Finite Group Databasebeta

← #7643323

Subgroups — #7643323

Order 512.

9412 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic, complemented
3#39725C214yesmaximal, complemented
4#39342C214yesmaximal, complemented
5#39138C214yesmaximal, complemented
6#38910C214yesmaximal, complemented
7#38026C218yesmaximal, complemented
8#37650C218yesmaximal, complemented
9#37278C218yesmaximal, complemented
10#36624C211yesmaximal, characteristic, complemented
11C2×#2856C211yesmaximal, characteristic, complemented
12#35565C212yesmaximal, complemented
13#35556C212yesmaximal, complemented
14#35513C212yesmaximal, complemented
15#35512C212yesmaximal, complemented
16#35292C214yesmaximal, complemented
17#35273C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35272C214yesmaximal, complemented
20#34188C211yesmaximal, characteristic, complemented
21C22×H(5,𝔽2)C2212yes—
22#3498—216no—
23C2×#550C2214yescomplemented
24C2×D42C2218yes—
25C2×D42C2214yescomplemented
26C2×#537C2212yescomplemented
27C2×#535C2212yes—
28C2×#535C2214yescomplemented
29C2×#535C2218yescomplemented
30C2×#535C2212yescomplemented
31#3444—216no—
32C2×#533C2212yescomplemented
33C2×#533C2211yescharacteristic, complemented
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#532C2212yescomplemented
37C2×#532C2212yescomplemented
38C22×#127C2211yescharacteristic
39C22×#127C2212yescomplemented
40C2×#529C2214yescomplemented
41C2×#529C2214yescomplemented
42C2×#529C2212yescomplemented
43C2×#529C2212yescomplemented
44C2×#525C2211yescharacteristic
45C2×#525C2214yescomplemented
46C2×#525C2211yescharacteristic, complemented
47C2×#525C2212yescomplemented
48C22×#121C2214yescomplemented
49C22×#121C2212yescomplemented
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2211yescharacteristic, complemented
52C2×C4×#41C2214yescomplemented
53C23×C42C2211yescharacteristic, complemented
54#2857C2212yescomplemented
55#2857C2212yescomplemented
56#2856C2214yescomplemented
57#2856C2214yescomplemented
58#2856C2214yescomplemented
59#2856C2214yescomplemented
60#2856C2212yescomplemented
61#2856C2212yescomplemented
62#2856C2214yescomplemented
63#2854C2214yescomplemented
64#2850C2214yescomplemented
65#2847C2214yescomplemented
66#2714C22116yescomplemented
67#2711C22116yescomplemented
68#2685C22116yescomplemented
69#2678C22116yescomplemented
70#2676C22116yescomplemented
71#2673C22116yescomplemented
72#2670C22116yescomplemented
73#2669C22116yescomplemented
74#2624C2218yescomplemented
75#2620C2214yescomplemented
76#2619C2218yescomplemented
77#2619C2218yescomplemented
78#2619C2214yescomplemented
79#2615C2218yescomplemented
80#2592C2218yescomplemented
81#2580C2218yescomplemented
82#2548C2218yescomplemented
83#2548C2214yescomplemented
84#2548C2218yescomplemented
85#2541C2218yescomplemented
86#2541C2218yescomplemented
87#2541C2214yescomplemented
88#2541C2218yescomplemented
89#2540C2218yescomplemented
90#2540C2218yescomplemented
91#2539C2218yescomplemented
92#2538C2214yescomplemented
93#2537C2214yescomplemented
94#2535C2218yescomplemented
95#2491C2218yescomplemented
96#2490C2218yescomplemented
97#2472C22116yescomplemented
98#2435C2214yescomplemented
99#2433C2218yescomplemented
100#2433C2214yescomplemented
101#2432C2214yescomplemented
102#2431C2214yescomplemented
103#2416C2218yescomplemented
104#2414C2218yescomplemented
105#2414C2218yescomplemented
106#2410C22116yescomplemented
107#2408C2218yescomplemented
108#2408C2218yescomplemented
109#2408C2218yescomplemented
110#2408C2218yescomplemented
111#2408C2218yescomplemented
