Finite Group Databasebeta

← #6568886

Subgroups — #6568886

Order 512.

1365 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36393C211yesmaximal, characteristic
2#36201C211yesmaximal, characteristic, complemented
3#30387C211yesmaximal, characteristic, complemented
4#30362C211yesmaximal, characteristic, complemented
5#30186C211yesmaximal, characteristic, complemented
6#29576C211yesmaximal, characteristic, complemented
7#29517C211yesmaximal, characteristic, complemented
8#29305C211yesmaximal, characteristic, complemented
9#29158C211yesmaximal, characteristic, complemented
10#29052C211yesmaximal, characteristic, complemented
11#29048C211yesmaximal, characteristic, complemented
12#29022C211yesmaximal, characteristic, complemented
13#29018C211yesmaximal, characteristic, complemented
14#28009C211yesmaximal, characteristic, complemented
15#28007C211yesmaximal, characteristic, complemented
16#27915C211yesmaximal, characteristic, complemented
17#27859C211yesmaximal, characteristic, complemented
18#27848C211yesmaximal, characteristic, complemented
19#27846C211yesmaximal, characteristic, complemented
20#25239C211yesmaximal, characteristic, complemented
21#25237C211yesmaximal, characteristic
22#25235C211yesmaximal, characteristic
23#25233C211yesmaximal, characteristic, complemented
24#23784C211yesmaximal, characteristic, complemented
25#23765C211yesmaximal, characteristic, complemented
26#23744C211yesmaximal, characteristic, complemented
27#22939C211yesmaximal, characteristic, complemented
28#22937C211yesmaximal, characteristic, complemented
29#22935C211yesmaximal, characteristic, complemented
30#22933C211yesmaximal, characteristic, complemented
31#20558C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2211yescharacteristic
40#2854C2211yescharacteristic
41#2851C2211yescharacteristic
42#2851C2211yescharacteristic
43#2850C2211yescharacteristic
44#2602—21no—
45#2598—21no—
46#2597—21no—
47#2596—21no—
48#2595—21no—
49#2578—21no—
50#2577—21no—
51#2530—21no—
52#2524—21no—
53#2515—21no—
54#2509C2211yescharacteristic
55#2507C2211yescharacteristic
56#2506C2211yescharacteristic
57#2497C2211yescharacteristic
58#2496C2211yescharacteristic
59#2495C2211yescharacteristic
60#2485C2211yescharacteristic
61#2485C2211yescharacteristic
62#2468—21no—
63#2460—21no—
64#2448C2211yescharacteristic
65#2427C2211yescharacteristic
66#2415C2211yescharacteristic
67#2414C2211yescharacteristic
68#2374—21no—
69#2373—21no—
70#2371—21no—
71#2363C2211yescharacteristic
72#2362C2211yescharacteristic
73#2347—21no—
74#2347C2211yescharacteristic
75#2346C2211yescharacteristic
76C4×#125C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78#2296C2211yescharacteristic
79#2293C2211yescharacteristic
80#2285C2211yescharacteristic
81#2283C2211yescharacteristic
82C42×D4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2087C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2074C2211yescharacteristic
108#2073C2211yescharacteristic
109#2068C2211yescharacteristic
110#2067C2211yescharacteristic
111#2066C2211yescharacteristic
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic
122#2025C2211yescharacteristic
123#1959C2211yescharacteristic
124#1959C2211yescharacteristic
125#1944C2211yescharacteristic
126#1944C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1943C2211yescharacteristic
130#1943C2211yescharacteristic
131#1943C2211yescharacteristic
132#1943C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1927C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1865C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic
168#1862C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1808C2211yescharacteristic
176#1808C2211yescharacteristic
177#1807C2211yescharacteristic
178#1807C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183#1770C2211yescharacteristic
184#1770C2211yescharacteristic
185#1767C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1752C2211yescharacteristic
191#1752C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194#1749C2211yescharacteristic
195#1749C2211yescharacteristic
196#1744C2211yescharacteristic
197#1735C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#126—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#123—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4D411yescharacteristic
218C2×C4×D4D411yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#485—24no—
229#485—24no—
230#482—24no—
231#482—24no—
232C8×D4—24no—
233C8×D4—24no—
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×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#394—21no—
299#394—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#392—21no—
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#390—21no—
308#390—21no—
309#390C2311yescharacteristic
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#389—21no—
313#389—21no—
314#389—21no—
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#383—21no—
391#383—21no—
392#383—21no—
393#383—21no—
394#382—21no—
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#381—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4D411yescharacteristic
