Finite Group Databasebeta

← #7624624

Subgroups — #7624624

Order 512.

1293 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62437C211yesmaximal, characteristic, complemented
2#61473C211yesmaximal, characteristic, complemented
3#33969C211yesmaximal, characteristic, complemented
4#33960C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33931C211yesmaximal, characteristic, complemented
7#33894C211yesmaximal, characteristic, complemented
8#33887C211yesmaximal, characteristic, complemented
9#33881C211yesmaximal, characteristic, complemented
10#33867C211yesmaximal, characteristic, complemented
11#33866C211yesmaximal, characteristic, complemented
12#33864C211yesmaximal, characteristic, complemented
13D4×Q32C211yesmaximal, characteristic, complemented
14#33851C211yesmaximal, characteristic, complemented
15#33848C211yesmaximal, characteristic, complemented
16#33843C211yesmaximal, characteristic, complemented
17#33836C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33828C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33814C211yesmaximal, characteristic, complemented
22#33791C211yesmaximal, characteristic, complemented
23#33789C211yesmaximal, characteristic, complemented
24#33777C211yesmaximal, characteristic, complemented
25#33684C211yesmaximal, characteristic, complemented
26#33681C211yesmaximal, characteristic, complemented
27#33664C211yesmaximal, characteristic, complemented
28#33590C211yesmaximal, characteristic, complemented
29#33588C211yesmaximal, characteristic, complemented
30C2×#2211C211yesmaximal, characteristic, complemented
31#33508C211yesmaximal, characteristic, complemented
32#3561—21no—
33#3516—21no—
34C2×#510C2211yescharacteristic
35C2×#510C2211yescharacteristic, complemented
36C2×#508C2211yescharacteristic
37C22×Q32C2211yescharacteristic
38C22×Q32C2211yescharacteristic, complemented
39C22×SD32C2211yescharacteristic
40#3402—21no—
41#3393C2211yescharacteristic
42#3393C2211yescharacteristic
43#3393C2211yescharacteristic, complemented
44#3383C2211yescharacteristic, complemented
45#3377—21no—
46#3339C2211yescharacteristic
47#3338C2211yescharacteristic
48#3336C2211yescharacteristic, complemented
49#3327—21no—
50#3320—21no—
51#3316—21no—
52D4×Q16C2211yescharacteristic
53D4×Q16C2211yescharacteristic
54D4×Q16C2211yescharacteristic
55#3285C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3285C2211yescharacteristic, complemented
59#3280C2211yescharacteristic
60#3280C2211yescharacteristic
61#3277—21no—
62#3266—21no—
63#3266—21no—
64#3225—21no—
65#3225—21no—
66#3215—21no—
67#3177C2211yescharacteristic, complemented
68#3175C2211yescharacteristic
69#3175C2211yescharacteristic
70#3175C2211yescharacteristic, complemented
71#3170C2211yescharacteristic
72#3168C2211yescharacteristic
73#3156C2211yescharacteristic
74#3156C2211yescharacteristic
75C2×#495C2211yescharacteristic
76#3121—21no—
77#3120—21no—
78#3117—21no—
79#2966C2211yescharacteristic
80#2951C2211yescharacteristic, complemented
81#2950C2211yescharacteristic, complemented
82C2×C4×Q16C2211yescharacteristic
83#2251C2211yescharacteristic
84#2251C2211yescharacteristic, complemented
85#2249C2211yescharacteristic
86#2249C2211yescharacteristic
87#2249C2211yescharacteristic
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2243C2211yescharacteristic
91#2242C2211yescharacteristic
92#2242C2211yescharacteristic
93#2242C2211yescharacteristic
94#2241C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2236C2211yescharacteristic
97#2236C2211yescharacteristic
98#2236C2211yescharacteristic, complemented
99#2234C2211yescharacteristic
100#2232C2211yescharacteristic
101#2229C2211yescharacteristic, complemented
