412yes—
913C23#58512yes—
914C23C2611yescharacteristic
915Q8—48no—
916Q8—88no—
917Q8—88no—
918Q8—88no—
919D4—416no—
920D4—48no—
921D4—88no—
922D4—88no—
923D4—88no—
924C2×C4—24no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—24no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—48no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—416no—
979C2×C4—416no—
980C2×C4—48no—
981C2×C4—44no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—416no—
985C2×C4—84no—
986C2×C4—84no—
987C2×C4—82no—
988C2×C4—82no—
989C2×C4—168no—
990C2×C4#542116yescomplemented
991C2×C4C22×#4118yes—
992C2×C4C22×#4114yes—
993C2×C4C2×H(5,𝔽2)12yes—
994C2×C4C2×H(5,𝔽2)12yes—
995C2×C4C2×H(5,𝔽2)14yes—
996C2×C4C2×2−1+414yes—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—416no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22C2×#54214yes—
1026C22C23×#4111yescharacteristic
1027C22C22×H(5,𝔽2)11yescharacteristic
1028C22C22×H(5,𝔽2)11yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C2×#58511yescharacteristic
1031C222−1+611yescharacteristic
1032C222−1+611yescharacteristic
1033C4—28no—
1034C4—22no—
1035C4—22no—
1036C4—44no—
1037C4—44no—
1038C4—44no—
1039C4—41no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—41no—
1044C4—44no—
1045C4—42no—
1046C4—44no—
1047C4—44no—
1048C4—42no—
1049C4—42no—
1050C4—44no—
1051C4C2×#54218yes—
1052C2—24no—
1053C2—42no—
1054C2—42no—
1055C2—84no—
1056C2C22×#54211yescharacteristic
1057C2#6277311yescharacteristic
1058C2#6285011yescharacteristic
1059C2#6291411yescharacteristic
1060C2#6291511yescharacteristic
1061C2#6292711yescharacteristic
1062C2#6292811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42637C2semidirect
2. #42625C2semidirect
3. #42583C2semidirect
4. #42568C2semidirect
5. #40166C2semidirect
6. #40058C2semidirect
7. #39398C2semidirect
8. #39026C2semidirect
9. #37464C2semidirect
10. #36764C2semidirect
11. #36730C2semidirect
12. #35519C2semidirect
13. #35516C2semidirect
14. #35267C2semidirect
15. #35260C2semidirect
16. #35224C2semidirect
18. #35173C2semidirect
19. #35158C2semidirect
20. #34813C2semidirect
21. #34274C2semidirect
22. C2×#2344C2semidirect
23. C4×#544C2semidirect
32. #2863C22semidirect
33. #2860C22semidirect
38. #2839C22semidirect
39. #2830C22semidirect
40. #2796C22semidirect
41. #2793C22semidirect
42. #2777C22semidirect
43. #2765C22semidirect
44. #2762C22semidirect
45. #2755C22semidirect
50. #2729C22semidirect
53. #2700C22semidirect
56. #2665C22semidirect
58. #2652C22semidirect
59. #2650C22semidirect
60. #2645C22semidirect
61. #2644C22semidirect
63. #2637C22semidirect
70. #2584C22semidirect
71. #2584C22semidirect
72. #2582C22semidirect
73. #2581C22semidirect
74. #2580C22semidirect
75. #2567C22semidirect
76. #2546C22semidirect
77. #2538C22semidirect
78. #2520C22semidirect
80. #2497C22semidirect
81. #2496C22semidirect
82. #2495C22semidirect
83. #2494C22semidirect
86. #2492C22semidirect
89. #2491C22semidirect
92. #2490C22semidirect
95. #2489C22semidirect
109. #2468C22semidirect
114. #2442C22semidirect
115. #2441C22semidirect
118. #2440C22semidirect
119. #2439C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2361C22semidirect
135. #2360C22semidirect
140. #2331C22semidirect
141. #2330C22semidirect
154. C4×C4⋊Q8C22semidirect
155. C4×#125C22semidirect
990. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#426372
#426252
#425832
#425682
#401662
#400582
#393982
#390262
#374642
#367642
#367302
#355192
#355162
#352672
#352602
#352242
#352232
#351732
#351582
#348132
#342742
C2×#23442
C4×#5442