Finite Group Databasebeta

← #7652072

Subgroups — #7652072

Order 512.

8266 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3486C211yesmaximal, characteristic, complemented
3#42926C214yesmaximal, complemented
4#42912C214yesmaximal, complemented
5#42807C214yesmaximal, complemented
6#42787C214yesmaximal, complemented
7#42295C218yesmaximal, complemented
8#39956C214yesmaximal, complemented
9#39864C214yesmaximal, complemented
10#39615C214yesmaximal, complemented
11#39593C214yesmaximal, complemented
12#38365C218yesmaximal, complemented
13#35674C211yesmaximal, characteristic, complemented
14#35673C211yesmaximal, characteristic, complemented
15#35666C211yesmaximal, characteristic, complemented
16#35659C211yesmaximal, characteristic, complemented
17#35633C211yesmaximal, characteristic, complemented
18#35621C211yesmaximal, characteristic, complemented
19#35316C211yesmaximal, characteristic, complemented
20#35307C211yesmaximal, characteristic, complemented
21#35242C211yesmaximal, characteristic, complemented
22#34743C211yesmaximal, characteristic, complemented
23#34742C211yesmaximal, characteristic, complemented
24C2×#2434C211yesmaximal, characteristic, complemented
25#34259C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C22×2−1+4C2211yescharacteristic
28C24×Q8C2211yescharacteristic
29#3499—216no—
30#3486—216no—
31C2×D4×Q8C2214yes—
32C2×D4×Q8C2214yes—
33C2×D4×Q8C2214yescomplemented
34C2×#548C2214yes—
35C2×#548C2214yes—
36C2×#547C2218yes—
37C2×#547C2214yescomplemented
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2214yes—
41C2×#536C2211yescharacteristic
42C2×#536C2211yescharacteristic
43C2×#536C2211yescharacteristic
44C2×#536C2212yescomplemented
45C2×#536C2212yescomplemented
46C2×#532C2211yescharacteristic
47C2×#532C2212yescomplemented
48C22×C4⋊Q8C2211yescharacteristic
49C22×C4⋊Q8C2211yescharacteristic
50C22×C4⋊Q8C2212yescomplemented
51C2×#525C2211yescharacteristic
52C2×#525C2211yescharacteristic
53C2×#525C2214yes—
54C2×#525C2211yescharacteristic
55C22×C22⋊Q8C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60#2857C2214yescomplemented
61#2855C2214yescomplemented
62#2849C2214yes—
63#2817C2218yescomplemented
64#2814C2218yescomplemented
65#2734C2218yescomplemented
66#2734C2218yescomplemented
67#2732C2218yes—
68#2729C2218yes—
69#2729C2218yes—
70#2729C2218yescomplemented
71#2729C2218yescomplemented
72#2728C2218yes—
73#2717C2218yescomplemented
74#2717C2218yescomplemented
75#2708C2218yes—
76#2708C2218yes—
77#2688C2218yes—
78#2686C2218yescomplemented
79#2686C2218yescomplemented
80#2671C2218yes—
81#2663C2218yescomplemented
82#2659C2218yescomplemented
83#2638C2218yes—
84#2638C2218yescomplemented
85#2630C2218yes—
86#2627C2218yescomplemented
87#2625C2214yescomplemented
88#2621C2214yescomplemented
89#2614C2214yes—
90#2602C2218yes—
91#2600C2218yes—
92#2583C2218yescomplemented
93#2579C2218yes—
94#2564C2218yes—
95#2564C2218yescomplemented
96#2547C2212yescomplemented
97#2547C2214yescomplemented
98#2546C2214yescomplemented
99#2546C2212yescomplemented
100#2545C2212yescomplemented
101#2544C2212yescomplemented
102#2534C2214yes—
103#2498C2218yes—
104#2486C2214yes—
105#2486C2218yes—
106#2484C2218yes—
107#2448C2214yescomplemented
108#2447C2214yescomplemented
109#2446C2214yescomplemented
110#2446C2214yescomplemented
111#2446C2214yescomplemented
112#2446C2214yescomplemented
113#2446C2214yescomplemented
114#2446C2214yescomplemented
115#2436C2214yes—
116#2434C2214yes—
117#2434C2214yes—
118#2434C2214yes—
119#2434C2214yes—
120#2434C2214yes—
121#2434C2212yescomplemented
122#2434C2214yescomplemented
123#2434C2212yescomplemented
124#2432C2212yescomplemented
