Finite Group Databasebeta

← #8094860

Subgroups — #8094860

Order 512.

6738 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53090C214yesmaximal, complemented
2#53059C214yesmaximal, complemented
3#53000C214yesmaximal, complemented
4#52969C214yesmaximal, complemented
5#52315C218yesmaximal, complemented
6#46050C214yesmaximal, complemented
7#45992C214yesmaximal, complemented
8#45604C214yesmaximal, complemented
9#45487C214yesmaximal, complemented
10#45444C218yesmaximal, complemented
11#35541C211yesmaximal, characteristic, complemented
12#35528C211yesmaximal, characteristic, complemented
13#35528C211yesmaximal, characteristic, complemented
14#35527C211yesmaximal, characteristic, complemented
15#35527C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic, complemented
17#35274C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35266C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35168C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23C2×#2541C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#560C2218yescomplemented
28C2×#537C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic, complemented
35C2×#535C2211yescharacteristic, complemented
36C2×#532C2211yescharacteristic
37C22×#127C2211yescharacteristic
38C22×#127C2211yescharacteristic
39C22×#127C2211yescharacteristic, complemented
40C22×#121C2214yescomplemented
41C2×#518C2211yescharacteristic, complemented
42C2×C4×#41C2211yescharacteristic, complemented
43C22×C4×D4C2211yescharacteristic, complemented
44#2867C2212yescomplemented
45#2860C2214yescomplemented
46#2858C2212yescomplemented
47#2856C2214yescomplemented
48#2856C2212yescomplemented
49#2850C2212yescomplemented
50#2849C2214yescomplemented
51#2847C2214yescomplemented
52#2828C2218yescomplemented
53#2828C2218yescomplemented
54#2825C2218yescomplemented
55#2825C2218yescomplemented
56#2818C2218yescomplemented
57#2815C2218yescomplemented
58#2815C2218yescomplemented
59#2815C2218yescomplemented
60#2813C2218yescomplemented
61#2812C2218yescomplemented
62#2797C2218yescomplemented
63#2749C2218yescomplemented
64#2714C2218yescomplemented
65#2714C2218yescomplemented
66#2703C2218yescomplemented
67#2699C2218yescomplemented
68#2691C2218yescomplemented
69#2688C2218yescomplemented
70#2688C2218yescomplemented
71#2688C2218yescomplemented
72#2678C2218yescomplemented
73#2678C2218yescomplemented
74#2675C2218yescomplemented
75#2673C2218yescomplemented
76#2673C2218yescomplemented
77#2673C2218yescomplemented
78#2669C2218yescomplemented
79#2669C2218yescomplemented
80#2669C2218yescomplemented
81#2668C2218yescomplemented
82#2657C2212yescomplemented
83#2657C2212yescomplemented
84#2644C2214yescomplemented
85#2622C2214yescomplemented
86#2620C2212yescomplemented
87#2619C2214yescomplemented
88#2619C2212yescomplemented
89#2617C2214yescomplemented
90#2548C2214yescomplemented
91#2544C2214yescomplemented
92#2544C2214yescomplemented
93#2541C2214yescomplemented
94#2541C2214yescomplemented
95#2541C2214yescomplemented
96#2541C2214yescomplemented
97#2541C2214yescomplemented
98#2541C2214yescomplemented
99#2541C2214yescomplemented
100#2541C2214yescomplemented
101#2541C2214yescomplemented
102#2514C2212yescomplemented
103#2513C2212yescomplemented
104#2513C2214yescomplemented
105#2512C2212yescomplemented
106#2512C2214yescomplemented
107#2511C2212yescomplemented
108#2510C2214yescomplemented
109#2481C2214yescomplemented
110#2480C2218yescomplemented
111#2448C2212yescomplemented
112#2447C2214yescomplemented
113#2447C2212yescomplemented
114#2447C2214yescomplemented
115#2446C2212yescomplemented
116#2445C2214yescomplemented
117#2445C2214yescomplemented
118#2445C2212yescomplemented
119#2444C2214yescomplemented
120#2443C2214yescomplemented
121#2435C2212yescomplemented
