Finite Group Databasebeta

← #7624642

Subgroups — #7624642

Order 512.

1353 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62440C211yesmaximal, characteristic, complemented
2#61471C211yesmaximal, characteristic, complemented
3#33968C211yesmaximal, characteristic, complemented
4#33966C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33933C211yesmaximal, characteristic, complemented
7#33899C211yesmaximal, characteristic, complemented
8#33890C211yesmaximal, characteristic, complemented
9#33885C211yesmaximal, characteristic, complemented
10#33884C211yesmaximal, characteristic, complemented
11#33874C211yesmaximal, characteristic, complemented
12#33873C211yesmaximal, characteristic, complemented
13#33840C211yesmaximal, characteristic, complemented
14#33839C211yesmaximal, characteristic, complemented
15#33834C211yesmaximal, characteristic, complemented
16#33833C211yesmaximal, characteristic, complemented
17#33830C211yesmaximal, characteristic, complemented
18#33830C211yesmaximal, characteristic, complemented
19#33829C211yesmaximal, characteristic, complemented
20#33823C211yesmaximal, characteristic, complemented
21#33817C211yesmaximal, characteristic, complemented
22#33790C211yesmaximal, characteristic, complemented
23#33786C211yesmaximal, characteristic, complemented
24#33785C211yesmaximal, characteristic, complemented
25#33685C211yesmaximal, characteristic, complemented
26#33678C211yesmaximal, characteristic, complemented
27#33669C211yesmaximal, characteristic, complemented
28#33589C211yesmaximal, characteristic, complemented
29#33585C211yesmaximal, characteristic, complemented
30#33580C211yesmaximal, characteristic, complemented
31#33509C211yesmaximal, characteristic, complemented
32#3546—21no—
33#3513—21no—
34C2×#509C2211yescharacteristic
35C2×#509C2211yescharacteristic, complemented
36C2×#509C2211yescharacteristic, complemented
37C2×#509C2211yescharacteristic, complemented
38C2×#508C2211yescharacteristic, complemented
39C22×D16C2211yescharacteristic
40#3397—21no—
41#3396C2211yescharacteristic, complemented
42#3393C2211yescharacteristic, complemented
43#3391C2211yescharacteristic, complemented
44#3380C2211yescharacteristic, complemented
45#3370—21no—
46#3339C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3334C2211yescharacteristic, complemented
49#3322—21no—
50#3310—21no—
51#3306—21no—
52#3287C2211yescharacteristic
53#3287C2211yescharacteristic, complemented
54#3283C2211yescharacteristic, complemented
55#3280C2211yescharacteristic
56#3280C2211yescharacteristic
57#3280C2211yescharacteristic, complemented
58#3280C2211yescharacteristic, complemented
59D4×D8C2211yescharacteristic, complemented
60D4×D8C2211yescharacteristic, complemented
61#3272—21no—
62#3268—21no—
63#3268—21no—
64#3224—21no—
65#3224—21no—
66#3214—21no—
67#3176C2211yescharacteristic, complemented
68#3175C2211yescharacteristic, complemented
69#3175C2211yescharacteristic, complemented
70#3175C2211yescharacteristic, complemented
71#3169C2211yescharacteristic, complemented
72#3168C2211yescharacteristic, complemented
73#3155C2211yescharacteristic, complemented
74#3155C2211yescharacteristic, complemented
75#3147C2211yescharacteristic, complemented
76#3119—21no—
77#3118—21no—
78#3114—21no—
79#2966C2211yescharacteristic
80#2951C2211yescharacteristic, complemented