125#2432C2214yescomplemented
126#2432C2212yescomplemented
127#2429C2214yes—
128#2429C2212yes—
129#2428C2212yes—
130#2427C2214yes—
131#2427C2212yes—
132#2426C2212yes—
133#2425C2218yes—
134#2425C2214yes—
135#2424C2214yes—
136#2423C2212yes—
137#2423C2214yescomplemented
138#2422C2212yes—
139#2421C2212yes—
140#2421C2214yescomplemented
141#2420C2212yes—
142#2419C2214yes—
143#2419C2218yes—
144#2418C2214yes—
145#2417C2214yes—
146#2417C2214yescomplemented
147#2415C2214yes—
148#2415C2214yescomplemented
149#2409C2214yes—
150#2409C2214yes—
151#2409C2214yes—
152#2409C2214yes—
153#2407C2214yes—
154#2407C2214yes—
155#2406C2214yes—
156#2406C2218yes—
157#2404C2214yes—
158#2395C2214yes—
159#2392C2214yes—
160C2×#395C2214yes—
161Q8×C22⋊C4C2214yescomplemented
162#2339C2218yes—
163#2339C2214yescomplemented
164#2325C2218yes—
165#2322C2218yes—
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2212yescomplemented
170#2310C2211yescharacteristic
171#2310C2211yescharacteristic
172#2310C2211yescharacteristic
173#2310C2211yescharacteristic
174#2310C2212yescomplemented
175C4×#123C2214yes—
176C4×#121C2214yes—
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2212yescomplemented
180#2296C2211yescharacteristic
181#2296C2211yescharacteristic
182C2×#391C2211yescharacteristic
183C2×#391C2211yescharacteristic
184C2×#391C2212yescomplemented
185C2×#385C2214yes—
186#2285C2211yescharacteristic
187#2280C2211yescharacteristic
188C2×C4×C22⋊C4C2211yescharacteristic
189C2×2−1+4—28no—
190C2×2−1+4—44no—
191C2×2−1+4—44no—
192C2×2−1+4—44no—
193C2×2−1+4—44no—
194C2×2−1+4D4116yescomplemented
195C22×#41C2311yescharacteristic
196C22×#41C2311yescharacteristic
197C22×#41C2311yescharacteristic
198C22×#41C2314yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201C22×#41C2312yes—
202C22×#41C2314yes—
203C22×#41C2312yes—
204C23×Q8—28no—
205C23×Q8—44no—
206C23×Q8—44no—
207C23×Q8C2311yescharacteristic
208C23×Q8C2311yescharacteristic
209C23×Q8C2311yescharacteristic
210C23×Q8C2312yes—
211C23×Q8C2314yes—
212C23×Q8C2314yes—
213C23×Q8C2312yes—
214C23×Q8C2312yes—
215C23×Q8C2312yes—
216C23×Q8C2312yes—
217C24×C4C2311yescharacteristic
218C24×C4C2312yes—
219D4×Q8—232no—
220D4×Q8—232no—
221D4×Q8—232no—
222#548—232no—
223#548—232no—
224#547—264no—
225#547—232no—
226#536—28no—
227#536—28no—
228#536—232no—
229#536—28no—
230#536—216no—
231#536—28no—
232#536—216no—
233#536—44no—
234#532—28no—
235#532—216no—
236C2×C4⋊Q8—28no—
237C2×C4⋊Q8—216no—
238C2×C4⋊Q8—44no—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2318yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2318yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2312yes—
253C2×#127C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2318yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262#525—28no—
263#525—28no—
264#525—232no—
265#525—44no—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2318yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2318yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×C22⋊Q8—44no—
278C2×C22⋊Q8C2318yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C2318yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2318yes—
288C2×C22⋊Q8C2318yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2318yes—
297C2×#121C2312yes—
298C2×#121C2318yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#120C2312yes—
302C2×#120C2312yes—
303C2×#120C2312yes—
304#520—44no—
305#519—28no—
306C4×#41—28no—
307C4×#41—44no—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2318yes—
314C2×C4×D4C2318yes—
315C2×C4×D4C2318yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2312yes—
