Finite Group Databasebeta

← #7647597

Subgroups — #7647597

Order 512.

7082 conjugacy classes of subgroups.

The subgroup lattice has 1065 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42878C214yesmaximal, complemented
4#42428C214yesmaximal, complemented
5#40493C218yesmaximal, complemented
6#39598C214yesmaximal, complemented
7#38922C214yesmaximal, complemented
8#38042C218yesmaximal, complemented
9#37640C212yesmaximal, complemented
10#37633C212yesmaximal, complemented
11#37389C214yesmaximal, complemented
12#37299C214yesmaximal, complemented
13#35621C212yesmaximal, complemented
14#35532C212yesmaximal, complemented
15#35308C212yesmaximal, complemented
16#35279C211yesmaximal, characteristic, complemented
17#35273C212yesmaximal, complemented
18#35238C212yesmaximal, complemented
19#35178C211yesmaximal, characteristic, complemented
20#35173C212yesmaximal, complemented
21C2×#2567C211yesmaximal, characteristic, complemented
22#34937C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24#3511—216no—
25C2×#556C2212yes—
26C2×#555C2212yes—
27C2×#554C2212yes—
28C2×#553C2214yes—
29C2×#548C2214yes—
30C2×#547C2212yes—
31#3461—216no—
32C2×#544C2211yescharacteristic
33C2×#542C2214yes—
34C2×#542C2212yes—
35C2×#542C2212yes—
36C2×#541C2212yes—
37C2×#541C2212yes—
38C2×#539C2214yes—
39C2×#537C2212yes—
40C2×#537C2211yescharacteristic
41C2×#536C2211yescharacteristic
42C2×#536C2211yescharacteristic
43C2×#536C2212yes—
44C2×#533C2212yes—
45C2×#533C2212yes—
46C2×#533C2212yes—
47C2×#532C2212yes—
48C2×#532C2211yescharacteristic
49C2×#532C2212yes—
50C22×C4⋊Q8C2211yescharacteristic
51C2×#529C2212yes—
52C2×#529C2212yes—
53C2×#529C2214yes—
54C2×#520C2212yes—
55C2×C4×#41C2211yescharacteristic
56C2×C4×#41C2212yes—
57C2×C4×#41C2211yescharacteristic
58C22×C4×Q8C2211yescharacteristic
59#2857C2214yes—
60#2857C2214yes—
61#2857C2214yes—
62#2856C2214yes—
63#2854C2214yes—
64#2850C2214yes—
65#2820C2218yes—
66#2814C2218yes—
67#2727C22116yes—
68#2725C22116yes—
69#2715C22116yes—
70#2704C22116yes—
71#2695C22116yes—
72#2683C22116yes—
73#2672C22116yes—
74#2672C22116yes—
75#2662C2218yes—
76#2659C2218yes—
77#2637C2218yes—
78#2629C2218yes—
79#2628C2214yes—
80#2624C2218yes—
81#2621C2214yes—
82#2620C2214yes—
83#2620C2214yes—
84#2620C2214yes—
85#2618C2214yes—
86#2616C2218yes—
87#2584C2218yes—
88#2584C2218yes—
89#2568C2212yes—
90#2567C2212yes—
91#2567C2212yes—
92#2567C2214yes—
93#2567C2214yes—
94#2567C2212yes—
95#2567C2214yes—
96#2567C2214yes—
97#2566C2214yes—
98#2565C2214yes—
99#2563C2212yes—
100#2548C2211yescharacteristic
101#2548C2212yes—
102#2547C2211yescharacteristic
103#2547C2214yes—
104#2546C2212yes—
105#2546C2214yes—
106#2546C2211yescharacteristic
107#2545C2214yes—
108#2545C2212yes—
109#2545C2214yes—
110#2544C2214yes—
111#2544C2212yes—
112#2543C2214yes—
113#2542C2214yes—
114#2542C2212yes—
115#2541C2211yescharacteristic
116#2538C2218yes—
117#2538C2214yes—
118#2538C2218yes—
119#2537C2218yes—
120#2536C2214yes—
121#2487C2214yes—
122#2485C2218yes—
123#2449C22116yes—
124#2441C2218yes—
125#2440C2218yes—
126#2430C2218yes—
127#2429C2218yes—
128#2427C2218yes—
129#2425C22116yes—
130#2425C22116yes—
131#2417C2218yes—
132#2416C2218yes—
133#2416C22116yes—
134#2416C2214yes—
135#2415C2218yes—
136#2409C2214yes—
137#2392C2214yes—
138C2×#395C2214yes—
139#2351C2212yes—
140Q8×C4⋊C4C2212yes—
141#2349C2214yes—
142#2349C2212yes—
143D4×C4⋊C4C2212yes—
144D4×C4⋊C4C2214yes—
145#2324C2218yes—
146#2317C2212yes—
147#2316C2218yes—
148#2311C2212yes—
149#2311C2212yes—
150C4×#121C2214yes—
151#2297C2212yes—
152#2296C2214yes—
153#2296C2212yes—
154C2×#391C2212yes—
155C2×#389C2214yes—
156#2285C2212yes—
157#2285C2211yescharacteristic
158C2×#384C2212yes—
159C2×C4×C4⋊C4C2212yes—
160C2×C4×C4⋊C4C2211yescharacteristic
161C22×#41C2311yescharacteristic
162C22×#41C2312yes—
163C22×#41C2311yescharacteristic
164C22×#41C2314yes—
165C23×Q8C2311yescharacteristic
166C23×Q8C2312yes—
167#556—216no—
168#555—216no—
169#554—216no—
170#553—232no—
171#548—232no—
172#547—216no—
173#544—28no—
