Finite Group Databasebeta

← #7656018

Subgroups — #7656018

Order 512.

6582 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42884C212yesmaximal, complemented
4#42812C212yesmaximal, complemented
5#42802C214yesmaximal, complemented
6#42301C218yesmaximal, complemented
7#42174C214yesmaximal, complemented
8#42170C214yesmaximal, complemented
9#39593C212yesmaximal, complemented
10#39123C212yesmaximal, complemented
11#38047C214yesmaximal, complemented
12#37841C214yesmaximal, complemented
13#37548C212yesmaximal, complemented
14#37546C211yesmaximal, characteristic
15#37538C212yesmaximal, complemented
16#37537C211yesmaximal, characteristic, complemented
17#36423C212yesmaximal, complemented
18#36162C212yesmaximal, complemented
19#36048C212yesmaximal, complemented
20#35938C212yesmaximal, complemented
21#35817C214yesmaximal, complemented
22#35179C211yesmaximal, characteristic, complemented
23#35118C212yesmaximal, complemented
24#34634C212yesmaximal, complemented
25#34602C211yesmaximal, characteristic, complemented
26#34196C211yesmaximal, characteristic, complemented
27#3523—216no—
28C2×#557C2211yescharacteristic, complemented
29C2×#557C2211yescharacteristic, complemented
30C2×#557C2212yescomplemented
31C2×#556—216no—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#556C2214yes—
35C2×#556C2212yes—
36C2×#556C2214yes—
37C2×#556C2212yes—
38C2×#556C2212yescomplemented
39C2×#556C2211yescharacteristic, complemented
40C2×#552C2212yes—
41C2×#552C2214yes—
42C2×D4×Q8C2212yes—
43C2×D4×Q8C2211yescharacteristic, complemented
44C2×#541C2212yescomplemented
45C2×#541C2214yescomplemented
46C2×#533C2212yes—
47C2×#533C2211yescharacteristic
48C22×C4⋊Q8C2211yescharacteristic
49C2×#529C2211yescharacteristic
50C2×#529C2212yes—
51C22×#126C2212yes—
52C22×#126C2212yes—
53C22×#124C2211yescharacteristic
54C22×#124C2211yescharacteristic
55C22×C22⋊Q8C2212yes—
56C2×#519C2212yescomplemented
57C22×C4×Q8C2211yescharacteristic
58C22×C4×Q8C2211yescharacteristic
59C22×C4×Q8C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic
61C22×#117C2212yes—
62#2855C2212yes—
63#2855C2212yes—
64#2853C2214yes—
65#2849C2214yes—
66#2823C2218yescomplemented
67#2821C2214yescomplemented
68#2821C2214yescomplemented
69#2820C2214yes—
70#2820C2212yes—
71#2819C2212yes—
72#2734C2218yescomplemented
73#2731C2218yes—
74#2730C2218yes—
75#2729C2218yescomplemented
76#2727C2218yescomplemented
77#2725C2218yescomplemented
78#2723C2218yescomplemented
79#2721C2218yescomplemented
80#2704C2218yescomplemented
81#2702C2218yescomplemented
82#2692C2218yescomplemented
83#2690C2218yescomplemented
84#2664C2218yescomplemented
85#2664C2214yescomplemented
86#2662C2214yes—
87#2662C2214yescomplemented
88#2658C2212yes—
89#2640C2212yes—
90#2637C2214yescomplemented
91#2637C2218yescomplemented
92#2637C2214yescomplemented
93#2636C2214yescomplemented
94#2634C2212yescomplemented
95#2632C2214yes—
96#2632C2212yescomplemented
97#2629C2218yescomplemented
98#2628C2214yescomplemented
99#2628C2214yescomplemented
100#2627C2211yescharacteristic
101#2627C2211yescharacteristic
102#2627C2212yes—
103#2627C2214yes—
104#2627C2212yes—
105#2626C2212yes—
106#2626C2214yes—
107#2626C2212yes—
108#2626C2212yes—
109#2623C2212yes—
110#2620C2214yes—
111#2618C2211yescharacteristic
112#2618C2211yescharacteristic
113#2617C2212yes—
114#2614C2212yes—
115#2611C2214yescomplemented
116#2610C2214yescomplemented
117#2609C2218yescomplemented
118#2604C2214yescomplemented
119#2604C2214yescomplemented
120#2601C2218yescomplemented
121#2601C2218yescomplemented
122#2599C2214yescomplemented
123#2598C2214yescomplemented
124#2592C2212yes—
125#2583C2214yes—
126#2582C2214yescomplemented
127#2581C2214yescomplemented
128#2579C2214yes—
129#2568C2212yescomplemented
130#2567C2212yescomplemented
131#2565C2214yescomplemented