332C2×#117C2314yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2318yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2314yes—
341C22×C22⋊C4C2312yes—
342C22×C22⋊C4C2312yes—
343C22×C42C2312yes—
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2312yes—
347#400C2314yes—
348#400C2318yes—
349#400C2318yes—
350#400C2318yes—
351#400C2318yes—
352#399C2314yes—
353#399C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#398C2314yes—
361#398C2318yes—
362#398C2314yes—
363#398C2318yes—
364#397C2314yes—
365#397C2318yes—
366#397C2318yes—
367#397C2318yes—
368#397C2318yes—
369#397C2318yes—
370#397C2318yes—
371#397C2314yes—
372#397C2318yes—
373#397C2314yes—
374#397C2314yes—
375#396C2314yes—
376#396C2318yes—
377#396C2318yes—
378#396C2314yes—
379#395C2318yes—
380#395C2318yes—
381#395C2318yes—
382#395C2318yes—
383#395C2318yes—
384#395C2318yes—
385#395C2318yes—
386#395C2318yes—
387#395C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2314yes—
391#394C2318yes—
392#394C2314yes—
393#394C2314yes—
394#394C2318yes—
395#394C2314yes—
396#394C2314yes—
397#394C2318yes—
398#393C2318yes—
399#393C2318yes—
400#393C2318yes—
401#392C2314yes—
402#392C2318yes—
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2311yescharacteristic
414#391C2312yes—
415#391C2312yes—
416#391C2318yes—
417#391C2312yes—
418#391C2318yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2311yescharacteristic
424#391C2312yes—
425#391C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2311yescharacteristic
429#390C2314yes—
430#390C2311yescharacteristic
431#390C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2318yes—
435#389C2318yes—
436#389C2314yes—
437#389C2318yes—
438#389C2318yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#388C2314yes—
444#388C2318yes—
445#388C2314yes—
446#388C2318yes—
447#388C2314yes—
448#388C2318yes—
449#388C2318yes—
450#388C2314yes—
451#387C2318yes—
452#387C2318yes—
453#387C2314yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2318yes—
460#387C2314yes—
461#386C2314yes—
462#386C2318yes—
463#386C2314yes—
464#386C2318yes—
465#386C2314yes—
466#386C2314yes—
467#386C2318yes—
468#386C2318yes—
469#386C2314yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2314yes—
474#386C2318yes—
475#386C2314yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2314yes—
487#385C2318yes—
488#385C2318yes—
489#385C2318yes—
490#385C2314yes—
491#385C2314yes—
492#384C2312yes—
493#382C2312yes—
494#381C2318yes—
495#381C2314yes—
496#381C2314yes—
497#381C2314yes—
498#381C2314yes—
499#381C2318yes—
500#381C2312yes—
501#381C2314yes—
502#380C2318yes—
503#380C2318yes—
504#380C2318yes—
505#380C2314yes—
506#380C2314yes—
507#380C2318yes—
508#380C2314yes—
509#380C2318yes—
510#380C2314yes—
511#380C2312yes—
512#380C2312yes—
513#380C2314yes—
514#379C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C2×#95C2318yes—
529C2×#95C2314yes—
530C2×#95C2312yes—
531C2×#95C2314yes—
532C25C2411yescharacteristic
5332−1+4—464no—
5342−1+4—464no—
535C2×#41—216no—
536C2×#41—28no—
537C2×#41—28no—
538C2×#41—24no—
539C2×#41—24no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—48no—
546C2×#41—48no—
547C2×#41—48no—
548C2×#41—48no—
549C2×#41—44no—
550C2×#41—44no—
551C2×#41—44no—
552C2×#41—44no—
553C2×#41—44no—
554C2×#41—44no—
555C2×#41—44no—
556C2×#41—44no—
557C2×#41C2×D418yes—
558C2×#41C2×D418yes—
559C2×#41C2×D4132yes—
560C2×#41C2×D4116yes—
561C2×#41C2×D4116yes—
562C22×Q8—216no—
563C22×Q8—216no—
564C22×Q8—28no—
565C22×Q8—28no—
566C22×Q8—24no—
567C22×Q8—28no—
568C22×Q8—24no—
569C22×Q8—24no—
570C22×Q8—24no—
571C22×Q8—24no—
572C22×Q8—24no—
573C22×Q8—24no—
574C22×Q8—24no—
575C22×Q8—44no—
576C22×Q8—44no—
577C22×Q8—48no—
