Finite Group Databasebeta

← #7624908

Subgroups — #7624908

Order 512.

1301 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62271C211yesmaximal, characteristic, complemented
2#62266C211yesmaximal, characteristic
3#33918C211yesmaximal, characteristic, complemented
4#33915C211yesmaximal, characteristic, complemented
5#33910C211yesmaximal, characteristic, complemented
6#33903C211yesmaximal, characteristic, complemented
7#33896C211yesmaximal, characteristic, complemented
8#33890C211yesmaximal, characteristic, complemented
9#33887C211yesmaximal, characteristic, complemented
10#33884C211yesmaximal, characteristic, complemented
11#33879C211yesmaximal, characteristic, complemented
12#33877C211yesmaximal, characteristic, complemented
13#33865C211yesmaximal, characteristic, complemented
14#33863C211yesmaximal, characteristic, complemented
15D4×SD32C211yesmaximal, characteristic, complemented
16#33844C211yesmaximal, characteristic, complemented
17#33832C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33826C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33767C211yesmaximal, characteristic, complemented
22#33766C211yesmaximal, characteristic, complemented
23#33756C211yesmaximal, characteristic, complemented
24#33753C211yesmaximal, characteristic, complemented
25#33745C211yesmaximal, characteristic, complemented
26#33743C211yesmaximal, characteristic, complemented
27#33613C211yesmaximal, characteristic, complemented
28#33609C211yesmaximal, characteristic, complemented
29#33606C211yesmaximal, characteristic, complemented
30C2×#2220C211yesmaximal, characteristic, complemented
31#33436C211yesmaximal, characteristic, complemented
32#3542—21no—
33#3538—21no—
34C2×#510C2211yescharacteristic, complemented
35C2×#510C2211yescharacteristic, complemented
36C22×SD32C2211yescharacteristic
37C22×SD32C2211yescharacteristic, complemented
38C2×#504C2211yescharacteristic, complemented
39C22×M32C2211yescharacteristic, complemented
40#3341C2211yescharacteristic
41#3339C2211yescharacteristic
42#3336C2211yescharacteristic
43#3336C2211yescharacteristic
44#3336C2211yescharacteristic, complemented
45#3336C2211yescharacteristic, complemented
46#3336C2211yescharacteristic, complemented
47#3334C2211yescharacteristic
48#3319—21no—
49#3312—21no—
50#3312—21no—
51#3312—21no—
52#3312—21no—
53#3310—21no—
54#3309—21no—
55#3306—21no—
56#3287C2211yescharacteristic
57D4×Q16C2211yescharacteristic
58D4×Q16C2211yescharacteristic, complemented
59D4×Q16C2211yescharacteristic, complemented
60D4×Q16C2211yescharacteristic, complemented
61#3280C2211yescharacteristic
62#3280C2211yescharacteristic
63D4×D8C2211yescharacteristic
64#3261—21no—
65#3257—21no—
66#3202—21no—
67#3198—21no—
68#3195—21no—
69#3194—21no—
70#3177C2211yescharacteristic, complemented
71#3177C2211yescharacteristic, complemented
72#3176C2211yescharacteristic
73#3175C2211yescharacteristic
74#3061C2211yescharacteristic
75#3059C2211yescharacteristic, complemented
76#3059C2211yescharacteristic, complemented
77#3058C2211yescharacteristic
78#3050C2211yescharacteristic
79C2×#467C2211yescharacteristic, complemented
80C2×#467C2211yescharacteristic, complemented
81C2×#466C2211yescharacteristic
82#2929C2211yescharacteristic
83#2255C2211yescharacteristic, complemented
84#2253C2211yescharacteristic, complemented
85#2251C2211yescharacteristic, complemented
86#2248C2211yescharacteristic, complemented
87#2245C2211yescharacteristic, complemented
88#2244C2211yescharacteristic, complemented
89#2242C2211yescharacteristic, complemented
90#2241C2211yescharacteristic, complemented
91#2237C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2236C2211yescharacteristic, complemented
97#2235C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2235C2211yescharacteristic, complemented
101#2234C2211yescharacteristic, complemented
