Finite Group Databasebeta

← #7652618

Subgroups — #7652618

Order 512.

8416 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#42927C214yesmaximal, complemented
4#42913C214yesmaximal, complemented
5#42806C214yesmaximal, complemented
6#42797C214yesmaximal, complemented
7#41933C218yesmaximal, complemented
8#39961C214yesmaximal, complemented
9#39865C214yesmaximal, complemented
10#39721C214yesmaximal, complemented
11#39166C214yesmaximal, complemented
12#38365C218yesmaximal, complemented
13#35676C211yesmaximal, characteristic, complemented
14#35674C211yesmaximal, characteristic, complemented
15#35673C211yesmaximal, characteristic, complemented
16#35659C211yesmaximal, characteristic, complemented
17#35633C211yesmaximal, characteristic, complemented
18#35533C211yesmaximal, characteristic, complemented
19#35327C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#34743C211yesmaximal, characteristic, complemented
23#34742C211yesmaximal, characteristic, complemented
24C2×#2432C211yesmaximal, characteristic, complemented
25#34259C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C22×2−1+4C2211yescharacteristic
28C23×#41C2211yescharacteristic
29#3499—216no—
30#3487—216no—
31C2×#550C2214yes—
32C2×#550C2214yes—
33C2×D4×Q8C2214yescomplemented
34C2×#548C2214yes—
35C2×#548C2214yes—
36C2×#547C2218yes—
37C2×#547C2214yescomplemented
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2212yescomplemented
41C2×#536C2212yescomplemented
42C2×#535C2211yescharacteristic
43C2×#535C2211yescharacteristic
44C2×#535C2214yes—
45C2×#535C2211yescharacteristic
46C2×#532C2211yescharacteristic
47C2×#532C2212yescomplemented
48C22×C4⋊Q8C2211yescharacteristic
49C22×C4⋊Q8C2212yescomplemented
50C22×#124C2211yescharacteristic
51C2×#525C2211yescharacteristic
52C2×#525C2211yescharacteristic
53C2×#525C2214yes—
54C2×#525C2211yescharacteristic
55C22×C22⋊Q8C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60#2854C2214yescomplemented
61#2850C2214yescomplemented
62#2849C2214yes—
63#2816C2218yescomplemented
64#2813C2218yescomplemented
65#2732C2218yescomplemented
66#2731C2218yescomplemented
67#2731C2218yescomplemented
68#2730C2218yescomplemented
69#2730C2218yescomplemented
70#2729C2218yescomplemented
71#2729C2218yescomplemented
72#2728C2218yescomplemented
73#2709C2218yescomplemented
74#2709C2218yescomplemented
75#2708C2218yescomplemented
76#2708C2218yescomplemented
77#2688C2218yescomplemented
78#2673C2218yescomplemented
79#2673C2218yescomplemented
80#2671C2218yescomplemented
81#2661C2218yescomplemented
82#2639C2218yescomplemented
83#2638C2218yescomplemented
84#2635C2218yescomplemented
85#2630C2218yescomplemented
86#2624C2214yescomplemented
87#2620C2214yescomplemented
88#2618C2218yescomplemented
89#2613C2214yes—
90#2602C2218yescomplemented
91#2600C2218yescomplemented
92#2591C2218yescomplemented
93#2579C2218yescomplemented
94#2564C2218yescomplemented
95#2548C2212yescomplemented
96#2545C2212yescomplemented
97#2545C2214yescomplemented
98#2544C2212yescomplemented
99#2544C2214yescomplemented
100#2543C2218yescomplemented
101#2541C2212yescomplemented
102#2534C2214yes—
103#2534C2218yes—
104#2498C2218yes—
105#2486C2214yes—
106#2484C2218yes—
107#2448C2214yescomplemented
108#2448C2214yescomplemented
109#2446C2214yescomplemented
