Finite Group Databasebeta

← #8095565

Subgroups — #8095565

Order 512.

5510 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53087C214yesmaximal, complemented
2#53047C214yesmaximal, complemented
3#53043C214yesmaximal, complemented
4#53018C214yesmaximal, complemented
5#52347C218yesmaximal, complemented
6#46061C214yesmaximal, complemented
7#46020C214yesmaximal, complemented
8#45697C214yesmaximal, complemented
9#45628C214yesmaximal, complemented
10#45588C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35616C211yesmaximal, characteristic, complemented
15#35616C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic
17#35327C211yesmaximal, characteristic, complemented
18#35317C211yesmaximal, characteristic, complemented
19#35308C211yesmaximal, characteristic, complemented
20#35266C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic, complemented
22#35153C211yesmaximal, characteristic, complemented
23C2×#2545C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic, complemented
33C2×#536C2211yescharacteristic, complemented
34C2×#535C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic, complemented
37C22×#124C2211yescharacteristic
38C22×#124C2211yescharacteristic
39C2×#519C2211yescharacteristic, complemented
40C2×C4×#41C2211yescharacteristic, complemented
41C22×C4×Q8C2211yescharacteristic, complemented
42#2868C2212yescomplemented
43#2860C2214yescomplemented
44#2858C2212yescomplemented
45#2857C2212yescomplemented
46#2854C2214yescomplemented
47#2853C2214yescomplemented
48#2850C2214yescomplemented
49#2850C2212yescomplemented
50#2842C2218yescomplemented
51#2837C2218yescomplemented
52#2837C2218yescomplemented
53#2837C2218yescomplemented
54#2829C2218yescomplemented
55#2829C2218yescomplemented
56#2829C2218yescomplemented
57#2827C2218yescomplemented
58#2826C2218yescomplemented
59#2823C2218yescomplemented
60#2803C2218yescomplemented
61#2801C2218yescomplemented
62#2796C2218yescomplemented
63#2795C2218yescomplemented
64#2795C2218yescomplemented
65#2795C2218yescomplemented
66#2790C2218yescomplemented
67#2790C2218yescomplemented
68#2790C2218yescomplemented
69#2780C2218yescomplemented
70#2756C2218yescomplemented
71#2752C2218yescomplemented
72#2746C2218yescomplemented
73#2735C2218yescomplemented
74#2735C2218yescomplemented
75#2735C2218yescomplemented
76#2705C2218yescomplemented
77#2697C2218yescomplemented
78#2685C2218yescomplemented
79#2685C2218yescomplemented
80#2658C2212yescomplemented
81#2658C2212yescomplemented
82#2644C2214yescomplemented
83#2623C2214yescomplemented
84#2621C2212yescomplemented
85#2620C2212yescomplemented
86#2620C2214yescomplemented
87#2618C2214yescomplemented
88#2548C2214yescomplemented
89#2546C2214yescomplemented
90#2545C2214yescomplemented
91#2545C2214yescomplemented
92#2545C2214yescomplemented
93#2545C2214yescomplemented
94#2545C2214yescomplemented
95#2545C2214yescomplemented
96#2545C2214yescomplemented
97#2544C2214yescomplemented
98#2542C2214yescomplemented
99#2542C2214yescomplemented
100#2534C2218yescomplemented
101#2514C2212yescomplemented
102#2513C2212yescomplemented
103#2513C2214yescomplemented
104#2512C2212yescomplemented
105#2512C2214yescomplemented
106#2511C2212yescomplemented
107#2510C2214yescomplemented
108#2501C2218yescomplemented
109#2498C2218yescomplemented
110#2481C2214yescomplemented
111#2480C2218yescomplemented
112#2448C2212yescomplemented
113#2448C2214yescomplemented
114#2448C2214yescomplemented
115#2447C2212yescomplemented
116#2446C2214yescomplemented
117#2446C2214yescomplemented
118#2446C2212yescomplemented
119#2445C2212yescomplemented
120#2444C2214yescomplemented
121#2443C2214yescomplemented
122#2435C2212yes—