81#2948C2211yescharacteristic, complemented
82C2×C4×D8C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2250C2211yescharacteristic
85#2250C2211yescharacteristic, complemented
86#2250C2211yescharacteristic, complemented
87#2249C2211yescharacteristic, complemented
88#2246C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2244C2211yescharacteristic, complemented
91#2244C2211yescharacteristic, complemented
92#2243C2211yescharacteristic, complemented
93#2242C2211yescharacteristic, complemented
94#2240C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2235C2211yescharacteristic, complemented
97#2234C2211yescharacteristic, complemented
98#2233C2211yescharacteristic, complemented
99#2233C2211yescharacteristic, complemented
100#2233C2211yescharacteristic, complemented
101#2229C2211yescharacteristic, complemented
102#2228C2211yescharacteristic, complemented
103#2228C2211yescharacteristic, complemented
104#2228C2211yescharacteristic, complemented
105#2226C2211yescharacteristic, complemented
106#2226C2211yescharacteristic, complemented
107#2226C2211yescharacteristic, complemented
108#2225C2211yescharacteristic, complemented
109#2225C2211yescharacteristic, complemented
110#2224C2211yescharacteristic, complemented
111#2220C2211yescharacteristic, complemented
112#2220C2211yescharacteristic, complemented
113#2220C2211yescharacteristic, complemented
114#2219C2211yescharacteristic, complemented
115#2218C2211yescharacteristic
116#2218C2211yescharacteristic
117#2218C2211yescharacteristic, complemented
118#2218C2211yescharacteristic, complemented
119#2217C2211yescharacteristic, complemented
120#2217C2211yescharacteristic, complemented
121#2217C2211yescharacteristic, complemented
122#2215C2211yescharacteristic, complemented
123#2211C2211yescharacteristic, complemented
124#2211C2211yescharacteristic, complemented
125#2211C2211yescharacteristic, complemented
126#2211C2211yescharacteristic, complemented
127#2210C2211yescharacteristic
128#2210C2211yescharacteristic
129#2210C2211yescharacteristic, complemented
130#2210C2211yescharacteristic, complemented
131#2210C2211yescharacteristic, complemented
132#2210C2211yescharacteristic, complemented
133#2210C2211yescharacteristic, complemented
134#2210C2211yescharacteristic, complemented
135#2210C2211yescharacteristic, complemented
136#2210C2211yescharacteristic, complemented
137#2210C2211yescharacteristic, complemented
138#2210C2211yescharacteristic, complemented
139#2208C2211yescharacteristic, complemented
140#2208C2211yescharacteristic, complemented
141#2207C2211yescharacteristic, complemented
142#2207C2211yescharacteristic, complemented
143#2207C2211yescharacteristic, complemented
144#2206C2211yescharacteristic
145#2206C2211yescharacteristic
146#2206C2211yescharacteristic, complemented
147#2206C2211yescharacteristic, complemented
148#2206C2211yescharacteristic, complemented
149#2206C2211yescharacteristic, complemented
150#2206C2211yescharacteristic, complemented
151#2206C2211yescharacteristic, complemented
152#2206C2211yescharacteristic, complemented
153#2189C2211yescharacteristic, complemented
154#2189C2211yescharacteristic, complemented
155#2189C2211yescharacteristic, complemented
156#2189C2211yescharacteristic, complemented
157#2187C2211yescharacteristic, complemented
158#2187C2211yescharacteristic, complemented
