Finite Group Databasebeta

← #7624551

Subgroups — #7624551

Order 512.

1335 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62419C211yesmaximal, characteristic, complemented
2#61430C211yesmaximal, characteristic, complemented
3#33970C211yesmaximal, characteristic, complemented
4#33968C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33938C211yesmaximal, characteristic, complemented
7#33887C211yesmaximal, characteristic, complemented
8#33885C211yesmaximal, characteristic, complemented
9#33880C211yesmaximal, characteristic, complemented
10#33878C211yesmaximal, characteristic, complemented
11#33868C211yesmaximal, characteristic, complemented
12#33864C211yesmaximal, characteristic, complemented
13#33851C211yesmaximal, characteristic, complemented
14#33848C211yesmaximal, characteristic, complemented
15#33837C211yesmaximal, characteristic, complemented
16#33836C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33831C211yesmaximal, characteristic, complemented
19#33822C211yesmaximal, characteristic, complemented
20#33816C211yesmaximal, characteristic, complemented
21#33813C211yesmaximal, characteristic, complemented
22#33785C211yesmaximal, characteristic, complemented
23#33779C211yesmaximal, characteristic, complemented
24#33777C211yesmaximal, characteristic, complemented
25#33677C211yesmaximal, characteristic, complemented
26#33671C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33584C211yesmaximal, characteristic, complemented
29#33579C211yesmaximal, characteristic, complemented
30C2×#2211C211yesmaximal, characteristic, complemented
31#33504C211yesmaximal, characteristic, complemented
32#3514—21no—
33#3480—21no—
34C2×#510C2211yescharacteristic, complemented
35C2×#509C2211yescharacteristic
36C2×#508C2211yescharacteristic, complemented
37C2×#508C2211yescharacteristic, complemented
38C22×Q32C2211yescharacteristic, complemented
39C22×SD32C2211yescharacteristic
40#3396C2211yescharacteristic
41#3396C2211yescharacteristic, complemented
42#3394—21no—
43#3393C2211yescharacteristic
44#3383C2211yescharacteristic, complemented
45#3365—21no—
46#3342C2211yescharacteristic, complemented
47#3339C2211yescharacteristic
48#3339C2211yescharacteristic, complemented
49#3304—21no—
50#3301—21no—
51#3301—21no—
52#3287C2211yescharacteristic, complemented
53D4×Q16C2211yescharacteristic
54#3285C2211yescharacteristic
55#3285C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic, complemented
58#3282—21no—
59#3282—21no—
60D4×SD16—21no—
61#3280C2211yescharacteristic
62#3280C2211yescharacteristic
63D4×D8C2211yescharacteristic
64#3212—21no—
65#3211—21no—
66#3211—21no—
67#3169C2211yescharacteristic, complemented
68#3168C2211yescharacteristic
69#3168C2211yescharacteristic
70#3168C2211yescharacteristic
71#3168C2211yescharacteristic, complemented
72#3168C2211yescharacteristic, complemented
73#3147C2211yescharacteristic
74C2×#495C2211yescharacteristic
75C2×#495C2211yescharacteristic
76#3103—21no—
77#3102—21no—
78#3102—21no—
79C8×#41C2211yescharacteristic
80C4×#135C2211yescharacteristic, complemented
81C4×#135C2211yescharacteristic, complemented
82C2×C4×Q16C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2250C2211yescharacteristic
85#2250C2211yescharacteristic
86#2250C2211yescharacteristic, complemented
87#2249C2211yescharacteristic
88#2249C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2244C2211yescharacteristic
91#2243C2211yescharacteristic
92#2243C2211yescharacteristic, complemented
93#2242C2211yescharacteristic
94#2242C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic
100#2233C2211yescharacteristic
101#2229C2211yescharacteristic, complemented
102#2229C2211yescharacteristic, complemented
103#2229C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2228C2211yescharacteristic
106#2228C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2228C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2226C2211yescharacteristic, complemented
111#2220C2211yescharacteristic
112#2220C2211yescharacteristic, complemented
113#2219C2211yescharacteristic, complemented
114#2218C2211yescharacteristic
115#2217C2211yescharacteristic
116#2217C2211yescharacteristic, complemented
117#2217C2211yescharacteristic, complemented
118#2217C2211yescharacteristic, complemented
119#2216C2211yescharacteristic, complemented
120#2215C2211yescharacteristic
121#2215C2211yescharacteristic
122#2215C2211yescharacteristic
123#2211C2211yescharacteristic
124#2211C2211yescharacteristic
125#2211C2211yescharacteristic
126#2211C2211yescharacteristic
127#2211C2211yescharacteristic
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2211C2211yescharacteristic, complemented
132#2211C2211yescharacteristic, complemented
133#2211C2211yescharacteristic, complemented
134#2211C2211yescharacteristic, complemented
135#2211C2211yescharacteristic, complemented
136#2211C2211yescharacteristic, complemented
137#2210C2211yescharacteristic
138#2210C2211yescharacteristic
139#2210C2211yescharacteristic
140#2210C2211yescharacteristic
141#2210C2211yescharacteristic, complemented
142#2210C2211yescharacteristic, complemented
143#2210C2211yescharacteristic, complemented
144#2210C2211yescharacteristic, complemented
145#2210C2211yescharacteristic, complemented
146#2210C2211yescharacteristic, complemented
147#2209C2211yescharacteristic, complemented
148#2208C2211yescharacteristic, complemented
149#2207C2211yescharacteristic
150#2207C2211yescharacteristic, complemented
151#2206C2211yescharacteristic
152#2206C2211yescharacteristic, complemented
153#2189C2211yescharacteristic, complemented
154#2189C2211yescharacteristic, complemented
155#2189C2211yescharacteristic, complemented
156#2189C2211yescharacteristic, complemented
157#2188C2211yescharacteristic, complemented
158#2188C2211yescharacteristic, complemented
159#2187C2211yescharacteristic
160#2186C2211yescharacteristic
161#2186C2211yescharacteristic
162#2186C2211yescharacteristic, complemented
163#2186C2211yescharacteristic, complemented
164#2185C2211yescharacteristic
165#2185C2211yescharacteristic, complemented
166#2185C2211yescharacteristic, complemented
167#2185C2211yescharacteristic, complemented
168#2184C2211yescharacteristic
169#2184C2211yescharacteristic
170#2184C2211yescharacteristic
171#2183C2211yescharacteristic, complemented
172#2183C2211yescharacteristic, complemented
173#2177C2211yescharacteristic
174#2176C2211yescharacteristic, complemented
175#2176C2211yescharacteristic, complemented
176#2176C2211yescharacteristic, complemented
177#2175C2211yescharacteristic
178#2175C2211yescharacteristic, complemented
179#2175C2211yescharacteristic, complemented
180#2175C2211yescharacteristic, complemented
181C4×Q32C2211yescharacteristic, complemented
182C4×SD32C2211yescharacteristic, complemented
183C4×SD32C2211yescharacteristic, complemented
184C4×D16C2211yescharacteristic, complemented
185#2168C2211yescharacteristic
186#2168C2211yescharacteristic
187#2168C2211yescharacteristic, complemented
188#2168C2211yescharacteristic, complemented
189D4×C16C2211yescharacteristic, complemented
190D4×C16C2211yescharacteristic, complemented
191#2163C2211yescharacteristic, complemented
