Finite Group Databasebeta

← #7683763

Subgroups — #7683763

Order 512.

5482 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59948C214yesmaximal, complemented
2#59236C214yesmaximal, complemented
3#59234C214yesmaximal, complemented
4#59231C214yesmaximal, complemented
5#59229C214yesmaximal, complemented
6#59160C214yesmaximal, complemented
7#45208C214yesmaximal, complemented
8#45122C214yesmaximal, complemented
9#45078C214yesmaximal, complemented
10#44909C214yesmaximal, complemented
11#43222C218yesmaximal, complemented
12#35592C211yesmaximal, characteristic, complemented
13#35576C211yesmaximal, characteristic, complemented
14#35542C212yesmaximal, complemented
15#35518C212yesmaximal, complemented
16C2×#2547C211yesmaximal, characteristic, complemented
17#34737C212yesmaximal, complemented
18#34252C212yesmaximal, complemented
19#34202C212yesmaximal, complemented
20#34180C212yesmaximal, complemented
21C2×#555C2214yes—
22C2×#544C2211yescharacteristic
23C2×#537C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×#124C2212yes—
26C2×#525C2212yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2809C2214yescomplemented
32#2803C2218yescomplemented
33#2783C2218yescomplemented
34#2781C2218yescomplemented
35#2775C2218yescomplemented
36#2775C2218yescomplemented
37#2756C2218yescomplemented
38#2744C2218yescomplemented
39#2737C2218yescomplemented
40#2733C2214yes—
41#2731C2214yes—
42#2731C2214yescomplemented
43#2686C2218yes—
44#2686C2218yescomplemented
45#2612C2218yescomplemented
46#2610C2218yes—
47#2591C2214yes—
48#2583C2214yes—
49#2574C2218yescomplemented
50#2563C2214yescomplemented
51#2562C2214yescomplemented
52#2562C2214yescomplemented
53#2555C2218yes—
54#2551C2214yescomplemented
55#2551C2214yescomplemented
56#2550C2214yescomplemented
57#2550C2214yescomplemented
58#2547C2214yes—
59#2547C2214yes—
60#2547C2214yes—
61#2547C2214yes—
62#2547C2214yescomplemented
63#2538C2214yescomplemented
64#2537C2214yescomplemented
65#2536C2214yescomplemented
66#2535C2214yescomplemented
67#2532C2218yescomplemented
68#2531C2218yescomplemented
69#2526C2218yescomplemented
70#2518C2218yescomplemented
71#2513C2218yescomplemented
72#2495C2218yescomplemented
73#2492C2214yescomplemented
74#2492C2214yescomplemented
75#2492C2214yescomplemented
76#2491C2218yes—
77#2491C2214yescomplemented
78#2491C2214yescomplemented
79#2491C2214yescomplemented
80#2490C2214yescomplemented
81#2489C2214yescomplemented
82#2488C2218yes—
83#2485C2218yescomplemented
84#2474C2218yes—
85#2474C2218yescomplemented
86#2474C2218yescomplemented
87#2472C2218yes—
88#2459C2218yes—
89#2439C2218yescomplemented
90#2436C2214yes—
91#2434C2214yes—
92#2425C2218yes—
93#2424C2218yes—
94#2420C2218yescomplemented
95#2417C2212yes—
96#2417C2212yes—
97#2417C2214yescomplemented
98#2416C2212yes—
99#2416C2212yes—
100#2416C2214yescomplemented
101#2415C2212yes—
102#2415C2212yes—
103#2415C2214yescomplemented
104#2414C2212yes—
105#2414C2212yes—
106#2414C2214yescomplemented
107#2413C2214yes—
108#2412C2214yes—
109#2411C2214yes—
110#2410C2214yes—
111#2392C2214yes—
112#2392C2214yes—
113C2×#397C2214yes—
114#2372C2214yes—
115#2372C2214yescomplemented
116#2369C2214yescomplemented
117#2359C2218yes—
118#2358C2218yes—
119#2357C2214yescomplemented
120#2356C2214yescomplemented
121#2355C2214yescomplemented
122#2354C2214yescomplemented
123#2354C2214yescomplemented
124#2352C2214yescomplemented
125#2352C2214yescomplemented
126D4×C4⋊C4C2214yescomplemented
127#2347C2214yescomplemented
128#2347C2214yescomplemented
129#2346C2214yescomplemented
130#2346C2214yescomplemented
131#2345C2214yescomplemented
132#2345C2214yescomplemented
133#2344C2214yescomplemented
134#2344C2214yescomplemented
135#2343C2218yes—
136#2342C2218yes—
137#2324C2214yescomplemented
138#2323C2214yescomplemented
139#2318C2218yes—
140#2317C2212yes—
141#2317C2212yes—
