Finite Group Databasebeta

← #8701566

Subgroups — #8701566

Order 512.

5509 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59834C212yesmaximal, complemented
2#59822C212yesmaximal, complemented
3#59478C214yesmaximal, complemented
4#58884C218yesmaximal, complemented
5#55615C214yesmaximal, complemented
6#52306C211yesmaximal, characteristic, complemented
7#51783C214yesmaximal, complemented
8#47874C218yesmaximal, complemented
9#45997C212yesmaximal, complemented
10#45996C211yesmaximal, characteristic, complemented
11#45088C212yesmaximal, complemented
12#44957C214yesmaximal, complemented
13#42969C212yesmaximal, complemented
14#42585C214yesmaximal, complemented
15#39405C214yesmaximal, complemented
16#39168C212yesmaximal, complemented
17#37216C212yesmaximal, complemented
18#37132C214yesmaximal, complemented
19#36457C211yesmaximal, characteristic, complemented
20#36300C212yesmaximal, complemented
21C2×#562C2214yescomplemented
22C2×H(3,𝔽4)C2212yes—
23C2×#559C2212yes—
24C2×Q82C2211yescharacteristic, complemented
25C2×#555C2214yescomplemented
26C2×#550C2211yescharacteristic
27C2×#538C2218yescomplemented
28C2×#535C2212yescomplemented
29#2860C2214yescomplemented
30#2858C2212yes—
31#2858C2212yes—
32#2858C2212yes—
33#2858C2211yescharacteristic, complemented
34#2832C2218yescomplemented
35#2819C2212yes—
36#2819C2214yescomplemented
37#2815C2214yes—
38#2809C2211yescharacteristic, complemented
39#2782C2214yescomplemented
40#2775C2214yescomplemented
41#2769C2212yescomplemented
42#2737C2218yescomplemented
43#2736C2214yescomplemented
44#2734C2211yescharacteristic, complemented
45#2733C2212yes—
46#2733C2214yescomplemented
47#2733C2214yescomplemented
48#2731C2212yes—
49#2727C2212yes—
50#2721C2214yescomplemented
51#2718C2218yescomplemented
52#2714C2218yescomplemented
53#2712C2218yescomplemented
54#2705C2218yescomplemented
55#2703C2218yescomplemented
56#2696C2218yes—
57#2692C2218yescomplemented
58#2682C2214yescomplemented
59#2682C2214yescomplemented
60#2679C2212yes—
61#2678C2218yescomplemented
62#2678C2218yescomplemented
63#2676C2218yescomplemented
64#2676C2218yescomplemented
65#2676C2218yescomplemented
66#2674C2218yescomplemented
67#2674C2218yescomplemented
68#2672C2218yescomplemented
69#2671C2218yescomplemented
70#2670C2218yes—
71#2670C2218yescomplemented
72#2670C2218yescomplemented
73#2669C2218yes—
74#2668C2218yescomplemented
75#2662C2218yescomplemented
76#2656C2214yes—
77#2640C2214yescomplemented
78#2635C2214yescomplemented
79#2631C2218yescomplemented
80#2624C2212yescomplemented
81#2620C2218yescomplemented
82#2610C2218yescomplemented
83#2609C2214yescomplemented
84#2602C2218yescomplemented
85#2567C2212yescomplemented
86#2567C2212yescomplemented
87#2564C2218yescomplemented
88#2563C2211yescharacteristic
89#2563C2212yescomplemented
90#2555C2218yescomplemented
91#2548C2212yes—
92#2548C2212yes—
93#2548C2212yes—
94#2548C2214yescomplemented
95#2548C2211yescharacteristic, complemented
96#2545C2214yescomplemented
97#2543C2214yescomplemented
98#2542C2214yescomplemented
99#2541C2214yes—
100#2541C2214yes—
101#2541C2214yescomplemented
102#2539C2218yescomplemented
103#2537C2214yescomplemented
104#2526C2218yescomplemented
105#2521C2218yescomplemented
106#2513C2214yescomplemented
107#2512C2214yescomplemented
108#2497C2214yescomplemented
109#2491C2214yes—
110#2491C2218yescomplemented
