Finite Group Databasebeta

← #7653294

Subgroups — #7653294

Order 512.

6790 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42812C212yesmaximal, complemented
4#42809C212yesmaximal, complemented
5#42174C214yesmaximal, complemented
6#41988C214yesmaximal, complemented
7#39879C214yesmaximal, complemented
8#39593C212yesmaximal, complemented
9#39588C214yesmaximal, complemented
10#39123C212yesmaximal, complemented
11#39117C214yesmaximal, complemented
12#38375C218yesmaximal, complemented
13#37548C212yesmaximal, complemented
14#37537C211yesmaximal, characteristic, complemented
15#36547C212yesmaximal, complemented
16#36528C212yesmaximal, complemented
17#36233C214yesmaximal, complemented
18#35938C212yesmaximal, complemented
19#35909C212yesmaximal, complemented
20#35325C212yesmaximal, complemented
21#35248C211yesmaximal, characteristic, complemented
22#35143C212yesmaximal, complemented
23#35129C211yesmaximal, characteristic
24#34971C211yesmaximal, characteristic, complemented
25#34875C212yesmaximal, complemented
26#34192C211yesmaximal, characteristic, complemented
27Q8×#41—216no—
28C2×Q82C2211yescharacteristic, complemented
29C2×#557C2211yescharacteristic, complemented
30C2×#557C2212yescomplemented
31C2×#556—216no—
32C2×#556C2214yes—
33C2×#556C2212yes—
34C2×#556C2212yes—
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#556C2214yes—
38C2×#554C2214yes—
39C2×#554C2212yes—
40C2×#554C2212yescomplemented
41C2×#554C2211yescharacteristic, complemented
42C2×D4×Q8C2212yes—
43C2×D4×Q8C2211yescharacteristic, complemented
44C2×#533C2211yescharacteristic
45C2×#533C2212yes—
46C2×#533C2212yescomplemented
47C2×#533C2214yescomplemented
48C22×C4⋊Q8C2211yescharacteristic
49C22×#126C2212yes—
50C22×#126C2212yes—
51C22×#124C2211yescharacteristic
52C22×#124C2211yescharacteristic
53C22×C22⋊Q8C2212yes—
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2212yes—
56C22×C4×Q8C2211yescharacteristic
57C22×C4×Q8C2211yescharacteristic
58C22×C4×Q8C2211yescharacteristic
59C22×C4×Q8C2212yescomplemented
60C22×C4×D4C2211yescharacteristic
61C22×#117C2212yes—
62#2855C2212yes—
63#2855C2212yes—
64#2855C2214yes—
65#2852C2218yescomplemented
66#2850C2214yes—
67#2848C2214yes—
68#2821C2214yescomplemented
69#2821C2214yescomplemented
70#2820C2214yes—
71#2734C2218yescomplemented
72#2731C2218yes—
73#2730C2218yes—
74#2729C2218yescomplemented
75#2725C2218yescomplemented
76#2723C2218yescomplemented
77#2716C2218yescomplemented
78#2704C2218yescomplemented
79#2702C2218yescomplemented
80#2692C2218yescomplemented
81#2683C2218yescomplemented
82#2677C2218yescomplemented
83#2664C2214yescomplemented
84#2664C2214yescomplemented
85#2658C2212yes—
86#2640C2212yes—
87#2637C2214yescomplemented
88#2637C2218yescomplemented
89#2636C2214yescomplemented
90#2634C2214yescomplemented
91#2632C2212yes—
92#2632C2214yes—
93#2631C2212yes—
94#2628C2214yescomplemented
95#2627C2214yes—
96#2626C2214yes—
97#2626C2214yes—
98#2621C2214yescomplemented
99#2611C2214yescomplemented
100#2611C2214yescomplemented
101#2610C2214yes—
102#2609C2218yescomplemented
103#2604C2214yescomplemented
104#2604C2218yescomplemented
105#2603C2214yescomplemented
106#2601C2218yescomplemented
107#2599C2214yescomplemented
108#2599C2218yescomplemented
109#2599C2214yescomplemented
110#2598C2214yescomplemented
111#2592C2212yes—
112#2583C2214yes—
113#2583C2214yes—
114#2581C2214yescomplemented
115#2581C2212yescomplemented
116#2579C2214yes—
117#2579C2214yes—
118#2568C2212yescomplemented
119#2561C2214yes—
120#2561C2214yes—
121#2560C2218yescomplemented
122#2556C2218yescomplemented
123#2546C2212yescomplemented
124#2546C2214yescomplemented
125#2545C2214yes—
126#2545C2214yes—
127#2540C2212yes—
128#2536C2212yescomplemented
129#2534C2214yes—
130#2534C2214yes—
131#2519C2218yescomplemented
132#2503C2212yes—
133#2486C2212yes—
134#2484C2212yes—
135#2484C2212yes—
136#2484C2211yescharacteristic