102#2234C2211yescharacteristic, complemented
103#2234C2211yescharacteristic, complemented
104#2233C2211yescharacteristic
105#2233C2211yescharacteristic, complemented
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2228C2211yescharacteristic, complemented
111#2228C2211yescharacteristic, complemented
112#2228C2211yescharacteristic, complemented
113#2227C2211yescharacteristic, complemented
114#2225C2211yescharacteristic, complemented
115#2220C2211yescharacteristic
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic
119#2220C2211yescharacteristic, complemented
120#2220C2211yescharacteristic, complemented
121#2220C2211yescharacteristic, complemented
122#2220C2211yescharacteristic, complemented
123#2220C2211yescharacteristic, complemented
124#2220C2211yescharacteristic, complemented
125#2220C2211yescharacteristic, complemented
126#2220C2211yescharacteristic, complemented
127#2220C2211yescharacteristic, complemented
128#2219C2211yescharacteristic, complemented
129#2219C2211yescharacteristic, complemented
130#2219C2211yescharacteristic, complemented
131#2217C2211yescharacteristic
132#2217C2211yescharacteristic
133#2217C2211yescharacteristic
134#2217C2211yescharacteristic
135#2217C2211yescharacteristic, complemented
136#2217C2211yescharacteristic, complemented
137#2217C2211yescharacteristic, complemented
138#2217C2211yescharacteristic, complemented
139#2217C2211yescharacteristic, complemented
140#2217C2211yescharacteristic, complemented
141#2217C2211yescharacteristic, complemented
142#2216C2211yescharacteristic, complemented
143#2216C2211yescharacteristic, complemented
144#2216C2211yescharacteristic, complemented
145#2216C2211yescharacteristic, complemented
146#2216C2211yescharacteristic, complemented
147#2211C2211yescharacteristic, complemented
148#2211C2211yescharacteristic, complemented
149#2209C2211yescharacteristic, complemented
150#2208C2211yescharacteristic, complemented
151#2208C2211yescharacteristic, complemented
152#2208C2211yescharacteristic, complemented
153#2207C2211yescharacteristic, complemented
154#2207C2211yescharacteristic, complemented
155#2189C2211yescharacteristic, complemented
156#2189C2211yescharacteristic, complemented
157#2189C2211yescharacteristic, complemented
158#2189C2211yescharacteristic, complemented
159#2188C2211yescharacteristic, complemented
160#2188C2211yescharacteristic, complemented
161#2187C2211yescharacteristic
162#2187C2211yescharacteristic
163#2187C2211yescharacteristic, complemented
164#2187C2211yescharacteristic, complemented
165#2185C2211yescharacteristic
166#2185C2211yescharacteristic
167#2185C2211yescharacteristic, complemented
168#2185C2211yescharacteristic, complemented
169#2185C2211yescharacteristic, complemented
170#2185C2211yescharacteristic, complemented
171#2176C2211yescharacteristic, complemented
172#2175C2211yescharacteristic, complemented
173#2175C2211yescharacteristic, complemented
174#2175C2211yescharacteristic, complemented
175C4×Q32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic, complemented
177C4×SD32C2211yescharacteristic, complemented
178C4×SD32C2211yescharacteristic, complemented
179#2169C2211yescharacteristic, complemented
180#2169C2211yescharacteristic, complemented
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic, complemented
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185D4×C16C2211yescharacteristic
186D4×C16C2211yescharacteristic, complemented
187#2159C2211yescharacteristic, complemented
188#2159C2211yescharacteristic, complemented
189#2158C2211yescharacteristic, complemented
190C2×#366C2211yescharacteristic, complemented
191#2151C2211yescharacteristic, complemented
192#2141C2211yescharacteristic, complemented
193#2141C2211yescharacteristic, complemented
194#2140C2211yescharacteristic, complemented
