Finite Group Databasebeta

← #7624891

Subgroups — #7624891

Order 512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62330C211yesmaximal, characteristic, complemented
2#62325C211yesmaximal, characteristic, complemented
3#33919C211yesmaximal, characteristic, complemented
4#33914C211yesmaximal, characteristic, complemented
5#33911C211yesmaximal, characteristic, complemented
6#33904C211yesmaximal, characteristic, complemented
7#33894C211yesmaximal, characteristic, complemented
8#33893C211yesmaximal, characteristic, complemented
9#33888C211yesmaximal, characteristic, complemented
10#33887C211yesmaximal, characteristic, complemented
11#33882C211yesmaximal, characteristic, complemented
12#33881C211yesmaximal, characteristic, complemented
13#33867C211yesmaximal, characteristic, complemented
14#33863C211yesmaximal, characteristic, complemented
15#33851C211yesmaximal, characteristic, complemented
16#33841C211yesmaximal, characteristic, complemented
17#33836C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33816C211yesmaximal, characteristic, complemented
20#33814C211yesmaximal, characteristic, complemented
21#33769C211yesmaximal, characteristic, complemented
22#33767C211yesmaximal, characteristic, complemented
23#33767C211yesmaximal, characteristic, complemented
24#33766C211yesmaximal, characteristic, complemented
25#33750C211yesmaximal, characteristic, complemented
26#33738C211yesmaximal, characteristic, complemented
27#33613C211yesmaximal, characteristic, complemented
28#33612C211yesmaximal, characteristic, complemented
29#33611C211yesmaximal, characteristic, complemented
30#33608C211yesmaximal, characteristic, complemented
31#33438C211yesmaximal, characteristic, complemented
32#3551—21no—
33#3547—21no—
34C2×#510C2211yescharacteristic
35C2×#509C2211yescharacteristic
36C2×#508C2211yescharacteristic
37C22×Q32C2211yescharacteristic, complemented
38C2×#504C2211yescharacteristic
39C2×#504C2211yescharacteristic, complemented
40#3341C2211yescharacteristic, complemented
41#3339C2211yescharacteristic
42#3339C2211yescharacteristic
43#3338C2211yescharacteristic
44#3336C2211yescharacteristic
45#3336C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3331—21no—
49#3329—21no—
50#3327—21no—
51#3327—21no—
52#3326—21no—
53#3326—21no—
54#3323—21no—
55#3323—21no—
56D4×Q16C2211yescharacteristic, complemented
57#3285C2211yescharacteristic
58#3285C2211yescharacteristic
59#3285C2211yescharacteristic
60#3285C2211yescharacteristic, complemented
61#3283C2211yescharacteristic
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3256—21no—
65#3252—21no—
66#3204—21no—
67#3201—21no—
68#3201—21no—
69#3200—21no—
70#3170C2211yescharacteristic, complemented
71#3168C2211yescharacteristic
72#3168C2211yescharacteristic
73#3168C2211yescharacteristic, complemented
74#3061C2211yescharacteristic
75#3061C2211yescharacteristic
76#3061C2211yescharacteristic
77#3061C2211yescharacteristic, complemented
78#3059C2211yescharacteristic
79#3059C2211yescharacteristic
80#3059C2211yescharacteristic, complemented
81#3058C2211yescharacteristic
82#2931C2211yescharacteristic
83#2255C2211yescharacteristic, complemented
84#2253C2211yescharacteristic, complemented
85#2251C2211yescharacteristic
86#2249C2211yescharacteristic
87#2245C2211yescharacteristic, complemented
88#2243C2211yescharacteristic
89#2242C2211yescharacteristic
90#2242C2211yescharacteristic, complemented
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2236C2211yescharacteristic
96#2236C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2236C2211yescharacteristic, complemented
99#2235C2211yescharacteristic
100#2235C2211yescharacteristic, complemented
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic
103#2234C2211yescharacteristic
104#2234C2211yescharacteristic, complemented
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2229C2211yescharacteristic, complemented
111#2228C2211yescharacteristic
112#2228C2211yescharacteristic, complemented
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic
115#2220C2211yescharacteristic
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic
119#2220C2211yescharacteristic
120#2220C2211yescharacteristic, complemented
121#2219C2211yescharacteristic
122#2219C2211yescharacteristic
123#2219C2211yescharacteristic, complemented
124#2219C2211yescharacteristic, complemented
125#2219C2211yescharacteristic, complemented
126#2219C2211yescharacteristic, complemented
127#2219C2211yescharacteristic, complemented
128#2218C2211yescharacteristic
129#2218C2211yescharacteristic
130#2218C2211yescharacteristic
131#2217C2211yescharacteristic
132#2217C2211yescharacteristic
133#2217C2211yescharacteristic
134#2217C2211yescharacteristic
135#2217C2211yescharacteristic
136#2217C2211yescharacteristic
137#2217C2211yescharacteristic, complemented
138#2217C2211yescharacteristic, complemented
139#2216C2211yescharacteristic
140#2216C2211yescharacteristic
141#2216C2211yescharacteristic, complemented
142#2216C2211yescharacteristic, complemented
143#2216C2211yescharacteristic, complemented
144#2216C2211yescharacteristic, complemented
145#2215C2211yescharacteristic
146#2215C2211yescharacteristic
147#2211C2211yescharacteristic
148#2211C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic, complemented
151#2210C2211yescharacteristic
152#2210C2211yescharacteristic
153#2209C2211yescharacteristic, complemented
154#2208C2211yescharacteristic
155#2189C2211yescharacteristic
156#2189C2211yescharacteristic
157#2189C2211yescharacteristic
158#2189C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2188C2211yescharacteristic, complemented
163#2187C2211yescharacteristic
164#2187C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic
167#2185C2211yescharacteristic
168#2185C2211yescharacteristic
169#2185C2211yescharacteristic
170#2185C2211yescharacteristic, complemented
171#2177C2211yescharacteristic
172#2176C2211yescharacteristic, complemented
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic, complemented
175C4×Q32C2211yescharacteristic, complemented
176C4×Q32C2211yescharacteristic, complemented
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179#2169C2211yescharacteristic
180#2169C2211yescharacteristic, complemented
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185D4×C16C2211yescharacteristic
186D4×C16C2211yescharacteristic, complemented
187#2159C2211yescharacteristic
188#2159C2211yescharacteristic, complemented
189#2158C2211yescharacteristic, complemented
190C2×#367C2211yescharacteristic, complemented
191C2×C4⋊C16C2211yescharacteristic, complemented
192#2141C2211yescharacteristic, complemented
193#2141C2211yescharacteristic, complemented
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic
197#2138C2211yescharacteristic
198C2×#358C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200#2113C2211yescharacteristic
201#2113C2211yescharacteristic, complemented
202C4×M32C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C2×#131C2311yescharacteristic
212C2×#131C2311yescharacteristic
213#563—41no—
214#562—41no—
215#562—41no—
216#560—41no—
217#555—21no—
218#555—41no—
219#555—41no—
220#554—21no—
221#553—21no—
222#553—21no—
223#553—41no—
224#552—21no—
225#552—21no—
226#552—21no—
227#552—21no—
228#551—41no—
229D4×Q8—21no—
230#548—21no—
231#548—21no—
232#548—21no—
233#548—21no—
234#547—21no—
235#546—21no—
236#546—21no—
237#544—41no—
238#542—41no—
239#542—41no—
240#540—41no—
241#540—41no—
242#540—41no—
243#538—41no—
244#538—41no—
245#537—21no—
246#537—21no—
247#537—21no—
248#537—21no—
249#536—21no—
250#536—21no—
251#536—21no—
252#535—21no—
253#533—21no—
254#532D411yescharacteristic
255#529—21no—
256#529—21no—
257#529—21no—
258#510—42no—
259#509—42no—
260#508—42no—
261C2×Q32—42no—
262C2×Q32C2311yescharacteristic
263C2×Q32C2311yescharacteristic
264C2×Q32C2311yescharacteristic
265C2×Q32C2311yescharacteristic
266C2×Q32C2311yescharacteristic
267C2×Q32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×SD32C2311yescharacteristic
276C2×D16C2311yescharacteristic
277C2×D16C2311yescharacteristic
278#504—42no—