122#2433C2214yescomplemented
123#2433C2214yescomplemented
124#2433C2218yescomplemented
125#2433C2212yescomplemented
126#2433C2212yescomplemented
127#2433C2214yescomplemented
128#2433C2212yescomplemented
129#2432C2212yescomplemented
130#2431C2212yescomplemented
131#2431C2214yescomplemented
132#2431C2212yescomplemented
133#2431C2212yescomplemented
134#2431C2214yescomplemented
135#2431C2214yescomplemented
136#2428C2214yescomplemented
137#2428C2214yescomplemented
138#2428C2214yescomplemented
139#2428C2214yescomplemented
140#2428C2214yescomplemented
141#2428C2214yescomplemented
142#2428C2214yescomplemented
143#2427C2214yescomplemented
144#2427C2214yescomplemented
145#2426C2214yescomplemented
146#2424C2218yescomplemented
147#2422C2214yescomplemented
148#2422C2214yescomplemented
149#2420C2214yescomplemented
150#2420C2214yescomplemented
151#2412C2218yescomplemented
152#2410C2218yes—
153#2410C2214yescomplemented
154#2410C2218yescomplemented
155#2410C2214yescomplemented
156#2408C2218yescomplemented
157#2408C2214yescomplemented
158#2407C2214yescomplemented
159#2403C2214yes—
160#2403C2218yes—
161#2403C2214yes—
162#2401C2214yescomplemented
163#2395C2214yescomplemented
164C2×#392C2214yescomplemented
165#2377C2218yescomplemented
166#2317C2211yescharacteristic, complemented
167#2316C2211yescharacteristic, complemented
168#2311C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic
171#2309C2211yescharacteristic, complemented
172C4×#126C2214yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2211yescharacteristic, complemented
180#2296C2211yescharacteristic, complemented
181#2296C2211yescharacteristic, complemented
182C2×#390C2211yescharacteristic
183C2×#390C2211yescharacteristic, complemented
184#2285C2211yescharacteristic, complemented
185C4×#117C2211yescharacteristic, complemented
186C2×C4×C4⋊C4C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—44no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×D4C2311yescharacteristic
196C23×D4C2311yescharacteristic
197C23×D4C2311yescharacteristic
198C23×D4C2314yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201C23×D4C2312yes—
202C23×D4C2314yes—
203C23×D4C2314yes—
204C23×D4C2312yes—
205C24×C4C2312yes—
206#560—432no—
207#537—44no—
208#535—44no—
209#535—44no—
210#535—44no—
211#535—44no—
212#535—44no—
213#535—44no—
214#535—44no—
215#532—44no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127—44no—
218C2×#127—44no—
219C2×#127—44no—
220C2×#127C2318yes—
221C2×#127C2312yes—
222C2×#127C2312yes—
223C2×#127C2312yes—
224C2×#127C2311yescharacteristic
225C2×#127C2312yes—
226C2×#127C2312yes—
227C2×#127C2312yes—
228C2×#127C2312yes—
229C2×#127C2312yes—
230C2×#127C2312yes—
231C2×#127C2314yes—
232C2×#127C2314yes—
233C2×#127C2314yes—
234C2×#127C2314yes—
235C2×#127C2312yes—
236C2×#127C2312yes—
237C2×#127C2318yes—
238C2×#126C2314yes—
239C2×#126C2318yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#123C2314yes—
250C2×#123C2318yes—
251C2×#123C2318yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×#121—416no—
255C2×#121C2318yes—
256C2×#121C2314yes—
257C2×#121C2318yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#121C2318yes—
264C2×#121C2318yes—
265C2×#121C2318yes—
266C2×#121C2318yes—
267C2×#121C2318yes—
268C2×#121C2314yes—
269C2×#121C2318yes—
270C2×#121C2318yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2318yes—
278C2×#121C2318yes—
279C2×#121C2318yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2318yes—
286C2×#120C2318yes—
287C2×#120C2314yes—
288C2×#120C2318yes—
289C2×#120C2314yes—
290C2×#120C2318yes—
291C2×#120C2318yes—
292#518—44no—
293C4×#41—44no—
294C2×C4×Q8C2312yes—
295C2×C4×D4—44no—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2314yes—
