Finite Group Databasebeta

← #7623528

Subgroups — #7623528

Order 512.

1269 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60696C211yesmaximal, characteristic, complemented
2#60695C211yesmaximal, characteristic, complemented
3#33828C211yesmaximal, characteristic, complemented
4#33826C211yesmaximal, characteristic, complemented
5#33824C211yesmaximal, characteristic, complemented
6#33823C211yesmaximal, characteristic, complemented
7#33809C211yesmaximal, characteristic, complemented
8#33809C211yesmaximal, characteristic, complemented
9#33808C211yesmaximal, characteristic, complemented
10#33807C211yesmaximal, characteristic, complemented
11#33791C211yesmaximal, characteristic, complemented
12#33790C211yesmaximal, characteristic, complemented
13#33788C211yesmaximal, characteristic, complemented
14#33787C211yesmaximal, characteristic, complemented
15#33769C211yesmaximal, characteristic, complemented
16#33767C211yesmaximal, characteristic, complemented
17#33766C211yesmaximal, characteristic, complemented
18#33764C211yesmaximal, characteristic, complemented
19#33751C211yesmaximal, characteristic, complemented
20#33750C211yesmaximal, characteristic, complemented
21#33747C211yesmaximal, characteristic, complemented
22#33746C211yesmaximal, characteristic, complemented
23#33677C211yesmaximal, characteristic, complemented
24#33676C211yesmaximal, characteristic, complemented
25#33675C211yesmaximal, characteristic, complemented
26#33674C211yesmaximal, characteristic, complemented
27#33672C211yesmaximal, characteristic, complemented
28#33671C211yesmaximal, characteristic, complemented
29#33671C211yesmaximal, characteristic, complemented
30#33670C211yesmaximal, characteristic, complemented
31#33421C211yesmaximal, characteristic, complemented
32#3461—21no—
33#3460—21no—
34#3179—21no—
35#3179—21no—
36#3178—21no—
37#3178—21no—
38#3177C2211yescharacteristic
39#3177C2211yescharacteristic, complemented
40#3176C2211yescharacteristic
41#3176C2211yescharacteristic
42#3175C2211yescharacteristic
43#3175C2211yescharacteristic
44#3175C2211yescharacteristic
45#3175C2211yescharacteristic, complemented
46#3172—21no—
47#3172—21no—
48#3171—21no—
49#3171—21no—
50#3170C2211yescharacteristic
51#3170C2211yescharacteristic, complemented
52#3169C2211yescharacteristic
53#3169C2211yescharacteristic
54#3168C2211yescharacteristic
55#3168C2211yescharacteristic
56#3168C2211yescharacteristic
57#3168C2211yescharacteristic, complemented
58#3164C2211yescharacteristic
59#3164C2211yescharacteristic, complemented
60#3156C2211yescharacteristic, complemented
61#3155C2211yescharacteristic
62#3137—21no—
63#3136—21no—
64#3063—21no—
65#3062—21no—
66#3061C2211yescharacteristic
67#3061C2211yescharacteristic
68#3059C2211yescharacteristic
69#3058C2211yescharacteristic
70C4×#137—21no—
71C4×AGL(1,ℤ/8)—21no—
72C4×#135C2211yescharacteristic
73C4×#135C2211yescharacteristic, complemented
74C2×C4×Q16C2211yescharacteristic, complemented
75C2×C4×D8C2211yescharacteristic
76C4×#131C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2253C2211yescharacteristic, complemented
80#2252C2211yescharacteristic, complemented
81#2251C2211yescharacteristic
82#2250C2211yescharacteristic
83#2249C2211yescharacteristic
84#2248C2211yescharacteristic
85#2245C2211yescharacteristic, complemented
86#2244C2211yescharacteristic
87#2243C2211yescharacteristic
88#2243C2211yescharacteristic, complemented
89#2242C2211yescharacteristic
90#2242C2211yescharacteristic, complemented
91#2241C2211yescharacteristic, complemented
92#2240C2211yescharacteristic
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic
95#2237C2211yescharacteristic
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic
98#2236C2211yescharacteristic
99#2236C2211yescharacteristic, complemented
