Finite Group Databasebeta

← #7624107

Subgroups — #7624107

Order 512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61482C211yesmaximal, characteristic, complemented
2#61473C211yesmaximal, characteristic, complemented
3#33969C211yesmaximal, characteristic, complemented
4#33953C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33934C211yesmaximal, characteristic, complemented
7#33913C211yesmaximal, characteristic, complemented
8#33910C211yesmaximal, characteristic, complemented
9#33905C211yesmaximal, characteristic, complemented
10#33883C211yesmaximal, characteristic, complemented
11#33882C211yesmaximal, characteristic, complemented
12#33881C211yesmaximal, characteristic, complemented
13#33875C211yesmaximal, characteristic, complemented
14#33866C211yesmaximal, characteristic, complemented
15#33864C211yesmaximal, characteristic, complemented
16#33848C211yesmaximal, characteristic, complemented
17#33835C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33747C211yesmaximal, characteristic, complemented
20#33745C211yesmaximal, characteristic, complemented
21#33739C211yesmaximal, characteristic, complemented
22#33684C211yesmaximal, characteristic, complemented
23#33684C211yesmaximal, characteristic, complemented
24#33681C211yesmaximal, characteristic, complemented
25#33680C211yesmaximal, characteristic, complemented
26#33665C211yesmaximal, characteristic, complemented
27#33664C211yesmaximal, characteristic, complemented
28#33482C211yesmaximal, characteristic, complemented
29#33459C211yesmaximal, characteristic, complemented
30#33455C211yesmaximal, characteristic, complemented
31C2×#2175C211yesmaximal, characteristic, complemented
32#3520—21no—
33#3516—21no—
34C2×#510C2211yescharacteristic
35C2×#508C2211yescharacteristic
36C22×SD32C2211yescharacteristic
37#3393C2211yescharacteristic
38#3393C2211yescharacteristic, complemented
39#3383C2211yescharacteristic, complemented
40Q8×D8C2211yescharacteristic
41#3377—21no—
42#3367—21no—
43#3339C2211yescharacteristic
44#3338C2211yescharacteristic
45#3338C2211yescharacteristic
46#3338C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3334C2211yescharacteristic
49#3330—21no—
50#3327—21no—
51#3320—21no—
52#3316—21no—
53#3314—21no—
54#3314—21no—
55D4×Q16C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic, complemented
58#3283C2211yescharacteristic
59#3280C2211yescharacteristic
60#3280C2211yescharacteristic
61#3177C2211yescharacteristic, complemented
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic, complemented
65#3170C2211yescharacteristic
66#3168C2211yescharacteristic
67#3124—21no—
68#3124—21no—
69#3121—21no—
70#3120—21no—
71#3117—21no—
72#3110—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76#2951C2211yescharacteristic, complemented
77#2950C2211yescharacteristic, complemented
78C2×C4×Q16C2211yescharacteristic
79C2×C4×D8C2211yescharacteristic
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2252C2211yescharacteristic, complemented
83#2251C2211yescharacteristic
84#2251C2211yescharacteristic, complemented
85#2249C2211yescharacteristic
86#2245C2211yescharacteristic, complemented
87#2243C2211yescharacteristic
88#2243C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2242C2211yescharacteristic
91#2241C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2236C2211yescharacteristic
94#2236C2211yescharacteristic
95#2236C2211yescharacteristic
96#2236C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2236C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2234C2211yescharacteristic
101#2233C2211yescharacteristic
102#2232C2211yescharacteristic
103#2232C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2228C2211yescharacteristic
106#2228C2211yescharacteristic
107#2228C2211yescharacteristic
108#2227C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2227C2211yescharacteristic, complemented
111#2227C2211yescharacteristic, complemented
112#2227C2211yescharacteristic, complemented
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic
