Finite Group Databasebeta

← #7644407

Subgroups — #7644407

Order 512.

5570 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42872C214yesmaximal, complemented
2#42847C214yesmaximal, complemented
3#42595C214yesmaximal, complemented
4#42560C214yesmaximal, complemented
5#40842C218yesmaximal, complemented
6#40692C218yesmaximal, complemented
7#37501C214yesmaximal, complemented
8#37494C214yesmaximal, complemented
9#37414C214yesmaximal, complemented
10#37346C214yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic, complemented
13#35630C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35592C211yesmaximal, characteristic, complemented
16#35574C211yesmaximal, characteristic, complemented
17#35541C211yesmaximal, characteristic, complemented
18#35533C211yesmaximal, characteristic, complemented
19#35307C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#34639C211yesmaximal, characteristic, complemented
22C2×#2640C211yesmaximal, characteristic, complemented
23#34269C211yesmaximal, characteristic, complemented
24#34259C211yesmaximal, characteristic, complemented
25#34070C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#518C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2856C2212yes—
40#2855C2214yescomplemented
41#2850C2212yes—
42#2832C2218yescomplemented
43#2831C2218yescomplemented
44#2825C2218yescomplemented
45#2824C2218yescomplemented
46#2804C2218yescomplemented
47#2797C2218yescomplemented
48#2786C2218yescomplemented
49#2784C2218yescomplemented
50#2760C2218yescomplemented
51#2759C2218yescomplemented
52#2751C2218yescomplemented
53#2751C2218yescomplemented
54#2750C2218yescomplemented
55#2749C2218yescomplemented
56#2745C2218yescomplemented
57#2708C2218yescomplemented
58#2696C2218yescomplemented
59#2688C2218yescomplemented
60#2686C2218yescomplemented
61#2676C2218yescomplemented
62#2665C2218yescomplemented
63#2653C2218yescomplemented
64#2653C2218yescomplemented
65#2648C2218yescomplemented
66#2645C2212yescomplemented
67#2645C2212yescomplemented
68#2644C2212yescomplemented
69#2644C2212yescomplemented
70#2643C2214yes—
71#2643C2214yes—
72#2643C2218yescomplemented
73#2640C2214yes—
74#2640C2214yes—
75#2640C2214yes—
76#2640C2214yes—
77#2639C2218yescomplemented
78#2631C2218yescomplemented
79#2630C2218yescomplemented
80#2625C2214yescomplemented
81#2620C2212yes—
82#2619C2212yes—
83#2591C2214yes—
84#2579C2214yes—
85#2578C2218yescomplemented
86#2557C2218yescomplemented
87#2548C2212yes—
88#2547C2214yes—
89#2545C2212yes—
90#2544C2214yes—
91#2544C2212yes—
92#2541C2212yes—
93#2514C2214yescomplemented
94#2514C2214yescomplemented
95#2511C2214yescomplemented
96#2511C2214yescomplemented
97#2493C2218yes—
98#2492C2214yescomplemented
99#2492C2214yescomplemented
100#2491C2214yescomplemented
101#2491C2214yescomplemented
102#2452C2214yescomplemented
103#2451C2214yescomplemented
104#2450C2218yescomplemented
105#2447C2214yes—
106#2447C2214yescomplemented
107#2446C2214yescomplemented
108#2445C2214yes—
109#2444C2218yescomplemented
110#2440C2214yescomplemented
111#2439C2214yescomplemented
112#2436C2214yes—
113#2436C2214yes—
114#2436C2214yes—
115#2436C2212yescomplemented
116#2434C2212yescomplemented
117#2432C2212yescomplemented
118#2431C2214yes—
119#2431C2214yes—
120#2431C2212yescomplemented
121#2430C2218yes—
122#2428C2214yes—
123#2427C2214yes—
124#2427C2214yes—
125#2426C2214yes—
126#2424C2218yes—
127#2424C2218yes—
128#2422C2214yes—
129#2420C2214yes—
130#2419C2218yes—
131#2416C2214yes—
132#2414C2214yes—
133#2412C2214yes—
134#2412C2214yes—
135#2412C2218yes—
136#2409C2214yes—
137#2409C2214yescomplemented
138#2407C2214yescomplemented
139#2404C2214yes—
140#2404C2214yes—
141#2401C2214yescomplemented
142#2401C2214yescomplemented
143C2×#397C2214yes—
144C2×#393C2214yes—
145#2367C2214yes—
146#2366C2214yes—
147#2358C2218yes—
148Q8×C22⋊C4C2214yescomplemented
149#2339C2218yes—
150#2339C2214yescomplemented
151#2328C2212yescomplemented
152#2327C2212yescomplemented
153#2326C2212yescomplemented
154#2326C2212yescomplemented
155#2325C2214yes—
156#2325C2214yes—
157#2324C2214yes—
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2212yescomplemented