102#2229C2211yescharacteristic, complemented
103#2229C2211yescharacteristic, complemented
104#2228C2211yescharacteristic
105#2227C2211yescharacteristic, complemented
106#2227C2211yescharacteristic, complemented
107#2227C2211yescharacteristic, complemented
108#2225C2211yescharacteristic, complemented
109#2224C2211yescharacteristic
110#2224C2211yescharacteristic, complemented
111#2220C2211yescharacteristic
112#2220C2211yescharacteristic
113#2220C2211yescharacteristic, complemented
114#2219C2211yescharacteristic, complemented
115#2217C2211yescharacteristic
116#2217C2211yescharacteristic
117#2217C2211yescharacteristic
118#2216C2211yescharacteristic
119#2216C2211yescharacteristic
120#2216C2211yescharacteristic, complemented
121#2216C2211yescharacteristic, complemented
122#2215C2211yescharacteristic
123#2211C2211yescharacteristic
124#2211C2211yescharacteristic
125#2211C2211yescharacteristic
126#2211C2211yescharacteristic
127#2211C2211yescharacteristic
128#2211C2211yescharacteristic
129#2211C2211yescharacteristic
130#2211C2211yescharacteristic
131#2211C2211yescharacteristic
132#2211C2211yescharacteristic
133#2211C2211yescharacteristic
134#2211C2211yescharacteristic
135#2211C2211yescharacteristic
136#2211C2211yescharacteristic, complemented
137#2211C2211yescharacteristic, complemented
138#2211C2211yescharacteristic, complemented
139#2210C2211yescharacteristic
140#2210C2211yescharacteristic
141#2210C2211yescharacteristic
142#2210C2211yescharacteristic
143#2209C2211yescharacteristic, complemented
144#2209C2211yescharacteristic, complemented
145#2209C2211yescharacteristic, complemented
146#2209C2211yescharacteristic, complemented
147#2209C2211yescharacteristic, complemented
148#2209C2211yescharacteristic, complemented
149#2209C2211yescharacteristic, complemented
150#2208C2211yescharacteristic
151#2208C2211yescharacteristic, complemented
152#2208C2211yescharacteristic, complemented
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2189C2211yescharacteristic
156#2189C2211yescharacteristic, complemented
157#2188C2211yescharacteristic
158#2188C2211yescharacteristic
159#2188C2211yescharacteristic
160#2188C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2188C2211yescharacteristic, complemented
163#2188C2211yescharacteristic, complemented
164#2187C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic
167#2185C2211yescharacteristic
168#2185C2211yescharacteristic
169#2185C2211yescharacteristic, complemented
170#2184C2211yescharacteristic
171#2183C2211yescharacteristic, complemented
172Q8×C16C2211yescharacteristic, complemented
173#2176C2211yescharacteristic, complemented
174#2175C2211yescharacteristic
175#2175C2211yescharacteristic
176#2175C2211yescharacteristic, complemented
177C4×Q32C2211yescharacteristic, complemented
178C4×Q32C2211yescharacteristic, complemented
179C4×Q32C2211yescharacteristic, complemented
180C4×Q32C2211yescharacteristic, complemented
181C4×Q32C2211yescharacteristic, complemented
182C4×Q32C2211yescharacteristic, complemented
183C4×SD32C2211yescharacteristic
184C4×D16C2211yescharacteristic
185#2169C2211yescharacteristic, complemented
186#2168C2211yescharacteristic
187#2168C2211yescharacteristic
188D4×C16C2211yescharacteristic
189D4×C16C2211yescharacteristic
190D4×C16C2211yescharacteristic, complemented
191#2164C2211yescharacteristic, complemented
192#2164C2211yescharacteristic, complemented
193#2162C2211yescharacteristic
194#2151C2211yescharacteristic, complemented
195#2151C2211yescharacteristic, complemented
196C2×C4⋊C16C2211yescharacteristic
197#2141C2211yescharacteristic, complemented
