Finite Group Databasebeta

← #7644405

Subgroups — #7644405

Order 512.

5606 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42976C214yesmaximal, complemented
2#42940C214yesmaximal, complemented
3#42520C214yesmaximal, complemented
4#42519C214yesmaximal, complemented
5#42012C218yesmaximal, complemented
6#40641C218yesmaximal, complemented
7#37516C214yesmaximal, complemented
8#37512C214yesmaximal, complemented
9#37285C214yesmaximal, complemented
10#37282C214yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35628C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35557C211yesmaximal, characteristic, complemented
17#35556C211yesmaximal, characteristic, complemented
18#35541C211yesmaximal, characteristic, complemented
19#35305C211yesmaximal, characteristic, complemented
20#35250C211yesmaximal, characteristic
21#34634C211yesmaximal, characteristic, complemented
22C2×#2620C211yesmaximal, characteristic, complemented
23#34204C211yesmaximal, characteristic, complemented
24#34203C211yesmaximal, characteristic, complemented
25#34044C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#533C2211yescharacteristic, complemented
32C22×#124C2211yescharacteristic, complemented
33C22×C22⋊Q8C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C2×#519C2211yescharacteristic, complemented
36C2×#518C2211yescharacteristic, complemented
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic
39#2848C2214yescomplemented
40#2847C2214yes—
41#2831C2218yescomplemented
42#2829C2218yescomplemented
43#2826C2218yescomplemented
44#2824C2218yescomplemented
45#2786C2218yescomplemented
46#2784C2218yescomplemented
47#2781C2218yescomplemented
48#2780C2218yescomplemented
49#2779C2218yescomplemented
50#2761C2218yescomplemented
51#2751C2218yescomplemented
52#2750C2218yescomplemented
53#2750C2218yescomplemented
54#2743C2218yescomplemented
55#2715C2218yescomplemented
56#2697C2218yescomplemented
57#2695C2218yescomplemented
58#2685C2218yescomplemented
59#2685C2218yescomplemented
60#2684C2218yescomplemented
61#2665C2218yescomplemented
62#2662C2218yescomplemented
63#2650C2218yescomplemented
64#2648C2218yescomplemented
65#2648C2218yescomplemented
66#2648C2218yescomplemented
67#2636C2218yescomplemented
68#2630C2218yescomplemented
69#2629C2212yescomplemented
70#2629C2212yescomplemented
71#2628C2212yescomplemented
72#2628C2212yescomplemented
73#2627C2214yescomplemented
74#2626C2214yes—
75#2620C2212yes—
76#2620C2212yes—
77#2620C2214yes—
78#2620C2214yescomplemented
79#2620C2212yescomplemented
80#2620C2212yescomplemented
81#2616C2214yescomplemented
82#2615C2214yes—
83#2592C2214yescomplemented
84#2592C2214yescomplemented
85#2574C2218yescomplemented
86#2568C2214yescomplemented
87#2554C2218yescomplemented
88#2548C2214yescomplemented
89#2548C2214yescomplemented
90#2547C2214yescomplemented
91#2545C2214yescomplemented
92#2544C2214yescomplemented
93#2512C2214yescomplemented
94#2512C2214yescomplemented
95#2511C2214yescomplemented
96#2511C2214yescomplemented
97#2498C2218yescomplemented
98#2497C2214yescomplemented
99#2497C2214yescomplemented
100#2496C2214yescomplemented
101#2496C2214yescomplemented
102#2492C2214yescomplemented
103#2491C2214yescomplemented
104#2490C2214yescomplemented
105#2489C2214yescomplemented
106#2488C2218yescomplemented
107#2481C2218yescomplemented
108#2481C2218yescomplemented
109#2472C2218yescomplemented
110#2467C2218yescomplemented
111#2459C2218yescomplemented
112#2448C2214yescomplemented
113#2447C2214yescomplemented
114#2446C2214yescomplemented
115#2445C2214yescomplemented
116#2436C2212yes—
117#2435C2212yescomplemented
118#2434C2212yescomplemented
119#2433C2212yes—
120#2432C2212yescomplemented
121#2432C2212yescomplemented
122#2431C2212yes—
123#2431C2212yes—
124#2427C2214yescomplemented