578C22×Q8—48no—
579C22×Q8—48no—
580C22×Q8—48no—
581C22×Q8—44no—
582C22×Q8—44no—
583C22×Q8—44no—
584C22×Q8—44no—
585C22×Q8—44no—
586C22×Q8—44no—
587C22×Q8—44no—
588C22×Q8—44no—
589C22×Q8—464no—
590C22×Q8C2×D418yes—
591C22×Q8C2×D4116yes—
592C22×Q8C2×D4116yes—
593C22×Q8C2412yes—
594C22×Q8C2412yes—
595C22×Q8C2412yes—
596C22×Q8C2412yes—
597C22×Q8C2411yescharacteristic
598C22×Q8C2411yescharacteristic
599C22×Q8C2412yes—
600C22×Q8C2411yescharacteristic
601C22×Q8C2412yes—
602C22×Q8C2418yes—
603C22×Q8C2414yes—
604C22×Q8C2414yes—
605C22×D4C2412yes—
606C22×D4C2411yescharacteristic
607C22×D4C2414yes—
608C22×D4C2414yes—
609C22×D4C2414yes—
610C22×D4C2412yes—
611C22×D4C2411yescharacteristic
612C22×D4C2412yes—
613C22×D4C2411yescharacteristic
614C22×D4C2414yes—
615C22×D4C2414yes—
616C22×D4C2414yes—
617C23×C4—28no—
618C23×C4—24no—
619C23×C4—24no—
620C23×C4—24no—
621C23×C4—44no—
622C23×C4—44no—
623C23×C4C2412yes—
624C23×C4C2411yescharacteristic
625C23×C4C2412yes—
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2412yes—
631C23×C4C2414yes—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2414yes—
637C23×C4C2418yes—
638C23×C4C2414yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2414yes—
642C23×C4C2414yes—
643C23×C4C2411yescharacteristic
644C4⋊Q8—28no—
645C4⋊Q8—24no—
646C4⋊Q8—28no—
647C4⋊Q8—28no—
648C4⋊Q8—28no—
649C4⋊Q8—216no—
650C4⋊Q8—232no—
651C4⋊Q8—28no—
652C4⋊Q8—28no—
653C4⋊Q8—232no—
654C4⋊Q8—44no—
655C4⋊Q8—44no—
656C4⋊Q8—48no—
657C4⋊Q8—44no—
658#127—24no—
659#124—28no—
660#124—24no—
661#124—24no—
662#124—28no—
663#124—28no—
664#124—28no—
665#124—232no—
666#124—44no—
667#123—28no—
668#123—216no—
669#123—28no—
670#123—216no—
671#123—216no—
672#123—232no—
673#123—216no—
674#123—232no—
675#123—216no—
676#123—44no—
677#123—48no—
678C22⋊Q8—28no—
679C22⋊Q8—28no—
680C22⋊Q8—232no—
681C22⋊Q8—216no—
682C22⋊Q8—232no—
683C22⋊Q8—216no—
684C22⋊Q8—232no—
685C22⋊Q8—216no—
686C22⋊Q8—216no—
687C22⋊Q8—232no—
688C22⋊Q8—232no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—44no—
692C22⋊Q8—44no—
693C22⋊Q8—44no—
694#121—28no—
695#121—28no—
696#121—232no—
697#121—216no—
698#121—232no—
699#121—216no—
700#121—44no—
701#120—28no—
702#120—28no—
703#120—44no—
704C4×Q8—28no—
705C4×Q8—216no—
706C4×Q8—216no—
707C4×Q8—44no—
708C4×Q8—44no—
709C4×D4—216no—
710C4×D4—28no—
711C4×D4—216no—
712C4×D4—216no—
713C4×D4—232no—
714C4×D4—232no—
715C4×D4—216no—
716C4×D4—232no—
717C4×D4—44no—
718C4×D4—44no—
719C4×D4—48no—
720C4×D4—48no—
721C4×D4—48no—
722#117—28no—
723#117—24no—
724#117—216no—
725#117—24no—
726#117—24no—
727#117—24no—
728#117—24no—
729#117—44no—
730#117—44no—
731C2×C4⋊C4—216no—
732C2×C4⋊C4—232no—
733C2×C4⋊C4—24no—
734C2×C4⋊C4—44no—
735C2×C4⋊C4—44no—
736C2×C4⋊C4—48no—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2418yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2418yes—
743C2×C4⋊C4C2418yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—44no—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2412yes—
808C2×C42—28no—
809C2×C42—24no—
810C2×C42—24no—
811C2×C42—44no—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2418yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2414yes—
826C2×C42C2414yes—
827#95C2414yes—
828#95C2418yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858C24—22no—
859C24—24no—
860C24—22no—
861C24—22no—
862C24—42no—
863C24C2512yes—
864C24C2512yes—
865C24C2512yes—
866C24C2512yes—
867C24C2511yescharacteristic
868#41—232no—
869#41—232no—
870#41—464no—
871#41—432no—
872#41—432no—
873#41—432no—
874#41—464no—
875#41—432no—
876#41—416no—
877C2×Q8—232no—
