Finite Group Databasebeta

← #6773642

Subgroups — #6773642

Order 512.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36264C211yesmaximal, characteristic
2#34966C211yesmaximal, characteristic, complemented
3#33096C211yesmaximal, characteristic, complemented
4#32375C211yesmaximal, characteristic, complemented
5#32231C211yesmaximal, characteristic, complemented
6#31577C211yesmaximal, characteristic, complemented
7#31573C211yesmaximal, characteristic, complemented
8#31459C211yesmaximal, characteristic, complemented
9#30947C211yesmaximal, characteristic, complemented
10#30815C211yesmaximal, characteristic, complemented
11#30807C211yesmaximal, characteristic, complemented
12#30150C211yesmaximal, characteristic, complemented
13#30066C211yesmaximal, characteristic, complemented
14#29516C211yesmaximal, characteristic, complemented
15#29389C211yesmaximal, characteristic, complemented
16#28769C211yesmaximal, characteristic, complemented
17#28654C211yesmaximal, characteristic, complemented
18#28207C211yesmaximal, characteristic, complemented
19#27859C211yesmaximal, characteristic, complemented
20#27588C211yesmaximal, characteristic, complemented
21#27254C211yesmaximal, characteristic
22#27254C211yesmaximal, characteristic
23#26422C211yesmaximal, characteristic, complemented
24#26348C211yesmaximal, characteristic, complemented
25#26060C211yesmaximal, characteristic, complemented
26#25960C211yesmaximal, characteristic, complemented
27#25952C211yesmaximal, characteristic, complemented
28#22589C211yesmaximal, characteristic, complemented
29#22219C211yesmaximal, characteristic, complemented
30#22114C211yesmaximal, characteristic, complemented
31C2×#1926C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#498C2211yescharacteristic, complemented
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic, complemented
39C22×#106C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2860C2211yescharacteristic
43#2858C2211yescharacteristic
44#2854C2211yescharacteristic
45#2610—21no—
46#2606—21no—
47#2605—21no—
48#2603—21no—
49#2570C2211yescharacteristic, complemented
50#2570C2211yescharacteristic, complemented
51#2554—21no—
52#2550C2211yescharacteristic, complemented
53#2550C2211yescharacteristic, complemented
54#2512C2211yescharacteristic
55#2472—21no—
56#2461—21no—
57#2452C2211yescharacteristic
58#2445C2211yescharacteristic
59#2445C2211yescharacteristic
60#2442C2211yescharacteristic
61#2442C2211yescharacteristic
62#2440C2211yescharacteristic
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2438—21no—
66#2438—21no—
67#2433C2211yescharacteristic
68#2411—21no—
69#2402—21no—
70#2399—21no—
71#2361C2211yescharacteristic
72#2358—21no—
73D4×C22⋊C4C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic, complemented
75C4×C4⋊Q8C2211yescharacteristic, complemented
76C4×#127C2211yescharacteristic
77C4×#125C2211yescharacteristic, complemented
78C4×#125C2211yescharacteristic, complemented
79C4×C22⋊Q8—21no—
80C4×C22⋊Q8—21no—
81#2293C2211yescharacteristic
82C2×#390C2211yescharacteristic
83#2283C2211yescharacteristic
84C4×#117C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2058C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2057C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#1990C2211yescharacteristic, complemented
127#1990C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1957C2211yescharacteristic
130#1957C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1942C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic, complemented
151#1926C2211yescharacteristic, complemented
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1925C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1844C2211yescharacteristic, complemented
187#1839C2211yescharacteristic, complemented
188#1831C2211yescharacteristic, complemented
189#1817C2211yescharacteristic
190#1808C2211yescharacteristic
191#1807C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×C4⋊C8C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1744C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#551—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×#120—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117D411yescharacteristic
238C2×#117D411yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C42—21no—
246C22×C42C2311yescharacteristic
247#498—42no—
248#486—24no—
249#486—42no—
250#478—24no—
251#478—42no—
252#478—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106—42no—
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#102—24no—
275C2×#102—42no—
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#392—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—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#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383—21no—
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#379—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4D411yescharacteristic
439C4×C22⋊C4D411yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376D411yescharacteristic
444#376D411yescharacteristic
445C2×#95—21no—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#127—22no—
537#127—41no—
538#127—41no—
539#127—41no—
540#126—44no—
541#126—44no—
542#125—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#124—44no—
547#124—82no—
548#123—44no—
549#123—44no—
550#123—44no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555#121—22no—
556#121—22no—
557#120—44no—
558#120—44no—
559C4×Q8—82no—
560C4×Q8—82no—
561C4×D4—22no—
562C4×D4—41no—
563C4×D4—44no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—44no—
569C4×D4—82no—