100#2235C2211yescharacteristic
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic
103#2234C2211yescharacteristic
104#2234C2211yescharacteristic, complemented
105#2233C2211yescharacteristic
106#2232C2211yescharacteristic
107#2232C2211yescharacteristic
108#2232C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2229C2211yescharacteristic, complemented
111#2229C2211yescharacteristic, complemented
112#2229C2211yescharacteristic, complemented
113#2228C2211yescharacteristic
114#2228C2211yescharacteristic
115#2228C2211yescharacteristic, complemented
116#2228C2211yescharacteristic, complemented
117#2227C2211yescharacteristic, complemented
118#2227C2211yescharacteristic, complemented
119#2227C2211yescharacteristic, complemented
120#2226C2211yescharacteristic, complemented
121#2225C2211yescharacteristic, complemented
122#2224C2211yescharacteristic
123#2224C2211yescharacteristic
124#2224C2211yescharacteristic, complemented
125#2220C2211yescharacteristic
126#2220C2211yescharacteristic
127#2220C2211yescharacteristic
128#2220C2211yescharacteristic, complemented
129#2220C2211yescharacteristic, complemented
130#2220C2211yescharacteristic, complemented
131#2219C2211yescharacteristic, complemented
132#2218C2211yescharacteristic
133#2217C2211yescharacteristic
134#2217C2211yescharacteristic
135#2217C2211yescharacteristic
136#2217C2211yescharacteristic, complemented
137#2216C2211yescharacteristic, complemented
138#2216C2211yescharacteristic, complemented
139#2215C2211yescharacteristic
140#2215C2211yescharacteristic, complemented
141#2211C2211yescharacteristic
142#2211C2211yescharacteristic
143#2211C2211yescharacteristic
144#2211C2211yescharacteristic, complemented
145#2210C2211yescharacteristic
146#2210C2211yescharacteristic
147#2210C2211yescharacteristic
148#2210C2211yescharacteristic, complemented
149#2209C2211yescharacteristic, complemented
150#2208C2211yescharacteristic
151#2208C2211yescharacteristic
152#2208C2211yescharacteristic, complemented
153#2207C2211yescharacteristic
154#2207C2211yescharacteristic
155#2207C2211yescharacteristic
156#2206C2211yescharacteristic
157#2189C2211yescharacteristic
158#2189C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2187C2211yescharacteristic
163#2187C2211yescharacteristic
164#2187C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic
167#2186C2211yescharacteristic
168#2186C2211yescharacteristic, complemented
169#2185C2211yescharacteristic
170#2185C2211yescharacteristic
171#2185C2211yescharacteristic, complemented
172#2184C2211yescharacteristic
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic
175#2177C2211yescharacteristic, complemented
176#2176C2211yescharacteristic, complemented
177#2176C2211yescharacteristic, complemented
178#2176C2211yescharacteristic, complemented
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic
183#2175C2211yescharacteristic
184#2175C2211yescharacteristic
185#2175C2211yescharacteristic, complemented
186#2175C2211yescharacteristic, complemented
187#2175C2211yescharacteristic, complemented
188#2175C2211yescharacteristic, complemented
189#2164C2211yescharacteristic
190#2164C2211yescharacteristic
191#2164C2211yescharacteristic, complemented
192#2164C2211yescharacteristic, complemented
193#2163C2211yescharacteristic
194#2163C2211yescharacteristic
195#2163C2211yescharacteristic, complemented
196#2163C2211yescharacteristic, complemented
197#2151C2211yescharacteristic, complemented
198#2151C2211yescharacteristic, complemented
199#2113C2211yescharacteristic
200#2113C2211yescharacteristic
201C4×M32C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#137—21no—
204C2×AGL(1,ℤ/8)—21no—
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×#131D411yescharacteristic
210C2×#131C2311yescharacteristic
211#544—21no—
212#544—21no—
