Finite Group Databasebeta

← #7643483

Subgroups — #7643483

Order 512.

4832 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40203C214yesmaximal, complemented
2#40154C214yesmaximal, complemented
3#39251C214yesmaximal, complemented
4#39010C214yesmaximal, complemented
5#38514C218yesmaximal, complemented
6#38134C218yesmaximal, complemented
7#37412C214yesmaximal, complemented
8#37357C214yesmaximal, complemented
9#36641C211yesmaximal, characteristic, complemented
10C2×#2861C211yesmaximal, characteristic, complemented
11#35677C211yesmaximal, characteristic
12#35662C211yesmaximal, characteristic, complemented
13#35640C211yesmaximal, characteristic, complemented
14#35639C211yesmaximal, characteristic, complemented
15#35626C211yesmaximal, characteristic, complemented
16#35619C211yesmaximal, characteristic, complemented
17#35556C211yesmaximal, characteristic
18#35529C211yesmaximal, characteristic, complemented
19#35312C211yesmaximal, characteristic, complemented
20#35266C211yesmaximal, characteristic, complemented
21#35186C214yesmaximal, complemented
22#35117C214yesmaximal, complemented
23#34275C211yesmaximal, characteristic
24#34254C211yesmaximal, characteristic, complemented
25C4×#533C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#518C2211yescharacteristic
35#2863C2212yescomplemented
36#2863C2212yescomplemented
37#2862C2212yescomplemented
38#2861C2214yes—
39#2861C2214yes—
40#2861C2214yes—
41#2861C2214yes—
42#2861C2212yescomplemented
43#2860C2214yes—
44#2860C2212yescomplemented
45#2860C2212yescomplemented
46#2852C2214yes—
47#2852C2214yes—
48#2796C2218yescomplemented
49#2793C2218yescomplemented
50#2790C2218yescomplemented
51#2777C2218yescomplemented
52#2772C2218yescomplemented
53#2770C2218yescomplemented
54#2764C2218yescomplemented
55#2761C2218yescomplemented
56#2757C2218yescomplemented
57#2754C2218yescomplemented
58#2751C2218yescomplemented
59#2739C2218yescomplemented
60#2737C2218yescomplemented
61#2723C2218yescomplemented
62#2715C2218yescomplemented
63#2700C2218yescomplemented
64#2651C2218yescomplemented
65#2651C2218yescomplemented
66#2650C2218yescomplemented
67#2644C2214yes—
68#2642C2212yescomplemented
69#2640C2212yescomplemented
70#2637C2218yescomplemented
71#2592C2214yes—
72#2583C2214yes—
73#2582C2214yescomplemented
74#2581C2214yescomplemented
75#2579C2214yes—
76#2566C2212yes—
77#2566C2212yes—
78#2563C2212yes—
79#2552C2214yescomplemented
80#2552C2214yescomplemented
81#2550C2214yescomplemented
82#2550C2214yescomplemented
83#2548C2214yes—
84#2548C2214yes—
85#2545C2214yes—
86#2542C2212yes—
87#2532C2218yescomplemented
88#2529C2218yescomplemented
89#2515C2218yescomplemented
90#2513C2214yes—
91#2512C2214yes—
92#2512C2218yescomplemented
93#2503C2212yescomplemented
94#2502C2214yes—
95#2502C2212yescomplemented
96#2499C2212yescomplemented
97#2499C2212yescomplemented
98#2492C2214yescomplemented
99#2491C2214yes—
100#2490C2214yes—
101#2489C2214yescomplemented
102#2488C2218yes—
103#2487C2214yes—
104#2483C2214yes—
105#2483C2214yes—
106#2480C2218yes—
107#2472C2218yes—
108#2468C2218yescomplemented
109#2468C2218yescomplemented
110#2465C2218yescomplemented
111#2454C2214yes—
112#2454C2214yescomplemented
113#2453C2214yescomplemented
114#2453C2214yescomplemented
115#2452C2214yes—
116#2451C2214yescomplemented
117#2448C2218yescomplemented
118#2447C2214yes—
119#2447C2214yes—
120#2447C2214yes—
121#2447C2214yes—
122#2447C2214yescomplemented
123#2446C2214yescomplemented
124#2442C2214yescomplemented
125#2441C2214yescomplemented
126#2438C2218yes—
127#2437C2218yes—
128#2426C2214yes—
129#2426C2214yes—
130#2419C2218yes—
131#2411C2214yes—
132#2411C2214yes—
133#2363C2214yes—
134#2361C2214yes—
135#2358C2218yes—
136#2356C2214yescomplemented
137#2355C2214yescomplemented
138#2343C2218yes—
139#2334C2218yescomplemented
140#2332C2218yescomplemented
141#2328C2212yes—
142#2326C2212yes—
143#2326C2218yescomplemented
144#2320C2214yescomplemented
145#2319C2218yescomplemented
146#2317C2211yescharacteristic
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2311C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2309C2211yescharacteristic
154#2309C2211yescharacteristic
155C4×C4⋊Q8C2212yescomplemented
156C4×C4⋊Q8C2212yescomplemented
157C4×#127C2212yes—
158C4×#125C2212yescomplemented
159C4×#125C2212yescomplemented
160C4×#126C2214yescomplemented
161C4×#126C2214yescomplemented
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2295C2214yescomplemented
174#2295C2214yescomplemented
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#390C2211yescharacteristic