110#2446C2214yescomplemented
111#2446C2214yescomplemented
112#2446C2214yescomplemented
113#2446C2214yescomplemented
114#2445C2214yescomplemented
115#2436C2214yescomplemented
116#2436C2212yescomplemented
117#2436C2212yescomplemented
118#2432C2214yes—
119#2432C2214yes—
120#2432C2214yes—
121#2432C2214yes—
122#2432C2214yes—
123#2431C2214yes—
124#2431C2212yescomplemented
125#2431C2214yescomplemented
126#2431C2212yescomplemented
127#2429C2212yescomplemented
128#2429C2214yescomplemented
129#2428C2212yescomplemented
130#2427C2214yescomplemented
131#2427C2212yescomplemented
132#2426C2212yescomplemented
133#2425C2214yes—
134#2424C2214yes—
135#2424C2218yes—
136#2423C2212yescomplemented
137#2423C2214yescomplemented
138#2422C2212yescomplemented
139#2421C2214yescomplemented
140#2421C2212yescomplemented
141#2420C2212yescomplemented
142#2419C2214yes—
143#2418C2214yes—
144#2418C2218yes—
145#2417C2214yescomplemented
146#2416C2214yescomplemented
147#2415C2214yescomplemented
148#2414C2214yescomplemented
149#2409C2214yescomplemented
150#2409C2214yescomplemented
151#2407C2214yes—
152#2407C2214yes—
153#2407C2214yescomplemented
154#2407C2214yescomplemented
155#2406C2214yes—
156#2404C2214yes—
157#2404C2218yes—
158#2395C2214yescomplemented
159#2392C2214yescomplemented
160C2×#394C2214yes—
161Q8×C22⋊C4C2214yescomplemented
162#2339C2218yes—
163#2339C2214yescomplemented
164#2325C2218yescomplemented
165#2322C2218yescomplemented
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2212yescomplemented
170#2310C2211yescharacteristic
171#2310C2211yescharacteristic
172#2310C2211yescharacteristic
173#2310C2212yescomplemented
174#2309C2211yescharacteristic
175C4×#123C2214yescomplemented
176C4×#121C2214yescomplemented
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2212yescomplemented
180#2296C2211yescharacteristic
181#2296C2211yescharacteristic
182C2×#391C2211yescharacteristic
183C2×#391C2212yescomplemented
184C2×#390C2211yescharacteristic
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×#41—28no—
196C22×#41—44no—
197C22×#41—44no—
198C22×#41C2311yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2314yes—
202C22×#41C2314yes—
203C22×#41C2314yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C22×#41C2312yes—
207C22×#41C2314yes—
208C22×#41C2312yes—
209C23×Q8C2311yescharacteristic
210C23×Q8C2311yescharacteristic
211C23×Q8C2312yes—
212C23×Q8C2312yes—
213C23×Q8C2312yes—
214C23×Q8C2312yes—
215C23×D4C2311yescharacteristic
216C23×D4C2312yes—
217C24×C4C2311yescharacteristic
218C24×C4C2312yes—
219#550—232no—
220#550—232no—
221D4×Q8—232no—
222#548—232no—
223#548—232no—
224#547—264no—
225#547—232no—
226#536—28no—
227#536—216no—
228#536—28no—
229#536—216no—
230#535—28no—
231#535—28no—
232#535—232no—
233#535—44no—
234#532—28no—
235#532—216no—
236C2×C4⋊Q8—28no—
237C2×C4⋊Q8—216no—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2318yes—
245C2×#127C2318yes—
246C2×#127C2311yescharacteristic
247C2×#127C2312yes—
248C2×#127C2312yes—
249C2×#127C2312yes—
250C2×#124—44no—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2318yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262#525—28no—
263#525—28no—
264#525—232no—
265#525—44no—
266C2×#123C2314yes—
267C2×#123C2318yes—