421C4×C4⋊C4D411yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4D411yescharacteristic
434C4×C22⋊C4D411yescharacteristic
435C4×C22⋊C4D411yescharacteristic
436C4×C22⋊C4D411yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376—21no—
440#376—21no—
441C43C2311yescharacteristic
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
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C2×D411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2×D411yescharacteristic
493C23×C4C2×D411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—41no—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516#126—44no—
517#125—41no—
518#125—41no—
519#125—44no—
520#124—41no—
521#124—41no—
522#123—44no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—22no—
529#121—41no—
530#121—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—42no—
537C4×D4—41no—
538C4×D4—42no—
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—22no—
544#117—44no—
545#117—41no—
546#117—41no—
547#117—41no—
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⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651#107—22no—
652#107—22no—
653#107—22no—
654#107—22no—
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#106—22no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—41no—
665#106—41no—
666#106—41no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685C22⋊C8—22no—
686C22⋊C8—22no—
687C22⋊C8#4114yes—
688C22⋊C8#4114yes—
689#97—41no—
690#97—41no—
691#97—41no—
692#97—41no—
693#97—41no—
694#97—41no—
695C4×C8—22no—
696C4×C8—22no—
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#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#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24C22×D411yescharacteristic
751C24C22×D411yescharacteristic
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—81no—
770C2×D4—81no—
771C2×D4—81no—
772C2×D4—81no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—81no—
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C2×#4112yes—
826C22×C4C2×#4112yes—
827C22×C4C2511yescharacteristic
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—82no—
849C2×C8—82no—
850C2×C8—82no—
851C2×C8—82no—
852C2×C8C2×#4112yes—
853C2×C8C2×#4112yes—
854C2×C8C2×#4112yes—
855C2×C8C2×#4112yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—41no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C42−1+412yes—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—41no—
918C22⋊C4—41no—
919C22⋊C4—41no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C42—22no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23#53212yes—
994C23#57512yes—
995C23C23×D411yescharacteristic
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000D4—28no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—162no—
1006D4—162no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
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—82no—
1095C2×C4—82no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—84no—
1099C2×C4#53212yes—
1100C2×C4#57512yes—
1101C2×C4C22×#4111yescharacteristic
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C2×2−1+411yescharacteristic
1104C2×C4#58511yescharacteristic
1105C2×C4#58511yescharacteristic
1106C2×C4#58511yescharacteristic
1107C8—22no—
1108C8—22no—
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22C2×#53211yescharacteristic
1137C22#348511yescharacteristic
1138C22#348911yescharacteristic
1139C22C2×#57511yescharacteristic
1140C22C2×#57511yescharacteristic
1141C22#358411yescharacteristic
1142C22#358411yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4#351511yescharacteristic
1171C4#351511yescharacteristic
1172C4#352111yescharacteristic
1173C4#352111yescharacteristic
1174C2—42no—
1175C2—42no—
1176C2—161no—
1177C2#3604511yescharacteristic
1178C2#6068811yescharacteristic
1179C2#6072411yescharacteristic
1180C2#6173211yescharacteristic
1181C2#6174311yescharacteristic
1182C2#6214011yescharacteristic
1183C2#6214111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2414C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36201C2semidirect
3. #30387C2semidirect
4. #30362C2semidirect
5. #30186C2semidirect
6. #29576C2semidirect
7. #29517C2semidirect
8. #29305C2semidirect
9. #29158C2semidirect
10. #29052C2semidirect
11. #29048C2semidirect
12. #29022C2semidirect
13. #29018C2semidirect
14. #28009C2semidirect
15. #28007C2semidirect
16. #27915C2semidirect
17. #27859C2semidirect
18. #27848C2semidirect
19. #27846C2semidirect
20. #25239C2semidirect
23. #25233C2semidirect
24. #23784C2semidirect
25. #23765C2semidirect
26. #23744C2semidirect
27. #22939C2semidirect
28. #22937C2semidirect
29. #22935C2semidirect
30. #22933C2semidirect
31. #20558C2semidirect

Maximal subgroups

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

subgroupindex
#363932
#362012
#303872
#303622
#301862
#295762
#295172
#293052
#291582
#290522
#290482
#290222
#290182
#280092
#280072
#279152
#278592
#278482
#278462
#252392
#252372
#252352
#252332
#237842
#237652
#237442
#229392
#229372
#229352
#229332
#205582