878C2×Q8—216no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—28no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—22no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—22no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—22no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—22no—
903C2×Q8—48no—
904C2×Q8—48no—
905C2×Q8—44no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—432no—
910C2×Q8—432no—
911C2×Q8—432no—
912C2×Q8—432no—
913C2×Q8—464no—
914C2×Q8—464no—
915C2×Q8—432no—
916C2×Q8—416no—
917C2×Q8—416no—
918C2×Q8C22×D418yes—
919C2×Q8C22×D414yes—
920C2×Q8C22×D418yes—
921C2×Q8C22×D414yes—
922C2×Q8C22×D4116yes—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—22no—
944C2×D4—28no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4C22×D418yes—
955C2×D4C22×D414yes—
956C2×D4C22×D418yes—
957C2×D4C22×D414yes—
958C2×D4C22×D4116yes—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—28no—
966C22×C4—24no—
967C22×C4—28no—
968C22×C4—24no—
969C22×C4—22no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—22no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—216no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—28no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—28no—
994C22×C4—48no—
995C22×C4—48no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—48no—
1012C22×C4—432no—
1013C22×C4—416no—
1014C22×C4C22×D418yes—
1015C22×C4C22×D418yes—
1016C22×C4C22×D418yes—
1017C22×C4C22×D4116yes—
1018C22×C4C22×D4116yes—
1019C22×C4C22×D414yes—
1020C22×C4H(5,𝔽2)14yes—
1021C22×C4H(5,𝔽2)14yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C4⋊C4—216no—
1043C4⋊C4—28no—
1044C4⋊C4—216no—
1045C4⋊C4—216no—
1046C4⋊C4—216no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—216no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—216no—
1053C4⋊C4—28no—
1054C4⋊C4—216no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—44no—
1065C4⋊C4—48no—
1066C4⋊C4—48no—
1067C4⋊C4—48no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—48no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—24no—
1080C22⋊C4—216no—
1081C22⋊C4—28no—
1082C22⋊C4—216no—
1083C22⋊C4—28no—
1084C22⋊C4—216no—
1085C22⋊C4—28no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—216no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—48no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—48no—
1102C22⋊C4—48no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C42−1+418yescomplemented
1111C42—22no—
1112C42—24no—
1113C42—22no—
1114C42—28no—
1115C42—24no—
1116C42—216no—
1117C42—24no—
1118C42—24no—
1119C42—22no—
1120C42—22no—
1121C42—24no—
1122C42—24no—
1123C42—24no—
1124C42—44no—
1125C42—44no—
1126C23—22no—
1127C23—22no—
1128C23—28no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—24no—
1138C23—24no—
1139C23—24no—
1140C23—22no—
1141C23—24no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—24no—
1147C23—24no—
1148C23—48no—
1149C23—48no—
1150C23—44no—
1151C23—44no—
1152C23C23×D414yes—
1153C23C23×D414yes—
1154C23C23×D412yes—
1155C23C2×H(5,𝔽2)12yes—
1156C23C2×H(5,𝔽2)12yes—
1157C23C2×2−1+414yes—
1158C23C2611yescharacteristic
1159Q8—216no—
1160Q8—216no—
1161Q8—28no—
1162Q8—28no—
1163Q8—416no—
1164Q8—432no—
1165Q8—416no—
1166Q8—48no—
1167Q8—48no—
1168Q8—48no—
1169Q8—48no—
1170Q8—44no—
1171D4—216no—
1172D4—216no—
1173D4—28no—
1174D4—28no—
1175D4—416no—
1176D4—416no—
1177D4—416no—
1178D4—416no—
1179D4—416no—
1180D4—48no—
1181D4—44no—
1182D4—88no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—216no—
1194C2×C4—216no—
1195C2×C4—216no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—28no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—416no—
1233C2×C4—416no—
1234C2×C4—48no—
1235C2×C4—416no—