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic, complemented
197C2×#358C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200#2113C2211yescharacteristic, complemented
201C2×C22⋊C16C2211yescharacteristic, complemented
202#2108C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C2×#131C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#563—41no—
214#563—41no—
215#562—41no—
216#560—41no—
217#555—21no—
218#553—21no—
219#552—21no—
220#552—21no—
221#552—21no—
222#552—21no—
223#552—21no—
224#551—41no—
225#551—41no—
226#551—41no—
227#550—21no—
228D4×Q8—21no—
229D4×Q8—21no—
230D4×Q8—21no—
231D4×Q8—21no—
232#547—21no—
233#546—21no—
234#546—21no—
235#546—41no—
236D42—21no—
237#544—41no—
238#544—41no—
239#542—21no—
240#541—21no—
241#541—21no—
242#540—21no—
243#540—41no—
244#539—41no—
245#539—41no—
246#538—41no—
247#537—21no—
248#536—21no—
249#536—21no—
250#535—21no—
251#535—41no—
252#534—41no—
253#525—21no—
254#525D411yescharacteristic
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257C2×#121—21no—
258#510—42no—
259#510—42no—
260C2×Q32C2311yescharacteristic
261C2×Q32C2311yescharacteristic
262C2×Q32C2311yescharacteristic
263C2×Q32C2311yescharacteristic
264C2×SD32—42no—
265C2×SD32—42no—
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×SD32C2311yescharacteristic
276C2×SD32C2311yescharacteristic
277C2×SD32C2311yescharacteristic
278#504—42no—
279C2×M32—42no—
280C2×M32C2311yescharacteristic
281C2×M32C2311yescharacteristic
282C2×M32C2311yescharacteristic
283C2×M32C2311yescharacteristic
284C2×M32C2311yescharacteristic
285C2×M32C2311yescharacteristic
286C22×C16C2311yescharacteristic
287C22×C16C2311yescharacteristic
288C22×C16C2311yescharacteristic
289C22×C16C2311yescharacteristic
290C22×C16C2311yescharacteristic
291C22×C16C2311yescharacteristic
292#500C2311yescharacteristic
293#499C2311yescharacteristic
294#499C2311yescharacteristic
295#499C2311yescharacteristic
296#495C2311yescharacteristic
297#494C2311yescharacteristic
298#494C2311yescharacteristic
299#493C2311yescharacteristic
300#491—21no—
301#491—21no—
302#490—21no—
303#489—21no—
304#485—21no—
305#485—21no—
306#485—21no—
307#485—21no—
308#485—21no—
309#483—21no—
310#483—21no—
311#483—21no—
312#483—21no—
313#483—21no—
314#482—21no—
315#482—21no—
316#482—21no—
317#481—21no—
318#480—21no—
319#480—21no—
320#479—21no—
321#479—21no—
322#479—21no—
323#479—21no—
324#479—21no—
325#478—21no—
326#476—21no—
327#474—21no—
328#470—21no—
329#470—21no—
330#470—21no—
331#470—21no—
332#470—21no—
333#470—21no—
334#469—21no—
335#469—21no—
336#469—21no—
337#468—21no—
338#468—21no—
339#468—21no—
340#467—21no—
341#467—21no—
342#467—21no—
343#467—21no—
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#467C2311yescharacteristic
349#467C2311yescharacteristic
350#467C2311yescharacteristic
351#467C2311yescharacteristic
352#467C2311yescharacteristic
353#467C2311yescharacteristic
354#467C2311yescharacteristic
355#467C2311yescharacteristic
356#467C2311yescharacteristic
357#467C2311yescharacteristic
358#467C2311yescharacteristic
359#466—21no—
360#466—21no—
361#466C2311yescharacteristic
362#466C2311yescharacteristic
363#466C2311yescharacteristic
364#466C2311yescharacteristic
365#466C2311yescharacteristic
366#466C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#466C2311yescharacteristic
370#465—21no—
371#465—21no—
372#463—21no—
373#463—21no—
374#462—21no—
375#462—21no—
376#462—21no—
377#462—21no—
378#460—21no—
379#459—21no—
380#451—21no—
381#451—21no—
382#451—21no—
383#451—21no—
384#451—21no—
385#451—21no—
386#451—21no—
387#451—21no—
388#450—21no—
389#450—21no—
390#449—21no—
391#449—21no—
392#449—21no—
393#449—21no—
394#447—21no—
395#447—21no—
396#442—21no—
397#441—21no—
398#441—21no—
399#440—21no—
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×Q16C2311yescharacteristic
