Finite Group Databasebeta

← #7646161

Subgroups — #7646161

Order 512.

4888 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42756C214yesmaximal, complemented
2#42722C214yesmaximal, complemented
3#42613C214yesmaximal, complemented
4#42537C214yesmaximal, complemented
5#40188C214yesmaximal, complemented
6#40106C214yesmaximal, complemented
7#39652C214yesmaximal, complemented
8#39240C214yesmaximal, complemented
9#37463C214yesmaximal, complemented
10#36763C214yesmaximal, complemented
11#36729C214yesmaximal, complemented
12#35519C212yesmaximal, complemented
13#35516C212yesmaximal, complemented
14#35267C212yesmaximal, complemented
15#35224C211yesmaximal, characteristic, complemented
16#35223C211yesmaximal, characteristic
17#35173C211yesmaximal, characteristic, complemented
18#35158C211yesmaximal, characteristic, complemented
19#35080C214yesmaximal, complemented
20#34813C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2345C211yesmaximal, characteristic, complemented
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#533C2212yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30#2863C2214yescomplemented
31#2860C2214yescomplemented
32#2857C2214yes—
33#2850C2214yes—
34#2848C2214yes—
35#2847C2214yes—
36#2838C2218yescomplemented
37#2831C2218yescomplemented
38#2799C2218yescomplemented
39#2790C2218yescomplemented
40#2772C2218yescomplemented
41#2767C2218yescomplemented
42#2751C2218yescomplemented
43#2747C2218yes—
44#2742C2218yes—
45#2741C2218yes—
46#2739C2218yescomplemented
47#2717C2218yes—
48#2716C2218yescomplemented
49#2715C2218yescomplemented
50#2702C2218yes—
51#2692C2218yes—
52#2691C2218yes—
53#2672C2218yes—
54#2666C2218yescomplemented
55#2659C2214yes—
56#2655C2218yescomplemented
57#2653C2218yes—
58#2651C2218yescomplemented
59#2649C2218yes—
60#2645C2214yescomplemented
61#2644C2214yescomplemented
62#2639C2214yes—
63#2638C2218yescomplemented
64#2627C2214yes—
65#2618C2214yes—
66#2584C2214yescomplemented
67#2584C2214yescomplemented
68#2582C2214yescomplemented
69#2581C2214yescomplemented
70#2580C2214yescomplemented
71#2567C2214yescomplemented
72#2546C2214yescomplemented
73#2538C2214yescomplemented
74#2515C2218yescomplemented
75#2510C2218yes—
76#2497C2214yescomplemented
77#2496C2214yescomplemented
78#2495C2214yes—
79#2495C2214yescomplemented
80#2494C2214yes—
81#2494C2214yescomplemented
82#2492C2214yes—
83#2492C2212yes—
84#2492C2212yes—
85#2492C2214yescomplemented
86#2491C2214yes—
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#2472C2214yes—
104#2472C2214yes—
105#2465C2218yescomplemented
106#2450C2218yes—
107#2449C2218yes—
108#2442C2214yes—
109#2442C2214yes—
110#2442C2214yescomplemented
111#2441C2214yescomplemented
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yescomplemented
115#2439C2214yescomplemented
116#2427C2214yes—
117#2426C2214yes—
118#2423C2214yes—
119#2423C2214yes—
120#2422C2214yes—
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#2345C2214yes—
137#2345C2214yes—
138#2345C2214yes—
139#2345C2214yes—
140#2337C2218yes—
141#2335C2218yes—
142#2331C2214yescomplemented
143#2330C2214yescomplemented
144#2329C2214yes—
145#2325C2214yes—
146#2317C2212yes—
147#2317C2212yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2212yes—
151#2311C2212yes—
152#2311C2212yes—
153C4×C4⋊Q8C2214yescomplemented
154C4×#125C2214yescomplemented
155C4×#124C2214yes—
156C4×#124C2214yes—
157C4×C22⋊Q8C2214yes—
158C4×#121C2214yes—
159#2297C2212yes—
160#2297C2212yes—
161C2×#389C2211yescharacteristic
162C2×#389C2211yescharacteristic
163C2×#387C2212yes—
164C2×#387C2212yes—
165#2280C2212yes—
166C2×#380C2212yes—
167C2×#380C2211yescharacteristic
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×C4×C22⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#537—28no—
178#533—48no—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#125C2312yes—
186C2×#125C2312yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190#525—48no—
191C2×#123C2318yes—
192C2×#123C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#120C2314yes—
209#520—48no—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C22×C4⋊C4—28no—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2312yes—
241#401C2318yes—
242#400C2314yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#399C2318yes—
