Finite Group Databasebeta

← #6484855

Subgroups — #6484855

Order 512.

1353 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35282C211yesmaximal, characteristic
2#34272C211yesmaximal, characteristic
3#33159C211yesmaximal, characteristic
4#33158C211yesmaximal, characteristic
5#33156C211yesmaximal, characteristic
6#33155C211yesmaximal, characteristic
7#29974C211yesmaximal, characteristic
8#29973C211yesmaximal, characteristic
9#29970C211yesmaximal, characteristic
10#29966C211yesmaximal, characteristic
11#29291C211yesmaximal, characteristic, complemented
12#29289C211yesmaximal, characteristic, complemented
13#29289C211yesmaximal, characteristic, complemented
14#29286C211yesmaximal, characteristic, complemented
15#29285C211yesmaximal, characteristic, complemented
16#29283C211yesmaximal, characteristic, complemented
17#29282C211yesmaximal, characteristic, complemented
18#29281C211yesmaximal, characteristic, complemented
19#29229C211yesmaximal, characteristic, complemented
20#29228C211yesmaximal, characteristic, complemented
21#29217C211yesmaximal, characteristic, complemented
22#29216C211yesmaximal, characteristic, complemented
23#29184C211yesmaximal, characteristic, complemented
24#29181C211yesmaximal, characteristic, complemented
25#29180C211yesmaximal, characteristic, complemented
26#29178C211yesmaximal, characteristic, complemented
27#21992C211yesmaximal, characteristic
28#21991C211yesmaximal, characteristic
29#21843C211yesmaximal, characteristic
30#21843C211yesmaximal, characteristic
31#20812C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#433C2211yescharacteristic
34C2×#433C2211yescharacteristic
35#2864C2211yescharacteristic
36#2859C2211yescharacteristic
37#2857C2211yescharacteristic
38#2851C2211yescharacteristic
39#2660C2211yescharacteristic
40#2660C2211yescharacteristic
41#2629C2211yescharacteristic
42#2628C2211yescharacteristic
43#2586—21no—
44#2585—21no—
45#2574—21no—
46#2556—21no—
47#2522—21no—
48#2520—21no—
49#2465—21no—
50#2462—21no—
51#2370—21no—
52#2370—21no—
53#2369—21no—
54#2368—21no—
55#2368—21no—
56#2365—21no—
57#2360—21no—
58#2360—21no—
59#2331C2211yescharacteristic
60#2331C2211yescharacteristic
61#2331C2211yescharacteristic
62#2330C2211yescharacteristic
63#2330C2211yescharacteristic
64#2330C2211yescharacteristic
65#2317C2211yescharacteristic
66#2314C2211yescharacteristic
67#2314C2211yescharacteristic
68C4×C4⋊Q8C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C4×C4⋊Q8C2211yescharacteristic
71C4×#125C2211yescharacteristic
72C4×#125C2211yescharacteristic
73C4×#125C2211yescharacteristic
74#2296C2211yescharacteristic
75C2×#389C2211yescharacteristic
76#2274C2211yescharacteristic
77#2274C2211yescharacteristic
78C4×#117C2211yescharacteristic
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#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2086C2211yescharacteristic
102#2086C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#1993C2211yescharacteristic
112#1993C2211yescharacteristic
113#1992C2211yescharacteristic
114#1992C2211yescharacteristic
115#1991C2211yescharacteristic
116#1991C2211yescharacteristic
117#1990C2211yescharacteristic
118#1990C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1989C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1988C2211yescharacteristic
130#1988C2211yescharacteristic
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#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1947C2211yescharacteristic
148#1947C2211yescharacteristic
149#1947C2211yescharacteristic
150#1947C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1853C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1846C2211yescharacteristic
178#1845C2211yescharacteristic
179#1842C2211yescharacteristic
180#1842C2211yescharacteristic
181#1836C2211yescharacteristic
182#1836C2211yescharacteristic
183#1835C2211yescharacteristic
184#1834C2211yescharacteristic
185#1832C2211yescharacteristic
186#1832C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1824C2211yescharacteristic
192#1824C2211yescharacteristic
193#1823C2211yescharacteristic
194#1823C2211yescharacteristic
195#1798C2211yescharacteristic
196#1798C2211yescharacteristic
197#1797C2211yescharacteristic
198#1797C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1767C2211yescharacteristic
202C4×C4⋊C8C2211yescharacteristic
203#544—24no—
204#544Q818yescomplemented
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4—21no—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#433—24no—
231#433—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268#400—21no—
269#399—21no—
270#398—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#396—21no—
277#396—21no—
278#395—21no—
279#395—21no—
280#395—21no—
281#395—21no—
282#395—21no—
283#393—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#391—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#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389C2311yescharacteristic
311#389C2311yescharacteristic
312#389C2311yescharacteristic
313#389C2311yescharacteristic
314#389C2311yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#388—21no—
327#388—21no—
328#388—21no—
329#388—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#387—21no—
356#387—21no—
357#387—21no—
358#385—21no—
359#385—21no—
360#385—21no—
361#385—21no—
362#385—21no—
363#385—21no—
364#384C2311yescharacteristic
365#384C2311yescharacteristic
366#384C2311yescharacteristic
367#384C2311yescharacteristic
368#384C2311yescharacteristic
369#384C2311yescharacteristic
370#382—21no—
371#382C2311yescharacteristic
372#382C2311yescharacteristic
373#382C2311yescharacteristic
374#382C2311yescharacteristic
375#382C2311yescharacteristic
376#382C2311yescharacteristic
377#380—21no—
378#380C2311yescharacteristic
379#380C2311yescharacteristic
380#380C2311yescharacteristic
