Finite Group Databasebeta

← #7646913

Subgroups — #7646913

Order 512.

8350 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3486C211yesmaximal, characteristic, complemented
2C22×#536C211yesmaximal, characteristic, complemented
3#42797C214yesmaximal, complemented
4#42796C214yesmaximal, complemented
5#42787C214yesmaximal, complemented
6#42786C214yesmaximal, complemented
7#39723C212yesmaximal, complemented
8#39721C212yesmaximal, complemented
9#39595C212yesmaximal, complemented
10#39593C212yesmaximal, complemented
11#39135C212yesmaximal, complemented
12#39133C212yesmaximal, complemented
13#39123C212yesmaximal, complemented
14#39121C212yesmaximal, complemented
15#37452C214yesmaximal, complemented
16#37190C218yesmaximal, complemented
17#35673C212yesmaximal, complemented
18#35660C212yesmaximal, complemented
19#35263C211yesmaximal, characteristic, complemented
20#35251C211yesmaximal, characteristic, complemented
21#35178C212yesmaximal, complemented
22#35153C212yesmaximal, complemented
23#35064C214yesmaximal, complemented
24#34810C211yesmaximal, characteristic, complemented
25#34738C211yesmaximal, characteristic, complemented
26C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
27C22×2−1+4C2211yescharacteristic, complemented
28C23×#41C2211yescharacteristic
29C24×Q8C2211yescharacteristic
30#3486—216no—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yescomplemented
34C2×D4×Q8C2212yescomplemented
35C2×#548C2212yes—
36C2×#548C2212yes—
37C2×#548C2212yescomplemented
38C2×#548C2212yescomplemented
39C2×#537C2212yes—
40C2×#536—216no—
41C2×#536C2214yes—
42C2×#536C2214yes—
43C2×#536C2214yes—
44C2×#536C2212yes—
45C2×#536C2212yes—
46C2×#536C2214yescomplemented
47C2×#536C2211yescharacteristic, complemented
48C2×#536C2211yescharacteristic, complemented
49C2×#532C2212yes—
50C22×C4⋊Q8C2212yes—
51C22×#124C2212yes—
52C2×#525C2214yes—
53C2×#525C2211yescharacteristic
54C2×#525C2211yescharacteristic
55C22×#123C2214yes—
56C22×C22⋊Q8C2212yes—
57C22×C22⋊Q8C2212yes—
58C2×#519C2211yescharacteristic, complemented
59C22×C4×Q8C2212yescomplemented
60C22×#117C2211yescharacteristic
61#2855C2212yes—
62#2854C2212yes—
63#2854C2218yescomplemented
64#2854C2218yescomplemented
65#2848C2212yes—
66#2847C2212yes—
67#2814C2218yescomplemented
68#2813C2218yescomplemented
69#2734C2218yescomplemented
70#2733C2218yescomplemented
71#2732C2218yescomplemented
72#2732C2218yescomplemented
73#2731C2218yescomplemented
74#2731C2218yescomplemented
75#2730C2218yescomplemented
76#2730C2218yescomplemented
77#2730C2218yescomplemented
78#2730C2218yescomplemented
79#2729C2218yescomplemented
80#2729C2218yescomplemented
81#2729C2218yescomplemented
82#2729C2218yescomplemented
83#2728C2218yescomplemented
84#2728C2218yescomplemented
85#2663C2218yescomplemented
86#2661C2218yescomplemented
87#2630C2218yescomplemented
88#2630C2218yescomplemented
89#2627C2214yes—
90#2626C2214yes—
91#2625C2212yescomplemented
92#2624C2212yescomplemented
93#2618C2214yes—
94#2618C2218yescomplemented
95#2618C2218yescomplemented
96#2617C2214yes—
97#2616C2212yes—
98#2615C2212yes—
99#2602C2218yescomplemented
100#2602C2218yescomplemented
101#2591C2214yes—
102#2583C2214yes—
103#2579C2214yes—
104#2579C2214yes—
105#2561C2214yes—
106#2548C2214yescomplemented
107#2546C2214yescomplemented
108#2545C2214yescomplemented
109#2545C2214yescomplemented
110#2539C2214yes—
111#2538C2214yescomplemented