268C2×#123C2312yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2318yes—
272C2×#123C2318yes—
273C2×#123C2312yes—
274C2×#123C2314yes—
275C2×C22⋊Q8—44no—
276C2×C22⋊Q8C2318yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2318yes—
282C2×C22⋊Q8C2318yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×#121C2318yes—
287C2×#121C2318yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2318yes—
292C2×#121C2312yes—
293C2×#121C2318yes—
294C2×#121C2314yes—
295C2×#121C2318yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#120C2312yes—
301C2×#120C2314yes—
302C2×#120C2312yes—
303C2×#120C2314yes—
304C2×#120C2314yes—
305C2×#120C2312yes—
306#520—44no—
307#519—28no—
308C4×#41—28no—
309C4×#41—44no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2318yes—
316C2×C4×D4C2318yes—
317C2×C4×D4C2318yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2318yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C22⋊C4C2312yes—
343C22×C22⋊C4C2312yes—
344C22×C22⋊C4C2314yes—
345C22×C22⋊C4C2314yes—
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348C22×C42C2311yescharacteristic
349C22×C42C2312yes—
350#400C2314yes—
351#400C2318yes—
352#400C2318yes—
353#400C2318yes—
354#399C2314yes—
355#399C2318yes—
356#399C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2314yes—
360#398C2318yes—
361#398C2318yes—
362#398C2314yes—
363#397C2318yes—
364#397C2314yes—
365#397C2318yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2318yes—
370#396C2318yes—
371#396C2318yes—
372#396C2314yes—
373#396C2318yes—
374#396C2318yes—
375#396C2314yes—
376#395C2318yes—
377#394C2314yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2314yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2318yes—
397#393C2318yes—
398#393C2318yes—
399#392C2318yes—
400#392C2318yes—
401#392C2318yes—
402#392C2318yes—
403#392C2318yes—
404#392C2314yes—
405#392C2318yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2311yescharacteristic
415#391C2312yes—
416#391C2312yes—
417#391C2318yes—
418#391C2312yes—
419#391C2318yes—
420#391C2314yes—
421#391C2312yes—
422#391C2311yescharacteristic
423#391C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2311yescharacteristic
429#390C2312yes—
430#390C2318yes—
431#390C2312yes—
432#390C2314yes—
433#390C2314yes—
434#390C2311yescharacteristic
435#390C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2318yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2314yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2318yes—
460#387C2318yes—
461#387C2314yes—
462#387C2314yes—
463#387C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2314yes—
467#386C2314yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2314yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2314yes—
477#386C2318yes—
478#386C2318yes—
479#386C2314yes—
480#386C2318yes—
481#386C2318yes—
482#386C2318yes—
483#386C2314yes—
484#386C2318yes—
485#386C2314yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2314yes—
492#385C2318yes—
493#385C2318yes—
494#385C2318yes—
495#385C2314yes—
496#385C2314yes—
497#384C2312yes—
498#382C2312yes—
499#381C2318yes—
500#381C2314yes—
501#381C2314yes—
502#381C2314yes—
503#381C2314yes—
504#381C2312yes—
505#380C2314yes—
506#380C2318yes—
507#380C2314yes—
508#380C2314yes—
509#380C2318yes—
510#380C2314yes—
511#380C2312yes—
512#380C2312yes—