570#117—24no—
571#117—24no—
572#117—44no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
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—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—44no—
655C2×C22⋊C4—44no—
656C2×C22⋊C4—82no—
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C42—22no—
662C2×C42—22no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—82no—
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102#4114yes—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C4×C8—22no—
734C4×C8—41no—
735C4×C8—41no—
736C4×C8—41no—
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#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C24—42no—
780C24—42no—
781C24—42no—
782C24—42no—
783C24—81no—
784C24—81no—
785C24—81no—
786C24C22×D411yescharacteristic
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4C2×#4112yes—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—41no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C42−1+412yes—
891C22×C42−1+412yes—
892C22×C4C2511yescharacteristic
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—44no—
917C2×C8—82no—
918C2×C8C2×#4112yes—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
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—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4C2×#4112yes—
977C4⋊C4H(5,𝔽2)12yes—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4#13514yes—
1010C22⋊C4AGL(1,ℤ/8)14yes—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—41no—
1032C42—41no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—84no—
1066C23—84no—
1067C23—84no—
1068C23—84no—
1069C23—162no—
1070C23—162no—
1071C23—162no—
1072C23#53612yes—
1073C23C2×#13512yes—
1074C23C2×AGL(1,ℤ/8)12yes—
1075C23C23×D411yescharacteristic
1076Q8—84no—
1077Q8—84no—
1078Q8—162no—
1079D4—22no—
1080D4—22no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—84no—
1092D4—84no—
1093D4—84no—
1094D4—84no—
1095D4—162no—
1096D4—162no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—44no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—44no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—84no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4—162no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4#53612yes—
1182C2×C4C2×#13512yes—
1183C2×C4C2×#13512yes—
1184C2×C4C2×AGL(1,ℤ/8)12yes—
1185C2×C4C2×AGL(1,ℤ/8)12yes—
1186C2×C4#57712yes—
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C2×H(5,𝔽2)11yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4C2×2−1+411yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—168no—
1229C22#322814yes—
1230C22C2×#53611yescharacteristic
1231C22D4×#4111yescharacteristic
1232C22#348811yescharacteristic
1233C22C22×#13511yescharacteristic
1234C22C22×AGL(1,ℤ/8)11yescharacteristic
1235C22C2×#57711yescharacteristic
1236C22#358511yescharacteristic
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—41no—
1244C4—42no—
1245C4—41no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4#349511yescharacteristic
1264C4#352011yescharacteristic
1265C4#356111yescharacteristic
1266C4#356411yescharacteristic
1267C2—24no—
1268C2—82no—
1269C2—161no—
1270C2—161no—
1271C2#3837011yescharacteristic
1272C2C2×#322811yescharacteristic
1273C2#6087311yescharacteristic
1274C2#6143211yescharacteristic
1275C2#6145111yescharacteristic
1276C2#6195511yescharacteristic
1277C2#6198311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
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
2. #34966C2semidirect
3. #33096C2semidirect
4. #32375C2semidirect
5. #32231C2semidirect
6. #31577C2semidirect
7. #31573C2semidirect
8. #31459C2semidirect
9. #30947C2semidirect
10. #30815C2semidirect
11. #30807C2semidirect
12. #30150C2semidirect
13. #30066C2semidirect
14. #29516C2semidirect
15. #29389C2semidirect
16. #28769C2semidirect
17. #28654C2semidirect
18. #28207C2semidirect
19. #27859C2semidirect
20. #27588C2semidirect
23. #26422C2semidirect
24. #26348C2semidirect
25. #26060C2semidirect
26. #25960C2semidirect
27. #25952C2semidirect
28. #22589C2semidirect
29. #22219C2semidirect
30. #22114C2semidirect
31. C2×#1926C2semidirect
33. C2×#498C22semidirect
38. C2×#478C22semidirect
49. #2570C22semidirect
50. #2570C22semidirect
52. #2550C22semidirect
53. #2550C22semidirect
74. C4×C4⋊Q8C22semidirect
75. C4×C4⋊Q8C22semidirect
77. C4×#125C22semidirect
78. C4×#125C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
92. #2092C22semidirect
93. #2092C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
103. #2073C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2058C22semidirect
114. #2058C22semidirect
115. #2057C22semidirect
116. #2057C22semidirect
123. #2025C22semidirect
126. #1990C22semidirect
127. #1990C22semidirect
128. #1989C22semidirect
131. #1949C22semidirect
132. #1942C22semidirect
133. #1942C22semidirect
134. #1941C22semidirect
135. #1941C22semidirect
150. #1926C22semidirect
151. #1926C22semidirect
152. #1926C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1925C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1920C22semidirect
163. #1920C22semidirect
164. #1919C22semidirect
165. #1919C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
186. #1844C22semidirect
187. #1839C22semidirect
188. #1831C22semidirect
194. #1804C22semidirect
197. C4×C4⋊C8C22semidirect
200. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#362642
#349662
#330962
#323752
#322312
#315772
#315732
#314592
#309472
#308152
#308072
#301502
#300662
#295162
#293892
#287692
#286542
#282072
#278592
#275882
#272542
#264222
#263482
#260602
#259602
#259522
#225892
#222192
#221142
C2×#19262