Finite Group Databasebeta

← #7624222

Subgroups — #7624222

Order 512.

1495 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62330C211yesmaximal, characteristic, complemented
2#61086C211yesmaximal, characteristic, complemented
3#33894C211yesmaximal, characteristic, complemented
4#33893C211yesmaximal, characteristic, complemented
5#33887C211yesmaximal, characteristic, complemented
6#33884C211yesmaximal, characteristic, complemented
7#33879C211yesmaximal, characteristic, complemented
8#33876C211yesmaximal, characteristic, complemented
9#33868C211yesmaximal, characteristic, complemented
10#33867C211yesmaximal, characteristic, complemented
11#33851C211yesmaximal, characteristic, complemented
12#33848C211yesmaximal, characteristic, complemented
13#33843C211yesmaximal, characteristic, complemented
14#33841C211yesmaximal, characteristic, complemented
15#33837C211yesmaximal, characteristic, complemented
16#33836C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33785C211yesmaximal, characteristic, complemented
20#33778C211yesmaximal, characteristic, complemented
21#33770C211yesmaximal, characteristic, complemented
22#33769C211yesmaximal, characteristic, complemented
23#33767C211yesmaximal, characteristic, complemented
24#33764C211yesmaximal, characteristic, complemented
25#33677C211yesmaximal, characteristic, complemented
26#33668C211yesmaximal, characteristic, complemented
27#33527C211yesmaximal, characteristic, complemented
28#33527C211yesmaximal, characteristic, complemented
29#33525C211yesmaximal, characteristic, complemented
30#33524C211yesmaximal, characteristic, complemented
31#33495C211yesmaximal, characteristic, complemented
32C2×#578C2211yescharacteristic
33C2×#578C2211yescharacteristic, complemented
34#3551—21no—
35#3497—21no—
36C2×#510C2211yescharacteristic
37C2×#510C2211yescharacteristic
38C2×#510C2211yescharacteristic, complemented
39C2×#509C2211yescharacteristic
40C2×#508C2211yescharacteristic
41C2×#508C2211yescharacteristic
42C22×Q32C2211yescharacteristic, complemented
43C22×SD32C2211yescharacteristic
44#3339C2211yescharacteristic
45#3339C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic
48#3326—21no—
49#3326—21no—
50#3323—21no—
51#3323—21no—
52#3287C2211yescharacteristic
53#3287C2211yescharacteristic, complemented
54D4×Q16C2211yescharacteristic
55D4×Q16C2211yescharacteristic, complemented
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3285C2211yescharacteristic
59#3285C2211yescharacteristic
60#3285C2211yescharacteristic, complemented
61#3285C2211yescharacteristic, complemented
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3278—21no—
65#3278—21no—
66#3277—21no—
67#3277—21no—
68#3256—21no—
69#3204—21no—
70#3200—21no—
71#3168C2211yescharacteristic
72#3168C2211yescharacteristic
73#3147C2211yescharacteristic, complemented
74#3061C2211yescharacteristic
75#3061C2211yescharacteristic
76#3061C2211yescharacteristic
77#3061C2211yescharacteristic, complemented
78#3059C2211yescharacteristic
79#3058C2211yescharacteristic
80#3037—21no—
81#3013—21no—
82#3013—21no—
83C2×C4×Q16C2211yescharacteristic, complemented
84#2931C2211yescharacteristic
85#2251C2211yescharacteristic
86#2250C2211yescharacteristic
87#2249C2211yescharacteristic
88#2249C2211yescharacteristic
89#2245C2211yescharacteristic, complemented
90#2244C2211yescharacteristic, complemented
91#2242C2211yescharacteristic, complemented
92#2242C2211yescharacteristic, complemented
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic, complemented
