Finite Group Databasebeta

← #6777119

Subgroups — #6777119

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38205C211yesmaximal, characteristic
2#35185C211yesmaximal, characteristic, complemented
3#33081C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#32401C211yesmaximal, characteristic, complemented
6#32270C211yesmaximal, characteristic, complemented
7#31998C211yesmaximal, characteristic, complemented
8#31536C211yesmaximal, characteristic, complemented
9#31465C211yesmaximal, characteristic, complemented
10#31268C211yesmaximal, characteristic
11#30425C211yesmaximal, characteristic
12#30182C211yesmaximal, characteristic, complemented
13#30035C211yesmaximal, characteristic, complemented
14#29513C211yesmaximal, characteristic, complemented
15#29390C211yesmaximal, characteristic, complemented
16#28982C211yesmaximal, characteristic, complemented
17#28847C211yesmaximal, characteristic, complemented
18#28071C211yesmaximal, characteristic, complemented
19#27888C211yesmaximal, characteristic, complemented
20#27869C211yesmaximal, characteristic, complemented
21#27642C211yesmaximal, characteristic, complemented
22#27597C211yesmaximal, characteristic, complemented
23#27527C211yesmaximal, characteristic, complemented
24#27458C211yesmaximal, characteristic, complemented
25#27161C211yesmaximal, characteristic, complemented
26#25039C211yesmaximal, characteristic, complemented
27#24908C211yesmaximal, characteristic, complemented
28#22789C211yesmaximal, characteristic, complemented
29#22203C211yesmaximal, characteristic, complemented
30#22059C211yesmaximal, characteristic, complemented
31#21116C211yesmaximal, characteristic, complemented
32C2×#470C2211yescharacteristic
33C2×#452C2211yescharacteristic
34C2×C4×Q16C2211yescharacteristic
35#2864—21no—
36#2860—21no—
37#2860C2211yescharacteristic
38#2741—21no—
39#2740—21no—
40#2722—21no—
41#2705—21no—
42#2650—21no—
43#2650—21no—
44#2629C2211yescharacteristic
45#2624C2211yescharacteristic
46#2571C2211yescharacteristic
47#2567C2211yescharacteristic
48#2563C2211yescharacteristic
49#2554—21no—
50#2538C2211yescharacteristic
51#2531—21no—
52#2526—21no—
53#2522—21no—
54#2513—21no—
55#2512C2211yescharacteristic
56#2509—21no—
57#2496C2211yescharacteristic
58#2496C2211yescharacteristic
59#2490C2211yescharacteristic
60#2486C2211yescharacteristic
61#2469—21no—
62#2469—21no—
63#2453C2211yescharacteristic
64#2423C2211yescharacteristic
65#2421C2211yescharacteristic
66#2421C2211yescharacteristic
67#2407C2211yescharacteristic
68#2345C2211yescharacteristic
69#2341C2211yescharacteristic
70#2323C2211yescharacteristic
71#2323C2211yescharacteristic
72#2323C2211yescharacteristic
73#2314C2211yescharacteristic
74#2314C2211yescharacteristic
75#2311C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77#2295C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×Q8C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2096C2211yescharacteristic
83#2094C2211yescharacteristic
84#2094C2211yescharacteristic
85#2092C2211yescharacteristic
86#2088C2211yescharacteristic
87#2084C2211yescharacteristic
88#2084C2211yescharacteristic
89#2084C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic
102#2072C2211yescharacteristic
103#2071C2211yescharacteristic
104#2066C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2026C2211yescharacteristic
117#2024C2211yescharacteristic
118#2023C2211yescharacteristic
119#2000C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1971C2211yescharacteristic
123#1968C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1941C2211yescharacteristic
127#1941C2211yescharacteristic
128#1936C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1933C2211yescharacteristic
132#1927C2211yescharacteristic
133#1927C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1921C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1872C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1847C2211yescharacteristic
183#1839C2211yescharacteristic
184#1834C2211yescharacteristic
185#1818C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1807C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1798C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1750C2211yescharacteristic
201#1744C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229#470—24no—
230#452—24no—
231C4×Q16—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#395—21no—
306#395—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#393—21no—
312#393—21no—
313#392—21no—
314#391—21no—
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390—21no—
321#390—21no—
322#390—21no—
323#390—21no—
324#390—21no—
325#390D411yescharacteristic
326#390D411yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389D411yescharacteristic
342#389D411yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
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#388D411yescharacteristic