279#504—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#495C2311yescharacteristic
298#495C2311yescharacteristic
299#494C2311yescharacteristic
300#488—21no—
301#488—21no—
302#488—21no—
303#487—21no—
304#485—21no—
305#485—21no—
306#485—21no—
307#485—21no—
308#484—21no—
309#484—21no—
310#483—21no—
311#483—21no—
312#483—21no—
313#483—21no—
314#482—21no—
315#482—21no—
316#482—21no—
317#482—21no—
318#481—21no—
319#481—21no—
320#479—21no—
321#479—21no—
322#479—21no—
323#479—21no—
324#478—21no—
325#478—21no—
326#477—21no—
327#476—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#468—21no—
337#468—21no—
338#468—21no—
339#468—21no—
340#468—21no—
341#468—21no—
342#468—21no—
343#468—21no—
344#467—21no—
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#467C2311yescharacteristic
360#466C2311yescharacteristic
361#466C2311yescharacteristic
362#466C2311yescharacteristic
363#466C2311yescharacteristic
364#466C2311yescharacteristic
365#466C2311yescharacteristic
366#466C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#465—21no—
370#465—21no—
371#465—21no—
372#464—21no—
373#464—21no—
374#464—21no—
375#464—21no—
376#463—21no—
377#463—21no—
378#462—21no—
379#461—21no—
380#452—21no—
381#452—21no—
382#452—21no—
383#452—21no—
384#452—21no—
385#452—21no—
386#451—21no—
387#451—21no—
388#450—21no—
389#450—21no—
390#449—21no—
391#449—21no—
392#448—21no—
393#448—21no—
394#448—21no—
395#448—21no—
396C4×Q16—21no—
397C4×Q16C2311yescharacteristic
398C4×Q16C2311yescharacteristic
399C4×Q16C2311yescharacteristic
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×SD16—21no—
403C4×SD16—21no—
404C4×SD16—21no—
405C4×D8C2311yescharacteristic
406C4×D8C2311yescharacteristic
407C4×D8C2311yescharacteristic
408#436D411yescharacteristic
409#436D411yescharacteristic
410#436D411yescharacteristic
411#436D411yescharacteristic
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#423D411yescharacteristic
425#419—21no—
426#419—21no—
427#419—21no—
428#418—21no—
429#417—21no—
430#417—21no—
431#417—21no—
432#417—21no—
433#408D411yescharacteristic
434#408D411yescharacteristic
435C2×C4×C8C2311yescharacteristic
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—21no—
503C2×#41—21no—
504C2×#41C2×D411yescharacteristic
505C2×#41C2×D411yescharacteristic
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×D4—21no—
510#135—41no—
511#135—41no—
512#135—41no—
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517#135—41no—
518C2×Q16—21no—
519C2×Q16—21no—
520C2×Q16—21no—
521C2×Q16—21no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16C2411yescharacteristic
529C2×Q16C2411yescharacteristic
530C2×Q16C2411yescharacteristic
531C2×Q16C2411yescharacteristic
532C2×Q16C2411yescharacteristic
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×D8—21no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8C2411yescharacteristic
544C2×D8C2411yescharacteristic
545C2×D8C2411yescharacteristic
546#131—41no—
547#131—41no—
548#131—41no—
549#131—41no—
550C2×M16C2×D411yescharacteristic
551C2×M16C2×D411yescharacteristic
552C2×M16C2×D411yescharacteristic
553C2×M16C2×D411yescharacteristic
554C2×M16C2×D411yescharacteristic
555C2×M16C2×D411yescharacteristic
556C22×C8C2×D411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—21no—
563C4⋊Q8—21no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8D811yescharacteristic
569#127—41no—
570#127D811yescharacteristic
571#126—41no—
572#126—41no—
573#126—41no—
574#126—41no—
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#126—41no—
580#125—21no—
581#125—21no—
582#125—21no—
583#125—41no—
584#125—41no—
585#125—41no—
586#125—41no—
587#125—41no—
588#125—41no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—41no—
599#124—41no—
600#124—41no—
601#124—41no—
602#124D811yescharacteristic
603#124D811yescharacteristic
604#123—41no—
605#123—41no—
606#123—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—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—21no—
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—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