112#2408C2218yescomplemented
113#2407C2218yescomplemented
114#2407C2218yescomplemented
115#2407C2218yescomplemented
116#2405C2218yescomplemented
117#2403C2218yescomplemented
118#2355C2214yescomplemented
119#2354C2214yescomplemented
120#2352C2218yescomplemented
121#2324C2218yescomplemented
122#2324C2218yescomplemented
123#2314C2214yescomplemented
124#2311C2212yes—
125#2311C2212yescomplemented
126#2309C2218yescomplemented
127#2309C2212yescomplemented
128C4×#121C2214yescomplemented
129C4×#121C2214yescomplemented
130#2297C2212yescomplemented
131C2×#390C2214yescomplemented
132C2×#390C2212yescomplemented
133#2285C2211yescharacteristic, complemented
134#2285C2214yescomplemented
135C2×#384C2211yescharacteristic, complemented
136#2274C2212yescomplemented
137C2×H(5,𝔽2)—216no—
138C2×H(5,𝔽2)—48no—
139C2×H(5,𝔽2)—48no—
140C22×#41C2312yes—
141C22×#41C2311yescharacteristic
142C22×#41C2314yes—
143C22×#41C2311yescharacteristic
144C22×#41C2314yes—
145C22×#41C2314yes—
146C23×D4C2312yes—
147C23×D4C2318yes—
148C23×D4C2318yes—
149C23×D4C2314yes—
150C23×D4C2314yes—
151C23×D4C2314yes—
152C23×D4C2314yes—
153C24×C4C2311yescharacteristic
154C24×C4C2312yes—
155#550—232no—
156D42—264no—
157D42—232no—
158#537—48no—
159#535—216no—
160#535—232no—
161#535—48no—
162#535—432no—
163#533—216no—
164#533—28no—
165#532—28no—
166#532—216no—
167#532—28no—
168#532—216no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2312yes—
172C2×#127—28no—
173C2×#127—216no—
174C2×#127C2312yes—
175C2×#127C2311yescharacteristic
176C2×#127C2312yes—
177C2×#127C2314yes—
178C2×#127C2318yes—
179C2×#127C2314yes—
180C2×#127C2311yescharacteristic
181C2×#127C23116yes—
182C2×#127C2314yes—
183#529—216no—
184#529—232no—
185#529—216no—
186#529—232no—
187C2×#126C2314yes—
188C2×#126C2314yes—
189C2×#125C2314yes—
190C2×#125C2312yes—
191C2×#124C2314yes—
192C2×#124C2312yes—
193C2×#124C2314yes—
194C2×#124C2311yescharacteristic
195C2×#124C2311yescharacteristic
196C2×#124C23116yes—
197C2×#124C2314yes—
198#525—28no—
199#525—232no—
200#525—28no—
201#525—48no—
202C2×#123C2312yes—
203C2×#123C2314yes—
204C2×#123C2314yes—
205C2×#123C2312yes—
206C2×#123C2314yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×#121—48no—
215C2×#121—416no—
216C2×#121C2318yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C23116yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2318yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×#121C2318yes—
237C2×#121C2314yes—
238C2×#121C2318yes—
239C2×#121C2314yes—
240C2×#120C2312yes—
241C2×#120C2312yes—
242C2×#120C23116yes—
243C2×#120C2318yes—
244C2×#120C2314yes—
245C2×#120C23116yes—
246C2×#120C2318yes—
247C2×#120C23116yes—
248C4×#41—28no—
249C4×#41—232no—
250C4×#41D4116yescomplemented
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×#117C2311yescharacteristic
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2318yes—
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2314yes—
279C22×C22⋊C4C2314yes—
280C22×C22⋊C4C2318yes—
281C22×C42—28no—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2312yes—
287C22×C42C2312yes—
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2312yes—
291#399C23116yes—
292#397C23116yes—
293#396C23116yes—
294#394C23116yes—
295#394C23116yes—
296#394C23116yes—
297#394C23116yes—
298#394C23116yes—
299#394C23116yes—
300#394C23116yes—
301#394C23116yes—
302#393C23116yes—
303#392C23116yes—
304#392C23116yes—
305#392C23116yes—
306#392C23116yes—
307#392C23116yes—
308#392C23116yes—
309#392C23116yes—
310#392C23116yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#390C2314yes—
