Finite Group Databasebeta

← #7035755

Subgroups — #7035755

Order 512.

1242 conjugacy classes of subgroups.

The subgroup lattice has 1163 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45130C211yesmaximal, characteristic
2#42686C211yesmaximal, characteristic
3#32329C211yesmaximal, characteristic, complemented
4#32324C211yesmaximal, characteristic, complemented
5#32307C211yesmaximal, characteristic, complemented
6#32287C211yesmaximal, characteristic, complemented
7#31999C211yesmaximal, characteristic, complemented
8#31999C211yesmaximal, characteristic, complemented
9#31451C211yesmaximal, characteristic, complemented
10#31427C211yesmaximal, characteristic, complemented
11#29170C211yesmaximal, characteristic, complemented
12#27959C211yesmaximal, characteristic, complemented
13#27848C211yesmaximal, characteristic, complemented
14#27838C211yesmaximal, characteristic, complemented
15#27714C211yesmaximal, characteristic, complemented
16#27698C211yesmaximal, characteristic, complemented
17#27380C211yesmaximal, characteristic, complemented
18#27361C211yesmaximal, characteristic, complemented
19#26222C211yesmaximal, characteristic, complemented
20#26206C211yesmaximal, characteristic, complemented
21#25241C211yesmaximal, characteristic, complemented
22#25239C211yesmaximal, characteristic, complemented
23#24961C211yesmaximal, characteristic, complemented
24#24948C211yesmaximal, characteristic, complemented
25#24946C211yesmaximal, characteristic, complemented
26#24944C211yesmaximal, characteristic, complemented
27#23748C211yesmaximal, characteristic, complemented
28#23123C211yesmaximal, characteristic
29#22712C211yesmaximal, characteristic, complemented
30#22704C211yesmaximal, characteristic, complemented
31#22094C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#435C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35#2824—21no—
36#2800—21no—
37#2797—21no—
38#2795—21no—
39#2794—21no—
40#2783—21no—
41#2781—21no—
42#2775—21no—
43#2775—21no—
44#2649—21no—
45#2649—21no—
46#2628C2211yescharacteristic
47#2595—21no—
48#2590—21no—
49#2577—21no—
50#2570C2211yescharacteristic
51#2536C2211yescharacteristic
52#2525—21no—
53#2523—21no—
54#2509C2211yescharacteristic
55#2509C2211yescharacteristic
56#2499C2211yescharacteristic
57#2499C2211yescharacteristic
58#2497C2211yescharacteristic
59#2495C2211yescharacteristic
60#2495C2211yescharacteristic
61#2495C2211yescharacteristic
62#2485C2211yescharacteristic
63#2485C2211yescharacteristic
64#2485C2211yescharacteristic
65#2485C2211yescharacteristic
66#2439C2211yescharacteristic
67#2439C2211yescharacteristic
68#2417C2211yescharacteristic
69#2415C2211yescharacteristic
70#2392C2211yescharacteristic
71#2355C2211yescharacteristic
72#2354C2211yescharacteristic
73#2354C2211yescharacteristic
74#2352C2211yescharacteristic
75#2352C2211yescharacteristic
76#2352C2211yescharacteristic
77#2323C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2088C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2077C2211yescharacteristic
108#2076C2211yescharacteristic
109#2075C2211yescharacteristic
110#2074C2211yescharacteristic
111#2074C2211yescharacteristic
112#2068C2211yescharacteristic
113#2066C2211yescharacteristic
114#2058C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1990C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1947C2211yescharacteristic
126#1944C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1933C2211yescharacteristic
133#1933C2211yescharacteristic
134#1928C2211yescharacteristic
135#1927C2211yescharacteristic
136#1924C2211yescharacteristic
137#1923C2211yescharacteristic
138#1921C2211yescharacteristic
139#1920C2211yescharacteristic
140#1920C2211yescharacteristic
141#1920C2211yescharacteristic
142#1920C2211yescharacteristic
143#1919C2211yescharacteristic
144#1919C2211yescharacteristic
145#1919C2211yescharacteristic
146#1918C2211yescharacteristic
147#1918C2211yescharacteristic
148#1917C2211yescharacteristic
149#1916C2211yescharacteristic
150#1894C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1873C2211yescharacteristic
155#1873C2211yescharacteristic
156#1872C2211yescharacteristic
157#1870C2211yescharacteristic
158#1869C2211yescharacteristic
159#1869C2211yescharacteristic
160#1869C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic
176#1847C2211yescharacteristic
177#1846C2211yescharacteristic
178#1836C2211yescharacteristic
179#1835C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1809C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195#1750C2211yescharacteristic
196#1736C2211yescharacteristic
197#1736C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C22⋊Q8C2311yescharacteristic
209C2×C22⋊Q8C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224#485—24no—
225#435—24no—
226C8×D4—24no—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#399—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398D411yescharacteristic
280#397—21no—
281#397—21no—
282#397—21no—
283#397—21no—
284#397—21no—
285#397—21no—
286#397—21no—
287#397—21no—
288#397—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#397D411yescharacteristic
293#396—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396D411yescharacteristic
