Finite Group Databasebeta

← #7624112

Subgroups — #7624112

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61487C211yesmaximal, characteristic, complemented
2#61475C211yesmaximal, characteristic, complemented
3#33968C211yesmaximal, characteristic, complemented
4#33951C211yesmaximal, characteristic, complemented
5#33937C211yesmaximal, characteristic, complemented
6#33934C211yesmaximal, characteristic, complemented
7#33916C211yesmaximal, characteristic, complemented
8#33914C211yesmaximal, characteristic, complemented
9#33907C211yesmaximal, characteristic, complemented
10#33886C211yesmaximal, characteristic, complemented
11#33878C211yesmaximal, characteristic, complemented
12#33878C211yesmaximal, characteristic, complemented
13#33877C211yesmaximal, characteristic, complemented
14#33870C211yesmaximal, characteristic, complemented
15#33864C211yesmaximal, characteristic, complemented
16#33846C211yesmaximal, characteristic, complemented
17#33833C211yesmaximal, characteristic, complemented
18#33830C211yesmaximal, characteristic, complemented
19#33746C211yesmaximal, characteristic, complemented
20#33745C211yesmaximal, characteristic, complemented
21#33742C211yesmaximal, characteristic, complemented
22#33684C211yesmaximal, characteristic, complemented
23#33683C211yesmaximal, characteristic, complemented
24#33678C211yesmaximal, characteristic, complemented
25#33678C211yesmaximal, characteristic, complemented
26#33666C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33482C211yesmaximal, characteristic, complemented
29#33456C211yesmaximal, characteristic, complemented
30#33454C211yesmaximal, characteristic, complemented
31#33451C211yesmaximal, characteristic, complemented
32#3521—21no—
33#3514—21no—
34C2×#509C2211yescharacteristic
35C2×#508C2211yescharacteristic
36C22×D16C2211yescharacteristic
37#3396C2211yescharacteristic, complemented
38#3393C2211yescharacteristic, complemented
39#3380C2211yescharacteristic, complemented
40Q8×D8C2211yescharacteristic, complemented
41#3376—21no—
42#3373—21no—
43#3342C2211yescharacteristic
44#3342C2211yescharacteristic, complemented
45#3341C2211yescharacteristic
46#3341C2211yescharacteristic, complemented
47#3339C2211yescharacteristic, complemented
48#3336C2211yescharacteristic
49#3324—21no—
50#3323—21no—
51#3319—21no—
52#3319—21no—
53#3311—21no—
54#3307—21no—
55#3283C2211yescharacteristic, complemented
56#3280C2211yescharacteristic
57#3280C2211yescharacteristic
58#3280C2211yescharacteristic, complemented
59#3280C2211yescharacteristic, complemented
60D4×D8C2211yescharacteristic
61#3177C2211yescharacteristic, complemented
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic, complemented
64#3175C2211yescharacteristic, complemented
65#3169C2211yescharacteristic, complemented
66#3168C2211yescharacteristic, complemented
67#3125—21no—
68#3123—21no—
69#3118—21no—
70#3118—21no—
71#3115—21no—
72#3111—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic, complemented
75#2948C2211yescharacteristic
76#2948C2211yescharacteristic, complemented
77#2948C2211yescharacteristic, complemented
78C4×#135C2211yescharacteristic, complemented
79C4×#135C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2254C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2250C2211yescharacteristic
85#2249C2211yescharacteristic, complemented
86#2244C2211yescharacteristic, complemented
87#2243C2211yescharacteristic, complemented
88#2243C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2242C2211yescharacteristic, complemented
91#2241C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic, complemented
100#2234C2211yescharacteristic, complemented
101#2234C2211yescharacteristic, complemented
102#2234C2211yescharacteristic, complemented
103#2232C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2228C2211yescharacteristic, complemented