403C4×Q16C2311yescharacteristic
404C4×Q16C2311yescharacteristic
405C4×D8C2311yescharacteristic
406C4×D8C2311yescharacteristic
407C4×D8C2311yescharacteristic
408#435D411yescharacteristic
409#435D411yescharacteristic
410#435D411yescharacteristic
411#435D411yescharacteristic
412C8×D4C2311yescharacteristic
413C8×D4C2311yescharacteristic
414C8×D4C2311yescharacteristic
415C8×D4C2311yescharacteristic
416#427C2311yescharacteristic
417#427C2311yescharacteristic
418#427C2311yescharacteristic
419#427C2311yescharacteristic
420C2×#107C2311yescharacteristic
421C2×#107C2311yescharacteristic
422C2×#107C2311yescharacteristic
423C2×#107C2311yescharacteristic
424#424D411yescharacteristic
425#419—21no—
426#419—21no—
427#418—21no—
428#417—21no—
429#416—21no—
430C2×#103—21no—
431C2×#103—21no—
432C2×#102—21no—
433#408D411yescharacteristic
434#407D411yescharacteristic
435#405C2311yescharacteristic
436#367C2311yescharacteristic
437#367C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
442#367C2311yescharacteristic
443#367C2311yescharacteristic
444#366C2311yescharacteristic
445#366C2311yescharacteristic
446#366C2311yescharacteristic
447#366C2311yescharacteristic
448#366C2311yescharacteristic
449#366C2311yescharacteristic
450#366C2311yescharacteristic
451#366C2311yescharacteristic
452C4⋊C16C2311yescharacteristic
453C4⋊C16C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#358C2311yescharacteristic
470#358C2311yescharacteristic
471#358C2311yescharacteristic
472#358C2311yescharacteristic
473#358C2311yescharacteristic
474#358C2311yescharacteristic
475#358C2311yescharacteristic
476#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
494C22⋊C16C2311yescharacteristic
495C22⋊C16C2311yescharacteristic
496#346C2311yescharacteristic
497#346C2311yescharacteristic
498C4×C16C2311yescharacteristic
499C4×C16C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—41no—
503C2×#41C2×D411yescharacteristic
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C23×C4C2×D411yescharacteristic
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517C2×Q16—21no—
518C2×Q16—21no—
519C2×Q16—21no—
520C2×Q16—21no—
521C2×Q16—21no—
522C2×Q16—21no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
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×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8C2411yescharacteristic
547C2×D8C2411yescharacteristic
548C2×D8C2411yescharacteristic
549#131—41no—
550#131—41no—
551C2×M16C2×D411yescharacteristic
552C2×M16C2×D411yescharacteristic
553C2×M16C2×D411yescharacteristic
554C2×M16C2×D411yescharacteristic
555C22×C8—41no—
556C22×C8—41no—
557C22×C8C2×D411yescharacteristic
558C22×C8C2×D411yescharacteristic
559C22×C8C2×D411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574#127—21no—
575#127—41no—
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#125—41no—
594#125—41no—
595#125—41no—
596#125—41no—
597#125—41no—
598#125—41no—
599#125—41no—
600#124—21no—
601#124—41no—
602#124—41no—
603#124—41no—
604#124—41no—
605#124—41no—
606#124—41no—
607#123—41no—
608#123—41no—
609#123—41no—
610#123—41no—
611#123—41no—
612#123—41no—
613#123—41no—
614#123—41no—
615#123—41no—
616#123—41no—
617#123—41no—
618#123—41no—
619#123—41no—
620#123—41no—
621#123—41no—
622#123—41no—
623#123—41no—
624#123—41no—
625#123D811yescharacteristic
626#123D811yescharacteristic
627C22⋊Q8—21no—
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8—21no—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647C22⋊Q8—41no—
648C22⋊Q8—41no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—41no—
653C22⋊Q8—41no—
654C22⋊Q8—41no—
655C22⋊Q8—41no—
656C22⋊Q8—41no—
657C22⋊Q8D811yescharacteristic
658C22⋊Q8D811yescharacteristic
659#121—21no—
660#121—21no—
661#121—21no—
662#121—21no—
663#121—21no—
664#121—21no—
665#121—21no—
666#121—21no—