123#2435C2214yes—
124#2435C2214yes—
125#2435C2214yes—
126#2435C2212yes—
127#2435C2212yes—
128#2433C2212yes—
129#2432C2212yes—
130#2432C2214yes—
131#2432C2212yes—
132#2432C2214yes—
133#2432C2214yes—
134#2432C2212yes—
135#2431C2212yes—
136#2429C2214yescomplemented
137#2429C2214yescomplemented
138#2429C2214yescomplemented
139#2429C2214yescomplemented
140#2429C2214yescomplemented
141#2427C2214yescomplemented
142#2426C2214yescomplemented
143#2426C2214yescomplemented
144#2426C2214yescomplemented
145#2426C2214yescomplemented
146#2425C2218yescomplemented
147#2423C2214yescomplemented
148#2423C2214yescomplemented
149#2421C2214yescomplemented
150#2421C2214yescomplemented
151#2413C2218yescomplemented
152#2411C2214yescomplemented
153#2411C2214yescomplemented
154#2410C2218yes—
155#2408C2214yes—
156#2407C2214yes—
157#2405C2214yes—
158#2405C2218yes—
159#2405C2214yes—
160#2401C2214yescomplemented
161#2395C2214yescomplemented
162C2×#396C2214yescomplemented
163#2383C2218yescomplemented
164#2375C2218yescomplemented
165#2317C2211yescharacteristic, complemented
166#2316C2211yescharacteristic, complemented
167#2311C2211yescharacteristic
168#2310C2211yescharacteristic, complemented
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic
171C4×#126C2214yescomplemented
172C4×#123C2214yescomplemented
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic, complemented
179#2296C2211yescharacteristic, complemented
180#2296C2211yescharacteristic, complemented
181C2×#391C2211yescharacteristic, complemented
182C2×#390C2211yescharacteristic
183C2×#388C2214yescomplemented
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×Q8C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×D4C2311yescharacteristic
198C23×D4C2314yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201#537—44no—
202#536—44no—
203#536—44no—
204#536—44no—
205#536—44no—
206#536—44no—
207#536—44no—
208#535—44no—
209#532—44no—
210C2×C4⋊Q8—44no—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×#127C2311yescharacteristic
222C2×#127C2312yes—
223C2×#126C2314yes—
224C2×#126C2318yes—
225C2×#124—44no—
226C2×#124—44no—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×#121C2314yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#120C2318yes—
264C2×#120C2314yes—
265#519—44no—
266C4×#41—44no—
267C2×C4×Q8—44no—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2312yes—
282C2×#117C2314yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2314yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2312yes—
295C22×C42C2312yes—
296#401C2314yes—
297#400C2318yes—
298#400C2318yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#399C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2314yes—
307#399C2318yes—
308#399C2318yes—
309#399C2318yes—
310#398C2314yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#397C2314yes—
318#397C2318yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2314yes—
323#397C2314yes—
324#397C2318yes—
325#397C2318yes—
326#397C2314yes—
327#397C2318yes—
328#397C2314yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2314yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2314yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2314yes—
362#392C2318yes—
363#392C2318yes—
364#391C2314yes—
365#391C2314yes—
366#391C2312yes—
367#391C2312yes—
368#391C2311yescharacteristic
369#391C2312yes—
370#391C2311yescharacteristic
371#391C2312yes—
372#391C2314yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2318yes—
384#390C2318yes—
385#390C2318yes—
386#390C2311yescharacteristic
387#390C2318yes—
388#390C2312yes—
389#390C2311yescharacteristic
390#390C2318yes—
391#390C2312yes—
392#390C2314yes—
393#390C2312yes—