95#2236C2211yescharacteristic, complemented
96#2236C2211yescharacteristic, complemented
97#2235C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2234C2211yescharacteristic
100#2234C2211yescharacteristic, complemented
101#2233C2211yescharacteristic
102#2233C2211yescharacteristic, complemented
103#2232C2211yescharacteristic
104#2232C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2220C2211yescharacteristic
110#2220C2211yescharacteristic
111#2220C2211yescharacteristic
112#2220C2211yescharacteristic, complemented
113#2219C2211yescharacteristic
114#2219C2211yescharacteristic, complemented
115#2218C2211yescharacteristic
116#2218C2211yescharacteristic
117#2217C2211yescharacteristic
118#2217C2211yescharacteristic
119#2217C2211yescharacteristic
120#2217C2211yescharacteristic, complemented
121#2216C2211yescharacteristic
122#2216C2211yescharacteristic, complemented
123#2215C2211yescharacteristic
124#2215C2211yescharacteristic
125#2211C2211yescharacteristic
126#2211C2211yescharacteristic
127#2211C2211yescharacteristic
128#2211C2211yescharacteristic
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2210C2211yescharacteristic
132#2210C2211yescharacteristic
133#2209C2211yescharacteristic, complemented
134#2208C2211yescharacteristic
135#2207C2211yescharacteristic, complemented
136#2206C2211yescharacteristic
137#2189C2211yescharacteristic
138#2189C2211yescharacteristic
139#2189C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic, complemented
142#2189C2211yescharacteristic, complemented
143#2189C2211yescharacteristic, complemented
144#2189C2211yescharacteristic, complemented
145#2189C2211yescharacteristic, complemented
146#2189C2211yescharacteristic, complemented
147#2188C2211yescharacteristic
148#2188C2211yescharacteristic
149#2188C2211yescharacteristic, complemented
150#2188C2211yescharacteristic, complemented
151#2188C2211yescharacteristic, complemented
152#2188C2211yescharacteristic, complemented
153#2188C2211yescharacteristic, complemented
154#2187C2211yescharacteristic
155#2186C2211yescharacteristic
156#2186C2211yescharacteristic
157#2186C2211yescharacteristic
158#2186C2211yescharacteristic
159#2186C2211yescharacteristic
160#2186C2211yescharacteristic
161#2186C2211yescharacteristic
162#2186C2211yescharacteristic
163#2186C2211yescharacteristic
164#2186C2211yescharacteristic
165#2185C2211yescharacteristic
166#2185C2211yescharacteristic
167#2185C2211yescharacteristic
168#2185C2211yescharacteristic
169#2185C2211yescharacteristic
170#2185C2211yescharacteristic
171#2185C2211yescharacteristic, complemented
172#2184C2211yescharacteristic
173#2176C2211yescharacteristic, complemented
174#2176C2211yescharacteristic, complemented
175#2175C2211yescharacteristic
176#2175C2211yescharacteristic
177C4×Q32C2211yescharacteristic, complemented
178C4×Q32C2211yescharacteristic, complemented
179C4×SD32C2211yescharacteristic
180C4×SD32C2211yescharacteristic
181#2169C2211yescharacteristic
182#2169C2211yescharacteristic, complemented
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic
185#2168C2211yescharacteristic, complemented
186#2168C2211yescharacteristic, complemented
187D4×C16C2211yescharacteristic
188D4×C16C2211yescharacteristic, complemented
189#2163C2211yescharacteristic, complemented
190#2162C2211yescharacteristic, complemented
191#2141C2211yescharacteristic
192#2141C2211yescharacteristic, complemented
193#2139C2211yescharacteristic, complemented
194#2139C2211yescharacteristic, complemented
195#2138C2211yescharacteristic