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319#401C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#399C2314yes—
325#398C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2318yes—
334#397C2318yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2314yes—
343#394C2314yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2314yes—
360#394C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#392C2318yes—
373#392C2318yes—
374#392C2318yes—
375#392C2318yes—
376#392C2318yes—
377#392C2318yes—
378#392C2318yes—
379#392C2318yes—
380#392C2318yes—
381#392C2318yes—
382#392C2318yes—
383#392C2318yes—
384#392C2318yes—
385#392C2318yes—
386#392C2318yes—
387#391C2312yes—
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2312yes—
399#390C2312yes—
400#390C2314yes—
401#390C2314yes—
402#390C2312yes—
403#390C2318yes—
404#390C2318yes—
405#390C2312yes—
406#390C2311yescharacteristic
407#390C2318yes—
408#390C2318yes—
409#390C2318yes—
410#390C2312yes—
411#390C2311yescharacteristic
412#390C2312yes—
413#390C2312yes—
414#390C2314yes—
415#390C2312yes—
416#390C2314yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#386C2314yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2312yes—
450#386C2312yes—
451#386C2318yes—
452#386C2318yes—
453#386C2312yes—
454#386C2318yes—
455#386C2318yes—
456#386C2312yes—
457#386C2312yes—
458#386C2312yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2318yes—
463#386C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#385C2314yes—
468#385C2312yes—
469#385C2318yes—
470#385C2312yes—
471#385C2318yes—
472#385C2318yes—
473#385C2314yes—
474#385C2314yes—
475#384C2312yes—
476#384C2312yes—
477#383C2314yes—
478#382C2312yes—
479#382C2312yes—
480#381C2318yes—
481#381C2318yes—
482#381C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2318yes—
486#380C2314yes—
487#379C2314yes—
488#379C2314yes—
489#379C2314yes—
490#379C2318yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509#376C2312yes—
510C2×#95C2312yes—
511C43C2312yes—
512C25C2412yes—
513C25C2412yes—
514C25C2412yes—
515C25C2414yes—
516H(5,𝔽2)—464no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—24no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—44no—
547C22×D4—44no—
548C22×D4—44no—
549C22×D4—44no—
550C22×D4—48no—
551C22×D4—48no—
552C22×D4—48no—
553C22×D4—44no—
554C22×D4—44no—
555C22×D4—48no—
556C22×D4—48no—
557C22×D4—48no—
558C22×D4—48no—
559C22×D4—48no—
560C22×D4—84no—
561C22×D4—84no—
562C22×D4—84no—
563C22×D4C2412yes—
564C22×D4C2412yes—
565C22×D4C2412yes—
566C22×D4C2412yes—
567C22×D4C2412yes—
568C22×D4C2411yescharacteristic
569C22×D4C2412yes—
570C22×D4C2412yes—
571C22×D4C2412yes—
572C22×D4C2411yescharacteristic
573C22×D4C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2414yes—
576C22×D4C2418yes—
577C22×D4C2418yes—
578C22×D4C2418yes—
579C22×D4C2418yes—
580C22×D4C2418yes—
581C22×D4C2414yes—
582C22×D4C2418yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2418yes—
586C22×D4C2414yes—
587C22×D4C2418yes—
588C22×D4C2414yes—
589C22×D4C2418yes—
590C22×D4C2418yes—
591C22×D4C2418yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C23×C4—48no—
595C23×C4—44no—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C23×C4C2414yes—
605C23×C4C2418yes—
606C23×C4C2418yes—
607C23×C4C2414yes—
608C23×C4C2411yescharacteristic
609C4⋊Q8—42no—
610#127—44no—
611#127—44no—
612#127—48no—
613#127—48no—
614#127—48no—
615#127—48no—
616#127—44no—
617#127—44no—
618#127—42no—
619#127—44no—
620#127—44no—
621#127—44no—
622#127—44no—
623#127—44no—
624#127—44no—
625#127—44no—
626#127—416no—
627#127—88no—
628#126—216no—
629#126—416no—
630#124—42no—
631#124—42no—
632#124—44no—
633#124—44no—
634#124—44no—
635#124—44no—
636#124—44no—
637#124—44no—
638#124—44no—
639#123—216no—
640#123—416no—
641#123—416no—