142#2314C2214yescomplemented
143#2314C2214yescomplemented
144#2311C2212yes—
145#2311C2212yes—
146C4×C22⋊Q8C2214yescomplemented
147C4×#121C2214yes—
148C4×#121C2214yes—
149C4×#121C2214yescomplemented
150#2297C2212yes—
151#2296C2212yes—
152C2×#391C2212yes—
153#2290C2218yes—
154#2285C2214yescomplemented
155#2283C2214yescomplemented
156#2280C2212yes—
157C2×#380C2212yes—
158C2×#380C2212yes—
159#2274C2211yescharacteristic
160#2274C2212yes—
161#2274C2211yescharacteristic
162C2×C4×C4⋊C4C2211yescharacteristic
163C22×#41C2312yes—
164C23×Q8C2312yes—
165C23×D4C2311yescharacteristic
166C24×C4C2312yes—
167#555—416no—
168#544—44no—
169#537—44no—
170C2×C4⋊Q8—44no—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×#125C2314yes—
177C2×#124—48no—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2318yes—
182C2×#124C2318yes—
183C2×#124C2314yes—
184#525—216no—
185#525—48no—
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2314yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2312yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2312yes—
200C2×#121C2312yes—
201C2×#121C2314yes—
202C2×#121C2318yes—
203C2×#120C2314yes—
204C2×#120C2314yes—
205#520—216no—
206C2×C4×Q8C2314yes—
207C2×C4×D4—44no—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×#117—216no—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2312yes—
227C2×#117C2318yes—
228C2×#117C2318yes—
229C2×#117C2312yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2312yes—
242C22×C42C2314yes—
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2314yes—
251#398C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2314yes—
257#397C2314yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#396C2314yes—
262#396C2314yes—
263#396C2314yes—
264#396C2314yes—
265#396C2318yes—
266#396C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2314yes—
274#394C2314yes—
275#394C2314yes—
276#394C2314yes—
277#394C2314yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#393C2318yes—
283#393C2318yes—
284#393C2318yes—
285#393C2318yes—
286#392C2314yes—
287#392C2314yes—
288#392C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2312yes—
293#391C2312yes—
294#391C2314yes—
295#391C2318yes—
296#391C2314yes—
297#391C2314yes—
298#391C2318yes—
299#391C2314yes—
300#391C2314yes—
301#390C2318yes—
302#390C2314yes—
303#390C2314yes—
304#390C2318yes—
305#390C2312yes—
306#390C2318yes—
307#390C2312yes—
308#390C2314yes—
309#390C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2314yes—
322#389C2318yes—
323#389C2314yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
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#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2314yes—
365#386C2318yes—
366#386C2314yes—
367#386C2314yes—
368#386C2314yes—
369#386C2314yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#384C2314yes—
377#384C2314yes—
378#383C2318yes—
379#383C2318yes—
380#382C2318yes—
381#382C2314yes—
382#382C2314yes—
383#382C2318yes—
384#382C2318yes—
385#381C2318yes—
386#381C2318yes—
387#381C2314yes—
388#380C2314yes—
389#380C2312yes—
390#380C2312yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2312yes—
396#380C2314yes—
397#380C2314yes—
398#380C2318yes—
399#380C2318yes—
400#380C2318yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2314yes—
409#379C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436#376C2318yes—
437#376C2318yes—
438C2×#95C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C25C2412yes—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—28no—
445C22×Q8—44no—
446C22×Q8—44no—
447C22×Q8—44no—
448C22×Q8C2412yes—
449C22×Q8C2414yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×D4—24no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2411yescharacteristic
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2414yes—
463C22×D4C2414yes—
464C22×D4C2411yescharacteristic
465C23×C4—28no—