192#2163C2211yescharacteristic, complemented
193#2162C2211yescharacteristic, complemented
194#2150C2211yescharacteristic, complemented
195C2×C4⋊C16C2211yescharacteristic, complemented
196C2×C4⋊C16C2211yescharacteristic, complemented
197#2141C2211yescharacteristic, complemented
198#2140C2211yescharacteristic
199#2138C2211yescharacteristic, complemented
200#2138C2211yescharacteristic, complemented
201C2×#358C2211yescharacteristic, complemented
202C2×#357C2211yescharacteristic
203C2×#135—21no—
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16—21no—
212C22×SD16—21no—
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#559—21no—
216#559—21no—
217#559—41no—
218#557—21no—
219#556—21no—
220#556—21no—
221#556—41no—
222#555—41no—
223#553—21no—
224#553—21no—
225#553—41no—
226#553—41no—
227#551—41no—
228#551—41no—
229#550—21no—
230D4×Q8—21no—
231#548—21no—
232#548—21no—
233#548—21no—
234#548—21no—
235#546—21no—
236#546—21no—
237#546—41no—
238D42—21no—
239#542—41no—
240#538—41no—
241#538—41no—
242#532—21no—
243#532—21no—
244#532—41no—
245#529—21no—
246#529—21no—
247#529—21no—
248#529—21no—
249#529—21no—
250#529—41no—
251#529—41no—
252C2×#124—21no—
253C2×#124—21no—
254#518—41no—
255C4×#41—21no—
256C4×#41—21no—
257C4×#41—41no—
258C4×#41D411yescharacteristic
259C2×C4×Q8—21no—
260#510—42no—
261#509—42no—
262#508—42no—
263#508—42no—
264C2×Q32—42no—
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×Q32C2311yescharacteristic
268C2×Q32C2311yescharacteristic
269C2×Q32C2311yescharacteristic
270C2×Q32C2311yescharacteristic
271C2×SD32—42no—
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×SD32C2311yescharacteristic
276C2×SD32C2311yescharacteristic
277C2×SD32C2311yescharacteristic
278C2×SD32C2311yescharacteristic
279C2×SD32C2311yescharacteristic
280C2×SD32C2311yescharacteristic
281C2×SD32C2311yescharacteristic
282C2×SD32C2311yescharacteristic
283C2×SD32C2311yescharacteristic
284C2×D16C2311yescharacteristic
285C2×D16C2311yescharacteristic
286C2×D16C2311yescharacteristic
287C2×D16C2311yescharacteristic
288C2×D16C2311yescharacteristic
289C2×D16C2311yescharacteristic
290C2×M32C2311yescharacteristic
291C2×M32C2311yescharacteristic
292C22×C16C2311yescharacteristic
293C22×C16C2311yescharacteristic
294C22×C16C2311yescharacteristic
295C22×C16C2311yescharacteristic
296#500C2311yescharacteristic
297#499C2311yescharacteristic
298#499C2311yescharacteristic
299#499C2311yescharacteristic
300#495—21no—
301#495—21no—
302#495—21no—
303#495—21no—
304#495—21no—
305#495C2311yescharacteristic
306#495C2311yescharacteristic
307#495C2311yescharacteristic
308#495C2311yescharacteristic
309#495C2311yescharacteristic
310#495C2311yescharacteristic
311#495C2311yescharacteristic
312#495C2311yescharacteristic
313#495C2311yescharacteristic
314#494C2311yescharacteristic
315#493C2311yescharacteristic
316#493C2311yescharacteristic
317#492—21no—
318#488—21no—
319#488—21no—
320#488—21no—
321#488—21no—
322#488—21no—
323#486—21no—
324#485—21no—
325#485—21no—
326#482—21no—
327#482—21no—
328#481—21no—
329#481—21no—
330#479—21no—
331#479—21no—
332#478—21no—
333#478—21no—
334#475—21no—
335#475—21no—
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#466—21no—
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#466C2311yescharacteristic
347#466C2311yescharacteristic
348#466C2311yescharacteristic
349#465—21no—
350#465—21no—
351#465—21no—
352#465—21no—
353#465—21no—
354#464—21no—
355#464—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#464—21no—
360#463—21no—
361#463—21no—
362#463—21no—
