Finite Group Databasebeta

← #7671246

Subgroups — #7671246

Order 512.

6034 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59224C214yesmaximal, complemented
2#59160C214yesmaximal, complemented
3#59151C211yesmaximal, characteristic, complemented
4#59135C211yesmaximal, characteristic, complemented
5#59124C212yesmaximal, complemented
6#59046C214yesmaximal, complemented
7#40122C214yesmaximal, complemented
8#40121C214yesmaximal, complemented
9#38819C218yesmaximal, complemented
10C2×#2858C211yesmaximal, characteristic, complemented
11#36463C212yesmaximal, complemented
12#36457C212yesmaximal, complemented
13#36412C212yesmaximal, complemented
14#36399C214yesmaximal, complemented
15#36300C212yesmaximal, complemented
16#36273C214yesmaximal, complemented
17#35466C214yesmaximal, complemented
18#35007C214yesmaximal, complemented
19#34320C214yesmaximal, complemented
20C4×#529C212yesmaximal, complemented
21C2×Q82C2211yescharacteristic, complemented
22C2×#555C2214yescomplemented
23C2×#555C2211yescharacteristic, complemented
24C2×#550C2212yes—
25C2×#546C2214yes—
26C2×#538C2214yes—
27C22×C4⋊Q8C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C2×#529C2212yes—
30C22×#124C2212yes—
31C22×#124C2212yes—
32#2860C2214yescomplemented
33#2858C2214yes—
34#2858C2212yes—
35#2858C2212yes—
36#2858C2214yes—
37#2858C2214yes—
38#2858C2214yescomplemented
39#2856C2214yescomplemented
40#2854C2214yescomplemented
41#2756C2218yescomplemented
42#2737C2218yescomplemented
43#2734C2214yescomplemented
44#2733C2214yescomplemented
45#2731C2214yescomplemented
46#2731C2214yescomplemented
47#2714C2218yescomplemented
48#2705C2218yescomplemented
49#2686C2218yescomplemented
50#2673C2218yes—
51#2662C2218yescomplemented
52#2661C2218yescomplemented
53#2610C2218yescomplemented
54#2610C2218yescomplemented
55#2567C2212yescomplemented
56#2563C2214yescomplemented
57#2563C2212yescomplemented
58#2561C2214yes—
59#2557C2218yescomplemented
60#2557C2218yescomplemented
61#2555C2218yescomplemented
62#2555C2218yescomplemented
63#2555C2218yescomplemented
64#2555C2218yescomplemented
65#2554C2218yescomplemented
66#2551C2214yescomplemented
67#2548C2212yes—
68#2548C2214yescomplemented
69#2541C2212yes—
70#2541C2214yes—
71#2539C2214yes—
72#2531C2218yescomplemented
73#2521C2218yescomplemented
74#2521C2218yescomplemented
75#2513C2214yescomplemented
76#2513C2214yescomplemented
77#2512C2214yescomplemented
78#2500C2214yescomplemented
79#2491C2218yescomplemented
80#2491C2214yescomplemented
81#2491C2218yescomplemented
82#2491C2214yescomplemented
83#2491C2218yescomplemented
84#2491C2214yescomplemented
85#2490C2214yescomplemented
86#2474C2218yescomplemented
87#2472C2218yes—
88#2471C2218yescomplemented
89#2459C2218yescomplemented
90#2454C2214yescomplemented
91#2451C2214yescomplemented
92#2448C2214yescomplemented
93#2445C2214yes—
94#2445C2214yescomplemented
95#2440C2214yes—
96#2439C2214yescomplemented
97#2436C2214yes—
98#2434C2214yes—
99#2433C2214yes—
100#2431C2214yes—
101#2431C2214yescomplemented
102#2428C2214yes—
103#2428C2214yescomplemented
104#2428C2214yescomplemented
105#2424C2218yes—
106#2420C2214yescomplemented
107#2416C2214yes—
108#2414C2218yescomplemented
109#2412C2218yes—
110#2410C2218yes—
111#2408C2214yes—
112#2374C2218yescomplemented
113#2372C2214yescomplemented
114#2369C2211yescharacteristic, complemented
