Finite Group Databasebeta

← #7652619

Subgroups — #7652619

Order 512.

8816 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#42969C214yesmaximal, complemented
4#42951C214yesmaximal, complemented
5#42883C214yesmaximal, complemented
6#42797C214yesmaximal, complemented
7#41932C218yesmaximal, complemented
8#39957C214yesmaximal, complemented
9#39865C214yesmaximal, complemented
10#39743C214yesmaximal, complemented
11#39135C214yesmaximal, complemented
12#38364C218yesmaximal, complemented
13#35679C211yesmaximal, characteristic, complemented
14#35673C211yesmaximal, characteristic, complemented
15#35563C211yesmaximal, characteristic, complemented
16#35533C211yesmaximal, characteristic, complemented
17#35527C211yesmaximal, characteristic, complemented
18#35512C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#34743C211yesmaximal, characteristic, complemented
23#34742C211yesmaximal, characteristic, complemented
24C2×#2431C211yesmaximal, characteristic, complemented
25#34259C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C22×H(5,𝔽2)C2211yescharacteristic
28C23×#41C2211yescharacteristic, complemented
29#3500—216no—
30#3487—216no—
31C2×#550C2214yescomplemented
32C2×#550C2214yescomplemented
33C2×#548C2214yescomplemented
34C2×#548C2214yescomplemented
35C2×#548C2214yescomplemented
36C2×#546C2218yes—
37C2×#546C2214yescomplemented
38C2×#536C2211yescharacteristic
39C2×#536C2212yescomplemented
40C2×#535C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2211yescharacteristic
43C2×#535C2211yescharacteristic, complemented
44C2×#535C2214yescomplemented
45C2×#535C2212yescomplemented
46C2×#532C2211yescharacteristic
47C2×#532C2212yescomplemented
48C22×#127C2211yescharacteristic
49C22×#124C2211yescharacteristic
50C22×#124C2212yescomplemented
51C2×#525C2211yescharacteristic
52C2×#525C2211yescharacteristic
53C2×#525C2211yescharacteristic, complemented
54C2×#525C2214yescomplemented
55C22×#121C2211yescharacteristic
56C2×#520C2211yescharacteristic, complemented
57C2×#519C2211yescharacteristic, complemented
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic, complemented
60#2856C2214yescomplemented
61#2854C2214yescomplemented
62#2849C2214yescomplemented
63#2815C2218yescomplemented
64#2813C2218yescomplemented
65#2733C2218yescomplemented
66#2733C2218yescomplemented
67#2732C2218yescomplemented
68#2730C2218yescomplemented
69#2730C2218yescomplemented
70#2730C2218yescomplemented
71#2730C2218yescomplemented
72#2728C2218yescomplemented
73#2688C2218yescomplemented
74#2673C2218yescomplemented
75#2673C2218yescomplemented
76#2671C2218yescomplemented
77#2669C2218yescomplemented
78#2669C2218yescomplemented
79#2668C2218yescomplemented
80#2668C2218yescomplemented
81#2661C2218yescomplemented
82#2656C2218yescomplemented
83#2635C2218yescomplemented
84#2635C2218yescomplemented
85#2630C2218yescomplemented
86#2624C2214yescomplemented
87#2619C2214yescomplemented
88#2617C2218yescomplemented
89#2613C2214yescomplemented
90#2602C2218yescomplemented
91#2600C2218yescomplemented
92#2548C2214yescomplemented
93#2548C2212yescomplemented
94#2545C2212yescomplemented
95#2544C2212yescomplemented
96#2543C2218yescomplemented
97#2543C2218yescomplemented
98#2541C2214yescomplemented
99#2541C2212yescomplemented
100#2539C2218yescomplemented
