Finite Group Databasebeta

← #7624004

Subgroups — #7624004

Order 512.

1331 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61433C211yesmaximal, characteristic, complemented
2#61431C211yesmaximal, characteristic, complemented
3#33968C211yesmaximal, characteristic, complemented
4#33955C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33938C211yesmaximal, characteristic, complemented
7#33918C211yesmaximal, characteristic, complemented
8#33912C211yesmaximal, characteristic, complemented
9#33911C211yesmaximal, characteristic, complemented
10#33893C211yesmaximal, characteristic, complemented
11#33890C211yesmaximal, characteristic, complemented
12#33887C211yesmaximal, characteristic, complemented
13#33883C211yesmaximal, characteristic, complemented
14#33877C211yesmaximal, characteristic, complemented
15#33873C211yesmaximal, characteristic, complemented
16#33841C211yesmaximal, characteristic, complemented
17#33832C211yesmaximal, characteristic, complemented
18#33831C211yesmaximal, characteristic, complemented
19#33738C211yesmaximal, characteristic, complemented
20#33737C211yesmaximal, characteristic, complemented
21#33735C211yesmaximal, characteristic, complemented
22#33668C211yesmaximal, characteristic, complemented
23#33665C211yesmaximal, characteristic, complemented
24#33663C211yesmaximal, characteristic, complemented
25#33662C211yesmaximal, characteristic, complemented
26#33662C211yesmaximal, characteristic, complemented
27#33661C211yesmaximal, characteristic, complemented
28#33479C211yesmaximal, characteristic, complemented
29C4×#510C211yesmaximal, characteristic, complemented
30C4×#509C211yesmaximal, characteristic, complemented
31C2×C4×SD32C211yesmaximal, characteristic, complemented
32#3482—21no—
33#3481—21no—
34C2×#510C2211yescharacteristic
35C2×#509C2211yescharacteristic
36C22×SD32C2211yescharacteristic
37#3396C2211yescharacteristic
38#3393C2211yescharacteristic, complemented
39#3383C2211yescharacteristic, complemented
40#3380C2211yescharacteristic
41#3364—21no—
42#3361—21no—
43#3339C2211yescharacteristic
44#3339C2211yescharacteristic
45#3338C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3334C2211yescharacteristic, complemented
49#3300—21no—
50#3300—21no—
51#3298—21no—
52#3297—21no—
53#3297—21no—
54#3295—21no—
55D4×Q16C2211yescharacteristic, complemented
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic, complemented
58#3280C2211yescharacteristic
59#3280C2211yescharacteristic
60D4×D8C2211yescharacteristic
61#3170C2211yescharacteristic, complemented
62#3169C2211yescharacteristic
63#3168C2211yescharacteristic
64#3168C2211yescharacteristic
65#3168C2211yescharacteristic, complemented
66#3168C2211yescharacteristic, complemented
67#3108—21no—
68#3108—21no—
69#3107—21no—
70#3106—21no—
71#3105—21no—
72#3105—21no—
73C8×#41C2211yescharacteristic
74C4×#135C2211yescharacteristic
75C4×#135C2211yescharacteristic, complemented
76C2×C4×Q16C2211yescharacteristic, complemented
77C2×C4×Q16C2211yescharacteristic, complemented
78C2×C4×D8C2211yescharacteristic
79C2×C4×D8C2211yescharacteristic
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2253C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2250C2211yescharacteristic
85#2249C2211yescharacteristic, complemented
86#2245C2211yescharacteristic, complemented
87#2244C2211yescharacteristic
88#2243C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2242C2211yescharacteristic, complemented
91#2242C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2236C2211yescharacteristic, complemented
95#2235C2211yescharacteristic, complemented
96#2235C2211yescharacteristic, complemented
97#2235C2211yescharacteristic, complemented
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic, complemented
100#2233C2211yescharacteristic, complemented
101#2233C2211yescharacteristic, complemented
102#2233C2211yescharacteristic, complemented
103#2232C2211yescharacteristic
104#2229C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2228C2211yescharacteristic
109#2228C2211yescharacteristic
110#2228C2211yescharacteristic, complemented
111#2228C2211yescharacteristic, complemented
112#2226C2211yescharacteristic
113#2226C2211yescharacteristic, complemented
114#2225C2211yescharacteristic, complemented
115#2225C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic, complemented