115#2224C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic, complemented
119#2219C2211yescharacteristic, complemented
120#2217C2211yescharacteristic
121#2217C2211yescharacteristic
122#2217C2211yescharacteristic
123#2216C2211yescharacteristic
124#2216C2211yescharacteristic
125#2216C2211yescharacteristic, complemented
126#2216C2211yescharacteristic, complemented
127#2215C2211yescharacteristic
128#2211C2211yescharacteristic
129#2211C2211yescharacteristic
130#2211C2211yescharacteristic
131#2211C2211yescharacteristic, complemented
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic
135#2210C2211yescharacteristic
136#2209C2211yescharacteristic, complemented
137#2209C2211yescharacteristic, complemented
138#2209C2211yescharacteristic, complemented
139#2208C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2189C2211yescharacteristic
143#2189C2211yescharacteristic, complemented
144#2188C2211yescharacteristic
145#2188C2211yescharacteristic
146#2188C2211yescharacteristic, complemented
147#2187C2211yescharacteristic
148#2186C2211yescharacteristic
149#2186C2211yescharacteristic
150#2185C2211yescharacteristic
151#2184C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2176C2211yescharacteristic, complemented
155#2176C2211yescharacteristic, complemented
156#2176C2211yescharacteristic, complemented
157#2175C2211yescharacteristic
158#2175C2211yescharacteristic
159#2175C2211yescharacteristic
160#2175C2211yescharacteristic
161#2175C2211yescharacteristic
162#2175C2211yescharacteristic
163#2175C2211yescharacteristic
164#2175C2211yescharacteristic
165#2175C2211yescharacteristic
166#2175C2211yescharacteristic
167#2175C2211yescharacteristic, complemented
168#2175C2211yescharacteristic, complemented
169#2175C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×Q32C2211yescharacteristic, complemented
172C4×Q32C2211yescharacteristic, complemented
173C4×Q32C2211yescharacteristic, complemented
174C4×Q32C2211yescharacteristic, complemented
175C4×Q32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179C4×D16C2211yescharacteristic
180C4×D16C2211yescharacteristic
181C4×D16C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic, complemented
185#2168C2211yescharacteristic, complemented
186D4×C16C2211yescharacteristic
187D4×C16C2211yescharacteristic
188#2164C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2162C2211yescharacteristic
191#2159C2211yescharacteristic, complemented
192C2×#366C2211yescharacteristic
193C2×#366C2211yescharacteristic, complemented
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic
197C2×#358C2211yescharacteristic
198C2×#358C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200#2108C2211yescharacteristic, complemented
201#2108C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#557—21no—
210#556—21no—
211#556—21no—
212#556—41no—
213#554—21no—
214#554—21no—
215#554—21no—
216#554—41no—
217#553—21no—
218#553—41no—
219#552—21no—
220#552—41no—
221#552—41no—
222#551—41no—
223#551—41no—
224D4×Q8—21no—
225D4×Q8—21no—
226#548—21no—
227#548—21no—
228#548—41no—
229#547—21no—
230#547—21no—
231#546—21no—
232#546—21no—
233#542—21no—
234#542—21no—
235#542—21no—
236#542—41no—
237#541—21no—
238#541—41no—
239#539—41no—
240#539—41no—
241#533—21no—
242#529—21no—
243#529—41no—
244#529—41no—
245#529D411yescharacteristic
246#525—41no—
247C2×C22⋊Q8—41no—
248#520—21no—
249#520—21no—
250#520—21no—
251#519—21no—
252C2×C4×Q8—21no—
253C2×C4×D4—21no—
254#510—24no—
255#508—24no—
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×Q32C2311yescharacteristic
262C2×SD32—24no—
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C22×C16C2311yescharacteristic
276C22×C16C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#494C2311yescharacteristic
290#494C2311yescharacteristic
291#491—21no—
292#489—21no—
293#489—21no—
294#489—21no—
295#488—21no—
296#487—21no—
297#485—21no—
298#484—21no—
299#484—21no—
300#484—21no—
301#484—21no—
302#484—21no—
303#484—21no—
304#483—21no—