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200C2×#358C2211yescharacteristic
201C2×#358C2211yescharacteristic, complemented
202C2×#357C2211yescharacteristic
203C2×#137—21no—
204C2×#137—21no—
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×SD16—21no—
214C22×D8C2311yescharacteristic
215#563—41no—
216#562—41no—
217#557—21no—
218#556—21no—
219#556—21no—
220#556—21no—
221#556—41no—
222#554—21no—
223#554—41no—
224#553—21no—
225#553—41no—
226#552—21no—
227#552—41no—
228#551—41no—
229#551—41no—
230D4×Q8—21no—
231D4×Q8—21no—
232D4×Q8—21no—
233#548—21no—
234#548—21no—
235#548—21no—
236#548—21no—
237#546—21no—
238#546—21no—
239#543—41no—
240#542—21no—
241#542—21no—
242#542—21no—
243#542—41no—
244#542—41no—
245#542—41no—
246#541—21no—
247#541—41no—
248#538—41no—
249#536—21no—
250#536—21no—
251#533—21no—
252#529—21no—
253#529—41no—
254#529—41no—
255#529D411yescharacteristic
256C2×#124—21no—
257#520—21no—
258#519—21no—
259C2×C4×Q8—21no—
260#510—42no—
261#510—42no—
262#508—42no—
263C2×Q32—42no—
264C2×Q32—42no—
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×Q32C2311yescharacteristic
268C2×Q32C2311yescharacteristic
269C2×Q32C2311yescharacteristic
270C2×Q32C2311yescharacteristic
271C2×Q32C2311yescharacteristic
272C2×Q32C2311yescharacteristic
273C2×Q32C2311yescharacteristic
274C2×Q32C2311yescharacteristic
275C2×Q32C2311yescharacteristic
276C2×Q32C2311yescharacteristic
277C2×SD32—42no—
278C2×SD32C2311yescharacteristic
279C2×SD32C2311yescharacteristic
280C2×SD32C2311yescharacteristic
281C2×SD32C2311yescharacteristic
282C2×SD32C2311yescharacteristic
283C2×SD32C2311yescharacteristic
284C2×SD32C2311yescharacteristic
285C2×SD32C2311yescharacteristic
286C2×SD32C2311yescharacteristic
287C2×SD32C2311yescharacteristic
288C2×D16C2311yescharacteristic
289C2×D16C2311yescharacteristic
290C2×M32C2311yescharacteristic
291C2×M32C2311yescharacteristic
292C22×C16C2311yescharacteristic
293C22×C16C2311yescharacteristic
294C22×C16C2311yescharacteristic
295C22×C16C2311yescharacteristic
296#500C2311yescharacteristic
297#500C2311yescharacteristic
298#499C2311yescharacteristic
299#499C2311yescharacteristic
300#497—21no—
301#497—21no—
302#497—21no—
303#497—21no—
304#495—21no—
305#495—21no—
306#495C2311yescharacteristic
307#495C2311yescharacteristic
308#495C2311yescharacteristic
309#495C2311yescharacteristic
310#495C2311yescharacteristic
311#495C2311yescharacteristic
312#495C2311yescharacteristic
313#495C2311yescharacteristic
314#494C2311yescharacteristic
315#494C2311yescharacteristic
316#494C2311yescharacteristic
317#494C2311yescharacteristic
318#491—21no—
319#489—21no—
320#489—21no—
321#489—21no—
322#488—21no—
323#487—21no—
324#485—21no—
325#484—21no—
326#484—21no—
327#483—21no—
328#482—21no—
329#481—21no—
330#479—21no—
331#479—21no—
332#479—21no—
333#478—21no—
334#477—21no—
335#475—21no—
336#470—21no—
337#468—21no—
338#468—21no—
339#468—21no—
340#467—21no—
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#467C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#466C2311yescharacteristic
353#465—21no—
354#464—21no—
355#464—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#464—21no—
360#464—21no—
361#464—21no—
362#464—21no—
363#464—21no—
364#463—21no—
365#463—21no—
366#462—21no—
367#462—21no—
368#462—21no—
369#461—21no—
370#461—21no—
371#461—21no—
372#452—21no—
373#452—21no—
374#452—21no—
375#452—21no—
376#451—21no—
377#451—21no—
378#451—21no—
379#451—21no—
380#451—21no—
381#451—21no—
382#450—21no—
383#450—21no—
384#449—21no—
385#449—21no—
386#448—21no—
387#448—21no—
388#448—21no—
389#448—21no—
390#446D411yescharacteristic
391C8×Q8C2311yescharacteristic
392#441—21no—
393#441—21no—
394#441—21no—
395#440—21no—