119#2220C2211yescharacteristic, complemented
120#2219C2211yescharacteristic, complemented
121#2219C2211yescharacteristic, complemented
122#2218C2211yescharacteristic, complemented
123#2218C2211yescharacteristic, complemented
124#2217C2211yescharacteristic
125#2217C2211yescharacteristic, complemented
126#2216C2211yescharacteristic, complemented
127#2215C2211yescharacteristic
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2211C2211yescharacteristic, complemented
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic, complemented
135#2210C2211yescharacteristic, complemented
136#2208C2211yescharacteristic
137#2208C2211yescharacteristic, complemented
138#2207C2211yescharacteristic
139#2207C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic, complemented
142#2188C2211yescharacteristic, complemented
143#2187C2211yescharacteristic
144#2187C2211yescharacteristic
145#2187C2211yescharacteristic
146#2186C2211yescharacteristic
147#2186C2211yescharacteristic
148#2185C2211yescharacteristic
149#2185C2211yescharacteristic, complemented
150#2185C2211yescharacteristic, complemented
151#2184C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2177C2211yescharacteristic
155#2177C2211yescharacteristic, complemented
156#2176C2211yescharacteristic, complemented
157#2176C2211yescharacteristic, complemented
158#2175C2211yescharacteristic
159#2175C2211yescharacteristic
160#2175C2211yescharacteristic
161#2175C2211yescharacteristic, complemented
162C4×Q32C2211yescharacteristic, complemented
163C4×Q32C2211yescharacteristic, complemented
164C4×Q32C2211yescharacteristic, complemented
165C4×SD32C2211yescharacteristic
166C4×SD32C2211yescharacteristic
167C4×SD32C2211yescharacteristic
168C4×SD32C2211yescharacteristic
169C4×SD32C2211yescharacteristic
170C4×SD32C2211yescharacteristic, complemented
171C4×SD32C2211yescharacteristic, complemented
172C4×SD32C2211yescharacteristic, complemented
173C4×SD32C2211yescharacteristic, complemented
174C4×SD32C2211yescharacteristic, complemented
175C4×SD32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic, complemented
177C4×SD32C2211yescharacteristic, complemented
178C4×SD32C2211yescharacteristic, complemented
179C4×D16C2211yescharacteristic
180C4×D16C2211yescharacteristic, complemented
181C4×D16C2211yescharacteristic, complemented
182#2169C2211yescharacteristic, complemented
183#2169C2211yescharacteristic, complemented
184#2168C2211yescharacteristic
185#2168C2211yescharacteristic
186#2168C2211yescharacteristic, complemented
187#2168C2211yescharacteristic, complemented
188#2162C2211yescharacteristic, complemented
189#2162C2211yescharacteristic, complemented
190#2162C2211yescharacteristic, complemented
191#2159C2211yescharacteristic, complemented
192#2159C2211yescharacteristic, complemented
193C2×#367C2211yescharacteristic, complemented
194#2141C2211yescharacteristic, complemented
195#2140C2211yescharacteristic
196#2139C2211yescharacteristic
197#2139C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200C4×M32C2211yescharacteristic, complemented
201C4×M32C2211yescharacteristic, complemented
202C2×C4×C16C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#559—21no—
210#557—21no—
211#556—21no—
212#556—41no—
213#554—21no—
214#554—21no—
215#553—21no—
216#553—21no—
217#553—41no—
218#552—21no—
219#552—21no—
220#552—41no—
221#552—41no—
222#551—41no—
223#551—41no—
224D4×Q8—21no—
225#548—21no—
226#548—21no—
227#547—21no—
228#547—41no—
229#546—21no—
230#546—21no—
231#546—41no—
232D42—21no—
233#533—21no—
234#533—41no—
235#532—21no—
236#529—21no—
237#529—21no—
238#529—21no—
239#529—21no—
240#529—41no—
241#529—41no—
242#529—41no—
243#525—41no—
244#525—41no—
245C4×#41—21no—
246C4×#41—21no—
247C4×#41—41no—
248C4×#41D411yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—41no—
254#510—24no—
255#509—24no—
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×SD32—24no—
260C2×SD32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×D16C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C2×M32C2311yescharacteristic
276C2×M32C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#499C2311yescharacteristic
282#499C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#494C2311yescharacteristic
290#493C2311yescharacteristic
291#488—21no—
292#488—21no—
293#488—21no—
294#488—21no—
295#487—21no—
296#486—21no—