305#482—21no—
306#481—21no—
307#480—21no—
308#480—21no—
309#479—21no—
310#479—21no—
311#479—21no—
312#478—21no—
313#477—21no—
314#477—21no—
315#477—21no—
316#475—21no—
317#474—21no—
318#474—21no—
319#474—21no—
320#474—21no—
321#470—21no—
322#468—21no—
323#468—21no—
324#468—21no—
325#467—21no—
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#466C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#464—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462—21no—
348#461—21no—
349#461—21no—
350#461—21no—
351#452—21no—
352#452—21no—
353#452—21no—
354#452—21no—
355#451—21no—
356#451—21no—
357#450—21no—
358#450—21no—
359#449—21no—
360#449—21no—
361#448—21no—
362#448—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#441—21no—
366#441—21no—
367#441—21no—
368#440—21no—
369#440—21no—
370#440—21no—
371#440—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16—21no—
378C4×Q16—21no—
379C4×Q16—21no—
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×Q16C2311yescharacteristic
384C4×Q16C2311yescharacteristic
385C4×Q16C2311yescharacteristic
386C4×Q16C2311yescharacteristic
387C4×Q16C2311yescharacteristic
388C4×Q16C2311yescharacteristic
389C4×Q16C2311yescharacteristic
390C4×Q16C2311yescharacteristic
391C4×Q16C2311yescharacteristic
392C4×SD16—21no—
393C4×D8—21no—
394C4×D8—21no—
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403#436D411yescharacteristic
404#435D411yescharacteristic
405#435D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#433D411yescharacteristic
410#433D411yescharacteristic
411#432D411yescharacteristic
412#427C2311yescharacteristic
413C2×#107C2311yescharacteristic
414C2×#107C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#419—21no—
419#417—21no—
420#417—21no—
421#417—21no—
422C2×#103—21no—
423C2×#102—21no—
424#405C2311yescharacteristic
425#405C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
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#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
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
491#346C2311yescharacteristic
492#346C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—41no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—41no—
504C22×D4—21no—
505C23×C4—41no—
506#135—22no—
507#135—22no—
508#135—22no—
509#135—41no—
510#135—41no—
511#135—41no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—21no—
515C2×Q16—21no—
516C2×Q16—21no—
517C2×Q16—21no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16C2411yescharacteristic
521C2×Q16C2411yescharacteristic
522C2×Q16C2411yescharacteristic
523C2×Q16C2411yescharacteristic
524C2×Q16C2411yescharacteristic
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—22no—
533C2×D8—21no—
534C2×D8—41no—
535C2×D8C2411yescharacteristic
536C2×D8C2411yescharacteristic
537C2×D8C2411yescharacteristic
538C2×M16C2×D411yescharacteristic
539C2×M16C2×D411yescharacteristic
540C22×C8C2×D411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552#126—41no—
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#126—41no—
564#126D811yescharacteristic
565#126D811yescharacteristic
566#125—21no—
567#125—21no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—41no—
577#125D811yescharacteristic
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124D811yescharacteristic
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123D811yescharacteristic
601#123D811yescharacteristic
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8D811yescharacteristic
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121—41no—
639#121—41no—
640#121—41no—
641#121D811yescharacteristic
642#120—41no—
643#120—41no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8—21no—
652C4×Q8—21no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—21no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8C2×D411yescharacteristic
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
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×D4—41no—