315#390C2318yes—
316#390C2318yes—
317#390C2318yes—
318#390C2318yes—
319#390C2318yes—
320#390C23116yes—
321#390C23116yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C23116yes—
326#390C23116yes—
327#390C2318yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2314yes—
338#388C23116yes—
339#388C23116yes—
340#388C23116yes—
341#388C2318yes—
342#388C2318yes—
343#387C23116yes—
344#386C2318yes—
345#386C2318yes—
346#386C23116yes—
347#386C23116yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#385C23116yes—
352#385C23116yes—
353#384C2312yes—
354#384C2312yes—
355#384C2312yes—
356#384C2314yes—
357#382C2312yes—
358#382C2318yes—
359#380C2318yes—
360#380C2318yes—
361#380C2314yes—
362#380C2318yes—
363#380C2314yes—
364#380C2314yes—
365#380C2318yes—
366#379C2318yes—
367#379C23116yes—
368#379C23116yes—
369C4×C4⋊C4C2318yes—
370C4×C4⋊C4C2318yes—
371C4×C4⋊C4C2318yes—
372C4×C4⋊C4C2314yes—
373C4×C22⋊C4C2318yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2314yes—
376C25C2411yescharacteristic
377C25C2414yes—
378C25C2418yes—
379H(5,𝔽2)—4128no—
380C2×#41—216no—
381C2×#41—216no—
382C2×#41—24no—
383C2×#41—216no—
384C2×#41—28no—
385C2×#41—24no—
386C2×#41—24no—
387C2×#41—28no—
388C2×#41—24no—
389C2×#41—24no—
390C2×#41—28no—
391C2×#41—216no—
392C2×#41—48no—
393C2×#41—48no—
394C2×#41—48no—
395C2×#41—48no—
396C2×#41—48no—
397C2×#41C2×D418yes—
398C22×Q8C2411yescharacteristic
399C22×Q8C2412yes—
400C22×Q8C2414yes—
401C22×Q8C2411yescharacteristic
402C22×D4—232no—
403C22×D4—216no—
404C22×D4—216no—
405C22×D4—28no—
406C22×D4—216no—
407C22×D4—232no—
408C22×D4—28no—
409C22×D4—28no—
410C22×D4—48no—
411C22×D4—48no—
412C22×D4—48no—
413C22×D4—48no—
414C22×D4—48no—
415C22×D4—416no—
416C22×D4—48no—
417C22×D4—416no—
418C22×D4—48no—
419C22×D4—416no—
420C22×D4—416no—
421C22×D4—416no—
422C22×D4C2412yes—
423C22×D4C2411yescharacteristic
424C22×D4C2418yes—
425C22×D4C2414yes—
426C22×D4C2414yes—
427C22×D4C2414yes—
428C22×D4C2414yes—
429C22×D4C2412yes—
430C22×D4C2414yes—
431C22×D4C2414yes—
432C22×D4C2414yes—
433C22×D4C2412yes—
434C22×D4C2411yescharacteristic
435C22×D4C2418yes—
436C22×D4C2418yes—
437C22×D4C24116yes—
438C22×D4C2418yes—
439C22×D4C24116yes—
440C22×D4C2418yes—
441C22×D4C2418yes—
442C22×D4C24116yes—
443C23×C4—28no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—28no—
448C23×C4—44no—
449C23×C4C2411yescharacteristic
450C23×C4C2412yes—
451C23×C4C2414yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2418yes—
465C23×C4C2411yescharacteristic
466C4⋊Q8—24no—
467C4⋊Q8—28no—
468C4⋊Q8—24no—
469#127—24no—
470#127—28no—
471#127—24no—
472#127—28no—
473#127—216no—
474#127—216no—
475#127—232no—
476#127—48no—
477#127—432no—
478#126—216no—
479#126—216no—
480#125—216no—
481#125—28no—
482#124—24no—
483#124—24no—
484#124—216no—
485#124—28no—
486#124—216no—
487#124—48no—
488#124—432no—
489#123—28no—
490#123—216no—
491#123—216no—
492#123—28no—
493#123—48no—
494C22⋊Q8—28no—
495C22⋊Q8—216no—
496C22⋊Q8—28no—
497C22⋊Q8—216no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501#121—28no—
502#121—216no—
503#121—216no—
504#121—232no—
505#121—232no—
506#121—216no—
507#121—28no—
508#121—232no—
509#121—264no—
510#121—216no—
511#121—416no—
512#121—416no—
513#121—416no—
514#121—416no—
515#121—48no—
516#121—416no—
517#121—48no—
518#121—416no—
519#121—416no—
520#121—416no—
521#121—48no—
522#121—48no—
523#121—416no—
524#121—416no—
525#120—28no—
526#120—28no—
527#120—232no—
528#120—264no—
529#120—432no—
530#120—48no—
531#120—416no—
532#120—432no—
533C4×Q8—216no—
534C4×Q8—216no—
535C4×Q8—28no—