132#2561C2214yes—
133#2560C2218yescomplemented
134#2556C2218yescomplemented
135#2546C2214yescomplemented
136#2545C2214yes—
137#2545C2214yes—
138#2540C2212yes—
139#2534C2214yes—
140#2519C2218yescomplemented
141#2512C2218yescomplemented
142#2484C2214yes—
143#2482C2214yes—
144#2482C2214yes—
145#2479C2218yescomplemented
146#2477C2218yescomplemented
147#2469C2218yescomplemented
148#2469C2218yescomplemented
149#2467C2218yes—
150#2465C2218yescomplemented
151#2462C2218yescomplemented
152#2460C2218yes—
153#2454C2214yes—
154#2453C2214yescomplemented
155#2448C2214yes—
156#2446C2214yescomplemented
157#2436C2214yes—
158#2435C2212yes—
159#2434C2212yes—
160#2434C2214yescomplemented
161#2429C2214yescomplemented
162#2429C2214yescomplemented
163#2427C2214yes—
164#2426C2214yes—
165#2413C2214yes—
166#2411C2214yes—
167#2411C2214yes—
168#2409C2212yes—
169#2408C2212yes—
170#2399C2212yescomplemented
171#2398C2212yescomplemented
172#2396C2214yescomplemented
173#2396C2218yescomplemented
174#2396C2214yescomplemented
175#2396C2214yescomplemented
176#2367C2214yes—
177#2365C2214yescomplemented
178#2363C2214yes—
179#2362C2214yescomplemented
180#2355C2214yescomplemented
181#2355C2212yescomplemented
182Q8×C4⋊C4C2212yescomplemented
183#2344C2212yes—
184#2344C2214yes—
185Q8×C22⋊C4C2212yes—
186#2322C2214yes—
187#2321C2214yes—
188#2320C2212yescomplemented
189#2320C2214yescomplemented
190#2317C2212yes—
191#2310C2212yes—
192C4×#123C2212yes—
193C4×#123C2212yes—
194#2296C2214yes—
195#2285C2212yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199#2280C2214yes—
200#2276C2212yescomplemented
201C23×Q8C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4C2312yes—
207#557—28no—
208#557—28no—
209#557—216no—
210#556—216no—
211#556—216no—
212#556—232no—
213#556—216no—
214#556—216no—
215#556—232no—
216#556—216no—
217#556—28no—
218#552—216no—
219#552—232no—
220D4×Q8—216no—
221D4×Q8—28no—
222#541—216no—
223#541—232no—
224#533—216no—
225#533—28no—
226C2×C4⋊Q8—28no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237#529—216no—
238#529—28no—
239C2×#126—216no—
240C2×#126—216no—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#124—28no—
264C2×#124—28no—
265C2×#124C2311yescharacteristic
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#123C2312yes—
276C2×#123C2314yes—
277C2×#123C2312yes—
278C2×#123C2312yes—
279C2×C22⋊Q8—216no—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2311yescharacteristic
294C2×#121C2314yes—
295C2×#120C2314yes—
296#519—216no—
297C2×C4×Q8—28no—
298C2×C4×Q8—28no—
299C2×C4×Q8D4116yescomplemented
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4—28no—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×#117—216no—
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C2314yes—
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2312yes—
353C22×C22⋊C4C2312yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360C22×C42C2311yescharacteristic
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#400C2312yes—
364#400C2314yes—
365#400C2318yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2318yes—
370#399C2314yes—
371#399C2318yes—
372#399C2314yes—
373#399C2318yes—
374#399C2314yes—
375#399C2314yes—
376#399C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2318yes—
389#398C2314yes—
390#397C2318yes—
391#397C2318yes—
392#397C2314yes—
393#397C2318yes—
394#397C2314yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#396C2314yes—
399#396C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2314yes—
404#396C2318yes—
405#396C2318yes—
406#396C2318yes—
407#395C2318yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2318yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2318yes—
417#394C2318yes—
418#394C2318yes—
419#394C2318yes—
420#394C2314yes—
421#394C2318yes—
422#394C2318yes—