680C4×D4—41no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4—41no—
684C4×D4—41no—
685C4×D4—41no—
686C4×D4—41no—
687C4×D4C2×D411yescharacteristic
688C4×D4C2×D411yescharacteristic
689C4×D4C2×D411yescharacteristic
690#117—21no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117—41no—
698#117—41no—
699#117—41no—
700#117—41no—
701#117C2×D411yescharacteristic
702#117C2×D411yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—22no—
720Q32—22no—
721Q32—41no—
722Q32—41no—
723Q32—41no—
724SD32—22no—
725SD32—22no—
726SD32—22no—
727SD32—22no—
728SD32—22no—
729SD32—41no—
730SD32—41no—
731SD32#4114yescomplemented
732D16—22no—
733D16—41no—
734M32—22no—
735M32—41no—
736C2×C16—22no—
737C2×C16—22no—
738C2×C16—41no—
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#107—21no—
755#107—21no—
756#107—21no—
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#107C2411yescharacteristic
763#107C2411yescharacteristic
764#107C2411yescharacteristic
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#103—21no—
791#103—21no—
792#103—21no—
793#103—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
812#97C2×D411yescharacteristic
813#97C2×D411yescharacteristic
814#97C2×D411yescharacteristic
815#97C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822C24—41no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41—81no—
827#41—81no—
828#41—81no—
829#41—162no—
830C2×Q8—21no—
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—41no—
842C2×Q8—41no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—162no—
846C2×Q8C2×D811yescharacteristic
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—42no—
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—81no—
860C2×D4C2×D811yescharacteristic
861C2×D4C2×D811yescharacteristic
862C2×D4C2×D811yescharacteristic
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—162no—
882C22×C4C2×D811yescharacteristic
883C22×C4C2×D811yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887Q16—21no—
888Q16—21no—
889Q16—21no—
890Q16—21no—
891Q16—21no—
892Q16—21no—
893Q16—21no—
894Q16—21no—
895Q16—21no—
896Q16—42no—
897Q16—42no—
898Q16—81no—
899Q16—81no—
900Q16C2×#4112yes—
901SD16—42no—
902SD16—42no—
903SD16—42no—
904SD16—81no—
905SD16—81no—
906SD16—81no—
907SD16—81no—
908D8—21no—
909D8—21no—
910D8—21no—
911D8—21no—
912D8—21no—
913D8—42no—
914D8C2×#4112yes—
915M16—41no—
916M16—41no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—41no—
924C2×C8C22×D411yescharacteristic
925C2×C8C22×D411yescharacteristic
926C2×C8C22×D411yescharacteristic
927C2×C8C22×D411yescharacteristic
928C2×C8C22×D411yescharacteristic
929C2×C8C22×D411yescharacteristic
930C2×C8C22×D411yescharacteristic
931C2×C8C2511yescharacteristic
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C4⋊C4C2×D811yescharacteristic
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
985C4⋊C4C2×D811yescharacteristic
986C4⋊C4C2×D811yescharacteristic
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4C2×D811yescharacteristic
1017C22⋊C4C2×D811yescharacteristic
1018C22⋊C4C2×D811yescharacteristic
1019C22⋊C4C2×D811yescharacteristic
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—
1038C42—41no—
1039C42C2×D811yescharacteristic
1040C42C2×D811yescharacteristic
1041C42C22×D411yescharacteristic
1042C42C22×D411yescharacteristic
1043C42C22×D411yescharacteristic
1044C42C22×D411yescharacteristic
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16—21no—
1050C16—21no—
1051C16—21no—
1052C16C2×#4112yes—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—82no—
1057C23—82no—
1058C23—161no—
1059C23C22×D811yescharacteristic
1060C23C22×D811yescharacteristic
1061C23C22×D811yescharacteristic
1062Q8—22no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—82no—
1074Q8—82no—
1075Q8—82no—
1076Q8—161no—
1077Q8—161no—
1078Q8—161no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—82no—
1089D4—82no—
1090D4—82no—
1091D4—82no—
1092D4—82no—
1093D4—161no—
1094D4—161no—
1095D4—161no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—161no—
1125C2×C4—161no—