112#2538C2214yescomplemented
113#2536C2214yescomplemented
114#2536C2214yescomplemented
115#2534C2214yes—
116#2534C2214yes—
117#2504C2211yescharacteristic
118#2503C2211yescharacteristic
119#2502C2211yescharacteristic
120#2501C2211yescharacteristic
121#2500C2212yescomplemented
122#2499C2212yescomplemented
123#2498C2214yescomplemented
124#2498C2214yescomplemented
125#2498C2218yescomplemented
126#2498C2218yescomplemented
127#2487C2212yes—
128#2486C2212yes—
129#2485C2214yescomplemented
130#2448C2214yescomplemented
131#2448C2214yescomplemented
132#2446C2214yescomplemented
133#2446C2214yescomplemented
134#2436C2211yescharacteristic
135#2436C2214yescomplemented
136#2435C2211yescharacteristic
137#2434C2211yescharacteristic
138#2434C2214yescomplemented
139#2433C2211yescharacteristic
140#2432C2212yes—
141#2432C2214yescomplemented
142#2431C2212yes—
143#2431C2214yescomplemented
144#2430C2214yes—
145#2430C2214yes—
146#2430C2218yescomplemented
147#2430C2218yescomplemented
148#2429C2214yescomplemented
149#2429C2214yescomplemented
150#2429C2214yescomplemented
151#2429C2214yescomplemented
152#2426C2214yescomplemented
153#2426C2214yescomplemented
154#2426C2214yescomplemented
155#2426C2214yescomplemented
156#2423C2214yescomplemented
157#2423C2214yescomplemented
158#2421C2214yescomplemented
159#2421C2214yescomplemented
160#2412C2212yes—
161#2412C2214yes—
162#2412C2212yes—
163#2410C2212yes—
164#2410C2214yes—
165#2410C2212yes—
166#2409C2212yes—
167#2409C2214yescomplemented
168#2409C2214yescomplemented
169#2408C2212yes—
170#2407C2214yes—
171#2407C2214yescomplemented
172#2407C2214yescomplemented
173#2395C2214yescomplemented
174#2388C2214yes—
175Q8×C22⋊C4C2212yes—
176Q8×C22⋊C4C2212yes—
177Q8×C22⋊C4C2212yes—
178Q8×C22⋊C4C2212yes—
179Q8×C22⋊C4C2214yescomplemented
180Q8×C22⋊C4C2214yescomplemented
181#2322C2214yes—
182#2322C2214yes—
183#2321C2214yes—
184#2321C2214yes—
185#2316C2212yescomplemented
186#2311C2212yes—
187#2311C2212yescomplemented
188C4×#123C2212yes—
189C4×#123C2212yes—
190C4×#120C2212yes—
191C4×#120C2212yes—
192#2297C2212yes—
193#2297C2212yescomplemented
194C2×#391C2214yescomplemented
195C2×#391C2212yescomplemented
196#2285C2212yescomplemented
197C2×#380C2212yes—
198C2×#380C2211yescharacteristic
199C2×C4×C22⋊C4C2211yescharacteristic
200C2×C4×C22⋊C4C2212yes—
201C2×2−1+4—28no—
202C2×2−1+4—48no—
203C22×#41—28no—
204C22×#41—48no—
205C22×#41C2312yes—
206C22×#41C2311yescharacteristic
207C22×#41C2311yescharacteristic
208C22×#41C2312yes—
209C22×#41C2312yes—
210C22×#41C2312yes—
211C22×#41C2312yes—
212C22×#41C2314yes—
213C22×#41C2312yes—
214C23×Q8—48no—
215C23×Q8D4116yescomplemented
216C23×Q8C2311yescharacteristic
217C23×Q8C2311yescharacteristic
218C23×Q8C2311yescharacteristic
219C23×Q8C2312yes—
220C23×Q8C2312yes—
221C23×Q8C2312yes—
222C23×Q8C2312yes—
223C23×Q8C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×D4C2311yescharacteristic
227C23×D4C2312yes—
228C24×C4C2311yescharacteristic
229C24×C4C2312yes—
230C24×C4C2312yes—
231D4×Q8—216no—
232D4×Q8—216no—
233D4×Q8—216no—
234D4×Q8—216no—
235#548—216no—
236#548—216no—
237#548—216no—
238#548—216no—
239#537—48no—
240#536—216no—
241#536—216no—
242#536—232no—
243#536—232no—
244#536—232no—
245#536—28no—
246#536—28no—
247#536—232no—
248#532—48no—
249C2×C4⋊Q8—216no—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2318yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2314yes—
