Finite Group Databasebeta

← #7683759

Subgroups — #7683759

Order 512.

6264 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59479C214yesmaximal, complemented
2#59476C214yesmaximal, complemented
3#59275C214yesmaximal, complemented
4#59273C214yesmaximal, complemented
5#59133C218yesmaximal, complemented
6#45081C214yesmaximal, complemented
7#44998C214yesmaximal, complemented
8#44988C214yesmaximal, complemented
9#44903C214yesmaximal, complemented
10#43147C218yesmaximal, complemented
11#35592C211yesmaximal, characteristic, complemented
12#35574C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35541C211yesmaximal, characteristic, complemented
15#35530C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic
17C2×#2542C211yesmaximal, 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#34188C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#551C2218yescomplemented
28C2×#537C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic, complemented
32C22×C22⋊Q8C2214yescomplemented
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic, complemented
35C2×#518C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2752C2218yescomplemented
39#2746C2218yescomplemented
40#2746C2218yescomplemented
41#2743C2218yescomplemented
42#2738C2218yescomplemented
43#2735C2218yescomplemented
44#2730C2218yescomplemented
45#2728C2218yescomplemented
46#2723C2218yescomplemented
47#2706C2218yescomplemented
48#2696C2218yescomplemented
49#2685C2218yescomplemented
50#2598C2218yescomplemented
51#2591C2214yescomplemented
52#2579C2214yescomplemented
53#2575C2218yescomplemented
54#2564C2218yescomplemented
55#2561C2218yescomplemented
56#2560C2218yescomplemented
57#2542C2214yescomplemented
58#2542C2214yescomplemented
59#2542C2214yescomplemented
60#2542C2214yescomplemented
61#2516C2218yescomplemented
62#2516C2218yescomplemented
63#2514C2212yescomplemented
64#2513C2212yescomplemented
65#2512C2212yescomplemented
66#2512C2214yescomplemented
67#2511C2212yescomplemented
68#2511C2214yescomplemented
69#2510C2214yescomplemented
70#2502C2212yescomplemented
71#2501C2212yescomplemented
72#2500C2212yescomplemented
73#2499C2212yescomplemented
74#2497C2214yescomplemented
75#2496C2214yescomplemented
76#2492C2214yescomplemented
77#2492C2214yescomplemented
78#2491C2214yescomplemented
79#2491C2214yescomplemented
80#2488C2218yescomplemented
81#2482C2218yescomplemented
82#2481C2214yescomplemented
83#2481C2218yescomplemented
84#2479C2218yescomplemented
85#2477C2218yescomplemented
86#2472C2218yescomplemented
87#2471C2218yescomplemented
88#2463C2218yescomplemented
89#2461C2218yescomplemented
90#2452C2214yescomplemented
91#2451C2214yescomplemented
92#2448C2212yescomplemented
93#2447C2212yescomplemented
94#2447C2214yescomplemented
95#2446C2212yescomplemented
96#2445C2212yescomplemented
97#2445C2214yescomplemented
98#2444C2214yescomplemented
99#2443C2218yescomplemented
100#2443C2214yescomplemented
101#2440C2214yescomplemented
102#2439C2214yescomplemented
103#2438C2218yescomplemented
104#2437C2218yescomplemented
105#2436C2214yescomplemented
106#2435C2212yes—
107#2433C2212yes—
108#2432C2212yes—
109#2431C2212yes—
110#2423C2214yescomplemented
111#2422C2214yescomplemented
112#2422C2214yescomplemented
113#2420C2214yescomplemented
114#2418C2218yescomplemented
115#2412C2218yescomplemented
116#2410C2218yes—
117#2409C2214yescomplemented
118#2408C2214yes—
119#2407C2214yes—
120#2401C2214yescomplemented
121#2395C2214yescomplemented
122C2×#399C2214yescomplemented
123#2368C2218yescomplemented
124#2367C2214yescomplemented
125#2366C2214yescomplemented
126#2363C2214yescomplemented
127#2361C2214yescomplemented
128#2361C2218yescomplemented
129#2357C2214yescomplemented
130#2355C2214yescomplemented
131#2354C2214yescomplemented
132#2354C2214yescomplemented
