Finite Group Databasebeta

← #7053086

Subgroups — #7053086

Order 512.

1293 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45368C211yesmaximal, characteristic
2#45304C211yesmaximal, characteristic, complemented
3#32658C211yesmaximal, characteristic, complemented
4#32609C211yesmaximal, characteristic, complemented
5#32387C211yesmaximal, characteristic, complemented
6#32292C211yesmaximal, characteristic, complemented
7#31943C211yesmaximal, characteristic, complemented
8#31597C211yesmaximal, characteristic, complemented
9#31317C211yesmaximal, characteristic
10#31015C211yesmaximal, characteristic
11#29419C211yesmaximal, characteristic, complemented
12#29020C211yesmaximal, characteristic, complemented
13#28047C211yesmaximal, characteristic, complemented
14#27597C211yesmaximal, characteristic, complemented
15#27575C211yesmaximal, characteristic, complemented
16#27528C211yesmaximal, characteristic, complemented
17#27494C211yesmaximal, characteristic, complemented
18#27470C211yesmaximal, characteristic, complemented
19#27369C211yesmaximal, characteristic, complemented
20#27198C211yesmaximal, characteristic, complemented
21#27181C211yesmaximal, characteristic, complemented
22#26755C211yesmaximal, characteristic, complemented
23#26329C211yesmaximal, characteristic, complemented
24#26159C211yesmaximal, characteristic, complemented
25#24998C211yesmaximal, characteristic, complemented
26#24903C211yesmaximal, characteristic, complemented
27#23767C211yesmaximal, characteristic, complemented
28#23106C211yesmaximal, characteristic, complemented
29#22812C211yesmaximal, characteristic, complemented
30#22324C211yesmaximal, characteristic, complemented
31#22057C211yesmaximal, characteristic, complemented
32C2×#460C2211yescharacteristic
33C2×#452C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2777—21no—
36#2773—21no—
37#2766—21no—
38#2762—21no—
39#2760—21no—
40#2749—21no—
41#2746—21no—
42#2737—21no—
43#2606—21no—
44#2598—21no—
45#2592C2211yescharacteristic
46#2582C2211yescharacteristic
47#2580C2211yescharacteristic
48#2571C2211yescharacteristic
49#2533—21no—
50#2532—21no—
51#2529—21no—
52#2514C2211yescharacteristic
53#2514C2211yescharacteristic
54#2510—21no—
55#2509C2211yescharacteristic
56#2507C2211yescharacteristic
57#2504C2211yescharacteristic
58#2495C2211yescharacteristic
59#2494C2211yescharacteristic
60#2471—21no—
61#2447C2211yescharacteristic
62#2445C2211yescharacteristic
63#2431C2211yescharacteristic
64#2423C2211yescharacteristic
65#2421C2211yescharacteristic
66#2419—21no—
67#2396C2211yescharacteristic
68#2366C2211yescharacteristic
69#2357C2211yescharacteristic
70#2356C2211yescharacteristic
71#2356C2211yescharacteristic
72#2355C2211yescharacteristic
73#2351C2211yescharacteristic
74#2344C2211yescharacteristic
75#2339C2211yescharacteristic
76#2324C2211yescharacteristic
77#2323C2211yescharacteristic
78#2314C2211yescharacteristic
79#2311C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2099C2211yescharacteristic
83#2097C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2096C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2056C2211yescharacteristic
111#2042C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2015C2211yescharacteristic
119#2000C2211yescharacteristic
120#1985C2211yescharacteristic
121#1984C2211yescharacteristic
122#1983C2211yescharacteristic
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic
125#1969C2211yescharacteristic
126#1968C2211yescharacteristic
127#1961C2211yescharacteristic
128#1959C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1947C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1917C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1872C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1846C2211yescharacteristic
185#1835C2211yescharacteristic
186#1818C2211yescharacteristic
187#1805C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#124C2311yescharacteristic
209C2×#123—21no—
210C2×C22⋊Q8C2311yescharacteristic
211C2×#121C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117—21no—
221C2×#117C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223#460—24no—
224#452—24no—
225C4×SD16—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#401—21no—
280#401—21no—
281#401—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400D411yescharacteristic
291#399—21no—
292#399—21no—
293#399D411yescharacteristic
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398D411yescharacteristic
300#398D411yescharacteristic
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396D411yescharacteristic
310#396D411yescharacteristic
311#395D411yescharacteristic
312#394—21no—
313#394—21no—
314#393—21no—
315#393—21no—
316#393D411yescharacteristic
317#392—21no—
318#392—21no—
319#391—21no—
320#391—21no—
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
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#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#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#383—21no—
406#383—21no—
407#383—21no—
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#381—21no—