255C2×C4⋊Q8C2314yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×#127C2312yes—
259C2×#124—216no—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2318yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269#525—28no—
270#525—28no—
271#525—232no—
272C2×#123—232no—
273C2×#123C2312yes—
274C2×#123C2318yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2318yes—
278C2×#123C2318yes—
279C2×#123C2318yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×C22⋊Q8—216no—
285C2×C22⋊Q8—216no—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×#121C2314yes—
309C2×#121C2311yescharacteristic
310C2×#121C2311yescharacteristic
311C2×#121C2311yescharacteristic
312C2×#121C2311yescharacteristic
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2318yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#120C2312yes—
320C2×#120C2312yes—
321C2×#120C2312yes—
322C2×#120C2314yes—
323C2×#120C2312yes—
324#519—28no—
325C2×C4×Q8—48no—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2314yes—
332C2×C4×Q8C2314yes—
333C2×C4×Q8C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×#117—28no—
345C2×#117C2311yescharacteristic
346C2×#117C2312yes—
347C2×#117C2311yescharacteristic
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2311yescharacteristic
357C22×C4⋊C4C2314yes—
358C22×C22⋊C4C2314yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2312yes—
361C22×C22⋊C4C2311yescharacteristic
362C22×C22⋊C4C2311yescharacteristic
363C22×C22⋊C4C2312yes—
364C22×C42C2312yes—
365C22×C42C2312yes—
366C22×C42C2314yes—
367#400C2318yes—
368#400C2314yes—
369#400C2318yes—
370#400C2314yes—
371#399C2314yes—
372#399C2318yes—
373#399C2314yes—
374#399C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2314yes—
382#398C2314yes—
383#397C2318yes—
384#397C2314yes—
385#397C2318yes—
386#397C2318yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#395C2318yes—
399#395C2314yes—
400#395C2318yes—
401#395C2314yes—
402#394C2318yes—
403#394C2314yes—
404#394C2314yes—
405#394C2318yes—
406#394C2318yes—
407#394C2314yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2318yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2318yes—
417#393C2314yes—
418#393C2318yes—
419#393C2314yes—
420#392C2314yes—
421#392C2318yes—
422#392C2314yes—
423#392C2318yes—
424#392C2314yes—
425#392C2314yes—
426#392C2318yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2318yes—
434#391C2318yes—
435#391C2318yes—
436#391C2318yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#390C2314yes—
442#390C2314yes—
443#390C2318yes—
444#390C2318yes—
445#390C2318yes—
446#390C2318yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2318yes—
456#389C2318yes—
457#389C2318yes—
458#389C2318yes—
459#388C2318yes—
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#388C2314yes—
473#388C2314yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2314yes—
480#387C2314yes—
481#386C2318yes—
482#386C2318yes—
483#386C2312yes—
484#386C2314yes—
485#386C2318yes—
486#386C2318yes—
487#386C2312yes—
488#386C2314yes—
489#386C2312yes—
490#386C2312yes—
491#386C2318yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2314yes—
500#385C2312yes—
501#385C2314yes—
502#385C2312yes—
503#385C2314yes—
504#385C2318yes—
505#385C2318yes—
506#385C2312yes—
507#385C2312yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2314yes—
512#385C2314yes—
513#384C2312yes—
514#384C2312yes—
515#382C2312yes—