106#2228C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2227C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2226C2211yescharacteristic, complemented
111#2226C2211yescharacteristic, complemented
112#2226C2211yescharacteristic, complemented
113#2224C2211yescharacteristic, complemented
114#2224C2211yescharacteristic, complemented
115#2224C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2219C2211yescharacteristic, complemented
118#2219C2211yescharacteristic, complemented
119#2218C2211yescharacteristic
120#2217C2211yescharacteristic
121#2217C2211yescharacteristic, complemented
122#2217C2211yescharacteristic, complemented
123#2217C2211yescharacteristic, complemented
124#2217C2211yescharacteristic, complemented
125#2216C2211yescharacteristic, complemented
126#2215C2211yescharacteristic, complemented
127#2215C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2210C2211yescharacteristic
131#2210C2211yescharacteristic
132#2210C2211yescharacteristic, complemented
133#2210C2211yescharacteristic, complemented
134#2210C2211yescharacteristic, complemented
135#2210C2211yescharacteristic, complemented
136#2208C2211yescharacteristic, complemented
137#2208C2211yescharacteristic, complemented
138#2207C2211yescharacteristic, complemented
139#2206C2211yescharacteristic
140#2189C2211yescharacteristic, complemented
141#2189C2211yescharacteristic, complemented
142#2187C2211yescharacteristic
143#2187C2211yescharacteristic
144#2187C2211yescharacteristic, complemented
145#2187C2211yescharacteristic, complemented
146#2186C2211yescharacteristic
147#2186C2211yescharacteristic
148#2186C2211yescharacteristic, complemented
149#2186C2211yescharacteristic, complemented
150#2184C2211yescharacteristic
151#2184C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2177C2211yescharacteristic
155#2177C2211yescharacteristic
156#2177C2211yescharacteristic
157#2177C2211yescharacteristic, complemented
158#2177C2211yescharacteristic, complemented
159#2177C2211yescharacteristic, complemented
160#2177C2211yescharacteristic, complemented
161#2176C2211yescharacteristic, complemented
162#2176C2211yescharacteristic, complemented
163#2175C2211yescharacteristic, complemented
164#2175C2211yescharacteristic, complemented
165#2175C2211yescharacteristic, complemented
166#2175C2211yescharacteristic, complemented
167#2175C2211yescharacteristic, complemented
168#2175C2211yescharacteristic, complemented
169#2175C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×SD32C2211yescharacteristic, complemented
172C4×SD32C2211yescharacteristic, complemented
173C4×SD32C2211yescharacteristic, complemented
174C4×SD32C2211yescharacteristic, complemented
175C4×SD32C2211yescharacteristic, complemented
176C4×D16C2211yescharacteristic
177C4×D16C2211yescharacteristic
178C4×D16C2211yescharacteristic
179C4×D16C2211yescharacteristic, complemented
180C4×D16C2211yescharacteristic, complemented
181C4×D16C2211yescharacteristic, complemented
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic, complemented
185#2168C2211yescharacteristic, complemented
186D4×C16C2211yescharacteristic, complemented
187D4×C16C2211yescharacteristic, complemented
188#2164C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2162C2211yescharacteristic, complemented
191#2159C2211yescharacteristic, complemented
192#2158C2211yescharacteristic, complemented
193#2158C2211yescharacteristic, complemented
194#2140C2211yescharacteristic
195#2140C2211yescharacteristic, complemented
196#2138C2211yescharacteristic, complemented
197#2138C2211yescharacteristic, complemented
198#2138C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic, complemented
200#2108C2211yescharacteristic, complemented
201#2108C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#559—21no—
210#556—21no—
211#556—21no—
212#556—21no—
213#555—21no—
214#555—21no—
215#554—21no—
216#553—21no—
217#553—41no—
218#552—21no—
219#552—41no—
220#551—41no—
221#551—41no—
222#551—41no—
223#551—41no—
224D4×Q8—21no—
