Finite Group Databasebeta

← #7658136

Subgroups — #7658136

Order 512.

6992 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#42985C214yesmaximal, complemented
4#42424C214yesmaximal, complemented
5#42393C218yesmaximal, complemented
6#42152C218yesmaximal, complemented
7#39173C212yesmaximal, complemented
8#39169C212yesmaximal, complemented
9#38092C214yesmaximal, complemented
10#38089C214yesmaximal, complemented
11#37632C211yesmaximal, characteristic, complemented
12#37618C212yesmaximal, complemented
13#37618C211yesmaximal, characteristic, complemented
14#37545C212yesmaximal, complemented
15#36415C212yesmaximal, complemented
16#36412C212yesmaximal, complemented
17#36083C214yesmaximal, complemented
18#36019C214yesmaximal, complemented
19#35303C212yesmaximal, complemented
20#35289C211yesmaximal, characteristic, complemented
21#34637C212yesmaximal, complemented
22#34624C211yesmaximal, characteristic, complemented
23#34123C211yesmaximal, characteristic, complemented
24#3517—216no—
25#3511—216no—
26C2×#557C2211yescharacteristic
27C2×#556C2212yes—
28C2×#555C2212yes—
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#553C2212yes—
32C2×#553C2214yes—
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2212yes—
36C2×#550C2212yes—
37C2×#548C2214yes—
38C2×#547C2211yescharacteristic
39C2×#547C2212yes—
40C2×#547C2212yes—
41C2×#542C2214yes—
42C2×#540C2214yes—
43C2×#540C2212yes—
44C2×#537C2212yes—
45C2×#533C2212yes—
46C2×#532C2211yescharacteristic
47C2×#532C2212yes—
48C2×#532C2211yescharacteristic
49C2×#532C2212yes—
50C22×C4⋊Q8C2211yescharacteristic
51C2×#529C2211yescharacteristic
52C2×#529C2212yes—
53C2×#520C2212yes—
54C2×#520C2212yes—
55C2×C4×#41C2211yescharacteristic
56#2862C2212yes—
57#2858C2212yes—
58#2856C2214yes—
59#2850C2214yes—
60#2821C2214yes—
61#2815C2218yes—
62#2815C2214yes—
63#2814C2218yes—
64#2693C22116yes—
65#2690C22116yes—
66#2688C22116yes—
67#2676C22116yes—
68#2673C22116yes—
69#2671C22116yes—
70#2662C2214yes—
71#2661C2214yes—
72#2660C2212yes—
73#2660C2211yescharacteristic
74#2657C2211yescharacteristic
75#2657C2212yes—
76#2642C2214yes—
77#2641C2214yes—
78#2641C2211yescharacteristic
79#2640C2212yes—
80#2640C2211yescharacteristic
81#2640C2212yes—
82#2640C2212yes—
83#2640C2212yes—
84#2639C2218yes—
85#2639C2218yes—
86#2638C2218yes—
87#2637C2218yes—
88#2631C2214yes—
89#2631C2218yes—
90#2628C2214yes—
91#2620C2212yes—
92#2619C2212yes—
93#2615C2218yes—
94#2615C2214yes—
95#2614C2214yes—
96#2610C2218yes—
97#2603C2218yes—
98#2599C2218yes—
99#2567C2212yes—
100#2566C2214yes—
101#2565C2214yes—
102#2563C2212yes—
103#2563C2214yes—
104#2557C22116yes—
105#2555C22116yes—
106#2547C2212yes—
107#2547C2214yes—
108#2547C2214yes—
109#2543C2218yes—
110#2541C2212yes—
111#2541C2214yes—
112#2535C2218yes—
113#2535C2218yes—
114#2535C2214yes—
115#2504C2214yes—
116#2503C2212yes—
117#2501C2212yes—
118#2500C2214yes—
119#2499C2214yes—
120#2486C2214yes—
121#2481C22116yes—
122#2467C22116yes—
123#2464C22116yes—
124#2457C22116yes—
125#2442C2218yes—
126#2436C2214yes—
127#2431C2214yes—
128#2431C2214yes—
129#2431C2214yes—
130#2430C2218yes—
131#2428C2218yes—
132#2421C2218yes—
133#2416C2218yes—
134#2407C2218yes—
135#2398C2218yes—
136#2398C2218yes—
137#2392C2214yes—
138#2388C2214yes—
139#2363C2218yes—
140#2356C2212yes—
141#2353C2214yes—
142#2352C2218yes—
143#2349C2212yes—
144#2346C2212yes—
145#2343C2214yes—
146#2339C2212yes—
147#2328C2214yes—
148#2326C2214yes—
149#2311C2214yes—
150C4×#127C2212yes—
151C4×#124C2212yes—
152#2297C2214yes—
153#2297C2214yes—
154#2295C2212yes—
155#2290C2214yes—
156#2283C2211yescharacteristic
157#2283C2212yes—
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×#376C2212yes—
161C22×#41C2312yes—
162C22×#41C2312yes—
163C22×#41C2312yes—
164C22×#41C2312yes—
165C22×#41C2312yes—
166C22×#41C2314yes—
167C22×#41C2311yescharacteristic
168C23×Q8C2312yes—
169#557—28no—
170#556—216no—
171#555—216no—
172#554—216no—
173#553—232no—
174#553—216no—