213#542—21no—
214#542—21no—
215#542—21no—
216#542—21no—
217#542—41no—
218#542—41no—
219#541—21no—
220#541—21no—
221#541—41no—
222#540—21no—
223#540—21no—
224#540—41no—
225#539—41no—
226#539—41no—
227#538—41no—
228#538—41no—
229#537—21no—
230#537—21no—
231#536—21no—
232#536—21no—
233#535—21no—
234#535—21no—
235#533—21no—
236#533—21no—
237#533—41no—
238#532—21no—
239#532—21no—
240#532—41no—
241#529—21no—
242#529—21no—
243#529—21no—
244#529—21no—
245#529—41no—
246#529—41no—
247#529—41no—
248#529—41no—
249#525—41no—
250#525—41no—
251C4×#41—21no—
252C4×#41—21no—
253C4×#41D411yescharacteristic
254C2×C4×Q8—21no—
255C2×C4×D4—21no—
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×SD32C2311yescharacteristic
260C2×SD32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×D16C2311yescharacteristic
270C2×D16C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×M32C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C22×C16C2311yescharacteristic
275C22×C16C2311yescharacteristic
276#501—21no—
277#501—21no—
278#501—21no—
279#501—21no—
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#500C2311yescharacteristic
284#499C2311yescharacteristic
285#499C2311yescharacteristic
286#499C2311yescharacteristic
287#499C2311yescharacteristic
288#497—21no—
289#497—21no—
290#496—21no—
291#496—21no—
292#495C2311yescharacteristic
293#495C2311yescharacteristic
294#495C2311yescharacteristic
295#495C2311yescharacteristic
296#494C2311yescharacteristic
297#494C2311yescharacteristic
298#493C2311yescharacteristic
299#493C2311yescharacteristic
300#491—21no—
301#491—21no—
302#490—21no—
303#490—21no—
304#489—21no—
305#489—21no—
306#489—21no—
307#489—21no—
308#488—21no—
309#488—21no—
310#488—21no—
311#488—21no—
312#487—21no—
313#487—21no—
314#486—21no—
315#486—21no—
316#470—21no—
317#470—21no—
318#470—21no—
319#470—21no—
320#469—21no—
321#469—21no—
322#469—21no—
323#469—21no—
324#468—21no—
325#468—21no—
326#468—21no—
327#468—21no—
328#468—21no—
329#468—21no—
330#468—21no—
331#468—21no—
332#467—21no—
333#467—21no—
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#466—21no—
343#466—21no—
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#466C2311yescharacteristic
347#466C2311yescharacteristic
348#466C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#465—21no—
353#465—21no—
354#465—21no—
355#465—21no—
356#442—21no—
357#442—21no—
358#441—21no—
359#441—21no—
360#440—21no—
361#440—21no—
362#440—21no—
363#440—21no—
364C4×Q16—21no—
365C4×Q16—21no—
366C4×Q16—21no—
367C4×Q16—21no—
368C4×Q16C2311yescharacteristic
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×SD16—21no—
377C4×SD16—21no—
378C4×SD16—21no—
379C4×SD16—21no—
380C4×SD16—21no—
381C4×SD16—21no—
382C4×SD16—21no—
383C4×SD16—21no—
384C4×D8—21no—
385C4×D8—21no—
386C4×D8—21no—
387C4×D8—21no—
388C4×D8C2311yescharacteristic
389C4×D8C2311yescharacteristic
390C4×D8C2311yescharacteristic
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396#428—21no—
397#428—21no—
398#427C2311yescharacteristic
399#427C2311yescharacteristic
400C2×#107C2311yescharacteristic
401C2×#107C2311yescharacteristic
402#419—21no—
403#418—21no—
404#417—21no—
405#417—21no—
406#416—21no—
407#416—21no—
408C2×#103—21no—
409C2×#102—21no—
410#405D411yescharacteristic
411#405D411yescharacteristic
412#405D411yescharacteristic
413#405C2311yescharacteristic
414#405C2311yescharacteristic
415#405C2311yescharacteristic
416C4×M16D411yescharacteristic
417C4×M16D411yescharacteristic
418C4×M16D411yescharacteristic
419C2×C4×C8C2311yescharacteristic
420C2×C4×C8C2311yescharacteristic
421C2×C4×C8C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438C4⋊C16C2311yescharacteristic
439C4⋊C16C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446#358C2311yescharacteristic
447#358C2311yescharacteristic