254#399C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#397C2314yes—
273#397C2314yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#395C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2318yes—
287#394C2314yes—
288#394C2318yes—
289#394C2314yes—
290#394C2314yes—
291#393C2318yes—
292#393C2318yes—
293#393C2314yes—
294#393C2314yes—
295#393C2314yes—
296#393C2314yes—
297#391C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2318yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2318yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2312yes—
313#390C2314yes—
314#390C2314yes—
315#390C2312yes—
316#390C2312yes—
317#390C2314yes—
318#390C2314yes—
319#390C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2318yes—
336#389C2314yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2314yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2314yes—
384#386C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#384C2314yes—
394#384C2314yes—
395#384C2314yes—
396#383C2318yes—
397#382C2314yes—
398#382C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2314yes—
402#381C2314yes—
403#381C2318yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2318yes—
420#380C2312yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#379C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2318yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453#376C2314yes—
454C2×#95C2312yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
460C2×#95C2312yes—
461C43C2314yes—
462C25C2411yescharacteristic
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—28no—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×Q8C2414yes—
469C22×Q8C2414yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—28no—
479C23×C4—82no—
480C23×C4—82no—
481C23×C4C2412yes—
482C23×C4C2412yes—
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2418yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—216no—
498C4⋊Q8—44no—
499C4⋊Q8—44no—
500C4⋊Q8—84no—
501#126—88no—
502#125—216no—
503#125—44no—
504#125—44no—
505#124—216no—
506#124—48no—
507#124—84no—
508#123—416no—
509#123—48no—
510C22⋊Q8—216no—
511C22⋊Q8—216no—
512C22⋊Q8—48no—
513C22⋊Q8—48no—
514C22⋊Q8—44no—
515C22⋊Q8—44no—
516C22⋊Q8—88no—
517C22⋊Q8—84no—
518C22⋊Q8—84no—
519#121—216no—
520#121—216no—
521#121—44no—
522#121—44no—
523#121—84no—
524#121—84no—
525#120—48no—
526C4×Q8—48no—
527C4×Q8—48no—
528C4×Q8—48no—
529C4×Q8—84no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—416no—
534C4×D4—84no—
535#117—28no—
536#117—28no—
537#117—28no—
538#117—48no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—216no—
544C2×C4⋊C4—216no—
545C2×C4⋊C4—48no—
546C2×C4⋊C4—82no—
547C2×C4⋊C4—82no—
548C2×C4⋊C4#4118yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—44no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2411yescharacteristic
590C2×C22⋊C4C2411yescharacteristic
591C2×C22⋊C4C2411yescharacteristic
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2411yescharacteristic
620C2×C42—24no—
621C2×C42—24no—
622C2×C42—82no—
623C2×C42—82no—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2414yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2418yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640#95C2414yes—
641#95C2412yes—
642#95C2412yes—
643#95C2414yes—
644#95C2414yes—
645#95C2412yes—
646#95C2412yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—41no—
685C24—41no—
686C24C2514yes—
687C24C2511yescharacteristic
688C24C2511yescharacteristic
689C24C2511yescharacteristic
690#41—432no—
691C2×Q8—24no—
692C2×Q8—28no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—28no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C22×C4—24no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—41no—
750C22×C4—42no—
751C22×C4—41no—
752C22×C4—42no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—416no—
763C22×C4—816no—
764C22×C4C2×#4118yes—
765C22×C4C2×#4114yes—
766C22×C4H(5,𝔽2)14yes—
767C22×C42−1+414yes—
768C22×C4C2511yescharacteristic
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2511yescharacteristic
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C4⋊C4—216no—
788C4⋊C4—28no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—216no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—44no—