137#2484C2211yescharacteristic
138#2482C2212yes—
139#2482C2212yes—
140#2482C2212yes—
141#2481C2218yescomplemented
142#2469C2218yescomplemented
143#2465C2218yescomplemented
144#2465C2218yescomplemented
145#2463C2218yes—
146#2462C2218yescomplemented
147#2460C2218yes—
148#2452C2214yes—
149#2452C2218yescomplemented
150#2451C2214yescomplemented
151#2449C2218yescomplemented
152#2448C2214yes—
153#2446C2214yescomplemented
154#2436C2214yes—
155#2435C2212yes—
156#2434C2212yes—
157#2434C2212yes—
158#2434C2214yescomplemented
159#2429C2214yescomplemented
160#2429C2214yescomplemented
161#2427C2214yes—
162#2426C2214yes—
163#2409C2212yes—
164#2409C2212yes—
165#2408C2212yes—
166#2406C2211yescharacteristic
167#2406C2211yescharacteristic
168#2404C2212yes—
169#2399C2212yescomplemented
170#2398C2212yescomplemented
171#2396C2214yescomplemented
172#2392C2214yescomplemented
173#2367C2214yes—
174#2365C2214yescomplemented
175#2361C2214yes—
176#2360C2214yescomplemented
177#2356C2212yescomplemented
178#2356C2214yescomplemented
179#2351C2212yescomplemented
180#2345C2214yes—
181#2345C2212yes—
182Q8×C22⋊C4C2212yes—
183#2327C2214yescomplemented
184#2323C2218yescomplemented
185#2322C2214yes—
186#2321C2214yes—
187#2321C2214yes—
188#2320C2214yescomplemented
189#2320C2212yescomplemented
190C4×C22⋊Q8C2214yescomplemented
191C4×#123C2214yes—
192C4×#123C2212yes—
193C4×#123C2212yes—
194C4×#120C2214yes—
195#2290C2218yescomplemented
196#2283C2211yescharacteristic
197#2283C2212yes—
198#2283C2212yes—
199#2283C2211yescharacteristic
200#2276C2212yescomplemented
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2312yes—
205C23×Q8C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C24×C4C2312yes—
208Q82—28no—
209#557—28no—
210#557—216no—
211#556—216no—
212#556—216no—
213#556—232no—
214#556—216no—
215#556—232no—
216#556—216no—
217#554—216no—
218#554—28no—
219#554—216no—
220#554—232no—
221D4×Q8—216no—
222D4×Q8—28no—
223#533—216no—
224#533—232no—
225#533—216no—
226#533—28no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×#126—216no—
242C2×#126—216no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#124—28no—
258C2×#124—28no—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#123C2312yes—
268C2×#123C2312yes—
269C2×C22⋊Q8—216no—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2314yes—
289C2×#120C2314yes—
290C4×#41—216no—
291C4×#41—28no—
292C2×C4×Q8—216no—
293C2×C4×Q8—28no—
294C2×C4×Q8—28no—
295C2×C4×Q8D4116yescomplemented
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4—28no—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2318yes—
334C2×#117—216no—
335C2×#117C2314yes—
336C2×#117C2314yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2314yes—
340C2×#117C2314yes—
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2312yes—
353C22×C22⋊C4C2312yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C42C2312yes—
359C22×C42C2314yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364C22×C42C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2318yes—
368#400C2314yes—
369#400C2312yes—
370#400C2318yes—
371#399C2314yes—
372#399C2314yes—
373#399C2318yes—
374#399C2314yes—
375#399C2318yes—
376#398C2318yes—
377#398C2312yes—
378#398C2318yes—
379#398C2314yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2318yes—
387#397C2314yes—
388#397C2318yes—
389#397C2318yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#396C2318yes—
399#396C2318yes—
400#396C2318yes—
401#395C2318yes—
402#395C2318yes—
403#395C2318yes—
404#395C2312yes—
405#395C2312yes—
406#395C2318yes—
407#395C2318yes—
408#395C2314yes—
409#395C2314yes—
410#394C2318yes—
411#394C2318yes—
412#394C2312yes—
413#394C2318yes—
414#394C2312yes—
415#394C2314yes—
416#393C2318yes—
417#393C2318yes—
418#393C2318yes—
419#393C2318yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#392C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2318yes—