363#463—21no—
364#463—21no—
365#463—21no—
366#462—21no—
367#461—21no—
368#460—21no—
369#460—21no—
370#460—21no—
371#459—21no—
372#452—21no—
373#452—21no—
374#452—21no—
375#452—21no—
376#451—21no—
377#451—21no—
378#450—21no—
379#450—21no—
380#449—21no—
381#449—21no—
382#449—21no—
383#449—21no—
384#448—21no—
385#448—21no—
386#448—21no—
387#448—21no—
388#447—21no—
389#447—21no—
390C8×Q8D411yescharacteristic
391C8×Q8C2311yescharacteristic
392C4×Q16—21no—
393C4×Q16—21no—
394C4×Q16C2311yescharacteristic
395C4×Q16C2311yescharacteristic
396C4×Q16C2311yescharacteristic
397C4×Q16C2311yescharacteristic
398C4×Q16C2311yescharacteristic
399C4×Q16C2311yescharacteristic
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×Q16C2311yescharacteristic
403C4×SD16—21no—
404C4×SD16—21no—
405C4×SD16—21no—
406C4×SD16—21no—
407C4×SD16—21no—
408C4×SD16—21no—
409C4×SD16—21no—
410C4×SD16—21no—
411C4×SD16—21no—
412C4×D8—21no—
413C4×D8C2311yescharacteristic
414C4×D8C2311yescharacteristic
415C4×D8C2311yescharacteristic
416C4×D8C2311yescharacteristic
417C4×D8C2311yescharacteristic
418C4×D8C2311yescharacteristic
419C4×D8C2311yescharacteristic
420C8×D4D411yescharacteristic
421C8×D4D411yescharacteristic
422C8×D4D411yescharacteristic
423C8×D4C2311yescharacteristic
424C8×D4C2311yescharacteristic
425C8×D4C2311yescharacteristic
426#431D411yescharacteristic
427#431D411yescharacteristic
428#431D411yescharacteristic
429#427C2311yescharacteristic
430#427C2311yescharacteristic
431C2×#107C2311yescharacteristic
432#416—21no—
433#416—21no—
434C2×#103—21no—
435C2×C4×C8C2311yescharacteristic
436C2×C4×C8C2311yescharacteristic
437C2×C4×C8C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
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#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—41no—
505C2×#41D811yescharacteristic
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512#135—22no—
513#135—22no—
514#135—41no—
515#135—41no—
516#135—41no—
517#135—41no—
518#135—41no—
519#135—41no—
520#135—82no—
521C2×Q16—22no—
522C2×Q16—21no—
523C2×Q16—21no—
524C2×Q16—21no—
525C2×Q16—21no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16C2411yescharacteristic
532C2×Q16C2411yescharacteristic
533C2×Q16C2411yescharacteristic
534C2×Q16C2411yescharacteristic
535C2×Q16C2411yescharacteristic
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×SD16—21no—
541C2×SD16—21no—
542C2×SD16—21no—
543C2×SD16—21no—
544C2×SD16—21no—
545C2×SD16—21no—
546C2×SD16—21no—
547C2×SD16—21no—
548C2×SD16—21no—
549C2×SD16—82no—
550C2×SD16—82no—
551C2×D8—21no—
552C2×D8—21no—
553C2×D8—21no—
554C2×D8—21no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8C2411yescharacteristic
560C2×D8C2411yescharacteristic
561C2×D8C2411yescharacteristic
562C2×D8C2411yescharacteristic
563C2×D8C2411yescharacteristic
564C22×C8C2×D411yescharacteristic
565C22×C8C2×D411yescharacteristic
566C22×C8C2×D411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C4⋊Q8—21no—
571C4⋊Q8—21no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574#127—21no—
575#127—21no—
576#127—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#125—21no—
589#125—21no—
590#125—21no—
591#125—41no—
592#125—41no—
593#124—21no—
594#124—21no—
595#124—21no—
596#124—21no—
597#124—21no—
598#124—21no—
599#124—21no—
600#124—21no—
601#124—21no—
602#124—41no—
603#124—41no—
604#124—41no—
605#124—41no—
606#124—41no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—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—
627C22⋊Q8—21no—
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—41no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—41no—
