Finite Group Databasebeta

← #6530041

Subgroups — #6530041

Order 512.

1330 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35235C211yesmaximal, characteristic
2#34403C211yesmaximal, characteristic
3#29293C211yesmaximal, characteristic, complemented
4#29293C211yesmaximal, characteristic, complemented
5#29292C211yesmaximal, characteristic, complemented
6#29292C211yesmaximal, characteristic, complemented
7#29282C211yesmaximal, characteristic, complemented
8#29282C211yesmaximal, characteristic, complemented
9#29281C211yesmaximal, characteristic, complemented
10#29281C211yesmaximal, characteristic, complemented
11#26517C211yesmaximal, characteristic, complemented
12#26516C211yesmaximal, characteristic, complemented
13#26515C211yesmaximal, characteristic, complemented
14#26514C211yesmaximal, characteristic, complemented
15#26451C211yesmaximal, characteristic, complemented
16#26450C211yesmaximal, characteristic, complemented
17#26449C211yesmaximal, characteristic, complemented
18#26448C211yesmaximal, characteristic, complemented
19#26019C211yesmaximal, characteristic
20#26017C211yesmaximal, characteristic
21#26015C211yesmaximal, characteristic
22#26013C211yesmaximal, characteristic
23#26011C211yesmaximal, characteristic
24#26009C211yesmaximal, characteristic
25#26007C211yesmaximal, characteristic
26#26005C211yesmaximal, characteristic
27#21975C211yesmaximal, characteristic
28#21965C211yesmaximal, characteristic
29#21837C211yesmaximal, characteristic
30#21361C211yesmaximal, characteristic
31#21312C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C2×#431C2211yescharacteristic
34C2×#423C2211yescharacteristic
35#2855—21no—
36#2855—21no—
37#2666—21no—
38#2666—21no—
39#2606—21no—
40#2605—21no—
41#2570C2211yescharacteristic
42#2570C2211yescharacteristic
43#2569—21no—
44#2550C2211yescharacteristic
45#2550C2211yescharacteristic
46#2549—21no—
47#2442C2211yescharacteristic
48#2442C2211yescharacteristic
49#2440C2211yescharacteristic
50#2440C2211yescharacteristic
51#2378—21no—
52#2378—21no—
53#2370C2211yescharacteristic
54#2370C2211yescharacteristic
55#2370C2211yescharacteristic
56#2370C2211yescharacteristic
57#2356—21no—
58#2356—21no—
59#2347C2211yescharacteristic
60#2347C2211yescharacteristic
61#2346C2211yescharacteristic
62#2346C2211yescharacteristic
63#2332—21no—
64#2332—21no—
65#2331C2211yescharacteristic
66#2331C2211yescharacteristic
67#2331C2211yescharacteristic
68#2331C2211yescharacteristic
69#2331C2211yescharacteristic
70#2331C2211yescharacteristic
71#2330C2211yescharacteristic
72#2330C2211yescharacteristic
73#2320—21no—
74#2320—21no—
75#2283C2211yescharacteristic
76#2283C2211yescharacteristic
77#2283C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2086C2211yescharacteristic
102#2086C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#1991C2211yescharacteristic
112#1991C2211yescharacteristic
113#1991C2211yescharacteristic
114#1991C2211yescharacteristic
115#1989C2211yescharacteristic
116#1989C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1987C2211yescharacteristic
132#1987C2211yescharacteristic
133#1987C2211yescharacteristic
134#1987C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1949C2211yescharacteristic
151#1948C2211yescharacteristic
152#1948C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1939C2211yescharacteristic
156#1939C2211yescharacteristic
157#1939C2211yescharacteristic
158#1939C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1851C2211yescharacteristic
180#1851C2211yescharacteristic
181#1851C2211yescharacteristic
182#1851C2211yescharacteristic
183#1843C2211yescharacteristic
184#1843C2211yescharacteristic
185#1832C2211yescharacteristic
186#1832C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198C4×#106C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205#533—24no—
206#533Q818yescomplemented
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C42—21no—
226C22×C42C2311yescharacteristic
227#431—24no—
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244#423—24no—
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#398—21no—
268#398—21no—
269#398—21no—
270#398—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#395—21no—
276#395—21no—
277#395—21no—
278#395—21no—
279#391—21no—
280#391—21no—
281#391—21no—
282#391—21no—
283#391—21no—
284#391—21no—
285#391—21no—
286#391—21no—
287#391—21no—
288#391—21no—
289#391—21no—
290#391—21no—
291#391—21no—
292#391—21no—
293#389—21no—
294#389—21no—
295#389—21no—
296#389—21no—
297#389—21no—
298#389—21no—
299#389—21no—
300#389—21no—
301#389—21no—
302#389—21no—
303#389C2311yescharacteristic
304#389C2311yescharacteristic
305#389C2311yescharacteristic
306#389C2311yescharacteristic
307#389C2311yescharacteristic
308#389C2311yescharacteristic
309#389C2311yescharacteristic
310#389C2311yescharacteristic
311#389C2311yescharacteristic
312#389C2311yescharacteristic
313#389C2311yescharacteristic
314#389C2311yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#388—21no—
320#388—21no—
321#388—21no—
322#388—21no—
323#388—21no—
324#388—21no—
325#388—21no—
326#388—21no—
327#387—21no—
328#387—21no—
329#387—21no—
330#387—21no—
331#387—21no—
332#387—21no—
333#387—21no—
334#387—21no—
335#387—21no—
336#387—21no—
337#387—21no—
338#387—21no—
339#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#385—21no—
356#385—21no—
357#385—21no—
358#385—21no—
359#384C2311yescharacteristic
360#384C2311yescharacteristic
361#383—21no—
362#383—21no—
363#383—21no—
364#383—21no—
365#383D411yescharacteristic