423#394C2312yes—
424#394C2312yes—
425#393C2314yes—
426#393C2318yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2318yes—
433#392C2314yes—
434#392C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2318yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2318yes—
442#391C2314yes—
443#391C2314yes—
444#390C2318yes—
445#390C2318yes—
446#390C2314yes—
447#390C2318yes—
448#390C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2318yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#389C2318yes—
456#389C2318yes—
457#389C2318yes—
458#389C2318yes—
459#389C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2314yes—
476#388C2314yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2314yes—
489#387C2314yes—
490#386C2318yes—
491#386C2312yes—
492#386C2318yes—
493#386C2314yes—
494#386C2312yes—
495#386C2318yes—
496#386C2318yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2318yes—
501#385C2318yes—
502#385C2314yes—
503#385C2312yes—
504#385C2314yes—
505#385C2318yes—
506#385C2318yes—
507#385C2312yes—
508#384C2314yes—
509#384C2314yes—
510#384C2312yes—
511#383C2314yes—
512#383C2312yes—
513#382C2312yes—
514#382C2312yes—
515#382C2314yes—
516#382C2314yes—
517#382C2314yes—
518#381C2312yes—
519#381C2314yes—
520#381C2314yes—
521#381C2314yes—
522#381C2312yes—
523#381C2312yes—
524#380C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2311yescharacteristic
528#380C2311yescharacteristic
529#380C2318yes—
530#380C2318yes—
531#379C2314yes—
532#379C2314yes—
533#379C2314yes—
534C4×C4⋊C4C2318yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2318yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2314yes—
553#376C2312yes—
554C25C2412yes—
555C22×Q8—28no—
556C22×Q8—24no—
557C22×Q8—24no—
558C22×Q8—24no—
559C22×Q8—42no—
560C22×Q8—44no—
561C22×Q8—44no—
562C22×Q8—48no—
563C22×Q8C2×D418yes—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2412yes—
571C22×Q8C2411yescharacteristic
572C22×Q8C2414yes—
573C22×Q8C2412yes—
574C22×Q8C2412yes—
575C22×D4—24no—
576C22×D4—44no—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2418yes—
582C23×C4—28no—
583C23×C4—28no—
584C23×C4—44no—
585C23×C4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2411yescharacteristic
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C23×C4C2414yes—
597C23×C4C2412yes—
598C23×C4C2411yescharacteristic
599C4⋊Q8—28no—
600C4⋊Q8—28no—
601C4⋊Q8—216no—
602C4⋊Q8—28no—
603C4⋊Q8—216no—
604C4⋊Q8—28no—
605C4⋊Q8—24no—
606C4⋊Q8—28no—
607C4⋊Q8—24no—
608C4⋊Q8—48no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—28no—
622#125—216no—
623#125—216no—
624#125—216no—
625#125—28no—
626#125—216no—
627#125—28no—
628#125—24no—
629#125—216no—
630#125—28no—
631#124—28no—
632#124—28no—
633#124—216no—
634#124—28no—
635#124—28no—
636#124—28no—
637#124—28no—
638#124—28no—
639#124—24no—
640#124—48no—
641#123—216no—
642#123—28no—
643#123—28no—
644#123—44no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—28no—
648C22⋊Q8—24no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—48no—
658#121—24no—
659#121—48no—
660#120—48no—
661C4×Q8—28no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8—28no—
666C4×Q8—216no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—216no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—24no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—48no—
679C4×Q8C2×D418yes—
680C4×Q8C2×D4116yes—
681C4×Q8C2×D418yes—
682C4×Q8C2×D418yes—
683C4×Q8C2×D4116yes—
684C4×Q8C2×D418yes—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—24no—
692#117—216no—
693#117—28no—
694#117—28no—
695#117—216no—
696#117—216no—
697#117—216no—
698#117—216no—
699#117—216no—
700#117—216no—
701#117—28no—
702#117—44no—
703#117—48no—
704C2×C4⋊C4—24no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—28no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4C2×D418yes—
