Finite Group Databasebeta

← #7682804

Subgroups — #7682804

Order 512.

5804 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59850C218yesmaximal, complemented
2#59480C214yesmaximal, complemented
3#59475C214yesmaximal, complemented
4#59280C214yesmaximal, complemented
5#59208C214yesmaximal, complemented
6#45176C214yesmaximal, complemented
7#45171C214yesmaximal, complemented
8#45026C214yesmaximal, complemented
9#44901C214yesmaximal, complemented
10#43149C218yesmaximal, complemented
11#35649C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35618C211yesmaximal, characteristic, complemented
14#35557C211yesmaximal, characteristic, complemented
15#35541C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic
17C2×#2566C211yesmaximal, characteristic, complemented
18#34816C211yesmaximal, characteristic, complemented
19#34744C211yesmaximal, characteristic, complemented
20#34265C211yesmaximal, characteristic, complemented
21#34258C211yesmaximal, characteristic, complemented
22#34256C211yesmaximal, characteristic, complemented
23#34255C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34189C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#532C2211yescharacteristic
30C22×#125C2211yescharacteristic, complemented
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic, complemented
33C2×#518C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#2797C2218yescomplemented
37#2782C2218yescomplemented
38#2757C2218yescomplemented
39#2750C2218yescomplemented
40#2749C2218yescomplemented
41#2749C2218yescomplemented
42#2743C2218yescomplemented
43#2743C2218yescomplemented
44#2739C2218yescomplemented
45#2735C2218yescomplemented
46#2705C2218yescomplemented
47#2685C2218yescomplemented
48#2603C2218yescomplemented
49#2601C2218yescomplemented
50#2600C2218yescomplemented
51#2595C2218yescomplemented
52#2591C2214yescomplemented
53#2579C2214yescomplemented
54#2576C2218yescomplemented
55#2573C2218yescomplemented
56#2566C2214yescomplemented
57#2566C2214yescomplemented
58#2566C2214yescomplemented
59#2566C2214yescomplemented
60#2534C2218yescomplemented
61#2526C2218yescomplemented
62#2526C2218yescomplemented
63#2514C2212yescomplemented
64#2513C2212yescomplemented
65#2512C2212yescomplemented
66#2512C2214yescomplemented
67#2511C2212yescomplemented
68#2511C2214yescomplemented
69#2510C2214yescomplemented
70#2510C2218yescomplemented
71#2505C2218yescomplemented
72#2504C2212yescomplemented
73#2504C2214yescomplemented
74#2503C2212yescomplemented
75#2500C2212yescomplemented
76#2499C2212yescomplemented
77#2497C2214yescomplemented
78#2496C2214yescomplemented
79#2490C2214yescomplemented
80#2490C2214yescomplemented
81#2489C2214yescomplemented
82#2489C2214yescomplemented
83#2487C2214yescomplemented
84#2483C2218yescomplemented
85#2481C2214yescomplemented
86#2481C2218yescomplemented
87#2480C2218yescomplemented
88#2480C2218yescomplemented
89#2471C2218yescomplemented
90#2457C2218yescomplemented
91#2454C2214yescomplemented
92#2453C2214yescomplemented
93#2448C2212yescomplemented
94#2447C2214yescomplemented
95#2447C2212yescomplemented
96#2446C2212yescomplemented
97#2445C2212yescomplemented
98#2445C2214yescomplemented
99#2444C2218yescomplemented
100#2444C2214yescomplemented
101#2443C2214yescomplemented
102#2442C2214yescomplemented
103#2441C2214yescomplemented
104#2435C2212yes—
105#2433C2212yes—
106#2432C2212yes—
107#2431C2212yes—
108#2422C2214yescomplemented
109#2421C2214yescomplemented
110#2420C2214yescomplemented
111#2420C2214yescomplemented
112#2419C2218yescomplemented
113#2412C2218yescomplemented
114#2411C2218yescomplemented
115#2410C2218yes—
116#2408C2214yes—
117#2407C2214yes—
118#2401C2214yescomplemented
119#2395C2214yescomplemented
120C2×#396C2214yescomplemented
121#2367C2214yescomplemented
122#2366C2214yescomplemented
123#2363C2214yescomplemented
124#2361C2214yescomplemented
125#2361C2218yescomplemented
126#2358C2218yescomplemented
127#2357C2214yescomplemented
128#2357C2214yescomplemented
129#2356C2214yescomplemented
130#2354C2214yescomplemented
131#2354C2214yescomplemented
132#2353C2218yescomplemented
133D4×C4⋊C4C2214yescomplemented
134#2343C2218yescomplemented
135#2342C2218yescomplemented
136#2341C2214yes—
137#2339C2214yes—
138#2339C2214yes—
139D4×C22⋊C4C2214yes—
140D4×C22⋊C4C2214yes—
141D4×C22⋊C4C2214yes—
142D4×C22⋊C4C2218yes—
143#2326C2212yescomplemented
144#2326C2212yescomplemented
145#2321C2214yescomplemented
146#2319C2214yescomplemented
147#2317C2211yescharacteristic, complemented
148#2316C2211yescharacteristic, complemented
