Finite Group Databasebeta

← #7648447

Subgroups — #7648447

Order 512.

6648 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3475C211yesmaximal, characteristic
3#42891C212yesmaximal, complemented
4#42814C212yesmaximal, complemented
5#42681C212yesmaximal, complemented
6#42482C212yesmaximal, complemented
7#41411C214yesmaximal, complemented
8#40592C214yesmaximal, complemented
9#39955C214yesmaximal, complemented
10#39952C214yesmaximal, complemented
11#38422C218yesmaximal, complemented
12#37560C212yesmaximal, complemented
13#37549C212yesmaximal, complemented
14#37281C214yesmaximal, complemented
15#37279C214yesmaximal, complemented
16#35516C212yesmaximal, complemented
17#35516C212yesmaximal, complemented
18#35335C211yesmaximal, characteristic, complemented
19#35297C212yesmaximal, complemented
20#35253C212yesmaximal, complemented
21#35253C212yesmaximal, complemented
22#35173C211yesmaximal, characteristic, complemented
23#35138C212yesmaximal, complemented
24#34946C211yesmaximal, characteristic, complemented
25C2×#2562C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27#3504—216no—
28C2×#557C2212yescomplemented
29C2×#557C2212yescomplemented
30#3475—216no—
31C2×#556C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×#554C2214yes—
34C2×#554C2211yescharacteristic
35C2×#554C2214yes—
36C2×#554C2212yescomplemented
37C2×#554C2212yescomplemented
38C2×#553C2212yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×#551C2214yes—
42C2×#547C2211yescharacteristic
43C2×#546C2212yes—
44C2×#544C2211yescharacteristic
45C2×#544C2211yescharacteristic
46C2×#544C2212yescomplemented
47C2×#544C2212yescomplemented
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#533C2212yescomplemented
51C2×#529C2214yes—
52C2×#529C2212yes—
53C22×#125C2211yescharacteristic
54C22×#125C2212yescomplemented
55C2×#525C2212yes—
56C2×#520C2211yescharacteristic
57C2×#520C2211yescharacteristic
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic
61C22×#117C2212yes—
62#2859C2214yescomplemented
63#2857C2214yes—
64#2857C2214yescomplemented
65#2857C2214yescomplemented
66#2851C2214yescomplemented
67#2851C2214yescomplemented
68#2822C2214yescomplemented
69#2820C2214yes—
70#2817C2214yescomplemented
71#2816C2214yes—
72#2721C2218yescomplemented
73#2719C2218yescomplemented
74#2716C2218yescomplemented
75#2713C2218yescomplemented
76#2700C2218yescomplemented
77#2698C2218yescomplemented
78#2694C2218yes—
79#2690C2218yescomplemented
80#2689C2218yescomplemented
81#2687C2218yescomplemented
82#2681C2218yes—
83#2680C2218yescomplemented
84#2677C2218yescomplemented
85#2674C2218yes—
86#2674C2218yescomplemented
87#2672C2218yes—
88#2664C2218yescomplemented
89#2663C2218yescomplemented
90#2660C2212yescomplemented
91#2660C2212yescomplemented
92#2659C2214yes—
93#2634C2214yescomplemented
94#2634C2214yescomplemented
95#2633C2214yes—
96#2632C2214yes—
97#2629C2214yescomplemented
98#2629C2214yescomplemented
99#2628C2214yescomplemented
100#2628C2214yescomplemented
101#2627C2214yescomplemented
102#2625C2214yescomplemented
103#2618C2214yes—
104#2616C2214yes—
105#2611C2218yescomplemented
106#2604C2218yescomplemented
107#2584C2212yescomplemented
108#2584C2214yescomplemented
109#2584C2212yescomplemented
110#2584C2214yescomplemented
111#2584C2212yescomplemented
112#2584C2212yescomplemented
113#2583C2214yes—
114#2583C2214yes—
115#2581C2214yescomplemented
116#2567C2212yescomplemented
117#2567C2212yescomplemented
118#2563C2212yes—
119#2562C2214yes—
120#2562C2212yes—
121#2562C2211yescharacteristic
122#2562C2212yes—
123#2562C2212yes—
124#2562C2214yes—
125#2562C2212yes—
126#2562C2211yescharacteristic
127#2562C2211yescharacteristic
128#2562C2211yescharacteristic
129#2561C2214yes—
130#2547C2212yes—
131#2546C2212yescomplemented
132#2546C2212yescomplemented
133#2536C2214yes—
134#2503C2212yes—
135#2487C2214yescomplemented
136#2487C2214yescomplemented