159#2186C2211yescharacteristic
160#2186C2211yescharacteristic, complemented
161#2186C2211yescharacteristic, complemented
162#2186C2211yescharacteristic, complemented
163#2186C2211yescharacteristic, complemented
164#2186C2211yescharacteristic, complemented
165#2184C2211yescharacteristic
166#2184C2211yescharacteristic
167#2184C2211yescharacteristic
168#2184C2211yescharacteristic, complemented
169#2184C2211yescharacteristic, complemented
170#2184C2211yescharacteristic, complemented
171#2183C2211yescharacteristic, complemented
172#2183C2211yescharacteristic, complemented
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic, complemented
175#2177C2211yescharacteristic, complemented
176#2177C2211yescharacteristic, complemented
177#2177C2211yescharacteristic, complemented
178#2177C2211yescharacteristic, complemented
179#2176C2211yescharacteristic, complemented
180#2175C2211yescharacteristic, complemented
181C4×SD32C2211yescharacteristic, complemented
182C4×SD32C2211yescharacteristic, complemented
183C4×SD32C2211yescharacteristic, complemented
184C4×D16C2211yescharacteristic, complemented
185#2169C2211yescharacteristic, complemented
186#2169C2211yescharacteristic, complemented
187#2168C2211yescharacteristic, complemented
188#2168C2211yescharacteristic, complemented
189#2168C2211yescharacteristic, complemented
190#2168C2211yescharacteristic, complemented
191#2164C2211yescharacteristic, complemented
192#2164C2211yescharacteristic, complemented
193#2163C2211yescharacteristic, complemented
194#2151C2211yescharacteristic, complemented
195#2151C2211yescharacteristic, complemented
196#2150C2211yescharacteristic, complemented
197#2140C2211yescharacteristic, complemented
198#2139C2211yescharacteristic, complemented
199#2139C2211yescharacteristic, complemented
200#2139C2211yescharacteristic, complemented
201#2138C2211yescharacteristic, complemented
202C2×#357C2211yescharacteristic, complemented
203C2×AGL(1,ℤ/8)—21no—
204C2×AGL(1,ℤ/8)—21no—
205C2×#135—21no—
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C2×#135C2311yescharacteristic
209C2×#135C2311yescharacteristic
210C2×#135C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#560—41no—
216#560—41no—
217#559—21no—
218#556—21no—
219#554—21no—
220#553—21no—
221#553—41no—
222#553—41no—
223#552—21no—
224#551—41no—
225#551—41no—
226#550—21no—
227#550—21no—
228#550—21no—
229#547—21no—
230#547—21no—
231#546—21no—
232#546—21no—
233#546—21no—
234#546—21no—
235#546—41no—
236#546—41no—
237D42—21no—
238D42—21no—
239#542—21no—
240#542—21no—
241#542—21no—
242#540—21no—
243#539—41no—
244#538—41no—
245#538—41no—
246#538—41no—
247#537—41no—
248#535—21no—
249#535—21no—
250#535—41no—
251#532—21no—
252#532—21no—
253#529—21no—
254#529D411yescharacteristic
255#525—41no—
256C2×#123—41no—
257#520—21no—
258#518—21no—
259C2×C4×D4—21no—
260#509—42no—
261#509—42no—
262#509—42no—
263#509—42no—
264#508—42no—
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×SD32C2311yescharacteristic
276C2×SD32C2311yescharacteristic
277C2×D16—42no—
278C2×D16C2311yescharacteristic
279C2×D16C2311yescharacteristic
280C2×D16C2311yescharacteristic
281C2×D16C2311yescharacteristic
282C2×D16C2311yescharacteristic
283C2×D16C2311yescharacteristic
284C2×D16C2311yescharacteristic
285C2×D16C2311yescharacteristic
286C2×D16C2311yescharacteristic
