Finite Group Databasebeta

← #8069243

Subgroups — #8069243

Order 512.

5143 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C212yesmaximal, complemented
2#59562C214yesmaximal, complemented
3#59202C212yesmaximal, complemented
4#59026C214yesmaximal, complemented
5#51831C214yesmaximal, complemented
6#49845C218yesmaximal, complemented
7#49518C218yesmaximal, complemented
8#48922C214yesmaximal, complemented
9#46152C211yesmaximal, characteristic, complemented
10#46015C212yesmaximal, complemented
11#45986C214yesmaximal, complemented
12#45977C212yesmaximal, complemented
13#40002C214yesmaximal, complemented
14#39934C214yesmaximal, complemented
15#38958C212yesmaximal, complemented
16#38904C212yesmaximal, complemented
17#36174C212yesmaximal, complemented
18D4×#124C211yesmaximal, characteristic, complemented
19#34366C212yesmaximal, complemented
20C4×H(3,𝔽4)C211yesmaximal, characteristic, complemented
21C2×H(3,𝔽4)C2211yescharacteristic
22C2×#555C2212yes—
23C2×D4×Q8C2211yescharacteristic, complemented
24C2×D42C2211yescharacteristic
25C22×#124C2212yes—
26C22×#121C2212yescomplemented
27#2862C2212yescomplemented
28#2859C2212yescomplemented
29#2858C2211yescharacteristic, complemented
30#2850C2212yescomplemented
31#2850C2214yescomplemented
32#2847C2212yescomplemented
33#2844C2212yescomplemented
34#2819C2214yescomplemented
35#2809C2212yescomplemented
36#2808C2214yescomplemented
37#2785C2214yescomplemented
38#2778C2218yescomplemented
39#2759C2218yescomplemented
40#2754C2218yescomplemented
41#2751C2218yescomplemented
42#2749C2218yescomplemented
43#2735C2218yescomplemented
44#2735C2214yescomplemented
45#2733C2214yescomplemented
46#2730C2218yescomplemented
47#2720C2218yescomplemented
48#2712C2218yescomplemented
49#2711C2218yescomplemented
50#2710C2218yescomplemented
51#2700C2218yescomplemented
52#2700C2218yescomplemented
53#2699C2218yescomplemented
54#2697C2218yescomplemented
55#2688C2218yescomplemented
56#2686C2218yescomplemented
57#2684C2214yes—
58#2683C2212yes—
59#2682C2214yescomplemented
60#2670C2218yescomplemented
61#2668C2218yes—
62#2653C2218yescomplemented
63#2648C2218yescomplemented
64#2622C2214yescomplemented
65#2620C2214yescomplemented
66#2610C2218yescomplemented
67#2595C2218yescomplemented
68#2580C2214yescomplemented
69#2576C2218yescomplemented
70#2576C2218yescomplemented
71#2567C2212yescomplemented
72#2557C2218yescomplemented
73#2555C2214yescomplemented
74#2555C2218yescomplemented
75#2548C2211yescharacteristic, complemented
76#2547C2211yescharacteristic
77#2547C2212yescomplemented
78#2538C2212yescomplemented
79#2537C2212yes—
80#2535C2214yes—
81#2527C2218yescomplemented
82#2526C2218yescomplemented
83#2518C2218yescomplemented
84#2517C2214yescomplemented
85#2504C2212yescomplemented
86#2500C2218yescomplemented
87#2500C2214yescomplemented
88#2499C2214yescomplemented
89#2497C2214yescomplemented
90#2495C2214yescomplemented
91#2494C2214yescomplemented
92#2491C2214yescomplemented
93#2491C2214yescomplemented
94#2490C2214yescomplemented
95#2489C2214yescomplemented
96#2487C2212yes—
97#2485C2214yescomplemented
98#2477C2218yescomplemented
99#2477C2218yescomplemented
100#2476C2218yescomplemented
101#2474C2218yescomplemented
102#2472C2218yescomplemented
103#2472C2218yescomplemented
104#2472C2218yescomplemented
105#2471C2218yescomplemented
106#2440C2214yescomplemented
107#2439C2214yescomplemented
108#2439C2214yescomplemented
109#2436C2212yescomplemented
110#2436C2214yescomplemented
111#2435C2212yes—
112#2435C2218yescomplemented
113#2428C2214yescomplemented
114#2422C2214yescomplemented