137#2486C2214yescomplemented
138#2486C2214yescomplemented
139#2485C2214yescomplemented
140#2485C2214yescomplemented
141#2485C2214yescomplemented
142#2485C2214yescomplemented
143#2484C2214yescomplemented
144#2442C2214yescomplemented
145#2442C2214yescomplemented
146#2441C2214yescomplemented
147#2441C2214yescomplemented
148#2440C2214yescomplemented
149#2440C2214yescomplemented
150#2439C2214yescomplemented
151#2439C2214yescomplemented
152#2438C2218yes—
153#2438C2218yes—
154#2437C2218yes—
155#2437C2218yes—
156#2435C2212yes—
157#2423C2214yescomplemented
158#2423C2214yescomplemented
159#2422C2214yescomplemented
160#2422C2214yescomplemented
161#2421C2214yescomplemented
162#2421C2214yescomplemented
163#2420C2214yescomplemented
164#2420C2214yescomplemented
165#2419C2218yes—
166#2419C2218yes—
167#2418C2218yes—
168#2418C2218yes—
169#2415C2218yescomplemented
170#2413C2218yescomplemented
171#2406C2214yes—
172#2398C2212yes—
173#2398C2212yes—
174C2×#400C2212yes—
175C2×#394C2212yes—
176#2323C2218yescomplemented
177#2322C2218yescomplemented
178#2320C2212yescomplemented
179#2319C2212yescomplemented
180#2318C2214yes—
181#2317C2212yes—
182#2317C2212yes—
183#2317C2212yes—
184#2316C2212yes—
185#2316C2212yes—
186#2314C2214yescomplemented
187#2311C2212yes—
188C4×#124C2214yes—
189#2295C2212yescomplemented
190#2293C2212yescomplemented
191#2290C2214yes—
192C2×#388C2214yes—
193#2285C2212yescomplemented
194#2283C2212yescomplemented
195#2280C2212yes—
196#2280C2212yes—
197C2×#380C2212yes—
198C2×#380C2212yes—
199C4×#117C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C23×D4C2311yescharacteristic
204C24×C4C2312yes—
205#557—216no—
206#557—216no—
207#556—28no—
208#555—28no—
209#554—28no—
210#554—232no—
211#554—232no—
212#554—216no—
213#554—216no—
214#553—216no—
215#552—216no—
216#552—216no—
217#551—232no—
218#547—28no—
219#546—216no—
220#544—28no—
221#544—28no—
222#544—216no—
223#544—216no—
224#533—28no—
225#533—28no—
226#533—216no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238#529—232no—
239#529—216no—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#125—28no—
244C2×#125—216no—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2311yescharacteristic
248C2×#125C2311yescharacteristic
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265#525—216no—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2318yes—
271C2×#123C2318yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2318yes—
289C2×C22⋊Q8C2318yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#120C2314yes—
295#520—28no—
296#520—28no—
297C4×#41—216no—
298C4×#41D4116yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×D4—28no—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×#117—216no—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2314yes—
335C2×#117C2312yes—
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2311yescharacteristic
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2314yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2314yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2314yes—
361C22×C42C2314yes—
362C22×C42C2312yes—
363C22×C42C2311yescharacteristic
364C22×C42C2312yes—
365#400C2312yes—
366#400C2314yes—
367#400C2318yes—
368#400C2314yes—
369#400C2318yes—
370#400C2312yes—
371#400C2312yes—
372#400C2312yes—
373#400C2318yes—
374#400C2318yes—
375#400C2318yes—
376#399C2318yes—
377#399C2318yes—
378#399C2318yes—
379#399C2318yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#398C2318yes—
388#398C2318yes—
389#398C2318yes—
390#398C2318yes—
391#398C2318yes—
392#397C2314yes—
393#397C2314yes—
394#397C2318yes—
395#397C2318yes—
396#397C2318yes—
397#397C2318yes—
398#397C2318yes—
399#397C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#395C2314yes—
405#395C2314yes—
406#395C2318yes—
407#395C2314yes—
408#395C2314yes—
409#395C2318yes—
410#395C2318yes—
411#395C2318yes—
412#394C2312yes—
413#394C2314yes—