297#485—21no—
298#485—21no—
299#484—21no—
300#484—21no—
301#483—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#481—21no—
306#481—21no—
307#480—21no—
308#480—21no—
309#479—21no—
310#479—21no—
311#479—21no—
312#479—21no—
313#478—21no—
314#478—21no—
315#478—21no—
316#478—21no—
317#477—21no—
318#476—21no—
319#475—21no—
320#474—21no—
321#467—21no—
322#467C2311yescharacteristic
323#467C2311yescharacteristic
324#467C2311yescharacteristic
325#467C2311yescharacteristic
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#466—21no—
329#466C2311yescharacteristic
330#466C2311yescharacteristic
331#466C2311yescharacteristic
332#466C2311yescharacteristic
333#466C2311yescharacteristic
334#466C2311yescharacteristic
335#465—21no—
336#465—21no—
337#465—21no—
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#463—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#462—21no—
348#461—21no—
349#460—21no—
350#459—21no—
351#452—21no—
352#452—21no—
353#451—21no—
354#451—21no—
355#450—21no—
356#450—21no—
357#449—21no—
358#449—21no—
359#448—21no—
360#448—21no—
361#447—21no—
362#447—21no—
363C8×Q8D411yescharacteristic
364C8×Q8C2311yescharacteristic
365C4×Q16—21no—
366C4×Q16—21no—
367C4×Q16—21no—
368C4×Q16—21no—
369C4×Q16—21no—
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×SD16—21no—
381C4×SD16—21no—
382C4×SD16—21no—
383C4×SD16—21no—
384C4×SD16—21no—
385C4×SD16—21no—
386C4×SD16—21no—
387C4×SD16—21no—
388C4×D8—21no—
389C4×D8—21no—
390C4×D8—21no—
391C4×D8—21no—
392C4×D8—21no—
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403C8×D4D411yescharacteristic
404C8×D4D411yescharacteristic
405C8×D4D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#431D411yescharacteristic
410#431D411yescharacteristic
411#431D411yescharacteristic
412#427C2311yescharacteristic
413#427C2311yescharacteristic
414C2×#107C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#416—21no—
419#416—21no—
420C2×#103—21no—
421C2×#103—21no—
422C2×#102—21no—
423C2×#102—21no—
424C2×C4×C8C2311yescharacteristic
425C2×C4×C8C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#367C2311yescharacteristic
432#367C2311yescharacteristic
433#367C2311yescharacteristic
434#367C2311yescharacteristic
435#367C2311yescharacteristic
436#367C2311yescharacteristic
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#358C2311yescharacteristic
462#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
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
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41D811yescharacteristic
502C22×Q8—21no—
503C22×Q8—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C23×C4—41no—
508C23×C4—41no—
509#135—22no—
510#135—22no—
511#135—41no—
512#135—41no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—21no—
516C2×Q16—21no—
517C2×Q16—21no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16C2411yescharacteristic
521C2×Q16C2411yescharacteristic
522C2×Q16C2411yescharacteristic
523C2×Q16C2411yescharacteristic
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8C2411yescharacteristic
538C2×D8C2411yescharacteristic
539C2×D8C2411yescharacteristic
540C2×D8C2411yescharacteristic
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—41no—
551C4⋊Q8—41no—
552#127—21no—
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#125—21no—
564#125—21no—
565#125—21no—
566#125—21no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#124—21no—
574#124—21no—
575#124—21no—
576#124—21no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#123—41no—
582#123—41no—
583#123—41no—
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—41no—
626#121—41no—
627#120—41no—
628#120—41no—
629#120—41no—
630#120—41no—
631C4×Q8—21no—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—21no—
640C4×Q8—21no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8D811yescharacteristic
648C4×Q8C2×D411yescharacteristic
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
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×D4D811yescharacteristic
680C4×D4D811yescharacteristic
681C4×D4D811yescharacteristic
682C4×D4C2×D411yescharacteristic
683C4×D4C2×D411yescharacteristic
684C4×D4C2×D411yescharacteristic
685#117—21no—
686#117—21no—
687#117—41no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117D811yescharacteristic
698#117D811yescharacteristic
699#117D811yescharacteristic