115#2369C2211yescharacteristic, complemented
116#2367C2214yescomplemented
117#2366C2212yes—
118#2366C2214yescomplemented
119#2363C2214yescomplemented
120#2363C2218yescomplemented
121#2363C2214yescomplemented
122#2360C2214yes—
123#2358C2218yes—
124#2357C2214yescomplemented
125#2354C2214yescomplemented
126#2352C2214yes—
127#2342C2218yes—
128#2341C2214yescomplemented
129#2341C2214yescomplemented
130D4×C22⋊C4C2214yes—
131#2335C2218yescomplemented
132#2333C2218yescomplemented
133#2321C2218yes—
134C4×#125C2212yescomplemented
135C4×#125C2212yescomplemented
136C4×#126C2214yescomplemented
137C4×#126C2214yescomplemented
138C4×#124C2214yescomplemented
139C4×#124C2212yescomplemented
140C4×#124C2212yescomplemented
141C4×C22⋊Q8C2212yes—
142C4×C22⋊Q8C2212yes—
143C4×#123C2214yes—
144C4×#123C2214yes—
145C4×#121C2212yes—
146C4×#121C2212yes—
147C4×#121C2214yescomplemented
148#2298C2214yescomplemented
149#2297C2214yescomplemented
150#2295C2212yescomplemented
151#2293C2214yescomplemented
152#2293C2212yescomplemented
153C2×#390C2214yes—
154C2×#390C2214yes—
155#2290C2214yes—
156#2283C2212yes—
157#2273C2214yes—
158C42×Q8C2212yescomplemented
159C42×D4C2214yes—
160C42×D4C2212yescomplemented
161C4×#117C2214yescomplemented
162C2×C43C2211yescharacteristic
163C22×#41C2314yes—
164C23×Q8C2312yes—
165C23×D4C2314yes—
166C23×D4C2312yes—
167Q82—44no—
168#555—416no—
169#555—44no—
170#550—48no—
171#546—232no—
172#538—416no—
173C2×C4⋊Q8—44no—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×#127—44no—
182C2×#127C2312yes—
183C2×#127C2314yes—
184C2×#127C2312yes—
185C2×#127C2314yes—
186C2×#127C2314yes—
187#529—216no—
188C2×#126C2314yes—
189C2×#126C2318yes—
190C2×#125C2312yes—
191C2×#124—48no—
192C2×#124—48no—
193C2×#124C2314yes—
194C2×#124C2314yes—
195C2×#124C2312yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×#124C2314yes—
200C2×#124C2318yes—
201C2×#124C2314yes—
202C2×#124C2318yes—
203C2×#124C2318yes—
204C2×#124C2314yes—
205C2×#124C2314yes—
206C2×#123C2318yes—
207C2×#123C2314yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×#121C2318yes—
212C2×#121C2314yes—
213C2×#121C2312yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2318yes—
221C2×#121C2314yes—
222C2×#120C2318yes—
223C2×#120C2318yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2312yes—
238C2×#117C2314yes—
239C2×#117C2314yes—
240C2×#117C2318yes—
241C2×#117C2314yes—
242C22×C4⋊C4C2314yes—
243C22×C22⋊C4C2314yes—
244C22×C22⋊C4C2318yes—
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2318yes—
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2314yes—
252C22×C42C2312yes—
253#399C2318yes—
254#398C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#396C2318yes—
260#396C2318yes—
261#395C2318yes—
262#395C2318yes—
263#395C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#393C2318yes—
275#393C2318yes—
276#393C2318yes—
277#393C2318yes—
278#392C2318yes—
279#392C2318yes—
280#392C2318yes—
281#392C2318yes—
282#392C2318yes—
283#392C2318yes—
284#392C2318yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2312yes—
291#391C2312yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2318yes—
296#390C2318yes—
297#390C2318yes—
298#390C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2318yes—
304#390C2314yes—
305#390C2318yes—
306#390C2314yes—
307#390C2314yes—
308#390C2312yes—