101#2534C2218yescomplemented
102#2534C2214yescomplemented
103#2498C2218yescomplemented
104#2482C2218yescomplemented
105#2448C2214yescomplemented
106#2448C2214yescomplemented
107#2448C2214yescomplemented
108#2448C2214yescomplemented
109#2448C2214yescomplemented
110#2448C2214yescomplemented
111#2446C2214yescomplemented
112#2445C2214yescomplemented
113#2433C2212yescomplemented
114#2433C2212yescomplemented
115#2433C2214yescomplemented
116#2432C2214yescomplemented
117#2431C2214yescomplemented
118#2431C2214yescomplemented
119#2431C2214yescomplemented
120#2431C2212yescomplemented
121#2431C2214yescomplemented
122#2431C2212yescomplemented
123#2431C2214yescomplemented
124#2431C2214yescomplemented
125#2429C2212yescomplemented
126#2428C2212yescomplemented
127#2428C2214yescomplemented
128#2427C2212yescomplemented
129#2426C2214yescomplemented
130#2426C2212yescomplemented
131#2425C2214yescomplemented
132#2424C2214yescomplemented
133#2424C2218yescomplemented
134#2423C2214yescomplemented
135#2423C2212yescomplemented
136#2422C2212yescomplemented
137#2421C2214yescomplemented
138#2421C2212yescomplemented
139#2420C2212yescomplemented
140#2419C2214yescomplemented
141#2418C2214yescomplemented
142#2418C2218yescomplemented
143#2416C2214yescomplemented
144#2416C2214yescomplemented
145#2414C2214yescomplemented
146#2414C2214yescomplemented
147#2408C2214yescomplemented
148#2408C2214yescomplemented
149#2408C2218yescomplemented
150#2408C2214yescomplemented
151#2407C2214yescomplemented
152#2407C2214yescomplemented
153#2407C2214yescomplemented
154#2407C2214yescomplemented
155#2405C2214yes—
156#2403C2214yes—
157#2403C2218yes—
158#2395C2214yescomplemented
159#2392C2214yescomplemented
160C2×#392C2214yescomplemented
161Q8×C22⋊C4C2214yescomplemented
162#2339C2214yescomplemented
163#2339C2218yescomplemented
164#2325C2218yescomplemented
165#2321C2218yescomplemented
166#2316C2211yescharacteristic, complemented
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2212yescomplemented
170#2310C2211yescharacteristic, complemented
171#2310C2212yescomplemented
172#2309C2211yescharacteristic
173#2309C2211yescharacteristic
174#2309C2211yescharacteristic, complemented
175C4×#123C2214yescomplemented
176C4×#121C2214yescomplemented
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2212yescomplemented
180#2296C2211yescharacteristic, complemented
181#2296C2211yescharacteristic, complemented
182C2×#391C2212yescomplemented
183C2×#391C2211yescharacteristic, complemented
184C2×#390C2211yescharacteristic, complemented
185C2×#386C2214yescomplemented
186#2285C2211yescharacteristic, complemented
187#2280C2211yescharacteristic, complemented
188C2×C4×C22⋊C4C2211yescharacteristic, complemented
189C2×2−1+4—44no—
190C2×2−1+4—44no—
191C2×2−1+4D4116yescomplemented
192C2×H(5,𝔽2)—28no—
193C2×H(5,𝔽2)—44no—
194C2×H(5,𝔽2)—44no—
195C22×#41—28no—
196C22×#41—44no—
197C22×#41—44no—
198C22×#41C2311yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2314yes—
202C22×#41C2314yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2314yes—
206C22×#41C2312yes—
207C22×#41C2312yes—
208C23×Q8C2311yescharacteristic
209C23×Q8C2312yes—
210C23×Q8C2312yes—
211C23×D4C2311yescharacteristic
212C23×D4C2311yescharacteristic
213C23×D4C2312yes—
214C23×D4C2314yes—
215C23×D4C2312yes—
216C23×D4C2312yes—