149#2314C2214yescomplemented
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2212yes—
154#2311C2211yescharacteristic
155#2311C2211yescharacteristic, complemented
156#2309C2212yes—
157#2309C2211yescharacteristic
158#2308C2214yes—
159C4×C4⋊Q8C2212yescomplemented
160C4×#127C2212yescomplemented
161C4×#126C2214yescomplemented
162C4×#123C2214yescomplemented
163C4×#120C2214yescomplemented
164#2297C2211yescharacteristic
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2212yes—
169#2297C2211yescharacteristic, complemented
170#2297C2211yescharacteristic, complemented
171#2296C2211yescharacteristic, complemented
172#2296C2211yescharacteristic, complemented
173#2293C2214yescomplemented
174C2×#390C2212yes—
175C2×#390C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#386C2214yes—
178C2×#385C2214yescomplemented
179#2285C2211yescharacteristic, complemented
180C2×#384C2211yescharacteristic, complemented
181#2283C2214yescomplemented
182C2×#382C2211yescharacteristic, complemented
183#2274C2211yescharacteristic, complemented
184#2274C2211yescharacteristic, complemented
185C4×#117C2211yescharacteristic, complemented
186C2×C4×C4⋊C4C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—28no—
188C2×H(5,𝔽2)—28no—
189C2×H(5,𝔽2)—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2311yescharacteristic
195C23×D4C2314yes—
196C23×D4C2312yes—
197C23×D4C2312yes—
198C23×D4C2311yescharacteristic
199C24×C4C2312yes—
200#537—44no—
201#535—28no—
202#532—28no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#127C2312yes—
206C2×#126C2314yes—
207C2×#126C2318yes—
208C2×#125—44no—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#120C2314yes—
224C2×#120C2318yes—
225#520—44no—
226#520—44no—
227#518—28no—
228C4×#41—28no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×D4—44no—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2318yes—
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2318yes—
254C2×#117C2312yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2318yes—
268C22×C22⋊C4C2318yes—
269C22×C22⋊C4C2314yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274#401C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#399C2314yes—
285#399C2318yes—
286#398C2318yes—
287#398C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2314yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2318yes—
314#394C2314yes—
315#394C2318yes—
316#392C2318yes—
317#392C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2311yescharacteristic
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2311yescharacteristic
330#390C2312yes—
331#390C2312yes—
332#390C2318yes—
333#390C2312yes—
334#390C2311yescharacteristic
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2318yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2318yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2311yescharacteristic
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2318yes—
395#386C2312yes—
396#386C2312yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2314yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2318yes—
407#386C2312yes—
408#386C2318yes—
409#386C2312yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#386C2314yes—
419#386C2312yes—
420#386C2312yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2312yes—
428#385C2312yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#383C2314yes—
442#383C2318yes—
443#382C2312yes—
444#382C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2318yes—
448#382C2312yes—
449#381C2318yes—
450#381C2318yes—
451#381C2314yes—
452#381C2318yes—
453#381C2318yes—
454#381C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2314yes—
464#380C2318yes—
465#379C2318yes—
466#379C2314yes—
467#379C2318yes—
468#379C2318yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499#376C2318yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C2×#95C2312yes—
503C43C2312yes—
504C25C2414yes—
505C25C2412yes—
506H(5,𝔽2)—464no—
507C2×#41—28no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
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—44no—
520C2×#41—44no—
521C2×#41#4118yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×D4—216no—
526C22×D4—28no—
527C22×D4—28no—
528C22×D4—28no—
529C22×D4—216no—
530C22×D4—24no—
531C22×D4—28no—
532C22×D4—24no—
533C22×D4—44no—
534C22×D4—44no—
535C22×D4—48no—
536C22×D4#4118yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2411yescharacteristic
548C22×D4C2418yes—
549C22×D4C2414yes—
550C23×C4—44no—
551C23×C4—84no—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2411yescharacteristic