642C22⋊Q8—44no—
643C22⋊Q8—44no—
644#121—232no—
645#121—416no—
646#121—416no—
647#121—416no—
648#121—416no—
649#121—416no—
650#121—416no—
651#121—416no—
652#121—48no—
653#121—48no—
654#121—48no—
655#121—48no—
656#121—44no—
657#121—44no—
658#121—44no—
659#121—48no—
660#121—44no—
661#121—44no—
662#121—44no—
663#121—416no—
664#121—48no—
665#121—48no—
666#121—88no—
667#121—88no—
668#121—88no—
669#120—416no—
670#120—416no—
671#120—416no—
672#120—48no—
673#120—48no—
674#120—48no—
675#120—48no—
676#120—48no—
677#120—48no—
678#120—48no—
679#120—88no—
680#120—88no—
681C4×Q8—44no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—44no—
685C4×D4—48no—
686C4×D4—48no—
687C4×D4—48no—
688C4×D4—48no—
689#117—24no—
690#117—24no—
691#117—24no—
692#117—24no—
693#117—24no—
694#117—44no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—28no—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2418yes—
718C2×C4⋊C4C2418yes—
719C2×C4⋊C4C2412yes—
720C2×C22⋊C4—48no—
721C2×C22⋊C4—48no—
722C2×C22⋊C4—48no—
723C2×C22⋊C4—44no—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2418yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2418yes—
768C2×C42—24no—
769C2×C42—24no—
770C2×C42—24no—
771C2×C42—44no—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2414yes—
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2414yes—
787C2×C42C2414yes—
788#95C2412yes—
789#95C2412yes—
790#95C2412yes—
791#95C2412yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815C24—24no—
816C24—24no—
817C24—24no—
818C24—24no—
819C24—24no—
820C24—24no—
821C24—24no—
822C24—24no—
823C24—24no—
824C24—44no—
825C24—44no—
826C24—44no—
827C24—44no—
828C24—44no—
829C24—44no—
830C24—44no—
831C24—44no—
832C24—44no—
833C24—48no—
834C24—48no—
835C24C2512yes—
836C24C2512yes—
837C24C2514yes—
838C24C2514yes—
839C24C2514yes—
840C24C2512yes—
841C24C2511yescharacteristic
842#41—432no—
843#41—432no—
844#41—416no—
845#41—416no—
846#41—416no—
847C2×Q8—22no—
848C2×Q8—22no—
849C2×Q8—22no—
850C2×Q8—22no—
851C2×Q8—22no—
852C2×Q8—22no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×Q8—22no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—24no—
871C2×D4—24no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—22no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—24no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—22no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—28no—
893C2×D4—216no—
894C2×D4—216no—
895C2×D4—216no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—48no—
904C2×D4—48no—
905C2×D4—48no—
906C2×D4—48no—
907C2×D4—48no—
908C2×D4—48no—
909C2×D4—48no—
910C2×D4—48no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—48no—
914C2×D4—48no—
915C2×D4—48no—
916C2×D4—48no—
917C2×D4—44no—
918C2×D4—48no—
919C2×D4—48no—
920C2×D4—48no—
921C2×D4—48no—
922C2×D4—48no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—44no—
927C2×D4—48no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—48no—
933C2×D4—48no—
934C2×D4—48no—
935C2×D4—48no—
936C2×D4—48no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—464no—
945C2×D4—432no—
946C2×D4—432no—
947C2×D4—416no—
948C2×D4—416no—
949C2×D4—416no—
950C2×D4—816no—
951C2×D4—832no—
952C2×D4—832no—
953C2×D4—816no—
954C22×C4—22no—
955C22×C4—24no—
956C22×C4—22no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—216no—
972C22×C4—28no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—48no—
982C22×C4—48no—
983C22×C4—44no—
984C22×C4—48no—
985C22×C4—48no—
986C22×C4—48no—
987C22×C4—816no—
988C22×C4H(5,𝔽2)14yes—
989C22×C4H(5,𝔽2)14yes—
990C22×C4H(5,𝔽2)14yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—24no—
1019C4⋊C4—22no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4H(5,𝔽2)18yescomplemented
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—216no—