396#440—21no—
397#440—21no—
398#440—21no—
399#440—21no—
400C4×Q16—21no—
401C4×Q16—21no—
402C4×Q16—21no—
403C4×Q16C2311yescharacteristic
404C4×Q16C2311yescharacteristic
405C4×Q16C2311yescharacteristic
406C4×Q16C2311yescharacteristic
407C4×Q16C2311yescharacteristic
408C4×Q16C2311yescharacteristic
409C4×Q16C2311yescharacteristic
410C4×Q16C2311yescharacteristic
411C4×Q16C2311yescharacteristic
412C4×Q16C2311yescharacteristic
413C4×Q16C2311yescharacteristic
414C4×Q16C2311yescharacteristic
415C4×SD16—21no—
416C4×D8C2311yescharacteristic
417C4×D8C2311yescharacteristic
418C4×D8C2311yescharacteristic
419C4×D8C2311yescharacteristic
420#436D411yescharacteristic
421#435D411yescharacteristic
422#435D411yescharacteristic
423C8×D4C2311yescharacteristic
424C8×D4C2311yescharacteristic
425C8×D4C2311yescharacteristic
426#433D411yescharacteristic
427#433D411yescharacteristic
428#432D411yescharacteristic
429#427C2311yescharacteristic
430C2×#107C2311yescharacteristic
431C2×#107C2311yescharacteristic
432#419—21no—
433#417—21no—
434C2×#103—21no—
435#405C2311yescharacteristic
436#405C2311yescharacteristic
437C2×C4×C8C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
442#366C2311yescharacteristic
443#366C2311yescharacteristic
444#366C2311yescharacteristic
445#366C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
450C4⋊C16C2311yescharacteristic
451C4⋊C16C2311yescharacteristic
452C4⋊C16C2311yescharacteristic
453C4⋊C16C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#358C2311yescharacteristic
470#358C2311yescharacteristic
471#358C2311yescharacteristic
472#358C2311yescharacteristic
473#358C2311yescharacteristic
474#358C2311yescharacteristic
475#358C2311yescharacteristic
476#358C2311yescharacteristic
477#358C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488C22⋊C16C2311yescharacteristic
489C22⋊C16C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494#346C2311yescharacteristic
495#346C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C4×C16C2311yescharacteristic
498C4×C16C2311yescharacteristic
499C4×C16C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×D4—21no—
509#137—82no—
510#137—82no—
511#135—22no—
512#135—41no—
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—21no—
520C2×Q16—21no—
521C2×Q16—21no—
522C2×Q16—21no—
523C2×Q16—21no—
524C2×Q16—21no—
525C2×Q16—21no—
526C2×Q16—21no—
527C2×Q16—21no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16C2411yescharacteristic
537C2×Q16C2411yescharacteristic
538C2×Q16C2411yescharacteristic
539C2×Q16C2411yescharacteristic
540C2×Q16C2411yescharacteristic
541C2×Q16C2411yescharacteristic
542C2×Q16C2411yescharacteristic
543C2×SD16—21no—
544C2×SD16—21no—
545C2×SD16—21no—
546C2×SD16—21no—
547C2×SD16—21no—
548C2×SD16—21no—
549C2×SD16—21no—
550C2×SD16—21no—
551C2×SD16—21no—
552C2×SD16—21no—
553C2×SD16—21no—
554C2×SD16—82no—
555C2×D8—21no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8C2411yescharacteristic
559C2×D8C2411yescharacteristic
560C2×D8C2411yescharacteristic
561C2×M16C2×D411yescharacteristic
562C2×M16C2×D411yescharacteristic
563C22×C8C2×D411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—21no—
568C4⋊Q8—21no—
569C4⋊Q8—21no—
570C4⋊Q8—21no—
571C4⋊Q8—21no—
572C4⋊Q8—21no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#126—41no—
578#126—41no—
579#126—41no—
580#126—41no—
581#126—41no—
582#126—41no—
583#126—41no—
584#126—41no—
585#126—41no—
586#126—41no—
587#126—41no—
588#126—41no—
589#126—41no—
590#126—41no—
591#126D811yescharacteristic
592#126D811yescharacteristic
593#125—21no—
594#125—21no—
595#125—41no—
596#125—41no—
597#125—41no—
598#125—41no—
599#125—41no—
600#125—41no—
601#125—41no—