381#380C2311yescharacteristic
382C4×C4⋊C4—21no—
383C4×C4⋊C4—21no—
384C4×C4⋊C4—21no—
385C4×C4⋊C4—21no—
386C4×C4⋊C4—21no—
387C4×C4⋊C4—21no—
388C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
398C4×C4⋊C4D411yescharacteristic
399C4×C4⋊C4D411yescharacteristic
400C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
414C4×C22⋊C4—21no—
415C4×C22⋊C4—21no—
416C4×C22⋊C4—21no—
417C4×C22⋊C4D411yescharacteristic
418C4×C22⋊C4D411yescharacteristic
419C4×C22⋊C4D411yescharacteristic
420C4×C22⋊C4D411yescharacteristic
421#376C2311yescharacteristic
422#376C2311yescharacteristic
423C2×#95—21no—
424C43C2311yescharacteristic
425C43C2311yescharacteristic
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
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C4⋊Q8—28no—
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—22no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8C2×Q814yes—
507C4⋊Q8C2×Q814yes—
508#125—28no—
509#125—22no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—41no—
514#125—41no—
515#125—82no—
516#125C2×Q814yes—
517#125C2×Q814yes—
518C22⋊Q8—28no—
519C22⋊Q8—28no—
520C22⋊Q8—82no—
521C4×Q8—82no—
522C4×Q8—82no—
523C4×Q8—82no—
524#117—22no—
525#117—22no—
526#117—22no—
527#117—41no—
528#117—41no—
529#117C2×Q814yes—
530#117C2×Q814yes—
531#117#4114yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
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—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—82no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×Q814yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
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—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—41no—
624C2×C42—41no—
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—22no—
672C22⋊C8—22no—
673#97—22no—
674#97—22no—
675C4×C8—22no—
676C4×C8—22no—
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#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C24C22×D411yescharacteristic
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×Q8—81no—
740C2×Q8—81no—
741C2×Q8—81no—
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—24no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4—81no—
773C22×C4—81no—
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×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×Q812yes—
788C22×C4C2×#4112yes—
789C22×C4C2511yescharacteristic
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—
813C2×C8—21no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
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—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
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⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4C22⋊Q814yes—
887C4⋊C4C22⋊Q814yes—
888C4⋊C4C22×Q812yes—
889C4⋊C4C22×Q812yes—
890C4⋊C4C22×Q812yes—
891C4⋊C4C22×Q812yes—
892C22⋊C4—24no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—42no—
896C22⋊C4—81no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C22⋊C4C22⋊Q814yes—
901C22⋊C4C22⋊Q814yes—
902C42—24no—
903C42—22no—
904C42—22no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—41no—
912C42—41no—
913C42—41no—
914C42—41no—
915C42—41no—
916C42—41no—
917C42—41no—
918C42—41no—
919C42—42no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42C22×Q812yes—
933C42C22×Q812yes—
934C42C2×#4112yes—
935C42C2×#4112yes—
936C422−1+412yes—
937C422−1+412yes—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23C2×C22⋊Q812yes—
945C23C23×D411yescharacteristic
946Q8—84no—
947Q8—84no—
948Q8—84no—
949Q8—162no—
950C2×C4—21no—
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—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
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—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—82no—
1034C2×C4—84no—
1035C2×C4—82no—
1036C2×C4—162no—
1037C2×C4C2×C22⋊Q812yes—
1038C2×C4C2×C22⋊Q812yes—
1039C2×C4C2×C22⋊Q812yes—
1040C2×C4C2×C22⋊Q812yes—
1041C2×C4C2×C22⋊Q812yes—
1042C2×C4#53612yes—
1043C2×C4#53612yes—
1044C2×C4#57612yes—
1045C2×C4C23×Q811yescharacteristic
1046C2×C4C22×#4111yescharacteristic
1047C2×C4C2×2−1+411yescharacteristic
1048C2×C4C2×2−1+411yescharacteristic
1049C2×C4#58511yescharacteristic
1050C2×C4#58511yescharacteristic
1051C8—41no—
1052C8—41no—
1053C8—41no—
1054C8—41no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C8—41no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22C22×C22⋊Q811yescharacteristic
1067C22C2×#53611yescharacteristic
1068C22#344911yescharacteristic
1069C22C2×#57611yescharacteristic
1070C22#358411yescharacteristic
1071C22#358611yescharacteristic
1072C22#358611yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—41no—
1089C4—41no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4#350211yescharacteristic
1103C4#350211yescharacteristic
1104C4#350711yescharacteristic
1105C4#350711yescharacteristic
1106C2—42no—
1107C2#3517911yescharacteristic
1108C2#6049411yescharacteristic
1109C2#6049911yescharacteristic
1110C2#6088811yescharacteristic
1111C2#6089111yescharacteristic
1112C2#6100011yescharacteristic
1113C2#6100511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
11. #29291C2semidirect
12. #29289C2semidirect
13. #29289C2semidirect
14. #29286C2semidirect
15. #29285C2semidirect
16. #29283C2semidirect
17. #29282C2semidirect
18. #29281C2semidirect
19. #29229C2semidirect
20. #29228C2semidirect
21. #29217C2semidirect
22. #29216C2semidirect
23. #29184C2semidirect
24. #29181C2semidirect
25. #29180C2semidirect
26. #29178C2semidirect
204. #544Q8semidirect

Maximal subgroups

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

subgroupindex
#352822
#342722
#331592
#331582
#331562
#331552
#299742
#299732
#299702
#299662
#292912
#292892
#292862
#292852
#292832
#292822
#292812
#292292
#292282
#292172
#292162
#291842
#291812
#291802
#291782
#219922
#219912
#218432
#208122