1038C22⋊C4—216no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—48no—
1060C22⋊C4—44no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C22⋊C4—48no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—48no—
1069C22⋊C4—48no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C42—22no—
1077C42—22no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—24no—
1082C42—22no—
1083C42—22no—
1084C42—24no—
1085C42—24no—
1086C42—24no—
1087C42—24no—
1088C42—24no—
1089C42—28no—
1090C42—44no—
1091C42—44no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—28no—
1097C23—28no—
1098C23—24no—
1099C23—22no—
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—28no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—28no—
1120C23—24no—
1121C23—24no—
1122C23—28no—
1123C23—28no—
1124C23—416no—
1125C23—416no—
1126C23—48no—
1127C23—48no—
1128C23—48no—
1129C23—84no—
1130C23—84no—
1131C23—88no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23—88no—
1137C23—88no—
1138C23—88no—
1139C23—88no—
1140C23—164no—
1141C23—164no—
1142C23—168no—
1143C23—168no—
1144C23C2×H(5,𝔽2)12yes—
1145C23C2×H(5,𝔽2)12yes—
1146C23C2×H(5,𝔽2)12yes—
1147C23C2611yescharacteristic
1148Q8—44no—
1149Q8—44no—
1150Q8—44no—
1151D4—416no—
1152D4—416no—
1153D4—48no—
1154D4—48no—
1155D4—48no—
1156D4—48no—
1157D4—48no—
1158D4—48no—
1159D4—48no—
1160D4—48no—
1161D4—44no—
1162D4—48no—
1163D4—44no—
1164D4—44no—
1165D4—88no—
1166D4—816no—
1167D4—816no—
1168D4—816no—
1169D4—816no—
1170D4—816no—
1171D4—816no—
1172D4—164no—
1173D4—164no—
1174D4—164no—
1175D4—164no—
1176D4—164no—
1177D4—168no—
1178D4—168no—
1179D4—168no—
1180D4—168no—
1181D4—168no—
1182C2×C4—28no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—28no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—48no—
1226C2×C4—48no—
1227C2×C4—44no—
1228C2×C4—416no—
1229C2×C4—48no—
1230C2×C4—48no—
1231C2×C4—48no—
1232C2×C4—88no—
1233C2×C4—816no—
1234C2×C4—84no—
1235C2×C4—168no—
1236C2×C4#560116yescomplemented
1237C2×C4C2×H(5,𝔽2)14yes—
1238C2×C4C2×H(5,𝔽2)14yes—
1239C2×C4C2×H(5,𝔽2)14yes—
1240C2×C4C2×H(5,𝔽2)12yes—
1241C2×C4C2×H(5,𝔽2)12yes—
1242C2×C4C2×H(5,𝔽2)12yes—
1243C2×C4C2×H(5,𝔽2)12yes—
1244C2×C4C2×H(5,𝔽2)12yes—
1245C2×C4C2×H(5,𝔽2)12yes—
1246C22—22no—
1247C22—22no—
1248C22—24no—
1249C22—24no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—48no—
1264C22—48no—
1265C22—48no—
1266C22—44no—
1267C22—44no—
1268C22—48no—
1269C22—44no—
1270C22—48no—
1271C22—44no—
1272C22—44no—
1273C22—48no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—816no—
1281C22—168no—
1282C22—168no—
1283C22—1616no—
1284C22C2×#56014yes—
1285C22C22×H(5,𝔽2)11yescharacteristic
1286C22C22×H(5,𝔽2)12yes—
1287C22C22×H(5,𝔽2)11yescharacteristic
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22H(7,𝔽2)12yes—
1290C4—24no—
1291C4—24no—
1292C4—24no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—44no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4C2×#56014yes—
1307C4C2×#56014yes—
1308C2—24no—
1309C2—82no—
1310C2—84no—
1311C2—84no—
1312C2—84no—
1313C2—82no—
1314C2—82no—
1315C2C22×#56011yescharacteristic
1316C2#6283211yescharacteristic
1317C2#6287611yescharacteristic
1318C2#6291212yes—
1319C2#6291612yes—
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. #53090C2semidirect
2. #53059C2semidirect
3. #53000C2semidirect
4. #52969C2semidirect
5. #52315C2semidirect
6. #46050C2semidirect
7. #45992C2semidirect
8. #45604C2semidirect
9. #45487C2semidirect
10. #45444C2semidirect
11. #35541C2semidirect
12. #35528C2semidirect
13. #35528C2semidirect
14. #35527C2semidirect
15. #35527C2semidirect
16. #35513C2semidirect
17. #35274C2semidirect
18. #35272C2semidirect
19. #35266C2semidirect
20. #35256C2semidirect
21. #35168C2semidirect