125#2427C2214yescomplemented
126#2426C2214yescomplemented
127#2426C2214yescomplemented
128#2423C2214yescomplemented
129#2422C2214yescomplemented
130#2421C2214yescomplemented
131#2420C2214yescomplemented
132#2412C2218yescomplemented
133#2412C2218yescomplemented
134#2411C2218yescomplemented
135#2406C2214yes—
136#2405C2214yes—
137#2404C2214yes—
138#2403C2214yes—
139#2396C2214yescomplemented
140#2396C2214yescomplemented
141C2×#396C2214yescomplemented
142C2×#394C2214yes—
143#2363C2214yes—
144#2362C2214yescomplemented
145#2361C2214yescomplemented
146#2360C2214yescomplemented
147#2344C2214yescomplemented
148#2342C2214yes—
149#2342C2214yescomplemented
150D4×C22⋊C4C2214yes—
151#2324C2214yes—
152#2323C2214yescomplemented
153#2316C2211yescharacteristic, complemented
154#2316C2211yescharacteristic, complemented
155#2311C2214yes—
156#2311C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2212yescomplemented
161#2311C2212yescomplemented
162#2310C2211yescharacteristic, complemented
163#2310C2212yescomplemented
164#2309C2211yescharacteristic, complemented
165#2309C2212yescomplemented
166#2308C2214yes—
167C4×C22⋊Q8C2214yescomplemented
168C4×#121C2214yescomplemented
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2212yescomplemented
174#2297C2212yescomplemented
175#2296C2211yescharacteristic, complemented
176#2296C2211yescharacteristic, complemented
177C2×#391C2211yescharacteristic, complemented
178C2×#390C2211yescharacteristic, complemented
179#2285C2211yescharacteristic, complemented
180C2×#384C2211yescharacteristic, complemented
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2212yescomplemented
184#2280C2212yescomplemented
185#2274C2211yescharacteristic, complemented
186#2274C2211yescharacteristic, complemented
187C22×#41—28no—
188C22×#41—44no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2312yes—
193C22×#41C2311yescharacteristic
194C22×#41C2311yescharacteristic
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×D4C2311yescharacteristic
199C23×D4C2312yes—
200C23×D4C2311yescharacteristic
201C23×D4C2312yes—
202C24×C4C2311yescharacteristic
203C24×C4C2312yes—
204#536—44no—
205#536—44no—
206#535—44no—
207#535—44no—
208#533—44no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#126C2318yes—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#124—44no—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2318yes—
229C2×C22⋊Q8—28no—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×#121—28no—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#120C2314yes—
245C2×#120C2314yes—
246C2×#120C2318yes—
247#519—44no—
248#518—44no—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2318yes—
255C2×#117—44no—
256C2×#117—44no—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2314yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2314yes—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2318yes—
300#399C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2318yes—
304#398C2314yes—
305#398C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#395C2318yes—
328#395C2314yes—
329#395C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#393C2314yes—
346#393C2318yes—
347#393C2318yes—
348#393C2318yes—
349#393C2314yes—
350#392C2318yes—
351#392C2318yes—
352#392C2318yes—
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2318yes—
367#391C2312yes—
368#391C2312yes—
369#390C2314yes—
370#390C2314yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2314yes—
376#390C2314yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2318yes—
382#390C2314yes—
383#390C2312yes—
384#390C2312yes—
385#390C2318yes—
386#390C2318yes—
387#390C2318yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2318yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2314yes—