179C2×#388C2214yes—
180C2×#388C2214yes—
181#2285C2211yescharacteristic
182#2274C2211yescharacteristic
183C42×Q8C2214yescomplemented
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C43C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190#544—44no—
191#536—44no—
192#535—28no—
193#533—28no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×#127C2312yes—
199C2×#126C2314yes—
200C2×#126C2314yes—
201C2×#126C2318yes—
202C2×#125—44no—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#124—44no—
209C2×#124C2312yes—
210C2×#124C2318yes—
211C2×#124C2314yes—
212C2×#124C2314yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×#121C2314yes—
221C2×#120C2314yes—
222#520—44no—
223#519—28no—
224#518—44no—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C22⋊C4C2314yes—
253C22×C22⋊C4C2314yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2314yes—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2312yes—
261C22×C42C2312yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#395C2318yes—
294#395C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2311yescharacteristic
314#391C2318yes—
315#391C2318yes—
316#391C2318yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2311yescharacteristic
323#391C2312yes—
324#390C2311yescharacteristic
325#390C2312yes—
326#390C2318yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2318yes—
336#390C2318yes—
337#390C2312yes—
338#390C2318yes—
339#390C2311yescharacteristic
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2318yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2314yes—
410#386C2312yes—
411#386C2318yes—
412#386C2318yes—
413#386C2314yes—
414#386C2312yes—
415#386C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2312yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2312yes—
427#385C2312yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2312yes—
432#385C2312yes—
433#385C2312yes—
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2312yes—
439#384C2318yes—
440#383C2314yes—
441#383C2314yes—
442#383C2318yes—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2318yes—
449#382C2318yes—
450#381C2314yes—
451#381C2314yes—
452#381C2318yes—
453#381C2318yes—
454#381C2318yes—
455#380C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460#379C2314yes—
461#379C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490#376C2318yes—
491#376C2312yes—
492#376C2312yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C43C2312yes—
496C43C2312yes—
497C43C2312yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×Q8C2414yes—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2418yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2414yes—
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537#127—28no—
538#126—48no—
539#126—48no—
540#126—416no—
541#125—28no—
542#125—48no—
543#125—48no—
544#125—44no—
545#125—44no—
546#124—28no—
547#124—48no—
548#124—48no—
549#124—44no—
550#124—416no—
551#123—48no—
552C22⋊Q8—216no—
553C22⋊Q8—48no—
554C22⋊Q8—416no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557#121—216no—
558#120—216no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—48no—
563C4×Q8—48no—
564C4×Q8—44no—
565C4×D4—416no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—48no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—216no—
579#117—44no—
580#117#4118yes—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C22⋊C4—48no—
629C2×C22⋊C4—48no—
630C2×C22⋊C4—48no—
631C2×C22⋊C4—44no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2412yes—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—44no—
667C2×C42—44no—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2418yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2411yescharacteristic
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2418yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734C24—24no—
735C24—24no—
736C24—24no—
737C24—44no—
738C24—44no—
739C24C2514yes—
740C24C2512yes—
741C24C2511yescharacteristic
742#41—416no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—28no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—28no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—48no—
757C2×Q8—416no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—216no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—22no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—416no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4C2×#4114yes—
801C22×C4H(5,𝔽2)14yes—
802C22×C42−1+414yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C4⋊C4—24no—