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—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—21no—
659#121—21no—
660#121—41no—
661#121—41no—
662#121—41no—
663#121—41no—
664#121—41no—
665#121—41no—
666#121—41no—
667#121—41no—
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#121D811yescharacteristic
685#121D811yescharacteristic
686#120—41no—
687#120—41no—
688#120—41no—
689#120—41no—
690C4×Q8—21no—
691C4×Q8—21no—
692C4×Q8—21no—
693C4×Q8—21no—
694C4×Q8—21no—
695C4×Q8—41no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—41no—
700C4×D4—41no—
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×D4—41no—
710C4×D4C2×D411yescharacteristic
711C4×D4C2×D411yescharacteristic
712C4×D4C2×D411yescharacteristic
713C4×D4C2×D411yescharacteristic
714#117—21no—
715#117—21no—
716#117—21no—
717#117—21no—
718#117—41no—
719#117—41no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117—41no—
724#117—41no—
725#117—41no—
726#117—41no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C42C2×D411yescharacteristic
735Q32—22no—
736Q32—22no—
737Q32—41no—
738Q32—41no—
739Q32—41no—
740Q32—41no—
741SD32—22no—
742SD32—41no—
743SD32—41no—
744SD32—41no—
745SD32—41no—
746SD32—41no—
747SD32—41no—
748SD32—41no—
749D16—22no—
750D16—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
835C4×C8C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2411yescharacteristic
838C4×C8C2411yescharacteristic
839C24—41no—
840#41—41no—
841#41—41no—
842#41—41no—
843#41—41no—
844#41—81no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851#41—81no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8C2×D811yescharacteristic
868C2×Q8C2×D811yescharacteristic
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
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×D4C2×D811yescharacteristic
889C2×D4C2×D811yescharacteristic
890C2×D4C2×D811yescharacteristic
891C2×D4C2×D811yescharacteristic
892C2×D4C2×D811yescharacteristic
893C2×D4C2×D811yescharacteristic
894C2×D4C2×D811yescharacteristic
895C2×D4C2×D811yescharacteristic
896C2×D4C2×D811yescharacteristic
897C2×D4C2×D811yescharacteristic
898C22×C4—41no—
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×C4C2×D811yescharacteristic
913C22×C4C2×D811yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919Q16—21no—
920Q16—21no—
921Q16—21no—
922Q16—21no—
923Q16—21no—
924Q16—21no—
925Q16—21no—
926Q16—21no—
927Q16—21no—
928Q16—21no—
929Q16—81no—
930Q16—81no—
931Q16—81no—
932Q16—81no—
933SD16—81no—
934SD16—81no—
935SD16—81no—
936SD16—81no—
937SD16—81no—
938SD16—81no—
939SD16—81no—
940D8—21no—
941D8—21no—
942D8—21no—
943D8—21no—
944D8—21no—
945D8—21no—
946D8—81no—
947M16—41no—
948M16—41no—
949M16—41no—
950M16—41no—
951M16—41no—
952M16—41no—
953C2×C8—21no—
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—41no—
964C2×C8C22×D411yescharacteristic
965C2×C8C22×D411yescharacteristic
966C2×C8C22×D411yescharacteristic
967C2×C8C22×D411yescharacteristic
968C2×C8C22×D411yescharacteristic
969C2×C8C22×D411yescharacteristic
970C2×C8C22×D411yescharacteristic
971C2×C8C2511yescharacteristic
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
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⋊C4C2×D811yescharacteristic
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
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⋊C4C2×D811yescharacteristic
1055C22⋊C4C2×D811yescharacteristic
1056C22⋊C4C2×D811yescharacteristic
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42C2×D811yescharacteristic
1072C42C2×D811yescharacteristic
1073C42C22×D411yescharacteristic
1074C42C22×D411yescharacteristic
1075C16—21no—
1076C16—21no—
1077C16—21no—
1078C16—21no—
1079C16—21no—
1080C16—21no—
1081C16—21no—
1082C16H(5,𝔽2)12yes—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—161no—
1087C23—161no—
1088C23—161no—
1089C23C22×D811yescharacteristic
1090C23C22×D811yescharacteristic
1091C23C22×D811yescharacteristic
1092C23C22×D811yescharacteristic
1093C23C22×D811yescharacteristic
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—161no—