448#358C2311yescharacteristic
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#358C2311yescharacteristic
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
478C22⋊C16C2311yescharacteristic
479C22⋊C16C2311yescharacteristic
480C22⋊C16C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486#346C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41C2×D411yescharacteristic
499C22×Q8—21no—
500C22×D4—21no—
501C23×C4—41no—
502#137—44no—
503AGL(1,ℤ/8)—44no—
504#135—41no—
505#135—41no—
506#135—41no—
507#135—41no—
508C2×Q16—21no—
509C2×Q16—21no—
510C2×Q16—21no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16C2411yescharacteristic
514C2×Q16C2411yescharacteristic
515C2×Q16C2411yescharacteristic
516C2×Q16C2411yescharacteristic
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—21no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8C2411yescharacteristic
529C2×D8C2411yescharacteristic
530C2×D8C2411yescharacteristic
531C2×D8C2411yescharacteristic
532#131—41no—
533#131—41no—
534#131—42no—
535C2×M16C2×D411yescharacteristic
536C2×M16C2×D411yescharacteristic
537C2×M16C2×D411yescharacteristic
538C2×M16C2×D411yescharacteristic
539C2×M16C2×D411yescharacteristic
540C2×M16C2×D411yescharacteristic
541C22×C8C2×D411yescharacteristic
542C22×C8C2×D411yescharacteristic
543C22×C8C2×D411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552C4⋊Q8—21no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#127—21no—
557#127—21no—
558#127—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#126—41no—
564#126—41no—
565#126—41no—
566#126—41no—
567#126—41no—
568#126—41no—
569#126—41no—
570#126—41no—
571#125—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125—41no—
576#125—41no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—41no—
583#124—21no—
584#124—21no—
585#124—21no—
586#124—21no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123—41no—
604#123—41no—
605#123—41no—
606#123—41no—
607#123—41no—
608#123—41no—
609#123—41no—
610#123—41no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—41no—
642#121—41no—
643#121—41no—
644#121—41no—
645#121—41no—
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#120—41no—
656#120—41no—
657#120—41no—
658#120—41no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—21no—
664C4×Q8—21no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—41no—
668C4×Q8—41no—
669C4×Q8—41no—
670C4×Q8—41no—
671C4×Q8D811yescharacteristic
672C4×Q8D811yescharacteristic
673C4×D4—21no—
674C4×D4—21no—
675C4×D4—21no—
676C4×D4—21no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—21no—
680C4×D4—21no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4—41no—
684C4×D4—41no—
685C4×D4—41no—
686C4×D4—41no—
687C4×D4—41no—
688C4×D4—41no—
689C4×D4—41no—
690C4×D4—41no—
691C4×D4—41no—
692C4×D4—41no—
693C4×D4D811yescharacteristic
694C4×D4D811yescharacteristic
695C4×D4D811yescharacteristic
696C4×D4D811yescharacteristic
697C4×D4D811yescharacteristic
698C4×D4D811yescharacteristic
699#117—21no—
700#117—21no—
701#117—41no—
702#117—41no—
703#117—41no—
704#117—41no—
705#117—41no—
706#117—41no—
707#117—41no—
708#117—41no—
709#117C2×D411yescharacteristic
710#117C2×D411yescharacteristic
711#117C2×D411yescharacteristic
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42—41no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722Q32—41no—
723Q32—41no—
724Q32—41no—
725SD32—41no—
726SD32—41no—
727SD32—41no—
728SD32—41no—
729SD32—41no—
730SD32—41no—
731SD32—41no—
732SD32—41no—
733SD32—41no—
734SD32—41no—
735D16—41no—
736D16—41no—
737D16—41no—
738M32—41no—
739M32—41no—
740C2×C16—41no—
741C2×C16—41no—
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748C2×C16C2411yescharacteristic
749C2×C16C2411yescharacteristic
750#107—21no—
751#107—21no—
752#107—21no—
753#107—21no—
754#107—21no—
755#107—21no—