115#2420C2214yescomplemented
116#2420C2214yescomplemented
117#2414C2214yescomplemented
118#2414C2214yescomplemented
119#2411C2218yescomplemented
120#2410C2218yescomplemented
121#2410C2214yescomplemented
122#2408C2214yes—
123#2403C2214yes—
124#2379C2211yescharacteristic
125#2379C2212yes—
126#2379C2214yescomplemented
127#2379C2212yescomplemented
128#2379C2212yescomplemented
129#2379C2214yescomplemented
130#2375C2212yes—
131#2375C2214yescomplemented
132#2372C2214yes—
133#2372C2214yescomplemented
134#2363C2214yescomplemented
135#2363C2214yescomplemented
136#2355C2212yescomplemented
137#2354C2212yescomplemented
138#2352C2214yescomplemented
139#2346C2214yescomplemented
140#2342C2218yescomplemented
141#2342C2218yescomplemented
142D4×C22⋊C4C2214yescomplemented
143D4×C22⋊C4C2212yescomplemented
144#2337C2218yescomplemented
145#2337C2218yescomplemented
146#2310C2214yescomplemented
147#2308C2214yes—
148C4×#124C2211yescharacteristic
149C4×#124C2212yescomplemented
150C4×#124C2214yescomplemented
151C4×#124C2212yescomplemented
152C4×#120C2212yes—
153C4×#120C2214yescomplemented
154#2293C2212yescomplemented
155#2293C2214yescomplemented
156#2283C2214yescomplemented
157#2280C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C23×Q8C2312yes—
160C23×D4C2312yes—
161C23×D4C2312yes—
162C23×D4C2314yes—
163C24×C4C2312yes—
164H(3,𝔽4)—28no—
165#555—48no—
166D4×Q8—44no—
167D42—44no—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2312yes—
171C2×#127C2311yescharacteristic
172C2×#125C2314yes—
173C2×#124—216no—
174C2×#124C2312yes—
175C2×#124C2312yes—
176C2×#124C2318yes—
177C2×#124C2312yes—
178C2×#124C2312yes—
179C2×#124C2312yes—
180C2×#124C2314yes—
181C2×#124C2318yes—
182C2×#124C2312yes—
183C2×#124C2318yes—
184C2×#124C2314yes—
185C2×#124C2311yescharacteristic
186C2×#123C2318yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2318yes—
191C2×#121—48no—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2312yes—
195C2×#121C2312yes—
196C2×#121C2314yes—
197C2×#121C2318yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#120C2312yes—
202C2×#120C2314yes—
203C2×#120C2314yes—
204C2×#120C2314yes—
205C2×#120C2318yes—
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2314yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2311yescharacteristic
216C2×#117C2314yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2318yes—
221C22×C4⋊C4C2312yes—
222C22×C22⋊C4C2318yes—
223C22×C22⋊C4C2314yes—
224C22×C22⋊C4C2314yes—
225C22×C42C2312yes—
226#401C2318yes—
227#400C2318yes—
228#400C2314yes—
229#400C2318yes—
230#399C2318yes—
231#399C2314yes—
232#398C2318yes—
233#397C2314yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#395C2314yes—
248#395C2314yes—
249#395C2318yes—
250#394C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2314yes—
264#393C2318yes—
265#393C2318yes—
266#393C2318yes—
267#393C2318yes—
268#393C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#391C2312yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#391C2314yes—
279#391C2318yes—
280#391C2314yes—
281#391C2312yes—
282#391C2314yes—
283#391C2318yes—
284#391C2311yescharacteristic
285#391C2314yes—
286#391C2312yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2314yes—
292#390C2312yes—
293#390C2318yes—
294#390C2314yes—
295#390C2318yes—
296#390C2318yes—
297#390C2312yes—
298#390C2311yescharacteristic
299#390C2314yes—
300#390C2312yes—
301#390C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#388C2318yes—
336#388C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#386C2312yes—
345#386C2314yes—
346#386C2314yes—
347#386C2318yes—