196#2138C2211yescharacteristic, complemented
197C2×#358C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199#2113C2211yescharacteristic
200#2113C2211yescharacteristic
201#2113C2211yescharacteristic, complemented
202#2113C2211yescharacteristic, complemented
203C2×2−1+4—21no—
204C2×2−1+4—21no—
205#578—42no—
206#578—42no—
207#578—42no—
208#578—42no—
209C2×#137—21no—
210C2×#137—21no—
211C2×#137—21no—
212C2×#137—21no—
213C2×#137—21no—
214C2×#137—21no—
215C2×#135—21no—
216C2×#135C2311yescharacteristic
217C2×#135C2311yescharacteristic
218C2×#135C2311yescharacteristic
219C2×#135C2311yescharacteristic
220C2×#135C2311yescharacteristic
221C2×#135C2311yescharacteristic
222C2×#135C2311yescharacteristic
223C2×#135C2311yescharacteristic
224C22×Q16C2311yescharacteristic
225C22×Q16C2311yescharacteristic
226C22×Q16C2311yescharacteristic
227C22×Q16C2311yescharacteristic
228C22×Q16C2311yescharacteristic
229C22×Q16C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C2×#131C2311yescharacteristic
232C2×#131C2311yescharacteristic
233#563—41no—
234#560—41no—
235#555—41no—
236#553—21no—
237#553—21no—
238#552—21no—
239#552—21no—
240#551—41no—
241#550—21no—
242#550—21no—
243#550—41no—
244D4×Q8—21no—
245D4×Q8—21no—
246D4×Q8—41no—
247#548—21no—
248#548—21no—
249#548—21no—
250#548—21no—
251#548—21no—
252#548—21no—
253#548—41no—
254#548—41no—
255#546—21no—
256#546—21no—
257#540—41no—
258#540—41no—
259#538—41no—
260#538—41no—
261#537—21no—
262#537—21no—
263#537—21no—
264#537—21no—
265#537—41no—
266#537—41no—
267#536—21no—
268#535—21no—
269#532—21no—
270#532—41no—
271#532—41no—
272#532D411yescharacteristic
273#529—21no—
274#529—21no—
275C2×C4×Q8—21no—
276#510—42no—
277#510—42no—
278#510—42no—
279#509—42no—
280#508—42no—
281#508—42no—
282C2×Q32—42no—
283C2×Q32C2311yescharacteristic
284C2×Q32C2311yescharacteristic
285C2×Q32C2311yescharacteristic
286C2×Q32C2311yescharacteristic
287C2×Q32C2311yescharacteristic
288C2×Q32C2311yescharacteristic
289C2×Q32C2311yescharacteristic
290C2×Q32C2311yescharacteristic
291C2×SD32—42no—
292C2×SD32C2311yescharacteristic
293C2×SD32C2311yescharacteristic
294C2×SD32C2311yescharacteristic
295C2×SD32C2311yescharacteristic
296C2×SD32C2311yescharacteristic
297C2×SD32C2311yescharacteristic
298C2×SD32C2311yescharacteristic
299C2×SD32C2311yescharacteristic
300C2×SD32C2311yescharacteristic
301C2×SD32C2311yescharacteristic
302C2×SD32C2311yescharacteristic
303C2×SD32C2311yescharacteristic
304C2×D16C2311yescharacteristic
305C2×D16C2311yescharacteristic
306C2×D16C2311yescharacteristic
307C2×D16C2311yescharacteristic
308C2×M32C2311yescharacteristic
309C2×M32C2311yescharacteristic
310C2×M32C2311yescharacteristic
311C2×M32C2311yescharacteristic
312C22×C16C2311yescharacteristic
313C22×C16C2311yescharacteristic
314C22×C16C2311yescharacteristic
315C22×C16C2311yescharacteristic
316#499C2311yescharacteristic
317#499C2311yescharacteristic
318#495—21no—
319#495C2311yescharacteristic
320#495C2311yescharacteristic
321#495C2311yescharacteristic
322#495C2311yescharacteristic
323#494C2311yescharacteristic
324#493C2311yescharacteristic
325#492—21no—
326#488—21no—
327#488—21no—
328#485—21no—
329#485—21no—
330#483—21no—
331#483—21no—
332#482—21no—
333#482—21no—
334#481—21no—
335#481—21no—
336#479—21no—
337#479—21no—
338#478—21no—
339#478—21no—
340#470—21no—
341#470—21no—
342#469—21no—
343#469—21no—
344#468—21no—
345#468—21no—
346#468—21no—
347#468—21no—
348#468—21no—
349#468—21no—
350#468—21no—
351#468—21no—
352#467C2311yescharacteristic
