Finite Group Databasebeta

← #7035442

Subgroups — #7035442

Order 512.

1387 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59325C211yesmaximal, characteristic, complemented
2#39984C211yesmaximal, characteristic
3#32663C211yesmaximal, characteristic, complemented
4#32653C211yesmaximal, characteristic, complemented
5#32357C211yesmaximal, characteristic, complemented
6#32351C211yesmaximal, characteristic, complemented
7#31531C211yesmaximal, characteristic, complemented
8#31528C211yesmaximal, characteristic, complemented
9#30969C211yesmaximal, characteristic, complemented
10#30955C211yesmaximal, characteristic, complemented
11#29164C211yesmaximal, characteristic, complemented
12#28971C211yesmaximal, characteristic, complemented
13#28944C211yesmaximal, characteristic, complemented
14#28549C211yesmaximal, characteristic, complemented
15#28532C211yesmaximal, characteristic, complemented
16#27952C211yesmaximal, characteristic, complemented
17#26385C211yesmaximal, characteristic, complemented
18#26369C211yesmaximal, characteristic, complemented
19#26356C211yesmaximal, characteristic, complemented
20#26356C211yesmaximal, characteristic, complemented
21#26079C211yesmaximal, characteristic, complemented
22#26074C211yesmaximal, characteristic, complemented
23#25972C211yesmaximal, characteristic
24#25967C211yesmaximal, characteristic
25#25071C211yesmaximal, characteristic, complemented
26#25065C211yesmaximal, characteristic, complemented
27#23733C211yesmaximal, characteristic
28#23239C211yesmaximal, characteristic, complemented
29#22879C211yesmaximal, characteristic
30#22862C211yesmaximal, characteristic
31#22042C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#500C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45#2851C2211yescharacteristic
46#2804—21no—
47#2784—21no—
48#2780—21no—
49#2774—21no—
50#2755—21no—
51#2692—21no—
52#2665—21no—
53#2607—21no—
54#2581C2211yescharacteristic
55#2581C2211yescharacteristic
56#2580C2211yescharacteristic
57#2569—21no—
58#2568C2211yescharacteristic
59#2568C2211yescharacteristic
60#2565C2211yescharacteristic
61#2563C2211yescharacteristic
62#2550C2211yescharacteristic
63#2549—21no—
64#2520—21no—
65#2509C2211yescharacteristic
66#2508—21no—
67#2508C2211yescharacteristic
68#2505—21no—
69#2505—21no—
70#2454C2211yescharacteristic
71#2453C2211yescharacteristic
72#2452C2211yescharacteristic
73#2451C2211yescharacteristic
74#2442C2211yescharacteristic
75#2440C2211yescharacteristic
76#2439C2211yescharacteristic
77#2439C2211yescharacteristic
78#2368—21no—
79#2360C2211yescharacteristic
80#2360C2211yescharacteristic
81#2355C2211yescharacteristic
82#2351C2211yescharacteristic
83#2341C2211yescharacteristic
84#2339C2211yescharacteristic
85#2329—21no—
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88#2297C2211yescharacteristic
89C2×#382C2211yescharacteristic
90#2101C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2097C2211yescharacteristic
97#2097C2211yescharacteristic
98#2097C2211yescharacteristic
99#2094C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic
104#2087C2211yescharacteristic
105#2087C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2085C2211yescharacteristic
113#2083C2211yescharacteristic
114#2067C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2065C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2058C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2023C2211yescharacteristic
130#1991C2211yescharacteristic
131#1991C2211yescharacteristic
132#1985C2211yescharacteristic
133#1984C2211yescharacteristic
134#1973C2211yescharacteristic
135#1969C2211yescharacteristic
136#1969C2211yescharacteristic
137#1968C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1942C2211yescharacteristic
143#1941C2211yescharacteristic
144#1935C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1921C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1877C2211yescharacteristic
168#1873C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic
186#1847C2211yescharacteristic
187#1846C2211yescharacteristic
188#1846C2211yescharacteristic
189#1846C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic
194#1788C2211yescharacteristic
195#1771C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8D411yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#501—42no—
230#500—42no—
231#478—42no—
232#475—42no—
233#475—42no—
234#475—42no—
235#452Q818yescomplemented
236#440—42no—
237C4×Q16—42no—
238#428—42no—
239#428—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266#417—42no—
267#417—42no—
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#393—21no—
