Finite Group Databasebeta

← #8096274

Subgroups — #8096274

Order 512.

5733 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53106C214yesmaximal, complemented
2#52969C212yesmaximal, complemented
3#52712C214yesmaximal, complemented
4#52325C218yesmaximal, complemented
5#52306C211yesmaximal, characteristic, complemented
6#52167C212yesmaximal, complemented
7#46345C212yesmaximal, complemented
8#46318C212yesmaximal, complemented
9#46225C214yesmaximal, complemented
10#45997C212yesmaximal, complemented
11#45996C211yesmaximal, characteristic, complemented
12#45992C214yesmaximal, complemented
13#45791C218yesmaximal, complemented
14#45785C214yesmaximal, complemented
15#36463C212yesmaximal, complemented
16#36462C214yesmaximal, complemented
17#36412C211yesmaximal, characteristic, complemented
18#36128C212yesmaximal, complemented
19#36004C212yesmaximal, complemented
20#35741C214yesmaximal, complemented
21C2×#562C2214yescomplemented
22C2×H(3,𝔽4)C2212yes—
23C2×#560C2218yescomplemented
24C2×#555C2211yescharacteristic
25C2×#550C2212yes—
26C2×#550C2211yescharacteristic, complemented
27C2×#532C2214yescomplemented
28C2×#518C2212yescomplemented
29#2867C2212yes—
30#2860C2214yescomplemented
31#2858C2212yes—
32#2858C2211yescharacteristic, complemented
33#2856C2212yes—
34#2856C2214yescomplemented
35#2854C2214yescomplemented
36#2850C2218yescomplemented
37#2832C2214yescomplemented
38#2828C2214yescomplemented
39#2824C2218yescomplemented
40#2819C2212yes—
41#2819C2214yescomplemented
42#2819C2218yescomplemented
43#2818C2218yescomplemented
44#2816C2218yescomplemented
45#2815C2218yes—
46#2813C2218yescomplemented
47#2812C2214yescomplemented
48#2809C2211yescharacteristic, complemented
49#2775C2214yescomplemented
50#2769C2212yescomplemented
51#2734C2211yescharacteristic, complemented
52#2733C2212yes—
53#2731C2212yes—
54#2731C2214yescomplemented
55#2727C2212yes—
56#2723C2218yescomplemented
57#2721C2214yescomplemented
58#2718C2218yescomplemented
59#2706C2218yescomplemented
60#2699C2214yescomplemented
61#2686C2218yescomplemented
62#2682C2214yescomplemented
63#2682C2214yescomplemented
64#2680C2214yescomplemented
65#2679C2212yes—
66#2676C2218yescomplemented
67#2676C2218yescomplemented
68#2676C2218yescomplemented
69#2673C2218yescomplemented
70#2673C2218yescomplemented
71#2673C2218yescomplemented
72#2671C2218yescomplemented
73#2670C2218yes—
74#2669C2218yes—
75#2669C2218yescomplemented
76#2669C2218yescomplemented
77#2669C2218yescomplemented
78#2668C2214yescomplemented
79#2635C2218yescomplemented
80#2631C2214yes—
81#2624C2212yescomplemented
82#2619C2214yes—
83#2598C2214yescomplemented
84#2580C2214yescomplemented
85#2572C2218yescomplemented
86#2567C2211yescharacteristic, complemented
87#2563C2212yescomplemented
88#2560C2218yescomplemented
89#2559C2218yescomplemented
90#2557C2218yescomplemented
91#2555C2218yescomplemented
92#2554C2218yescomplemented
93#2548C2212yes—
94#2548C2212yescomplemented
95#2541C2211yescharacteristic
96#2541C2212yes—
97#2541C2214yes—
98#2541C2214yescomplemented
99#2541C2214yescomplemented
100#2540C2214yes—
101#2539C2218yescomplemented
102#2518C2218yescomplemented
103#2513C2214yescomplemented
104#2508C2214yescomplemented
105#2500C2212yescomplemented
106#2491C2214yes—
107#2490C2214yescomplemented
108#2472C2218yescomplemented
109#2464C2218yescomplemented
110#2464C2218yescomplemented