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—22no—
720Q32—41no—
721SD32—22no—
722SD32—22no—
723SD32—22no—
724SD32—22no—
725SD32—22no—
726SD32—41no—
727SD32—41no—
728SD32—41no—
729SD32—41no—
730SD32#4114yescomplemented
731D16—22no—
732D16—22no—
733D16—41no—
734M32—22no—
735M32—22no—
736M32—41no—
737M32—41no—
738C2×C16—22no—
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#107—21no—
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
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#103—21no—
787#103—21no—
788#103—21no—
789#103—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
812C4×C8C2×D411yescharacteristic
813C4×C8C2×D411yescharacteristic
814C4×C8C2×D411yescharacteristic
815C4×C8C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822C24—41no—
823C24—41no—
824#41—42no—
825#41—42no—
826#41—42no—
827#41—81no—
828#41—81no—
829#41—84no—
830#41—162no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8C2×D811yescharacteristic
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—42no—
849C2×D4—42no—
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—81no—
863C2×D4—81no—
864C2×D4—84no—
865C2×D4C2×D811yescharacteristic
866C2×D4C2×D811yescharacteristic
867C2×D4C2×D811yescharacteristic
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—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—162no—
887C22×C4—162no—
888C22×C4C2×D811yescharacteristic
889C22×C4C2×D811yescharacteristic
890C22×C4C2×D811yescharacteristic
891C22×C4C2×D811yescharacteristic
892C22×C4C2×D811yescharacteristic
893C22×C4C2×D811yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897Q16—21no—
898Q16—21no—
899Q16—21no—
900Q16—21no—
901Q16—21no—
902Q16—21no—
903Q16—21no—
904Q16—42no—
905Q16—42no—
906Q16—81no—
907Q16C2×#4112yes—
908SD16—42no—
909SD16—42no—
910SD16—81no—
911SD16—81no—
912SD16—81no—
913SD16—81no—
914D8—21no—
915D8—21no—
916D8—21no—
917D8—21no—
918D8—21no—
919D8—21no—
920D8—21no—
921D8—42no—
922D8—42no—
923D8—81no—
924D8C2×#4112yes—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—41no—
932C2×C8—41no—
933C2×C8—41no—
934C2×C8C22×D411yescharacteristic
935C2×C8C22×D411yescharacteristic
936C2×C8C22×D411yescharacteristic
937C2×C8C22×D411yescharacteristic
938C2×C8C22×D411yescharacteristic
939C2×C8C22×D411yescharacteristic
940C2×C8C22×D411yescharacteristic
941C2×C8C2511yescharacteristic
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
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⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
985C4⋊C4C2×D811yescharacteristic
986C4⋊C4C2×D811yescharacteristic
987C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C22⋊C4C2×D811yescharacteristic
1024C22⋊C4C2×D811yescharacteristic
1025C22⋊C4C2×D811yescharacteristic
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42C2×D811yescharacteristic
1039C42C2×D811yescharacteristic
1040C42C2×D811yescharacteristic
1041C42C2×D811yescharacteristic
1042C42C2×D811yescharacteristic
1043C42C2×D811yescharacteristic
1044C42C22×D411yescharacteristic
1045C42C22×D411yescharacteristic
1046C42C22×D411yescharacteristic
1047C42C22×D411yescharacteristic
1048C16—21no—
1049C16—21no—
1050C16—21no—
1051C16—21no—
1052C16—21no—
1053C16—21no—
1054C16—21no—
1055C16C2×#4112yes—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—82no—
1061C23—82no—
1062C23—82no—
1063C23—82no—
1064C23—161no—
1065C23—161no—
1066C23C22×D811yescharacteristic
1067C23C22×D811yescharacteristic
1068C23C22×D811yescharacteristic
1069Q8—22no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—82no—
1079Q8—82no—
1080Q8—82no—
1081Q8—161no—
1082D4—22no—
1083D4—22no—
1084D4—22no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—82no—
1094D4—82no—
1095D4—82no—
1096D4—82no—
1097D4—82no—
1098D4—82no—
1099D4—82no—
1100D4—82no—
1101D4—82no—
1102D4—161no—
1103D4—161no—
1104D4—161no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
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—41no—
1128C2×C4—41no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4—82no—
1136C2×C4—82no—
1137C2×C4—82no—
1138C2×C4—82no—
1139C2×C4—82no—
1140C2×C4—82no—
1141C2×C4—161no—
1142C2×C4—161no—
1143C2×C4—161no—
1144C2×C4—161no—
1145C2×C4—161no—
1146C2×C4—161no—
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×C4C22×D811yescharacteristic
1157C2×C4C22×D811yescharacteristic
1158C2×C4C23×D411yescharacteristic