225#548—41no—
226#547—21no—
227#546—21no—
228#546—21no—
229#546—21no—
230#546—21no—
231#546—41no—
232D42—21no—
233#542—21no—
234#542—21no—
235#542—21no—
236#541—21no—
237#539—41no—
238#538—41no—
239#538—41no—
240#538—41no—
241#532—21no—
242#529—21no—
243#529—41no—
244#529—41no—
245#529D411yescharacteristic
246C2×#126—41no—
247C2×#124—41no—
248#520—21no—
249#518—21no—
250#518—21no—
251#518—21no—
252C4×#41—21no—
253C4×#41—21no—
254#509—24no—
255#508—24no—
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×SD32C2311yescharacteristic
259C2×SD32C2311yescharacteristic
260C2×SD32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×D16—24no—
267C2×D16C2311yescharacteristic
268C2×D16C2311yescharacteristic
269C2×D16C2311yescharacteristic
270C2×D16C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C22×C16C2311yescharacteristic
276C22×C16C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#494C2311yescharacteristic
290#493C2311yescharacteristic
291#491—21no—
292#489—21no—
293#489—21no—
294#489—21no—
295#488—21no—
296#486—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#485—21no—
301#485—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—21no—
306#482—21no—
307#482—21no—
308#481—21no—
309#479—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#476—21no—
314#476—21no—
315#476—21no—
316#475—21no—
317#475—21no—
318#474—21no—
319#474—21no—
320#474—21no—
321#470—21no—
322#468—21no—
323#468—21no—
324#468—21no—
325#467C2311yescharacteristic
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#466—21no—
332#466C2311yescharacteristic
333#466C2311yescharacteristic
334#466C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#461—21no—
348#461—21no—
349#460—21no—
350#459—21no—
351#452—21no—
352#452—21no—
353#450—21no—
354#450—21no—
355#450—21no—
356#450—21no—
357#449—21no—
358#449—21no—
359#449—21no—
360#449—21no—
361#447—21no—
362#447—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#442—21no—
366#442—21no—
367#442—21no—
368#442—21no—
369#442—21no—
370#442—21no—
371#441—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×SD16—21no—
384C4×SD16—21no—
385C4×SD16—21no—
386C4×SD16—21no—
387C4×SD16—21no—
388C4×D8—21no—
389C4×D8C2311yescharacteristic
390C4×D8C2311yescharacteristic
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403#436D411yescharacteristic
404#435D411yescharacteristic
405#435D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#433D411yescharacteristic
410#433D411yescharacteristic
411#432D411yescharacteristic
412#427C2311yescharacteristic
413#427C2311yescharacteristic
414#427C2311yescharacteristic
415#427C2311yescharacteristic
416#427C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#418—21no—
419#418—21no—
420#418—21no—
421#417—21no—
422#416—21no—
423#416—21no—
424#405C2311yescharacteristic
425#405C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#367C2311yescharacteristic
432#367C2311yescharacteristic
433#367C2311yescharacteristic
434#367C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
442#366C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449#358C2311yescharacteristic
450#358C2311yescharacteristic
451#358C2311yescharacteristic
452#358C2311yescharacteristic
453#358C2311yescharacteristic
454#358C2311yescharacteristic
455#358C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#357C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
464#357C2311yescharacteristic
465#357C2311yescharacteristic
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
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492#346C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—41no—
501C22×Q8—41no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506#135—22no—
507#135—22no—
508#135—22no—
509#135—41no—
510#135—41no—
511#135—41no—
512C2×Q16—21no—
513C2×Q16C2411yescharacteristic
514C2×Q16C2411yescharacteristic
515C2×Q16C2411yescharacteristic