111#2459C2218yescomplemented
112#2459C2218yescomplemented
113#2452C2214yescomplemented
114#2452C2214yescomplemented
115#2445C2214yes—
116#2445C2214yescomplemented
117#2445C2214yescomplemented
118#2445C2214yescomplemented
119#2433C2214yes—
120#2433C2214yescomplemented
121#2433C2212yescomplemented
122#2431C2212yes—
123#2431C2214yescomplemented
124#2431C2214yescomplemented
125#2428C2214yes—
126#2428C2214yes—
127#2428C2218yescomplemented
128#2428C2218yescomplemented
129#2428C2214yescomplemented
130#2424C2218yes—
131#2424C2218yescomplemented
132#2424C2218yescomplemented
133#2420C2214yescomplemented
134#2420C2214yescomplemented
135#2408C2212yes—
136#2404C2218yescomplemented
137#2396C2214yescomplemented
138#2395C2212yes—
139#2392C2214yescomplemented
140#2388C2218yescomplemented
141#2379C2214yescomplemented
142#2369C2212yescomplemented
143#2366C2212yes—
144#2366C2214yescomplemented
145#2366C2214yescomplemented
146#2363C2214yes—
147#2363C2214yescomplemented
148#2357C2214yescomplemented
149#2347C2212yescomplemented
150C4×C4⋊Q8C2212yescomplemented
151C4×#125C2212yescomplemented
152C4×#126C2214yescomplemented
153C4×#124C2211yescharacteristic
154C4×#123C2218yescomplemented
155C4×#121C2214yescomplemented
156#2297C2212yescomplemented
157C42×D4C2212yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2314yes—
161C23×D4C2312yes—
162#562—416no—
163H(3,𝔽4)—48no—
164#560—432no—
165#555—44no—
166#550—48no—
167#550—44no—
168#532—416no—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×#127C2318yes—
173C2×#127C2314yes—
174C2×#127C2312yes—
175C2×#127C2311yescharacteristic
176C2×#127C2314yes—
177C2×#127C2314yes—
178C2×#127C2312yes—
179C2×#127C2312yes—
180C2×#127C2314yes—
181C2×#127C2312yes—
182C2×#127C2314yes—
183C2×#126C2314yes—
184C2×#126C2318yes—
185C2×#125C2312yes—
186C2×#124C2314yes—
187C2×#124C2311yescharacteristic
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2318yes—
191C2×#124C2314yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×#121C2314yes—
201C2×#121C2318yes—
202C2×#121C2318yes—
203C2×#121C2318yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2318yes—
218C2×#121C2314yes—
219C2×#120C2318yes—
220C2×#120C2314yes—
221C2×#120C2318yes—
222C2×#120C2318yes—
223C2×#120C2318yes—
224C2×#120C2318yes—
225#518—48no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C22×C22⋊C4C2318yes—
244C22×C42C2314yes—
245C22×C42C2312yes—
246#400C2314yes—
247#400C2318yes—
248#400C2312yes—
249#399C2314yes—
250#399C2318yes—
251#399C2312yes—
252#399C2314yes—
253#398C2318yes—
254#398C2314yes—
255#398C2312yes—
256#398C2314yes—
257#397C2318yes—
258#397C2314yes—
259#397C2318yes—
260#397C2312yes—
261#397C2314yes—
262#397C2318yes—
263#396C2318yes—
264#396C2314yes—
265#396C2314yes—
266#396C2318yes—
267#395C2314yes—
268#395C2314yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2314yes—
280#394C2314yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2314yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2314yes—
294#393C2318yes—
295#393C2318yes—
296#392C2314yes—
297#392C2318yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#392C2314yes—
311#392C2318yes—
312#392C2318yes—
313#392C2314yes—
314#392C2314yes—
315#392C2318yes—
316#391C2318yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2311yescharacteristic
321#390C2318yes—
322#390C2314yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2311yescharacteristic