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2212yescomplemented
167C4×#121C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2212yescomplemented
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#391C2212yescomplemented
180C2×#390C2211yescharacteristic
181C2×#390C2211yescharacteristic
182#2290C2214yescomplemented
183#2290C2214yescomplemented
184#2285C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2314yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200C23×D4C2311yescharacteristic
201#537—44no—
202#536—44no—
203#535—28no—
204#535—44no—
205#535—44no—
206#532—28no—
207C2×C4⋊Q8—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2311yescharacteristic
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#124—44no—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2318yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2318yes—
241C2×#121C2318yes—
242C2×#120C2314yes—
243C2×#120C2314yes—
244C2×#120C2314yes—
245#520—44no—
246#518—44no—
247C4×#41—44no—
248C4×#41—44no—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2318yes—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C22⋊C4C2314yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2314yes—
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2312yes—
283C22×C42C2312yes—
284#401C2318yes—
285#401C2314yes—
286#401C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2314yes—
290#400C2318yes—
291#400C2318yes—
292#400C2314yes—
293#400C2318yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#398C2318yes—
299#398C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2314yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2314yes—
320#396C2314yes—
321#395C2318yes—
322#395C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#393C2318yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#393C2318yes—
343#392C2318yes—
344#392C2318yes—
345#392C2318yes—
346#392C2318yes—
347#392C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2311yescharacteristic
354#391C2312yes—
355#391C2312yes—
356#391C2318yes—
357#391C2312yes—
358#391C2312yes—
359#391C2318yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2311yescharacteristic
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2318yes—
371#391C2318yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2311yescharacteristic
376#390C2312yes—
377#390C2318yes—
378#390C2312yes—
379#390C2312yes—
380#390C2318yes—
381#390C2311yescharacteristic
382#390C2312yes—
383#390C2314yes—
384#390C2314yes—
385#390C2312yes—
386#390C2312yes—
387#390C2312yes—
388#390C2312yes—
389#390C2318yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2318yes—
427#386C2318yes—
428#386C2312yes—
429#386C2318yes—
430#386C2312yes—
431#386C2312yes—
432#386C2312yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2312yes—
437#386C2318yes—
438#386C2314yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2312yes—
443#386C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2312yes—
453#385C2318yes—
454#385C2318yes—
455#385C2314yes—
456#385C2314yes—
457#385C2314yes—
458#385C2318yes—
459#385C2314yes—
460#385C2312yes—
461#385C2314yes—
462#385C2318yes—
463#385C2318yes—
464#384C2312yes—
465#384C2312yes—
466#383C2318yes—
467#382C2312yes—
468#382C2312yes—
469#381C2314yes—
470#381C2314yes—
471#381C2318yes—
472#381C2318yes—
473#381C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2318yes—
478#380C2314yes—
479#380C2318yes—
480#380C2314yes—
481#380C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498#376C2312yes—
499#376C2312yes—
500#376C2312yes—
501#376C2312yes—
502C2×#95C2312yes—
503C2×#95C2312yes—
504C2×#95C2314yes—
505C2×#95C2318yes—
506C2×#95C2314yes—
507C25C2412yes—
5082−1+4—464no—
509C2×#41—216no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41#4118yes—
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8—84no—
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2411yescharacteristic
543C22×Q8C2414yes—
544C22×Q8C2418yes—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4C2412yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2412yes—
553C22×D4C2411yescharacteristic
554C22×D4C2412yes—