175#553—232no—
176#550—216no—
177#550—28no—
178#550—216no—
179#550—28no—
180#548—232no—
181#547—216no—
182#547—216no—
183#547—28no—
184#542—232no—
185#540—216no—
186#540—232no—
187#537—216no—
188#533—216no—
189#532—28no—
190#532—216no—
191#532—28no—
192#532—216no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×#127C2311yescharacteristic
202C2×#127C2312yes—
203C2×#127C2311yescharacteristic
204C2×#127C2314yes—
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#127C2314yes—
208#529—28no—
209#529—216no—
210C2×#126C2312yes—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#125C2314yes—
214C2×#125C2311yescharacteristic
215C2×#125C2314yes—
216C2×#125C2312yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#124C2311yescharacteristic
220C2×#124C2312yes—
221C2×#124C2318yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#123C2312yes—
226C2×#123C2318yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2318yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2314yes—
241C2×#121C2312yes—
242C2×#121C2311yescharacteristic
243C2×#121C2312yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2318yes—
258C2×#121C23116yes—
259C2×#121C23116yes—
260#520—216no—
261#520—216no—
262C4×#41D4116yescomplemented
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2318yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2318yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×#117C2314yes—
292C2×#117C2314yes—
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C42C2314yes—
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306#400C2318yes—
307#400C23116yes—
308#400C23116yes—
309#399C2318yes—
310#398C23116yes—
311#398C2318yes—
312#398C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C23116yes—
317#397C2318yes—
318#397C2318yes—
319#397C23116yes—
320#397C2314yes—
321#396C23116yes—
322#396C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2318yes—
329#394C2318yes—
330#394C23116yes—
331#394C23116yes—
332#394C23116yes—
333#393C2318yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#393C2314yes—
339#392C2318yes—
340#392C2318yes—
341#392C2314yes—
342#392C23116yes—
343#392C23116yes—
344#392C23116yes—
345#392C2318yes—
346#392C23116yes—
347#392C2318yes—
348#392C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2318yes—
355#391C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2318yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2312yes—
365#390C23116yes—
366#389C2318yes—
367#389C2314yes—
368#388C23116yes—
369#388C23116yes—
370#388C23116yes—
371#388C2318yes—
372#388C2318yes—
373#387C23116yes—
374#387C2318yes—
375#387C2318yes—
376#387C23116yes—
377#386C23116yes—
378#386C23116yes—
379#386C23116yes—
380#386C23116yes—
381#386C2318yes—
382#386C23116yes—
383#386C23116yes—
384#386C23116yes—
385#386C23116yes—
386#386C23116yes—
387#385C23116yes—
388#385C23116yes—
389#385C2318yes—
390#384C2312yes—
391#384C2314yes—
392#383C2312yes—
393#383C2314yes—
394#382C2314yes—
395#382C2318yes—
396#382C2312yes—
397#382C2314yes—
398#382C2312yes—
399#381C2314yes—
400#381C2312yes—
401#381C2318yes—
402#380C23116yes—
403#380C2318yes—
404#380C2312yes—
405#380C2314yes—
406#380C2318yes—
407#380C23116yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C23116yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C23116yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421#376C2314yes—
422#376C2314yes—
423#376C2314yes—
424#376C2311yescharacteristic
425#376C2312yes—
426#376C2311yescharacteristic
427C2×#95C2314yes—
428C2×#95C2314yes—
429C43C2312yes—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—216no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—48no—
437C2×#41—44no—
438C2×#41—48no—
439C2×#41—48no—
440C2×#41—48no—
441C2×#41—48no—
442C2×#41—88no—
443C2×#41C2×D418yes—
444C22×Q8—28no—
445C22×Q8—84no—
446C22×Q8C2412yes—
447C22×Q8C2411yescharacteristic
448C22×Q8C2411yescharacteristic
449C22×Q8C2412yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C22×D4C2412yes—
