Finite Group Databasebeta

← #7051608

Subgroups — #7051608

Order 512.

1433 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C211yesmaximal, characteristic, complemented
2#59234C211yesmaximal, characteristic, complemented
3#32614C211yesmaximal, characteristic, complemented
4#32544C211yesmaximal, characteristic, complemented
5#32306C211yesmaximal, characteristic, complemented
6#32226C211yesmaximal, characteristic, complemented
7#32048C211yesmaximal, characteristic, complemented
8#31294C211yesmaximal, characteristic, complemented
9#30829C211yesmaximal, characteristic, complemented
10#30535C211yesmaximal, characteristic
11#29414C211yesmaximal, characteristic, complemented
12#28876C211yesmaximal, characteristic, complemented
13#28017C211yesmaximal, characteristic, complemented
14#27585C211yesmaximal, characteristic, complemented
15#27523C211yesmaximal, characteristic, complemented
16#27507C211yesmaximal, characteristic, complemented
17#27493C211yesmaximal, characteristic, complemented
18#27474C211yesmaximal, characteristic, complemented
19#27330C211yesmaximal, characteristic, complemented
20#27243C211yesmaximal, characteristic
21#27195C211yesmaximal, characteristic, complemented
22#27130C211yesmaximal, characteristic, complemented
23#27076C211yesmaximal, characteristic, complemented
24#26695C211yesmaximal, characteristic, complemented
25#26327C211yesmaximal, characteristic, complemented
26#25073C211yesmaximal, characteristic, complemented
27#23756C211yesmaximal, characteristic, complemented
28#23230C211yesmaximal, characteristic, complemented
29#23061C211yesmaximal, characteristic, complemented
30#22321C211yesmaximal, characteristic, complemented
31#22040C211yesmaximal, characteristic
32C2×#489C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×#447C2211yescharacteristic
35#2786—21no—
36#2775—21no—
37#2775—21no—
38#2740—21no—
39#2601—21no—
40#2592C2211yescharacteristic
41#2560—21no—
42#2551C2211yescharacteristic, complemented
43#2547—21no—
44#2538C2211yescharacteristic
45#2538C2211yescharacteristic, complemented
46#2513C2211yescharacteristic, complemented
47#2513C2211yescharacteristic, complemented
48#2512C2211yescharacteristic
49#2512C2211yescharacteristic
50#2502C2211yescharacteristic
51#2495C2211yescharacteristic
52#2495C2211yescharacteristic
53#2492—21no—
54#2491C2211yescharacteristic
55#2491C2211yescharacteristic
56#2480—21no—
57#2480—21no—
58#2474—21no—
59#2474—21no—
60#2448C2211yescharacteristic
61#2447C2211yescharacteristic
62#2437—21no—
63#2435C2211yescharacteristic
64#2415—21no—
65#2369C2211yescharacteristic, complemented
66#2369C2211yescharacteristic, complemented
67#2367C2211yescharacteristic
68#2355C2211yescharacteristic, complemented
69#2354C2211yescharacteristic
70#2354C2211yescharacteristic, complemented
71#2347—21no—
72#2345C2211yescharacteristic
73#2342—21no—
74D4×C22⋊C4C2211yescharacteristic
75C4×C22⋊Q8C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2285C2211yescharacteristic
80#2099C2211yescharacteristic, complemented
81#2099C2211yescharacteristic, complemented
82#2097C2211yescharacteristic, complemented
83#2096C2211yescharacteristic, complemented
84#2094C2211yescharacteristic
85#2094C2211yescharacteristic
86#2094C2211yescharacteristic, complemented
87#2092C2211yescharacteristic
88#2086C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2084C2211yescharacteristic, complemented
91#2083C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2024C2211yescharacteristic, complemented
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2000C2211yescharacteristic
120#1990C2211yescharacteristic, complemented
121#1988C2211yescharacteristic, complemented
122#1985C2211yescharacteristic, complemented
123#1984C2211yescharacteristic, complemented
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1970C2211yescharacteristic
129#1970C2211yescharacteristic
130#1968C2211yescharacteristic, complemented
131#1958C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic, complemented
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1880C2211yescharacteristic, complemented
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1817C2211yescharacteristic
188#1804C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#106C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197C8×C4⋊C4C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#124—21no—
213C2×#124—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8D411yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117—21no—
229C2×#117—21no—
230C22×C4⋊C4C2311yescharacteristic
231C22×C22⋊C4—21no—
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234C22×C42C2311yescharacteristic
235#489—24no—
236#476—24no—
237#447—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#400—21no—
292#400—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391D411yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#390—21no—
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
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#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385D411yescharacteristic
396#385D411yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#383—21no—
402#383—21no—
403#382—21no—
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#381—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380D411yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#379—21no—
419#379—21no—
420#379—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2×D411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×D4—22no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—82no—
526#126—82no—
527#126—82no—
528#124—22no—
529#124—41no—
530#124—41no—
531#124—41no—
532#124—82no—
533#124—82no—
534C22⋊Q8—42no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—82no—
538C22⋊Q8—82no—
539#121—22no—
540#121—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—82no—
552#117—44no—
553#117—82no—
554#117—82no—
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—21no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
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⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
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⋊C4—21no—