711C2×C4⋊C4C2×D4116yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C22⋊C4—28no—
768C2×C22⋊C4—28no—
769C2×C22⋊C4—28no—
770C2×C22⋊C4—28no—
771C2×C22⋊C4—28no—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C42—28no—
807C2×C42—24no—
808C2×C42—24no—
809C2×C42C2×D4116yes—
810C2×C42C2×D418yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2418yes—
824C2×C42C2414yes—
825C2×C42C2418yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834#95C2412yes—
835#95C2414yes—
836#95C2412yes—
837#95C2418yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2418yes—
843#95C2418yes—
844#95C2414yes—
845#95C2418yes—
846#95C2414yes—
847#95C2414yes—
848#95C2418yes—
849#95C2414yes—
850#95C2418yes—
851#95C2414yes—
852#95C2414yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24—24no—
864C24—24no—
865C24—24no—
866C24—44no—
867C24—44no—
868C24C2514yes—
869C24C2512yes—
870C24C2511yescharacteristic
871C2×Q8—24no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—28no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—28no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—48no—
890C2×Q8—44no—
891C2×Q8—42no—
892C2×Q8—416no—
893C2×Q8—416no—
894C2×Q8—416no—
895C2×Q8—432no—
896C2×Q8C22×D414yes—
897C2×Q8C22×D414yes—
898C2×Q8C22×D418yes—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—22no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—416no—
909C2×D4—48no—
910C2×D4—48no—
911C2×D4—48no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—24no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—28no—
931C22×C4—28no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—44no—
938C22×C4—48no—
939C22×C4—44no—
940C22×C4—432no—
941C22×C4C22×D414yes—
942C22×C4C22×D418yes—
943C22×C4C22×D414yes—
944C22×C4C22×D414yes—
945C22×C4C22×D418yes—
946C22×C42−1+414yes—
947C22×C4C2514yes—
948C22×C4C2518yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2511yescharacteristic
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—22no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4C22×D414yes—
1019C4⋊C4C22×D418yes—
1020C4⋊C4C22×D414yes—
1021C4⋊C4C22×D418yes—
1022C4⋊C4C22×D418yes—
1023C4⋊C4C22×D418yes—
1024C4⋊C4C22×D418yes—
1025C22⋊C4—28no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—44no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C42—28no—
1060C42—28no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—24no—
1065C42—28no—
1066C42—28no—
1067C42—28no—
1068C42—28no—
1069C42—24no—
1070C42—28no—
1071C42—48no—
1072C42—44no—
1073C42—48no—
1074C42C22×D418yes—
1075C42C22×D418yes—
1076C42C22×D414yes—
1077C42C22×D418yes—
1078C42C22×D418yes—
1079C42C22×D414yes—
1080C42C22×D414yes—
1081C42C22×D414yes—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—24no—
1086C23—22no—
1087C23—24no—
1088C23—28no—
1089C23—24no—
1090C23—24no—
1091C23—22no—
1092C23—28no—
1093C23—24no—
1094C23—48no—
1095C23—48no—
1096C23—48no—
1097C23—88no—
1098C23—88no—
1099C23C23×D412yes—
1100C23C2×2−1+412yes—
1101C23#58512yes—
1102C23C2611yescharacteristic
1103Q8—28no—
1104Q8—28no—
1105Q8—48no—
1106Q8—48no—
1107Q8—48no—
1108Q8—48no—
1109Q8—44no—
1110Q8—48no—
1111Q8—416no—
1112Q8—48no—
1113Q8—48no—
1114D4—44no—
1115D4—48no—
1116D4—48no—
1117D4—48no—
1118D4—168no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—28no—
1135C2×C4—216no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—28no—
1154C2×C4—28no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—28no—
1159C2×C4—28no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—416no—
1170C2×C4—416no—
1171C2×C4—416no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—48no—
1175C2×C4—44no—
1176C2×C4—48no—
1177C2×C4C23×D414yes—
1178C2×C4C23×D412yes—
1179C2×C4C23×D412yes—
1180C2×C4C23×D414yes—
1181C2×C4C23×D414yes—
1182C2×C4C23×D412yes—