353#467C2311yescharacteristic
354#467C2311yescharacteristic
355#467C2311yescharacteristic
356#467C2311yescharacteristic
357#467C2311yescharacteristic
358#467C2311yescharacteristic
359#467C2311yescharacteristic
360#467C2311yescharacteristic
361#467C2311yescharacteristic
362#466C2311yescharacteristic
363#466C2311yescharacteristic
364#466C2311yescharacteristic
365#466C2311yescharacteristic
366#466C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#466C2311yescharacteristic
370#466C2311yescharacteristic
371#466C2311yescharacteristic
372#465—21no—
373#465—21no—
374#464—21no—
375#464—21no—
376#464—21no—
377#464—21no—
378#464—21no—
379#464—21no—
380#463—21no—
381#463—21no—
382#462—21no—
383#462—21no—
384#460—21no—
385#460—21no—
386#452—21no—
387#452—21no—
388#452—21no—
389#452—21no—
390#452—21no—
391#452—21no—
392#451—21no—
393#451—21no—
394#451—21no—
395#451—21no—
396#450—21no—
397#450—21no—
398#449—21no—
399#449—21no—
400#449—21no—
401#449—21no—
402#449—21no—
403#449—21no—
404#448—21no—
405#448—21no—
406#448—21no—
407#448—21no—
408#448—21no—
409#448—21no—
410C4×Q16—21no—
411C4×Q16—21no—
412C4×Q16C2311yescharacteristic
413C4×Q16C2311yescharacteristic
414C4×Q16C2311yescharacteristic
415C4×Q16C2311yescharacteristic
416C4×Q16C2311yescharacteristic
417C4×Q16C2311yescharacteristic
418C4×SD16—21no—
419C4×SD16—21no—
420C4×D8C2311yescharacteristic
421C4×D8C2311yescharacteristic
422#436D411yescharacteristic
423#436D411yescharacteristic
424#436D411yescharacteristic
425#436D411yescharacteristic
426C8×D4C2311yescharacteristic
427C8×D4C2311yescharacteristic
428C8×D4C2311yescharacteristic
429C8×D4C2311yescharacteristic
430#427C2311yescharacteristic
431#427C2311yescharacteristic
432C2×#107C2311yescharacteristic
433C2×#107C2311yescharacteristic
434C2×#107C2311yescharacteristic
435#423D411yescharacteristic
436#419—21no—
437#418—21no—
438#417—21no—
439#417—21no—
440#417—21no—
441#417—21no—
442C2×#103—21no—
443#408D411yescharacteristic
444#408D411yescharacteristic
445C2×C4×C8C2311yescharacteristic
446#367C2311yescharacteristic
447#367C2311yescharacteristic
448#367C2311yescharacteristic
449#367C2311yescharacteristic
450#366C2311yescharacteristic
451#366C2311yescharacteristic
452#366C2311yescharacteristic
453#366C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
456C4⋊C16C2311yescharacteristic
457C4⋊C16C2311yescharacteristic
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#358C2311yescharacteristic
477#358C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488#357C2311yescharacteristic
489#357C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494C22⋊C16C2311yescharacteristic
495C22⋊C16C2311yescharacteristic
496C22⋊C16C2311yescharacteristic
497C22⋊C16C2311yescharacteristic
498C22⋊C16C2311yescharacteristic
499C22⋊C16C2311yescharacteristic
500C22⋊C16C2311yescharacteristic
501C22⋊C16C2311yescharacteristic
502#346C2311yescharacteristic
503#346C2311yescharacteristic
504C4×C16C2311yescharacteristic
505C4×C16C2311yescharacteristic
5062−1+4—44no—
5072−1+4—44no—
5082−1+4—82no—
5092−1+4—82no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—21no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41—21no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C2×D411yescharacteristic
525C2×#41C2×D411yescharacteristic
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—41no—
533C22×Q8—41no—
534C22×D4—21no—
535#137—44no—
536#137—44no—
537#137—44no—
538#137—44no—
539#137—44no—
540#137—44no—
541#135—22no—
542#135—22no—