513#380C2314yes—
514#379C2314yes—
515#379C2312yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2312yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C2×#95C2318yes—
530C2×#95C2314yes—
531C2×#95C2312yes—
532C25C2411yescharacteristic
533C25C2412yes—
5342−1+4—464no—
5352−1+4—464no—
536C2×#41—216no—
537C2×#41—216no—
538C2×#41—216no—
539C2×#41—28no—
540C2×#41—28no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—24no—
546C2×#41—24no—
547C2×#41—24no—
548C2×#41—48no—
549C2×#41—48no—
550C2×#41—48no—
551C2×#41—48no—
552C2×#41—48no—
553C2×#41—48no—
554C2×#41—48no—
555C2×#41—48no—
556C2×#41—44no—
557C2×#41—44no—
558C2×#41—44no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—44no—
562C2×#41—44no—
563C2×#41—44no—
564C2×#41—464no—
565C2×#41C2×D418yes—
566C2×#41C2×D418yes—
567C2×#41C2×D4132yes—
568C2×#41C2×D4116yes—
569C2×#41C2×D4116yes—
570C22×Q8—28no—
571C22×Q8—28no—
572C22×Q8—24no—
573C22×Q8—24no—
574C22×Q8—24no—
575C22×Q8—24no—
576C22×Q8—24no—
577C22×Q8—44no—
578C22×Q8—44no—
579C22×Q8—44no—
580C22×Q8—44no—
581C22×Q8—44no—
582C22×Q8—44no—
583C22×Q8—44no—
584C22×Q8—44no—
585C22×Q8C2×D418yes—
586C22×Q8C2×D4116yes—
587C22×Q8C2×D4116yes—
588C22×Q8C2412yes—
589C22×Q8C2412yes—
590C22×Q8C2411yescharacteristic
591C22×Q8C2411yescharacteristic
592C22×Q8C2411yescharacteristic
593C22×Q8C2412yes—
594C22×Q8C2412yes—
595C22×Q8C2414yes—
596C22×Q8C2414yes—
597C22×D4—28no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4C2412yes—
604C22×D4C2412yes—
605C22×D4C2412yes—
606C22×D4C2411yescharacteristic
607C22×D4C2414yes—
608C22×D4C2412yes—
609C22×D4C2411yescharacteristic
610C22×D4C2412yes—
611C22×D4C2411yescharacteristic
612C22×D4C2418yes—
613C22×D4C2414yes—
614C22×D4C2418yes—
615C22×D4C2414yes—
616C22×D4C2414yes—
617C22×D4C2418yes—
618C22×D4C2414yes—
619C22×D4C2414yes—
620C22×D4C2414yes—
621C22×D4C2414yes—
622C23×C4—28no—
623C23×C4—24no—
624C23×C4—24no—
625C23×C4—24no—
626C23×C4—44no—
627C23×C4—44no—
628C23×C4C2412yes—
629C23×C4C2411yescharacteristic
630C23×C4C2412yes—
631C23×C4C2412yes—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2414yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2414yes—
641C23×C4C2418yes—
642C23×C4C2414yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2411yescharacteristic
648C4⋊Q8—28no—
649C4⋊Q8—24no—
650C4⋊Q8—28no—
651C4⋊Q8—28no—
652C4⋊Q8—28no—
653C4⋊Q8—216no—
654C4⋊Q8—232no—
655#127—24no—
656#127—28no—
657#127—28no—
658#127—232no—
659#127—44no—
660#124—28no—
661#124—24no—
662#124—28no—
663#124—28no—
664#124—232no—
665#124—24no—
666#124—28no—
667#124—44no—
668#124—44no—
669#124—48no—
670#124—44no—
671#123—28no—
672#123—28no—
673#123—216no—
674#123—232no—
675#123—216no—
676#123—232no—
677#123—416no—
678#123—48no—
679#123—44no—
680C22⋊Q8—28no—
681C22⋊Q8—28no—
682C22⋊Q8—232no—
683C22⋊Q8—216no—
684C22⋊Q8—232no—
685C22⋊Q8—216no—
686C22⋊Q8—232no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—44no—
690#121—28no—
691#121—28no—
692#121—232no—
693#121—216no—
694#121—232no—
695#121—216no—
696#121—216no—
697#121—232no—
698#121—232no—
699#121—48no—
700#121—416no—
701#121—44no—
702#121—44no—
703#121—44no—
704#120—28no—
705#120—216no—
706#120—28no—
707#120—216no—
708#120—44no—
709#120—48no—
710C4×Q8—28no—
711C4×Q8—216no—
712C4×Q8—216no—
713C4×Q8—44no—
