Finite Group Databasebeta

← #6573278

Subgroups — #6573278

Order 512.

1497 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39153C211yesmaximal, characteristic, complemented
2#34398C211yesmaximal, characteristic
3#30160C211yesmaximal, characteristic, complemented
4#30159C211yesmaximal, characteristic, complemented
5#29694C211yesmaximal, characteristic
6#29504C211yesmaximal, characteristic, complemented
7#29504C211yesmaximal, characteristic, complemented
8#28214C211yesmaximal, characteristic, complemented
9#28210C211yesmaximal, characteristic, complemented
10#27952C211yesmaximal, characteristic, complemented
11#27653C211yesmaximal, characteristic, complemented
12#27113C211yesmaximal, characteristic, complemented
13#27112C211yesmaximal, characteristic, complemented
14#27097C211yesmaximal, characteristic, complemented
15#27096C211yesmaximal, characteristic, complemented
16#26803C211yesmaximal, characteristic, complemented
17#26800C211yesmaximal, characteristic, complemented
18#26786C211yesmaximal, characteristic, complemented
19#26785C211yesmaximal, characteristic, complemented
20#26051C211yesmaximal, characteristic, complemented
21#26049C211yesmaximal, characteristic, complemented
22#24822C211yesmaximal, characteristic, complemented
23#24822C211yesmaximal, characteristic, complemented
24#23845C211yesmaximal, characteristic, complemented
25#23842C211yesmaximal, characteristic, complemented
26#23570C211yesmaximal, characteristic
27#23071C211yesmaximal, characteristic, complemented
28#23065C211yesmaximal, characteristic, complemented
29#22812C211yesmaximal, characteristic, complemented
30#22806C211yesmaximal, characteristic, complemented
31#22633C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2851C2211yescharacteristic
44#2789—21no—
45#2788—21no—
46#2787—21no—
47#2767—21no—
48#2645C2211yescharacteristic
49#2645C2211yescharacteristic
50#2573—21no—
51#2565C2211yescharacteristic
52#2550C2211yescharacteristic
53#2533—21no—
54#2527—21no—
55#2514—21no—
56#2497C2211yescharacteristic
57#2494C2211yescharacteristic
58#2492C2211yescharacteristic
59#2489C2211yescharacteristic
60#2379—21no—
61#2379—21no—
62#2370C2211yescharacteristic
63#2361C2211yescharacteristic
64#2361C2211yescharacteristic
65#2361C2211yescharacteristic
66#2361C2211yescharacteristic
67#2357C2211yescharacteristic
68#2357C2211yescharacteristic
69#2356C2211yescharacteristic
70#2349C2211yescharacteristic
71#2349C2211yescharacteristic
72#2339—21no—
73#2339—21no—
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76#2331C2211yescharacteristic
77#2330C2211yescharacteristic
78#2328C2211yescharacteristic
79#2328C2211yescharacteristic
80#2325—21no—
81#2325—21no—
82#2318—21no—
83#2318—21no—
84C4×C22⋊Q8C2211yescharacteristic
85#2283C2211yescharacteristic
86C2×#382C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2074C2211yescharacteristic
102#2074C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic
124#2014C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#1991C2211yescharacteristic
128#1991C2211yescharacteristic
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1939C2211yescharacteristic
136#1939C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic
173#1846C2211yescharacteristic
174#1846C2211yescharacteristic
175#1832C2211yescharacteristic
176#1832C2211yescharacteristic
177#1824C2211yescharacteristic
178#1823C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1797C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×#41—21no—
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#532—24no—
207#532—24no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#484—42no—
234#483—42no—
235#478—24no—
236#478—24no—
237#478—42no—
238#478—42no—
239#476—42no—
240#474—42no—
241C4×SD16—24no—
242C4×SD16—24no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#401—21no—
298#401—21no—
299#401—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#396—21no—
315#395—21no—
316#393—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
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#388—21no—
360#388—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#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384C2311yescharacteristic
404#383—21no—
405#383D411yescharacteristic
406#383D411yescharacteristic
407#382—21no—
408#382—21no—
409#382—21no—
410#382D411yescharacteristic
411#382D411yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#381D411yescharacteristic
421#381D411yescharacteristic
422#380—21no—
423#380—21no—
424#380D411yescharacteristic
425#380D411yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#376—21no—
448#376C2311yescharacteristic
449#376C2311yescharacteristic
450C2×#95—21no—
451C2×#95—21no—
452C2×#95—21no—