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—21no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—21no—
527C2×D8—21no—
528C2×D8—21no—
529C2×D8—21no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8C2411yescharacteristic
534C2×D8C2411yescharacteristic
535C2×D8C2411yescharacteristic
536C2×D8C2411yescharacteristic
537C2×D8C2411yescharacteristic
538C2×M16C2×D411yescharacteristic
539C2×M16C2×D411yescharacteristic
540C22×C8C2×D411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549#127—21no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#126—41no—
556#126—41no—
557#126—41no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#126—41no—
564#126D811yescharacteristic
565#126D811yescharacteristic
566#125—21no—
567#125—21no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125D811yescharacteristic
572#124—21no—
573#124—21no—
574#124—21no—
575#124—21no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124D811yescharacteristic
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123D811yescharacteristic
603#123D811yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8D811yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—41no—
628#121—41no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121D811yescharacteristic
638#120—41no—
639#120—41no—
640#120—41no—
641#120—41no—
642#120—41no—
643#120—41no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8C2×D411yescharacteristic
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4—41no—
677C4×D4—41no—
678C4×D4—41no—
679C4×D4—41no—
680C4×D4—41no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4C2×D411yescharacteristic
684C4×D4C2×D411yescharacteristic
685C4×D4C2×D411yescharacteristic
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117—41no—
698#117—41no—
699#117C2×D411yescharacteristic
700#117C2×D411yescharacteristic
701C2×C4⋊C4—21no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—41no—
720SD32—22no—
721SD32—22no—
722SD32—22no—
723SD32—22no—
724SD32—41no—
725SD32—41no—
726SD32—41no—
727SD32—41no—
728D16—22no—
729D16—22no—
730D16—22no—
731D16—22no—
732D16—41no—
733D16#4114yescomplemented
734M32—22no—
735M32—41no—
736C2×C16—22no—
737C2×C16—22no—
738C2×C16—41no—
739C2×C16—41no—
740C2×C16C2411yescharacteristic
741C2×C16C2411yescharacteristic
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748#107—21no—
749#107—21no—
750#107—21no—
751#107—21no—
752#107—21no—
753#107C2411yescharacteristic
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#106—21no—
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768C4⋊C8C2×D411yescharacteristic
769C4⋊C8C2×D411yescharacteristic
770C4⋊C8C2×D411yescharacteristic
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774#103—21no—
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#103—21no—
780#103—21no—
781#103—21no—
782#103—21no—
783#103—21no—
784#103—21no—
785#103—21no—
786#102—21no—
787#102—21no—
788#102—21no—
789#102—21no—
790#102—21no—
791#102—21no—
792#102—21no—
793#102—21no—
794#102—21no—
795#102—21no—
796#102—21no—
797#102—21no—
798#102—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802#102—21no—
803#102—21no—
804#102—21no—
805#102—21no—
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808C22⋊C8C2×D411yescharacteristic
809C22⋊C8C2×D411yescharacteristic
810C22⋊C8C2×D411yescharacteristic
811C22⋊C8C2×D411yescharacteristic
812#97C2×D411yescharacteristic
813#97C2×D411yescharacteristic
814#97C2×D411yescharacteristic
815#97C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822C24—41no—
823C24—41no—
824C24—41no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—81no—
829#41—81no—
830#41—81no—
831#41—162no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—41no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—162no—
840C2×Q8C2×D811yescharacteristic
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—162no—
867C2×D4C2×D811yescharacteristic
868C2×D4C2×D811yescharacteristic
869C2×D4C2×D811yescharacteristic