330#390C2312yes—
331#390C2318yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#384C2312yes—
393#384C2312yes—
394#383C2314yes—
395#383C2314yes—
396#382C2312yes—
397#382C2314yes—
398#382C2311yescharacteristic
399#382C2318yes—
400#381C2318yes—
401#381C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2312yes—
405#379C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2314yes—
427C43C2312yes—
428C43C2311yescharacteristic
429C25C2414yes—
430C2×#41—28no—
431C2×#41—44no—
432C2×#41—48no—
433C2×#41—48no—
434C2×#41—82no—
435C2×#41—84no—
436C22×Q8C2412yes—
437C22×Q8C2412yes—
438C22×Q8C2414yes—
439C22×Q8C2411yescharacteristic
440C22×D4—44no—
441C22×D4—48no—
442C22×D4C2411yescharacteristic
443C22×D4C2412yes—
444C22×D4C2414yes—
445C22×D4C2411yescharacteristic
446C22×D4C2414yes—
447C22×D4C2418yes—
448C22×D4C2418yes—
449C22×D4C2414yes—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2418yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2418yes—
459C22×D4C2418yes—
460C22×D4C2418yes—
461C22×D4C2418yes—
462C22×D4C2412yes—
463C22×D4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2418yes—
468C23×C4C2418yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C4⋊Q8—28no—
472C4⋊Q8—44no—
473C4⋊Q8—42no—
474#127—48no—
475#127—48no—
476#127—44no—
477#127—48no—
478#127—48no—
479#127—42no—
480#127—44no—
481#127—44no—
482#127—416no—
483#127—82no—
484#127—84no—
485#126—216no—
486#126—416no—
487#125—28no—
488#124—216no—
489#124—24no—
490#124—48no—
491#124—416no—
492#124—48no—
493#124—48no—
494#124—48no—
495#124—48no—
496#123—232no—
497#123—416no—
498#123—416no—
499#123—416no—
500C22⋊Q8—416no—
501C22⋊Q8—416no—
502#121—216no—
503#121—48no—
504#121—416no—
505#121—44no—
506#121—48no—
507#121—44no—
508#121—416no—
509#121—416no—
510#121—416no—
511#121—416no—
512#121—416no—
513#121—416no—
514#121—416no—
515#121—48no—
516#121—48no—
517#121—44no—
518#121—416no—
519#121—416no—
520#121—84no—
521#120—416no—
522#120—416no—
523#120—416no—
524#120—48no—
525#120—416no—
526#120—88no—
527C4×Q8—44no—
528C4×Q8—42no—
529C4×D4—216no—
530C4×D4—28no—
531C4×D4—24no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—44no—
535C4×D4—48no—
536C4×D4—48no—
537C4×D4—42no—
538C4×D4—416no—
539C4×D4—416no—
540C4×D4—84no—
541#117—28no—
542#117—44no—
543#117—44no—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C22⋊C4—416no—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C42—48no—
609C2×C42—82no—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2411yescharacteristic
617C2×C42C2412yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2412yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2411yescharacteristic
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2414yes—
631#95C2412yes—
632#95C2414yes—
633#95C2412yes—
634#95C2418yes—
635#95C2414yes—
636#95C2418yes—
637#95C2412yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651C24—44no—
652C24—48no—
653C24—48no—
654C24—44no—
655C24—44no—
656C24C2512yes—
657C24C2518yes—
658C24C2514yes—
659C24C2512yes—
660#41—816no—
661#41—832no—
662C2×Q8—24no—
663C2×Q8—41no—
664C2×Q8—42no—
665C2×Q8—41no—
666C2×Q8—42no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C2×Q8—42no—
671C2×Q8—44no—
672C2×Q8H(5,𝔽2)14yes—
673C2×D4—28no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—216no—