133#2354C2214yescomplemented
134#2352C2218yescomplemented
135D4×C4⋊C4C2214yescomplemented
136#2342C2218yescomplemented
137#2341C2214yes—
138#2339C2214yes—
139#2339C2214yes—
140D4×C22⋊C4C2214yes—
141D4×C22⋊C4C2214yes—
142D4×C22⋊C4C2214yes—
143D4×C22⋊C4C2218yes—
144#2326C2212yescomplemented
145#2326C2212yescomplemented
146#2321C2214yescomplemented
147#2319C2214yescomplemented
148#2317C2211yescharacteristic, complemented
149#2316C2211yescharacteristic, complemented
150#2314C2214yescomplemented
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2211yescharacteristic
154#2311C2212yes—
155#2311C2211yescharacteristic
156#2311C2211yescharacteristic, complemented
157#2309C2212yes—
158#2309C2211yescharacteristic
159#2308C2214yes—
160C4×C4⋊Q8C2212yescomplemented
161C4×#127C2212yescomplemented
162C4×#126C2214yescomplemented
163C4×#123C2214yescomplemented
164C4×#120C2214yescomplemented
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2212yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic, complemented
171#2297C2211yescharacteristic, complemented
172#2296C2211yescharacteristic, complemented
173#2296C2211yescharacteristic, complemented
174#2293C2214yescomplemented
175C2×#390C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#390C2212yes—
178C2×#386C2214yes—
179#2285C2211yescharacteristic, complemented
180#2285C2214yescomplemented
181C2×#384C2211yescharacteristic, complemented
182C2×#384C2211yescharacteristic, 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×Q8C2312yes—
196C23×D4C2314yes—
197C23×D4C2312yes—
198C23×D4C2312yes—
199C23×D4C2311yescharacteristic
200C24×C4C2312yes—
201#551—432no—
202#537—44no—
203#535—28no—
204#532—28no—
205C2×C4⋊Q8—44no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×#127C2311yescharacteristic
210C2×#127C2312yes—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2312yes—
216C2×#124C2318yes—
217C2×#123C2314yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×C22⋊Q8—416no—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#120C2314yes—
234C2×#120C2318yes—
235#520—44no—
236#520—44no—
237#518—28no—
238C4×#41—28no—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4—44no—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×#117C2312yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C2×#117C2318yes—
264C2×#117C2318yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2318yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2318yes—
280C22×C22⋊C4C2314yes—
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284C22×C42C2311yescharacteristic
285#401C2314yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2318yes—
293#399C2314yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#398C2314yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2318yes—
315#395C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2314yes—
319#394C2314yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#393C2318yes—
325#393C2318yes—
326#393C2318yes—
327#392C2318yes—
328#392C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2311yescharacteristic
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2311yescharacteristic
343#390C2318yes—
344#390C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2311yescharacteristic
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2318yes—
357#390C2312yes—
358#390C2312yes—
359#390C2314yes—
360#390C2318yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2311yescharacteristic
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2318yes—
406#386C2318yes—
407#386C2312yes—
408#386C2312yes—
409#386C2314yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2314yes—
419#386C2312yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2318yes—
424#386C2318yes—
425#386C2312yes—
426#386C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2312yes—