543#135—22no—
544#135—22no—
545#135—41no—
546#135—41no—
547#135—41no—
548#135—41no—
549#135—41no—
550#135—41no—
551#135—41no—
552#135—41no—
553#135—41no—
554#135—41no—
555#135—41no—
556#135—41no—
557#135—82no—
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—22no—
564C2×Q16—21no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16—21no—
571C2×Q16—41no—
572C2×Q16—41no—
573C2×Q16—41no—
574C2×Q16—41no—
575C2×Q16—41no—
576C2×Q16—41no—
577C2×Q16C2411yescharacteristic
578C2×Q16C2411yescharacteristic
579C2×Q16C2411yescharacteristic
580C2×Q16C2411yescharacteristic
581C2×Q16C2411yescharacteristic
582C2×Q16C2411yescharacteristic
583C2×SD16—21no—
584C2×SD16—21no—
585C2×SD16—21no—
586C2×SD16—21no—
587C2×SD16—21no—
588C2×SD16—21no—
589C2×SD16—21no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×D8—21no—
596C2×D8—21no—
597C2×D8—41no—
598C2×D8—41no—
599C2×D8C2411yescharacteristic
600C2×D8C2411yescharacteristic
601C2×D8C2411yescharacteristic
602C2×D8C2411yescharacteristic
603#131—41no—
604#131—41no—
605#131—41no—
606#131—41no—
607C2×M16C2×D411yescharacteristic
608C2×M16C2×D411yescharacteristic
609C2×M16C2×D411yescharacteristic
610C2×M16C2×D411yescharacteristic
611C2×M16C2×D411yescharacteristic
612C2×M16C2×D411yescharacteristic
613C22×C8C2×D411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C4⋊Q8—21no—
620C4⋊Q8—41no—
621C4⋊Q8—41no—
622C4⋊Q8—41no—
623C4⋊Q8D811yescharacteristic
624#127—21no—
625#127—41no—
626#127—41no—
627#127—41no—
628#127D811yescharacteristic
629#126—41no—
630#126—41no—
631#126—41no—
632#126—41no—
633#126—41no—
634#126—41no—
635#125—21no—
636#125—21no—
637#125—41no—
638#125—41no—
639#124—21no—
640#124—21no—
641#124—21no—
642#124—21no—
643#124—41no—
644#124—41no—
645#124—41no—
646#124—41no—
647#124—41no—
648#124—41no—
649#124—41no—
650#124—41no—
651#124D811yescharacteristic
652#124D811yescharacteristic
653#123—41no—
654#123—41no—
655#123—41no—
656#123—41no—
657#123—41no—
658#123—41no—
659#123—41no—
660#123—41no—
661#123—41no—
662#123—41no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8—21no—
673C22⋊Q8—41no—
674C22⋊Q8—41no—
675C22⋊Q8—41no—
676C22⋊Q8—41no—
677C22⋊Q8—41no—
678C22⋊Q8—41no—
679C22⋊Q8—41no—
680C22⋊Q8—41no—
681C22⋊Q8—41no—
682C22⋊Q8—41no—
683C22⋊Q8—41no—
684C22⋊Q8—41no—
685C22⋊Q8—41no—
686C22⋊Q8—41no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—41no—
698#121—41no—
699#121—41no—
700#121—41no—
701#121—41no—
702#121—41no—
703#121—41no—
704#121—41no—
705#121—41no—
706#121—41no—
707#121—41no—
708#121—41no—
709#121—41no—
710#121—41no—
711#121—41no—
712#121—41no—
713#121—41no—
714#121—41no—
715#121—41no—
716#121—41no—
717#121—41no—
718#121—41no—
719#121—41no—
720#121—41no—
721#121—41no—
722#121—41no—
723#121—41no—
724#121—41no—
725#121D811yescharacteristic
726#121D811yescharacteristic
727#121D811yescharacteristic
728#121D811yescharacteristic
729#120—41no—
730#120—41no—
731#120—41no—
732#120—41no—
733C4×Q8—21no—
734C4×Q8—21no—
735C4×Q8—21no—
736C4×Q8—21no—
737C4×Q8—21no—
738C4×Q8—21no—
739C4×Q8—41no—
740C4×Q8—41no—
741C4×D4—21no—
742C4×D4—21no—
743C4×D4—41no—
744C4×D4—41no—
745C4×D4—41no—
746C4×D4—41no—
747C4×D4—41no—
748C4×D4—41no—
749C4×D4—41no—
750C4×D4—41no—
751C4×D4—41no—
752C4×D4—41no—
753C4×D4—41no—
754C4×D4—41no—
755C4×D4—41no—
756C4×D4—41no—
757C4×D4—41no—
758C4×D4—41no—
759C4×D4C2×D411yescharacteristic
760C4×D4C2×D411yescharacteristic
761C4×D4C2×D411yescharacteristic
762C4×D4C2×D411yescharacteristic
763#117—21no—
764#117—21no—
765#117—41no—
766#117—41no—
767#117—41no—