667#121—21no—
668#121—41no—
669#121—41no—
670#121—41no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121—41no—
675#121—41no—
676#121—41no—
677#121—41no—
678#121—41no—
679#121—41no—
680#121—41no—
681#121—41no—
682#121D811yescharacteristic
683#121D811yescharacteristic
684#120—41no—
685#120—41no—
686#120—41no—
687#120—41no—
688#120—41no—
689#120—41no—
690#120—41no—
691#120D811yescharacteristic
692#120D811yescharacteristic
693C4×Q8—21no—
694C4×Q8—21no—
695C4×Q8—21no—
696C4×Q8—21no—
697C4×Q8—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—41no—
702C4×D4—41no—
703C4×D4—41no—
704C4×D4—41no—
705C4×D4—41no—
706C4×D4—41no—
707C4×D4—41no—
708C4×D4—41no—
709C4×D4C2×D411yescharacteristic
710C4×D4C2×D411yescharacteristic
711C4×D4C2×D411yescharacteristic
712C4×D4C2×D411yescharacteristic
713#117—21no—
714#117—21no—
715#117—21no—
716#117—21no—
717#117—41no—
718#117—41no—
719#117—41no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117C2×D411yescharacteristic
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—41no—
729C2×C4⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735Q32—22no—
736Q32—41no—
737Q32—41no—
738Q32—41no—
739SD32—22no—
740SD32—22no—
741SD32—22no—
742SD32—41no—
743SD32—41no—
744SD32—41no—
745SD32—41no—
746SD32—41no—
747SD32—41no—
748SD32—41no—
749SD32—41no—
750SD32—41no—
751M32—22no—
752M32—22no—
753M32—22no—
754M32—41no—
755M32—41no—
756M32—41no—
757C2×C16—22no—
758C2×C16—22no—
759C2×C16—41no—
760C2×C16—41no—
761C2×C16—41no—
762C2×C16—41no—
763C2×C16C2411yescharacteristic
764C2×C16C2411yescharacteristic
765C2×C16C2411yescharacteristic
766C2×C16C2411yescharacteristic
767C2×C16C2411yescharacteristic
768C2×C16C2411yescharacteristic
769C2×C16C2411yescharacteristic
770C2×C16C2411yescharacteristic
771#107—21no—
772#107—21no—
773#107—21no—
774#107—21no—
775#107—21no—
776#107C2411yescharacteristic
777#107C2411yescharacteristic
778#107C2411yescharacteristic
779#107C2411yescharacteristic
780#107C2411yescharacteristic
781#107C2411yescharacteristic
782#107C2411yescharacteristic
783#107C2411yescharacteristic
784#106—21no—
785#106—21no—
786#106—21no—
787#106—21no—
788#106—21no—
789#106—21no—
790#106—21no—
791C4⋊C8C2×D411yescharacteristic
792C4⋊C8C2×D411yescharacteristic
793C4⋊C8C2×D411yescharacteristic
794C4⋊C8C2×D411yescharacteristic
795#103—21no—
796#103—21no—
797#103—21no—
798#103—21no—
799#103—21no—
800#103—21no—
801#103—21no—
802#103—21no—
803#103—21no—
804#103—21no—
805#103—21no—
806#103—21no—
807#103—21no—
808#103—21no—
809#103—21no—
810#103—21no—
811#103—21no—
812#103—21no—
813#103—21no—
814#103—21no—
815#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—
826#102—21no—
827C22⋊C8C2×D411yescharacteristic
828C22⋊C8C2×D411yescharacteristic
829C22⋊C8C2×D411yescharacteristic
830C22⋊C8C2×D411yescharacteristic
831C22⋊C8C2×D411yescharacteristic
832C22⋊C8C2×D411yescharacteristic
833C22⋊C8C2×D411yescharacteristic
834C22⋊C8C2×D411yescharacteristic
835#97C2×D411yescharacteristic
836#97C2×D411yescharacteristic
837C4×C8C2411yescharacteristic
838C4×C8C2411yescharacteristic
839C24—41no—
840C24—41no—
841C24C2×D811yescharacteristic
842#41—41no—
843#41—41no—
844#41—81no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—162no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8C2×D811yescharacteristic
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—162no—
891C2×D4—162no—
892C2×D4C2×D811yescharacteristic
893C2×D4C2×D811yescharacteristic
894C2×D4C2×D811yescharacteristic
895C2×D4C2×D811yescharacteristic
896C2×D4C2×D811yescharacteristic
897C2×D4C2×D811yescharacteristic
898C2×D4C2×D811yescharacteristic
899C22×C4—41no—
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×C4C2×D811yescharacteristic
915C22×C4C2×D811yescharacteristic
916C22×C4C2×D811yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922Q16—21no—