174#542—216no—
175#542—216no—
176#542—232no—
177#541—216no—
178#541—216no—
179#539—232no—
180#537—28no—
181#537—216no—
182#536—28no—
183#536—28no—
184#536—48no—
185#533—216no—
186#533—216no—
187#533—216no—
188#532—28no—
189#532—216no—
190#532—48no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×#127C2311yescharacteristic
204C2×#127C2312yes—
205#529—232no—
206#529—216no—
207#529—216no—
208C2×#126C2314yes—
209C2×#126C2314yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2318yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×#123C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×C22⋊Q8C23116yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2318yes—
259C2×#121C2314yes—
260C2×#121C2318yes—
261C2×#121C23116yes—
262#520—216no—
263C4×#41—28no—
264C4×#41—48no—
265C4×#41D4116yescomplemented
266C2×C4×Q8—28no—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2318yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2318yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2318yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2314yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2314yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2318yes—
314C22×C42C2312yes—
315C22×C42C2312yes—
316C22×C42C2312yes—
317C22×C42C2314yes—
318C22×C42C2311yescharacteristic
319C22×C42C2312yes—
320#400C2318yes—
321#399C23116yes—
322#399C2318yes—
323#398C23116yes—
324#398C2314yes—
325#398C2318yes—
326#398C23116yes—
327#398C23116yes—
328#397C23116yes—
329#397C23116yes—
330#397C2314yes—
331#396C23116yes—
332#396C23116yes—
333#396C23116yes—
334#396C23116yes—
335#396C23116yes—
336#396C23116yes—
337#396C2318yes—
338#395C2318yes—
339#395C2318yes—
340#395C2318yes—
341#395C23116yes—
342#395C23116yes—
343#394C2314yes—
344#394C2318yes—
345#394C23116yes—
346#394C23116yes—
347#394C23116yes—
348#394C2318yes—
349#394C23116yes—
350#393C2318yes—
351#392C2314yes—
352#391C2312yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2314yes—
358#391C2318yes—
359#391C2318yes—
360#390C2314yes—
361#390C2312yes—
362#390C2314yes—
363#390C2318yes—
364#390C23116yes—
365#390C2312yes—
366#390C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C23116yes—
370#389C2318yes—
371#389C23116yes—
372#389C2314yes—
373#389C2318yes—
374#389C23116yes—
375#389C2318yes—
376#389C23116yes—
377#389C23116yes—
378#389C2314yes—
379#389C2318yes—
380#389C2314yes—
381#389C2318yes—
382#388C23116yes—
383#388C23116yes—
384#388C23116yes—
385#388C2318yes—
386#387C23116yes—
387#386C2318yes—
388#386C2318yes—
389#386C23116yes—
390#386C23116yes—
391#386C2318yes—
392#386C2318yes—
393#385C23116yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#384C2314yes—
399#384C2314yes—
400#384C2314yes—
401#384C2318yes—
402#384C2312yes—
403#384C2314yes—
404#382C2314yes—
405#382C2314yes—
406#382C2312yes—
407#380C2318yes—
408#380C2318yes—
409#380C2318yes—
410#380C23116yes—
411#380C23116yes—
412#380C2312yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C23116yes—
417#380C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C2×#95C2312yes—
431C2×#95C2314yes—
432C2×#95C2318yes—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—216no—
436C2×#41—24no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—24no—
440C2×#41—24no—
441C2×#41—28no—
442C2×#41—88no—
443C2×#41C2×D418yes—
444C22×Q8—24no—
445C22×Q8—28no—
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—84no—
449C22×Q8C2412yes—
450C22×Q8C2412yes—
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2411yescharacteristic
454C22×Q8C2414yes—
455C22×Q8C2414yes—
456C22×Q8C2414yes—
457C22×D4C2412yes—
458C22×D4C2414yes—
459C22×D4C2412yes—
460C22×D4C2411yescharacteristic
461C22×D4C2412yes—
462C22×D4C2412yes—
463C22×D4C2411yescharacteristic
464C22×D4C2414yes—
465C22×D4C2418yes—
466C22×D4C2412yes—
467C22×D4C2418yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2412yes—
477C23×C4C2414yes—
478C23×C4C2418yes—
479C23×C4C2418yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2411yescharacteristic
484C4⋊Q8—28no—