348#386C2318yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2314yes—
372#385C2312yes—
373#385C2314yes—
374#385C2314yes—
375#384C2314yes—
376#384C2312yes—
377#384C2312yes—
378#383C2318yes—
379#382C2314yes—
380#382C2314yes—
381#382C2318yes—
382#382C2314yes—
383#382C2311yescharacteristic
384#382C2314yes—
385#382C2312yes—
386#382C2312yes—
387#381C2318yes—
388#381C2318yes—
389#381C2318yes—
390#380C2312yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#379C2318yes—
399#379C2314yes—
400#379C2318yes—
401#379C2314yes—
402#379C2312yes—
403#379C2318yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C22⋊C4C2314yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424#376C2318yes—
425C43C2311yescharacteristic
426C43C2312yes—
427C25C2414yes—
428C25C2412yes—
429C22×Q8—28no—
430C22×Q8—44no—
431C22×Q8—82no—
432C22×Q8C2412yes—
433C22×Q8C2414yes—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2411yescharacteristic
437C22×D4—28no—
438C22×D4—28no—
439C22×D4—48no—
440C22×D4—44no—
441C22×D4—48no—
442C22×D4—82no—
443C22×D4—88no—
444C22×D4C2412yes—
445C22×D4C2411yescharacteristic
446C22×D4C2414yes—
447C22×D4C2412yes—
448C22×D4C2412yes—
449C22×D4C2414yes—
450C22×D4C2418yes—
451C22×D4C2414yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2418yes—
455C22×D4C2418yes—
456C22×D4C2411yescharacteristic
457C23×C4—44no—
458C23×C4—48no—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2414yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C4⋊Q8—42no—
469C4⋊Q8—44no—
470C4⋊Q8—44no—
471#127—42no—
472#125—84no—
473#124—28no—
474#124—28no—
475#124—28no—
476#124—232no—
477#124—216no—
478#124—28no—
479#124—28no—
480#124—416no—
481#124—88no—
482#124—84no—
483#124—82no—
484#124#4118yes—
485#123—88no—
486C22⋊Q8—48no—
487C22⋊Q8—44no—
488C22⋊Q8—84no—
489C22⋊Q8—88no—
490#121—216no—
491#121—416no—
492#121—48no—
493#121—48no—
494#121—44no—
495#121—44no—
496#121—48no—
497#121—88no—
498#121—84no—
499#120—28no—
500#120—216no—
501#120—48no—
502#120—84no—
503#120—88no—
504C4×Q8—44no—
505C4×Q8—42no—
506C4×D4—24no—
507C4×D4—28no—
508C4×D4—44no—
509C4×D4—48no—
510C4×D4—48no—
511C4×D4—44no—
512C4×D4—42no—
513C4×D4—44no—
514#117—48no—
515#117—48no—
516#117—48no—
517#117—84no—
518#117—88no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C22⋊C4—232no—
547C2×C22⋊C4—48no—
548C2×C22⋊C4—84no—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C42—28no—
589C2×C42C2411yescharacteristic
590C2×C42C2412yes—
591C2×C42C2414yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2418yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2414yes—
601C2×C42C2418yes—
602C2×C42C2411yescharacteristic
603C2×C42C2412yes—
604C2×C42C2411yescharacteristic
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2412yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633C24—28no—
634C24—28no—
635C24—24no—
636C24—42no—
637C24—44no—
638C24—44no—
639C24—42no—
640C24—44no—
641C24—48no—
642C24—48no—
643C24C2514yes—
644C24C2514yes—
645C24C2512yes—
646C24C2512yes—
647C2×Q8—24no—
648C2×Q8—28no—
649C2×Q8—24no—
650C2×Q8—41no—
651C2×Q8—41no—
652C2×Q8—42no—
653C2×Q8—44no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—44no—
657C2×Q8—42no—
658C2×Q8—48no—
659C2×Q8—44no—
660C2×Q8—816no—
661C2×Q8C2×#4114yes—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—216no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—28no—
672C2×D4—41no—
673C2×D4—41no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—44no—
681C2×D4—48no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—42no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—816no—