309#390C2314yes—
310#390C2318yes—
311#390C2314yes—
312#390C2318yes—
313#390C2314yes—
314#390C2318yes—
315#390C2314yes—
316#390C2318yes—
317#390C2314yes—
318#390C2318yes—
319#390C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2314yes—
325#389C2314yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#388C2318yes—
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#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#387C2314yes—
359#387C2314yes—
360#387C2314yes—
361#387C2318yes—
362#387C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2314yes—
376#386C2314yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2314yes—
381#384C2314yes—
382#383C2314yes—
383#382C2312yes—
384#382C2312yes—
385#382C2314yes—
386#381C2314yes—
387#381C2318yes—
388#380C2318yes—
389#380C2314yes—
390#380C2314yes—
391#380C2318yes—
392#380C2312yes—
393#380C2318yes—
394#380C2312yes—
395#379C2318yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435#376C2314yes—
436#376C2314yes—
437C43C2312yes—
438C43C2312yes—
439C43C2312yes—
440C43C2312yes—
441C43C2314yes—
442C25C2414yes—
443C2×#41—216no—
444C2×#41—48no—
445C2×#41—48no—
446C22×Q8—44no—
447C22×Q8—44no—
448C22×Q8—44no—
449C22×Q8C2412yes—
450C22×Q8C2412yes—
451C22×Q8C2414yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×D4—216no—
455C22×D4—44no—
456C22×D4—48no—
457C22×D4—44no—
458C22×D4—48no—
459C22×D4—44no—
460C22×D4C2414yes—
461C22×D4C2412yes—
462C22×D4C2414yes—
463C22×D4C2414yes—
464C22×D4C2418yes—
465C22×D4C2418yes—
466C22×D4C2414yes—
467C22×D4C2414yes—
468C22×D4C2418yes—
469C22×D4C2418yes—
470C22×D4C2418yes—
471C22×D4C2414yes—
472C23×C4C2411yescharacteristic
473C23×C4C2414yes—
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2418yes—
480C23×C4C2418yes—
481C23×C4C2414yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—24no—
484C4⋊Q8—24no—
485C4⋊Q8—48no—
486C4⋊Q8—48no—
487C4⋊Q8—44no—
488C4⋊Q8—48no—
489C4⋊Q8—48no—
490#127—28no—
491#127—48no—
492#127—44no—
493#127—48no—
494#127—48no—
495#126—216no—
496#126—416no—
497#125—28no—
498#124—28no—
499#124—216no—
500#124—216no—
501#124—48no—
502#124—416no—
503#124—48no—
504#124—48no—
505#124—48no—
506#124—416no—
507#124—416no—
508#124—48no—
509#124—48no—
510#124—48no—
511#123—232no—
512#123—216no—
513#123—416no—
514C22⋊Q8—48no—
515C22⋊Q8#41116yescomplemented
516#121—28no—
517#121—216no—
518#121—232no—
519#121—416no—
520#121—416no—
521#121—416no—
522#121—416no—
523#121—48no—
524#121—48no—
525#121—48no—
526#121—48no—
527#120—232no—
528#120—416no—
529C4×Q8—28no—
530C4×Q8—28no—
531C4×Q8—44no—
532C4×Q8—48no—
533C4×D4—216no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—216no—
537C4×D4—216no—
538C4×D4—28no—
539C4×D4—44no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—416no—
543#117—216no—
544#117—216no—
545#117—416no—
546#117—48no—
547C2×C4⋊C4—48no—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C22⋊C4—216no—
573C2×C22⋊C4—232no—
574C2×C22⋊C4—416no—
575C2×C22⋊C4—48no—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C42—28no—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—24no—
614C2×C42—44no—
615C2×C42—48no—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2411yescharacteristic
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2411yescharacteristic
633C2×C42C2412yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2418yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671C24—216no—