298#396D411yescharacteristic
299#395—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#394D411yescharacteristic
307#394D411yescharacteristic
308#394D411yescharacteristic
309#393—21no—
310#393—21no—
311#393—21no—
312#392D411yescharacteristic
313#391—21no—
314#391—21no—
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#390—21no—
319#390—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
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#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—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#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#383—21no—
393#383—21no—
394#383—21no—
395#382—21no—
396#382—21no—
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#380—21no—
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8C2411yescharacteristic
483C22×D4C2×D411yescharacteristic
484C22×D4C2×D411yescharacteristic
485C22×D4C2×D411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—41no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518C22⋊Q8—41no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—41no—
526C4×D4—41no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
531#117—41no—
532#117—41no—
533#117—41no—
534#117—41no—
535#117—41no—
536#117—41no—
537#117—41no—
538#117—41no—
539#117—41no—
540#117—41no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#107—22no—
644#107—41no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#106—22no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661#103—22no—
662#103—22no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—22no—
672C22⋊C8—41no—
673C22⋊C8—41no—
674C22⋊C8—41no—
675C22⋊C8—41no—
676C22⋊C8#4114yes—
677#97—22no—
678#97—41no—
679C4×C8—22no—
680C4×C8—41no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#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#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736C24C22×D411yescharacteristic
737C24C22×D411yescharacteristic
738C24C22×D411yescharacteristic
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—81no—
746C2×Q8—81no—
747C2×Q8—81no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
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—81no—
790C22×C4—81no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C2×#4112yes—
807C22×C42−1+412yes—
808C22×C4C2511yescharacteristic
809M16—82no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—82no—
833C2×C8—82no—
834C2×C8—82no—
835C2×C8C2×#4112yes—
836C2×C8C2×#4112yes—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
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—41no—
870C4⋊C4—41no—
871C4⋊C4—41no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—22no—
904C22⋊C4—41no—
905C22⋊C4—41no—
906C22⋊C4—41no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—42no—
943C42—42no—
944C42—81no—
945C42—81no—
946C42—81no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23#54712yes—
975C23C23×D411yescharacteristic
976Q8—41no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—162no—
981D4—44no—
982D4—82no—
983D4—82no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
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—162no—
1077C2×C4—162no—
1078C2×C4#54712yes—
1079C2×C4C22×#4111yescharacteristic
1080C2×C4C2×2−1+411yescharacteristic
1081C2×C4#58511yescharacteristic
1082C2×C4#58511yescharacteristic
1083C2×C4#58511yescharacteristic
1084C2×C4#58511yescharacteristic
1085C8—22no—
1086C8—22no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22C2×#54711yescharacteristic
1115C22#348511yescharacteristic
1116C22#350011yescharacteristic
1117C22#358411yescharacteristic
1118C22#358411yescharacteristic
1119C22#358411yescharacteristic
1120C22#358611yescharacteristic
1121C4—22no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4#352111yescharacteristic
1149C4#352111yescharacteristic
1150C4#355311yescharacteristic
1151C4#355311yescharacteristic
1152C2—42no—
1153C2—81no—
1154C2—81no—
1155C2#4349511yescharacteristic
1156C2#6126111yescharacteristic
1157C2#6127511yescharacteristic
1158C2#6176911yescharacteristic
1159C2#6180111yescharacteristic
1160C2#6255511yescharacteristic
1161C2#6260611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#392D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32329C2semidirect
4. #32324C2semidirect
5. #32307C2semidirect
6. #32287C2semidirect
7. #31999C2semidirect
8. #31999C2semidirect
9. #31451C2semidirect
10. #31427C2semidirect
11. #29170C2semidirect
12. #27959C2semidirect
13. #27848C2semidirect
14. #27838C2semidirect
15. #27714C2semidirect
16. #27698C2semidirect
17. #27380C2semidirect
18. #27361C2semidirect
19. #26222C2semidirect
20. #26206C2semidirect
21. #25241C2semidirect
22. #25239C2semidirect
23. #24961C2semidirect
24. #24948C2semidirect
25. #24946C2semidirect
26. #24944C2semidirect
27. #23748C2semidirect
29. #22712C2semidirect
30. #22704C2semidirect
31. #22094C2semidirect

Maximal subgroups

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

subgroupindex
#451302
#426862
#323292
#323242
#323072
#322872
#319992
#314512
#314272
#291702
#279592
#278482
#278382
#277142
#276982
#273802
#273612
#262222
#262062
#252412
#252392
#249612
#249482
#249462
#249442
#237482
#231232
#227122
#227042
#220942