680C2×D4—216no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—41no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—41no—
703C2×D4—42no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—42no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—44no—
732C2×D4—432no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—216no—
740C22×C4—28no—
741C22×C4—216no—
742C22×C4—42no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—48no—
753C22×C4C2514yes—
754C22×C4C2512yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2518yes—
759C22×C4C2511yescharacteristic
760C22×C4C2512yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—216no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—41no—
781C4⋊C4—42no—
782C4⋊C4—42no—
783C4⋊C4—42no—
784C4⋊C4—42no—
785C4⋊C4—41no—
786C4⋊C4—42no—
787C4⋊C4—42no—
788C4⋊C4—44no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—42no—
792C4⋊C4—48no—
793C4⋊C4—44no—
794C4⋊C4H(5,𝔽2)14yes—
795C4⋊C4H(5,𝔽2)18yes—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—28no—
799C22⋊C4—24no—
800C22⋊C4—216no—
801C22⋊C4—216no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—216no—
807C22⋊C4—216no—
808C22⋊C4—216no—
809C22⋊C4—216no—
810C22⋊C4—44no—
811C22⋊C4—48no—
812C22⋊C4—44no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—42no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—44no—
823C22⋊C4—48no—
824C22⋊C4—44no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C42—24no—
833C42—28no—
834C42—28no—
835C42—28no—
836C42—22no—
837C42—24no—
838C42—22no—
839C42—24no—
840C42—28no—
841C42—28no—
842C42—24no—
843C42—48no—
844C42—41no—
845C42—44no—
846C42—42no—
847C42—42no—
848C23—24no—
849C23—22no—
850C23—28no—
851C23—22no—
852C23—28no—
853C23—28no—
854C23—22no—
855C23—28no—
856C23—28no—
857C23—24no—
858C23—22no—
859C23—24no—
860C23—24no—
861C23—28no—
862C23—24no—
863C23—28no—
864C23—24no—
865C23—28no—
866C23—28no—
867C23—22no—
868C23—22no—
869C23—24no—
870C23—416no—
871C23—168no—
872C23—164no—
873C23—164no—
874C23—168no—
875C23C2611yescharacteristic
876Q8—44no—
877Q8—48no—
878Q8—164no—
879Q8—162no—
880D4—416no—
881D4—44no—
882D4—48no—
883D4—416no—
884D4—816no—
885D4—816no—
886D4—82no—
887D4—88no—
888D4—88no—
889D4—88no—
890D4—84no—
891D4—816no—
892D4—168no—
893D4—164no—
894D4—168no—
895D4—164no—
896D4—164no—
897D4—164no—
898D4—162no—
899D4—168no—
900D4—168no—
901D4—168no—
902C2×C4—24no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—28no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—48no—
939C2×C4—416no—
940C2×C4—48no—
941C2×C4—816no—
942C2×C4—88no—
943C2×C4—816no—
944C2×C4—168no—
945C2×C4C2×H(5,𝔽2)14yes—
946C2×C4C2×H(5,𝔽2)14yes—
947C2×C4C2×H(5,𝔽2)14yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)18yes—
950C2×C4C2×H(5,𝔽2)12yes—
951C2×C4#58514yes—
952C22—48no—
953C22—44no—
954C22—48no—
955C22—48no—
956C22—44no—
957C22—48no—
958C22—44no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22—42no—
963C22—48no—
964C22—42no—
965C22—42no—
966C22—48no—
967C22—42no—
968C22—44no—
969C22—44no—
970C22—48no—
971C22—48no—
972C22—44no—
973C22—48no—
974C22—1616no—
975C22C22×H(5,𝔽2)11yescharacteristic
976C22C22×H(5,𝔽2)12yes—
977C22C22×H(5,𝔽2)11yescharacteristic
978C22C2×#58512yes—
979C22H(7,𝔽2)11yescharacteristic
980C4—28no—
981C4—24no—
982C4—24no—
983C4—22no—
984C4—24no—
985C4—48no—
986C4—42no—
987C4—44no—
988C4—44no—
989C4—42no—
990C4—41no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—44no—