602#125D811yescharacteristic
603#124—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#124—21no—
608#124—21no—
609#124—21no—
610#124—21no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—41no—
618#124—41no—
619#124—41no—
620#124D811yescharacteristic
621#123—41no—
622#123—41no—
623#123—41no—
624#123—41no—
625#123—41no—
626#123—41no—
627#123—41no—
628#123—41no—
629#123—41no—
630#123—41no—
631#123—41no—
632#123—41no—
633#123D811yescharacteristic
634#123D811yescharacteristic
635C22⋊Q8—21no—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647C22⋊Q8—41no—
648C22⋊Q8—41no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—41no—
653C22⋊Q8—41no—
654C22⋊Q8—41no—
655C22⋊Q8—41no—
656C22⋊Q8—41no—
657C22⋊Q8—41no—
658C22⋊Q8—41no—
659C22⋊Q8—41no—
660C22⋊Q8—41no—
661C22⋊Q8—41no—
662C22⋊Q8—41no—
663C22⋊Q8—41no—
664C22⋊Q8—41no—
665C22⋊Q8—41no—
666C22⋊Q8D811yescharacteristic
667#121—21no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121—41no—
675#121—41no—
676#121—41no—
677#121—41no—
678#121D811yescharacteristic
679#120—41no—
680#120—41no—
681C4×Q8—21no—
682C4×Q8—21no—
683C4×Q8—21no—
684C4×Q8—21no—
685C4×Q8—21no—
686C4×Q8—21no—
687C4×Q8—21no—
688C4×Q8—21no—
689C4×Q8—21no—
690C4×Q8—21no—
691C4×Q8—21no—
692C4×Q8—21no—
693C4×Q8—41no—
694C4×Q8—41no—
695C4×Q8—41no—
696C4×Q8—41no—
697C4×Q8—41no—
698C4×Q8—41no—
699C4×Q8C2×D411yescharacteristic
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—41no—
705C4×D4—41no—
706C4×D4—41no—
707C4×D4—41no—
708C4×D4—41no—
709C4×D4—41no—
710C4×D4—41no—
711C4×D4—41no—
712C4×D4—41no—
713C4×D4—41no—
714C4×D4—41no—
715C4×D4—41no—
716C4×D4C2×D411yescharacteristic
717C4×D4C2×D411yescharacteristic
718C4×D4C2×D411yescharacteristic
719#117—21no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117—41no—
724#117—41no—
725#117—41no—
726#117—41no—
727#117—41no—
728#117—41no—
729#117C2×D411yescharacteristic
730#117C2×D411yescharacteristic
731C2×C4⋊C4—21no—
732C2×C4⋊C4—21no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C42—41no—
740C2×C42C2×D411yescharacteristic
741Q32—22no—
742Q32—22no—
743Q32—22no—
744Q32—22no—
745Q32—41no—
746Q32—41no—
747Q32—41no—
748Q32—41no—
749Q32—41no—
750Q32—41no—
751Q32—41no—
752Q32—41no—
753SD32—22no—
754SD32—22no—
755SD32—41no—
756SD32—41no—
757SD32—41no—
758SD32—41no—
759SD32—41no—
760SD32—41no—
761SD32—41no—
762SD32—41no—
763D16—41no—
764D16—41no—
765M32—41no—
766M32—41no—
767C2×C16—41no—
768C2×C16—41no—
769C2×C16—41no—
770C2×C16—41no—
771C2×C16C2411yescharacteristic
772C2×C16C2411yescharacteristic
773C2×C16C2411yescharacteristic
774C2×C16C2411yescharacteristic
775C2×C16C2411yescharacteristic
776C2×C16C2411yescharacteristic
777C2×C16C2411yescharacteristic
778C2×C16C2411yescharacteristic
779#107—21no—
780#107—21no—
781#107—21no—
782#107—21no—
783#107C2411yescharacteristic
784#107C2411yescharacteristic
785#107C2411yescharacteristic
786#107C2411yescharacteristic
787#107C2411yescharacteristic
788#107C2411yescharacteristic
789#106—21no—
790#106—21no—
791#106—21no—
792C4⋊C8C2×D411yescharacteristic
793C4⋊C8C2×D411yescharacteristic
794C4⋊C8C2×D411yescharacteristic
795C4⋊C8C2×D411yescharacteristic
796C4⋊C8C2×D411yescharacteristic
797C4⋊C8C2×D411yescharacteristic
798#103—21no—
799#103—21no—
800#103—21no—
801#103—21no—
802#103—21no—
803#103—21no—
804#103—21no—
805#103—21no—
806#103—21no—
807#103—21no—
808#103—21no—
809#103—21no—
810#103—21no—
811#103—21no—
812#103—21no—
813#103—21no—
814#103—21no—
815#103—21no—
816#103—21no—
817#103—21no—
818#102—21no—
819#102—21no—
820#102—21no—
821#102—21no—
822#102—21no—
823#102—21no—
824#102—21no—
825#102—21no—
826C22⋊C8C2×D411yescharacteristic
827C22⋊C8C2×D411yescharacteristic