696C2×D4—816no—
697C2×D4—832no—
698C2×D4C2×#4114yes—
699C2×D4H(5,𝔽2)14yes—
700C22×C4—28no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—28no—
704C22×C4—24no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—44no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—44no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—44no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—816no—
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2514yes—
728C22×C4C2514yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2518yes—
733C22×C4C2518yes—
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2511yescharacteristic
737C22×C4C2511yescharacteristic
738C22×C4C2512yes—
739C22×C4C2512yes—
740C22×C4C2511yescharacteristic
741C4⋊C4—28no—
742C4⋊C4—24no—
743C4⋊C4—22no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—42no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—42no—
753C4⋊C4—44no—
754C4⋊C4—41no—
755C4⋊C4—42no—
756C4⋊C4—44no—
757C4⋊C4—42no—
758C4⋊C4—41no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—42no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C22⋊C4—216no—
768C22⋊C4—24no—
769C22⋊C4—216no—
770C22⋊C4—24no—
771C22⋊C4—28no—
772C22⋊C4—216no—
773C22⋊C4—216no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—48no—
778C22⋊C4—42no—
779C22⋊C4—48no—
780C22⋊C4—44no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—42no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—44no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—44no—
805C22⋊C4C2×#41116yes—
806C42—24no—
807C42—28no—
808C42—24no—
809C42—22no—
810C42—24no—
811C42—24no—
812C42—28no—
813C42—48no—
814C42—48no—
815C42—42no—
816C42—44no—
817C42—44no—
818C42—48no—
819C42—41no—
820C42—42no—
821C42C2×#4114yes—
822C23—22no—
823C23—22no—
824C23—24no—
825C23—24no—
826C23—22no—
827C23—24no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—28no—
836C23—24no—
837C23—24no—
838C23—28no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—416no—
843C23—48no—
844C23—84no—
845C23—88no—
846C23—88no—
847C23—88no—
848C23—816no—
849C23—84no—
850C23—88no—
851C23—168no—
852C23C22×#4114yes—
853C23C2×H(5,𝔽2)14yes—
854C23C2611yescharacteristic
855Q8—44no—
856Q8—84no—
857Q8—84no—
858Q8—88no—
859Q8—164no—
860D4—28no—
861D4—44no—
862D4—48no—
863D4—84no—
864D4—84no—
865D4—84no—
866D4—88no—
867D4—88no—
868D4—88no—
869D4—816no—
870D4—816no—
871D4—162no—
872D4—168no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—28no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—28no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—48no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—48no—
916C2×C4—88no—
917C2×C4—816no—
918C2×C4—84no—
919C2×C4—88no—
920C2×C4—88no—
921C2×C4C22×#4114yes—
922C2×C4C22×#4112yes—
923C2×C4C22×#4114yes—
924C2×C4C2×H(5,𝔽2)12yes—
925C2×C4#58514yes—
926C22—24no—
927C22—24no—
928C22—28no—
929C22—24no—
930C22—24no—
931C22—44no—
932C22—42no—
933C22—42no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—48no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—48no—
946C22—44no—
947C22—44no—
948C22—816no—
949C22—1616no—
950C22C23×#4111yescharacteristic
951C22C22×H(5,𝔽2)11yescharacteristic
952C22C2×#58512yes—
953C22H(7,𝔽2)11yescharacteristic
954C22H(7,𝔽2)12yes—
955C4—22no—
956C4—24no—
957C4—24no—
958C4—42no—
959C4—44no—
960C4—44no—
961C4—44no—
962C4—44no—
963C4—42no—
964C4—48no—
965C4—41no—
966C4—42no—
967C4—42no—
968C4—44no—
969C4—48no—
970C4#354514yes—
971C2—44no—
972C2—44no—
973C2—84no—
974C2—84no—
975C2C2×#354511yescharacteristic
976C2#6298311yescharacteristic