516#382C2312yes—
517#381C2312yes—
518#381C2314yes—
519#381C2312yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2318yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2312yes—
529#380C2312yes—
530#380C2312yes—
531#380C2318yes—
532#380C2314yes—
533#380C2314yes—
534#379C2312yes—
535#379C2314yes—
536#379C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C22⋊C4C2314yes—
540C4×C22⋊C4C2314yes—
541C4×C22⋊C4C2311yescharacteristic
542C4×C22⋊C4C2311yescharacteristic
543C4×C22⋊C4C2311yescharacteristic
544C4×C22⋊C4C2311yescharacteristic
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552C2×#95C2312yes—
553C2×#95C2312yes—
554C2×#95C2314yes—
555C2×#95C2314yes—
556C25C2411yescharacteristic
557C25C2412yes—
5582−1+4—464no—
559C2×#41—28no—
560C2×#41—28no—
561C2×#41—216no—
562C2×#41—24no—
563C2×#41—24no—
564C2×#41—28no—
565C2×#41—28no—
566C2×#41—28no—
567C2×#41—28no—
568C2×#41—28no—
569C2×#41—28no—
570C2×#41—28no—
571C2×#41—28no—
572C2×#41—48no—
573C2×#41—48no—
574C2×#41—416no—
575C2×#41—44no—
576C2×#41—44no—
577C2×#41—48no—
578C2×#41—48no—
579C2×#41—464no—
580C22×Q8—28no—
581C22×Q8—28no—
582C22×Q8—24no—
583C22×Q8—28no—
584C22×Q8—28no—
585C22×Q8—48no—
586C22×Q8—464no—
587C22×Q8—48no—
588C22×Q8—48no—
589C22×Q8—48no—
590C22×Q8—48no—
591C22×Q8—44no—
592C22×Q8—48no—
593C22×Q8—48no—
594C22×Q8C2×D418yes—
595C22×Q8C2×D418yes—
596C22×Q8C2×D4116yes—
597C22×Q8C2×D4116yes—
598C22×Q8C2×D4116yes—
599C22×Q8C2×D4116yes—
600C22×Q8C2×D4116yes—
601C22×Q8C2411yescharacteristic
602C22×Q8C2411yescharacteristic
603C22×Q8C2412yes—
604C22×Q8C2412yes—
605C22×Q8C2412yes—
606C22×Q8C2412yes—
607C22×Q8C2412yes—
608C22×Q8C2414yes—
609C22×Q8C2412yes—
610C22×Q8C2414yes—
611C22×Q8C2414yes—
612C22×D4—28no—
613C22×D4—24no—
614C22×D4—44no—
615C22×D4—48no—
616C22×D4C2412yes—
617C22×D4C2412yes—
618C22×D4C2412yes—
619C22×D4C2412yes—
620C22×D4C2411yescharacteristic
621C22×D4C2414yes—
622C22×D4C2412yes—
623C22×D4C2411yescharacteristic
624C22×D4C2412yes—
625C22×D4C2412yes—
626C22×D4C2414yes—
627C22×D4C2414yes—
628C22×D4C2414yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2418yes—
632C23×C4—28no—
633C23×C4—28no—
634C23×C4—48no—
635C23×C4—48no—
636C23×C4C2×D418yes—
637C23×C4C2×D4116yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2414yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2411yescharacteristic
660C4⋊Q8—216no—
661C4⋊Q8—216no—
662C4⋊Q8—232no—
663C4⋊Q8—28no—
664C4⋊Q8—28no—
665C4⋊Q8—216no—
666C4⋊Q8—216no—
667C4⋊Q8—44no—
668#127—44no—
669#124—216no—
670#124—216no—
671#124—232no—
672#124—28no—
673#124—28no—
674#124—216no—
675#124—216no—
676#124—44no—
677#124—44no—
678#123—232no—
679#123—232no—
680#123—232no—
681#123—232no—
682#123—28no—
683#123—28no—
684#123—216no—
685#123—216no—
686#123—28no—
687#123—48no—
688#123—44no—
689C22⋊Q8—216no—
690C22⋊Q8—216no—
691C22⋊Q8—216no—
692C22⋊Q8—216no—
693C22⋊Q8—232no—
694C22⋊Q8—232no—
695C22⋊Q8—28no—
696C22⋊Q8—28no—
697C22⋊Q8—28no—
698C22⋊Q8—28no—
699C22⋊Q8—216no—
700C22⋊Q8—216no—
701C22⋊Q8—216no—
702C22⋊Q8—216no—
703C22⋊Q8—24no—
704C22⋊Q8—24no—
705C22⋊Q8—24no—
706C22⋊Q8—24no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711#121—24no—
712#121—24no—
713#121—24no—
714#121—24no—
715#121—216no—
716#121—216no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—416no—
722#120—28no—
723#120—28no—
724#120—28no—
725#120—44no—
726#120—48no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—28no—