995C4#352914yes—
996C2—84no—
997C2—82no—
998C2—88no—
999C2—82no—
1000C2C2×#352911yescharacteristic
1001C2#6289211yescharacteristic
1002C2#6296112yes—
1003C2#6301412yes—
1004C2#6304011yescharacteristic
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. #53106C2semidirect
2. #52969C2semidirect
3. #52712C2semidirect
4. #52325C2semidirect
5. #52306C2semidirect
6. #52167C2semidirect
7. #46345C2semidirect
8. #46318C2semidirect
9. #46225C2semidirect
10. #45997C2semidirect
11. #45996C2semidirect
12. #45992C2semidirect
13. #45791C2semidirect
14. #45785C2semidirect
15. #36463C2semidirect
16. #36462C2semidirect
17. #36412C2semidirect
18. #36128C2semidirect
19. #36004C2semidirect
20. #35741C2semidirect
21. C2×#562C22semidirect
23. C2×#560C22semidirect
26. C2×#550C22semidirect
27. C2×#532C22semidirect
28. C2×#518C22semidirect
30. #2860C22semidirect
32. #2858C22semidirect
34. #2856C22semidirect
35. #2854C22semidirect
36. #2850C22semidirect
37. #2832C22semidirect
38. #2828C22semidirect
39. #2824C22semidirect
41. #2819C22semidirect
42. #2819C22semidirect
43. #2818C22semidirect
44. #2816C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2809C22semidirect
49. #2775C22semidirect
50. #2769C22semidirect
51. #2734C22semidirect
54. #2731C22semidirect
56. #2723C22semidirect
57. #2721C22semidirect
58. #2718C22semidirect
59. #2706C22semidirect
60. #2699C22semidirect
61. #2686C22semidirect
62. #2682C22semidirect
63. #2682C22semidirect
64. #2680C22semidirect
66. #2676C22semidirect
67. #2676C22semidirect
68. #2676C22semidirect
69. #2673C22semidirect
70. #2673C22semidirect
71. #2673C22semidirect
72. #2671C22semidirect
75. #2669C22semidirect
76. #2669C22semidirect
77. #2669C22semidirect
78. #2668C22semidirect
79. #2635C22semidirect
81. #2624C22semidirect
83. #2598C22semidirect
84. #2580C22semidirect
85. #2572C22semidirect
86. #2567C22semidirect
87. #2563C22semidirect
88. #2560C22semidirect
89. #2559C22semidirect
90. #2557C22semidirect
91. #2555C22semidirect
92. #2554C22semidirect
94. #2548C22semidirect
98. #2541C22semidirect
99. #2541C22semidirect
101. #2539C22semidirect
102. #2518C22semidirect
103. #2513C22semidirect
104. #2508C22semidirect
105. #2500C22semidirect
107. #2490C22semidirect
108. #2472C22semidirect
109. #2464C22semidirect
110. #2464C22semidirect
111. #2459C22semidirect
112. #2459C22semidirect
113. #2452C22semidirect
114. #2452C22semidirect
116. #2445C22semidirect
117. #2445C22semidirect
118. #2445C22semidirect
120. #2433C22semidirect
121. #2433C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
127. #2428C22semidirect
128. #2428C22semidirect
129. #2428C22semidirect
131. #2424C22semidirect
132. #2424C22semidirect
133. #2420C22semidirect
134. #2420C22semidirect
136. #2404C22semidirect
137. #2396C22semidirect
139. #2392C22semidirect
140. #2388C22semidirect
141. #2379C22semidirect
142. #2369C22semidirect
144. #2366C22semidirect
145. #2366C22semidirect
147. #2363C22semidirect
148. #2357C22semidirect
149. #2347C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#125C22semidirect
152. C4×#126C22semidirect
154. C4×#123C22semidirect
155. C4×#121C22semidirect
156. #2297C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#531062
#529692
#527122
#523252
#523062
#521672
#463452
#463182
#462252
#459972
#459962
#459922
#457912
#457852
#364632
#364622
#364122
#361282
#360042
#357412