647#121—41no—
648#121—41no—
649#121—41no—
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#120—41no—
661#120—41no—
662#120—41no—
663#120—41no—
664C4×Q8—21no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—21no—
673C4×Q8—41no—
674C4×Q8—41no—
675C4×Q8—41no—
676C4×Q8—41no—
677C4×Q8D811yescharacteristic
678C4×Q8C2×D411yescharacteristic
679C4×D4—21no—
680C4×D4—21no—
681C4×D4—21no—
682C4×D4—21no—
683C4×D4—21no—
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—41no—
687C4×D4—41no—
688C4×D4—41no—
689C4×D4—41no—
690C4×D4—41no—
691C4×D4—41no—
692C4×D4—41no—
693C4×D4—41no—
694C4×D4—41no—
695C4×D4—41no—
696C4×D4—41no—
697C4×D4—41no—
698C4×D4—41no—
699C4×D4—41no—
700C4×D4—41no—
701C4×D4—41no—
702C4×D4—41no—
703C4×D4—41no—
704C4×D4—41no—
705C4×D4—41no—
706C4×D4—41no—
707C4×D4—41no—
708C4×D4D811yescharacteristic
709C4×D4D811yescharacteristic
710C4×D4D811yescharacteristic
711C4×D4C2×D411yescharacteristic
712C4×D4C2×D411yescharacteristic
713C4×D4C2×D411yescharacteristic
714#117—21no—
715#117—21no—
716#117—41no—
717#117—41no—
718#117—41no—
719#117—41no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117—41no—
724#117D811yescharacteristic
725#117D811yescharacteristic
726#117D811yescharacteristic
727C2×C4⋊C4—21no—
728C2×C4⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C42—41no—
736C2×C42—41no—
737C2×C42—41no—
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741Q32—22no—
742Q32—22no—
743Q32—22no—
744Q32—41no—
745Q32—41no—
746Q32—41no—
747SD32—22no—
748SD32—22no—
749SD32—22no—
750SD32—41no—
751SD32—41no—
752SD32—41no—
753SD32—41no—
754SD32—41no—
755SD32—41no—
756SD32—41no—
757SD32—41no—
758SD32—41no—
759D16—41no—
760D16—41no—
761D16—41no—
762D16—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#107C2411yescharacteristic
782#107C2411yescharacteristic
783#107C2411yescharacteristic
784#107C2411yescharacteristic
785#107C2411yescharacteristic
786#107C2411yescharacteristic
787#106—21no—
788#106—21no—
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#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
832C4×C8C2×D411yescharacteristic
833C4×C8C2×D411yescharacteristic
834C4×C8C2×D411yescharacteristic
835C4×C8C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2×D411yescharacteristic
838C4×C8C2411yescharacteristic
839C4×C8C2411yescharacteristic
840C4×C8C2411yescharacteristic
841C4×C8C2411yescharacteristic
842C24—41no—
843C24—41no—
844#41—42no—
845#41—42no—
846#41—42no—
847#41—81no—
848#41—81no—
849#41—84no—
850#41—81no—
851#41—81no—
852#41—81no—
853#41—81no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—42no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—41no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8C2×D811yescharacteristic
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
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—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—84no—
897C2×D4C2×D811yescharacteristic
898C2×D4C2×D811yescharacteristic
899C2×D4C2×D811yescharacteristic
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4C2×D811yescharacteristic
916C22×C4C2×D811yescharacteristic
917C22×C4C2×D811yescharacteristic
918C22×C4C2×D811yescharacteristic
919C22×C4C2×D811yescharacteristic
920C22×C4C2×D811yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924Q16—21no—
925Q16—21no—
926Q16—21no—
927Q16—21no—
928Q16—21no—
929Q16—21no—
930Q16—21no—
931Q16—21no—
932Q16—21no—
933Q16—42no—
934Q16—81no—
935Q16—81no—
936Q16—81no—
937Q16H(5,𝔽2)12yes—
938SD16—42no—
939SD16—42no—
940SD16—42no—