217C23×D4C2314yes—
218C23×D4C2312yes—
219C24×C4C2311yescharacteristic
220C24×C4C2312yes—
221#550—232no—
222#550—232no—
223#548—232no—
224#548—232no—
225#548—232no—
226#546—264no—
227#546—232no—
228#536—28no—
229#536—216no—
230#535—28no—
231#535—28no—
232#535—28no—
233#535—232no—
234#535—216no—
235#535—44no—
236#532—28no—
237#532—216no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×#127—44no—
241C2×#127C2318yes—
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2312yes—
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2312yes—
250C2×#124—28no—
251C2×#124—216no—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#124C2311yescharacteristic
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2318yes—
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2318yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264#525—28no—
265#525—28no—
266#525—232no—
267#525—44no—
268C2×#123C2314yes—
269C2×#123C2318yes—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×#123C2314yes—
274C2×#123C2318yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2318yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C2312yes—
281C2×#121—44no—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2318yes—
286C2×#121C2318yes—
287C2×#121C2318yes—
288C2×#121C2312yes—
289C2×#121C2318yes—
290C2×#121C2312yes—
291C2×#121C2318yes—
292C2×#121C2314yes—
293C2×#121C2318yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2318yes—
301C2×#121C2318yes—
302C2×#121C2318yes—
303C2×#120C2312yes—
304C2×#120C2314yes—
305C2×#120C2314yes—
306C2×#120C2314yes—
307C2×#120C2312yes—
308C2×#120C2318yes—
309C2×#120C2318yes—
310C2×#120C2314yes—
311C2×#120C2312yes—
312C2×#120C2318yes—
313C2×#120C2318yes—
314#520—44no—
315#519—28no—
316C4×#41—28no—
317C4×#41—44no—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4C2318yes—
324C2×C4×D4C2318yes—
325C2×C4×D4C2318yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C22⋊C4C2318yes—
348C22×C22⋊C4C2314yes—
349C22×C22⋊C4C2312yes—
350C22×C22⋊C4C2312yes—
351C22×C22⋊C4C2314yes—
352C22×C42C2312yes—
353C22×C42C2311yescharacteristic
354C22×C42C2311yescharacteristic
355C22×C42C2312yes—
356#400C2314yes—
357#400C2318yes—
358#399C2318yes—
359#399C2318yes—
360#399C2314yes—
361#399C2318yes—
362#399C2318yes—
363#398C2314yes—
364#398C2314yes—
365#398C2318yes—
366#397C2314yes—
367#397C2314yes—
368#397C2318yes—
369#397C2318yes—
370#397C2318yes—
371#397C2314yes—
372#397C2314yes—
373#397C2318yes—
374#396C2318yes—
375#396C2318yes—
376#396C2314yes—
377#396C2314yes—
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#394C2314yes—
391#394C2314yes—
392#394C2318yes—
393#394C2314yes—
394#394C2314yes—
395#392C2318yes—
396#392C2318yes—
397#392C2318yes—
398#392C2318yes—
399#392C2318yes—
400#392C2318yes—
401#392C2318yes—
402#392C2318yes—
403#392C2318yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#392C2318yes—
408#392C2314yes—
409#392C2318yes—
410#392C2318yes—
411#392C2318yes—
412#391C2312yes—
413#391C2311yescharacteristic
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2318yes—
419#391C2312yes—
420#391C2314yes—
421#391C2318yes—
422#391C2311yescharacteristic
423#391C2312yes—
424#391C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2312yes—
433#390C2312yes—
434#390C2311yescharacteristic
435#390C2318yes—
436#390C2318yes—