431#391C2318yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#390C2318yes—
436#390C2318yes—
437#390C2314yes—
438#390C2314yes—
439#389C2314yes—
440#389C2318yes—
441#389C2318yes—
442#389C2318yes—
443#389C2318yes—
444#389C2318yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2318yes—
449#389C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2314yes—
465#388C2314yes—
466#388C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2314yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2314yes—
478#387C2314yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2314yes—
483#387C2318yes—
484#386C2318yes—
485#386C2312yes—
486#386C2314yes—
487#386C2318yes—
488#386C2318yes—
489#386C2312yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2318yes—
497#385C2314yes—
498#385C2314yes—
499#385C2318yes—
500#385C2318yes—
501#385C2312yes—
502#385C2312yes—
503#385C2318yes—
504#385C2318yes—
505#385C2314yes—
506#385C2314yes—
507#385C2318yes—
508#383C2314yes—
509#383C2312yes—
510#383C2314yes—
511#383C2312yes—
512#382C2312yes—
513#382C2314yes—
514#382C2314yes—
515#382C2312yes—
516#382C2314yes—
517#381C2312yes—
518#381C2312yes—
519#381C2314yes—
520#381C2314yes—
521#381C2312yes—
522#381C2311yescharacteristic
523#381C2311yescharacteristic
524#380C2318yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2312yes—
529#380C2314yes—
530#379C2314yes—
531#379C2314yes—
532#379C2314yes—
533C4×C4⋊C4C2318yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2318yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2318yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2314yes—
551#376C2312yes—
552#376C2312yes—
553#376C2314yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—24no—
557C22×Q8—28no—
558C22×Q8—24no—
559C22×Q8—24no—
560C22×Q8—44no—
561C22×Q8—44no—
562C22×Q8—44no—
563C22×Q8—48no—
564C22×Q8C2×D418yes—
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2414yes—
573C22×Q8C2412yes—
574C22×Q8C2414yes—
575C22×Q8C2412yes—
576C22×Q8C2412yes—
577C22×D4—24no—
578C22×D4—44no—
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2418yes—
584C23×C4—28no—
585C23×C4—48no—
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2414yes—
598C23×C4C2412yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C23×C4C2412yes—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—216no—
606C4⋊Q8—28no—
607C4⋊Q8—216no—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—28no—
611C4⋊Q8—24no—
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—48no—
615C4⋊Q8—48no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#125—216no—
625#125—216no—
626#125—216no—
627#125—28no—
628#125—28no—
629#125—28no—
630#124—28no—
631#124—28no—
632#124—216no—
633#124—28no—
634#124—28no—
635#124—28no—
636#124—28no—
637#124—48no—
638#123—28no—
639#123—28no—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—28no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—48no—
656C22⋊Q8—416no—
657C22⋊Q8—48no—
658#121—48no—
659#120—216no—
660C4×Q8—28no—
661C4×Q8—28no—
662C4×Q8—216no—
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—28no—
672C4×Q8—28no—
673C4×Q8—24no—
674C4×Q8—28no—
675C4×Q8—24no—
676C4×Q8—216no—
677C4×Q8—28no—
678C4×Q8—48no—
679C4×Q8C2×D418yes—
680C4×Q8C2×D4116yes—
681C4×Q8C2×D418yes—
682C4×Q8C2×D418yes—
683C4×Q8C2×D418yes—
684C4×Q8C2×D4116yes—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—216no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—24no—
694C4×D4—28no—
695C4×D4—24no—
696C4×D4—416no—
697#117—24no—
698#117—28no—
699#117—216no—
700#117—216no—
701#117—216no—
702#117—216no—
703#117—216no—
704#117—28no—
705C2×C4⋊C4—24no—
706C2×C4⋊C4—28no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4C2×D418yes—
714C2×C4⋊C4C2×D4116yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2418yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C22⋊C4—28no—
766C2×C22⋊C4—28no—
767C2×C22⋊C4—28no—
768C2×C22⋊C4—28no—