1236C2×C4—48no—
1237C2×C4—432no—
1238C2×C4—416no—
1239C2×C4—416no—
1240C2×C4—44no—
1241C2×C4—48no—
1242C2×C4—48no—
1243C2×C4—48no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—88no—
1247C2×C4—84no—
1248C2×C4—164no—
1249C2×C4#534116yes—
1250C2×C4C23×D414yes—
1251C2×C4C23×D418yes—
1252C2×C4C23×D414yes—
1253C2×C4C23×D412yes—
1254C2×C4C23×D412yes—
1255C2×C4C2×H(5,𝔽2)12yes—
1256C2×C4C2×H(5,𝔽2)12yes—
1257C2×C4C2×H(5,𝔽2)12yes—
1258C2×C4C2×H(5,𝔽2)12yes—
1259C2×C4C2×2−1+414yes—
1260C2×C4C2×2−1+414yes—
1261C22—24no—
1262C22—22no—
1263C22—22no—
1264C22—24no—
1265C22—28no—
1266C22—24no—
1267C22—28no—
1268C22—24no—
1269C22—24no—
1270C22—24no—
1271C22—24no—
1272C22—416no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—44no—
1288C22C2×#53414yes—
1289C22C24×D411yescharacteristic
1290C22C22×H(5,𝔽2)11yescharacteristic
1291C22C22×H(5,𝔽2)11yescharacteristic
1292C22C22×2−1+412yes—
1293C222−1+612yes—
1294C4—24no—
1295C4—24no—
1296C4—28no—
1297C4—24no—
1298C4—24no—
1299C4—42no—
1300C4—44no—
1301C4—44no—
1302C4—44no—
1303C4—42no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—42no—
1311C4—44no—
1312C4C2×#53414yes—
1313C4C2×#53414yes—
1314C2—24no—
1315C2—44no—
1316C2—44no—
1317C2—44no—
1318C2—82no—
1319C2C22×#53411yescharacteristic
1320C2#6283311yescharacteristic
1321C2#6288711yescharacteristic
1322C2#6294212yes—
1323C2D4×2−1+412yes—
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×#3499C2semidirect
2. C2×#3486C2semidirect
3. #42926C2semidirect
4. #42912C2semidirect
5. #42807C2semidirect
6. #42787C2semidirect
7. #42295C2semidirect
8. #39956C2semidirect
9. #39864C2semidirect
10. #39615C2semidirect
11. #39593C2semidirect
12. #38365C2semidirect
13. #35674C2semidirect
14. #35673C2semidirect
15. #35666C2semidirect
16. #35659C2semidirect
17. #35633C2semidirect
18. #35621C2semidirect
19. #35316C2semidirect
20. #35307C2semidirect
21. #35242C2semidirect
22. #34743C2semidirect
23. #34742C2semidirect
24. C2×#2434C2semidirect
25. #34259C2semidirect
33. C2×D4×Q8C22semidirect
37. C2×#547C22semidirect
44. C2×#536C22semidirect
45. C2×#536C22semidirect
47. C2×#532C22semidirect
50. C22×C4⋊Q8C22semidirect
60. #2857C22semidirect
61. #2855C22semidirect
63. #2817C22semidirect
64. #2814C22semidirect
65. #2734C22semidirect
66. #2734C22semidirect
70. #2729C22semidirect
71. #2729C22semidirect
73. #2717C22semidirect
74. #2717C22semidirect
78. #2686C22semidirect
79. #2686C22semidirect
81. #2663C22semidirect
82. #2659C22semidirect
84. #2638C22semidirect
86. #2627C22semidirect
87. #2625C22semidirect
88. #2621C22semidirect
92. #2583C22semidirect
95. #2564C22semidirect
96. #2547C22semidirect
97. #2547C22semidirect
98. #2546C22semidirect
99. #2546C22semidirect
100. #2545C22semidirect
101. #2544C22semidirect
107. #2448C22semidirect
108. #2447C22semidirect
109. #2446C22semidirect
110. #2446C22semidirect
111. #2446C22semidirect
112. #2446C22semidirect
113. #2446C22semidirect
114. #2446C22semidirect
121. #2434C22semidirect
122. #2434C22semidirect
123. #2434C22semidirect
124. #2432C22semidirect
125. #2432C22semidirect
126. #2432C22semidirect
137. #2423C22semidirect
140. #2421C22semidirect
146. #2417C22semidirect
148. #2415C22semidirect
161. Q8×C22⋊C4C22semidirect
163. #2339C22semidirect
169. #2311C22semidirect
174. #2310C22semidirect
179. #2297C22semidirect
184. C2×#391C22semidirect
194. C2×2−1+4D4semidirect
1110. 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×#34992
C2×#34862
#429262
#429122
#428072
#427872
#422952
#399562
#398642
#396152
#395932
#383652
#356742
#356732
#356662
#356592
#356332
#356212
#353162
#353072
#352422
#347432
#347422
C2×#24342
#342592