394#390C2312yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2318yes—
402#389C2318yes—
403#389C2318yes—
404#389C2312yes—
405#389C2318yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2314yes—
433#388C2318yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2314yes—
441#387C2318yes—
442#387C2314yes—
443#386C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2312yes—
449#386C2312yes—
450#386C2312yes—
451#386C2312yes—
452#386C2312yes—
453#386C2312yes—
454#386C2314yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2312yes—
463#385C2312yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#384C2318yes—
469#384C2312yes—
470#384C2318yes—
471#384C2312yes—
472#383C2314yes—
473#382C2312yes—
474#382C2312yes—
475#381C2314yes—
476#381C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2318yes—
480#380C2314yes—
481#379C2314yes—
482#379C2314yes—
483#379C2318yes—
484#379C2318yes—
485#379C2318yes—
486#379C2318yes—
487#379C2318yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506#376C2312yes—
507C2×#95C2314yes—
508C2×#95C2312yes—
509C43C2312yes—
510C25C2412yes—
511C25C2414yes—
512H(5,𝔽2)—464no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
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×D4C2412yes—
554C22×D4C2411yescharacteristic
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2412yes—
560C22×D4C2411yescharacteristic
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2418yes—
564C22×D4C2414yes—
565C22×D4C2414yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2411yescharacteristic
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2411yescharacteristic
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2411yescharacteristic
579C4⋊Q8—48no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582C4⋊Q8—42no—
583C4⋊Q8—44no—
584C4⋊Q8—44no—
585C4⋊Q8—44no—
586C4⋊Q8—44no—
587C4⋊Q8—44no—
588C4⋊Q8—44no—
589#127—42no—
590#127—44no—
591#126—416no—
592#126—48no—
593#124—44no—
594#124—44no—
595#124—48no—
596#124—48no—
597#124—48no—
598#124—42no—
599#124—42no—
600#124—44no—
601#124—44no—
602#124—44no—
603#124—44no—
604#124—44no—
605#124—44no—
606#124—44no—
607#123—48no—
608#123—48no—
609#123—48no—
610#123—48no—
611#123—48no—
612#123—48no—
613#123—48no—
614C22⋊Q8—48no—
615C22⋊Q8—48no—
616C22⋊Q8—48no—
617C22⋊Q8—44no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620C22⋊Q8—48no—
621C22⋊Q8—44no—
622C22⋊Q8—44no—
623C22⋊Q8—44no—
624#121—48no—
625#121—44no—
626#121—44no—
627#121—48no—
628#121—48no—
629#120—416no—
630#120—48no—
631C4×Q8—48no—
632C4×Q8—48no—
633C4×Q8—44no—
634C4×Q8—48no—
635C4×Q8—48no—
636C4×D4—44no—
637C4×D4—48no—
638C4×D4—48no—
639#117—24no—
640#117—24no—
641#117—24no—
642#117—24no—
643#117—24no—
644#117—44no—
645#117—48no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—44no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—48no—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C22⋊C4—48no—
686C2×C22⋊C4—44no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—48no—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C42—24no—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—44no—
735C2×C42—44no—
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2414yes—
749C2×C42C2411yescharacteristic
750C2×C42C2418yes—
751C2×C42C2414yes—
752C2×C42C2418yes—
753C2×C42C2414yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24—24no—
786C24—24no—
787C24—24no—
788C24—44no—
789C24—44no—
790C24—44no—
791C24—44no—
792C24—44no—
793C24—48no—
794C24—48no—
795C24C2512yes—
796C24C2512yes—
797C24C2514yes—
798C24C2512yes—
799C24C2511yescharacteristic
800#41—432no—
801#41—432no—
802#41—416no—
803#41—416no—