414#394C2318yes—
415#394C2318yes—
416#394C2314yes—
417#394C2318yes—
418#394C2312yes—
419#394C2312yes—
420#394C2312yes—
421#394C2318yes—
422#394C2318yes—
423#393C2318yes—
424#393C2314yes—
425#393C2314yes—
426#393C2318yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2318yes—
431#391C2318yes—
432#391C2314yes—
433#390C2314yes—
434#390C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2318yes—
450#389C2318yes—
451#389C2318yes—
452#389C2318yes—
453#389C2318yes—
454#389C2318yes—
455#389C2318yes—
456#389C2318yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#386C2318yes—
482#386C2318yes—
483#386C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2318yes—
492#385C2318yes—
493#384C2314yes—
494#384C2314yes—
495#384C2314yes—
496#384C2314yes—
497#383C2314yes—
498#382C2314yes—
499#382C2314yes—
500#382C2314yes—
501#382C2314yes—
502#382C2314yes—
503#381C2314yes—
504#381C2314yes—
505#381C2314yes—
506#381C2318yes—
507#381C2318yes—
508#380C2314yes—
509#380C2314yes—
510#380C2314yes—
511#380C2314yes—
512#380C2314yes—
513#380C2314yes—
514#380C2314yes—
515#380C2314yes—
516#380C2312yes—
517#380C2312yes—
518#380C2312yes—
519#380C2312yes—
520#380C2312yes—
521#380C2312yes—
522#380C2312yes—
523#380C2312yes—
524#380C2314yes—
525#380C2314yes—
526#380C2318yes—
527#380C2318yes—
528#380C2314yes—
529#380C2318yes—
530#380C2318yes—
531#379C2314yes—
532#379C2314yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2311yescharacteristic
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C22⋊C4C2312yes—
542C4×C22⋊C4C2312yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548#376C2312yes—
549#376C2314yes—
550C2×#95C2312yes—
551C2×#95C2314yes—
552C2×#95C2314yes—
553C43C2312yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—48no—
558C2×#41C2×D418yes—
559C22×Q8C2411yescharacteristic
560C22×Q8C2412yes—
561C22×Q8C2414yes—
562C22×Q8C2414yes—
563C22×Q8C2412yes—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×D4—24no—
567C22×D4—44no—
568C22×D4C2411yescharacteristic
569C22×D4C2414yes—
570C22×D4C2412yes—
571C22×D4C2412yes—
572C22×D4C2411yescharacteristic
573C22×D4C2411yescharacteristic
574C22×D4C2414yes—
575C23×C4—28no—
576C23×C4—28no—
577C23×C4—28no—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2414yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C4⋊Q8—28no—
597C4⋊Q8—28no—
598C4⋊Q8—216no—
599C4⋊Q8—216no—
600C4⋊Q8—28no—
601C4⋊Q8—28no—
602C4⋊Q8—24no—
603C4⋊Q8—24no—
604C4⋊Q8—24no—
605C4⋊Q8—24no—
606C4⋊Q8—84no—
607#126—216no—
608#126—216no—
609#126—216no—
610#125—216no—
611#125—28no—
612#125—28no—
613#125—216no—
614#125—216no—
615#125—28no—
616#125—24no—
617#125—28no—
618#125—28no—
619#125—28no—
620#125—216no—
621#125—28no—
622#125—28no—
623#125—216no—
624#125—28no—
625#125—24no—
626#125—28no—
627#124—216no—
628#124—28no—
629#124—48no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—416no—
635#123—88no—
636C22⋊Q8—28no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—416no—
653C22⋊Q8—88no—
654#121—28no—
655#121—28no—
656#121—28no—
657#121—216no—
658#120—216no—
659C4×Q8—28no—
660C4×Q8—28no—
661C4×Q8—28no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—216no—
668C4×Q8C2×D418yes—
669C4×Q8C2×D418yes—
670C4×D4—216no—
671C4×D4—216no—
672C4×D4—28no—
673C4×D4—28no—
674C4×D4—216no—
675C4×D4—216no—
676C4×D4—216no—
677C4×D4—24no—
678C4×D4—24no—
679C4×D4—28no—
680C4×D4—24no—
681C4×D4—28no—
682C4×D4—24no—
683C4×D4—28no—
684C4×D4C2×D4116yes—
685C4×D4C2×D418yes—
686C4×D4C2×D4116yes—
687C4×D4C2×D418yes—
688#117—28no—
689#117—28no—
690#117—28no—
691#117—28no—
692#117—24no—
693#117—24no—
694#117—28no—
695#117—28no—
696#117—28no—
697#117—216no—
698#117—216no—
699#117—216no—
700#117—84no—
701#117C2×D418yes—
702#117C2×D4116yes—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—216no—
711C2×C4⋊C4—216no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—216no—
774C2×C22⋊C4—48no—