430#386C2312yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2318yes—
435#385C2312yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2312yes—
442#385C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#383C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2318yes—
455#381C2318yes—
456#381C2318yes—
457#381C2318yes—
458#381C2314yes—
459#380C2318yes—
460#380C2318yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#379C2318yes—
470#379C2318yes—
471#379C2318yes—
472#379C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2318yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502#376C2312yes—
503C2×#95C2318yes—
504C2×#95C2312yes—
505C43C2312yes—
506C25C2414yes—
507C25C2412yes—
508H(5,𝔽2)—464no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—28no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41#4118yes—
524C22×Q8—44no—
525C22×Q8—48no—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2418yes—
530C22×D4—216no—
531C22×D4—28no—
532C22×D4—28no—
533C22×D4—28no—
534C22×D4—216no—
535C22×D4—24no—
536C22×D4—28no—
537C22×D4—24no—
538C22×D4—44no—
539C22×D4—44no—
540C22×D4—48no—
541C22×D4#4118yes—
542C22×D4C2412yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2414yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2418yes—
554C22×D4C2414yes—
555C23×C4—48no—
556C23×C4—44no—
557C23×C4C2411yescharacteristic
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2414yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2411yescharacteristic
568C23×C4C2418yes—
569C23×C4C2412yes—
570C23×C4C2418yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2411yescharacteristic
574C4⋊Q8—24no—
575C4⋊Q8—48no—
576C4⋊Q8—48no—
577#127—24no—
578#127—28no—
579#126—216no—
580#126—416no—
581#124—24no—
582#124—24no—
583#124—28no—
584#124—416no—
585#123—216no—
586#123—416no—
587#123—416no—
588C22⋊Q8—232no—
589C22⋊Q8—416no—
590C22⋊Q8—416no—
591C22⋊Q8—416no—
592C22⋊Q8—416no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595#121—216no—
596#121—216no—
597#121—44no—
598#121—44no—
599#121—48no—
600#120—216no—
601#120—416no—
602C4×Q8—28no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×D4—216no—
606C4×D4—28no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—416no—
615C4×D4—416no—
616C4×D4—48no—
617C4×D4—48no—
618#117—28no—
619#117—24no—
620#117—24no—
621#117—24no—
622#117—24no—
623#117—24no—
624#117—416no—
625#117—44no—
626#117—44no—
627#117—416no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—28no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4—44no—
634C2×C4⋊C4—48no—
635C2×C4⋊C4—48no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C22⋊C4—216no—
672C2×C22⋊C4—48no—
673C2×C22⋊C4—48no—
674C2×C22⋊C4—416no—
675C2×C22⋊C4—416no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C42—28no—
716C2×C42—24no—
717C2×C42—24no—
718C2×C42—24no—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2418yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2418yes—
738C2×C42C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772C24—24no—
773C24—24no—
774C24—28no—
775C24—28no—
776C24—44no—
777C24—44no—
778C24—44no—
779C24—48no—
780C24—48no—
781C24C2×#4118yes—
782C24C2512yes—
783C24C2512yes—
784C24C2514yes—
785C24C2512yes—
786C24C2511yescharacteristic
787#41—232no—
788#41—432no—
789#41—432no—
790#41—416no—
791#41—416no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—216no—
801C2×Q8—48no—
802C2×Q8—48no—
803C2×Q8—816no—
804C2×Q8C2×#4114yes—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—216no—
818C2×D4—232no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—28no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—22no—
830C2×D4—28no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—432no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—44no—
841C2×D4—432no—
842C2×D4—464no—