1159C8—21no—
1160C8—21no—
1161C8—21no—
1162C8—21no—
1163C8—21no—
1164C8—21no—
1165C8—21no—
1166C8C22×#4111yescharacteristic
1167C8#58511yescharacteristic
1168C22—21no—
1169C22—21no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
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—164no—
1189C22—164no—
1190C22#341412yes—
1191C22C23×D811yescharacteristic
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—21no—
1196C4—21no—
1197C4—21no—
1198C4—21no—
1199C4—21no—
1200C4—21no—
1201C4—21no—
1202C4—42no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4#341612yes—
1215C4D4×#4111yescharacteristic
1216C4#358411yescharacteristic
1217C2—22no—
1218C2—41no—
1219C2—41no—
1220C2—82no—
1221C2—161no—
1222C2—161no—
1223C2—161no—
1224C2D8×#4111yescharacteristic
1225C2C2×#341411yescharacteristic
1226C2C2×#341611yescharacteristic
subgroupG/H
centerC2×C4C22×D8
commutator, Frattini, cosocleC2×C8C25
socleC22C23×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #61433C2semidirect
2. #61431C2semidirect
3. #33968C2semidirect
4. #33955C2semidirect
5. #33943C2semidirect
6. #33938C2semidirect
7. #33918C2semidirect
8. #33912C2semidirect
9. #33911C2semidirect
10. #33893C2semidirect
11. #33890C2semidirect
12. #33887C2semidirect
13. #33883C2semidirect
14. #33877C2semidirect
15. #33873C2semidirect
16. #33841C2semidirect
17. #33832C2semidirect
18. #33831C2semidirect
19. #33738C2semidirect
20. #33737C2semidirect
21. #33735C2semidirect
22. #33668C2semidirect
23. #33665C2semidirect
24. #33663C2semidirect
25. #33662C2semidirect
26. #33662C2semidirect
27. #33661C2semidirect
28. #33479C2semidirect
29. C4×#510C2semidirect
30. C4×#509C2semidirect
31. C2×C4×SD32C2semidirect
38. #3393C22semidirect
39. #3383C22semidirect
47. #3336C22semidirect
48. #3334C22semidirect
55. D4×Q16C22semidirect
57. #3285C22semidirect
61. #3170C22semidirect
65. #3168C22semidirect
66. #3168C22semidirect
75. C4×#135C22semidirect
76. C2×C4×Q16C22semidirect
77. C2×C4×Q16C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2253C22semidirect
83. #2251C22semidirect
85. #2249C22semidirect
86. #2245C22semidirect
88. #2243C22semidirect
89. #2243C22semidirect
90. #2242C22semidirect
91. #2242C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2236C22semidirect
95. #2235C22semidirect
96. #2235C22semidirect
97. #2235C22semidirect
99. #2234C22semidirect
100. #2233C22semidirect
101. #2233C22semidirect
102. #2233C22semidirect
104. #2229C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
107. #2229C22semidirect
110. #2228C22semidirect
111. #2228C22semidirect
113. #2226C22semidirect
114. #2225C22semidirect
115. #2225C22semidirect
118. #2220C22semidirect
119. #2220C22semidirect
120. #2219C22semidirect
121. #2219C22semidirect
122. #2218C22semidirect
123. #2218C22semidirect
125. #2217C22semidirect
126. #2216C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
131. #2211C22semidirect
134. #2210C22semidirect
135. #2210C22semidirect
137. #2208C22semidirect
141. #2189C22semidirect
142. #2188C22semidirect
149. #2185C22semidirect
150. #2185C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
155. #2177C22semidirect
156. #2176C22semidirect
157. #2176C22semidirect
161. #2175C22semidirect
162. C4×Q32C22semidirect
163. C4×Q32C22semidirect
164. C4×Q32C22semidirect
170. C4×SD32C22semidirect
171. C4×SD32C22semidirect
172. C4×SD32C22semidirect
173. C4×SD32C22semidirect
174. C4×SD32C22semidirect
175. C4×SD32C22semidirect
176. C4×SD32C22semidirect
177. C4×SD32C22semidirect
178. C4×SD32C22semidirect
180. C4×D16C22semidirect
181. C4×D16C22semidirect
182. #2169C22semidirect
183. #2169C22semidirect
186. #2168C22semidirect
187. #2168C22semidirect
188. #2162C22semidirect
189. #2162C22semidirect
190. #2162C22semidirect
191. #2159C22semidirect
192. #2159C22semidirect
193. C2×#367C22semidirect
194. #2141C22semidirect
197. #2139C22semidirect
198. C2×#358C22semidirect
200. C4×M32C22semidirect
201. C4×M32C22semidirect
202. C2×C4×C16C22semidirect
730. SD32#41semidirect

Maximal subgroups

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

subgroupindex
#614332
#614312
#339682
#339552
#339432
#339382
#339182
#339122
#339112
#338932
#338902
#338872
#338832
#338772
#338732
#338412
#338322
#338312
#337382
#337372
#337352
#336682
#336652
#336632
#336622
#336612
#334792
C4×#5102
C4×#5092
C2×C4×SD322