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#107C2411yescharacteristic
763#107C2411yescharacteristic
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768#106—21no—
769#106—21no—
770#103—21no—
771#103—21no—
772#103—21no—
773#103—21no—
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#97C2×D411yescharacteristic
803#97C2×D411yescharacteristic
804#97C2×D411yescharacteristic
805#97C2×D411yescharacteristic
806#97C2×D411yescharacteristic
807#97C2×D411yescharacteristic
808C4×C8C2×D411yescharacteristic
809C4×C8C2×D411yescharacteristic
810C4×C8C2×D411yescharacteristic
811C4×C8C2×D411yescharacteristic
812C4×C8C2×D411yescharacteristic
813C4×C8C2×D411yescharacteristic
814C4×C8C2411yescharacteristic
815C4×C8C2411yescharacteristic
816C4×C8C2411yescharacteristic
817C4×C8C2411yescharacteristic
818C24—41no—
819#41—41no—
820#41—41no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—162no—
826#41—162no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—41no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8C2×D811yescharacteristic
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
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×D4C2×D811yescharacteristic
861C2×D4C2×D811yescharacteristic
862C2×D4C2×D811yescharacteristic
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—162no—
877C22×C4C2×D811yescharacteristic
878C22×C4C2×D811yescharacteristic
879C22×C4C2×D811yescharacteristic
880C22×C4C2×D811yescharacteristic
881C22×C4C2×D811yescharacteristic
882C22×C4C2×D811yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886Q16—21no—
887Q16—21no—
888Q16—21no—
889Q16—21no—
890Q16—21no—
891Q16—21no—
892Q16—21no—
893Q16—21no—
894Q16—42no—
895Q16—42no—
896Q16—42no—
897SD16—42no—
898SD16—42no—
899SD16—42no—
900SD16—42no—
901SD16—42no—
902SD16—42no—
903D8—21no—
904D8—21no—
905D8—21no—
906D8—21no—
907D8—21no—
908D8—21no—
909D8—21no—
910D8—21no—
911D8—42no—
912D8—42no—
913D8—42no—
914M16—22no—
915M16—22no—
916M16—41no—
917M16—41no—
918M16—41no—
919M16—41no—
920C2×C8—22no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—41no—
928C2×C8—41no—
929C2×C8C22×D411yescharacteristic
930C2×C8C22×D411yescharacteristic
931C2×C8C22×D411yescharacteristic
932C2×C8C22×D411yescharacteristic
933C2×C8C22×D411yescharacteristic
934C2×C8C22×D411yescharacteristic
935C2×C8C22×D411yescharacteristic
936C2×C8C2511yescharacteristic
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—41no—
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⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4C2×D811yescharacteristic
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
1019C22⋊C4C2×D811yescharacteristic
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C22⋊C4C2×D811yescharacteristic
1024C22⋊C4C2×D811yescharacteristic
1025C42—41no—
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42C2×D811yescharacteristic
1036C42C2×D811yescharacteristic
1037C42C2×D811yescharacteristic
1038C42C2×D811yescharacteristic
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—
1052C16—21no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—82no—
1058C23—161no—
1059C23—161no—
1060C23C22×D811yescharacteristic
1061C23C22×D811yescharacteristic
1062C23C22×D811yescharacteristic
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—82no—
1073Q8—161no—
1074Q8—161no—
1075Q8—161no—
1076Q8—161no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—82no—
1089D4—82no—
1090D4—82no—
1091D4—161no—
1092D4—161no—
1093D4—161no—
1094D4—161no—
1095D4—161no—
1096D4—161no—
1097D4—161no—
1098D4—161no—
1099D4—161no—
1100D4—161no—
1101D4—161no—
1102D4—161no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
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—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—161no—
1135C2×C4—161no—