446#385C2314yes—
447#384C2312yes—
448#384C2312yes—
449#384C2314yes—
450#384C2312yes—
451#382C2318yes—
452#382C2312yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2312yes—
457#381C2312yes—
458#381C2318yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2318yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2318yes—
476#379C2314yes—
477#379C2314yes—
478#379C2314yes—
479#379C2318yes—
480#379C2312yes—
481#379C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C2×#95C2314yes—
507C25C2412yes—
508C25C2411yescharacteristic
509C25C2412yes—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—28no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—464no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—42no—
534C22×Q8—42no—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2414yes—
541C22×D4—28no—
542C22×D4—28no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—42no—
548C22×D4—42no—
549C22×D4—44no—
550C22×D4—44no—
551C22×D4—84no—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2411yescharacteristic
557C22×D4C2411yescharacteristic
558C22×D4C2414yes—
559C22×D4C2414yes—
560C22×D4C2412yes—
561C22×D4C2412yes—
562C22×D4C2412yes—
563C22×D4C2418yes—
564C22×D4C2418yes—
565C23×C4—24no—
566C23×C4—24no—
567C23×C4—28no—
568C23×C4—44no—
569C23×C4—44no—
570C23×C4#4118yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2414yes—
587C23×C4C2418yes—
588C23×C4C2411yescharacteristic
589C4⋊Q8—44no—
590C4⋊Q8—44no—
591C4⋊Q8—44no—
592#127—44no—
593#127—44no—
594#126—88no—
595#126—88no—
596#125—44no—
597#124—44no—
598#124—44no—
599#124—48no—
600#124—44no—
601#124—44no—
602#124—44no—
603#124—44no—
604#124—88no—
605#123—48no—
606#123—48no—
607#123—88no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—28no—
611C22⋊Q8—28no—
612C22⋊Q8—48no—
613C22⋊Q8—48no—
614C22⋊Q8—48no—
615#121—28no—
616#121—28no—
617#121—28no—
618#121—28no—
619#121—48no—
620#121—48no—
621#120—48no—
622#120—48no—
623#120—88no—
624C4×Q8—48no—
625C4×Q8—48no—
626C4×Q8—48no—
627C4×D4—48no—
628C4×D4—48no—
629C4×D4—88no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117—44no—
637#117—44no—
638#117—42no—
639#117—42no—
640#117—42no—
641#117—42no—
642#117—44no—
643#117—44no—
644#117—48no—
645#117—44no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—28no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—84no—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C22⋊C4—28no—
686C2×C22⋊C4—28no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—48no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—48no—
691C2×C22⋊C4—84no—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2418yes—
734C2×C42—24no—
735C2×C42—24no—
736C2×C42—44no—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2412yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2414yes—
750C2×C42C2418yes—
751C2×C42C2418yes—
752C2×C42C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783C24—22no—
784C24—22no—
785C24—24no—
786C24—24no—
787C24—24no—
788C24—24no—
789C24—42no—
790C24—42no—
791C24—42no—
792C24—42no—
793C24—44no—
794C24—44no—
795C24—44no—
796C24—44no—
797C24C2×#4114yes—
798C24C2514yes—
799C24C2512yes—
800C24C2512yes—
801C24C2511yescharacteristic
802C24C2511yescharacteristic
803C24C2511yescharacteristic
804#41—432no—
805#41—416no—
806#41—416no—
807#41—432no—
808#41—416no—
809#41—416no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—24no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—42no—
824C2×Q8—42no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—416no—
829C2×Q8—416no—
830C2×D4—28no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—48no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—416no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—48no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—432no—