768#117—41no—
769C2×C4⋊C4—21no—
770C2×C4⋊C4—21no—
771C2×C4⋊C4—21no—
772C2×C4⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C42—41no—
776C2×C42C2×D411yescharacteristic
777Q32—22no—
778Q32—22no—
779Q32—22no—
780Q32—22no—
781Q32—41no—
782Q32—41no—
783Q32—41no—
784Q32—41no—
785SD32—22no—
786SD32—22no—
787SD32—22no—
788SD32—22no—
789SD32—41no—
790SD32—41no—
791SD32—41no—
792SD32—41no—
793SD32—41no—
794SD32—41no—
795SD32—41no—
796SD32—41no—
797D16—41no—
798D16—41no—
799D16—41no—
800D16—41no—
801M32—41no—
802M32—41no—
803M32—41no—
804M32—41no—
805C2×C16—41no—
806C2×C16—41no—
807C2×C16—41no—
808C2×C16—41no—
809C2×C16C2411yescharacteristic
810C2×C16C2411yescharacteristic
811C2×C16C2411yescharacteristic
812C2×C16C2411yescharacteristic
813C2×C16C2411yescharacteristic
814C2×C16C2411yescharacteristic
815C2×C16C2411yescharacteristic
816C2×C16C2411yescharacteristic
817#107—21no—
818#107—21no—
819#107—21no—
820#107C2411yescharacteristic
821#107C2411yescharacteristic
822#107C2411yescharacteristic
823#107C2411yescharacteristic
824#107C2411yescharacteristic
825#107C2411yescharacteristic
826#106—21no—
827#106—21no—
828#106—21no—
829#106—21no—
830C4⋊C8C2×D411yescharacteristic
831C4⋊C8C2×D411yescharacteristic
832C4⋊C8C2×D411yescharacteristic
833C4⋊C8C2×D411yescharacteristic
834#103—21no—
835#103—21no—
836#103—21no—
837#103—21no—
838#103—21no—
839#103—21no—
840#103—21no—
841#103—21no—
842#103—21no—
843#103—21no—
844#103—21no—
845#103—21no—
846#103—21no—
847#103—21no—
848#103—21no—
849#103—21no—
850#102—21no—
851#102—21no—
852#102—21no—
853#102—21no—
854#102—21no—
855#102—21no—
856#102—21no—
857#102—21no—
858#102—21no—
859#102—21no—
860#102—21no—
861#102—21no—
862C22⋊C8C2×D411yescharacteristic
863C22⋊C8C2×D411yescharacteristic
864C22⋊C8C2×D411yescharacteristic
865C22⋊C8C2×D411yescharacteristic
866C22⋊C8C2×D411yescharacteristic
867C22⋊C8C2×D411yescharacteristic
868C22⋊C8C2×D411yescharacteristic
869C22⋊C8C2×D411yescharacteristic
870C4×C8C2×D411yescharacteristic
871C4×C8C2×D411yescharacteristic
872C4×C8C2411yescharacteristic
873C4×C8C2411yescharacteristic
874C24—41no—
875#41—41no—
876#41—41no—
877#41—41no—
878#41—41no—
879#41—42no—
880#41—42no—
881#41—42no—
882#41—42no—
883#41—42no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41—81no—
888#41—81no—
889#41—81no—
890#41—81no—
891#41—81no—
892#41—81no—
893#41—81no—
894#41—81no—
895#41—84no—
896#41—84no—
897#41—84no—
898#41—84no—
899#41—84no—
900#41—84no—
901C2×Q8—24no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—41no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—41no—
919C2×Q8—81no—
920C2×Q8—81no—
921C2×Q8—81no—
922C2×Q8—81no—
923C2×Q8—81no—
924C2×Q8—81no—
925C2×Q8—84no—
926C2×Q8—84no—
927C2×Q8C2×D811yescharacteristic
928C2×Q8C2×D811yescharacteristic
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—41no—
934C2×D4—41no—
935C2×D4—41no—
936C2×D4—41no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—41no—
940C2×D4—41no—
941C2×D4—41no—
942C2×D4—41no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—41no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—41no—
953C2×D4—41no—
954C2×D4—81no—
955C2×D4—81no—
956C2×D4C2×D811yescharacteristic
957C2×D4C2×D811yescharacteristic
958C2×D4C2×D811yescharacteristic
959C2×D4C2×D811yescharacteristic
960C2×D4C2×D811yescharacteristic
961C2×D4C2×D811yescharacteristic
962C2×D4C2×D811yescharacteristic
963C2×D4C2×D811yescharacteristic
964C2×D4C2×D811yescharacteristic
965C2×D4C2×D811yescharacteristic