826C4⋊C4—216no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4C2×#4118yes—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—216no—
874C22⋊C4—216no—
875C22⋊C4—216no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4C2×#4118yes—
897C42—24no—
898C42—22no—
899C42—22no—
900C42—24no—
901C42—216no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—24no—
910C42—22no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—28no—
918C42—42no—
919C42—42no—
920C42—42no—
921C42—42no—
922C42—44no—
923C42—44no—
924C42—44no—
925C42—48no—
926C42C2×#4118yes—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—24no—
936C23—28no—
937C23—28no—
938C23—24no—
939C23—48no—
940C23—88no—
941C23—88no—
942C23—84no—
943C23—84no—
944C23C22×#4112yes—
945C23C2×H(5,𝔽2)12yes—
946C23C2×2−1+412yes—
947C23C2611yescharacteristic
948Q8—416no—
949Q8—48no—
950Q8—48no—
951Q8—44no—
952Q8—164no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—44no—
957D4—816no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—164no—
1016C2×C4—164no—
1017C2×C4—164no—
1018C2×C4#542116yes—
1019C2×C4C22×#4118yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C2×H(5,𝔽2)12yes—
1023C2×C4C2×H(5,𝔽2)12yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4C2×2−1+412yes—
1026C2×C4#58514yes—
1027C2×C4#58514yes—
1028C22—24no—
1029C22—24no—
1030C22—22no—
1031C22—22no—
1032C22—44no—
1033C22—48no—
1034C22—44no—
1035C22—48no—
1036C22—42no—
1037C22—44no—
1038C22—44no—
1039C22—42no—
1040C22—42no—
1041C22—44no—
1042C22—168no—
1043C22C2×#54214yes—
1044C22C23×#4111yescharacteristic
1045C22C22×H(5,𝔽2)11yescharacteristic
1046C22C22×2−1+411yescharacteristic
1047C22C2×#58512yes—
1048C22C2×#58512yes—
1049C4—24no—
1050C4—28no—
1051C4—24no—
1052C4—44no—
1053C4—42no—
1054C4—44no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—44no—
1069C4C2×#54214yes—
1070C4C2×#54214yes—
1071C2—24no—
1072C2—82no—
1073C2—84no—
1074C2C22×#54211yescharacteristic
1075C2#6281012yes—
1076C2#6283112yes—
1077C2#6283611yescharacteristic
1078C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40203C2semidirect
2. #40154C2semidirect
3. #39251C2semidirect
4. #39010C2semidirect
5. #38514C2semidirect
6. #38134C2semidirect
7. #37412C2semidirect
8. #37357C2semidirect
9. #36641C2semidirect
10. C2×#2861C2semidirect
12. #35662C2semidirect
13. #35640C2semidirect
14. #35639C2semidirect
15. #35626C2semidirect
16. #35619C2semidirect
18. #35529C2semidirect
19. #35312C2semidirect
20. #35266C2semidirect
21. #35186C2semidirect
22. #35117C2semidirect
24. #34254C2semidirect
25. C4×#533C2semidirect
35. #2863C22semidirect
36. #2863C22semidirect
37. #2862C22semidirect
42. #2861C22semidirect
44. #2860C22semidirect
45. #2860C22semidirect
48. #2796C22semidirect
49. #2793C22semidirect
50. #2790C22semidirect
51. #2777C22semidirect
52. #2772C22semidirect
53. #2770C22semidirect
54. #2764C22semidirect
55. #2761C22semidirect
56. #2757C22semidirect
57. #2754C22semidirect
58. #2751C22semidirect
59. #2739C22semidirect
60. #2737C22semidirect
61. #2723C22semidirect
62. #2715C22semidirect
63. #2700C22semidirect
64. #2651C22semidirect
65. #2651C22semidirect
66. #2650C22semidirect
68. #2642C22semidirect
69. #2640C22semidirect
70. #2637C22semidirect
73. #2582C22semidirect
74. #2581C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2550C22semidirect
82. #2550C22semidirect
87. #2532C22semidirect
88. #2529C22semidirect
89. #2515C22semidirect
92. #2512C22semidirect
93. #2503C22semidirect
95. #2502C22semidirect
96. #2499C22semidirect
97. #2499C22semidirect
98. #2492C22semidirect
101. #2489C22semidirect
108. #2468C22semidirect
109. #2468C22semidirect
110. #2465C22semidirect
112. #2454C22semidirect
113. #2453C22semidirect
114. #2453C22semidirect
116. #2451C22semidirect
117. #2448C22semidirect
122. #2447C22semidirect
123. #2446C22semidirect
124. #2442C22semidirect
125. #2441C22semidirect
136. #2356C22semidirect
137. #2355C22semidirect
139. #2334C22semidirect
140. #2332C22semidirect
143. #2326C22semidirect
144. #2320C22semidirect
145. #2319C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×C4⋊Q8C22semidirect
158. C4×#125C22semidirect
159. C4×#125C22semidirect
160. C4×#126C22semidirect
161. C4×#126C22semidirect
173. #2295C22semidirect
174. #2295C22semidirect
183. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#402032
#401542
#392512
#390102
#385142
#381342
#374122
#373572
#366412
C2×#28612
#356772
#356622
#356402
#356392
#356262
#356192
#355562
#355292
#353122
#352662
#351862
#351172
#342752
#342542
C4×#5332