941SD16—42no—
942SD16—42no—
943SD16—81no—
944SD16—81no—
945SD16—81no—
946SD16—81no—
947SD16—81no—
948SD16—81no—
949SD16—81no—
950SD16—81no—
951D8—21no—
952D8—21no—
953D8—21no—
954D8—21no—
955D8—21no—
956D8—21no—
957D8—21no—
958D8—21no—
959D8—21no—
960D8—21no—
961D8—81no—
962D8—81no—
963D8—81no—
964D8—81no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—41no—
972C2×C8—41no—
973C2×C8—41no—
974C2×C8C22×D411yescharacteristic
975C2×C8C22×D411yescharacteristic
976C2×C8C22×D411yescharacteristic
977C2×C8C22×D411yescharacteristic
978C2×C8C22×D411yescharacteristic
979C2×C8C22×D411yescharacteristic
980C2×C8C22×D411yescharacteristic
981C2×C8C2511yescharacteristic
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
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⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4C2×D811yescharacteristic
1013C4⋊C4C2×D811yescharacteristic
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C4⋊C4C2×D811yescharacteristic
1018C22⋊C4—41no—
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⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C22⋊C4C2×D811yescharacteristic
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42C2×D811yescharacteristic
1075C42C2×D811yescharacteristic
1076C42C2×D811yescharacteristic
1077C42C2×D811yescharacteristic
1078C42C2×D811yescharacteristic
1079C42C2×D811yescharacteristic
1080C42C22×D411yescharacteristic
1081C42C22×D411yescharacteristic
1082C42C22×D411yescharacteristic
1083C42C22×D411yescharacteristic
1084C16—21no—
1085C16—21no—
1086C16—21no—
1087C16—21no—
1088C16—21no—
1089C16—21no—
1090C16—21no—
1091C16—21no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—82no—
1098C23—82no—
1099C23—161no—
1100C23—161no—
1101C23—161no—
1102C23—161no—
1103C23C22×D811yescharacteristic
1104C23C22×D811yescharacteristic
1105C23C22×D811yescharacteristic
1106Q8—22no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—82no—
1118Q8—82no—
1119Q8—161no—
1120Q8—161no—
1121D4—22no—
1122D4—22no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—82no—
1135D4—82no—
1136D4—82no—
1137D4—82no—
1138D4—82no—
1139D4—82no—
1140D4—82no—
1141D4—82no—
1142D4—161no—
1143D4—161no—
1144D4—161no—
1145D4—161no—
1146D4—161no—
1147D4—161no—
1148D4—161no—
1149D4—161no—
1150D4—161no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—82no—
1175C2×C4—82no—
1176C2×C4—82no—
1177C2×C4—82no—
1178C2×C4—82no—
1179C2×C4—82no—
1180C2×C4—161no—
1181C2×C4—161no—
1182C2×C4—161no—
1183C2×C4—161no—
1184C2×C4—161no—
1185C2×C4—161no—
1186C2×C4—161no—
1187C2×C4—161no—
1188C2×C4—161no—
1189C2×C4C22×D811yescharacteristic
1190C2×C4C22×D811yescharacteristic
1191C2×C4C22×D811yescharacteristic
1192C2×C4C22×D811yescharacteristic
1193C2×C4C22×D811yescharacteristic
1194C2×C4C22×D811yescharacteristic
1195C2×C4C22×D811yescharacteristic
1196C2×C4C22×D811yescharacteristic
1197C2×C4C22×D811yescharacteristic
1198C2×C4C22×D811yescharacteristic
1199C2×C4C22×D811yescharacteristic
1200C2×C4C23×D411yescharacteristic
1201C8—21no—
1202C8—21no—
1203C8—21no—
1204C8—21no—
1205C8—21no—
1206C8—21no—
1207C8—21no—
1208C8C2×H(5,𝔽2)11yescharacteristic
1209C8#58511yescharacteristic
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—322no—
1234C22—322no—
1235C22#341412yes—
1236C22C23×D811yescharacteristic
1237C4—21no—
1238C4—21no—
1239C4—21no—
1240C4—21no—
1241C4—21no—
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—21no—
1247C4—21no—
1248C4—42no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4#348811yescharacteristic
1260C4#358511yescharacteristic
1261C2—22no—