437#390C2312yes—
438#390C2318yes—
439#390C2312yes—
440#390C2318yes—
441#390C2314yes—
442#390C2311yescharacteristic
443#390C2314yes—
444#390C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#388C2314yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2314yes—
463#388C2318yes—
464#388C2314yes—
465#388C2314yes—
466#387C2314yes—
467#387C2318yes—
468#387C2314yes—
469#387C2318yes—
470#386C2314yes—
471#386C2314yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2318yes—
480#386C2314yes—
481#386C2318yes—
482#386C2318yes—
483#386C2318yes—
484#386C2318yes—
485#386C2314yes—
486#386C2318yes—
487#386C2318yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#385C2314yes—
492#385C2318yes—
493#385C2318yes—
494#385C2318yes—
495#385C2314yes—
496#385C2314yes—
497#384C2312yes—
498#382C2312yes—
499#381C2314yes—
500#381C2318yes—
501#381C2312yes—
502#381C2314yes—
503#380C2314yes—
504#380C2314yes—
505#380C2318yes—
506#380C2314yes—
507#380C2314yes—
508#380C2312yes—
509#380C2312yes—
510#380C2314yes—
511#379C2314yes—
512#379C2314yes—
513#379C2314yes—
514#379C2318yes—
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—
532C25C2412yes—
533C25C2411yescharacteristic
534C25C2412yes—
535C25C2414yes—
5362−1+4—464no—
537H(5,𝔽2)—464no—
538C2×#41—28no—
539C2×#41—216no—
540C2×#41—216no—
541C2×#41—28no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—24no—
546C2×#41—24no—
547C2×#41—24no—
548C2×#41—24no—
549C2×#41—48no—
550C2×#41—48no—
551C2×#41—48no—
552C2×#41—48no—
553C2×#41—48no—
554C2×#41—48no—
555C2×#41—44no—
556C2×#41—44no—
557C2×#41—44no—
558C2×#41—44no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—44no—
562C2×#41—44no—
563C2×#41—464no—
564C2×#41C2×D418yes—
565C2×#41C2×D418yes—
566C2×#41C2×D4132yes—
567C2×#41C2×D4116yescomplemented
568C2×#41C2×D4116yescomplemented
569C22×Q8—24no—
570C22×Q8—24no—
571C22×Q8—44no—
572C22×Q8—44no—
573C22×Q8—44no—
574C22×Q8—44no—
575C22×Q8C2×D418yes—
576C22×Q8C2×D4116yescomplemented
577C22×Q8C2×D4116yescomplemented
578C22×Q8C2411yescharacteristic
579C22×Q8C2411yescharacteristic
580C22×Q8C2412yes—
581C22×Q8C2411yescharacteristic
582C22×Q8C2412yes—
583C22×Q8C2414yes—
584C22×D4—216no—
585C22×D4—28no—
586C22×D4—28no—
587C22×D4—24no—
588C22×D4—28no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—24no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—44no—
595C22×D4—44no—
596C22×D4—44no—
597C22×D4—44no—
598C22×D4—48no—
599C22×D4—44no—
600C22×D4—44no—
601C22×D4—44no—
602C22×D4—48no—
603C22×D4—48no—
604C22×D4—48no—
605C22×D4—84no—
606C22×D4—84no—
607C22×D4C2412yes—
608C22×D4C2412yes—
609C22×D4C2412yes—
610C22×D4C2412yes—
611C22×D4C2411yescharacteristic
612C22×D4C2412yes—
613C22×D4C2412yes—
614C22×D4C2411yescharacteristic
615C22×D4C2412yes—
616C22×D4C2411yescharacteristic
617C22×D4C2418yes—
618C22×D4C2414yes—
619C22×D4C2418yes—
620C22×D4C2414yes—
621C22×D4C2418yes—
622C22×D4C2414yes—
623C22×D4C2418yes—
624C22×D4C2414yes—
625C22×D4C2414yes—
626C22×D4C2418yes—
627C22×D4C2414yes—
628C22×D4C2414yes—
629C22×D4C2414yes—
630C22×D4C2418yes—
631C22×D4C2418yes—
632C22×D4C2414yes—
633C23×C4—28no—
634C23×C4—24no—
635C23×C4—24no—
636C23×C4—24no—
637C23×C4—44no—
638C23×C4—44no—
639C23×C4C2411yescharacteristic
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2418yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2411yescharacteristic