456C22×D4C2411yescharacteristic
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2412yes—
464C22×D4C2412yes—
465C22×D4C2418yes—
466C22×D4C2414yes—
467C22×D4C2414yes—
468C22×D4C2414yes—
469C22×D4C2418yes—
470C22×D4C24116yes—
471C22×D4C2412yes—
472C23×C4C2412yes—
473C23×C4C2414yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2414yes—
478C23×C4C2414yes—
479C23×C4C2418yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2418yes—
484C23×C4C2412yes—
485C23×C4C2411yescharacteristic
486C23×C4C2412yes—
487C4⋊Q8—28no—
488C4⋊Q8—28no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—24no—
492C4⋊Q8—28no—
493C4⋊Q8—24no—
494#127—28no—
495#127—216no—
496#127—24no—
497#127—28no—
498#127—24no—
499#127—48no—
500#127—44no—
501#126—232no—
502#126—216no—
503#126—28no—
504#125—28no—
505#125—216no—
506#125—24no—
507#125—216no—
508#124—232no—
509#124—24no—
510#124—28no—
511#124—28no—
512#124—216no—
513#124—48no—
514#124—44no—
515#124—88no—
516#123—28no—
517#123—216no—
518#123—216no—
519#123—216no—
520#123—216no—
521#123—232no—
522#123—88no—
523C22⋊Q8—216no—
524C22⋊Q8—24no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—232no—
529#121—216no—
530#121—232no—
531#121—28no—
532#121—216no—
533#121—24no—
534#121—28no—
535#121—216no—
536#121—28no—
537#121—216no—
538#121—28no—
539#121—28no—
540#121—216no—
541#121—28no—
542#121—216no—
543#121—28no—
544#121—216no—
545#121—216no—
546#121—216no—
547#121—216no—
548#121—416no—
549#121—816no—
550#121—816no—
551C4×Q8—28no—
552C4×Q8—216no—
553C4×Q8—28no—
554C4×Q8—24no—
555C4×Q8—216no—
556C4×Q8C2×D418yes—
557C4×Q8C2×D418yes—
558C4×D4—28no—
559C4×D4—216no—
560C4×D4—28no—
561C4×D4—216no—
562C4×D4—232no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—216no—
566C4×D4—28no—
567C4×D4—24no—
568C4×D4—28no—
569C4×D4—216no—
570C4×D4—28no—
571C4×D4—216no—
572C4×D4—28no—
573C4×D4—48no—
574C4×D4—416no—
575C4×D4C2×D418yes—
576C4×D4C2×D4116yes—
577C4×D4C2×D4116yes—
578C4×D4C2×D418yes—
579#117—216no—
580#117—216no—
581#117—28no—
582#117—216no—
583#117—44no—
584#117C2×D418yes—
585#117C2×D4116yes—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—216no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C24116yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C24116yes—
641C2×C22⋊C4C24116yes—
642C2×C22⋊C4C24116yes—
643C2×C22⋊C4C24116yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C24116yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C42—48no—
651C2×C42C2×D418yes—
652C2×C42C2×D4116yes—
653C2×C42C2418yes—
654C2×C42C2412yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2418yes—
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#95C2412yes—
670#95C2412yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2412yes—
676#95C2412yes—
677#95C2418yes—
678#95C2414yes—
679#95C2418yes—
680#95C24116yes—
681#95C24116yes—
682#95C24116yes—
683#95C2414yes—
684#95C2418yes—
685#95C2418yes—
686#95C24116yes—
687#95C24116yes—
688C24C2514yes—
689C24C2512yes—
690C24C2514yes—
691C24C2511yescharacteristic
692C24C2512yes—
693#41—416no—
694#41—432no—
695#41—432no—
696#41—816no—
697#41—816no—
698#41—816no—
699#41—832no—
700C2×Q8—24no—
701C2×Q8—28no—
702C2×Q8—24no—
703C2×Q8—22no—
704C2×Q8—28no—
705C2×Q8—24no—
706C2×Q8—28no—
707C2×Q8—24no—
708C2×Q8—48no—
709C2×Q8—44no—
710C2×Q8—48no—
711C2×Q8—816no—
712C2×Q8C22×D414yes—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—216no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—28no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—416no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—416no—
752C2×D4—416no—
753C2×D4—416no—
754C2×D4C22×D414yes—
755C2×D4C22×D418yes—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—24no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—216no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—216no—
769C22×C4—42no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—44no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—416no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C22×D418yes—