1107Q8—161no—
1108Q8—161no—
1109Q8—161no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—161no—
1127D4—161no—
1128D4—161no—
1129D4—161no—
1130D4—161no—
1131D4—161no—
1132D4—161no—
1133D4—161no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137D4—161no—
1138D4—161no—
1139D4—161no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
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—82no—
1166C2×C4—161no—
1167C2×C4—161no—
1168C2×C4—161no—
1169C2×C4—161no—
1170C2×C4—161no—
1171C2×C4—161no—
1172C2×C4—161no—
1173C2×C4—161no—
1174C2×C4—161no—
1175C2×C4—161no—
1176C2×C4—161no—
1177C2×C4—161no—
1178C2×C4—161no—
1179C2×C4C22×D811yescharacteristic
1180C2×C4C22×D811yescharacteristic
1181C2×C4C22×D811yescharacteristic
1182C2×C4C22×D811yescharacteristic
1183C2×C4C22×D811yescharacteristic
1184C2×C4C22×D811yescharacteristic
1185C2×C4C22×D811yescharacteristic
1186C2×C4C22×D811yescharacteristic
1187C2×C4C22×D811yescharacteristic
1188C2×C4C23×D411yescharacteristic
1189C8—21no—
1190C8—21no—
1191C8—21no—
1192C8—21no—
1193C8—21no—
1194C8—21no—
1195C8—21no—
1196C8C2×H(5,𝔽2)11yescharacteristic
1197C8#58511yescharacteristic
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—322no—
1223C22C23×D811yescharacteristic
1224C4—21no—
1225C4—21no—
1226C4—21no—
1227C4—21no—
1228C4—21no—
1229C4—21no—
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4#349611yescharacteristic
1247C4#358411yescharacteristic
1248C2—41no—
1249C2—41no—
1250C2—41no—
1251C2—41no—
1252C2—41no—
1253C2—161no—
1254C2—161no—
1255C2—161no—
1256C2#6224511yescharacteristic
1257C2#6263511yescharacteristic
1258C2#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. #62325C2semidirect
3. #33919C2semidirect
4. #33914C2semidirect
5. #33911C2semidirect
6. #33904C2semidirect
7. #33894C2semidirect
8. #33893C2semidirect
9. #33888C2semidirect
10. #33887C2semidirect
11. #33882C2semidirect
12. #33881C2semidirect
13. #33867C2semidirect
14. #33863C2semidirect
15. #33851C2semidirect
16. #33841C2semidirect
17. #33836C2semidirect
18. #33833C2semidirect
19. #33816C2semidirect
20. #33814C2semidirect
21. #33769C2semidirect
22. #33767C2semidirect
23. #33767C2semidirect
24. #33766C2semidirect
25. #33750C2semidirect
26. #33738C2semidirect
27. #33613C2semidirect
28. #33612C2semidirect
29. #33611C2semidirect
30. #33608C2semidirect
31. #33438C2semidirect
37. C22×Q32C22semidirect
39. C2×#504C22semidirect
40. #3341C22semidirect
47. #3336C22semidirect
56. D4×Q16C22semidirect
60. #3285C22semidirect
70. #3170C22semidirect
73. #3168C22semidirect
77. #3061C22semidirect
80. #3059C22semidirect
83. #2255C22semidirect
84. #2253C22semidirect
87. #2245C22semidirect
90. #2242C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
96. #2236C22semidirect
97. #2236C22semidirect
98. #2236C22semidirect
100. #2235C22semidirect
104. #2234C22semidirect
106. #2232C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
112. #2228C22semidirect
113. #2225C22semidirect
120. #2220C22semidirect
123. #2219C22semidirect
124. #2219C22semidirect
125. #2219C22semidirect
126. #2219C22semidirect
127. #2219C22semidirect
137. #2217C22semidirect
138. #2217C22semidirect
141. #2216C22semidirect
142. #2216C22semidirect
143. #2216C22semidirect
144. #2216C22semidirect
150. #2211C22semidirect
153. #2209C22semidirect
160. #2189C22semidirect
161. #2188C22semidirect
162. #2188C22semidirect
170. #2185C22semidirect
172. #2176C22semidirect
174. #2175C22semidirect
175. C4×Q32C22semidirect
176. C4×Q32C22semidirect
180. #2169C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
186. D4×C16C22semidirect
188. #2159C22semidirect
189. #2158C22semidirect
190. C2×#367C22semidirect
191. C2×C4⋊C16C22semidirect
192. #2141C22semidirect
193. #2141C22semidirect
195. #2139C22semidirect
198. C2×#358C22semidirect
201. #2113C22semidirect
202. C4×M32C22semidirect

Maximal subgroups

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

subgroupindex
#623302
#623252
#339192
#339142
#339112
#339042
#338942
#338932
#338882
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