287C2×D16C2311yescharacteristic
288C2×D16C2311yescharacteristic
289C2×D16C2311yescharacteristic
290C2×M32C2311yescharacteristic
291C2×M32C2311yescharacteristic
292C2×M32C2311yescharacteristic
293C2×M32C2311yescharacteristic
294C22×C16C2311yescharacteristic
295C22×C16C2311yescharacteristic
296#500C2311yescharacteristic
297#500C2311yescharacteristic
298#499C2311yescharacteristic
299#499C2311yescharacteristic
300#496—21no—
301#496—21no—
302#496—21no—
303#496—21no—
304#495—21no—
305#495C2311yescharacteristic
306#495C2311yescharacteristic
307#495C2311yescharacteristic
308#495C2311yescharacteristic
309#495C2311yescharacteristic
310#495C2311yescharacteristic
311#494C2311yescharacteristic
312#493C2311yescharacteristic
313#493C2311yescharacteristic
314#493C2311yescharacteristic
315#493C2311yescharacteristic
316#493C2311yescharacteristic
317#492—21no—
318#490—21no—
319#489—21no—
320#489—21no—
321#489—21no—
322#488—21no—
323#486—21no—
324#485—21no—
325#483—21no—
326#482—21no—
327#481—21no—
328#480—21no—
329#480—21no—
330#479—21no—
331#478—21no—
332#478—21no—
333#478—21no—
334#476—21no—
335#474—21no—
336#469—21no—
337#468—21no—
338#468—21no—
339#468—21no—
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#466—21no—
345#466C2311yescharacteristic
346#466C2311yescharacteristic
347#466C2311yescharacteristic
348#466C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#466C2311yescharacteristic
353#465—21no—
354#464—21no—
355#464—21no—
356#463—21no—
357#463—21no—
358#463—21no—
359#463—21no—
360#463—21no—
361#463—21no—
362#461—21no—
363#461—21no—
364#460—21no—
365#460—21no—
366#460—21no—
367#459—21no—
368#459—21no—
369#459—21no—
370#459—21no—
371#459—21no—
372#452—21no—
373#452—21no—
374#450—21no—
375#450—21no—
376#450—21no—
377#450—21no—
378#449—21no—
379#449—21no—
380#449—21no—
381#449—21no—
382#449—21no—
383#449—21no—
384#449—21no—
385#449—21no—
386#447—21no—
387#447—21no—
388#447—21no—
389#447—21no—
390#446D411yescharacteristic
391C8×Q8C2311yescharacteristic
392#442—21no—
393#442—21no—
394#442—21no—
395#440—21no—
396#440—21no—
397#440—21no—
398#440—21no—
399#440—21no—
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×Q16C2311yescharacteristic
403C4×Q16C2311yescharacteristic
404C4×SD16—21no—
405C4×D8—21no—
406C4×D8—21no—
407C4×D8—21no—
408C4×D8C2311yescharacteristic
409C4×D8C2311yescharacteristic
410C4×D8C2311yescharacteristic
411C4×D8C2311yescharacteristic
412C4×D8C2311yescharacteristic
413C4×D8C2311yescharacteristic
414C4×D8C2311yescharacteristic
415C4×D8C2311yescharacteristic
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#418—21no—
433#417—21no—
434C2×#102—21no—
435#405C2311yescharacteristic
436#405C2311yescharacteristic
437C2×C4×C8C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
442#367C2311yescharacteristic
443#367C2311yescharacteristic
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#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
469#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
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
496#346C2311yescharacteristic
497#346C2311yescharacteristic
498C4×C16C2311yescharacteristic
499C4×C16C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C23×C4—41no—
515AGL(1,ℤ/8)—82no—
516AGL(1,ℤ/8)—82no—
517#135—22no—
518#135—41no—
519#135—41no—
520#135—41no—
521#135—41no—