536C4×Q8C2×D4116yescomplemented
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—216no—
542C4×D4—216no—
543C4×D4—216no—
544C4×D4—28no—
545C4×D4—216no—
546C4×D4—232no—
547C4×D4—416no—
548C4×D4C2×D4132yes—
549C4×D4C2×D4116yescomplemented
550#117—24no—
551#117—216no—
552#117—28no—
553#117—216no—
554#117—216no—
555#117—28no—
556#117—416no—
557#117C2×D418yes—
558#117C2×D4116yescomplemented
559C2×C4⋊C4—28no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C22⋊C4—416no—
582C2×C22⋊C4—48no—
583C2×C22⋊C4C24116yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C24116yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C24116yes—
597C2×C22⋊C4C24116yes—
598C2×C22⋊C4C24116yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C24116yes—
602C2×C22⋊C4C24116yes—
603C2×C22⋊C4C24116yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C24116yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2414yes—
610C2×C42—28no—
611C2×C42—24no—
612C2×C42—28no—
613C2×C42—28no—
614C2×C42—28no—
615C2×C42—28no—
616C2×C42—28no—
617C2×C42C2×D418yes—
618C2×C42C2×D4116yescomplemented
619C2×C42C2412yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2414yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2411yescharacteristic
629C2×C42C24116yes—
630C2×C42C2411yescharacteristic
631C2×C42C2414yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635#95C24116yes—
636#95C2418yes—
637#95C2418yes—
638#95C24116yes—
639#95C2418yes—
640#95C24116yes—
641C24—24no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—216no—
646C24—28no—
647C24—28no—
648C24—28no—
649C24—42no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—416no—
655C24—416no—
656C24C2514yes—
657C24C2518yes—
658C24C2512yes—
659C24C2512yes—
660C24C2512yes—
661C24C2511yescharacteristic
662#41—232no—
663#41—464no—
664#41—464no—
665#41—464no—
666#41—416no—
667#41—432no—
668C2×Q8—28no—
669C2×Q8—22no—
670C2×Q8—24no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—24no—
675C2×Q8—24no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—44no—
679C2×Q8C22×D414yes—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—24no—
684C2×D4—28no—
685C2×D4—216no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—24no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—216no—
694C2×D4—232no—
695C2×D4—28no—
696C2×D4—22no—
697C2×D4—28no—
698C2×D4—216no—
699C2×D4—216no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—216no—
704C2×D4—232no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—28no—
708C2×D4—216no—
709C2×D4—28no—
710C2×D4—22no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—28no—
717C2×D4—22no—
718C2×D4—28no—
719C2×D4—216no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—464no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4—48no—
733C2×D4—416no—
734C2×D4—48no—
735C2×D4—416no—
736C2×D4—416no—
737C2×D4—416no—
738C2×D4—416no—
739C2×D4—48no—
740C2×D4—416no—
741C2×D4—4128no—
742C2×D4—464no—
743C2×D4—432no—
744C2×D4—832no—
745C2×D4—864no—
746C2×D4—832no—
747C2×D4C22×D418yes—
748C2×D4C22×D414yes—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—216no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—24no—
785C22×C4—28no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—432no—
792C22×C4—48no—
793C22×C4—416no—
794C22×C4C22×D418yes—
795C22×C4C22×D4116yes—
796C22×C4C22×D418yes—
797C22×C4C22×D414yes—
798C22×C4H(5,𝔽2)14yes—
799C22×C4H(5,𝔽2)14yes—
800C22×C4H(5,𝔽2)18yescomplemented
801C22×C4C2518yes—
802C22×C4C2514yes—