466C23×C4—28no—
467C23×C4—28no—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2411yescharacteristic
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2418yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—48no—
484C4⋊Q8—48no—
485C4⋊Q8—48no—
486C4⋊Q8—48no—
487C4⋊Q8—48no—
488#125—48no—
489#124—216no—
490#124—48no—
491#124—416no—
492#124—416no—
493#124—48no—
494#124—48no—
495#123—216no—
496#123—48no—
497C22⋊Q8—28no—
498C22⋊Q8—28no—
499C22⋊Q8—48no—
500C22⋊Q8—44no—
501C22⋊Q8—44no—
502C22⋊Q8—48no—
503#121—216no—
504#121—28no—
505#121—28no—
506#121—48no—
507#121—416no—
508#121—44no—
509#121—44no—
510#121—48no—
511#121—48no—
512#120—216no—
513#120—48no—
514C4×Q8—216no—
515C4×D4—232no—
516C4×D4—216no—
517C4×D4—216no—
518C4×D4—216no—
519C4×D4—44no—
520C4×D4—44no—
521C4×D4—44no—
522C4×D4—44no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—416no—
526#117—28no—
527#117—28no—
528#117—28no—
529#117—28no—
530#117—216no—
531#117—216no—
532#117—216no—
533#117—416no—
534#117—416no—
535#117#41116yes—
536C2×C4⋊C4—28no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—216no—
542C2×C4⋊C4—42no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C22⋊C4—216no—
577C2×C22⋊C4—48no—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—44no—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C42—24no—
616C2×C42—216no—
617C2×C42—44no—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2418yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2418yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2414yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2414yes—
662#95C2414yes—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—42no—
668C24—42no—
669C24—42no—
670C24C2512yes—
671C24C2514yes—
672C24C2512yes—
673C24C2511yescharacteristic
674#41—432no—
675C2×Q8—24no—
676C2×Q8—24no—
677C2×Q8—24no—
678C2×Q8—28no—
679C2×Q8—28no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—816no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—28no—
696C2×D4—24no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—41no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—41no—
706C2×D4—44no—
707C2×D4—416no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4H(5,𝔽2)14yes—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—22no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—216no—
748C22×C4—44no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—48no—
757C22×C4—44no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—432no—
761C22×C4C2×#4118yes—
762C22×C4H(5,𝔽2)14yes—
763C22×C4C2514yes—
764C22×C4C2518yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2512yes—
779C4⋊C4—28no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—216no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—41no—
795C4⋊C4—42no—
796C4⋊C4—41no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4C2×#4118yes—
810C4⋊C4C2×#4118yes—
811C22⋊C4—28no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—28no—
818C22⋊C4—216no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4C2×#41116yes—
846C42—28no—
847C42—28no—
848C42—28no—
849C42—216no—
850C42—24no—
851C42—24no—
852C42—28no—
853C42—28no—
854C42—44no—
855C42—48no—
856C42—48no—
857C42—44no—
858C42—44no—
859C42—44no—
860C42—44no—
861C42C2×#41116yes—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—24no—
873C23—22no—
874C23—24no—
875C23—24no—
876C23—22no—
877C23—22no—
878C23—24no—
879C23—24no—
880C23—22no—
881C23—24no—
882C23—22no—
883C23—24no—
884C23—22no—
885C23—48no—
886C23—48no—
887C23—48no—
888C23—48no—
889C23—84no—
890C23—84no—
891C23—84no—
892C23C22×#4114yes—
893C23C2×H(5,𝔽2)14yes—
894C23C2×H(5,𝔽2)12yes—
895C23C2611yescharacteristic
896Q8—48no—
897Q8—88no—
898Q8—88no—
899Q8—164no—
900D4—44no—
901D4—416no—
902D4—48no—
903D4—44no—
904D4—416no—
905D4—48no—
906D4—88no—
907D4—88no—
908D4—88no—
909D4—164no—