522#135—41no—
523#135—41no—
524#135—41no—
525#135—41no—
526#135—41no—
527#135—82no—
528C2×Q16—21no—
529C2×Q16C2411yescharacteristic
530C2×Q16C2411yescharacteristic
531C2×Q16C2411yescharacteristic
532C2×SD16—21no—
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×SD16—21no—
541C2×SD16—21no—
542C2×SD16—21no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—21no—
546C2×D8—21no—
547C2×D8—21no—
548C2×D8—21no—
549C2×D8—21no—
550C2×D8—21no—
551C2×D8—21no—
552C2×D8—21no—
553C2×D8—21no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8C2411yescharacteristic
561C2×D8C2411yescharacteristic
562C2×D8C2411yescharacteristic
563C2×D8C2411yescharacteristic
564C2×D8C2411yescharacteristic
565C2×D8C2411yescharacteristic
566C2×D8C2411yescharacteristic
567C2×M16C2×D411yescharacteristic
568C2×M16C2×D411yescharacteristic
569C22×C8C2×D411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—21no—
574C4⋊Q8—21no—
575C4⋊Q8—21no—
576#127—21no—
577#127—21no—
578#127—21no—
579#127—21no—
580#127—21no—
581#127—41no—
582#127—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#125D811yescharacteristic
597#124—21no—
598#124—21no—
599#124—21no—
600#124—21no—
601#124—21no—
602#124—21no—
603#124—41no—
604#124—41no—
605#124—41no—
606#124—41no—
607#124—41no—
608#124D811yescharacteristic
609#123—41no—
610#123—41no—
611#123—41no—
612#123—41no—
613#123—41no—
614#123—41no—
615#123—41no—
616#123—41no—
617#123—41no—
618#123—41no—
619#123—41no—
620#123—41no—
621#123—41no—
622#123—41no—
623#123—41no—
624#123—41no—
625#123—41no—
626#123—41no—
627#123D811yescharacteristic
628#123D811yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8D811yescharacteristic
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—41no—
651#121—41no—
652#121—41no—
653#121—41no—
654#121—41no—
655#121—41no—
656#121—41no—
657#121—41no—
658#121—41no—
659#121—41no—
660#121—41no—
661#121—41no—
662#121—41no—
663#121—41no—
664#121—41no—
665#121—41no—
666#121—41no—
667#121—41no—
668#121—41no—
669#121—41no—
670#121—41no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121D811yescharacteristic
675#120—41no—
676#120—41no—
677#120—41no—
678#120—41no—
679#120—41no—
680#120—41no—
681#120—41no—
682#120—41no—
683#120—41no—
684#120—41no—
685#120—41no—
686#120—41no—
687C4×Q8—21no—
688C4×Q8—21no—
689C4×Q8—21no—
690C4×Q8—21no—
691C4×Q8C2×D411yescharacteristic
692C4×D4—21no—
693C4×D4—21no—
694C4×D4—21no—
695C4×D4—21no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
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×D4—41no—
717C4×D4—41no—
718C4×D4C2×D411yescharacteristic
719C4×D4C2×D411yescharacteristic
720C4×D4C2×D411yescharacteristic
721#117—21no—
722#117—41no—
723#117—41no—
724#117—41no—
725#117—41no—
726#117C2×D411yescharacteristic
727#117C2×D411yescharacteristic
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—41no—
732C2×C4⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C42C2×D411yescharacteristic
741Q32—41no—
742Q32—41no—
743SD32—22no—
744SD32—22no—
745SD32—41no—
746SD32—41no—
747SD32—41no—
748SD32—41no—
749SD32—41no—
750SD32—41no—
751SD32—41no—
752SD32—41no—
753D16—22no—
754D16—22no—
755D16—22no—
756D16—22no—
757D16—41no—
758D16—41no—
759D16—41no—
760D16—41no—
761D16—41no—
762D16—41no—
763D16—41no—
764D16—41no—
765M32—41no—
766M32—41no—
767M32—41no—
768M32—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#102—21no—