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2418yes—
562C23×C4C2414yes—
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2414yes—
566C23×C4C2418yes—
567C23×C4C2414yes—
568C23×C4C2411yescharacteristic
569C4⋊Q8—24no—
570#127—24no—
571#127—28no—
572#126—48no—
573#126—88no—
574#125—48no—
575#125—48no—
576#124—24no—
577#124—24no—
578#124—28no—
579#123—48no—
580#123—88no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583#121—216no—
584#121—216no—
585#121—44no—
586#121—44no—
587#121—48no—
588#120—216no—
589#120—416no—
590C4×Q8—28no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—216no—
596C4×D4—216no—
597C4×D4—216no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4—88no—
605C4×D4—88no—
606#117—28no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—416no—
613#117—44no—
614#117—44no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—84no—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C22⋊C4—216no—
658C2×C22⋊C4—48no—
659C2×C22⋊C4—44no—
660C2×C22⋊C4—88no—
661C2×C22⋊C4—88no—
662C2×C22⋊C4—84no—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C42—28no—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2418yes—
723C2×C42C2414yes—
724C2×C42C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760C24—24no—
761C24—24no—
762C24—28no—
763C24—28no—
764C24—44no—
765C24—44no—
766C24—44no—
767C24—48no—
768C24—48no—
769C24C2×#4118yes—
770C24C2512yes—
771C24C2512yes—
772C24C2512yes—
773C24C2514yes—
774C24C2511yescharacteristic
775#41—232no—
776#41—432no—
777#41—432no—
778#41—416no—
779#41—416no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8C2×#4114yes—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—28no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—216no—
802C2×D4—232no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—28no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—28no—
817C2×D4—432no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—48no—
824C2×D4—44no—
825C2×D4—432no—
826C2×D4—464no—
827C2×D4C2×#4118yes—
828C2×D4C2×#4118yes—
829C2×D4C2×#4114yes—
830C2×D4C2×#4118yes—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—216no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—42no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—42no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—48no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—816no—
872C22×C4C2×#4118yes—
873C22×C4C2×#4114yes—
874C22×C4C2×#4114yes—
875C22×C4H(5,𝔽2)14yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2514yes—
879C22×C4C2514yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2514yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2514yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—24no—
938C22⋊C4—28no—
939C22⋊C4—216no—
940C22⋊C4—28no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C42—22no—
968C42—24no—
969C42—22no—
970C42—24no—
971C42—28no—
972C42—24no—
973C42—22no—
974C42—22no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—28no—
982C42—48no—
983C42—44no—
984C42—44no—
985C42—44no—
986C42—48no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—28no—
994C23—24no—
995C23—28no—
996C23—24no—
997C23—216no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—416no—
1009C23—416no—
1010C23—84no—
1011C23—88no—
1012C23—84no—
1013C23—816no—
1014C23—816no—
1015C23—164no—
1016C23—164no—
1017C23C22×#4118yes—
1018C23C22×#4114yes—
1019C23C22×#4112yes—
1020C23C22×#4112yes—
1021C23C2×H(5,𝔽2)12yes—
1022C23C2611yescharacteristic
1023Q8—28no—
1024Q8—44no—
1025Q8—44no—
1026D4—216no—
1027D4—216no—
1028D4—216no—
1029D4—28no—
1030D4—416no—
1031D4—416no—
1032D4—416no—
1033D4—48no—
1034D4—48no—
1035D4—44no—
1036D4—44no—
1037D4—816no—
1038D4—164no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—216no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—28no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—28no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—48no—
1088C2×C4—416no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—48no—
1092C2×C4—48no—
1093C2×C4—816no—
1094C2×C4—84no—
1095C2×C4—88no—
1096C2×C4—84no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—816no—
1100C2×C4—164no—
1101C2×C4—164no—
1102C2×C4#551116yes—
1103C2×C4C22×#4114yes—
1104C2×C4C22×#4112yes—
1105C2×C4C22×#4112yes—
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4112yes—
1108C2×C4C2×H(5,𝔽2)12yes—
1109C2×C4C2×H(5,𝔽2)12yes—
1110C2×C4#58514yes—
1111C22—24no—
1112C22—24no—
1113C22—22no—
1114C22—22no—
1115C22—216no—
1116C22—28no—
1117C22—24no—