977C2#6299412yes—
978C2#6304511yescharacteristic
979C2#6305112yes—
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. #59952C2semidirect
2. #59562C2semidirect
3. #59202C2semidirect
4. #59026C2semidirect
5. #51831C2semidirect
6. #49845C2semidirect
7. #49518C2semidirect
8. #48922C2semidirect
9. #46152C2semidirect
10. #46015C2semidirect
11. #45986C2semidirect
12. #45977C2semidirect
13. #40002C2semidirect
14. #39934C2semidirect
15. #38958C2semidirect
16. #38904C2semidirect
17. #36174C2semidirect
18. D4×#124C2semidirect
19. #34366C2semidirect
20. C4×H(3,𝔽4)C2semidirect
23. C2×D4×Q8C22semidirect
26. C22×#121C22semidirect
27. #2862C22semidirect
28. #2859C22semidirect
29. #2858C22semidirect
30. #2850C22semidirect
31. #2850C22semidirect
32. #2847C22semidirect
33. #2844C22semidirect
34. #2819C22semidirect
35. #2809C22semidirect
36. #2808C22semidirect
37. #2785C22semidirect
38. #2778C22semidirect
39. #2759C22semidirect
40. #2754C22semidirect
41. #2751C22semidirect
42. #2749C22semidirect
43. #2735C22semidirect
44. #2735C22semidirect
45. #2733C22semidirect
46. #2730C22semidirect
47. #2720C22semidirect
48. #2712C22semidirect
49. #2711C22semidirect
50. #2710C22semidirect
51. #2700C22semidirect
52. #2700C22semidirect
53. #2699C22semidirect
54. #2697C22semidirect
55. #2688C22semidirect
56. #2686C22semidirect
59. #2682C22semidirect
60. #2670C22semidirect
62. #2653C22semidirect
63. #2648C22semidirect
64. #2622C22semidirect
65. #2620C22semidirect
66. #2610C22semidirect
67. #2595C22semidirect
68. #2580C22semidirect
69. #2576C22semidirect
70. #2576C22semidirect
71. #2567C22semidirect
72. #2557C22semidirect
73. #2555C22semidirect
74. #2555C22semidirect
75. #2548C22semidirect
77. #2547C22semidirect
78. #2538C22semidirect
81. #2527C22semidirect
82. #2526C22semidirect
83. #2518C22semidirect
84. #2517C22semidirect
85. #2504C22semidirect
86. #2500C22semidirect
87. #2500C22semidirect
88. #2499C22semidirect
89. #2497C22semidirect
90. #2495C22semidirect
91. #2494C22semidirect
92. #2491C22semidirect
93. #2491C22semidirect
94. #2490C22semidirect
95. #2489C22semidirect
97. #2485C22semidirect
98. #2477C22semidirect
99. #2477C22semidirect
100. #2476C22semidirect
101. #2474C22semidirect
102. #2472C22semidirect
103. #2472C22semidirect
104. #2472C22semidirect
105. #2471C22semidirect
106. #2440C22semidirect
107. #2439C22semidirect
108. #2439C22semidirect
109. #2436C22semidirect
110. #2436C22semidirect
112. #2435C22semidirect
113. #2428C22semidirect
114. #2422C22semidirect
115. #2420C22semidirect
116. #2420C22semidirect
117. #2414C22semidirect
118. #2414C22semidirect
119. #2411C22semidirect
120. #2410C22semidirect
121. #2410C22semidirect
126. #2379C22semidirect
127. #2379C22semidirect
128. #2379C22semidirect
129. #2379C22semidirect
131. #2375C22semidirect
133. #2372C22semidirect
134. #2363C22semidirect
135. #2363C22semidirect
136. #2355C22semidirect
137. #2354C22semidirect
138. #2352C22semidirect
139. #2346C22semidirect
140. #2342C22semidirect
141. #2342C22semidirect
142. D4×C22⋊C4C22semidirect
143. D4×C22⋊C4C22semidirect
144. #2337C22semidirect
145. #2337C22semidirect
146. #2310C22semidirect
149. C4×#124C22semidirect
150. C4×#124C22semidirect
151. C4×#124C22semidirect
153. C4×#120C22semidirect
154. #2293C22semidirect
155. #2293C22semidirect
156. #2283C22semidirect
157. #2280C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#599522
#595622
#592022
#590262
#518312
#498452
#495182
#489222
#461522
#460152
#459862
#459772
#400022
#399342
#389582
#389042
#361742
D4×#1242
#343662
C4×H(3,𝔽4)2