807#102—21no—
808#102—21no—
809#102—21no—
810#102—21no—
811#102—21no—
812#102—21no—
813#102—21no—
814#102—21no—
815#102—21no—
816#102—21no—
817#102—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—
843C24—41no—
844C24—41no—
845C24—41no—
846#41—42no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851#41—81no—
852#41—81no—
853#41—81no—
854#41—81no—
855#41—81no—
856#41—162no—
857#41—162no—
858#41—162no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—41no—
863C2×Q8—41no—
864C2×Q8C2×D811yescharacteristic
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
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—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—162no—
908C2×D4—162no—
909C2×D4C2×D811yescharacteristic
910C2×D4C2×D811yescharacteristic
911C2×D4C2×D811yescharacteristic
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—162no—
932C22×C4C2×D811yescharacteristic
933C22×C4C2×D811yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937Q16—21no—
938Q16—21no—
939Q16—21no—
940Q16—21no—
941Q16—21no—
942Q16—21no—
943Q16—81no—
944SD16—42no—
945SD16—42no—
946SD16—42no—
947SD16—81no—
948SD16—81no—
949SD16—81no—
950SD16—81no—
951SD16—81no—
952SD16—81no—
953SD16—81no—
954SD16—81no—
955D8—21no—
956D8—21no—
957D8—21no—
958D8—21no—
959D8—21no—
960D8—21no—
961D8—21no—
962D8—21no—
963D8—21no—
964D8—21no—
965D8—21no—
966D8—21no—
967D8—21no—
968D8—42no—
969D8—42no—
970D8—42no—
971D8—81no—
972D8—81no—
973D8—81no—
974D8—81no—
975D8—81no—
976D8—81no—
977D8H(5,𝔽2)12yes—
978M16—41no—
979M16—41no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—41no—
987C2×C8C22×D411yescharacteristic
988C2×C8C22×D411yescharacteristic
989C2×C8C22×D411yescharacteristic
990C2×C8C22×D411yescharacteristic
991C2×C8C22×D411yescharacteristic
992C2×C8C22×D411yescharacteristic
993C2×C8C22×D411yescharacteristic
994C2×C8C2511yescharacteristic
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
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⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4C2×D811yescharacteristic
1020C4⋊C4C2×D811yescharacteristic
1021C4⋊C4C2×D811yescharacteristic
1022C4⋊C4C2×D811yescharacteristic
1023C4⋊C4C2×D811yescharacteristic
1024C4⋊C4C2×D811yescharacteristic
1025C4⋊C4C2×D811yescharacteristic
1026C4⋊C4C2×D811yescharacteristic
1027C4⋊C4C2×D811yescharacteristic
1028C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4C2×D811yescharacteristic
1067C22⋊C4C2×D811yescharacteristic
1068C22⋊C4C2×D811yescharacteristic
1069C22⋊C4C2×D811yescharacteristic
1070C22⋊C4C2×D811yescharacteristic
1071C22⋊C4C2×D811yescharacteristic
1072C22⋊C4C2×D811yescharacteristic
1073C22⋊C4C2×D811yescharacteristic
1074C22⋊C4C2×D811yescharacteristic
1075C22⋊C4C2×D811yescharacteristic
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—41no—
1080C42—41no—
1081C42C2×D811yescharacteristic
1082C42C2×D811yescharacteristic
1083C42C22×D411yescharacteristic
1084C42C22×D411yescharacteristic
1085C42C22×D411yescharacteristic
1086C42C22×D411yescharacteristic
1087C16—21no—
1088C16—21no—
1089C16—21no—
1090C16—21no—
1091C16—21no—
1092C16—21no—
1093C16—21no—
1094C16—21no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—82no—
1103C23—82no—
1104C23—82no—
1105C23—161no—
1106C23—161no—
1107C23—161no—
1108C23—161no—
1109C23—161no—
1110C23—161no—