923Q16—21no—
924Q16—21no—
925Q16—21no—
926Q16—21no—
927Q16—21no—
928Q16—21no—
929Q16—21no—
930Q16—21no—
931Q16—21no—
932Q16—81no—
933Q16—81no—
934Q16—81no—
935Q16—81no—
936Q16—81no—
937Q16—81no—
938SD16—81no—
939SD16—81no—
940SD16—81no—
941D8—21no—
942D8—21no—
943D8—21no—
944D8—21no—
945D8—21no—
946D8—21no—
947D8—81no—
948D8—81no—
949D8—81no—
950M16—41no—
951M16—41no—
952M16—41no—
953M16—41no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—41no—
965C2×C8—41no—
966C2×C8—41no—
967C2×C8C22×D411yescharacteristic
968C2×C8C22×D411yescharacteristic
969C2×C8C22×D411yescharacteristic
970C2×C8C22×D411yescharacteristic
971C2×C8C22×D411yescharacteristic
972C2×C8C22×D411yescharacteristic
973C2×C8C22×D411yescharacteristic
974C2×C8C2511yescharacteristic
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4C2×D811yescharacteristic
1019C4⋊C4C2×D811yescharacteristic
1020C4⋊C4C2×D811yescharacteristic
1021C4⋊C4C2×D811yescharacteristic
1022C4⋊C4C2×D811yescharacteristic
1023C4⋊C4C2×D811yescharacteristic
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
1063C22⋊C4C2×D811yescharacteristic
1064C22⋊C4C2×D811yescharacteristic
1065C22⋊C4C2×D811yescharacteristic
1066C22⋊C4C2×D811yescharacteristic
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42—41no—
1075C42—41no—
1076C42C22×D411yescharacteristic
1077C42C22×D411yescharacteristic
1078C16—21no—
1079C16—21no—
1080C16—21no—
1081C16—21no—
1082C16—21no—
1083C16—21no—
1084C16—21no—
1085C16H(5,𝔽2)12yes—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—82no—
1093C23—161no—
1094C23—161no—
1095C23—161no—
1096C23—161no—
1097C23—161no—
1098C23C22×D811yescharacteristic
1099C23C22×D811yescharacteristic
1100C23C22×D811yescharacteristic
1101C23C22×D811yescharacteristic
1102C23C22×D811yescharacteristic
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—161no—
1115Q8—161no—
1116Q8—161no—
1117Q8—161no—
1118Q8—161no—
1119D4—22no—
1120D4—22no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—82no—
1133D4—161no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137D4—161no—
1138D4—161no—
1139D4—161no—
1140D4—161no—
1141D4—161no—
1142D4—161no—
1143D4—161no—
1144D4—161no—
1145D4—161no—
1146D4—161no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—41no—
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—82no—
1174C2×C4—82no—
1175C2×C4—82no—
1176C2×C4—161no—
1177C2×C4—161no—
1178C2×C4—161no—
1179C2×C4—161no—
1180C2×C4—161no—
1181C2×C4—161no—
1182C2×C4—161no—
1183C2×C4—161no—
1184C2×C4—161no—
1185C2×C4—161no—
1186C2×C4C22×D811yescharacteristic
1187C2×C4C22×D811yescharacteristic
1188C2×C4C22×D811yescharacteristic
1189C2×C4C22×D811yescharacteristic
1190C2×C4C22×D811yescharacteristic
1191C2×C4C22×D811yescharacteristic
1192C2×C4C22×D811yescharacteristic
1193C2×C4C22×D811yescharacteristic
1194C2×C4C22×D811yescharacteristic
1195C2×C4C23×D411yescharacteristic
1196C8—21no—
1197C8—21no—
1198C8—21no—
1199C8—21no—
1200C8—21no—
1201C8—21no—
1202C8—21no—
1203C8C2×H(5,𝔽2)11yescharacteristic
1204C8#58511yescharacteristic
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—82no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—322no—
1230C22—322no—
1231C22#341612yes—
1232C22C23×D811yescharacteristic
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—21no—
1239C4—21no—
1240C4—21no—
1241C4—21no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4#349611yescharacteristic
1256C4#358411yescharacteristic
1257C2—22no—
1258C2—41no—
1259C2—41no—
1260C2—41no—
1261C2—41no—
1262C2—161no—
1263C2—161no—
1264C2—161no—
1265C2#6224511yescharacteristic
1266C2C2×#341611yescharacteristic
1267C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#62266C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ #2929 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62271C2semidirect