1262C2—41no—
1263C2—41no—
1264C2—161no—
1265C2—161no—
1266C2—161no—
1267C2—161no—
1268C2—161no—
1269C2#6194711yescharacteristic
1270C2C2×#341411yescharacteristic
1271C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62419C2semidirect
2. #61430C2semidirect
3. #33970C2semidirect
4. #33968C2semidirect
5. #33944C2semidirect
6. #33938C2semidirect
7. #33887C2semidirect
8. #33885C2semidirect
9. #33880C2semidirect
10. #33878C2semidirect
11. #33868C2semidirect
12. #33864C2semidirect
13. #33851C2semidirect
14. #33848C2semidirect
15. #33837C2semidirect
16. #33836C2semidirect
17. #33834C2semidirect
18. #33831C2semidirect
19. #33822C2semidirect
20. #33816C2semidirect
21. #33813C2semidirect
22. #33785C2semidirect
23. #33779C2semidirect
24. #33777C2semidirect
25. #33677C2semidirect
26. #33671C2semidirect
27. #33662C2semidirect
28. #33584C2semidirect
29. #33579C2semidirect
30. C2×#2211C2semidirect
31. #33504C2semidirect
34. C2×#510C22semidirect
36. C2×#508C22semidirect
37. C2×#508C22semidirect
38. C22×Q32C22semidirect
41. #3396C22semidirect
44. #3383C22semidirect
46. #3342C22semidirect
48. #3339C22semidirect
52. #3287C22semidirect
57. #3285C22semidirect
67. #3169C22semidirect
71. #3168C22semidirect
72. #3168C22semidirect
80. C4×#135C22semidirect
81. C4×#135C22semidirect
82. C2×C4×Q16C22semidirect
83. #2251C22semidirect
86. #2250C22semidirect
88. #2249C22semidirect
89. #2245C22semidirect
92. #2243C22semidirect
94. #2242C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2236C22semidirect
101. #2229C22semidirect
102. #2229C22semidirect
103. #2229C22semidirect
104. #2229C22semidirect
106. #2228C22semidirect
107. #2228C22semidirect
108. #2228C22semidirect
109. #2227C22semidirect
110. #2226C22semidirect
112. #2220C22semidirect
113. #2219C22semidirect
116. #2217C22semidirect
117. #2217C22semidirect
118. #2217C22semidirect
119. #2216C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
131. #2211C22semidirect
132. #2211C22semidirect
133. #2211C22semidirect
134. #2211C22semidirect
135. #2211C22semidirect
136. #2211C22semidirect
141. #2210C22semidirect
142. #2210C22semidirect
143. #2210C22semidirect
144. #2210C22semidirect
145. #2210C22semidirect
146. #2210C22semidirect
147. #2209C22semidirect
148. #2208C22semidirect
150. #2207C22semidirect
152. #2206C22semidirect
153. #2189C22semidirect
154. #2189C22semidirect
155. #2189C22semidirect
156. #2189C22semidirect
157. #2188C22semidirect
158. #2188C22semidirect
162. #2186C22semidirect
163. #2186C22semidirect
165. #2185C22semidirect
166. #2185C22semidirect
167. #2185C22semidirect
171. #2183C22semidirect
172. #2183C22semidirect
174. #2176C22semidirect
175. #2176C22semidirect
176. #2176C22semidirect
178. #2175C22semidirect
179. #2175C22semidirect
180. #2175C22semidirect
181. C4×Q32C22semidirect
182. C4×SD32C22semidirect
183. C4×SD32C22semidirect
184. C4×D16C22semidirect
187. #2168C22semidirect
188. #2168C22semidirect
189. D4×C16C22semidirect
190. D4×C16C22semidirect
191. #2163C22semidirect
192. #2163C22semidirect
193. #2162C22semidirect
194. #2150C22semidirect
195. C2×C4⋊C16C22semidirect
196. C2×C4⋊C16C22semidirect
197. #2141C22semidirect
199. #2138C22semidirect
200. #2138C22semidirect
201. C2×#358C22semidirect

Maximal subgroups

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

subgroupindex
#624192
#614302
#339702
#339682
#339442
#339382
#338872
#338852
#338802
#338782
#338682
#338642
#338512
#338482
#338372
#338362
#338342
#338312
#338222
#338162
#338132
#337852
#337792
#337772
#336772
#336712
#336622
#335842
#335792
C2×#22112
#335042