657C4⋊Q8—28no—
658C4⋊Q8—24no—
659#127—24no—
660#127—28no—
661#127—28no—
662#127—28no—
663#127—232no—
664#127—44no—
665#127—44no—
666#127—48no—
667#127—44no—
668#124—28no—
669#124—24no—
670#124—28no—
671#124—28no—
672#124—28no—
673#124—216no—
674#124—232no—
675#124—28no—
676#124—28no—
677#124—232no—
678#124—24no—
679#124—44no—
680#123—28no—
681#123—28no—
682#123—216no—
683#123—232no—
684#123—48no—
685#123—44no—
686#123—88no—
687C22⋊Q8—28no—
688C22⋊Q8—28no—
689C22⋊Q8—232no—
690C22⋊Q8—216no—
691C22⋊Q8—232no—
692C22⋊Q8—44no—
693#121—28no—
694#121—28no—
695#121—232no—
696#121—216no—
697#121—232no—
698#121—216no—
699#121—232no—
700#121—216no—
701#121—216no—
702#121—232no—
703#121—232no—
704#121—48no—
705#121—48no—
706#121—48no—
707#121—416no—
708#121—44no—
709#121—44no—
710#121—44no—
711#121—88no—
712#121—88no—
713#121—88no—
714#120—28no—
715#120—216no—
716#120—216no—
717#120—28no—
718#120—216no—
719#120—232no—
720#120—416no—
721#120—44no—
722#120—48no—
723#120—88no—
724#120—88no—
725C4×Q8—28no—
726C4×Q8—216no—
727C4×Q8—216no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×D4—216no—
731C4×D4—28no—
732C4×D4—216no—
733C4×D4—216no—
734C4×D4—232no—
735C4×D4—232no—
736C4×D4—216no—
737C4×D4—232no—
738C4×D4—44no—
739C4×D4—44no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743#117—28no—
744#117—24no—
745#117—216no—
746#117—24no—
747#117—24no—
748#117—24no—
749#117—24no—
750#117—44no—
751#117—44no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—44no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C22⋊C4—216no—
779C2×C22⋊C4—232no—
780C2×C22⋊C4—44no—
781C2×C22⋊C4—44no—
782C2×C22⋊C4—84no—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2418yes—
825C2×C22⋊C4C2418yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2414yes—
828C2×C42—28no—
829C2×C42—24no—
830C2×C42—24no—
831C2×C42—44no—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2418yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845C2×C42C2414yes—
846C2×C42C2414yes—
847#95C2414yes—
848#95C2418yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2418yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2418yes—
869#95C2418yes—
870C24—22no—
871C24—24no—
872C24—28no—
873C24—24no—
874C24—24no—
875C24—22no—
876C24—24no—
877C24—22no—
878C24—24no—
879C24—24no—
880C24—42no—
881C24—44no—
882C24—44no—
883C24—42no—
884C24—44no—
885C24—44no—
886C24—44no—
887C24—44no—
888C24—48no—
889C24—48no—
890C24C2512yes—
891C24C2514yes—
892C24C2512yes—
893C24C2514yes—
894C24C2512yes—
895C24C2512yes—
896C24C2511yescharacteristic
897#41—232no—
898#41—232no—
899#41—464no—
900#41—432no—
901#41—432no—
902#41—432no—
903#41—464no—
904#41—464no—
905#41—432no—
906#41—416no—
907C2×Q8—232no—
908C2×Q8—22no—
909C2×Q8—22no—
910C2×Q8—22no—
911C2×Q8—24no—
912C2×Q8—24no—
913C2×Q8—24no—
914C2×Q8—24no—
915C2×Q8—22no—
916C2×Q8—22no—
917C2×Q8—22no—
918C2×Q8—22no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×Q8—432no—
922C2×Q8—432no—
923C2×Q8C22×D418yes—
924C2×Q8C22×D414yes—
925C2×Q8C22×D418yes—
926C2×Q8C22×D414yes—
927C2×Q8C22×D4116yes—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—28no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—28no—
937C2×D4—216no—
938C2×D4—216no—
939C2×D4—28no—
940C2×D4—28no—
941C2×D4—216no—