372#388D411yescharacteristic
373#388D411yescharacteristic
374#388D411yescharacteristic
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#382—21no—
401#382—21no—
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#380—21no—
406#380—21no—
407#380—21no—
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437C43—21no—
438C43C2311yescharacteristic
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#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
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C2×Q16—41no—
499C2×Q16—41no—
500C2×Q16#4114yes—
501C2×SD16—22no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520#126—82no—
521#126—82no—
522#126—82no—
523#126—82no—
524#125—41no—
525#125—41no—
526#123—82no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—41no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533#121—41no—
534#121—41no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—82no—
546C4×D4—41no—
547C4×D4—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
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⋊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—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—41no—
661#107—41no—
662#106—22no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695C22⋊C8—22no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700C22⋊C8—41no—
701#97—41no—
702C4×C8—22no—
703C4×C8—41no—
704C4×C8—41no—
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#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C24C22×D411yescharacteristic
755#41—82no—
756#41—82no—
757#41—82no—
758#41—82no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8C2×#4112yes—
773C2×Q8C2×#4112yes—
774C2×D4—22no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—81no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4—81no—
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—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C2511yescharacteristic
835Q16—44no—
836SD16—82no—
837M16—82no—
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—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—82no—
862C2×C8C2×#4112yes—
863C4⋊C4—22no—
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—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C42—22no—
961C42—22no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—41no—
973C42—41no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23C23×D411yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—22no—
1011Q8—22no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—84no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—82no—
1022D4—84no—
1023D4—162no—
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—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—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—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—84no—
1112C2×C4—162no—
1113C2×C4#57712yes—
1114C2×C4#57712yes—
1115C2×C4C22×#4111yescharacteristic
1116C2×C4#58511yescharacteristic
1117C2×C4#58511yescharacteristic
1118C2×C4#58511yescharacteristic
1119C2×C4#58511yescharacteristic
1120C2×C4#58511yescharacteristic
1121C8—22no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22#344911yescharacteristic
1151C22D4×#4111yescharacteristic
1152C22#348511yescharacteristic
1153C22C2×#57711yescharacteristic
1154C22C2×#57711yescharacteristic
1155C22#358411yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—42no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4#349111yescharacteristic
1185C4#352111yescharacteristic
1186C4#356611yescharacteristic
1187C4#356811yescharacteristic
1188C2—81no—
1189C2—81no—
1190C2—161no—
1191C2#3837611yescharacteristic
1192C2#6095611yescharacteristic
1193C2#6098211yescharacteristic
1194C2#6149511yescharacteristic
1195C2#6152611yescharacteristic
1196C2#6179211yescharacteristic
1197C2#6180111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35185C2semidirect
3. #33081C2semidirect
4. #32430C2semidirect
5. #32401C2semidirect
6. #32270C2semidirect
7. #31998C2semidirect
8. #31536C2semidirect
9. #31465C2semidirect
12. #30182C2semidirect
13. #30035C2semidirect
14. #29513C2semidirect
15. #29390C2semidirect
16. #28982C2semidirect
17. #28847C2semidirect
18. #28071C2semidirect
19. #27888C2semidirect
20. #27869C2semidirect
21. #27642C2semidirect
22. #27597C2semidirect
23. #27527C2semidirect
24. #27458C2semidirect
25. #27161C2semidirect
26. #25039C2semidirect
27. #24908C2semidirect
28. #22789C2semidirect
29. #22203C2semidirect
30. #22059C2semidirect
31. #21116C2semidirect

Maximal subgroups

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

subgroupindex
#382052
#351852
#330812
#324302
#324012
#322702
#319982
#315362
#314652
#312682
#304252
#301822
#300352
#295132
#293902
#289822
#288472
#280712
#278882
#278692
#276422
#275972
#275272
#274582
#271612
#250392
#249082
#227892
#222032
#220592
#211162