869C2×D4—416no—
870C2×D4—816no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—232no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
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—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—42no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—42no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—432no—
917C22×C4C2×#4114yes—
918C22×C4C2×#4114yes—
919C22×C4C2×#4114yes—
920C22×C4C2×#4114yes—
921C22×C4C2×#4114yes—
922C22×C4C2×#4114yes—
923C22×C4H(5,𝔽2)14yes—
924C22×C4H(5,𝔽2)14yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2514yes—
931C22×C4C2514yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—44no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—48no—
967C4⋊C4—48no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—44no—
974C4⋊C4—48no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—44no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—48no—
1013C22⋊C4—44no—
1014C22⋊C4—48no—
1015C22⋊C4—44no—
1016C22⋊C4—48no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C42—24no—
1020C42—24no—
1021C42—22no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—24no—
1026C42—24no—
1027C42—24no—
1028C42—24no—
1029C42—24no—
1030C42—24no—
1031C42—44no—
1032C42—48no—
1033C42—48no—
1034C42—48no—
1035C23—22no—
1036C23—22no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—28no—
1046C23—24no—
1047C23—22no—
1048C23—22no—
1049C23—24no—
1050C23—22no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—24no—
1056C23—24no—
1057C23—28no—
1058C23—24no—
1059C23—24no—
1060C23—28no—
1061C23—44no—
1062C23—44no—
1063C23—48no—
1064C23—48no—
1065C23—84no—
1066C23—84no—
1067C23—84no—
1068C23—84no—
1069C23—84no—
1070C23—84no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23C22×#4112yes—
1076C23C22×#4112yes—
1077C23C22×#4112yes—
1078C23C2×H(5,𝔽2)12yes—
1079C23C2×H(5,𝔽2)12yes—
1080C23C2611yescharacteristic
1081Q8—48no—
1082Q8—48no—
1083Q8—48no—
1084Q8—44no—
1085Q8—44no—
1086Q8—88no—
1087D4—48no—
1088D4—48no—
1089D4—48no—
1090D4—416no—
1091D4—48no—
1092D4—48no—
1093D4—48no—
1094D4—48no—
1095D4—44no—
1096D4—44no—
1097D4—88no—
1098D4—168no—
1099D4—168no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—28no—
1105C2×C4—28no—
1106C2×C4—28no—
1107C2×C4—28no—
1108C2×C4—28no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—48no—
1153C2×C4—48no—
1154C2×C4—48no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4—48no—
1159C2×C4—84no—
1160C2×C4—84no—
1161C2×C4—84no—
1162C2×C4—88no—
1163C2×C4—168no—
1164C2×C4#538116yes—
1165C2×C4C22×#4112yes—
1166C2×C4C22×#4112yes—
1167C2×C4C22×#4112yes—
1168C2×C4C22×#4112yes—
1169C2×C4C2×H(5,𝔽2)12yes—
1170C2×C4C2×H(5,𝔽2)12yes—
1171C2×C4C2×H(5,𝔽2)12yes—
1172C2×C4C2×H(5,𝔽2)12yes—
1173C22—22no—
1174C22—22no—
1175C22—24no—
1176C22—24no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—44no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—44no—
1193C22—44no—
1194C22—48no—
1195C22—44no—
1196C22—48no—
1197C22—44no—
1198C22—44no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—88no—
1203C22—816no—
1204C22—168no—
1205C22C2×#53814yes—
1206C22C23×#4111yescharacteristic
1207C22C22×H(5,𝔽2)11yescharacteristic
1208C22C22×H(5,𝔽2)11yescharacteristic
1209C22H(7,𝔽2)12yes—
1210C222−1+612yes—
1211C4—22no—
1212C4—22no—
1213C4—44no—
1214C4—44no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—44no—
1224C4—44no—
1225C4—42no—
1226C4—42no—
1227C4—44no—
1228C4C2×#53814yes—
1229C4C2×#53814yes—
1230C2—24no—
1231C2—42no—
1232C2—42no—
1233C2—82no—
1234C2—82no—
1235C2—84no—
1236C2C22×#53811yescharacteristic
1237C2#6285511yescharacteristic
1238C2#6286011yescharacteristic
1239C2#6287512yes—