485C4⋊Q8—28no—
486C4⋊Q8—28no—
487C4⋊Q8—28no—
488C4⋊Q8—28no—
489C4⋊Q8—28no—
490C4⋊Q8—24no—
491C4⋊Q8—28no—
492C4⋊Q8—28no—
493C4⋊Q8—44no—
494C4⋊Q8—48no—
495#127—24no—
496#127—44no—
497#126—216no—
498#126—232no—
499#126—216no—
500#126—216no—
501#126—216no—
502#125—216no—
503#125—28no—
504#125—216no—
505#125—28no—
506#125—216no—
507#125—216no—
508#124—28no—
509#124—216no—
510#124—232no—
511#124—28no—
512#124—28no—
513#124—216no—
514#124—44no—
515#124—44no—
516#124—48no—
517#123—216no—
518#123—216no—
519#123—216no—
520#123—216no—
521#123—232no—
522#123—416no—
523C22⋊Q8—28no—
524C22⋊Q8—216no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—28no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—28no—
532C22⋊Q8—28no—
533C22⋊Q8—216no—
534C22⋊Q8—232no—
535C22⋊Q8—216no—
536C22⋊Q8—416no—
537C22⋊Q8—88no—
538C22⋊Q8—816no—
539#121—216no—
540#121—28no—
541#121—216no—
542#121—232no—
543#121—28no—
544#121—216no—
545#121—28no—
546#121—28no—
547#121—216no—
548#121—216no—
549#121—416no—
550#121—816no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—24no—
556C4×Q8—24no—
557C4×Q8—216no—
558C4×Q8—216no—
559C4×Q8—216no—
560C4×Q8—48no—
561C4×Q8C2×D418yes—
562C4×Q8C2×D418yes—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—232no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—216no—
570C4×D4—28no—
571C4×D4—216no—
572C4×D4—28no—
573C4×D4—48no—
574C4×D4—416no—
575C4×D4—416no—
576C4×D4C2×D4116yes—
577C4×D4C2×D418yes—
578C4×D4C2×D4116yes—
579C4×D4C2×D418yes—
580#117—24no—
581#117—216no—
582#117—216no—
583#117—28no—
584#117—216no—
585#117—28no—
586#117—216no—
587#117—48no—
588#117C2×D418yes—
589#117C2×D4116yes—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—28no—
593C2×C4⋊C4—28no—
594C2×C4⋊C4—216no—
595C2×C4⋊C4—28no—
596C2×C4⋊C4—216no—
597C2×C4⋊C4—88no—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C24116yes—
628C2×C4⋊C4C24116yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C24116yes—
634C2×C4⋊C4C24116yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C24116yes—
660C2×C22⋊C4C24116yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C24116yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C42—28no—
667C2×C42—28no—
668C2×C42—28no—
669C2×C42—48no—
670C2×C42C2×D418yes—
671C2×C42C2×D4116yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2411yescharacteristic
690#95C2412yes—
691#95C2414yes—
692#95C2412yes—
693#95C2418yes—
694#95C2414yes—
695#95C24116yes—
696#95C24116yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C24116yes—
702#95C24116yes—
703#95C24116yes—
704C24C2512yes—
705C24C2514yes—
706C24C2512yes—
707C24C2511yescharacteristic
708#41—232no—
709#41—416no—
710#41—432no—
711#41—832no—
712C2×Q8—24no—
713C2×Q8—24no—
714C2×Q8—24no—
715C2×Q8—22no—
716C2×Q8—28no—
717C2×Q8—28no—
718C2×Q8—28no—
719C2×Q8—22no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—22no—
723C2×Q8—24no—
724C2×Q8—22no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—22no—
729C2×Q8—48no—
730C2×Q8—48no—
731C2×Q8—48no—
732C2×Q8—416no—
733C2×Q8—816no—
734C2×Q8C22×D414yes—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—28no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—28no—
741C2×D4—28no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—216no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—22no—
750C2×D4—24no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—28no—
754C2×D4—22no—
755C2×D4—24no—
756C2×D4—216no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—416no—
762C2×D4C22×D418yes—
763C2×D4C22×D414yes—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—24no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—216no—
785C22×C4—216no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—44no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—44no—
794C22×C4—416no—
795C22×C4C22×D414yes—
796C22×C4C22×D418yes—
797C22×C4C22×D418yes—
798C22×C4C22×D414yes—
799C22×C4C22×D418yes—
800C22×C4C22×D414yes—
801C22×C4H(5,𝔽2)14yes—