910C2×C4—28no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—28no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—28no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—416no—
953C2×C4—44no—
954C2×C4—48no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—416no—
960C2×C4—816no—
961C2×C4—88no—
962C2×C4—88no—
963C2×C4—84no—
964C2×C4—84no—
965C2×C4#555116yescomplemented
966C2×C4C22×#4118yes—
967C2×C4C22×#4118yes—
968C2×C4C22×#4114yes—
969C2×C4C22×#4114yes—
970C2×C4C2×H(5,𝔽2)12yes—
971C2×C4C2×H(5,𝔽2)14yes—
972C2×C4#58512yes—
973C22—24no—
974C22—24no—
975C22—22no—
976C22—22no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—44no—
985C22—44no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—44no—
991C22—42no—
992C22—42no—
993C22—44no—
994C22—42no—
995C22—44no—
996C22—42no—
997C22—44no—
998C22—816no—
999C22C2×#55514yes—
1000C22C23×#4112yes—
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C2×#58511yescharacteristic
1004C222−1+612yes—
1005C4—28no—
1006C4—28no—
1007C4—22no—
1008C4—22no—
1009C4—44no—
1010C4—48no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4C2×#55518yes—
1021C2—24no—
1022C2—44no—
1023C2—84no—
1024C2—82no—
1025C2C22×#55511yescharacteristic
1026C2#6281811yescharacteristic
1027C2#6288611yescharacteristic
1028C2#6298512yes—
1029C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59948C2semidirect
2. #59236C2semidirect
3. #59234C2semidirect
4. #59231C2semidirect
5. #59229C2semidirect
6. #59160C2semidirect
7. #45208C2semidirect
8. #45122C2semidirect
9. #45078C2semidirect
10. #44909C2semidirect
11. #43222C2semidirect
12. #35592C2semidirect
13. #35576C2semidirect
14. #35542C2semidirect
15. #35518C2semidirect
16. C2×#2547C2semidirect
17. #34737C2semidirect
18. #34252C2semidirect
19. #34202C2semidirect
20. #34180C2semidirect
31. #2809C22semidirect
32. #2803C22semidirect
33. #2783C22semidirect
34. #2781C22semidirect
35. #2775C22semidirect
36. #2775C22semidirect
37. #2756C22semidirect
38. #2744C22semidirect
39. #2737C22semidirect
42. #2731C22semidirect
44. #2686C22semidirect
45. #2612C22semidirect
49. #2574C22semidirect
50. #2563C22semidirect
51. #2562C22semidirect
52. #2562C22semidirect
54. #2551C22semidirect
55. #2551C22semidirect
56. #2550C22semidirect
57. #2550C22semidirect
62. #2547C22semidirect
63. #2538C22semidirect
64. #2537C22semidirect
65. #2536C22semidirect
66. #2535C22semidirect
67. #2532C22semidirect
68. #2531C22semidirect
69. #2526C22semidirect
70. #2518C22semidirect
71. #2513C22semidirect
72. #2495C22semidirect
73. #2492C22semidirect
74. #2492C22semidirect
75. #2492C22semidirect
77. #2491C22semidirect
78. #2491C22semidirect
79. #2491C22semidirect
80. #2490C22semidirect
81. #2489C22semidirect
83. #2485C22semidirect
85. #2474C22semidirect
86. #2474C22semidirect
89. #2439C22semidirect
94. #2420C22semidirect
97. #2417C22semidirect
100. #2416C22semidirect
103. #2415C22semidirect
106. #2414C22semidirect
115. #2372C22semidirect
116. #2369C22semidirect
119. #2357C22semidirect
120. #2356C22semidirect
121. #2355C22semidirect
122. #2354C22semidirect
123. #2354C22semidirect
124. #2352C22semidirect
125. #2352C22semidirect
126. D4×C4⋊C4C22semidirect
127. #2347C22semidirect
128. #2347C22semidirect
129. #2346C22semidirect
130. #2346C22semidirect
131. #2345C22semidirect
132. #2345C22semidirect
133. #2344C22semidirect
134. #2344C22semidirect
137. #2324C22semidirect
138. #2323C22semidirect
142. #2314C22semidirect
143. #2314C22semidirect
146. C4×C22⋊Q8C22semidirect
149. C4×#121C22semidirect
154. #2285C22semidirect
155. #2283C22semidirect
965. C2×C4#555semidirect

Maximal subgroups

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

subgroupindex
#599482
#592362
#592342
#592312
#592292
#591602
#452082
#451222
#450782
#449092
#432222
#355922
#355762
#355422
#355182
C2×#25472
#347372
#342522
#342022
#341802