555C22×D4C2411yescharacteristic
556C22×D4C2418yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2414yes—
560C22×D4C2418yes—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2411yescharacteristic
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2411yescharacteristic
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2418yes—
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2411yescharacteristic
580C4⋊Q8—24no—
581C4⋊Q8—48no—
582C4⋊Q8—48no—
583C4⋊Q8—44no—
584#127—24no—
585#127—28no—
586#127—44no—
587#127—44no—
588#124—24no—
589#124—28no—
590#124—24no—
591#124—48no—
592#124—48no—
593#124—44no—
594#124—44no—
595#124—44no—
596#124—88no—
597#123—48no—
598#123—88no—
599C22⋊Q8—48no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—88no—
603#121—216no—
604#121—216no—
605#121—44no—
606#121—44no—
607#121—48no—
608#121—44no—
609#121—44no—
610#121—48no—
611#121—88no—
612#121—88no—
613#120—216no—
614#120—48no—
615#120—48no—
616C4×Q8—44no—
617C4×Q8—44no—
618C4×Q8—44no—
619C4×D4—216no—
620C4×D4—44no—
621C4×D4—44no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—44no—
625C4×D4—48no—
626C4×D4—48no—
627C4×D4—48no—
628C4×D4—88no—
629#117—24no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—44no—
635#117—44no—
636#117—44no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4—44no—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C22⋊C4—48no—
669C2×C22⋊C4—44no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—84no—
672C2×C22⋊C4—84no—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C42—24no—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—44no—
714C2×C42—44no—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772C24—24no—
773C24—24no—
774C24—24no—
775C24—44no—
776C24—44no—
777C24C2514yes—
778C24C2512yes—
779C24C2512yes—
780C24C2512yes—
781C24C2511yescharacteristic
782#41—232no—
783#41—432no—
784#41—464no—
785#41—432no—
786#41—416no—
787#41—416no—
788C2×Q8—22no—
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—22no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—24no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—48no—
806C2×Q8—48no—
807C2×Q8—48no—
808C2×Q8—432no—
809C2×Q8—432no—
810C2×Q8—416no—
811C2×Q8—816no—
812C2×Q8C2×#4114yes—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—28no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—28no—
823C2×D4—216no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—22no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—48no—
844C2×D4—44no—
845C2×D4—48no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—48no—
852C2×D4—48no—
853C2×D4—416no—
854C2×D4C2×#4118yes—
855C2×D4C2×#4114yes—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—28no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—48no—
894C22×C4—44no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4C2×#4118yes—
899C22×C4C2×#4114yes—
900C22×C4H(5,𝔽2)14yes—
901C22×C4H(5,𝔽2)14yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2512yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C4⋊C4—24no—
923C4⋊C4—28no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—48no—
945C4⋊C4—48no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C22⋊C4—24no—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—28no—
956C22⋊C4—216no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—48no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C42—24no—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—44no—
1000C42—44no—
1001C42—44no—
1002C42—48no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—28no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—28no—
1024C23—48no—
1025C23—88no—
1026C23—84no—
1027C23—88no—
1028C23—84no—
1029C23C22×#4114yes—
1030C23C22×#4112yes—
1031C23C2×H(5,𝔽2)12yes—
1032C23C2×H(5,𝔽2)12yes—
1033C23C2611yescharacteristic
1034Q8—28no—
1035Q8—416no—
1036Q8—48no—
1037Q8—44no—
1038Q8—48no—
1039Q8—44no—
1040Q8—816no—
1041D4—216no—
1042D4—28no—
1043D4—416no—
1044D4—48no—
1045D4—48no—
1046D4—48no—
1047D4—48no—
1048D4—44no—
1049D4—44no—
1050D4—88no—
1051D4—816no—
1052D4—164no—
1053D4—164no—
1054D4—168no—