802C22×C42−1+414yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2518yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2518yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—216no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—416no—
852C4⋊C4—416no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—416no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—416no—
859C4⋊C4C22×D414yes—
860C4⋊C4C22×D414yes—
861C4⋊C4C22×D418yes—
862C4⋊C4C22×D418yes—
863C4⋊C42−1+418yes—
864C22⋊C4—24no—
865C22⋊C4—216no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—216no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—216no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—416no—
884C22⋊C4—416no—
885C22⋊C4—416no—
886C22⋊C4—48no—
887C22⋊C4C22×D418yes—
888C22⋊C4C22×D418yes—
889C22⋊C4C22×D418yes—
890C42—28no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—28no—
895C42—216no—
896C42—24no—
897C42—24no—
898C42—28no—
899C42—28no—
900C42—48no—
901C42C22×D414yes—
902C42C22×D414yes—
903C42C22×D418yes—
904C42C22×D414yes—
905C42C22×D418yes—
906C42C22×D414yes—
907C42C22×D418yes—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—22no—
918C23—28no—
919C23—24no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—28no—
924C23C23×D414yes—
925C23C23×D412yes—
926C23C2×H(5,𝔽2)12yes—
927C23C2×2−1+412yes—
928C23C2611yescharacteristic
929Q8—28no—
930Q8—416no—
931Q8—48no—
932Q8—48no—
933Q8—48no—
934Q8—44no—
935Q8—88no—
936Q8—88no—
937D4—216no—
938D4—28no—
939D4—48no—
940D4—416no—
941D4—48no—
942D4—44no—
943D4—48no—
944D4—48no—
945D4—816no—
946D4—88no—
947D4—816no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—216no—
958C2×C4—28no—
959C2×C4—216no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—28no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—216no—
983C2×C4—44no—
984C2×C4—48no—
985C2×C4—416no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—416no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4—816no—
992C2×C4—816no—
993C2×C4—84no—
994C2×C4—88no—
995C2×C4#537116yes—
996C2×C4C23×D412yes—
997C2×C4C23×D414yes—
998C2×C4C23×D412yes—
999C2×C4C23×D412yes—
1000C2×C4C23×D414yes—
1001C2×C4C23×D414yes—
1002C2×C4C23×D412yes—
1003C2×C4C23×D412yes—
1004C2×C4C23×D412yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×2−1+418yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2×2−1+414yes—
1011C22—22no—
1012C22—22no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—44no—
1019C22—44no—
1020C22—42no—
1021C22—44no—
1022C22—44no—
1023C22—42no—
1024C22—42no—
1025C22—44no—
1026C22—48no—
1027C22—44no—
1028C22—44no—
1029C22—48no—
1030C22C2×#53714yes—
1031C22C24×D411yescharacteristic
1032C22C22×H(5,𝔽2)11yescharacteristic
1033C22C22×2−1+412yes—
1034C22C22×2−1+411yescharacteristic
1035C22H(7,𝔽2)12yes—
1036C4—22no—
1037C4—24no—
1038C4—22no—
1039C4—24no—
1040C4—22no—
1041C4—24no—
1042C4—28no—
1043C4—42no—
1044C4—48no—
1045C4—44no—
1046C4—42no—
1047C4—44no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4—48no—
1052C4C2×#53714yes—
1053C4C2×#53714yes—
1054C4#349914yes—
1055C2—24no—
1056C2—44no—
1057C2—82no—
1058C2—84no—
1059C2C22×#53711yescharacteristic
1060C2C2×#349911yescharacteristic
1061C2#6285211yescharacteristic
1062C2#6294312yes—
1063C2#6294412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3511C2semidirect
2. C2×#3461C2semidirect
3. #42878C2semidirect
4. #42428C2semidirect
5. #40493C2semidirect
6. #39598C2semidirect
7. #38922C2semidirect
8. #38042C2semidirect
9. #37640C2semidirect
10. #37633C2semidirect
11. #37389C2semidirect
12. #37299C2semidirect
13. #35621C2semidirect
14. #35532C2semidirect
15. #35308C2semidirect
16. #35279C2semidirect
17. #35273C2semidirect
18. #35238C2semidirect
19. #35178C2semidirect
20. #35173C2semidirect
21. C2×#2567C2semidirect
22. #34937C2semidirect
23. C4⋊C4×#41C2semidirect
265. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34612
#428782
#424282
#404932
#395982
#389222
#380422
#376402
#376332
#373892
#372992
#356212
#355322
#353082
#352792
#352732
#352382
#351782
#351732
C2×#25672
#349372
C4⋊C4×#412