942C2×D4—28no—
943C2×D4—24no—
944C2×D4—216no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—22no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—22no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—24no—
956C2×D4—22no—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—22no—
963C2×D4—216no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—48no—
969C2×D4—48no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—432no—
973C2×D4—432no—
974C2×D4—44no—
975C2×D4—48no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—48no—
979C2×D4—48no—
980C2×D4—48no—
981C2×D4—48no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—48no—
986C2×D4—48no—
987C2×D4—44no—
988C2×D4—48no—
989C2×D4—48no—
990C2×D4—44no—
991C2×D4—48no—
992C2×D4—48no—
993C2×D4—44no—
994C2×D4—48no—
995C2×D4—48no—
996C2×D4—48no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—48no—
1000C2×D4—48no—
1001C2×D4—464no—
1002C2×D4—432no—
1003C2×D4—416no—
1004C2×D4—416no—
1005C2×D4—832no—
1006C2×D4—816no—
1007C2×D4C22×D418yes—
1008C2×D4C22×D414yes—
1009C2×D4C22×D418yes—
1010C2×D4C22×D414yes—
1011C2×D4C22×D4116yes—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—22no—
1019C22×C4—24no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—28no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—216no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—28no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—48no—
1039C22×C4—48no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—48no—
1056C22×C4—432no—
1057C22×C4—416no—
1058C22×C4C22×D418yes—
1059C22×C4C22×D418yes—
1060C22×C4C22×D418yes—
1061C22×C4C22×D4116yes—
1062C22×C4C22×D4116yes—
1063C22×C4C22×D414yes—
1064C22×C4H(5,𝔽2)14yes—
1065C22×C4H(5,𝔽2)14yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—216no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—216no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—48no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—28no—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—216no—
1118C22⋊C4—28no—
1119C22⋊C4—216no—
1120C22⋊C4—216no—
1121C22⋊C4—216no—
1122C22⋊C4—216no—
1123C22⋊C4—28no—
1124C22⋊C4—216no—
1125C22⋊C4—28no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—48no—
1133C22⋊C4—48no—
1134C22⋊C4—48no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—48no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—48no—
1145C22⋊C4—48no—
1146C22⋊C4—48no—
1147C22⋊C4—48no—
1148C22⋊C4—48no—
1149C22⋊C4—48no—
1150C22⋊C4—44no—
1151C22⋊C4—48no—
1152C22⋊C4—44no—
1153C42—22no—
1154C42—24no—
1155C42—22no—
1156C42—28no—
1157C42—24no—
1158C42—216no—
1159C42—24no—
1160C42—24no—
1161C42—22no—
1162C42—22no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—44no—
1167C42—44no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—22no—
1181C23—24no—
1182C23—22no—
1183C23—22no—
1184C23—24no—
1185C23—24no—
1186C23—22no—
1187C23—22no—
1188C23—24no—
1189C23—24no—
1190C23—22no—
1191C23—22no—
1192C23—24no—
1193C23—28no—
1194C23—28no—
1195C23—28no—
1196C23—24no—
1197C23—22no—
1198C23—28no—
1199C23—22no—
1200C23—44no—
1201C23—416no—
1202C23—44no—
1203C23—416no—
1204C23—48no—
1205C23—44no—
1206C23—48no—
1207C23—84no—
1208C23—88no—
1209C23—84no—
1210C23—84no—
1211C23—84no—
1212C23—84no—
1213C23—88no—
1214C23—88no—
1215C23—84no—
1216C23—816no—