775C2×C22⋊C4—84no—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C42—216no—
810C2×C42—82no—
811C2×C42C2×D418yes—
812C2×C42C2×D4116yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833#95C2414yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2412yes—
840#95C2412yes—
841#95C2414yes—
842#95C2418yes—
843#95C2418yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862C24—24no—
863C24—24no—
864C24—24no—
865C24—24no—
866C24—42no—
867C24—42no—
868C24—42no—
869C24C2512yes—
870C24C2512yes—
871C24C2512yes—
872C24C2511yescharacteristic
873#41—232no—
874#41—432no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—44no—
883C2×Q8—48no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8C22×D414yes—
892C2×D4—28no—
893C2×D4—24no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—24no—
897C2×D4—28no—
898C2×D4—22no—
899C2×D4—24no—
900C2×D4—22no—
901C2×D4—24no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—416no—
908C2×D4C22×D418yes—
909C2×D4C22×D414yes—
910C22×C4—28no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—28no—
915C22×C4—28no—
916C22×C4—28no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—28no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—28no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—41no—
938C22×C4—42no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—48no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—42no—
951C22×C4—432no—
952C22×C4C22×D418yes—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C22×D418yes—
956C22×C4C22×D418yes—
957C22×C4C22×D414yes—
958C22×C42−1+418yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2518yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C4⋊C4—22no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—22no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—48no—
1025C4⋊C4—48no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4—48no—
1032C4⋊C4—48no—
1033C4⋊C4—48no—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D414yes—
1036C4⋊C4C22×D418yes—
1037C4⋊C4C22×D418yes—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—216no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—24no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—48no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4C22×D418yes—
1069C22⋊C4C22×D418yes—
1070C22⋊C4C22×D418yes—
1071C42—28no—
1072C42—28no—
1073C42—28no—
1074C42—28no—
1075C42—28no—
1076C42—24no—
1077C42—24no—
1078C42—28no—
1079C42—44no—
1080C42—44no—
1081C42—42no—
1082C42—42no—
1083C42—44no—
1084C42C22×D418yes—
1085C42C22×D414yes—
1086C42C22×D418yes—
1087C42C22×D414yes—
1088C42C22×D414yes—
1089C42C22×D414yes—
1090C42C22×D418yes—
1091C23—22no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—24no—
1098C23—24no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—48no—
1112C23—48no—
1113C23—48no—
1114C23—48no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23C23×D414yes—
1119C23C23×D412yes—
1120C23C2×2−1+414yes—
1121C23#58514yes—
1122C23C2611yescharacteristic
1123Q8—28no—
1124Q8—48no—
1125Q8—88no—
1126Q8—84no—
1127Q8—88no—
1128Q8—84no—
1129Q8—84no—
1130D4—28no—
1131D4—216no—
1132D4—28no—
1133D4—48no—
1134D4—44no—
1135D4—416no—
1136D4—88no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—216no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—28no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—28no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—48no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—48no—
1188C2×C4—416no—
1189C2×C4—48no—
1190C2×C4—48no—
1191C2×C4—48no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—88no—
1195C2×C4—84no—
1196C2×C4—88no—
1197C2×C4—84no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4#536116yes—
1201C2×C4C23×D414yes—
1202C2×C4C23×D414yes—
1203C2×C4C23×D414yes—
1204C2×C4C23×D412yes—
1205C2×C4C23×D412yes—
1206C2×C4C23×D412yes—
1207C2×C4C23×D412yes—
1208C2×C4C23×D412yes—
1209C2×C4C23×D412yes—