366#383D411yescharacteristic
367#382—21no—
368#382—21no—
369#382D411yescharacteristic
370#382D411yescharacteristic
371#382C2311yescharacteristic
372#382C2311yescharacteristic
373#382C2311yescharacteristic
374#382C2311yescharacteristic
375#382C2311yescharacteristic
376#382C2311yescharacteristic
377#381—21no—
378#381—21no—
379#381D411yescharacteristic
380#381D411yescharacteristic
381#380—21no—
382#380—21no—
383#380D411yescharacteristic
384#380D411yescharacteristic
385#380C2311yescharacteristic
386#380C2311yescharacteristic
387#380C2311yescharacteristic
388#380C2311yescharacteristic
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4C2311yescharacteristic
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2311yescharacteristic
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2311yescharacteristic
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C22⋊C4—21no—
416C4×C22⋊C4—21no—
417C4×C22⋊C4C2311yescharacteristic
418C4×C22⋊C4C2311yescharacteristic
419#376—21no—
420#376—21no—
421#376—21no—
422#376—21no—
423#376C2311yescharacteristic
424#376C2311yescharacteristic
425C2×#95—21no—
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C2×D411yescharacteristic
489C23×C4C2×D411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×M16—22no—
492C2×M16—22no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—22no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8C2×Q814yes—
512C4⋊Q8C2×Q814yes—
513#125—22no—
514#125—22no—
515#125—22no—
516#125—22no—
517#125—41no—
518#125—41no—
519#125C2×Q814yes—
520#125C2×Q814yes—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—82no—
524C22⋊Q8—82no—
525C4×Q8—28no—
526C4×Q8—28no—
527#117—22no—
528#117—22no—
529#117C2×Q814yes—
530#117C2×Q814yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4C2×D411yescharacteristic
596C2×C22⋊C4C2×D411yescharacteristic
597C2×C22⋊C4C2×D411yescharacteristic
598C2×C22⋊C4C2×D411yescharacteristic
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—82no—
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×Q814yes—
621C2×C42#4114yes—
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#107—22no—
629#107—22no—
630#107—41no—
631#107—41no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107—41no—
636#106—22no—
637#106—22no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8—22no—
648C4⋊C8—22no—
649C4⋊C8—22no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C4×C8—22no—
661C4×C8—22no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726C24C22×D411yescharacteristic
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8—81no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—81no—
768C22×C4—81no—
769C22×C4C22⋊Q814yes—
770C22×C4C22⋊Q814yes—
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×Q812yes—
785C22×C4C2×#4112yes—
786C22×C4C2511yescharacteristic
787M16—82no—
788M16—82no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4C22×Q812yes—
878C4⋊C4C22×Q812yes—
879C4⋊C4C22×Q812yes—
880C4⋊C4C22×Q812yes—
881C4⋊C42−1+412yes—
882C4⋊C42−1+412yes—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—41no—
886C22⋊C4—41no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—81no—
892C22⋊C4—81no—
893C42—24no—
894C42—24no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42—81no—
907C42—81no—
908C42—81no—
909C42—81no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42C22⋊Q814yes—
920C42C22⋊Q814yes—
921C42C22×Q812yes—
922C42C22×Q812yes—
923C42C2×#4112yes—
924C42C2×#4112yes—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23C2×C22⋊Q812yes—
932C23C23×D411yescharacteristic
933Q8—84no—
934Q8—84no—
935Q8—162no—
936Q8—162no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—84no—
1026C2×C4—84no—
1027C2×C4C2×C22⋊Q812yes—
1028C2×C4C2×C22⋊Q812yes—
1029C2×C4C2×C22⋊Q812yes—
1030C2×C4C2×C22⋊Q812yes—
1031C2×C4C2×C22⋊Q812yes—
1032C2×C4C23×Q811yescharacteristic
1033C2×C4C22×#4111yescharacteristic
1034C2×C4C2×2−1+411yescharacteristic
1035C2×C4C2×2−1+411yescharacteristic
1036C2×C4#58511yescharacteristic
1037C2×C4#58511yescharacteristic
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8—41no—
1045C8—41no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22C22×C22⋊Q811yescharacteristic
1054C22#348911yescharacteristic
1055C22#348911yescharacteristic
1056C22#358411yescharacteristic
1057C22#358411yescharacteristic
1058C22#358511yescharacteristic
1059C22#358611yescharacteristic
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4—41no—
1074C4—42no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4#350211yescharacteristic
1090C4#350211yescharacteristic
1091C4#350911yescharacteristic
1092C4#351011yescharacteristic
1093C2—42no—
1094C2#3566211yescharacteristic
1095C2#6048911yescharacteristic
1096C2#6049311yescharacteristic
1097C2#6217511yescharacteristic
1098C2#6217611yescharacteristic
1099C2#6217711yescharacteristic
1100C2#6217811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29293C2semidirect
4. #29293C2semidirect
5. #29292C2semidirect
6. #29292C2semidirect
7. #29282C2semidirect
8. #29282C2semidirect
9. #29281C2semidirect
10. #29281C2semidirect
11. #26517C2semidirect
12. #26516C2semidirect
13. #26515C2semidirect
14. #26514C2semidirect
15. #26451C2semidirect
16. #26450C2semidirect
17. #26449C2semidirect
18. #26448C2semidirect
206. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#352352
#344032
#292932
#292922
#292822
#292812
#265172
#265162
#265152
#265142
#264512
#264502
#264492
#264482
#260192
#260172
#260152
#260132
#260112
#260092
#260072
#260052
#219752
#219652
#218372
#213612
#213122