730C4×Q8—28no—
731C4×Q8—48no—
732C4×Q8—48no—
733C4×Q8—48no—
734C4×Q8—48no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—28no—
738C4×D4—28no—
739C4×D4—216no—
740C4×D4—216no—
741C4×D4—216no—
742C4×D4—216no—
743C4×D4—48no—
744C4×D4—48no—
745#117—28no—
746#117—28no—
747#117—28no—
748#117—28no—
749#117—216no—
750#117—24no—
751#117—24no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—216no—
755C2×C4⋊C4—216no—
756C2×C4⋊C4—28no—
757C2×C4⋊C4—48no—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2418yes—
784C2×C4⋊C4C2418yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2418yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2418yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2418yes—
793C2×C22⋊C4—28no—
794C2×C22⋊C4—216no—
795C2×C22⋊C4—216no—
796C2×C22⋊C4—24no—
797C2×C22⋊C4—42no—
798C2×C22⋊C4—44no—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2418yes—
834C2×C22⋊C4C2418yes—
835C2×C22⋊C4C2418yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2418yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2418yes—
843C2×C22⋊C4C2418yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C42—28no—
846C2×C42—28no—
847C2×C42—48no—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2418yes—
859C2×C42C2418yes—
860#95C2412yes—
861#95C2412yes—
862#95C2418yes—
863#95C2418yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2418yes—
868#95C2418yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2418yes—
883#95C2418yes—
884#95C2418yes—
885#95C2418yes—
886#95C2418yes—
887#95C2418yes—
888C24—24no—
889C24—22no—
890C24—22no—
891C24—24no—
892C24—24no—
893C24—24no—
894C24—42no—
895C24—44no—
896C24—44no—
897C24C22×D414yes—
898C24C2514yes—
899C24C2512yes—
900C24C2512yes—
901C24C2511yescharacteristic
902C24C2511yescharacteristic
903C24C2511yescharacteristic
904#41—432no—
905#41—432no—
906#41—432no—
907#41—464no—
908#41—432no—
909#41—432no—
910#41—432no—
911#41—416no—
912#41—416no—
913C2×Q8—232no—
914C2×Q8—232no—
915C2×Q8—28no—
916C2×Q8—22no—
917C2×Q8—22no—
918C2×Q8—24no—
919C2×Q8—24no—
920C2×Q8—28no—
921C2×Q8—28no—
922C2×Q8—28no—
923C2×Q8—28no—
924C2×Q8—24no—
925C2×Q8—24no—
926C2×Q8—24no—
927C2×Q8—24no—
928C2×Q8—432no—
929C2×Q8—48no—
930C2×Q8—48no—
931C2×Q8—48no—
932C2×Q8—44no—
933C2×Q8—432no—
934C2×Q8—432no—
935C2×Q8—432no—
936C2×Q8—432no—
937C2×Q8—416no—
938C2×Q8—432no—
939C2×Q8—432no—
940C2×Q8C22×D418yes—
941C2×Q8C22×D418yes—
942C2×Q8C22×D418yes—
943C2×Q8C22×D418yes—
944C2×Q8C22×D4116yes—
945C2×Q8C22×D4116yes—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—28no—
957C2×D4—28no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—28no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—28no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—48no—
978C2×D4—416no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—48no—
985C2×D4—48no—
986C2×D4—48no—
987C2×D4—432no—
988C22×C4—28no—
989C22×C4—24no—
990C22×C4—28no—
991C22×C4—232no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—28no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—24no—
1015C22×C4—432no—
1016C22×C4—44no—
1017C22×C4—48no—
1018C22×C4—48no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—48no—
1024C22×C4—48no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—432no—
1030C22×C4C22×D414yes—
1031C22×C4C22×D414yes—
1032C22×C4C22×D414yes—
1033C22×C4C22×D414yes—
1034C22×C4C22×D414yes—