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4C2×D811yescharacteristic
889C22×C4C2×D811yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893Q16—21no—
894Q16—21no—
895Q16—21no—
896Q16—21no—
897Q16—21no—
898Q16—21no—
899Q16—81no—
900SD16—42no—
901SD16—42no—
902SD16—42no—
903SD16—81no—
904SD16—81no—
905SD16—81no—
906SD16—81no—
907D8—21no—
908D8—21no—
909D8—21no—
910D8—21no—
911D8—21no—
912D8—21no—
913D8—21no—
914D8—21no—
915D8—42no—
916D8—42no—
917D8—42no—
918D8—81no—
919D8C2×#4112yes—
920D8C2×#4112yes—
921M16—41no—
922M16—41no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—41no—
930C2×C8C22×D411yescharacteristic
931C2×C8C22×D411yescharacteristic
932C2×C8C22×D411yescharacteristic
933C2×C8C22×D411yescharacteristic
934C2×C8C22×D411yescharacteristic
935C2×C8C22×D411yescharacteristic
936C2×C8C22×D411yescharacteristic
937C2×C8C2511yescharacteristic
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4C2×D811yescharacteristic
970C4⋊C4C2×D811yescharacteristic
971C4⋊C4C2×D811yescharacteristic
972C4⋊C4C2×D811yescharacteristic
973C4⋊C4C2×D811yescharacteristic
974C4⋊C4C2×D811yescharacteristic
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4C2×D811yescharacteristic
1019C22⋊C4C2×D811yescharacteristic
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C22⋊C4C2×D811yescharacteristic
1024C22⋊C4C2×D811yescharacteristic
1025C22⋊C4C2×D811yescharacteristic
1026C22⋊C4C2×D811yescharacteristic
1027C22⋊C4C2×D811yescharacteristic
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42C2×D811yescharacteristic
1040C42C2×D811yescharacteristic
1041C42C22×D411yescharacteristic
1042C42C22×D411yescharacteristic
1043C42C22×D411yescharacteristic
1044C42C22×D411yescharacteristic
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16—21no—
1050C16—21no—
1051C16—21no—
1052C16C2×#4112yes—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—82no—
1059C23—82no—
1060C23—82no—
1061C23—161no—
1062C23—161no—
1063C23—161no—
1064C23—161no—
1065C23—161no—
1066C23—161no—
1067C23C22×D811yescharacteristic
1068C23C22×D811yescharacteristic
1069C23C22×D811yescharacteristic
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—82no—
1078Q8—161no—
1079Q8—161no—
1080Q8—161no—
1081D4—22no—
1082D4—22no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—82no—
1095D4—82no—
1096D4—82no—
1097D4—82no—
1098D4—82no—
1099D4—82no—
1100D4—82no—
1101D4—161no—
1102D4—161no—
1103D4—161no—
1104D4—161no—
1105D4—161no—
1106D4—161no—
1107D4—161no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—161no—
1132C2×C4—161no—
1133C2×C4—161no—
1134C2×C4—161no—
1135C2×C4—161no—
1136C2×C4—161no—
1137C2×C4—161no—
1138C2×C4—161no—
1139C2×C4—161no—
1140C2×C4—161no—
1141C2×C4—161no—
1142C2×C4—161no—
1143C2×C4—161no—
1144C2×C4—161no—
1145C2×C4C22×D811yescharacteristic
1146C2×C4C22×D811yescharacteristic
1147C2×C4C22×D811yescharacteristic
1148C2×C4C22×D811yescharacteristic
1149C2×C4C22×D811yescharacteristic
1150C2×C4C22×D811yescharacteristic
1151C2×C4C22×D811yescharacteristic
1152C2×C4C22×D811yescharacteristic
1153C2×C4C22×D811yescharacteristic
1154C2×C4C22×D811yescharacteristic
1155C2×C4C22×D811yescharacteristic
1156C2×C4C23×D411yescharacteristic
1157C8—21no—
1158C8—21no—
1159C8—21no—
1160C8—21no—
1161C8—21no—
1162C8—21no—
1163C8—21no—
1164C8C22×#4111yescharacteristic
1165C8#58511yescharacteristic
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—42no—
1176C22—42no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—322no—
1191C22—322no—
1192C22—322no—
1193C22C23×D811yescharacteristic
1194C4—21no—
1195C4—21no—
1196C4—21no—
1197C4—21no—
1198C4—21no—
1199C4—21no—
1200C4—21no—
1201C4—21no—
1202C4—21no—
1203C4—21no—
1204C4—21no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4D4×#4111yescharacteristic
1217C4#358411yescharacteristic
1218C2—41no—
1219C2—41no—
1220C2—41no—
1221C2—82no—
1222C2—82no—
1223C2—161no—
1224C2—161no—
1225C2—161no—
1226C2D8×#4111yescharacteristic