1217C23—164no—
1218C23—164no—
1219C23—168no—
1220C23C23×D414yes—
1221C23C23×D414yes—
1222C23C23×D412yes—
1223C23C2×H(5,𝔽2)12yes—
1224C23C2×H(5,𝔽2)12yes—
1225C23C2611yescharacteristic
1226Q8—216no—
1227Q8—216no—
1228Q8—28no—
1229Q8—28no—
1230Q8—416no—
1231Q8—44no—
1232D4—216no—
1233D4—216no—
1234D4—28no—
1235D4—28no—
1236D4—416no—
1237D4—416no—
1238D4—432no—
1239D4—416no—
1240D4—48no—
1241D4—48no—
1242D4—48no—
1243D4—44no—
1244D4—48no—
1245D4—48no—
1246D4—816no—
1247D4—88no—
1248D4—816no—
1249D4—816no—
1250D4—88no—
1251D4—88no—
1252D4—816no—
1253D4—88no—
1254D4—816no—
1255D4—816no—
1256D4—164no—
1257D4—164no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—216no—
1267C2×C4—216no—
1268C2×C4—216no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—28no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—416no—
1303C2×C4—416no—
1304C2×C4—48no—
1305C2×C4—432no—
1306C2×C4—416no—
1307C2×C4—44no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—88no—
1312C2×C4—84no—
1313C2×C4—88no—
1314C2×C4—84no—
1315C2×C4—164no—
1316C2×C4#534116yes—
1317C2×C4C23×D414yes—
1318C2×C4C23×D418yes—
1319C2×C4C23×D414yes—
1320C2×C4C23×D412yes—
1321C2×C4C23×D412yes—
1322C2×C4C2×H(5,𝔽2)12yes—
1323C2×C4C2×H(5,𝔽2)12yes—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×H(5,𝔽2)12yes—
1326C2×C4#58514yes—
1327C22—24no—
1328C22—22no—
1329C22—22no—
1330C22—24no—
1331C22—28no—
1332C22—28no—
1333C22—24no—
1334C22—24no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—42no—
1343C22—48no—
1344C22—44no—
1345C22—48no—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—42no—
1353C22—44no—
1354C22—48no—
1355C22—42no—
1356C22—48no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22—44no—
1362C22—42no—
1363C22—88no—
1364C22—816no—
1365C22—168no—
1366C22—1616no—
1367C22C2×#53414yes—
1368C22C24×D411yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C2×#58512yes—
1372C22H(7,𝔽2)12yes—
1373C4—24no—
1374C4—24no—
1375C4—28no—
1376C4—24no—
1377C4—42no—
1378C4—42no—
1379C4—44no—
1380C4—44no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4C2×#53414yes—
1390C4C2×#53414yes—
1391C2—24no—
1392C2—44no—
1393C2—44no—
1394C2—84no—
1395C2—82no—
1396C2—82no—
1397C2—84no—
1398C2C22×#53411yescharacteristic
1399C2#6283611yescharacteristic
1400C2#6287611yescharacteristic
1401C2#6292412yes—
1402C2#6300312yes—
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×#3500C2semidirect
2. C2×#3487C2semidirect
3. #42969C2semidirect
4. #42951C2semidirect
5. #42883C2semidirect
6. #42797C2semidirect
7. #41932C2semidirect
8. #39957C2semidirect
9. #39865C2semidirect
10. #39743C2semidirect
11. #39135C2semidirect
12. #38364C2semidirect
13. #35679C2semidirect
14. #35673C2semidirect
15. #35563C2semidirect
16. #35533C2semidirect
17. #35527C2semidirect
18. #35512C2semidirect
19. #35272C2semidirect
20. #35254C2semidirect
21. #35149C2semidirect
22. #34743C2semidirect
23. #34742C2semidirect
24. C2×#2431C2semidirect
25. #34259C2semidirect
28. C23×#41C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
37. C2×#546C22semidirect
39. C2×#536C22semidirect
43. C2×#535C22semidirect
44. C2×#535C22semidirect
45. C2×#535C22semidirect
47. C2×#532C22semidirect
50. C22×#124C22semidirect
53. C2×#525C22semidirect
54. C2×#525C22semidirect
56. C2×#520C22semidirect