111#2491C2214yescomplemented
112#2474C2218yescomplemented
113#2474C2218yescomplemented
114#2464C2218yescomplemented
115#2461C2218yescomplemented
116#2456C2218yescomplemented
117#2454C2214yescomplemented
118#2452C2214yescomplemented
119#2452C2214yescomplemented
120#2452C2214yescomplemented
121#2448C2214yescomplemented
122#2448C2214yescomplemented
123#2445C2214yescomplemented
124#2445C2214yescomplemented
125#2437C2214yescomplemented
126#2433C2214yes—
127#2433C2212yescomplemented
128#2431C2214yes—
129#2428C2214yes—
130#2424C2218yescomplemented
131#2424C2218yescomplemented
132#2422C2214yes—
133#2414C2218yescomplemented
134#2414C2218yescomplemented
135#2411C2218yes—
136#2408C2212yes—
137#2396C2214yescomplemented
138#2395C2212yes—
139#2369C2212yescomplemented
140#2367C2214yescomplemented
141#2366C2212yes—
142#2359C2218yescomplemented
143#2354C2214yescomplemented
144#2354C2214yescomplemented
145#2341C2214yescomplemented
146#2339C2212yescomplemented
147D4×C22⋊C4C2214yescomplemented
148#2326C2214yescomplemented
149#2324C2214yes—
150C4×C4⋊Q8C2212yescomplemented
151C4×#127C2214yescomplemented
152C4×#125C2212yescomplemented
153C4×#126C2214yescomplemented
154C4×#124C2211yescharacteristic
155C4×#124C2212yescomplemented
156#2295C2212yescomplemented
157#2293C2214yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C23×D4C2312yes—
161#562—416no—
162H(3,𝔽4)—48no—
163#559—48no—
164Q82—44no—
165#555—416no—
166#550—44no—
167#538—432no—
168#535—48no—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2314yes—
175C2×#127C2314yes—
176C2×#127C2312yes—
177C2×#127C2312yes—
178C2×#127C2312yes—
179C2×#127C2311yescharacteristic
180C2×#127C2314yes—
181C2×#126C2314yes—
182C2×#126C2318yes—
183C2×#125C2312yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2312yes—
187C2×#124C2311yescharacteristic
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2314yes—
191C2×#124C2318yes—
192C2×#124C2318yes—
193C2×#124C2318yes—
194C2×#124C2314yes—
195C2×#124C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2314yes—
215C2×#120C2314yes—
216C2×#120C2318yes—
217C2×#120C2318yes—
218C2×#120C2318yes—
219C2×#120C2318yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×#117C2312yes—
236C2×#117C2318yes—
237C2×#117C2318yes—
238C22×C22⋊C4C2318yes—
239#400C2318yes—
240#400C2314yes—
241#400C2312yes—
242#399C2318yes—
243#399C2314yes—
244#399C2312yes—
245#399C2314yes—
246#399C2318yes—
247#398C2312yes—
248#398C2314yes—
249#398C2314yes—
250#397C2314yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2314yes—
256#397C2312yes—
257#396C2318yes—
258#396C2314yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2314yes—
263#396C2318yes—
264#395C2318yes—
265#395C2318yes—
266#395C2314yes—
267#394C2314yes—
268#394C2314yes—
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#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#393C2314yes—
285#393C2318yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#392C2318yes—
292#392C2318yes—
293#392C2318yes—
294#392C2318yes—
295#392C2314yes—
296#392C2318yes—
297#392C2318yes—
298#392C2314yes—
299#392C2318yes—
300#392C2314yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2318yes—
310#391C2311yescharacteristic
311#390C2314yes—
312#390C2318yes—
313#390C2318yes—
314#390C2314yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#390C2314yes—
319#390C2318yes—
320#390C2314yes—