843C2×D4C2×#4118yes—
844C2×D4C2×#4118yes—
845C2×D4C2×#4114yes—
846C2×D4C2×#4118yes—
847C22×C4—22no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—28no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—28no—
855C22×C4—22no—
856C22×C4—216no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—28no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—216no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—44no—
874C22×C4—42no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—816no—
888C22×C4C2×#4118yes—
889C22×C4C2×#4114yes—
890C22×C4C2×#4114yes—
891C22×C4H(5,𝔽2)14yes—
892C22×C4C2512yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—216no—
929C4⋊C4—216no—
930C4⋊C4—22no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—48no—
945C4⋊C4H(5,𝔽2)18yescomplemented
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—216no—
949C22⋊C4—28no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—28no—
953C22⋊C4—216no—
954C22⋊C4—24no—
955C22⋊C4—28no—
956C22⋊C4—216no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—216no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C42—22no—
985C42—24no—
986C42—22no—
987C42—24no—
988C42—28no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—28no—
999C42—44no—
1000C42—48no—
1001C42—44no—
1002C42—44no—
1003C42—48no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—28no—
1009C23—24no—
1010C23—22no—
1011C23—24no—
1012C23—28no—
1013C23—24no—
1014C23—216no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—24no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—416no—
1026C23—416no—
1027C23—84no—
1028C23—88no—
1029C23—84no—
1030C23—816no—
1031C23—816no—
1032C23—164no—
1033C23—164no—
1034C23C22×#4118yes—
1035C23C22×#4114yes—
1036C23C22×#4112yes—
1037C23C22×#4112yes—
1038C23C2×H(5,𝔽2)12yes—
1039C23C2611yescharacteristic
1040Q8—28no—
1041Q8—44no—
1042Q8—44no—
1043Q8—816no—
1044D4—216no—
1045D4—216no—
1046D4—216no—
1047D4—28no—
1048D4—416no—
1049D4—416no—
1050D4—416no—
1051D4—48no—
1052D4—48no—
1053D4—44no—
1054D4—44no—
1055D4—816no—
1056D4—164no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—216no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—28no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—28no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—48no—
1105C2×C4—416no—
1106C2×C4—48no—
1107C2×C4—416no—
1108C2×C4—44no—
1109C2×C4—48no—
1110C2×C4—48no—
1111C2×C4—816no—
1112C2×C4—816no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4—164no—
1117C2×C4—164no—
1118C2×C4#551116yescomplemented
1119C2×C4C22×#4114yes—
1120C2×C4C22×#4112yes—
1121C2×C4C22×#4112yes—
1122C2×C4C22×#4112yes—
1123C2×C4C22×#4112yes—
1124C2×C4C2×H(5,𝔽2)14yes—
1125C2×C4C2×H(5,𝔽2)14yes—
1126C2×C4C2×H(5,𝔽2)14yes—
1127C2×C4C2×H(5,𝔽2)12yes—
1128C2×C4C2×H(5,𝔽2)12yes—
1129C22—24no—
1130C22—24no—
1131C22—22no—
1132C22—22no—
1133C22—216no—
1134C22—28no—
1135C22—24no—
1136C22—28no—
1137C22—44no—
1138C22—48no—
1139C22—44no—
1140C22—42no—
1141C22—44no—
1142C22—42no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—816no—
1154C22—1616no—
1155C22C2×#55114yes—
1156C22C23×#4111yescharacteristic
1157C22C23×#4111yescharacteristic
1158C22C22×H(5,𝔽2)12yes—
1159C22C22×H(5,𝔽2)11yescharacteristic
1160C222−1+612yes—
1161C4—24no—
1162C4—24no—
1163C4—24no—
1164C4—24no—
1165C4—44no—
1166C4—44no—
1167C4—44no—
1168C4—42no—
1169C4—44no—
1170C4—42no—
1171C4—44no—
1172C4—44no—
1173C4—44no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4C2×#55114yes—
1180C4C2×#55114yes—
1181C2—24no—
1182C2—48no—
1183C2—44no—
1184C2—82no—
1185C2—82no—
1186C2C22×#55111yescharacteristic
1187C2#6283211yescharacteristic
1188C2#6288711yescharacteristic
1189C2#6298412yes—
1190C2#6298512yes—
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. #59479C2semidirect
2. #59476C2semidirect