672C24—28no—
673C24—44no—
674C24—44no—
675C24—48no—
676C24C2518yes—
677C24C2514yes—
678C24C2511yescharacteristic
679#41—832no—
680C2×Q8—24no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—24no—
685C2×Q8—42no—
686C2×Q8—42no—
687C2×Q8—42no—
688C2×Q8—44no—
689C2×Q8—42no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—816no—
695C2×Q8C2×#4118yes—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—24no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—216no—
705C2×D4—24no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—24no—
712C2×D4—28no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—832no—
733C2×D4—816no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—22no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—216no—
750C22×C4—216no—
751C22×C4—28no—
752C22×C4—42no—
753C22×C4—44no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4C2×#4118yes—
764C22×C4H(5,𝔽2)14yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2512yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4C2×#41116yes—
805C4⋊C4C2×#4118yes—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—216no—
809C22⋊C4—216no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—216no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—216no—
820C22⋊C4—216no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4C2×#41116yes—
840C42—24no—
841C42—24no—
842C42—24no—
843C42—24no—
844C42—28no—
845C42—28no—
846C42—24no—
847C42—24no—
848C42—24no—
849C42—22no—
850C42—22no—
851C42—24no—
852C42—28no—
853C42—28no—
854C42—28no—
855C42—24no—
856C42—24no—
857C42—28no—
858C42—42no—
859C42—44no—
860C42—42no—
861C42—44no—
862C42—44no—
863C42—44no—
864C42—44no—
865C42—44no—
866C42—44no—
867C42H(5,𝔽2)14yes—
868C42H(5,𝔽2)14yes—
869C23—21no—
870C23—21no—
871C23—22no—
872C23—24no—
873C23—28no—
874C23—28no—
875C23—24no—
876C23—28no—
877C23—28no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—28no—
882C23—28no—
883C23—24no—
884C23—24no—
885C23—28no—
886C23—416no—
887C23—816no—
888C23—88no—
889C23—816no—
890C23—88no—
891C23C22×#4114yes—
892C23C2×H(5,𝔽2)12yes—
893C23C2611yescharacteristic
894Q8—216no—
895Q8—84no—
896Q8—88no—
897Q8—84no—
898Q8—164no—
899D4—416no—
900D4—48no—
901D4—416no—
902D4—416no—
903D4—816no—
904D4—816no—
905D4—88no—
906D4—88no—
907D4—816no—
908D4—168no—
909D4—164no—
910D4—168no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—216no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
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—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—44no—
955C2×C4—416no—
956C2×C4—48no—
957C2×C4—44no—
958C2×C4—416no—
959C2×C4—816no—
960C2×C4—88no—
961C2×C4—816no—
962C2×C4—88no—
963C2×C4C22×#4114yes—
964C2×C4C22×#4118yes—
965C2×C4C22×#4118yes—
966C2×C4C22×#4114yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×H(5,𝔽2)14yes—
969C2×C4C2×H(5,𝔽2)12yes—
970C2×C4C2×H(5,𝔽2)12yes—
971C2×C4C2×H(5,𝔽2)14yes—
972C2×C4#58514yes—
973C22—24no—
974C22—24no—
975C22—22no—
976C22—22no—
977C22—44no—
978C22—48no—
979C22—48no—
980C22—44no—
981C22—44no—
982C22—48no—
983C22—44no—
984C22—48no—
985C22—44no—
986C22—48no—
987C22—48no—
988C22—44no—
989C22—44no—
990C22—48no—
991C22—1616no—
992C22#348314yes—
993C22C23×#4112yes—
994C22C22×H(5,𝔽2)11yescharacteristic