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4C2×D811yescharacteristic
986C22×C4C2×D811yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992Q16—24no—
993Q16—21no—
994Q16—21no—
995Q16—21no—
996Q16—21no—
997Q16—21no—
998Q16—21no—
999Q16—21no—
1000Q16—21no—
1001Q16—21no—
1002Q16—21no—
1003Q16—42no—
1004Q16—42no—
1005Q16—42no—
1006Q16—42no—
1007Q16—81no—
1008Q16—81no—
1009Q16H(5,𝔽2)12yes—
1010Q16H(5,𝔽2)12yes—
1011SD16—42no—
1012SD16—42no—
1013SD16—42no—
1014SD16—42no—
1015SD16—42no—
1016SD16—42no—
1017SD16—81no—
1018SD16—81no—
1019SD16—81no—
1020SD16—81no—
1021SD16—81no—
1022SD16—81no—
1023D8—21no—
1024D8—21no—
1025D8—21no—
1026D8—21no—
1027D8—21no—
1028D8—21no—
1029D8—21no—
1030D8—21no—
1031D8—81no—
1032D8—81no—
1033M16—41no—
1034M16—41no—
1035M16—41no—
1036M16—41no—
1037M16—41no—
1038M16—41no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—41no—
1050C2×C8C22×D411yescharacteristic
1051C2×C8C22×D411yescharacteristic
1052C2×C8C22×D411yescharacteristic
1053C2×C8C22×D411yescharacteristic
1054C2×C8C22×D411yescharacteristic
1055C2×C8C22×D411yescharacteristic
1056C2×C8C22×D411yescharacteristic
1057C2×C8C2511yescharacteristic
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4C2×D811yescharacteristic
1090C4⋊C4C2×D811yescharacteristic
1091C4⋊C4C2×D811yescharacteristic
1092C4⋊C4C2×D811yescharacteristic
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4C2×D811yescharacteristic
1126C22⋊C4C2×D811yescharacteristic
1127C22⋊C4C2×D811yescharacteristic
1128C22⋊C4C2×D811yescharacteristic
1129C22⋊C4C2×D811yescharacteristic
1130C22⋊C4C2×D811yescharacteristic
1131C22⋊C4C2×D811yescharacteristic
1132C22⋊C4C2×D811yescharacteristic
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—41no—
1137C42—41no—
1138C42—41no—
1139C42—41no—
1140C42—41no—
1141C42C2×D811yescharacteristic
1142C42C2×D811yescharacteristic
1143C42C22×D411yescharacteristic
1144C42C22×D411yescharacteristic
1145C16—21no—
1146C16—21no—
1147C16—21no—
1148C16—21no—
1149C16—21no—
1150C16—21no—
1151C16—21no—
1152C16—21no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—161no—
1158C23—161no—
1159C23—161no—
1160C23C22×D811yescharacteristic
1161C23C22×D811yescharacteristic
1162C23C22×D811yescharacteristic
1163C23C22×D811yescharacteristic
1164C23C22×D811yescharacteristic
1165Q8—22no—
1166Q8—22no—
1167Q8—41no—
1168Q8—41no—
1169Q8—44no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—82no—
1181Q8—82no—
1182Q8—82no—
1183Q8—82no—
1184Q8—161no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—82no—
1208D4—82no—
1209D4—82no—
1210D4—161no—
1211D4—161no—
1212D4—161no—
1213D4—161no—
1214D4—161no—
1215D4—161no—
1216D4—161no—
1217D4—161no—
1218D4—161no—
1219D4—161no—
1220D4—161no—
1221D4—161no—
1222D4—161no—
1223D4—161no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—44no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—82no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—82no—
1253C2×C4—82no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4—82no—
1257C2×C4—82no—
1258C2×C4—82no—
1259C2×C4—161no—
1260C2×C4—161no—
1261C2×C4—161no—
1262C2×C4—161no—
1263C2×C4—161no—
1264C2×C4—161no—
1265C2×C4—161no—
1266C2×C4—161no—
1267C2×C4C22×D811yescharacteristic
1268C2×C4C22×D811yescharacteristic
1269C2×C4C22×D811yescharacteristic
1270C2×C4C22×D811yescharacteristic
1271C2×C4C22×D811yescharacteristic
1272C2×C4C22×D811yescharacteristic
1273C2×C4C22×D811yescharacteristic
1274C2×C4C22×D811yescharacteristic
1275C2×C4C22×D811yescharacteristic
1276C2×C4C23×D411yescharacteristic
1277C8—21no—