769C2×C22⋊C4—28no—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C42—28no—
802C2×C42—24no—
803C2×C42—24no—
804C2×C42—216no—
805C2×C42—28no—
806C2×C42C2×D4116yes—
807C2×C42C2×D418yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2418yes—
822C2×C42C2418yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2418yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2418yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2414yes—
845#95C2418yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2414yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2418yes—
857#95C2414yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864C24—24no—
865C24—28no—
866C24—44no—
867C24—44no—
868C24C2514yes—
869C24C2512yes—
870C24C2511yescharacteristic
871#41—232no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—28no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—28no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—48no—
893C2×Q8—48no—
894C2×Q8—44no—
895C2×Q8—416no—
896C2×Q8—416no—
897C2×Q8—416no—
898C2×Q8—432no—
899C2×Q8C22×D414yes—
900C2×Q8C22×D414yes—
901C2×Q8C22×D418yes—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—216no—
906C2×D4—22no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—28no—
910C2×D4—44no—
911C2×D4—416no—
912C2×D4—48no—
913C2×D4—48no—
914C2×D42−1+418yes—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—28no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—42no—
942C22×C4—48no—
943C22×C4—42no—
944C22×C4—44no—
945C22×C4—48no—
946C22×C4—44no—
947C22×C4—432no—
948C22×C4C22×D414yes—
949C22×C4C22×D414yes—
950C22×C4C22×D418yes—
951C22×C4C22×D418yes—
952C22×C4C22×D414yes—
953C22×C4C2518yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2511yescharacteristic
970C22×C4C2512yes—
971C22×C4C2511yescharacteristic
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—22no—
999C4⋊C4—24no—
1000C4⋊C4—22no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—216no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—48no—
1012C4⋊C4—48no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—48no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—48no—
1019C4⋊C4C22×D414yes—
1020C4⋊C4C22×D418yes—
1021C4⋊C4C22×D418yes—
1022C4⋊C4C22×D414yes—
1023C4⋊C4C22×D418yes—
1024C4⋊C4C22×D418yes—
1025C4⋊C4C22×D418yes—
1026C22⋊C4—24no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
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—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—24no—
1047C22⋊C4—216no—
1048C22⋊C4—28no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—44no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C42—28no—
1058C42—24no—
1059C42—28no—
1060C42—28no—
1061C42—24no—
1062C42—24no—
1063C42—28no—
1064C42—24no—
1065C42—28no—
1066C42—24no—
1067C42—24no—
1068C42—24no—
1069C42—28no—
1070C42—48no—
1071C42—48no—
1072C42—44no—
1073C42C22×D418yes—
1074C42C22×D414yes—
1075C42C22×D418yes—
1076C42C22×D418yes—
1077C42C22×D418yes—
1078C42C22×D414yes—
1079C42C22×D414yes—
1080C42C22×D414yes—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—28no—
1089C23—24no—
1090C23—28no—
1091C23—24no—
1092C23—48no—
1093C23—48no—
1094C23—48no—
1095C23—816no—
1096C23C23×D412yes—
1097C23C2×2−1+414yes—
1098C23C2×2−1+414yes—
1099C23C2611yescharacteristic
1100Q8—28no—
1101Q8—28no—
1102Q8—28no—
1103Q8—48no—
1104Q8—48no—
1105Q8—48no—
1106Q8—48no—
1107Q8—416no—
1108Q8—48no—
1109Q8—48no—
1110Q8—88no—
1111Q8—84no—
1112D4—28no—
1113D4—216no—
1114D4—48no—
1115D4—48no—
1116D4—816no—
1117C2×C4—28no—
1118C2×C4—216no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—28no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—24no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—22no—
1160C2×C4—48no—
1161C2×C4—44no—
1162C2×C4—48no—
1163C2×C4—416no—
1164C2×C4—416no—
1165C2×C4—416no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—48no—
1171C2×C4—88no—
1172C2×C4—84no—
1173C2×C4C23×D412yes—