714C4×Q8—44no—
715C4×D4—216no—
716C4×D4—28no—
717C4×D4—216no—
718C4×D4—216no—
719C4×D4—232no—
720C4×D4—232no—
721C4×D4—216no—
722C4×D4—232no—
723C4×D4—44no—
724C4×D4—44no—
725C4×D4—48no—
726C4×D4—48no—
727C4×D4—48no—
728#117—28no—
729#117—24no—
730#117—216no—
731#117—24no—
732#117—24no—
733#117—24no—
734#117—24no—
735#117—44no—
736#117—44no—
737C2×C4⋊C4—216no—
738C2×C4⋊C4—232no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—44no—
741C2×C4⋊C4—44no—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C22⋊C4—44no—
771C2×C22⋊C4—48no—
772C2×C22⋊C4—44no—
773C2×C22⋊C4—48no—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C42—28no—
816C2×C42—24no—
817C2×C42—24no—
818C2×C42—44no—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2418yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2414yes—
833C2×C42C2414yes—
834#95C2418yes—
835#95C2414yes—
836#95C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861C24—22no—
862C24—24no—
863C24—24no—
864C24—22no—
865C24—22no—
866C24—24no—
867C24—42no—
868C24—44no—
869C24—42no—
870C24—44no—
871C24C2512yes—
872C24C2514yes—
873C24C2512yes—
874C24C2512yes—
875C24C2512yes—
876C24C2511yescharacteristic
877#41—232no—
878#41—232no—
879#41—464no—
880#41—432no—
881#41—432no—
882#41—432no—
883#41—464no—
884#41—432no—
885#41—464no—
886#41—464no—
887#41—416no—
888C2×Q8—232no—
889C2×Q8—28no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—22no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—22no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×Q8—432no—
912C2×Q8—432no—
913C2×Q8—432no—
914C2×Q8—432no—
915C2×Q8—416no—
916C2×Q8C22×D414yes—
917C2×Q8C22×D418yes—
918C2×Q8C22×D418yes—
919C2×Q8C22×D414yes—
920C2×Q8C22×D4116yes—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—216no—
932C2×D4—28no—
933C2×D4—216no—
934C2×D4—216no—
935C2×D4—24no—
936C2×D4—24no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—24no—
943C2×D4—22no—
944C2×D4—24no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—22no—
948C2×D4—28no—
949C2×D4—48no—
950C2×D4—48no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—432no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—48no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—48no—
963C2×D4—44no—
964C2×D4—48no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—48no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—48no—
971C2×D4—48no—
972C2×D4—416no—
973C2×D4C22×D418yes—
974C2×D4C22×D414yes—
975C2×D4C22×D418yes—
976C2×D4C22×D414yes—
977C2×D4C22×D4116yes—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—28no—
985C22×C4—24no—
986C22×C4—28no—
987C22×C4—24no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—216no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—28no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—48no—
1009C22×C4—48no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—48no—
1028C22×C4—432no—
1029C22×C4—416no—
1030C22×C4C22×D418yes—
1031C22×C4C22×D418yes—
1032C22×C4C22×D418yes—
1033C22×C4C22×D4116yes—
1034C22×C4C22×D4116yes—
1035C22×C4C22×D414yes—
1036C22×C4H(5,𝔽2)14yes—
1037C22×C4H(5,𝔽2)14yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C4⋊C4—216no—
1058C4⋊C4—28no—
1059C4⋊C4—216no—
1060C4⋊C4—216no—