804#41—416no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—22no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—22no—
815C2×Q8—22no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—24no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—22no—
824C2×Q8—22no—
825C2×Q8—22no—
826C2×Q8—416no—
827C2×Q8—416no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—28no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—464no—
867C2×D4—432no—
868C2×D4—432no—
869C2×D4—416no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—42no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—42no—
903C22×C4H(5,𝔽2)14yes—
904C22×C4H(5,𝔽2)14yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—28no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—48no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—48no—
950C4⋊C4—48no—
951C4⋊C4—44no—
952C4⋊C4—48no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—48no—
957C4⋊C4—48no—
958C4⋊C4—48no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—216no—
967C22⋊C4—28no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—44no—
991C22⋊C4—48no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C42—22no—
1004C42—22no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—22no—
1010C42—22no—
1011C42—24no—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—24no—
1016C42—28no—
1017C42—44no—
1018C42—48no—
1019C42—44no—
1020C42—48no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—24no—
1035C23—28no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—28no—
1041C23—24no—
1042C23—24no—
1043C23—416no—
1044C23—48no—
1045C23—84no—
1046C23—84no—
1047C23—88no—
1048C23—88no—
1049C23—164no—
1050C23—164no—
1051C23—168no—
1052C23—168no—
1053C23C2×H(5,𝔽2)12yes—
1054C23C2×H(5,𝔽2)12yes—
1055C23C2×H(5,𝔽2)12yes—
1056C23C2611yescharacteristic
1057Q8—48no—
1058Q8—48no—
1059Q8—48no—
1060Q8—48no—
1061Q8—44no—
1062Q8—44no—
1063Q8—44no—
1064D4—416no—
1065D4—416no—
1066D4—48no—
1067D4—48no—
1068D4—48no—
1069D4—48no—
1070D4—44no—
1071D4—48no—
1072D4—44no—
1073D4—44no—
1074D4—88no—
1075D4—164no—
1076D4—168no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—48no—
1128C2×C4—44no—
1129C2×C4—44no—
1130C2×C4—416no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—48no—
1135C2×C4—48no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—88no—
1139C2×C4#560116yes—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×H(5,𝔽2)12yes—
1142C2×C4C2×H(5,𝔽2)12yes—
1143C2×C4C2×H(5,𝔽2)12yes—
1144C2×C4C2×H(5,𝔽2)12yes—
1145C2×C4C2×H(5,𝔽2)12yes—
1146C2×C4#58514yes—
1147C22—22no—
1148C22—22no—
1149C22—24no—
1150C22—24no—
1151C22—42no—
1152C22—42no—
1153C22—44no—
1154C22—42no—
1155C22—42no—
1156C22—44no—
1157C22—42no—
1158C22—42no—
1159C22—44no—
1160C22—48no—
1161C22—44no—
1162C22—44no—
1163C22—44no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—44no—
1168C22—44no—
1169C22—48no—
1170C22—44no—
1171C22—168no—
1172C22—1616no—
1173C22C2×#56014yes—
1174C22C22×H(5,𝔽2)11yescharacteristic
1175C22C22×H(5,𝔽2)11yescharacteristic
1176C22C22×H(5,𝔽2)11yescharacteristic
1177C22C2×#58512yes—
1178C222−1+612yes—
1179C4—24no—
1180C4—42no—
1181C4—42no—
1182C4—44no—
1183C4—42no—
1184C4—42no—
1185C4—44no—
1186C4—44no—
1187C4—44no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—44no—
1192C4—44no—
1193C4—42no—
1194C4—42no—
1195C4—44no—
1196C4—42no—
1197C4C2×#56014yes—
1198C4C2×#56014yes—
1199C2—24no—
1200C2—82no—
1201C2—82no—
1202C2—84no—
1203C2—82no—
1204C2C22×#56011yescharacteristic
1205C2#6283611yescharacteristic
1206C2#6288711yescharacteristic
1207C2#6293112yes—
1208C2#6295412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35513C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53087C2semidirect