803C22×C4C2518yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2512yes—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—216no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4C22×D418yes—
834C4⋊C4C22×D4116yes—
835C22⋊C4—24no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—216no—
845C22⋊C4—232no—
846C22⋊C4—232no—
847C22⋊C4—216no—
848C22⋊C4—416no—
849C22⋊C4—416no—
850C22⋊C4—416no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—416no—
854C22⋊C4—416no—
855C22⋊C4—416no—
856C22⋊C4—48no—
857C22⋊C4—416no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4C22×D418yes—
861C22⋊C4C22×D4116yes—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—22no—
867C42—24no—
868C42—22no—
869C42—24no—
870C42—28no—
871C42—28no—
872C42—416no—
873C42C22×D414yes—
874C42C22×D414yes—
875C42C22×D418yes—
876C42C22×D4116yes—
877C42C22×D418yes—
878C23—22no—
879C23—22no—
880C23—28no—
881C23—22no—
882C23—22no—
883C23—24no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—24no—
891C23—22no—
892C23—28no—
893C23—24no—
894C23—216no—
895C23—28no—
896C23—22no—
897C23—24no—
898C23—24no—
899C23—28no—
900C23—28no—
901C23—24no—
902C23—22no—
903C23—28no—
904C23—216no—
905C23—24no—
906C23—48no—
907C23—48no—
908C23—44no—
909C23—432no—
910C23—44no—
911C23—416no—
912C23—816no—
913C23—88no—
914C23—832no—
915C23—816no—
916C23—88no—
917C23—168no—
918C23—1616no—
919C23—168no—
920C23C23×D414yes—
921C23C23×D412yes—
922C23C2×H(5,𝔽2)14yes—
923C23C2×H(5,𝔽2)12yes—
924C23C2×H(5,𝔽2)12yes—
925C23C2611yescharacteristic
926Q8—28no—
927Q8—416no—
928Q8—44no—
929Q8—48no—
930D4—216no—
931D4—28no—
932D4—416no—
933D4—416no—
934D4—432no—
935D4—416no—
936D4—432no—
937D4—416no—
938D4—48no—
939D4—416no—
940D4—48no—
941D4—416no—
942D4—44no—
943D4—432no—
944D4—416no—
945D4—816no—
946D4—832no—
947D4—816no—
948D4—832no—
949D4—168no—
950D4—1616no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—216no—
960C2×C4—216no—
961C2×C4—216no—
962C2×C4—232no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—28no—
970C2×C4—216no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—48no—
986C2×C4—432no—
987C2×C4—44no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—416no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—416no—
994C2×C4—88no—
995C2×C4#535116yescomplemented
996C2×C4C23×D414yes—
997C2×C4C23×D418yes—
998C2×C4C23×D414yes—
999C2×C4C23×D412yes—
1000C2×C4C23×D412yes—
1001C2×C4C23×D414yes—
1002C2×C4C2×H(5,𝔽2)14yes—
1003C2×C4C2×H(5,𝔽2)12yes—
1004C2×C4C2×H(5,𝔽2)12yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)14yes—
1008C2×C4#58514yes—
1009C22—24no—
1010C22—22no—
1011C22—24no—
1012C22—22no—
1013C22—24no—
1014C22—28no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—416no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—44no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—44no—
1027C22—416no—
1028C22—48no—
1029C22—48no—
1030C22—42no—
1031C22—44no—
1032C22—48no—
1033C22—44no—
1034C22—416no—
1035C22—42no—
1036C22—48no—
1037C22—44no—
1038C22—48no—
1039C22—44no—
1040C22—42no—
1041C22—1616no—
1042C22—1632no—
1043C22C2×#53514yes—
1044C22C24×D411yescharacteristic
1045C22C22×H(5,𝔽2)12yes—
1046C22C22×H(5,𝔽2)11yescharacteristic
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C2×#58512yes—
1049C4—24no—
1050C4—24no—
1051C4—28no—
1052C4—24no—
1053C4—42no—
1054C4—44no—
1055C4—48no—
1056C4—48no—
1057C4—42no—
1058C4—44no—
1059C4—42no—
1060C4C2×#53514yes—
1061C4C2×#53514yes—
1062C4#348818yes—
1063C2—24no—
1064C2—44no—
1065C2—44no—
1066C2—82no—
1067C2—88no—
1068C2—84no—
1069C2C22×#53511yescharacteristic
1070C2C2×#348812yes—
1071C2#6283211yescharacteristic