1061C4⋊C4—216no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—216no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—44no—
1077C4⋊C4—48no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—48no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—216no—
1092C22⋊C4—28no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—216no—
1096C22⋊C4—28no—
1097C22⋊C4—216no—
1098C22⋊C4—28no—
1099C22⋊C4—216no—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—216no—
1103C22⋊C4—24no—
1104C22⋊C4—42no—
1105C22⋊C4—48no—
1106C22⋊C4—42no—
1107C22⋊C4—48no—
1108C22⋊C4—48no—
1109C22⋊C4—48no—
1110C22⋊C4—48no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—48no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—48no—
1124C22⋊C4—48no—
1125C22⋊C4—44no—
1126C42—22no—
1127C42—24no—
1128C42—22no—
1129C42—28no—
1130C42—24no—
1131C42—216no—
1132C42—24no—
1133C42—24no—
1134C42—22no—
1135C42—22no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—44no—
1140C42—44no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—22no—
1155C23—24no—
1156C23—22no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—22no—
1161C23—28no—
1162C23—22no—
1163C23—24no—
1164C23—22no—
1165C23—24no—
1166C23—28no—
1167C23—22no—
1168C23—44no—
1169C23—44no—
1170C23—416no—
1171C23—48no—
1172C23—44no—
1173C23—84no—
1174C23—88no—
1175C23—84no—
1176C23—84no—
1177C23—84no—
1178C23C23×D414yes—
1179C23C23×D414yes—
1180C23C23×D412yes—
1181C23C2×H(5,𝔽2)12yes—
1182C23C2×H(5,𝔽2)12yes—
1183C23C2611yescharacteristic
1184Q8—216no—
1185Q8—216no—
1186Q8—28no—
1187Q8—28no—
1188Q8—416no—
1189Q8—416no—
1190Q8—48no—
1191Q8—48no—
1192Q8—44no—
1193D4—216no—
1194D4—216no—
1195D4—28no—
1196D4—28no—
1197D4—416no—
1198D4—416no—
1199D4—432no—
1200D4—416no—
1201D4—48no—
1202D4—48no—
1203D4—48no—
1204D4—44no—
1205D4—88no—
1206D4—816no—
1207D4—816no—
1208D4—88no—
1209D4—88no—
1210D4—164no—
1211D4—164no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—216no—
1221C2×C4—216no—
1222C2×C4—216no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—416no—
1260C2×C4—416no—
1261C2×C4—48no—
1262C2×C4—416no—
1263C2×C4—432no—
1264C2×C4—416no—
1265C2×C4—416no—
1266C2×C4—44no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—48no—
1270C2×C4—48no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—88no—
1274C2×C4—164no—
1275C2×C4#534116yes—
1276C2×C4C23×D414yes—
1277C2×C4C23×D418yes—
1278C2×C4C23×D414yes—
1279C2×C4C23×D412yes—
1280C2×C4C23×D412yes—
1281C2×C4C2×H(5,𝔽2)12yes—
1282C2×C4C2×H(5,𝔽2)12yes—
1283C2×C4C2×H(5,𝔽2)12yes—
1284C2×C4C2×H(5,𝔽2)12yes—
1285C2×C4#58514yes—
1286C22—24no—
1287C22—22no—
1288C22—22no—
1289C22—24no—
1290C22—28no—
1291C22—28no—
1292C22—24no—
1293C22—24no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—42no—
1302C22—48no—
1303C22—42no—
1304C22—42no—
1305C22—44no—
1306C22—42no—
1307C22—42no—
1308C22—44no—
1309C22—42no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—48no—
1316C22—42no—
1317C22—816no—
1318C22—88no—
1319C22C2×#53414yes—
1320C22C24×D411yescharacteristic
1321C22C22×H(5,𝔽2)11yescharacteristic
1322C22C22×H(5,𝔽2)11yescharacteristic
1323C22C2×#58512yes—
1324C222−1+612yes—
1325C4—24no—
1326C4—24no—
1327C4—28no—
1328C4—24no—
1329C4—42no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4C2×#53414yes—
1343C4C2×#53414yes—