22. #35152C2semidirect
23. C2×#2541C2semidirect
24. #34816C2semidirect
25. #34744C2semidirect
27. C2×#560C22semidirect
34. C2×#535C22semidirect
35. C2×#535C22semidirect
39. C22×#127C22semidirect
40. C22×#121C22semidirect
41. C2×#518C22semidirect
42. C2×C4×#41C22semidirect
43. C22×C4×D4C22semidirect
44. #2867C22semidirect
45. #2860C22semidirect
46. #2858C22semidirect
47. #2856C22semidirect
48. #2856C22semidirect
49. #2850C22semidirect
50. #2849C22semidirect
51. #2847C22semidirect
52. #2828C22semidirect
53. #2828C22semidirect
54. #2825C22semidirect
55. #2825C22semidirect
56. #2818C22semidirect
57. #2815C22semidirect
58. #2815C22semidirect
59. #2815C22semidirect
60. #2813C22semidirect
61. #2812C22semidirect
62. #2797C22semidirect
63. #2749C22semidirect
64. #2714C22semidirect
65. #2714C22semidirect
66. #2703C22semidirect
67. #2699C22semidirect
68. #2691C22semidirect
69. #2688C22semidirect
70. #2688C22semidirect
71. #2688C22semidirect
72. #2678C22semidirect
73. #2678C22semidirect
74. #2675C22semidirect
75. #2673C22semidirect
76. #2673C22semidirect
77. #2673C22semidirect
78. #2669C22semidirect
79. #2669C22semidirect
80. #2669C22semidirect
81. #2668C22semidirect
82. #2657C22semidirect
83. #2657C22semidirect
84. #2644C22semidirect
85. #2622C22semidirect
86. #2620C22semidirect
87. #2619C22semidirect
88. #2619C22semidirect
89. #2617C22semidirect
90. #2548C22semidirect
91. #2544C22semidirect
92. #2544C22semidirect
93. #2541C22semidirect
94. #2541C22semidirect
95. #2541C22semidirect
96. #2541C22semidirect
97. #2541C22semidirect
98. #2541C22semidirect
99. #2541C22semidirect
100. #2541C22semidirect
101. #2541C22semidirect
102. #2514C22semidirect
103. #2513C22semidirect
104. #2513C22semidirect
105. #2512C22semidirect
106. #2512C22semidirect
107. #2511C22semidirect
108. #2510C22semidirect
109. #2481C22semidirect
110. #2480C22semidirect
111. #2448C22semidirect
112. #2447C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2446C22semidirect
116. #2445C22semidirect
117. #2445C22semidirect
118. #2445C22semidirect
119. #2444C22semidirect
120. #2443C22semidirect
121. #2435C22semidirect
122. #2433C22semidirect
123. #2433C22semidirect
124. #2433C22semidirect
125. #2433C22semidirect
126. #2433C22semidirect
127. #2433C22semidirect
128. #2433C22semidirect
129. #2432C22semidirect
130. #2431C22semidirect
131. #2431C22semidirect
132. #2431C22semidirect
133. #2431C22semidirect
134. #2431C22semidirect
135. #2431C22semidirect
136. #2428C22semidirect
137. #2428C22semidirect
138. #2428C22semidirect
139. #2428C22semidirect
140. #2428C22semidirect
141. #2428C22semidirect
142. #2428C22semidirect
143. #2427C22semidirect
144. #2427C22semidirect
145. #2426C22semidirect
146. #2424C22semidirect
147. #2422C22semidirect
148. #2422C22semidirect
149. #2420C22semidirect
150. #2420C22semidirect
151. #2412C22semidirect
153. #2410C22semidirect
154. #2410C22semidirect
155. #2410C22semidirect
156. #2408C22semidirect
157. #2408C22semidirect
158. #2407C22semidirect
162. #2401C22semidirect
163. #2395C22semidirect
164. C2×#392C22semidirect
165. #2377C22semidirect
166. #2317C22semidirect
167. #2316C22semidirect
171. #2309C22semidirect
172. C4×#126C22semidirect
173. C4×#123C22semidirect
179. #2297C22semidirect
180. #2296C22semidirect
181. #2296C22semidirect
183. C2×#390C22semidirect
184. #2285C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C4⋊C4C22semidirect
1031. C4⋊C4H(5,𝔽2)semidirect
1236. C2×C4#560semidirect

Maximal subgroups

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

subgroupindex
#530902
#530592
#530002
#529692
#523152
#460502
#459922
#456042
#454872
#454442
#355412
#355282
#355272
#355132
#352742
#352722
#352662
#352562
#351682
#351522
C2×#25412
#348162
#347442