420#380—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376—21no—
444C2×#95—21no—
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×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2411yescharacteristic
502C2×Q16—22no—
503C2×Q16—41no—
504C2×Q16—41no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16#4114yes—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519#127—22no—
520#127—41no—
521#124—41no—
522#124—41no—
523#123—82no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—41no—
527#121—41no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—82no—
543#117—41no—
544#117—41no—
545#117—82no—
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—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
591C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#106—22no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649C4⋊C8—22no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653#103—22no—
654#103—22no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#102—22no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679C22⋊C8—22no—
680C22⋊C8—41no—
681C22⋊C8—41no—
682C22⋊C8—41no—
683#97—41no—
684#97—41no—
685#97—41no—
686C4×C8—22no—
687C4×C8—41no—
688C4×C8—41no—
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#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#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24—21no—
751C24C22×D411yescharacteristic
752#41—82no—
753#41—82no—
754#41—82no—
755#41—82no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
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—41no—
768C2×Q8—41no—
769C2×Q8—41no—
770C2×Q8C2×#4112yes—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4C2×#4112yes—
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—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C2511yescharacteristic
844Q16—82no—
845SD16—44no—
846SD16—82no—
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—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8C2×#4112yes—
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—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
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—
925C22⋊C4—41no—
926C22⋊C4—41no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
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—
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—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—21no—
984C23—21no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23C23×D411yescharacteristic
999Q8—22no—
1000Q8—22no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—41no—
1007Q8—82no—
1008D4—22no—
1009D4—22no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—84no—
1017D4—84no—
1018D4—162no—
1019D4—162no—
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—21no—
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—21no—
1047C2×C4—21no—
1048C2×C4—22no—
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—84no—
1106C2×C4—84no—
1107C2×C4—162no—
1108C2×C4—162no—
1109C2×C4—162no—
1110C2×C4C22×#4111yescharacteristic
1111C2×C4#58511yescharacteristic
1112C2×C4#58511yescharacteristic
1113C2×C4#58511yescharacteristic
1114C2×C4#58511yescharacteristic
1115C2×C4#58511yescharacteristic
1116C8—22no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C22—41no—
1125C22—42no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22D4×#4111yescharacteristic
1146C22#348511yescharacteristic
1147C22#348711yescharacteristic
1148C22#358411yescharacteristic
1149C22#358411yescharacteristic
1150C22#358511yescharacteristic
1151C22#358611yescharacteristic
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4#349111yescharacteristic
1180C4#352111yescharacteristic
1181C4#356611yescharacteristic
1182C4#356611yescharacteristic
1183C2—81no—
1184C2—82no—
1185C2—161no—
1186C2#4354811yescharacteristic
1187C2#6152811yescharacteristic
1188C2#6153511yescharacteristic
1189C2#6176311yescharacteristic
1190C2#6181311yescharacteristic
1191C2#6193011yescharacteristic
1192C2#6193911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2431C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45304C2semidirect
3. #32658C2semidirect
4. #32609C2semidirect
5. #32387C2semidirect
6. #32292C2semidirect
7. #31943C2semidirect
8. #31597C2semidirect
11. #29419C2semidirect
12. #29020C2semidirect
13. #28047C2semidirect
14. #27597C2semidirect
15. #27575C2semidirect
16. #27528C2semidirect
17. #27494C2semidirect
18. #27470C2semidirect
19. #27369C2semidirect
20. #27198C2semidirect
21. #27181C2semidirect
22. #26755C2semidirect
23. #26329C2semidirect
24. #26159C2semidirect
25. #24998C2semidirect
26. #24903C2semidirect
27. #23767C2semidirect
28. #23106C2semidirect
29. #22812C2semidirect
30. #22324C2semidirect
31. #22057C2semidirect

Maximal subgroups

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

subgroupindex
#453682
#453042
#326582
#326092
#323872
#322922
#319432
#315972
#313172
#310152
#294192
#290202
#280472
#275972
#275752
#275282
#274942
#274702
#273692
#271982
#271812
#267552
#263292
#261592
#249982
#249032
#237672
#231062
#228122
#223242
#220572