784C22×C4C22×D418yes—
785C22×C4C22×D414yes—
786C22×C4C22×D418yes—
787C22×C4C2518yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2518yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—216no—
825C4⋊C4—28no—
826C4⋊C4—44no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—416no—
830C4⋊C4C22×D414yes—
831C4⋊C4C22×D414yes—
832C4⋊C4C22×D418yes—
833C4⋊C4C22×D418yes—
834C22⋊C4—216no—
835C22⋊C4—28no—
836C22⋊C4—24no—
837C22⋊C4—28no—
838C22⋊C4—24no—
839C22⋊C4—28no—
840C22⋊C4—24no—
841C22⋊C4—216no—
842C22⋊C4—28no—
843C22⋊C4—24no—
844C22⋊C4—216no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—416no—
854C22⋊C4—48no—
855C22⋊C4—416no—
856C22⋊C4—416no—
857C22⋊C4—416no—
858C22⋊C4—44no—
859C22⋊C4—416no—
860C22⋊C4—48no—
861C22⋊C4C22×D418yes—
862C22⋊C4C22×D418yes—
863C22⋊C4C22×D418yes—
864C42—216no—
865C42—28no—
866C42—24no—
867C42—24no—
868C42—28no—
869C42—24no—
870C42—28no—
871C42—48no—
872C42—44no—
873C42C22×D414yes—
874C42C22×D414yes—
875C42C22×D418yes—
876C42C22×D418yes—
877C42C22×D414yes—
878C42C22×D418yes—
879C42C22×D414yes—
880C23—22no—
881C23—24no—
882C23—24no—
883C23—22no—
884C23—22no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—22no—
889C23—24no—
890C23—24no—
891C23—28no—
892C23—28no—
893C23—24no—
894C23—28no—
895C23—24no—
896C23—24no—
897C23—28no—
898C23—28no—
899C23C23×D414yes—
900C23C23×D412yes—
901C23C2611yescharacteristic
902Q8—28no—
903Q8—416no—
904Q8—48no—
905Q8—48no—
906Q8—44no—
907Q8—88no—
908D4—28no—
909D4—48no—
910D4—48no—
911D4—416no—
912D4—48no—
913D4—416no—
914D4—48no—
915D4—48no—
916D4—44no—
917D4—48no—
918D4—88no—
919D4—84no—
920D4—84no—
921D4—88no—
922D4—88no—
923D4—88no—
924D4—88no—
925D4—816no—
926D4—816no—
927D4—1616no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—28no—
936C2×C4—216no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—216no—
958C2×C4—24no—
959C2×C4—44no—
960C2×C4—48no—
961C2×C4—48no—
962C2×C4—416no—
963C2×C4—48no—
964C2×C4—416no—
965C2×C4—88no—
966C2×C4—88no—
967C2×C4—88no—
968C2×C4—816no—
969C2×C4—88no—
970C2×C4—816no—
971C2×C4C23×D414yes—
972C2×C4C23×D414yes—
973C2×C4C23×D412yes—
974C2×C4C23×D412yes—
975C2×C4C23×D412yes—
976C2×C4C23×D412yes—
977C2×C4C23×D414yes—
978C2×C4C23×D412yes—
979C2×C4C23×D412yes—
980C2×C4#58514yes—
981C2×C4#58514yes—
982C22—22no—
983C22—24no—
984C22—22no—
985C22—24no—
986C22—22no—
987C22—24no—
988C22—48no—
989C22—44no—
990C22—42no—
991C22—44no—
992C22—44no—
993C22—44no—
994C22—42no—
995C22—44no—
996C22—48no—
997C22—48no—
998C22—416no—
999C22—48no—
1000C22—44no—
1001C22—42no—
1002C22—44no—
1003C22C24×D411yescharacteristic
1004C22C2×#58512yes—
1005C22C2×#58512yes—
1006C22H(7,𝔽2)12yes—
1007C4—24no—
1008C4—22no—
1009C4—22no—
1010C4—24no—
1011C4—22no—
1012C4—22no—
1013C4—24no—
1014C4—44no—
1015C4—42no—
1016C4—48no—
1017C4—42no—
1018C4—44no—
1019C4—48no—
1020C4—44no—
1021C4—42no—
1022C4—44no—
1023C4#344914yes—
1024C4#350014yes—
1025C2—42no—
1026C2—44no—
1027C2—82no—
1028C2—84no—
1029C2—84no—
1030C2C2×#344911yescharacteristic
1031C2C2×#350011yescharacteristic
1032C2#6285211yescharacteristic
1033C2#6293714yes—
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×#3517C2semidirect
3. #42985C2semidirect
4. #42424C2semidirect
5. #42393C2semidirect
6. #42152C2semidirect
7. #39173C2semidirect
8. #39169C2semidirect
9. #38092C2semidirect
10. #38089C2semidirect
11. #37632C2semidirect
12. #37618C2semidirect
13. #37618C2semidirect
14. #37545C2semidirect
15. #36415C2semidirect
16. #36412C2semidirect
17. #36083C2semidirect
18. #36019C2semidirect
19. #35303C2semidirect
20. #35289C2semidirect
21. #34637C2semidirect
22. #34624C2semidirect
23. #34123C2semidirect
262. 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×#35172
#429852
#424242
#423932
#421522
#391732
#391692
#380922
#380892
#376322
#376182
#375452
#364152
#364122
#360832
#360192
#353032
#352892
#346372
#346242
#341232