1210C2×C4C2×2−1+414yes—
1211C2×C4C2×2−1+414yes—
1212C22—22no—
1213C22—22no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—42no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—816no—
1236C22C2×#53614yes—
1237C22C24×D411yescharacteristic
1238C22C22×2−1+412yes—
1239C22C2×#58512yes—
1240C22H(7,𝔽2)11yescharacteristic
1241C222−1+611yescharacteristic
1242C4—22no—
1243C4—24no—
1244C4—22no—
1245C4—22no—
1246C4—24no—
1247C4—22no—
1248C4—24no—
1249C4—44no—
1250C4—44no—
1251C4—42no—
1252C4—42no—
1253C4—44no—
1254C4—42no—
1255C4—44no—
1256C4—42no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4—44no—
1261C4—48no—
1262C4C2×#53614yes—
1263C4C2×#53614yes—
1264C2—24no—
1265C2—44no—
1266C2—44no—
1267C2—82no—
1268C2C22×#53611yescharacteristic
1269C2#6281111yescharacteristic
1270C2#6285311yescharacteristic
1271C2#6292812yes—
1272C2#6295812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3475C2
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×#3504C2semidirect
3. #42891C2semidirect
4. #42814C2semidirect
5. #42681C2semidirect
6. #42482C2semidirect
7. #41411C2semidirect
8. #40592C2semidirect
9. #39955C2semidirect
10. #39952C2semidirect
11. #38422C2semidirect
12. #37560C2semidirect
13. #37549C2semidirect
14. #37281C2semidirect
15. #37279C2semidirect
16. #35516C2semidirect
17. #35516C2semidirect
18. #35335C2semidirect
19. #35297C2semidirect
20. #35253C2semidirect
21. #35253C2semidirect
22. #35173C2semidirect
23. #35138C2semidirect
24. #34946C2semidirect
25. C2×#2562C2semidirect
26. #34060C2semidirect
28. C2×#557C22semidirect
29. C2×#557C22semidirect
36. C2×#554C22semidirect
37. C2×#554C22semidirect
46. C2×#544C22semidirect
47. C2×#544C22semidirect
50. C2×#533C22semidirect
54. C22×#125C22semidirect
62. #2859C22semidirect
64. #2857C22semidirect
65. #2857C22semidirect
66. #2851C22semidirect
67. #2851C22semidirect
68. #2822C22semidirect
70. #2817C22semidirect
72. #2721C22semidirect
73. #2719C22semidirect
74. #2716C22semidirect
75. #2713C22semidirect
76. #2700C22semidirect
77. #2698C22semidirect
79. #2690C22semidirect
80. #2689C22semidirect
81. #2687C22semidirect
83. #2680C22semidirect
84. #2677C22semidirect
86. #2674C22semidirect
88. #2664C22semidirect
89. #2663C22semidirect
90. #2660C22semidirect
91. #2660C22semidirect
93. #2634C22semidirect
94. #2634C22semidirect
97. #2629C22semidirect
98. #2629C22semidirect
99. #2628C22semidirect
100. #2628C22semidirect
101. #2627C22semidirect
102. #2625C22semidirect
105. #2611C22semidirect
106. #2604C22semidirect
107. #2584C22semidirect
108. #2584C22semidirect
109. #2584C22semidirect
110. #2584C22semidirect
111. #2584C22semidirect
112. #2584C22semidirect
115. #2581C22semidirect
116. #2567C22semidirect
117. #2567C22semidirect
131. #2546C22semidirect
132. #2546C22semidirect
135. #2487C22semidirect
136. #2487C22semidirect
137. #2486C22semidirect
138. #2486C22semidirect
139. #2485C22semidirect
140. #2485C22semidirect
141. #2485C22semidirect
142. #2485C22semidirect
143. #2484C22semidirect
144. #2442C22semidirect
145. #2442C22semidirect
146. #2441C22semidirect
147. #2441C22semidirect
148. #2440C22semidirect
149. #2440C22semidirect
150. #2439C22semidirect
151. #2439C22semidirect
157. #2423C22semidirect
158. #2423C22semidirect
159. #2422C22semidirect
160. #2422C22semidirect
161. #2421C22semidirect
162. #2421C22semidirect
163. #2420C22semidirect
164. #2420C22semidirect
169. #2415C22semidirect
170. #2413C22semidirect
176. #2323C22semidirect
177. #2322C22semidirect
178. #2320C22semidirect
179. #2319C22semidirect
186. #2314C22semidirect
189. #2295C22semidirect
190. #2293C22semidirect
193. #2285C22semidirect
194. #2283C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#34752
#428912
#428142
#426812
#424822
#414112
#405922
#399552
#399522
#384222
#375602
#375492
#372812
#372792
#355162
#353352
#352972
#352532
#351732
#351382
#349462
C2×#25622
#340602