828C22⋊C8C2×D411yescharacteristic
829C22⋊C8C2×D411yescharacteristic
830C22⋊C8C2×D411yescharacteristic
831C22⋊C8C2×D411yescharacteristic
832#97C2×D411yescharacteristic
833#97C2×D411yescharacteristic
834#97C2×D411yescharacteristic
835#97C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2×D411yescharacteristic
838C4×C8C2411yescharacteristic
839C4×C8C2411yescharacteristic
840C4×C8C2411yescharacteristic
841C4×C8C2411yescharacteristic
842C24—41no—
843#41—42no—
844#41—81no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—81no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—41no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—41no—
864C2×Q8—41no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8C2×D811yescharacteristic
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4C2×D811yescharacteristic
888C2×D4C2×D811yescharacteristic
889C2×D4C2×D811yescharacteristic
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4C2×D811yescharacteristic
905C22×C4C2×D811yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909Q16—21no—
910Q16—21no—
911Q16—21no—
912Q16—21no—
913Q16—21no—
914Q16—21no—
915Q16—21no—
916Q16—21no—
917Q16—21no—
918Q16—21no—
919Q16—21no—
920Q16—21no—
921Q16—21no—
922Q16—42no—
923Q16—42no—
924Q16—42no—
925Q16—81no—
926Q16—81no—
927Q16—81no—
928Q16—81no—
929Q16—81no—
930Q16—81no—
931Q16H(5,𝔽2)12yes—
932SD16—42no—
933SD16—42no—
934SD16—42no—
935SD16—81no—
936SD16—81no—
937SD16—81no—
938SD16—81no—
939SD16—81no—
940SD16—81no—
941SD16—81no—
942SD16—81no—
943D8—21no—
944D8—21no—
945D8—21no—
946D8—21no—
947D8—21no—
948D8—21no—
949D8—81no—
950M16—41no—
951M16—41no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—41no—
959C2×C8C22×D411yescharacteristic
960C2×C8C22×D411yescharacteristic
961C2×C8C22×D411yescharacteristic
962C2×C8C22×D411yescharacteristic
963C2×C8C22×D411yescharacteristic
964C2×C8C22×D411yescharacteristic
965C2×C8C22×D411yescharacteristic
966C2×C8C2511yescharacteristic
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4C2×D811yescharacteristic
1010C4⋊C4C2×D811yescharacteristic
1011C4⋊C4C2×D811yescharacteristic
1012C4⋊C4C2×D811yescharacteristic
1013C4⋊C4C2×D811yescharacteristic
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C4⋊C4C2×D811yescharacteristic
1018C4⋊C4C2×D811yescharacteristic
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4C2×D811yescharacteristic
1053C22⋊C4C2×D811yescharacteristic
1054C22⋊C4C2×D811yescharacteristic
1055C22⋊C4C2×D811yescharacteristic
1056C22⋊C4C2×D811yescharacteristic
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42—41no—
1075C42C2×D811yescharacteristic
1076C42C2×D811yescharacteristic
1077C42C22×D411yescharacteristic
1078C42C22×D411yescharacteristic
1079C42C22×D411yescharacteristic
1080C42C22×D411yescharacteristic
1081C16—21no—
1082C16—21no—
1083C16—21no—
1084C16—21no—
1085C16—21no—
1086C16—21no—
1087C16—21no—
1088C16—21no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—82no—
1093C23—161no—
1094C23—161no—
1095C23C22×D811yescharacteristic
1096C23C22×D811yescharacteristic
1097C23C22×D811yescharacteristic
1098Q8—22no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—82no—
1114Q8—82no—
1115Q8—161no—
1116Q8—161no—
1117Q8—161no—
1118Q8—161no—
1119Q8—161no—
1120D4—22no—
1121D4—22no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—82no—
1130D4—82no—
1131D4—161no—
1132D4—161no—
1133D4—161no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—82no—
1159C2×C4—82no—
1160C2×C4—82no—
1161C2×C4—161no—
1162C2×C4—161no—
1163C2×C4—161no—
1164C2×C4—161no—
1165C2×C4—161no—
1166C2×C4—161no—
1167C2×C4—161no—
1168C2×C4—161no—
1169C2×C4—161no—
1170C2×C4—161no—
1171C2×C4—161no—