57. C2×#519C22semidirect
59. C2×C4×#41C22semidirect
60. #2856C22semidirect
61. #2854C22semidirect
62. #2849C22semidirect
63. #2815C22semidirect
64. #2813C22semidirect
65. #2733C22semidirect
66. #2733C22semidirect
67. #2732C22semidirect
68. #2730C22semidirect
69. #2730C22semidirect
70. #2730C22semidirect
71. #2730C22semidirect
72. #2728C22semidirect
73. #2688C22semidirect
74. #2673C22semidirect
75. #2673C22semidirect
76. #2671C22semidirect
77. #2669C22semidirect
78. #2669C22semidirect
79. #2668C22semidirect
80. #2668C22semidirect
81. #2661C22semidirect
82. #2656C22semidirect
83. #2635C22semidirect
84. #2635C22semidirect
85. #2630C22semidirect
86. #2624C22semidirect
87. #2619C22semidirect
88. #2617C22semidirect
89. #2613C22semidirect
90. #2602C22semidirect
91. #2600C22semidirect
92. #2548C22semidirect
93. #2548C22semidirect
94. #2545C22semidirect
95. #2544C22semidirect
96. #2543C22semidirect
97. #2543C22semidirect
98. #2541C22semidirect
99. #2541C22semidirect
100. #2539C22semidirect
101. #2534C22semidirect
102. #2534C22semidirect
103. #2498C22semidirect
104. #2482C22semidirect
105. #2448C22semidirect
106. #2448C22semidirect
107. #2448C22semidirect
108. #2448C22semidirect
109. #2448C22semidirect
110. #2448C22semidirect
111. #2446C22semidirect
112. #2445C22semidirect
113. #2433C22semidirect
114. #2433C22semidirect
115. #2433C22semidirect
116. #2432C22semidirect
117. #2431C22semidirect
118. #2431C22semidirect
119. #2431C22semidirect
120. #2431C22semidirect
121. #2431C22semidirect
122. #2431C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
125. #2429C22semidirect
126. #2428C22semidirect
127. #2428C22semidirect
128. #2427C22semidirect
129. #2426C22semidirect
130. #2426C22semidirect
131. #2425C22semidirect
132. #2424C22semidirect
133. #2424C22semidirect
134. #2423C22semidirect
135. #2423C22semidirect
136. #2422C22semidirect
137. #2421C22semidirect
138. #2421C22semidirect
139. #2420C22semidirect
140. #2419C22semidirect
141. #2418C22semidirect
142. #2418C22semidirect
143. #2416C22semidirect
144. #2416C22semidirect
145. #2414C22semidirect
146. #2414C22semidirect
147. #2408C22semidirect
148. #2408C22semidirect
149. #2408C22semidirect
150. #2408C22semidirect
151. #2407C22semidirect
152. #2407C22semidirect
153. #2407C22semidirect
154. #2407C22semidirect
158. #2395C22semidirect
159. #2392C22semidirect
160. C2×#392C22semidirect
161. Q8×C22⋊C4C22semidirect
162. #2339C22semidirect
163. #2339C22semidirect
164. #2325C22semidirect
165. #2321C22semidirect
166. #2316C22semidirect
169. #2311C22semidirect
170. #2310C22semidirect
171. #2310C22semidirect
174. #2309C22semidirect
175. C4×#123C22semidirect
176. C4×#121C22semidirect
179. #2297C22semidirect
180. #2296C22semidirect
181. #2296C22semidirect
182. C2×#391C22semidirect
183. C2×#391C22semidirect
184. C2×#390C22semidirect
185. C2×#386C22semidirect
186. #2285C22semidirect
187. #2280C22semidirect
188. C2×C4×C22⋊C4C22semidirect
191. C2×2−1+4D4semidirect
567. C2×#41C2×D4semidirect
568. C2×#41C2×D4semidirect
576. C22×Q8C2×D4semidirect
577. C22×Q8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34872
#429692
#429512
#428832
#427972
#419322
#399572
#398652
#397432
#391352
#383642
#356792
#356732
#355632
#355332
#355272
#355122
#352722
#352542
#351492
#347432
#347422
C2×#24312
#342592