1035C22×C4C22×D418yes—
1036C22×C4C22×D418yes—
1037C22×C4C22×D4116yes—
1038C22×C4C22×D4116yes—
1039C22×C4C22×D414yes—
1040C22×C4H(5,𝔽2)18yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2518yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—216no—
1066C4⋊C4—216no—
1067C4⋊C4—216no—
1068C4⋊C4—216no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—48no—
1087C4⋊C4—48no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—48no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—48no—
1094C4⋊C4—44no—
1095C4⋊C4—48no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—28no—
1107C22⋊C4—22no—
1108C22⋊C4—216no—
1109C22⋊C4—216no—
1110C22⋊C4—216no—
1111C22⋊C4—216no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—42no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—48no—
1128C22⋊C4—44no—
1129C22⋊C4—48no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—48no—
1136C22⋊C4—44no—
1137C22⋊C4—48no—
1138C22⋊C4—48no—
1139C22⋊C4—44no—
1140C22⋊C4—48no—
1141C22⋊C42−1+414yescomplemented
1142C42—28no—
1143C42—28no—
1144C42—28no—
1145C42—28no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—48no—
1153C42—48no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—22no—
1163C23—28no—
1164C23—28no—
1165C23—24no—
1166C23—22no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—22no—
1176C23—24no—
1177C23—22no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—44no—
1183C23—48no—
1184C23—48no—
1185C23—48no—
1186C23—48no—
1187C23—48no—
1188C23—88no—
1189C23—88no—
1190C23C23×D412yes—
1191C23C23×D412yes—
1192C23C23×D412yes—
1193C23C2×H(5,𝔽2)14yes—
1194C23C2×2−1+412yes—
1195C23#58512yes—
1196C23C2611yescharacteristic
1197Q8—216no—
1198Q8—216no—
1199Q8—216no—
1200Q8—216no—
1201Q8—416no—
1202Q8—416no—
1203Q8—416no—
1204Q8—48no—
1205Q8—44no—
1206Q8—44no—
1207Q8—48no—
1208D4—48no—
1209D4—416no—
1210D4—48no—
1211D4—48no—
1212D4—416no—
1213D4—416no—
1214D4—48no—
1215D4—48no—
1216D4—48no—
1217D4—48no—
1218D4—48no—
1219D4—44no—
1220D4—44no—
1221D4—88no—
1222D4—88no—
1223D4—168no—
1224C2×C4—22no—
1225C2×C4—28no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—28no—
1229C2×C4—22no—
1230C2×C4—28no—
1231C2×C4—216no—
1232C2×C4—216no—
1233C2×C4—28no—
1234C2×C4—28no—
1235C2×C4—28no—
1236C2×C4—28no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—28no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—28no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—416no—
1273C2×C4—416no—
1274C2×C4—48no—
1275C2×C4—416no—
1276C2×C4—416no—
1277C2×C4—416no—
1278C2×C4—48no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—416no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—84no—
1285C2×C4—88no—
1286C2×C4#534116yes—
1287C2×C4C23×D412yes—
1288C2×C4C23×D418yes—
1289C2×C4C23×D418yes—
1290C2×C4C23×D412yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D412yes—
1293C2×C4C2×H(5,𝔽2)14yes—
1294C2×C4C2×H(5,𝔽2)14yes—
1295C2×C4C2×2−1+414yes—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—416no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—44no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—816no—
1328C22C2×#53414yes—
1329C22#349714yes—
1330C22C24×D411yescharacteristic
1331C22C22×H(5,𝔽2)12yes—
1332C22C22×2−1+411yescharacteristic
1333C22C2×#58511yescharacteristic
1334C222−1+612yes—
1335C4—22no—
1336C4—22no—
1337C4—28no—
1338C4—28no—
1339C4—24no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—48no—