995C22C22×H(5,𝔽2)11yescharacteristic
996C22C22×H(5,𝔽2)11yescharacteristic
997C22C2×#58512yes—
998C4—24no—
999C4—28no—
1000C4—24no—
1001C4—28no—
1002C4—24no—
1003C4—22no—
1004C4—22no—
1005C4—44no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4—44no—
1014C4#351418yes—
1015C2—24no—
1016C2—84no—
1017C2—88no—
1018C2C2×#348311yescharacteristic
1019C2C2×#351412yes—
1020C2#6280012yes—
1021C2#6282211yescharacteristic
1022C2#6283211yescharacteristic
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. #59224C2semidirect
2. #59160C2semidirect
3. #59151C2semidirect
4. #59135C2semidirect
5. #59124C2semidirect
6. #59046C2semidirect
7. #40122C2semidirect
8. #40121C2semidirect
9. #38819C2semidirect
10. C2×#2858C2semidirect
11. #36463C2semidirect
12. #36457C2semidirect
13. #36412C2semidirect
14. #36399C2semidirect
15. #36300C2semidirect
16. #36273C2semidirect
17. #35466C2semidirect
18. #35007C2semidirect
19. #34320C2semidirect
20. C4×#529C2semidirect
21. C2×Q82C22semidirect
22. C2×#555C22semidirect
23. C2×#555C22semidirect
32. #2860C22semidirect
38. #2858C22semidirect
39. #2856C22semidirect
40. #2854C22semidirect
41. #2756C22semidirect
42. #2737C22semidirect
43. #2734C22semidirect
44. #2733C22semidirect
45. #2731C22semidirect
46. #2731C22semidirect
47. #2714C22semidirect
48. #2705C22semidirect
49. #2686C22semidirect
51. #2662C22semidirect
52. #2661C22semidirect
53. #2610C22semidirect
54. #2610C22semidirect
55. #2567C22semidirect
56. #2563C22semidirect
57. #2563C22semidirect
59. #2557C22semidirect
60. #2557C22semidirect
61. #2555C22semidirect
62. #2555C22semidirect
63. #2555C22semidirect
64. #2555C22semidirect
65. #2554C22semidirect
66. #2551C22semidirect
68. #2548C22semidirect
72. #2531C22semidirect
73. #2521C22semidirect
74. #2521C22semidirect
75. #2513C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2500C22semidirect
79. #2491C22semidirect
80. #2491C22semidirect
81. #2491C22semidirect
82. #2491C22semidirect
83. #2491C22semidirect
84. #2491C22semidirect
85. #2490C22semidirect
86. #2474C22semidirect
88. #2471C22semidirect
89. #2459C22semidirect
90. #2454C22semidirect
91. #2451C22semidirect
92. #2448C22semidirect
94. #2445C22semidirect
96. #2439C22semidirect
101. #2431C22semidirect
103. #2428C22semidirect
104. #2428C22semidirect
106. #2420C22semidirect
108. #2414C22semidirect
112. #2374C22semidirect
113. #2372C22semidirect
114. #2369C22semidirect
115. #2369C22semidirect
116. #2367C22semidirect
118. #2366C22semidirect
119. #2363C22semidirect
120. #2363C22semidirect
121. #2363C22semidirect
124. #2357C22semidirect
125. #2354C22semidirect
128. #2341C22semidirect
129. #2341C22semidirect
131. #2335C22semidirect
132. #2333C22semidirect
134. C4×#125C22semidirect
135. C4×#125C22semidirect
136. C4×#126C22semidirect
137. C4×#126C22semidirect
138. C4×#124C22semidirect
139. C4×#124C22semidirect
140. C4×#124C22semidirect
147. C4×#121C22semidirect
148. #2298C22semidirect
149. #2297C22semidirect
150. #2295C22semidirect
151. #2293C22semidirect
152. #2293C22semidirect
158. C42×Q8C22semidirect
160. C42×D4C22semidirect
161. C4×#117C22semidirect
515. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#592242
#591602
#591512
#591352
#591242
#590462
#401222
#401212
#388192
C2×#28582
#364632
#364572
#364122
#363992
#363002
#362732
#354662
#350072
#343202
C4×#5292