1172C2×C4C22×D811yescharacteristic
1173C2×C4C22×D811yescharacteristic
1174C2×C4C22×D811yescharacteristic
1175C2×C4C22×D811yescharacteristic
1176C2×C4C22×D811yescharacteristic
1177C2×C4C22×D811yescharacteristic
1178C2×C4C22×D811yescharacteristic
1179C2×C4C22×D811yescharacteristic
1180C2×C4C22×D811yescharacteristic
1181C2×C4C22×D811yescharacteristic
1182C2×C4C22×D811yescharacteristic
1183C2×C4C23×D411yescharacteristic
1184C8—21no—
1185C8—21no—
1186C8—21no—
1187C8—21no—
1188C8—21no—
1189C8—21no—
1190C8—21no—
1191C8C2×H(5,𝔽2)11yescharacteristic
1192C8#58511yescharacteristic
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—322no—
1211C22#341712yes—
1212C22C23×D811yescharacteristic
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—42no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4#348811yescharacteristic
1238C4#358511yescharacteristic
1239C2—22no—
1240C2—41no—
1241C2—41no—
1242C2—161no—
1243C2—161no—
1244C2—161no—
1245C2#6194711yescharacteristic
1246C2C2×#341711yescharacteristic
1247C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #62437C2semidirect
2. #61473C2semidirect
3. #33969C2semidirect
4. #33960C2semidirect
5. #33944C2semidirect
6. #33931C2semidirect
7. #33894C2semidirect
8. #33887C2semidirect
9. #33881C2semidirect
10. #33867C2semidirect
11. #33866C2semidirect
12. #33864C2semidirect
13. D4×Q32C2semidirect
14. #33851C2semidirect
15. #33848C2semidirect
16. #33843C2semidirect
17. #33836C2semidirect
18. #33832C2semidirect
19. #33828C2semidirect
20. #33824C2semidirect
21. #33814C2semidirect
22. #33791C2semidirect
23. #33789C2semidirect
24. #33777C2semidirect
25. #33684C2semidirect
26. #33681C2semidirect
27. #33664C2semidirect
28. #33590C2semidirect
29. #33588C2semidirect
30. C2×#2211C2semidirect
31. #33508C2semidirect
35. C2×#510C22semidirect
38. C22×Q32C22semidirect
43. #3393C22semidirect
44. #3383C22semidirect
48. #3336C22semidirect
58. #3285C22semidirect
67. #3177C22semidirect
70. #3175C22semidirect
80. #2951C22semidirect
81. #2950C22semidirect
84. #2251C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
94. #2241C22semidirect
95. #2237C22semidirect
98. #2236C22semidirect
101. #2229C22semidirect
102. #2229C22semidirect
103. #2229C22semidirect
105. #2227C22semidirect
106. #2227C22semidirect
107. #2227C22semidirect
108. #2225C22semidirect
110. #2224C22semidirect
113. #2220C22semidirect
114. #2219C22semidirect
120. #2216C22semidirect
121. #2216C22semidirect
136. #2211C22semidirect
137. #2211C22semidirect
138. #2211C22semidirect
143. #2209C22semidirect
144. #2209C22semidirect
145. #2209C22semidirect
146. #2209C22semidirect
147. #2209C22semidirect
148. #2209C22semidirect
149. #2209C22semidirect
151. #2208C22semidirect
152. #2208C22semidirect
156. #2189C22semidirect
160. #2188C22semidirect
161. #2188C22semidirect
162. #2188C22semidirect
163. #2188C22semidirect
169. #2185C22semidirect
171. #2183C22semidirect
172. Q8×C16C22semidirect
173. #2176C22semidirect
176. #2175C22semidirect
177. C4×Q32C22semidirect
178. C4×Q32C22semidirect
179. C4×Q32C22semidirect
180. C4×Q32C22semidirect
181. C4×Q32C22semidirect
182. C4×Q32C22semidirect
185. #2169C22semidirect
190. D4×C16C22semidirect
191. #2164C22semidirect
192. #2164C22semidirect
194. #2151C22semidirect
195. #2151C22semidirect
197. #2141C22semidirect
201. C2×#358C22semidirect

Maximal subgroups

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

subgroupindex
#624372
#614732
#339692
#339602
#339442
#339312
#338942
#338872
#338812
#338672
#338662
#338642
D4×Q322
#338512
#338482
#338432
#338362
#338322
#338282
#338242
#338142
#337912
#337892
#337772
#336842
#336812
#336642
#335902
#335882
C2×#22112
#335082