3. #59275C2semidirect
4. #59273C2semidirect
5. #59133C2semidirect
6. #45081C2semidirect
7. #44998C2semidirect
8. #44988C2semidirect
9. #44903C2semidirect
10. #43147C2semidirect
11. #35592C2semidirect
12. #35574C2semidirect
13. #35557C2semidirect
14. #35541C2semidirect
15. #35530C2semidirect
17. C2×#2542C2semidirect
18. #34816C2semidirect
19. #34744C2semidirect
20. #34265C2semidirect
21. #34258C2semidirect
22. #34256C2semidirect
23. #34255C2semidirect
24. #34207C2semidirect
25. #34188C2semidirect
27. C2×#551C22semidirect
31. C22×C4⋊Q8C22semidirect
32. C22×C22⋊Q8C22semidirect
34. C2×#520C22semidirect
38. #2752C22semidirect
39. #2746C22semidirect
40. #2746C22semidirect
41. #2743C22semidirect
42. #2738C22semidirect
43. #2735C22semidirect
44. #2730C22semidirect
45. #2728C22semidirect
46. #2723C22semidirect
47. #2706C22semidirect
48. #2696C22semidirect
49. #2685C22semidirect
50. #2598C22semidirect
51. #2591C22semidirect
52. #2579C22semidirect
53. #2575C22semidirect
54. #2564C22semidirect
55. #2561C22semidirect
56. #2560C22semidirect
57. #2542C22semidirect
58. #2542C22semidirect
59. #2542C22semidirect
60. #2542C22semidirect
61. #2516C22semidirect
62. #2516C22semidirect
63. #2514C22semidirect
64. #2513C22semidirect
65. #2512C22semidirect
66. #2512C22semidirect
67. #2511C22semidirect
68. #2511C22semidirect
69. #2510C22semidirect
70. #2502C22semidirect
71. #2501C22semidirect
72. #2500C22semidirect
73. #2499C22semidirect
74. #2497C22semidirect
75. #2496C22semidirect
76. #2492C22semidirect
77. #2492C22semidirect
78. #2491C22semidirect
79. #2491C22semidirect
80. #2488C22semidirect
81. #2482C22semidirect
82. #2481C22semidirect
83. #2481C22semidirect
84. #2479C22semidirect
85. #2477C22semidirect
86. #2472C22semidirect
87. #2471C22semidirect
88. #2463C22semidirect
89. #2461C22semidirect
90. #2452C22semidirect
91. #2451C22semidirect
92. #2448C22semidirect
93. #2447C22semidirect
94. #2447C22semidirect
95. #2446C22semidirect
96. #2445C22semidirect
97. #2445C22semidirect
98. #2444C22semidirect
99. #2443C22semidirect
100. #2443C22semidirect
101. #2440C22semidirect
102. #2439C22semidirect
103. #2438C22semidirect
104. #2437C22semidirect
105. #2436C22semidirect
110. #2423C22semidirect
111. #2422C22semidirect
112. #2422C22semidirect
113. #2420C22semidirect
114. #2418C22semidirect
115. #2412C22semidirect
117. #2409C22semidirect
120. #2401C22semidirect
121. #2395C22semidirect
122. C2×#399C22semidirect
123. #2368C22semidirect
124. #2367C22semidirect
125. #2366C22semidirect
126. #2363C22semidirect
127. #2361C22semidirect
128. #2361C22semidirect
129. #2357C22semidirect
130. #2355C22semidirect
131. #2354C22semidirect
132. #2354C22semidirect
133. #2354C22semidirect
134. #2352C22semidirect
135. D4×C4⋊C4C22semidirect
136. #2342C22semidirect
144. #2326C22semidirect
145. #2326C22semidirect
146. #2321C22semidirect
147. #2319C22semidirect
148. #2317C22semidirect
149. #2316C22semidirect
150. #2314C22semidirect
156. #2311C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×#127C22semidirect
162. C4×#126C22semidirect
163. C4×#123C22semidirect
164. C4×#120C22semidirect
170. #2297C22semidirect
171. #2297C22semidirect
172. #2296C22semidirect
173. #2296C22semidirect
174. #2293C22semidirect
179. #2285C22semidirect
180. #2285C22semidirect
181. C2×#384C22semidirect
182. C2×#384C22semidirect
183. #2274C22semidirect
184. #2274C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C4⋊C4C22semidirect
945. C4⋊C4H(5,𝔽2)semidirect
1118. C2×C4#551semidirect

Maximal subgroups

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

subgroupindex
#594792
#594762
#592752
#592732
#591332
#450812
#449982
#449882
#449032
#431472
#355922
#355742
#355572
#355412
#355302
#355132
C2×#25422
#348162
#347442
#342652
#342582
#342562
#342552
#342072
#341882