1240C2#6287812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35250C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42976C2semidirect
2. #42940C2semidirect
3. #42520C2semidirect
4. #42519C2semidirect
5. #42012C2semidirect
6. #40641C2semidirect
7. #37516C2semidirect
8. #37512C2semidirect
9. #37285C2semidirect
10. #37282C2semidirect
11. #35677C2semidirect
12. #35673C2semidirect
13. #35628C2semidirect
14. #35617C2semidirect
15. #35557C2semidirect
16. #35557C2semidirect
17. #35556C2semidirect
18. #35541C2semidirect
19. #35305C2semidirect
21. #34634C2semidirect
22. C2×#2620C2semidirect
23. #34204C2semidirect
24. #34203C2semidirect
25. #34044C2semidirect
31. C2×#533C22semidirect
32. C22×#124C22semidirect
35. C2×#519C22semidirect
36. C2×#518C22semidirect
39. #2848C22semidirect
41. #2831C22semidirect
42. #2829C22semidirect
43. #2826C22semidirect
44. #2824C22semidirect
45. #2786C22semidirect
46. #2784C22semidirect
47. #2781C22semidirect
48. #2780C22semidirect
49. #2779C22semidirect
50. #2761C22semidirect
51. #2751C22semidirect
52. #2750C22semidirect
53. #2750C22semidirect
54. #2743C22semidirect
55. #2715C22semidirect
56. #2697C22semidirect
57. #2695C22semidirect
58. #2685C22semidirect
59. #2685C22semidirect
60. #2684C22semidirect
61. #2665C22semidirect
62. #2662C22semidirect
63. #2650C22semidirect
64. #2648C22semidirect
65. #2648C22semidirect
66. #2648C22semidirect
67. #2636C22semidirect
68. #2630C22semidirect
69. #2629C22semidirect
70. #2629C22semidirect
71. #2628C22semidirect
72. #2628C22semidirect
73. #2627C22semidirect
78. #2620C22semidirect
79. #2620C22semidirect
80. #2620C22semidirect
81. #2616C22semidirect
83. #2592C22semidirect
84. #2592C22semidirect
85. #2574C22semidirect
86. #2568C22semidirect
87. #2554C22semidirect
88. #2548C22semidirect
89. #2548C22semidirect
90. #2547C22semidirect
91. #2545C22semidirect
92. #2544C22semidirect
93. #2512C22semidirect
94. #2512C22semidirect
95. #2511C22semidirect
96. #2511C22semidirect
97. #2498C22semidirect
98. #2497C22semidirect
99. #2497C22semidirect
100. #2496C22semidirect
101. #2496C22semidirect
102. #2492C22semidirect
103. #2491C22semidirect
104. #2490C22semidirect
105. #2489C22semidirect
106. #2488C22semidirect
107. #2481C22semidirect
108. #2481C22semidirect
109. #2472C22semidirect
110. #2467C22semidirect
111. #2459C22semidirect
112. #2448C22semidirect
113. #2447C22semidirect
114. #2446C22semidirect
115. #2445C22semidirect
117. #2435C22semidirect
118. #2434C22semidirect
120. #2432C22semidirect
121. #2432C22semidirect
124. #2427C22semidirect
125. #2427C22semidirect
126. #2426C22semidirect
127. #2426C22semidirect
128. #2423C22semidirect
129. #2422C22semidirect
130. #2421C22semidirect
131. #2420C22semidirect
132. #2412C22semidirect
133. #2412C22semidirect
134. #2411C22semidirect
139. #2396C22semidirect
140. #2396C22semidirect
141. C2×#396C22semidirect
144. #2362C22semidirect
145. #2361C22semidirect
146. #2360C22semidirect
147. #2344C22semidirect
149. #2342C22semidirect
152. #2323C22semidirect
153. #2316C22semidirect
154. #2316C22semidirect
160. #2311C22semidirect
161. #2311C22semidirect
162. #2310C22semidirect
163. #2310C22semidirect
164. #2309C22semidirect
165. #2309C22semidirect
167. C4×C22⋊Q8C22semidirect
168. C4×#121C22semidirect
173. #2297C22semidirect
174. #2297C22semidirect
175. #2296C22semidirect
176. #2296C22semidirect
177. C2×#391C22semidirect
178. C2×#390C22semidirect
179. #2285C22semidirect
180. C2×#384C22semidirect
183. #2280C22semidirect
184. #2280C22semidirect
185. #2274C22semidirect
186. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#429762
#429402
#425202
#425192
#420122
#406412
#375162
#375122
#372852
#372822
#356772
#356732
#356282
#356172
#355572
#355562
#355412
#353052
#352502
#346342
C2×#26202
#342042
#342032
#340442