1174C2×C4C23×D414yes—
1175C2×C4C23×D412yes—
1176C2×C4C23×D414yes—
1177C2×C4C23×D412yes—
1178C2×C4C23×D414yes—
1179C2×C4C23×D412yes—
1180C2×C4C23×D414yes—
1181C2×C4C23×D412yes—
1182C2×C4C23×D412yes—
1183C2×C4C2×2−1+414yes—
1184C2×C4#58514yes—
1185C2×C4#58514yes—
1186C22—28no—
1187C22—22no—
1188C22—22no—
1189C22—28no—
1190C22—24no—
1191C22—44no—
1192C22—42no—
1193C22—42no—
1194C22—48no—
1195C22—48no—
1196C22—44no—
1197C22—44no—
1198C22—44no—
1199C22—816no—
1200C22#348614yes—
1201C22C24×D411yescharacteristic
1202C22C22×2−1+412yes—
1203C22C2×#58512yes—
1204C22C2×#58512yes—
1205C4—22no—
1206C4—22no—
1207C4—24no—
1208C4—24no—
1209C4—24no—
1210C4—24no—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—24no—
1215C4—24no—
1216C4—44no—
1217C4—44no—
1218C4—48no—
1219C4—42no—
1220C4—42no—
1221C4—42no—
1222C4—44no—
1223C4—42no—
1224C4—44no—
1225C4—42no—
1226C4—44no—
1227C4#344914yes—
1228C2—24no—
1229C2—44no—
1230C2—84no—
1231C2C2×#344911yescharacteristic
1232C2C2×#348611yescharacteristic
1233C2#6281111yescharacteristic
1234C2#6302514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35129C2
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×Q8×#41C2semidirect
2. C22×#556C2semidirect
3. #42812C2semidirect
4. #42809C2semidirect
5. #42174C2semidirect
6. #41988C2semidirect
7. #39879C2semidirect
8. #39593C2semidirect
9. #39588C2semidirect
10. #39123C2semidirect
11. #39117C2semidirect
12. #38375C2semidirect
13. #37548C2semidirect
14. #37537C2semidirect
15. #36547C2semidirect
16. #36528C2semidirect
17. #36233C2semidirect
18. #35938C2semidirect
19. #35909C2semidirect
20. #35325C2semidirect
21. #35248C2semidirect
22. #35143C2semidirect
24. #34971C2semidirect
25. #34875C2semidirect
26. #34192C2semidirect
28. C2×Q82C22semidirect
29. C2×#557C22semidirect
30. C2×#557C22semidirect
40. C2×#554C22semidirect
41. C2×#554C22semidirect
43. C2×D4×Q8C22semidirect
46. C2×#533C22semidirect
47. C2×#533C22semidirect
59. C22×C4×Q8C22semidirect
65. #2852C22semidirect
68. #2821C22semidirect
69. #2821C22semidirect
71. #2734C22semidirect
74. #2729C22semidirect
75. #2725C22semidirect
76. #2723C22semidirect
77. #2716C22semidirect
78. #2704C22semidirect
79. #2702C22semidirect
80. #2692C22semidirect
81. #2683C22semidirect
82. #2677C22semidirect
83. #2664C22semidirect
84. #2664C22semidirect
87. #2637C22semidirect
88. #2637C22semidirect
89. #2636C22semidirect
90. #2634C22semidirect
94. #2628C22semidirect
98. #2621C22semidirect
99. #2611C22semidirect
100. #2611C22semidirect
102. #2609C22semidirect
103. #2604C22semidirect
104. #2604C22semidirect
105. #2603C22semidirect
106. #2601C22semidirect
107. #2599C22semidirect
108. #2599C22semidirect
109. #2599C22semidirect
110. #2598C22semidirect
114. #2581C22semidirect
115. #2581C22semidirect
118. #2568C22semidirect
121. #2560C22semidirect
122. #2556C22semidirect
123. #2546C22semidirect
124. #2546C22semidirect
128. #2536C22semidirect
131. #2519C22semidirect
141. #2481C22semidirect
142. #2469C22semidirect
143. #2465C22semidirect
144. #2465C22semidirect
146. #2462C22semidirect
149. #2452C22semidirect
150. #2451C22semidirect
151. #2449C22semidirect
153. #2446C22semidirect
158. #2434C22semidirect
159. #2429C22semidirect
160. #2429C22semidirect
169. #2399C22semidirect
170. #2398C22semidirect
171. #2396C22semidirect
172. #2392C22semidirect
174. #2365C22semidirect
176. #2360C22semidirect
177. #2356C22semidirect
178. #2356C22semidirect
179. #2351C22semidirect
183. #2327C22semidirect
184. #2323C22semidirect
188. #2320C22semidirect
189. #2320C22semidirect
190. C4×C22⋊Q8C22semidirect
195. #2290C22semidirect
200. #2276C22semidirect
295. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C22×#5562
#428122
#428092
#421742
#419882
#398792
#395932
#395882
#391232
#391172
#383752
#375482
#375372
#365472
#365282
#362332
#359382
#359092
#353252
#352482
#351432
#351292
#349712
#348752
#341922