638C2×C22⋊C4—44no—
639C2×C22⋊C4—82no—
640C2×C22⋊C4—82no—
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—41no—
657C2×C42—41no—
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#106—22no—
671#106—22no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102#4114yes—
709C22⋊C8—22no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713#97—22no—
714#97—41no—
715C4×C8—41no—
716C4×C8—41no—
717C4×C8—41no—
718C4×C8—41no—
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#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761C24—21no—
762C24—21no—
763C24—21no—
764C24—42no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24—81no—
769C24—81no—
770C24—81no—
771C24C22×D411yescharacteristic
772C2×Q8—22no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—41no—
780C2×Q8—41no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
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—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—81no—
809C2×D4—82no—
810C2×D4—82no—
811C2×D4—82no—
812C2×D4—82no—
813C2×D4—81no—
814C2×D4C2×#4112yes—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
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×C4C2511yescharacteristic
866SD16—82no—
867D8—82no—
868D8—82no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
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×C8C2×#4112yes—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—21no—
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—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
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⋊C4C2×#4112yes—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—41no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
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—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—41no—
1003C42—41no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—22no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—84no—
1043C23—84no—
1044C23—84no—
1045C23—84no—
1046C23—162no—
1047C23—162no—
1048C23—162no—
1049C23#57712yes—
1050C23C23×D411yescharacteristic
1051Q8—41no—
1052Q8—41no—
1053Q8—41no—
1054Q8—41no—
1055Q8—82no—
1056Q8—162no—
1057Q8—162no—
1058D4—22no—
1059D4—22no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—84no—
1071D4—84no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
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—44no—
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—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
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—82no—
1153C2×C4—84no—
1154C2×C4—84no—
1155C2×C4—162no—
1156C2×C4—162no—
1157C2×C4#57512yes—
1158C2×C4#57612yes—
1159C2×C4#57712yes—
1160C2×C4C22×#4111yescharacteristic
1161C2×C4#58511yescharacteristic
1162C2×C4#58511yescharacteristic
1163C2×C4#58511yescharacteristic
1164C2×C4#58511yescharacteristic
1165C2×C4#58511yescharacteristic
1166C8—22no—
1167C8—41no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—168no—
1203C22D4×#4111yescharacteristic
1204C22#348511yescharacteristic
1205C22#348711yescharacteristic
1206C22C2×#57511yescharacteristic
1207C22C2×#57611yescharacteristic
1208C22C2×#57711yescharacteristic
1209C22C2×#57711yescharacteristic
1210C4—22no—
1211C4—22no—
1212C4—22no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—42no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4#351011yescharacteristic
1237C4#352111yescharacteristic
1238C4#356611yescharacteristic
1239C4#356811yescharacteristic
1240C2—42no—
1241C2—82no—
1242C2—161no—
1243C2—161no—
1244C2#4354511yescharacteristic
1245C2#6144511yescharacteristic
1246C2#6149611yescharacteristic
1247C2#6174011yescharacteristic
1248C2#6176511yescharacteristic
1249C2#6189911yescharacteristic
1250C2#6193711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
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. #59424C2semidirect
2. #59234C2semidirect
3. #32614C2semidirect
4. #32544C2semidirect
5. #32306C2semidirect
6. #32226C2semidirect
7. #32048C2semidirect
8. #31294C2semidirect
9. #30829C2semidirect
11. #29414C2semidirect
12. #28876C2semidirect
13. #28017C2semidirect
14. #27585C2semidirect
15. #27523C2semidirect
16. #27507C2semidirect
17. #27493C2semidirect
18. #27474C2semidirect
19. #27330C2semidirect
21. #27195C2semidirect
22. #27130C2semidirect
23. #27076C2semidirect
24. #26695C2semidirect
25. #26327C2semidirect
26. #25073C2semidirect
27. #23756C2semidirect
28. #23230C2semidirect
29. #23061C2semidirect
30. #22321C2semidirect
42. #2551C22semidirect
45. #2538C22semidirect
46. #2513C22semidirect
47. #2513C22semidirect
65. #2369C22semidirect
66. #2369C22semidirect
68. #2355C22semidirect
70. #2354C22semidirect
80. #2099C22semidirect
81. #2099C22semidirect
82. #2097C22semidirect
83. #2096C22semidirect
86. #2094C22semidirect
88. #2086C22semidirect
89. #2085C22semidirect
90. #2084C22semidirect
91. #2083C22semidirect
96. #2072C22semidirect
99. #2071C22semidirect
100. #2068C22semidirect
103. #2065C22semidirect
104. #2058C22semidirect
105. #2055C22semidirect
114. #2024C22semidirect
120. #1990C22semidirect
121. #1988C22semidirect
122. #1985C22semidirect
123. #1984C22semidirect
130. #1968C22semidirect
132. #1949C22semidirect
133. #1948C22semidirect
134. #1948C22semidirect
135. #1943C22semidirect
136. #1935C22semidirect
141. #1934C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
144. #1927C22semidirect
152. #1926C22semidirect
153. #1926C22semidirect
157. #1925C22semidirect
162. #1920C22semidirect
163. #1920C22semidirect
164. #1920C22semidirect
165. #1919C22semidirect
166. #1918C22semidirect
167. #1918C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
172. #1880C22semidirect
177. #1877C22semidirect
180. #1863C22semidirect
182. #1862C22semidirect
186. #1847C22semidirect
192. #1776C22semidirect
193. C4×#106C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. C8×C4⋊C4C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#592342
#326142
#325442
#323062
#322262
#320482
#312942
#308292
#305352
#294142
#288762
#280172
#275852
#275232
#275072
#274932
#274742
#273302
#272432
#271952
#271302
#270762
#266952
#263272
#250732
#237562
#232302
#230612
#223212
#220402