1353C4C2×#53414yes—
1354C4C2×#53414yes—
1355C2—24no—
1356C2—24no—
1357C2—42no—
1358C2—82no—
1359C2—82no—
1360C2—84no—
1361C2C22×#53411yescharacteristic
1362C2C2×#349711yescharacteristic
1363C2#6284811yescharacteristic
1364C2#6294212yes—
1365C2#6295412yes—
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×#3486C2semidirect
2. C22×#536C2semidirect
3. #42797C2semidirect
4. #42796C2semidirect
5. #42787C2semidirect
6. #42786C2semidirect
7. #39723C2semidirect
8. #39721C2semidirect
9. #39595C2semidirect
10. #39593C2semidirect
11. #39135C2semidirect
12. #39133C2semidirect
13. #39123C2semidirect
14. #39121C2semidirect
15. #37452C2semidirect
16. #37190C2semidirect
17. #35673C2semidirect
18. #35660C2semidirect
19. #35263C2semidirect
20. #35251C2semidirect
21. #35178C2semidirect
22. #35153C2semidirect
23. #35064C2semidirect
24. #34810C2semidirect
25. #34738C2semidirect
26. C2×Q8×C22⋊C4C2semidirect
27. C22×2−1+4C22semidirect
33. C2×D4×Q8C22semidirect
34. C2×D4×Q8C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
46. C2×#536C22semidirect
47. C2×#536C22semidirect
48. C2×#536C22semidirect
58. C2×#519C22semidirect
59. C22×C4×Q8C22semidirect
63. #2854C22semidirect
64. #2854C22semidirect
67. #2814C22semidirect
68. #2813C22semidirect
69. #2734C22semidirect
70. #2733C22semidirect
71. #2732C22semidirect
72. #2732C22semidirect
73. #2731C22semidirect
74. #2731C22semidirect
75. #2730C22semidirect
76. #2730C22semidirect
77. #2730C22semidirect
78. #2730C22semidirect
79. #2729C22semidirect
80. #2729C22semidirect
81. #2729C22semidirect
82. #2729C22semidirect
83. #2728C22semidirect
84. #2728C22semidirect
85. #2663C22semidirect
86. #2661C22semidirect
87. #2630C22semidirect
88. #2630C22semidirect
91. #2625C22semidirect
92. #2624C22semidirect
94. #2618C22semidirect
95. #2618C22semidirect
99. #2602C22semidirect
100. #2602C22semidirect
106. #2548C22semidirect
107. #2546C22semidirect
108. #2545C22semidirect
109. #2545C22semidirect
111. #2538C22semidirect
112. #2538C22semidirect
113. #2536C22semidirect
114. #2536C22semidirect
121. #2500C22semidirect
122. #2499C22semidirect
123. #2498C22semidirect
124. #2498C22semidirect
125. #2498C22semidirect
126. #2498C22semidirect
129. #2485C22semidirect
130. #2448C22semidirect
131. #2448C22semidirect
132. #2446C22semidirect
133. #2446C22semidirect
135. #2436C22semidirect
138. #2434C22semidirect
141. #2432C22semidirect
143. #2431C22semidirect
146. #2430C22semidirect
147. #2430C22semidirect
148. #2429C22semidirect
149. #2429C22semidirect
150. #2429C22semidirect
151. #2429C22semidirect
152. #2426C22semidirect
153. #2426C22semidirect
154. #2426C22semidirect
155. #2426C22semidirect
156. #2423C22semidirect
157. #2423C22semidirect
158. #2421C22semidirect
159. #2421C22semidirect
167. #2409C22semidirect
168. #2409C22semidirect
171. #2407C22semidirect
172. #2407C22semidirect
173. #2395C22semidirect
179. Q8×C22⋊C4C22semidirect
180. Q8×C22⋊C4C22semidirect
185. #2316C22semidirect
187. #2311C22semidirect
193. #2297C22semidirect
194. C2×#391C22semidirect
195. C2×#391C22semidirect
196. #2285C22semidirect
215. C23×Q8D4semidirect
1141. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34862
C22×#5362
#427972
#427962
#427872
#427862
#397232
#397212
#395952
#395932
#391352
#391332
#391232
#391212
#374522
#371902
#356732
#356602
#352632
#352512
#351782
#351532
#350642
#348102
#347382
C2×Q8×C22⋊C42