2. #53047C2semidirect
3. #53043C2semidirect
4. #53018C2semidirect
5. #52347C2semidirect
6. #46061C2semidirect
7. #46020C2semidirect
8. #45697C2semidirect
9. #45628C2semidirect
10. #45588C2semidirect
11. #35677C2semidirect
12. #35673C2semidirect
13. #35667C2semidirect
14. #35616C2semidirect
15. #35616C2semidirect
17. #35327C2semidirect
18. #35317C2semidirect
19. #35308C2semidirect
20. #35266C2semidirect
21. #35182C2semidirect
22. #35153C2semidirect
23. C2×#2545C2semidirect
24. #34816C2semidirect
25. #34744C2semidirect
32. C2×#536C22semidirect
33. C2×#536C22semidirect
36. C22×C4⋊Q8C22semidirect
39. C2×#519C22semidirect
40. C2×C4×#41C22semidirect
41. C22×C4×Q8C22semidirect
42. #2868C22semidirect
43. #2860C22semidirect
44. #2858C22semidirect
45. #2857C22semidirect
46. #2854C22semidirect
47. #2853C22semidirect
48. #2850C22semidirect
49. #2850C22semidirect
50. #2842C22semidirect
51. #2837C22semidirect
52. #2837C22semidirect
53. #2837C22semidirect
54. #2829C22semidirect
55. #2829C22semidirect
56. #2829C22semidirect
57. #2827C22semidirect
58. #2826C22semidirect
59. #2823C22semidirect
60. #2803C22semidirect
61. #2801C22semidirect
62. #2796C22semidirect
63. #2795C22semidirect
64. #2795C22semidirect
65. #2795C22semidirect
66. #2790C22semidirect
67. #2790C22semidirect
68. #2790C22semidirect
69. #2780C22semidirect
70. #2756C22semidirect
71. #2752C22semidirect
72. #2746C22semidirect
73. #2735C22semidirect
74. #2735C22semidirect
75. #2735C22semidirect
76. #2705C22semidirect
77. #2697C22semidirect
78. #2685C22semidirect
79. #2685C22semidirect
80. #2658C22semidirect
81. #2658C22semidirect
82. #2644C22semidirect
83. #2623C22semidirect
84. #2621C22semidirect
85. #2620C22semidirect
86. #2620C22semidirect
87. #2618C22semidirect
88. #2548C22semidirect
89. #2546C22semidirect
90. #2545C22semidirect
91. #2545C22semidirect
92. #2545C22semidirect
93. #2545C22semidirect
94. #2545C22semidirect
95. #2545C22semidirect
96. #2545C22semidirect
97. #2544C22semidirect
98. #2542C22semidirect
99. #2542C22semidirect
100. #2534C22semidirect
101. #2514C22semidirect
102. #2513C22semidirect
103. #2513C22semidirect
104. #2512C22semidirect
105. #2512C22semidirect
106. #2511C22semidirect
107. #2510C22semidirect
108. #2501C22semidirect
109. #2498C22semidirect
110. #2481C22semidirect
111. #2480C22semidirect
112. #2448C22semidirect
113. #2448C22semidirect
114. #2448C22semidirect
115. #2447C22semidirect
116. #2446C22semidirect
117. #2446C22semidirect
118. #2446C22semidirect
119. #2445C22semidirect
120. #2444C22semidirect
121. #2443C22semidirect
136. #2429C22semidirect
137. #2429C22semidirect
138. #2429C22semidirect
139. #2429C22semidirect
140. #2429C22semidirect
141. #2427C22semidirect
142. #2426C22semidirect
143. #2426C22semidirect
144. #2426C22semidirect
145. #2426C22semidirect
146. #2425C22semidirect
147. #2423C22semidirect
148. #2423C22semidirect
149. #2421C22semidirect
150. #2421C22semidirect
151. #2413C22semidirect
152. #2411C22semidirect
153. #2411C22semidirect
160. #2401C22semidirect
161. #2395C22semidirect
162. C2×#396C22semidirect
163. #2383C22semidirect
164. #2375C22semidirect
165. #2317C22semidirect
166. #2316C22semidirect
168. #2310C22semidirect
171. C4×#126C22semidirect
172. C4×#123C22semidirect
178. #2297C22semidirect
179. #2296C22semidirect
180. #2296C22semidirect
181. C2×#391C22semidirect
183. C2×#388C22semidirect
184. #2285C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#530872
#530472
#530432
#530182
#523472
#460612
#460202
#456972
#456282
#455882
#356772
#356732
#356672
#356162
#355132
#353272
#353172
#353082
#352662
#351822
#351532
C2×#25452
#348162
#347442