321#390C2314yes—
322#390C2318yes—
323#390C2314yes—
324#390C2318yes—
325#390C2311yescharacteristic
326#390C2312yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2318yes—
338#390C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
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#388C2318yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2318yes—
374#387C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#384C2314yes—
392#384C2312yes—
393#384C2314yes—
394#383C2314yes—
395#382C2312yes—
396#382C2312yes—
397#382C2311yescharacteristic
398#381C2314yes—
399#380C2314yes—
400#380C2318yes—
401#380C2318yes—
402#380C2312yes—
403#380C2318yes—
404#379C2318yes—
405#379C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424#376C2314yes—
425C2×#95C2314yes—
426C43C2312yes—
427C43C2311yescharacteristic
428C43C2312yes—
429C25C2414yes—
430C2×#41—28no—
431C2×#41—48no—
432C22×Q8C2411yescharacteristic
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2414yes—
437C22×Q8C2411yescharacteristic
438C22×D4—44no—
439C22×D4—48no—
440C22×D4C2414yes—
441C22×D4C2412yes—
442C22×D4C2411yescharacteristic
443C22×D4C2414yes—
444C22×D4C2414yes—
445C22×D4C2418yes—
446C22×D4C2412yes—
447C22×D4C2414yes—
448C22×D4C2418yes—
449C22×D4C2418yes—
450C22×D4C2414yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2418yes—
454C22×D4C2418yes—
455C22×D4C2412yes—
456C22×D4C2414yes—
457C23×C4C2412yes—
458C23×C4C2418yes—
459C23×C4C2418yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C4⋊Q8—28no—
463C4⋊Q8—44no—
464C4⋊Q8—48no—
465C4⋊Q8—42no—
466C4⋊Q8—44no—
467C4⋊Q8—44no—
468#127—48no—
469#127—44no—
470#127—48no—
471#127—42no—
472#127—44no—
473#127—44no—
474#126—216no—
475#126—416no—
476#125—28no—
477#124—216no—
478#124—28no—
479#124—216no—
480#124—24no—
481#124—416no—
482#124—416no—
483#124—48no—
484#124—416no—
485#124—48no—
486#124—48no—
487#124—48no—
488#124—416no—
489#123—232no—
490#123—416no—
491#123—416no—
492#123—416no—
493C22⋊Q8—416no—
494C22⋊Q8—416no—
495C22⋊Q8—416no—
496#121—48no—
497#121—48no—
498#121—416no—
499#121—416no—
500#121—416no—
501#121—416no—
502#121—416no—
503#121—48no—
504#121—416no—
505#121—44no—
506#121—48no—
507#121—416no—
508#120—416no—
509#120—416no—
510#120—416no—
511#120—48no—
512#120—416no—
513C4×Q8—24no—
514C4×Q8—28no—
515C4×Q8—44no—
516C4×Q8—42no—
517C4×Q8—44no—
518C4×Q8—44no—
519C4×D4—216no—
520C4×D4—416no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—416no—
526C4×D4—42no—
527C4×D4—44no—
528#117—44no—
529#117—416no—
530#117—416no—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2411yescharacteristic
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2412yes—
563C2×C22⋊C4—416no—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2414yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2411yescharacteristic
611C2×C42C2412yes—
612C2×C42C2418yes—
613C2×C42C2414yes—
614C2×C42C2411yescharacteristic
615C2×C42C2412yes—
616#95C2412yes—
617#95C2418yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2412yes—
626#95C2414yes—
627#95C2414yes—
628#95C2412yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641C24—48no—
642C24—44no—
643C24—48no—
644C24—44no—
645C24—44no—
646C24C2512yes—
647C24C2518yes—
648C24C2514yes—
649#41—816no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—41no—
653C2×Q8—41no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—44no—