1278C8—21no—
1279C8—21no—
1280C8—21no—
1281C8—21no—
1282C8—21no—
1283C8—21no—
1284C8C2×H(5,𝔽2)11yescharacteristic
1285C8C2×H(5,𝔽2)11yescharacteristic
1286C22—21no—
1287C22—21no—
1288C22—21no—
1289C22—21no—
1290C22—21no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—21no—
1297C22—21no—
1298C22—21no—
1299C22—21no—
1300C22—21no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—322no—
1314C22C23×D811yescharacteristic
1315C4—21no—
1316C4—21no—
1317C4—21no—
1318C4—21no—
1319C4—21no—
1320C4—21no—
1321C4—21no—
1322C4—21no—
1323C4—21no—
1324C4—42no—
1325C4—42no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#348411yescharacteristic
1337C4#358511yescharacteristic
1338C2—41no—
1339C2—41no—
1340C2—41no—
1341C2—41no—
1342C2—41no—
1343C2—161no—
1344C2—161no—
1345C2—161no—
1346C2—161no—
1347C2#6155911yescharacteristic
1348C2#6263511yescharacteristic
1349C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ #2931 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62330C2semidirect
2. #61086C2semidirect
3. #33894C2semidirect
4. #33893C2semidirect
5. #33887C2semidirect
6. #33884C2semidirect
7. #33879C2semidirect
8. #33876C2semidirect
9. #33868C2semidirect
10. #33867C2semidirect
11. #33851C2semidirect
12. #33848C2semidirect
13. #33843C2semidirect
14. #33841C2semidirect
15. #33837C2semidirect
16. #33836C2semidirect
17. #33834C2semidirect
18. #33832C2semidirect
19. #33785C2semidirect
20. #33778C2semidirect
21. #33770C2semidirect
22. #33769C2semidirect
23. #33767C2semidirect
24. #33764C2semidirect
25. #33677C2semidirect
26. #33668C2semidirect
27. #33527C2semidirect
28. #33527C2semidirect
29. #33525C2semidirect
30. #33524C2semidirect
31. #33495C2semidirect
33. C2×#578C22semidirect
38. C2×#510C22semidirect
42. C22×Q32C22semidirect
53. #3287C22semidirect
55. D4×Q16C22semidirect
60. #3285C22semidirect
61. #3285C22semidirect
73. #3147C22semidirect
77. #3061C22semidirect
83. C2×C4×Q16C22semidirect
89. #2245C22semidirect
90. #2244C22semidirect
91. #2242C22semidirect
92. #2242C22semidirect
94. #2237C22semidirect
95. #2236C22semidirect
96. #2236C22semidirect
97. #2235C22semidirect
98. #2235C22semidirect
100. #2234C22semidirect
102. #2233C22semidirect
104. #2232C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
112. #2220C22semidirect
114. #2219C22semidirect
120. #2217C22semidirect
122. #2216C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
133. #2209C22semidirect
135. #2207C22semidirect
141. #2189C22semidirect
142. #2189C22semidirect
143. #2189C22semidirect
144. #2189C22semidirect
145. #2189C22semidirect
146. #2189C22semidirect
149. #2188C22semidirect
150. #2188C22semidirect
151. #2188C22semidirect
152. #2188C22semidirect
153. #2188C22semidirect
171. #2185C22semidirect
173. #2176C22semidirect
174. #2176C22semidirect
177. C4×Q32C22semidirect
178. C4×Q32C22semidirect
182. #2169C22semidirect
185. #2168C22semidirect
186. #2168C22semidirect
188. D4×C16C22semidirect
189. #2163C22semidirect
190. #2162C22semidirect
192. #2141C22semidirect
193. #2139C22semidirect
194. #2139C22semidirect
196. #2138C22semidirect
197. C2×#358C22semidirect
198. C2×#358C22semidirect
201. #2113C22semidirect
202. #2113C22semidirect

Maximal subgroups

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

subgroupindex
#623302
#610862
#338942
#338932
#338872
#338842
#338792
#338762
#338682
#338672
#338512
#338482
#338432
#338412
#338372
#338362
#338342
#338322
#337852
#337782
#337702
#337692
#337672
#337642
#336772
#336682
#335272
#335252
#335242
#334952