1344C2—24no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2—84no—
1349C2—82no—
1350C2C22×#53411yescharacteristic
1351C2#6283611yescharacteristic
1352C2#6288711yescharacteristic
1353C2#6292512yes—
1354C2#6300212yes—
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×#3487C2semidirect
3. #42927C2semidirect
4. #42913C2semidirect
5. #42806C2semidirect
6. #42797C2semidirect
7. #41933C2semidirect
8. #39961C2semidirect
9. #39865C2semidirect
10. #39721C2semidirect
11. #39166C2semidirect
12. #38365C2semidirect
13. #35676C2semidirect
14. #35674C2semidirect
15. #35673C2semidirect
16. #35659C2semidirect
17. #35633C2semidirect
18. #35533C2semidirect
19. #35327C2semidirect
20. #35254C2semidirect
21. #35149C2semidirect
22. #34743C2semidirect
23. #34742C2semidirect
24. C2×#2432C2semidirect
25. #34259C2semidirect
33. C2×D4×Q8C22semidirect
37. C2×#547C22semidirect
40. C2×#536C22semidirect
41. C2×#536C22semidirect
47. C2×#532C22semidirect
49. C22×C4⋊Q8C22semidirect
60. #2854C22semidirect
61. #2850C22semidirect
63. #2816C22semidirect
64. #2813C22semidirect
65. #2732C22semidirect
66. #2731C22semidirect
67. #2731C22semidirect
68. #2730C22semidirect
69. #2730C22semidirect
70. #2729C22semidirect
71. #2729C22semidirect
72. #2728C22semidirect
73. #2709C22semidirect
74. #2709C22semidirect
75. #2708C22semidirect
76. #2708C22semidirect
77. #2688C22semidirect
78. #2673C22semidirect
79. #2673C22semidirect
80. #2671C22semidirect
81. #2661C22semidirect
82. #2639C22semidirect
83. #2638C22semidirect
84. #2635C22semidirect
85. #2630C22semidirect
86. #2624C22semidirect
87. #2620C22semidirect
88. #2618C22semidirect
90. #2602C22semidirect
91. #2600C22semidirect
92. #2591C22semidirect
93. #2579C22semidirect
94. #2564C22semidirect
95. #2548C22semidirect
96. #2545C22semidirect
97. #2545C22semidirect
98. #2544C22semidirect
99. #2544C22semidirect
100. #2543C22semidirect
101. #2541C22semidirect
107. #2448C22semidirect
108. #2448C22semidirect
109. #2446C22semidirect
110. #2446C22semidirect
111. #2446C22semidirect
112. #2446C22semidirect
113. #2446C22semidirect
114. #2445C22semidirect
115. #2436C22semidirect
116. #2436C22semidirect
117. #2436C22semidirect
124. #2431C22semidirect
125. #2431C22semidirect
126. #2431C22semidirect
127. #2429C22semidirect
128. #2429C22semidirect
129. #2428C22semidirect
130. #2427C22semidirect
131. #2427C22semidirect
132. #2426C22semidirect
136. #2423C22semidirect
137. #2423C22semidirect
138. #2422C22semidirect
139. #2421C22semidirect
140. #2421C22semidirect
141. #2420C22semidirect
145. #2417C22semidirect
146. #2416C22semidirect
147. #2415C22semidirect
148. #2414C22semidirect
149. #2409C22semidirect
150. #2409C22semidirect
153. #2407C22semidirect
154. #2407C22semidirect
158. #2395C22semidirect
159. #2392C22semidirect
161. Q8×C22⋊C4C22semidirect
163. #2339C22semidirect
164. #2325C22semidirect
165. #2322C22semidirect
169. #2311C22semidirect
173. #2310C22semidirect
175. C4×#123C22semidirect
176. C4×#121C22semidirect
179. #2297C22semidirect
183. C2×#391C22semidirect
194. C2×2−1+4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34872
#429272
#429132
#428062
#427972
#419332
#399612
#398652
#397212
#391662
#383652
#356762
#356742
#356732
#356592
#356332
#355332
#353272
#352542
#351492
#347432
#347422
C2×#24322
#342592