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—48no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4C2×#41116yes—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—22no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—24no—
829C22⋊C4—28no—
830C22⋊C4—216no—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—42no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C42−1+414yes—
855C42—28no—
856C42—24no—
857C42—24no—
858C42—28no—
859C42—28no—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—44no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42—48no—
868C42—44no—
869C42—44no—
870C42—44no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—28no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—44no—
896C23—44no—
897C23—44no—
898C23—44no—
899C23—44no—
900C23—44no—
901C23C22×#4112yes—
902C23C2×H(5,𝔽2)12yes—
903C23C2×2−1+412yes—
904C23C2×2−1+412yes—
905C23#58512yes—
906C23C2611yescharacteristic
907Q8—48no—
908Q8—88no—
909Q8—88no—
910Q8—88no—
911D4—416no—
912D4—48no—
913D4—88no—
914D4—88no—
915D4—88no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—48no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—48no—
971C2×C4—44no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—416no—
975C2×C4—88no—
976C2×C4—88no—
977C2×C4—84no—
978C2×C4—82no—
979C2×C4—82no—
980C2×C4—84no—
981C2×C4—168no—
982C2×C4#542116yes—
983C2×C4C22×#4118yes—
984C2×C4C22×#4114yes—
985C2×C4C2×H(5,𝔽2)14yes—
986C2×C4C2×2−1+412yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+414yes—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—416no—
1002C22—41no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22C2×#54214yes—
1018C22C23×#4111yescharacteristic
1019C22C22×H(5,𝔽2)11yescharacteristic
1020C22C22×2−1+411yescharacteristic
1021C22C22×2−1+411yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22H(7,𝔽2)11yescharacteristic
1024C22H(7,𝔽2)11yescharacteristic
1025C4—28no—
1026C4—22no—
1027C4—22no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4—42no—
1032C4—44no—
1033C4—41no—
1034C4—44no—
1035C4—44no—
1036C4—41no—
1037C4—44no—
1038C4—42no—
1039C4—44no—
1040C4—44no—
1041C4—42no—
1042C4—44no—
1043C4C2×#54218yes—
1044C2—24no—
1045C2—42no—
1046C2—42no—
1047C2—84no—
1048C2C22×#54211yescharacteristic
1049C2#6278811yescharacteristic
1050C2#6284611yescharacteristic
1051C2#6294411yescharacteristic
1052C2#6294511yescharacteristic
1053C2#6295711yescharacteristic
1054C2#6295811yescharacteristic
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. #42756C2semidirect
2. #42722C2semidirect
3. #42613C2semidirect
4. #42537C2semidirect
5. #40188C2semidirect
6. #40106C2semidirect
7. #39652C2semidirect
8. #39240C2semidirect
9. #37463C2semidirect
10. #36763C2semidirect
11. #36729C2semidirect
12. #35519C2semidirect
13. #35516C2semidirect
14. #35267C2semidirect
15. #35224C2semidirect
17. #35173C2semidirect
18. #35158C2semidirect
19. #35080C2semidirect
20. #34813C2semidirect
21. #34274C2semidirect
22. C2×#2345C2semidirect
23. C4×#544C2semidirect
30. #2863C22semidirect
31. #2860C22semidirect
36. #2838C22semidirect
37. #2831C22semidirect
38. #2799C22semidirect
39. #2790C22semidirect
40. #2772C22semidirect
41. #2767C22semidirect
42. #2751C22semidirect
46. #2739C22semidirect
48. #2716C22semidirect
49. #2715C22semidirect
54. #2666C22semidirect
56. #2655C22semidirect
58. #2651C22semidirect
60. #2645C22semidirect
61. #2644C22semidirect
63. #2638C22semidirect
66. #2584C22semidirect
67. #2584C22semidirect
68. #2582C22semidirect
69. #2581C22semidirect
70. #2580C22semidirect
71. #2567C22semidirect
72. #2546C22semidirect
73. #2538C22semidirect
74. #2515C22semidirect
76. #2497C22semidirect
77. #2496C22semidirect
79. #2495C22semidirect
81. #2494C22semidirect
85. #2492C22semidirect
89. #2491C22semidirect
92. #2490C22semidirect
95. #2489C22semidirect
105. #2465C22semidirect
110. #2442C22semidirect
111. #2441C22semidirect
114. #2440C22semidirect
115. #2439C22semidirect
132. #2363C22semidirect
133. #2362C22semidirect
134. #2361C22semidirect
135. #2360C22semidirect
142. #2331C22semidirect
143. #2330C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#427562
#427222
#426132
#425372
#401882
#401062
#396522
#392402
#374632
#367632
#367292
#355192
#355162
#352672
#352242
#352232
#351732
#351582
#350802
#348132
#342742
C2×#23452
C4×#5442