657C2×Q8—44no—
658C2×Q8—48no—
659C2×Q8—44no—
660C2×Q8—42no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8H(5,𝔽2)14yes—
664C2×Q8H(5,𝔽2)14yes—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—216no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—41no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—816no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—216no—
714C22×C4—28no—
715C22×C4—216no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—48no—
719C22×C4—48no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4C2512yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2512yes—
728C22×C4C2518yes—
729C22×C4C2514yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2512yes—
738C22×C4C2512yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—22no—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—216no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—28no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—48no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4—41no—
761C4⋊C4—42no—
762C4⋊C4—48no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—42no—
766C4⋊C4—41no—
767C4⋊C4—44no—
768C4⋊C4—42no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4H(5,𝔽2)18yes—
773C22⋊C4—28no—
774C22⋊C4—216no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—216no—
778C22⋊C4—216no—
779C22⋊C4—216no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—216no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—42no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C42—24no—
808C42—28no—
809C42—28no—
810C42—28no—
811C42—24no—
812C42—28no—
813C42—28no—
814C42—24no—
815C42—22no—
816C42—24no—
817C42—22no—
818C42—24no—
819C42—28no—
820C42—24no—
821C42—41no—
822C42—42no—
823C42—48no—
824C42—44no—
825C23—24no—
826C23—28no—
827C23—24no—
828C23—28no—
829C23—22no—
830C23—28no—
831C23—28no—
832C23—28no—
833C23—22no—
834C23—24no—
835C23—28no—
836C23—28no—
837C23—24no—
838C23—28no—
839C23—22no—
840C23—24no—
841C23—28no—
842C23—88no—
843C23—816no—
844C23—168no—
845C23—164no—
846C23—164no—
847C23C2611yescharacteristic
848Q8—28no—
849Q8—44no—
850Q8—84no—
851Q8—164no—
852Q8—162no—
853Q8—164no—
854D4—416no—
855D4—48no—
856D4—816no—
857D4—84no—
858D4—82no—
859D4—88no—
860D4—88no—
861D4—88no—
862D4—816no—
863D4—88no—
864D4—168no—
865D4—164no—
866D4—168no—
867D4—164no—
868D4—162no—
869D4—164no—
870D4—168no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—28no—
882C2×C4—22no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—48no—
909C2×C4—816no—
910C2×C4—816no—
911C2×C4—88no—
912C2×C4—168no—
913C2×C4C2×H(5,𝔽2)14yes—
914C2×C4C2×H(5,𝔽2)14yes—
915C2×C4C2×H(5,𝔽2)12yes—
916C2×C4C2×H(5,𝔽2)14yes—
917C2×C4C2×H(5,𝔽2)18yes—
918C2×C4C2×H(5,𝔽2)12yes—
919C2×C4#58514yes—
920C22—42no—
921C22—44no—
922C22—48no—
923C22—48no—
924C22—48no—
925C22—48no—
926C22—44no—
927C22—48no—
928C22—44no—
929C22—42no—
930C22—44no—
931C22—48no—
932C22—42no—
933C22—48no—
934C22—48no—
935C22—48no—
936C22—44no—
937C22—1616no—
938C22C22×H(5,𝔽2)11yescharacteristic
939C22C22×H(5,𝔽2)11yescharacteristic
940C22C22×H(5,𝔽2)12yes—
941C22C2×#58512yes—
942C222−1+611yescharacteristic
943C4—24no—
944C4—28no—
945C4—22no—
946C4—24no—
947C4—24no—
948C4—42no—
949C4—44no—
950C4—48no—
951C4—42no—
952C4—44no—
953C4—44no—
954C4—42no—
955C4—42no—
956C4—41no—
957C4—44no—
958C4—44no—
959C4#354514yes—
960C2—84no—