1183C2×C4C23×D412yes—
1184C2×C4C23×D414yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C2×2−1+414yes—
1188C2×C4#58514yes—
1189C22—22no—
1190C22—22no—
1191C22—24no—
1192C22—24no—
1193C22—44no—
1194C22—42no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—44no—
1199C22—44no—
1200C22—48no—
1201C22—44no—
1202C22—48no—
1203C22—816no—
1204C22#348914yes—
1205C22C24×D411yescharacteristic
1206C22C22×2−1+411yescharacteristic
1207C22C2×#58511yescharacteristic
1208C22C2×#58512yes—
1209C222−1+612yes—
1210C4—24no—
1211C4—24no—
1212C4—24no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—24no—
1219C4—24no—
1220C4—42no—
1221C4—42no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—44no—
1226C4—44no—
1227C4—42no—
1228C4—44no—
1229C4—44no—
1230C4—44no—
1231C4—48no—
1232C4#344914yes—
1233C2—24no—
1234C2—82no—
1235C2—84no—
1236C2C2×#344911yescharacteristic
1237C2C2×#348911yescharacteristic
1238C2#6284811yescharacteristic
1239C2#6295912yes—
1240C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37546C2
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×#3523C2semidirect
2. C22×#556C2semidirect
3. #42884C2semidirect
4. #42812C2semidirect
5. #42802C2semidirect
6. #42301C2semidirect
7. #42174C2semidirect
8. #42170C2semidirect
9. #39593C2semidirect
10. #39123C2semidirect
11. #38047C2semidirect
12. #37841C2semidirect
13. #37548C2semidirect
15. #37538C2semidirect
16. #37537C2semidirect
17. #36423C2semidirect
18. #36162C2semidirect
19. #36048C2semidirect
20. #35938C2semidirect
21. #35817C2semidirect
22. #35179C2semidirect
23. #35118C2semidirect
24. #34634C2semidirect
25. #34602C2semidirect
26. #34196C2semidirect
28. C2×#557C22semidirect
29. C2×#557C22semidirect
30. C2×#557C22semidirect
38. C2×#556C22semidirect
39. C2×#556C22semidirect
43. C2×D4×Q8C22semidirect
44. C2×#541C22semidirect
45. C2×#541C22semidirect
56. C2×#519C22semidirect
66. #2823C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
72. #2734C22semidirect
75. #2729C22semidirect
76. #2727C22semidirect
77. #2725C22semidirect
78. #2723C22semidirect
79. #2721C22semidirect
80. #2704C22semidirect
81. #2702C22semidirect
82. #2692C22semidirect
83. #2690C22semidirect
84. #2664C22semidirect
85. #2664C22semidirect
87. #2662C22semidirect
90. #2637C22semidirect
91. #2637C22semidirect
92. #2637C22semidirect
93. #2636C22semidirect
94. #2634C22semidirect
96. #2632C22semidirect
97. #2629C22semidirect
98. #2628C22semidirect
99. #2628C22semidirect
115. #2611C22semidirect
116. #2610C22semidirect
117. #2609C22semidirect
118. #2604C22semidirect
119. #2604C22semidirect
120. #2601C22semidirect
121. #2601C22semidirect
122. #2599C22semidirect
123. #2598C22semidirect
126. #2582C22semidirect
127. #2581C22semidirect
129. #2568C22semidirect
130. #2567C22semidirect
131. #2565C22semidirect
133. #2560C22semidirect
134. #2556C22semidirect
135. #2546C22semidirect
140. #2519C22semidirect
141. #2512C22semidirect
145. #2479C22semidirect
146. #2477C22semidirect
147. #2469C22semidirect
148. #2469C22semidirect
150. #2465C22semidirect
151. #2462C22semidirect
154. #2453C22semidirect
156. #2446C22semidirect
160. #2434C22semidirect
161. #2429C22semidirect
162. #2429C22semidirect
170. #2399C22semidirect
171. #2398C22semidirect
172. #2396C22semidirect
173. #2396C22semidirect
174. #2396C22semidirect
175. #2396C22semidirect
177. #2365C22semidirect
179. #2362C22semidirect
180. #2355C22semidirect
181. #2355C22semidirect
182. Q8×C4⋊C4C22semidirect
188. #2320C22semidirect
189. #2320C22semidirect
200. #2276C22semidirect
299. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C22×#5562
#428842
#428122
#428022
#423012
#421742
#421702
#395932
#391232
#380472
#378412
#375482
#375462
#375382
#375372
#364232
#361622
#360482
#359382
#358172
#351792
#351182
#346342
#346022
#341962