1126C2×C4—161no—
1127C2×C4—161no—
1128C2×C4—161no—
1129C2×C4—161no—
1130C2×C4—161no—
1131C2×C4—161no—
1132C2×C4—161no—
1133C2×C4—161no—
1134C2×C4—161no—
1135C2×C4C22×D811yescharacteristic
1136C2×C4C22×D811yescharacteristic
1137C2×C4C22×D811yescharacteristic
1138C2×C4C22×D811yescharacteristic
1139C2×C4C22×D811yescharacteristic
1140C2×C4C22×D811yescharacteristic
1141C2×C4C22×D811yescharacteristic
1142C2×C4C22×D811yescharacteristic
1143C2×C4C22×D811yescharacteristic
1144C2×C4C22×D811yescharacteristic
1145C2×C4C22×D811yescharacteristic
1146C2×C4C23×D411yescharacteristic
1147C8—21no—
1148C8—21no—
1149C8—21no—
1150C8—21no—
1151C8—21no—
1152C8—21no—
1153C8—21no—
1154C8C22×#4111yescharacteristic
1155C8#58511yescharacteristic
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—42no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—164no—
1174C22#341712yes—
1175C22C23×D811yescharacteristic
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—21no—
1180C4—21no—
1181C4—21no—
1182C4—21no—
1183C4—21no—
1184C4—21no—
1185C4—21no—
1186C4—21no—
1187C4—42no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4D4×#4111yescharacteristic
1201C4#358411yescharacteristic
1202C2—22no—
1203C2—41no—
1204C2—41no—
1205C2—82no—
1206C2—161no—
1207C2—161no—
1208C2D8×#4111yescharacteristic
1209C2C2×#341711yescharacteristic
1210C2#6263611yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #61482C2semidirect
2. #61473C2semidirect
3. #33969C2semidirect
4. #33953C2semidirect
5. #33944C2semidirect
6. #33934C2semidirect
7. #33913C2semidirect
8. #33910C2semidirect
9. #33905C2semidirect
10. #33883C2semidirect
11. #33882C2semidirect
12. #33881C2semidirect
13. #33875C2semidirect
14. #33866C2semidirect
15. #33864C2semidirect
16. #33848C2semidirect
17. #33835C2semidirect
18. #33832C2semidirect
19. #33747C2semidirect
20. #33745C2semidirect
21. #33739C2semidirect
22. #33684C2semidirect
23. #33684C2semidirect
24. #33681C2semidirect
25. #33680C2semidirect
26. #33665C2semidirect
27. #33664C2semidirect
28. #33482C2semidirect
29. #33459C2semidirect
30. #33455C2semidirect
31. C2×#2175C2semidirect
38. #3393C22semidirect
39. #3383C22semidirect
47. #3336C22semidirect
57. #3285C22semidirect
61. #3177C22semidirect
64. #3175C22semidirect
76. #2951C22semidirect
77. #2950C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2252C22semidirect
84. #2251C22semidirect
86. #2245C22semidirect
88. #2243C22semidirect
89. #2243C22semidirect
91. #2241C22semidirect
92. #2237C22semidirect
96. #2236C22semidirect
97. #2236C22semidirect
98. #2236C22semidirect
99. #2235C22semidirect
103. #2232C22semidirect
104. #2229C22semidirect
108. #2227C22semidirect
109. #2227C22semidirect
110. #2227C22semidirect
111. #2227C22semidirect
112. #2227C22semidirect
113. #2225C22semidirect
115. #2224C22semidirect
118. #2220C22semidirect
119. #2219C22semidirect
125. #2216C22semidirect
126. #2216C22semidirect
131. #2211C22semidirect
136. #2209C22semidirect
137. #2209C22semidirect
138. #2209C22semidirect
143. #2189C22semidirect
146. #2188C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
154. #2176C22semidirect
155. #2176C22semidirect
156. #2176C22semidirect
167. #2175C22semidirect
168. #2175C22semidirect
169. #2175C22semidirect
170. C4×Q32C22semidirect
171. C4×Q32C22semidirect
172. C4×Q32C22semidirect
173. C4×Q32C22semidirect
174. C4×Q32C22semidirect
175. C4×Q32C22semidirect
184. #2168C22semidirect
185. #2168C22semidirect
188. #2164C22semidirect
189. #2164C22semidirect
191. #2159C22semidirect
193. C2×#366C22semidirect
195. #2139C22semidirect
198. C2×#358C22semidirect
200. #2108C22semidirect
201. #2108C22semidirect
731. SD32#41semidirect

Maximal subgroups

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

subgroupindex
#614822
#614732
#339692
#339532
#339442
#339342
#339132
#339102
#339052
#338832
#338822
#338812
#338752
#338662
#338642
#338482
#338352
#338322
#337472
#337452
#337392
#336842
#336812
#336802
#336652
#336642
#334822
#334592
#334552
C2×#21752