961C2—88no—
962C2—82no—
963C2C2×#354511yescharacteristic
964C2#6289511yescharacteristic
965C2#6296012yes—
966C2#6301412yes—
967C2#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. #59834C2semidirect
2. #59822C2semidirect
3. #59478C2semidirect
4. #58884C2semidirect
5. #55615C2semidirect
6. #52306C2semidirect
7. #51783C2semidirect
8. #47874C2semidirect
9. #45997C2semidirect
10. #45996C2semidirect
11. #45088C2semidirect
12. #44957C2semidirect
13. #42969C2semidirect
14. #42585C2semidirect
15. #39405C2semidirect
16. #39168C2semidirect
17. #37216C2semidirect
18. #37132C2semidirect
19. #36457C2semidirect
20. #36300C2semidirect
21. C2×#562C22semidirect
24. C2×Q82C22semidirect
25. C2×#555C22semidirect
27. C2×#538C22semidirect
28. C2×#535C22semidirect
29. #2860C22semidirect
33. #2858C22semidirect
34. #2832C22semidirect
36. #2819C22semidirect
38. #2809C22semidirect
39. #2782C22semidirect
40. #2775C22semidirect
41. #2769C22semidirect
42. #2737C22semidirect
43. #2736C22semidirect
44. #2734C22semidirect
46. #2733C22semidirect
47. #2733C22semidirect
50. #2721C22semidirect
51. #2718C22semidirect
52. #2714C22semidirect
53. #2712C22semidirect
54. #2705C22semidirect
55. #2703C22semidirect
57. #2692C22semidirect
58. #2682C22semidirect
59. #2682C22semidirect
61. #2678C22semidirect
62. #2678C22semidirect
63. #2676C22semidirect
64. #2676C22semidirect
65. #2676C22semidirect
66. #2674C22semidirect
67. #2674C22semidirect
68. #2672C22semidirect
69. #2671C22semidirect
71. #2670C22semidirect
72. #2670C22semidirect
74. #2668C22semidirect
75. #2662C22semidirect
77. #2640C22semidirect
78. #2635C22semidirect
79. #2631C22semidirect
80. #2624C22semidirect
81. #2620C22semidirect
82. #2610C22semidirect
83. #2609C22semidirect
84. #2602C22semidirect
85. #2567C22semidirect
86. #2567C22semidirect
87. #2564C22semidirect
89. #2563C22semidirect
90. #2555C22semidirect
94. #2548C22semidirect
95. #2548C22semidirect
96. #2545C22semidirect
97. #2543C22semidirect
98. #2542C22semidirect
101. #2541C22semidirect
102. #2539C22semidirect
103. #2537C22semidirect
104. #2526C22semidirect
105. #2521C22semidirect
106. #2513C22semidirect
107. #2512C22semidirect
108. #2497C22semidirect
110. #2491C22semidirect
111. #2491C22semidirect
112. #2474C22semidirect
113. #2474C22semidirect
114. #2464C22semidirect
115. #2461C22semidirect
116. #2456C22semidirect
117. #2454C22semidirect
118. #2452C22semidirect
119. #2452C22semidirect
120. #2452C22semidirect
121. #2448C22semidirect
122. #2448C22semidirect
123. #2445C22semidirect
124. #2445C22semidirect
125. #2437C22semidirect
127. #2433C22semidirect
130. #2424C22semidirect
131. #2424C22semidirect
133. #2414C22semidirect
134. #2414C22semidirect
137. #2396C22semidirect
139. #2369C22semidirect
140. #2367C22semidirect
142. #2359C22semidirect
143. #2354C22semidirect
144. #2354C22semidirect
145. #2341C22semidirect
146. #2339C22semidirect
147. D4×C22⋊C4C22semidirect
148. #2326C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#127C22semidirect
152. C4×#125C22semidirect
153. C4×#126C22semidirect
155. C4×#124C22semidirect
156. #2295C22semidirect
157. #2293C22semidirect
158. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598342
#598222
#594782
#588842
#556152
#523062
#517832
#478742
#459972
#459962
#450882
#449572
#429692
#425852
#394052
#391682
#372162
#371322
#364572
#363002