3. #33918C2semidirect
4. #33915C2semidirect
5. #33910C2semidirect
6. #33903C2semidirect
7. #33896C2semidirect
8. #33890C2semidirect
9. #33887C2semidirect
10. #33884C2semidirect
11. #33879C2semidirect
12. #33877C2semidirect
13. #33865C2semidirect
14. #33863C2semidirect
15. D4×SD32C2semidirect
16. #33844C2semidirect
17. #33832C2semidirect
18. #33832C2semidirect
19. #33826C2semidirect
20. #33824C2semidirect
21. #33767C2semidirect
22. #33766C2semidirect
23. #33756C2semidirect
24. #33753C2semidirect
25. #33745C2semidirect
26. #33743C2semidirect
27. #33613C2semidirect
28. #33609C2semidirect
29. #33606C2semidirect
30. C2×#2220C2semidirect
31. #33436C2semidirect
34. C2×#510C22semidirect
35. C2×#510C22semidirect
37. C22×SD32C22semidirect
38. C2×#504C22semidirect
39. C22×M32C22semidirect
44. #3336C22semidirect
45. #3336C22semidirect
46. #3336C22semidirect
58. D4×Q16C22semidirect
59. D4×Q16C22semidirect
60. D4×Q16C22semidirect
70. #3177C22semidirect
71. #3177C22semidirect
75. #3059C22semidirect
76. #3059C22semidirect
79. C2×#467C22semidirect
80. C2×#467C22semidirect
83. #2255C22semidirect
84. #2253C22semidirect
85. #2251C22semidirect
86. #2248C22semidirect
87. #2245C22semidirect
88. #2244C22semidirect
89. #2242C22semidirect
90. #2241C22semidirect
91. #2237C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
96. #2236C22semidirect
97. #2235C22semidirect
98. #2235C22semidirect
99. #2235C22semidirect
100. #2235C22semidirect
101. #2234C22semidirect
102. #2234C22semidirect
103. #2234C22semidirect
105. #2233C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2228C22semidirect
111. #2228C22semidirect
112. #2228C22semidirect
113. #2227C22semidirect
114. #2225C22semidirect
119. #2220C22semidirect
120. #2220C22semidirect
121. #2220C22semidirect
122. #2220C22semidirect
123. #2220C22semidirect
124. #2220C22semidirect
125. #2220C22semidirect
126. #2220C22semidirect
127. #2220C22semidirect
128. #2219C22semidirect
129. #2219C22semidirect
130. #2219C22semidirect
135. #2217C22semidirect
136. #2217C22semidirect
137. #2217C22semidirect
138. #2217C22semidirect
139. #2217C22semidirect
140. #2217C22semidirect
141. #2217C22semidirect
142. #2216C22semidirect
143. #2216C22semidirect
144. #2216C22semidirect
145. #2216C22semidirect
146. #2216C22semidirect
147. #2211C22semidirect
148. #2211C22semidirect
149. #2209C22semidirect
150. #2208C22semidirect
151. #2208C22semidirect
152. #2208C22semidirect
153. #2207C22semidirect
154. #2207C22semidirect
155. #2189C22semidirect
156. #2189C22semidirect
157. #2189C22semidirect
158. #2189C22semidirect
159. #2188C22semidirect
160. #2188C22semidirect
163. #2187C22semidirect
164. #2187C22semidirect
167. #2185C22semidirect
168. #2185C22semidirect
169. #2185C22semidirect
170. #2185C22semidirect
171. #2176C22semidirect
172. #2175C22semidirect
173. #2175C22semidirect
174. #2175C22semidirect
175. C4×Q32C22semidirect
176. C4×SD32C22semidirect
177. C4×SD32C22semidirect
178. C4×SD32C22semidirect
179. #2169C22semidirect
180. #2169C22semidirect
182. #2168C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
186. D4×C16C22semidirect
187. #2159C22semidirect
188. #2159C22semidirect
189. #2158C22semidirect
190. C2×#366C22semidirect
191. #2151C22semidirect
192. #2141C22semidirect
193. #2141C22semidirect
194. #2140C22semidirect
195. #2139C22semidirect
196. #2138C22semidirect
197. C2×#358C22semidirect
198. C2×#358C22semidirect
200. #2113C22semidirect
201. C2×C22⋊C16C22semidirect
202. #2108C22semidirect

Maximal subgroups

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

subgroupindex
#622712
#622662
#339182
#339152
#339102
#339032
#338962
#338902
#338872
#338842
#338792
#338772
#338652
#338632
D4×SD322
#338442
#338322
#338262
#338242
#337672
#337662
#337562
#337532
#337452
#337432
#336132
#336092
#336062
C2×#22202
#334362