1055D4—164no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—216no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—28no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—28no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—416no—
1107C2×C4—44no—
1108C2×C4—416no—
1109C2×C4—44no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4—88no—
1119C2×C4—164no—
1120C2×C4—168no—
1121C2×C4#538116yes—
1122C2×C4C22×#4114yes—
1123C2×C4C22×#4112yes—
1124C2×C4C22×#4112yes—
1125C2×C4C2×H(5,𝔽2)12yes—
1126C2×C4C2×H(5,𝔽2)12yes—
1127C2×C4C2×H(5,𝔽2)12yes—
1128C2×C4C2×H(5,𝔽2)12yes—
1129C22—24no—
1130C22—22no—
1131C22—24no—
1132C22—22no—
1133C22—28no—
1134C22—24no—
1135C22—42no—
1136C22—44no—
1137C22—42no—
1138C22—44no—
1139C22—48no—
1140C22—44no—
1141C22—42no—
1142C22—42no—
1143C22—44no—
1144C22—44no—
1145C22—48no—
1146C22—44no—
1147C22—42no—
1148C22—44no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—44no—
1153C22—168no—
1154C22C2×#53814yes—
1155C22C23×#4111yescharacteristic
1156C22C22×H(5,𝔽2)11yescharacteristic
1157C22C22×H(5,𝔽2)11yescharacteristic
1158C22H(7,𝔽2)12yes—
1159C222−1+612yes—
1160C4—24no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—42no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—44no—
1171C4—44no—
1172C4—44no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—44no—
1177C4—42no—
1178C4C2×#53814yes—
1179C4C2×#53814yes—
1180C2—24no—
1181C2—44no—
1182C2—82no—
1183C2—82no—
1184C2—84no—
1185C2C22×#53811yescharacteristic
1186C2#6285712yes—
1187C2#6287611yescharacteristic
1188C2#6287812yes—
1189C2#6288711yescharacteristic
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. #42872C2semidirect
2. #42847C2semidirect
3. #42595C2semidirect
4. #42560C2semidirect
5. #40842C2semidirect
6. #40692C2semidirect
7. #37501C2semidirect
8. #37494C2semidirect
9. #37414C2semidirect
10. #37346C2semidirect
11. #35676C2semidirect
12. #35660C2semidirect
13. #35630C2semidirect
14. #35617C2semidirect
15. #35592C2semidirect
16. #35574C2semidirect
17. #35541C2semidirect
18. #35533C2semidirect
19. #35307C2semidirect
20. #35256C2semidirect
21. #34639C2semidirect
22. C2×#2640C2semidirect
23. #34269C2semidirect
24. #34259C2semidirect
25. #34070C2semidirect
40. #2855C22semidirect
42. #2832C22semidirect
43. #2831C22semidirect
44. #2825C22semidirect
45. #2824C22semidirect
46. #2804C22semidirect
47. #2797C22semidirect
48. #2786C22semidirect
49. #2784C22semidirect
50. #2760C22semidirect
51. #2759C22semidirect
52. #2751C22semidirect
53. #2751C22semidirect
54. #2750C22semidirect
55. #2749C22semidirect
56. #2745C22semidirect
57. #2708C22semidirect
58. #2696C22semidirect
59. #2688C22semidirect
60. #2686C22semidirect
61. #2676C22semidirect
62. #2665C22semidirect
63. #2653C22semidirect
64. #2653C22semidirect
65. #2648C22semidirect
66. #2645C22semidirect
67. #2645C22semidirect
68. #2644C22semidirect
69. #2644C22semidirect
72. #2643C22semidirect
77. #2639C22semidirect
78. #2631C22semidirect
79. #2630C22semidirect
80. #2625C22semidirect
85. #2578C22semidirect
86. #2557C22semidirect
93. #2514C22semidirect
94. #2514C22semidirect
95. #2511C22semidirect
96. #2511C22semidirect
98. #2492C22semidirect
99. #2492C22semidirect
100. #2491C22semidirect
101. #2491C22semidirect
102. #2452C22semidirect
103. #2451C22semidirect
104. #2450C22semidirect
106. #2447C22semidirect
107. #2446C22semidirect
109. #2444C22semidirect
110. #2440C22semidirect
111. #2439C22semidirect
115. #2436C22semidirect
116. #2434C22semidirect
117. #2432C22semidirect
120. #2431C22semidirect
137. #2409C22semidirect
138. #2407C22semidirect
141. #2401C22semidirect
142. #2401C22semidirect
148. Q8×C22⋊C4C22semidirect
150. #2339C22semidirect
151. #2328C22semidirect
152. #2327C22semidirect
153. #2326C22semidirect
154. #2326C22semidirect
163. #2311C22semidirect
166. #2310C22semidirect
173. #2297C22semidirect
179. C2×#391C22semidirect
182. #2290C22semidirect
183. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#428722
#428472
#425952
#425602
#408422
#406922
#375012
#374942
#374142
#373462
#356762
#356602
#356302
#356172
#355922
#355742
#355412
#355332
#353072
#352562
#346392
C2×#26402
#342692
#342592
#340702