1111C23—161no—
1112C23—161no—
1113C23—161no—
1114C23C22×D811yescharacteristic
1115C23C22×D811yescharacteristic
1116C23C22×D811yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—161no—
1125Q8—161no—
1126D4—22no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—82no—
1144D4—82no—
1145D4—82no—
1146D4—82no—
1147D4—82no—
1148D4—161no—
1149D4—161no—
1150D4—161no—
1151D4—161no—
1152D4—161no—
1153D4—161no—
1154D4—161no—
1155D4—161no—
1156D4—161no—
1157D4—161no—
1158D4—161no—
1159D4—161no—
1160D4—161no—
1161D4—161no—
1162D4—161no—
1163D4—161no—
1164D4—161no—
1165D4—161no—
1166D4—161no—
1167D4—161no—
1168D4—161no—
1169D4—161no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—82no—
1188C2×C4—82no—
1189C2×C4—82no—
1190C2×C4—82no—
1191C2×C4—161no—
1192C2×C4—161no—
1193C2×C4—161no—
1194C2×C4—161no—
1195C2×C4—161no—
1196C2×C4—161no—
1197C2×C4—161no—
1198C2×C4—161no—
1199C2×C4—161no—
1200C2×C4—161no—
1201C2×C4—161no—
1202C2×C4—161no—
1203C2×C4—161no—
1204C2×C4—161no—
1205C2×C4—161no—
1206C2×C4C22×D811yescharacteristic
1207C2×C4C22×D811yescharacteristic
1208C2×C4C22×D811yescharacteristic
1209C2×C4C22×D811yescharacteristic
1210C2×C4C22×D811yescharacteristic
1211C2×C4C22×D811yescharacteristic
1212C2×C4C22×D811yescharacteristic
1213C2×C4C22×D811yescharacteristic
1214C2×C4C22×D811yescharacteristic
1215C2×C4C22×D811yescharacteristic
1216C2×C4C22×D811yescharacteristic
1217C2×C4C23×D411yescharacteristic
1218C8—21no—
1219C8—21no—
1220C8—21no—
1221C8—21no—
1222C8—21no—
1223C8—21no—
1224C8—21no—
1225C8C2×H(5,𝔽2)11yescharacteristic
1226C8#58511yescharacteristic
1227C22—21no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—42no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—164no—
1258C22—322no—
1259C22—322no—
1260C22—322no—
1261C22C23×D811yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—21no—
1265C4—21no—
1266C4—21no—
1267C4—21no—
1268C4—21no—
1269C4—21no—
1270C4—21no—
1271C4—21no—
1272C4—21no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4#348811yescharacteristic
1283C4#358511yescharacteristic
1284C2—41no—
1285C2—41no—
1286C2—41no—
1287C2—82no—
1288C2—161no—
1289C2—161no—
1290C2—161no—
1291C2—161no—
1292C2—161no—
1293C2—161no—
1294C2#6194711yescharacteristic
1295C2#6263611yescharacteristic
1296C2#6263611yescharacteristic
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. #62440C2semidirect
2. #61471C2semidirect
3. #33968C2semidirect
4. #33966C2semidirect
5. #33943C2semidirect
6. #33933C2semidirect
7. #33899C2semidirect
8. #33890C2semidirect
9. #33885C2semidirect
10. #33884C2semidirect
11. #33874C2semidirect
12. #33873C2semidirect
13. #33840C2semidirect
14. #33839C2semidirect
15. #33834C2semidirect
16. #33833C2semidirect
17. #33830C2semidirect
18. #33830C2semidirect
19. #33829C2semidirect
20. #33823C2semidirect
21. #33817C2semidirect
22. #33790C2semidirect
23. #33786C2semidirect
24. #33785C2semidirect
25. #33685C2semidirect
26. #33678C2semidirect
27. #33669C2semidirect
28. #33589C2semidirect
29. #33585C2semidirect
30. #33580C2semidirect
31. #33509C2semidirect
35. C2×#509C22semidirect
36. C2×#509C22semidirect
37. C2×#509C22semidirect
38. C2×#508C22semidirect
41. #3396C22semidirect
42. #3393C22semidirect
43. #3391C22semidirect
44. #3380C22semidirect
47. #3336C22semidirect
48. #3334C22semidirect
53. #3287C22semidirect