1072C2#6283412yes—
1073C2#6283611yescharacteristic
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×#3498C2semidirect
2. C2×#3444C2semidirect
3. #39725C2semidirect
4. #39342C2semidirect
5. #39138C2semidirect
6. #38910C2semidirect
7. #38026C2semidirect
8. #37650C2semidirect
9. #37278C2semidirect
10. #36624C2semidirect
11. C2×#2856C2semidirect
12. #35565C2semidirect
13. #35556C2semidirect
14. #35513C2semidirect
15. #35512C2semidirect
16. #35292C2semidirect
17. #35273C2semidirect
18. #35272C2semidirect
19. #35272C2semidirect
20. #34188C2semidirect
23. C2×#550C22semidirect
25. C2×D42C22semidirect
26. C2×#537C22semidirect
28. C2×#535C22semidirect
29. C2×#535C22semidirect
30. C2×#535C22semidirect
32. C2×#533C22semidirect
33. C2×#533C22semidirect
36. C2×#532C22semidirect
37. C2×#532C22semidirect
39. C22×#127C22semidirect
40. C2×#529C22semidirect
41. C2×#529C22semidirect
42. C2×#529C22semidirect
43. C2×#529C22semidirect
45. C2×#525C22semidirect
46. C2×#525C22semidirect
47. C2×#525C22semidirect
48. C22×#121C22semidirect
49. C22×#121C22semidirect
51. C2×C4×#41C22semidirect
52. C2×C4×#41C22semidirect
53. C23×C42C22semidirect
54. #2857C22semidirect
55. #2857C22semidirect
56. #2856C22semidirect
57. #2856C22semidirect
58. #2856C22semidirect
59. #2856C22semidirect
60. #2856C22semidirect
61. #2856C22semidirect
62. #2856C22semidirect
63. #2854C22semidirect
64. #2850C22semidirect
65. #2847C22semidirect
66. #2714C22semidirect
67. #2711C22semidirect
68. #2685C22semidirect
69. #2678C22semidirect
70. #2676C22semidirect
71. #2673C22semidirect
72. #2670C22semidirect
73. #2669C22semidirect
74. #2624C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2619C22semidirect
78. #2619C22semidirect
79. #2615C22semidirect
80. #2592C22semidirect
81. #2580C22semidirect
82. #2548C22semidirect
83. #2548C22semidirect
84. #2548C22semidirect
85. #2541C22semidirect
86. #2541C22semidirect
87. #2541C22semidirect
88. #2541C22semidirect
89. #2540C22semidirect
90. #2540C22semidirect
91. #2539C22semidirect
92. #2538C22semidirect
93. #2537C22semidirect
94. #2535C22semidirect
95. #2491C22semidirect
96. #2490C22semidirect
97. #2472C22semidirect
98. #2435C22semidirect
99. #2433C22semidirect
100. #2433C22semidirect
101. #2432C22semidirect
102. #2431C22semidirect
103. #2416C22semidirect
104. #2414C22semidirect
105. #2414C22semidirect
106. #2410C22semidirect
107. #2408C22semidirect
108. #2408C22semidirect
109. #2408C22semidirect
110. #2408C22semidirect
111. #2408C22semidirect
112. #2408C22semidirect
113. #2407C22semidirect
114. #2407C22semidirect
115. #2407C22semidirect
116. #2405C22semidirect
117. #2403C22semidirect
118. #2355C22semidirect
119. #2354C22semidirect
120. #2352C22semidirect
121. #2324C22semidirect
122. #2324C22semidirect
123. #2314C22semidirect
125. #2311C22semidirect
126. #2309C22semidirect
127. #2309C22semidirect
128. C4×#121C22semidirect
129. C4×#121C22semidirect
130. #2297C22semidirect
131. C2×#390C22semidirect
132. C2×#390C22semidirect
133. #2285C22semidirect
134. #2285C22semidirect
135. C2×#384C22semidirect
136. #2274C22semidirect
250. C4×#41D4semidirect
536. C4×Q8C2×D4semidirect
549. C4×D4C2×D4semidirect
558. #117C2×D4semidirect
618. C2×C42C2×D4semidirect
800. C22×C4H(5,𝔽2)semidirect
995. C2×C4#535semidirect

Maximal subgroups

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

subgroupindex
C2×#34982
C2×#34442
#397252
#393422
#391382
#389102
#380262
#376502
#372782
#366242
C2×#28562
#355652
#355562
#355132
#355122
#352922
#352732
#352722
#341882