327#393—21no—
328#393—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391D411yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389D411yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385D411yescharacteristic
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380D411yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C2×#95—21no—
455C2×#95—21no—
456C2×#95—21no—
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×Q814yes—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16C2×Q814yes—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16C2×Q814yes—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—41no—
543C22⋊Q8—22no—
544C22⋊Q8—42no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8C2×Q814yes—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564#117—41no—
565#117—41no—
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—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103C2×Q814yes—
699#102—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102C2×Q814yes—
706C22⋊C8—22no—
707C22⋊C8C2×Q814yes—
708#97—22no—
709#97—41no—
710C4×C8—22no—
711C4×C8—41no—
712C4×C8—41no—
713C4×C8—41no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24C22×D411yescharacteristic
775#41—44no—
776#41—44no—
777#41—82no—
778#41—82no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8C22×Q812yes—
802C2×Q8C22×Q812yes—
803C2×D4—24no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4C22×Q812yes—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×Q812yes—
866C22×C42−1+412yes—
867C22×C4C2511yescharacteristic
868Q16—44no—
869SD16—44no—
870M16—44no—
871M16—44no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8C22×Q812yes—
893C2×C8C22×Q812yes—
894C2×C8H(5,𝔽2)12yes—
895C2×C8H(5,𝔽2)12yes—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C22×Q812yes—
961C22⋊C4—24no—
962C22⋊C4—22no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—41no—
993C42—41no—
994C42—42no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23D4×Q812yes—
1017C23C23×D411yescharacteristic
1018Q8—22no—
1019Q8—22no—
1020Q8—22no—
1021Q8—22no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—82no—
1027Q8—162no—
1028Q8—162no—
1029Q8—162no—
1030D4—22no—
1031D4—22no—
1032D4—41no—
1033D4—41no—
1034D4—84no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
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—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—84no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—162no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4—162no—
1128C2×C4D4×Q812yes—
1129C2×C4#57512yes—
1130C2×C4C23×Q811yescharacteristic
1131C2×C4C2×H(5,𝔽2)11yescharacteristic
1132C2×C4C2×H(5,𝔽2)11yescharacteristic
1133C2×C4C2×2−1+411yescharacteristic
1134C2×C4#58511yescharacteristic
1135C2×C4#58511yescharacteristic
1136C8—22no—
1137C8—22no—
1138C8—22no—
1139C8—22no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22C2×D4×Q811yescharacteristic
1159C22#348511yescharacteristic
1160C22#349811yescharacteristic
1161C22C2×#57511yescharacteristic
1162C22#358411yescharacteristic
1163C22#358411yescharacteristic
1164C22#358611yescharacteristic
1165C4—22no—
1166C4—22no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—42no—
1178C4—41no—
1179C4—42no—
1180C4—42no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4#350111yescharacteristic
1194C4#350111yescharacteristic
1195C4#353511yescharacteristic
1196C4#353511yescharacteristic
1197C2—42no—
1198C2—82no—
1199C2#4349411yescharacteristic
1200C2#6136911yescharacteristic
1201C2#6137611yescharacteristic
1202C2#6174311yescharacteristic
1203C2#6176011yescharacteristic
1204C2#6242811yescharacteristic
1205C2#6246711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59325C2semidirect
3. #32663C2semidirect
4. #32653C2semidirect
5. #32357C2semidirect
6. #32351C2semidirect
7. #31531C2semidirect
8. #31528C2semidirect
9. #30969C2semidirect
10. #30955C2semidirect
11. #29164C2semidirect
12. #28971C2semidirect
13. #28944C2semidirect
14. #28549C2semidirect
15. #28532C2semidirect
16. #27952C2semidirect
17. #26385C2semidirect
18. #26369C2semidirect
19. #26356C2semidirect
20. #26356C2semidirect
21. #26079C2semidirect
22. #26074C2semidirect
25. #25071C2semidirect
26. #25065C2semidirect
28. #23239C2semidirect
235. #452Q8semidirect

Maximal subgroups

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

subgroupindex
#593252
#399842
#326632
#326532
#323572
#323512
#315312
#315282
#309692
#309552
#291642
#289712
#289442
#285492
#285322
#279522
#263852
#263692
#263562
#260792
#260742
#259722
#259672
#250712
#250652
#237332
#232392
#228792
#228622
#220422