1136C2×C4—161no—
1137C2×C4—161no—
1138C2×C4—161no—
1139C2×C4—161no—
1140C2×C4C22×D811yescharacteristic
1141C2×C4C22×D811yescharacteristic
1142C2×C4C22×D811yescharacteristic
1143C2×C4C22×D811yescharacteristic
1144C2×C4C22×D811yescharacteristic
1145C2×C4C22×D811yescharacteristic
1146C2×C4C22×D811yescharacteristic
1147C2×C4C22×D811yescharacteristic
1148C2×C4C22×D811yescharacteristic
1149C2×C4C22×D811yescharacteristic
1150C2×C4C22×D811yescharacteristic
1151C2×C4C23×D411yescharacteristic
1152C8—21no—
1153C8—21no—
1154C8—21no—
1155C8—21no—
1156C8—21no—
1157C8—21no—
1158C8#57512yes—
1159C8#58511yescharacteristic
1160C8#58511yescharacteristic
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—164no—
1183C22C23×D811yescharacteristic
1184C4—21no—
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—21no—
1190C4—21no—
1191C4—21no—
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4#344911yescharacteristic
1208C4C2×#57511yescharacteristic
1209C2—41no—
1210C2—41no—
1211C2—41no—
1212C2—161no—
1213C2—161no—
1214C2—161no—
1215C2—161no—
1216C2#6094011yescharacteristic
1217C2#6263611yescharacteristic
1218C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×#131 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60696C2semidirect
2. #60695C2semidirect
3. #33828C2semidirect
4. #33826C2semidirect
5. #33824C2semidirect
6. #33823C2semidirect
7. #33809C2semidirect
8. #33809C2semidirect
9. #33808C2semidirect
10. #33807C2semidirect
11. #33791C2semidirect
12. #33790C2semidirect
13. #33788C2semidirect
14. #33787C2semidirect
15. #33769C2semidirect
16. #33767C2semidirect
17. #33766C2semidirect
18. #33764C2semidirect
19. #33751C2semidirect
20. #33750C2semidirect
21. #33747C2semidirect
22. #33746C2semidirect
23. #33677C2semidirect
24. #33676C2semidirect
25. #33675C2semidirect
26. #33674C2semidirect
27. #33672C2semidirect
28. #33671C2semidirect
29. #33671C2semidirect
30. #33670C2semidirect
31. #33421C2semidirect
39. #3177C22semidirect
45. #3175C22semidirect
51. #3170C22semidirect
57. #3168C22semidirect
59. #3164C22semidirect
60. #3156C22semidirect
73. C4×#135C22semidirect
74. C2×C4×Q16C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2253C22semidirect
80. #2252C22semidirect
85. #2245C22semidirect
88. #2243C22semidirect
90. #2242C22semidirect
91. #2241C22semidirect
96. #2237C22semidirect
99. #2236C22semidirect
104. #2234C22semidirect
108. #2232C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
111. #2229C22semidirect
112. #2229C22semidirect
115. #2228C22semidirect
116. #2228C22semidirect
117. #2227C22semidirect
118. #2227C22semidirect
119. #2227C22semidirect
120. #2226C22semidirect
121. #2225C22semidirect
124. #2224C22semidirect
128. #2220C22semidirect
129. #2220C22semidirect
130. #2220C22semidirect
131. #2219C22semidirect
136. #2217C22semidirect
137. #2216C22semidirect
138. #2216C22semidirect
140. #2215C22semidirect
144. #2211C22semidirect
148. #2210C22semidirect
149. #2209C22semidirect
152. #2208C22semidirect
160. #2189C22semidirect
161. #2188C22semidirect
168. #2186C22semidirect
171. #2185C22semidirect
175. #2177C22semidirect
176. #2176C22semidirect
177. #2176C22semidirect
178. #2176C22semidirect
185. #2175C22semidirect
186. #2175C22semidirect
187. #2175C22semidirect
188. #2175C22semidirect
191. #2164C22semidirect
192. #2164C22semidirect
195. #2163C22semidirect
196. #2163C22semidirect
197. #2151C22semidirect
198. #2151C22semidirect
201. C4×M32C22semidirect
202. C2×#346C22semidirect

Maximal subgroups

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

subgroupindex
#606962
#606952
#338282
#338262
#338242
#338232
#338092
#338082
#338072
#337912
#337902
#337882
#337872
#337692
#337672
#337662
#337642
#337512
#337502
#337472
#337462
#336772
#336762
#336752
#336742
#336722
#336712
#336702
#334212