1227C2#6263511yescharacteristic
1228C2#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. #61487C2semidirect
2. #61475C2semidirect
3. #33968C2semidirect
4. #33951C2semidirect
5. #33937C2semidirect
6. #33934C2semidirect
7. #33916C2semidirect
8. #33914C2semidirect
9. #33907C2semidirect
10. #33886C2semidirect
11. #33878C2semidirect
12. #33878C2semidirect
13. #33877C2semidirect
14. #33870C2semidirect
15. #33864C2semidirect
16. #33846C2semidirect
17. #33833C2semidirect
18. #33830C2semidirect
19. #33746C2semidirect
20. #33745C2semidirect
21. #33742C2semidirect
22. #33684C2semidirect
23. #33683C2semidirect
24. #33678C2semidirect
25. #33678C2semidirect
26. #33666C2semidirect
27. #33662C2semidirect
28. #33482C2semidirect
29. #33456C2semidirect
30. #33454C2semidirect
31. #33451C2semidirect
37. #3396C22semidirect
38. #3393C22semidirect
39. #3380C22semidirect
40. Q8×D8C22semidirect
44. #3342C22semidirect
46. #3341C22semidirect
47. #3339C22semidirect
55. #3283C22semidirect
58. #3280C22semidirect
59. #3280C22semidirect
61. #3177C22semidirect
63. #3175C22semidirect
64. #3175C22semidirect
65. #3169C22semidirect
66. #3168C22semidirect
74. #2951C22semidirect
76. #2948C22semidirect
77. #2948C22semidirect
78. C4×#135C22semidirect
79. C4×#135C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2254C22semidirect
83. #2251C22semidirect
85. #2249C22semidirect
86. #2244C22semidirect
87. #2243C22semidirect
88. #2243C22semidirect
89. #2243C22semidirect
90. #2242C22semidirect
91. #2241C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2236C22semidirect
99. #2234C22semidirect
100. #2234C22semidirect
101. #2234C22semidirect
102. #2234C22semidirect
103. #2232C22semidirect
104. #2229C22semidirect
105. #2228C22semidirect
106. #2228C22semidirect
107. #2228C22semidirect
108. #2227C22semidirect
109. #2227C22semidirect
110. #2226C22semidirect
111. #2226C22semidirect
112. #2226C22semidirect
113. #2224C22semidirect
114. #2224C22semidirect
115. #2224C22semidirect
117. #2219C22semidirect
118. #2219C22semidirect
121. #2217C22semidirect
122. #2217C22semidirect
123. #2217C22semidirect
124. #2217C22semidirect
125. #2216C22semidirect
126. #2215C22semidirect
127. #2215C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
132. #2210C22semidirect
133. #2210C22semidirect
134. #2210C22semidirect
135. #2210C22semidirect
136. #2208C22semidirect
137. #2208C22semidirect
138. #2207C22semidirect
140. #2189C22semidirect
141. #2189C22semidirect
144. #2187C22semidirect
145. #2187C22semidirect
148. #2186C22semidirect
149. #2186C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
157. #2177C22semidirect
158. #2177C22semidirect
159. #2177C22semidirect
160. #2177C22semidirect
161. #2176C22semidirect
162. #2176C22semidirect
163. #2175C22semidirect
164. #2175C22semidirect
165. #2175C22semidirect
166. #2175C22semidirect
167. #2175C22semidirect
168. #2175C22semidirect
169. #2175C22semidirect
170. C4×Q32C22semidirect
171. C4×SD32C22semidirect
172. C4×SD32C22semidirect
173. C4×SD32C22semidirect
174. C4×SD32C22semidirect
175. C4×SD32C22semidirect
179. C4×D16C22semidirect
180. C4×D16C22semidirect
181. C4×D16C22semidirect
184. #2168C22semidirect
185. #2168C22semidirect
186. D4×C16C22semidirect
187. D4×C16C22semidirect
188. #2164C22semidirect
189. #2164C22semidirect
190. #2162C22semidirect
191. #2159C22semidirect
192. #2158C22semidirect
193. #2158C22semidirect
195. #2140C22semidirect
196. #2138C22semidirect
197. #2138C22semidirect
198. #2138C22semidirect
199. C2×#357C22semidirect
200. #2108C22semidirect
201. #2108C22semidirect
202. C2×#346C22semidirect
733. D16#41semidirect

Maximal subgroups

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

subgroupindex
#614872
#614752
#339682
#339512
#339372
#339342
#339162
#339142
#339072
#338862
#338782
#338772
#338702
#338642
#338462
#338332
#338302
#337462
#337452
#337422
#336842
#336832
#336782
#336662
#336622
#334822
#334562
#334542
#334512