54. #3283C22semidirect
57. #3280C22semidirect
58. #3280C22semidirect
59. D4×D8C22semidirect
60. D4×D8C22semidirect
67. #3176C22semidirect
68. #3175C22semidirect
69. #3175C22semidirect
70. #3175C22semidirect
71. #3169C22semidirect
72. #3168C22semidirect
73. #3155C22semidirect
74. #3155C22semidirect
75. #3147C22semidirect
80. #2951C22semidirect
81. #2948C22semidirect
82. C2×C4×D8C22semidirect
83. #2251C22semidirect
85. #2250C22semidirect
86. #2250C22semidirect
87. #2249C22semidirect
88. #2246C22semidirect
89. #2245C22semidirect
90. #2244C22semidirect
91. #2244C22semidirect
92. #2243C22semidirect
93. #2242C22semidirect
94. #2240C22semidirect
95. #2237C22semidirect
96. #2235C22semidirect
97. #2234C22semidirect
98. #2233C22semidirect
99. #2233C22semidirect
100. #2233C22semidirect
101. #2229C22semidirect
102. #2228C22semidirect
103. #2228C22semidirect
104. #2228C22semidirect
105. #2226C22semidirect
106. #2226C22semidirect
107. #2226C22semidirect
108. #2225C22semidirect
109. #2225C22semidirect
110. #2224C22semidirect
111. #2220C22semidirect
112. #2220C22semidirect
113. #2220C22semidirect
114. #2219C22semidirect
117. #2218C22semidirect
118. #2218C22semidirect
119. #2217C22semidirect
120. #2217C22semidirect
121. #2217C22semidirect
122. #2215C22semidirect
123. #2211C22semidirect
124. #2211C22semidirect
125. #2211C22semidirect
126. #2211C22semidirect
129. #2210C22semidirect
130. #2210C22semidirect
131. #2210C22semidirect
132. #2210C22semidirect
133. #2210C22semidirect
134. #2210C22semidirect
135. #2210C22semidirect
136. #2210C22semidirect
137. #2210C22semidirect
138. #2210C22semidirect
139. #2208C22semidirect
140. #2208C22semidirect
141. #2207C22semidirect
142. #2207C22semidirect
143. #2207C22semidirect
146. #2206C22semidirect
147. #2206C22semidirect
148. #2206C22semidirect
149. #2206C22semidirect
150. #2206C22semidirect
151. #2206C22semidirect
152. #2206C22semidirect
153. #2189C22semidirect
154. #2189C22semidirect
155. #2189C22semidirect
156. #2189C22semidirect
157. #2187C22semidirect
158. #2187C22semidirect
160. #2186C22semidirect
161. #2186C22semidirect
162. #2186C22semidirect
163. #2186C22semidirect
164. #2186C22semidirect
168. #2184C22semidirect
169. #2184C22semidirect
170. #2184C22semidirect
171. #2183C22semidirect
172. #2183C22semidirect
174. #2177C22semidirect
175. #2177C22semidirect
176. #2177C22semidirect
177. #2177C22semidirect
178. #2177C22semidirect
179. #2176C22semidirect
180. #2175C22semidirect
181. C4×SD32C22semidirect
182. C4×SD32C22semidirect
183. C4×SD32C22semidirect
184. C4×D16C22semidirect
185. #2169C22semidirect
186. #2169C22semidirect
187. #2168C22semidirect
188. #2168C22semidirect
189. #2168C22semidirect
190. #2168C22semidirect
191. #2164C22semidirect
192. #2164C22semidirect
193. #2163C22semidirect
194. #2151C22semidirect
195. #2151C22semidirect
196. #2150C22semidirect
197. #2140C22semidirect
198. #2139C22semidirect
199. #2139C22semidirect
200. #2139C22semidirect
201. #2138C22semidirect
202. C2×#357C22semidirect

Maximal subgroups

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

subgroupindex
#624402
#614712
#339682
#339662
#339432
#339332
#338992
#338902
#338852
#338842
#338742
#338732
#338402
#338392
#338342
#338332
#338302
#338292
#338232
#338172
#337902
#337862
#337852
#336852
#336782
#336692
#335892
#335852
#335802
#335092