1118C22—28no—
1119C22—44no—
1120C22—48no—
1121C22—44no—
1122C22—42no—
1123C22—44no—
1124C22—42no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—816no—
1136C22—1616no—
1137C22C2×#55114yes—
1138C22C23×#4111yescharacteristic
1139C22C23×#4111yescharacteristic
1140C22C22×H(5,𝔽2)11yescharacteristic
1141C22C2×#58512yes—
1142C22H(7,𝔽2)12yes—
1143C4—24no—
1144C4—24no—
1145C4—44no—
1146C4—44no—
1147C4—44no—
1148C4—42no—
1149C4—44no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—44no—
1155C4—42no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4C2×#55114yes—
1162C4C2×#55114yes—
1163C2—24no—
1164C2—48no—
1165C2—44no—
1166C2—82no—
1167C2—82no—
1168C2C22×#55111yescharacteristic
1169C2#6283611yescharacteristic
1170C2#6287611yescharacteristic
1171C2#6299212yes—
1172C2#6300812yes—
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. #59850C2semidirect
2. #59480C2semidirect
3. #59475C2semidirect
4. #59280C2semidirect
5. #59208C2semidirect
6. #45176C2semidirect
7. #45171C2semidirect
8. #45026C2semidirect
9. #44901C2semidirect
10. #43149C2semidirect
11. #35649C2semidirect
12. #35639C2semidirect
13. #35618C2semidirect
14. #35557C2semidirect
15. #35541C2semidirect
17. C2×#2566C2semidirect
18. #34816C2semidirect
19. #34744C2semidirect
20. #34265C2semidirect
21. #34258C2semidirect
22. #34256C2semidirect
23. #34255C2semidirect
24. #34207C2semidirect
25. #34189C2semidirect
30. C22×#125C22semidirect
32. C2×#520C22semidirect
36. #2797C22semidirect
37. #2782C22semidirect
38. #2757C22semidirect
39. #2750C22semidirect
40. #2749C22semidirect
41. #2749C22semidirect
42. #2743C22semidirect
43. #2743C22semidirect
44. #2739C22semidirect
45. #2735C22semidirect
46. #2705C22semidirect
47. #2685C22semidirect
48. #2603C22semidirect
49. #2601C22semidirect
50. #2600C22semidirect
51. #2595C22semidirect
52. #2591C22semidirect
53. #2579C22semidirect
54. #2576C22semidirect
55. #2573C22semidirect
56. #2566C22semidirect
57. #2566C22semidirect
58. #2566C22semidirect
59. #2566C22semidirect
60. #2534C22semidirect
61. #2526C22semidirect
62. #2526C22semidirect
63. #2514C22semidirect
64. #2513C22semidirect
65. #2512C22semidirect
66. #2512C22semidirect
67. #2511C22semidirect
68. #2511C22semidirect
69. #2510C22semidirect
70. #2510C22semidirect
71. #2505C22semidirect
72. #2504C22semidirect
73. #2504C22semidirect
74. #2503C22semidirect
75. #2500C22semidirect
76. #2499C22semidirect
77. #2497C22semidirect
78. #2496C22semidirect
79. #2490C22semidirect
80. #2490C22semidirect
81. #2489C22semidirect
82. #2489C22semidirect
83. #2487C22semidirect
84. #2483C22semidirect
85. #2481C22semidirect
86. #2481C22semidirect
87. #2480C22semidirect
88. #2480C22semidirect
89. #2471C22semidirect
90. #2457C22semidirect
91. #2454C22semidirect
92. #2453C22semidirect
93. #2448C22semidirect
94. #2447C22semidirect
95. #2447C22semidirect
96. #2446C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2444C22semidirect
100. #2444C22semidirect
101. #2443C22semidirect
102. #2442C22semidirect
103. #2441C22semidirect
108. #2422C22semidirect
109. #2421C22semidirect
110. #2420C22semidirect
111. #2420C22semidirect
112. #2419C22semidirect
113. #2412C22semidirect
114. #2411C22semidirect
118. #2401C22semidirect
119. #2395C22semidirect
120. C2×#396C22semidirect
121. #2367C22semidirect
122. #2366C22semidirect
123. #2363C22semidirect
124. #2361C22semidirect
125. #2361C22semidirect
126. #2358C22semidirect
127. #2357C22semidirect
128. #2357C22semidirect
129. #2356C22semidirect
130. #2354C22semidirect
131. #2354C22semidirect
132. #2353C22semidirect
133. D4×C4⋊C4C22semidirect
134. #2343C22semidirect
135. #2342C22semidirect
143. #2326C22semidirect
144. #2326C22semidirect
145. #2321C22semidirect
146. #2319C22semidirect
147. #2317C22semidirect
148. #2316C22semidirect
149. #2314C22semidirect
155. #2311C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#127C22semidirect
161. C4×#126C22semidirect
162. C4×#123C22semidirect
163. C4×#120C22semidirect
169. #2297C22semidirect
170. #2297C22semidirect
171. #2296C22semidirect
172. #2296C22semidirect
173. #2293C22semidirect
178. C2×#385C22semidirect
179. #2285C22semidirect
180. C2×#384C22semidirect
181. #2283C22semidirect
182. C2×#382C22semidirect
183. #2274C22semidirect
184. #2274C22semidirect
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
#598502
#594802
#594752
#592802
#592082
#451762
#451712
#450262
#449012
#431492
#356492
#356392
#356182
#355572
#355412
#355132
C2×#25662
#348162
#347442
#342652
#342582
#342562
#342552
#342072
#341892