453C2×#95—21no—
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—28no—
491C2×#41—82no—
492C2×#41—82no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531#127—22no—
532#127—22no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—41no—
537#124—28no—
538C22⋊Q8—22no—
539C22⋊Q8—41no—
540#121—28no—
541#121—22no—
542#121—22no—
543#121—22no—
544#121—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×D4—28no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—82no—
559C4×D4—82no—
560C4×D4—82no—
561C4×D4—82no—
562C4×D4#4114yes—
563C4×D4#4114yes—
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—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
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×C42—22no—
633C2×C42—22no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—22no—
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676#103—22no—
677#103—22no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700#97—22no—
701#97—22no—
702C4×C8—22no—
703C4×C8—22no—
704C4×C8—22no—
705C4×C8—22no—
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#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C24—21no—
769C24C22×D411yescharacteristic
770#41—816no—
771C2×Q8—24no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4C2×#4112yes—
806C2×D4C2×#4112yes—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C2511yescharacteristic
871SD16—44no—
872SD16—44no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C82−1+412yes—
896C2×C82−1+412yes—
897C4⋊C4—24no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4C2×#4112yes—
948C4⋊C4C2×#4112yes—
949C4⋊C4H(5,𝔽2)12yes—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C42—22no—
975C42—22no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—42no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42C2×#4112yes—
997C42C2×#4112yes—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23#57712yes—
1019C23C23×D411yescharacteristic
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—84no—
1025Q8—162no—
1026D4—22no—
1027D4—22no—
1028D4—22no—
1029D4—22no—
1030D4—48no—
1031D4—48no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—84no—
1037D4—84no—
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—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—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—44no—
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—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—82no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4—162no—
1128C2×C4—162no—
1129C2×C4—162no—
1130C2×C4—162no—
1131C2×C4#52512yes—
1132C2×C4#52512yes—
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C22×#4111yescharacteristic
1135C2×C4C2×H(5,𝔽2)11yescharacteristic
1136C2×C4C2×2−1+411yescharacteristic
1137C2×C4C2×2−1+411yescharacteristic
1138C2×C4#58511yescharacteristic
1139C8—22no—
1140C8—22no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22C2×#52511yescharacteristic
1169C22#348811yescharacteristic
1170C22#349911yescharacteristic
1171C22C2×#57711yescharacteristic
1172C22#358411yescharacteristic
1173C22#358411yescharacteristic
1174C22#358511yescharacteristic
1175C4—22no—
1176C4—22no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—42no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—42no—
1190C4—41no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4#349511yescharacteristic
1203C4#349511yescharacteristic
1204C4#351111yescharacteristic
1205C4#351111yescharacteristic
1206C2—42no—
1207C2—82no—
1208C2—82no—
1209C2#3608911yescharacteristic
1210C2#6055711yescharacteristic
1211C2#6057911yescharacteristic
1212C2#6204711yescharacteristic
1213C2#6206611yescharacteristic
1214C2#6249111yescharacteristic
1215C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39153C2semidirect
3. #30160C2semidirect
4. #30159C2semidirect
6. #29504C2semidirect
7. #29504C2semidirect
8. #28214C2semidirect
9. #28210C2semidirect
10. #27952C2semidirect
11. #27653C2semidirect
12. #27113C2semidirect
13. #27112C2semidirect
14. #27097C2semidirect
15. #27096C2semidirect
16. #26803C2semidirect
17. #26800C2semidirect
18. #26786C2semidirect
19. #26785C2semidirect
20. #26051C2semidirect
21. #26049C2semidirect
22. #24822C2semidirect
23. #24822C2semidirect
24. #23845C2semidirect
25. #23842C2semidirect
27. #23071C2semidirect
28. #23065C2semidirect
29. #22812C2semidirect
30. #22806C2semidirect
31. #22633C2semidirect

Maximal subgroups

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

subgroupindex
#391532
#343982
#301602
#301592
#296942
#295042
#282142
#282102
#279522
#276532
#271132
#271122
#270972
#270962
#268032
#268002
#267862
#267852
#260512
#260492
#248222
#238452
#238422
#235702
#230712
#230652
#228122
#228062
#226332