Finite Group Databasebeta

← #6464705

Subgroups — #6464705

Order 512.

1484 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#34619C211yesmaximal, characteristic
2#34085C211yesmaximal, characteristic, complemented
3#29526C211yesmaximal, characteristic, complemented
4#29524C211yesmaximal, characteristic, complemented
5#29509C211yesmaximal, characteristic, complemented
6#29508C211yesmaximal, characteristic, complemented
7#29491C211yesmaximal, characteristic
8#29487C211yesmaximal, characteristic, complemented
9#29474C211yesmaximal, characteristic
10#29470C211yesmaximal, characteristic, complemented
11#29362C211yesmaximal, characteristic, complemented
12#29325C211yesmaximal, characteristic, complemented
13#29138C211yesmaximal, characteristic, complemented
14#28396C211yesmaximal, characteristic, complemented
15#24718C211yesmaximal, characteristic, complemented
16#24714C211yesmaximal, characteristic, complemented
17#24669C211yesmaximal, characteristic
18#24665C211yesmaximal, characteristic
19#23765C211yesmaximal, characteristic, complemented
20#23764C211yesmaximal, characteristic
21#23577C211yesmaximal, characteristic, complemented
22#23574C211yesmaximal, characteristic
23#21616C211yesmaximal, characteristic, complemented
24#21615C211yesmaximal, characteristic, complemented
25#21508C211yesmaximal, characteristic, complemented
26#21508C211yesmaximal, characteristic, complemented
27#21288C211yesmaximal, characteristic, complemented
28#21288C211yesmaximal, characteristic, complemented
29#21287C211yesmaximal, characteristic, complemented
30#21287C211yesmaximal, characteristic, complemented
31#20465C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#441C2211yescharacteristic
38C2×#441C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#433C2211yescharacteristic
42C2×#433C2211yescharacteristic
43#2654—21no—
44#2653—21no—
45#2650—21no—
46#2649—21no—
47#2647C2211yescharacteristic
48#2645C2211yescharacteristic
49#2644C2211yescharacteristic
50#2640C2211yescharacteristic
51#2628C2211yescharacteristic
52#2625C2211yescharacteristic
53#2624C2211yescharacteristic
54#2620C2211yescharacteristic
55#2401—21no—
56#2398—21no—
57#2396—21no—
58#2395—21no—
59#2336—21no—
60#2336—21no—
61#2332—21no—
62#2332—21no—
63#2331C2211yescharacteristic
64#2331C2211yescharacteristic
65#2327C2211yescharacteristic
66#2327C2211yescharacteristic
67#2323C2211yescharacteristic
68#2323C2211yescharacteristic
69#2323C2211yescharacteristic
70#2323C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic
72C4×#124C2211yescharacteristic
73C4×C22⋊Q8C2211yescharacteristic
74C4×#121C2211yescharacteristic
75#2298—21no—
76#2298—21no—
77#2295—21no—
78#2295—21no—
79#2295C2211yescharacteristic
80#2295C2211yescharacteristic
81#2295C2211yescharacteristic
82#2293C2211yescharacteristic
83#2283C2211yescharacteristic
84C42×Q8C2211yescharacteristic
85C42×Q8C2211yescharacteristic
86C4×#117C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2097C2211yescharacteristic
90#2092C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2075C2211yescharacteristic
97#2074C2211yescharacteristic
98#2073C2211yescharacteristic
99#2058C2211yescharacteristic
100#2057C2211yescharacteristic
101#2043C2211yescharacteristic
102#2043C2211yescharacteristic
103#2036C2211yescharacteristic
104#2036C2211yescharacteristic
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2024C2211yescharacteristic
112#2023C2211yescharacteristic
113#2016C2211yescharacteristic
114#2013C2211yescharacteristic
115#2001C2211yescharacteristic
116#2001C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic
125#1971C2211yescharacteristic
126#1971C2211yescharacteristic
127#1969C2211yescharacteristic
128#1969C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1941C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1928C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1805C2211yescharacteristic
176#1805C2211yescharacteristic
177#1803C2211yescharacteristic
178#1803C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183#1768C2211yescharacteristic
184#1768C2211yescharacteristic
185#1767C2211yescharacteristic
186#1767C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic
199#1746C2211yescharacteristic
200#1746C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#533—24no—
208#533—24no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#124C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#477—24no—
236#475—24no—
237#464—24no—
238#464—24no—
239#441—24no—
240#441—24no—
241#440—24no—
242#440—24no—
243#433—24no—
244#433—24no—
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×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301#401—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#399—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#395—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#393—21no—
331#393—21no—
332#393—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—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#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#386—21no—
404#385—21no—
405#384C2311yescharacteristic
406#383—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4D411yescharacteristic
429C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4D411yescharacteristic
445C4×C22⋊C4D411yescharacteristic
446C4×C22⋊C4D411yescharacteristic
447C4×C22⋊C4D411yescharacteristic
448#376—21no—
449#376—21no—
450#376—21no—
451#376—21no—
452#376C2311yescharacteristic
453#376C2311yescharacteristic
454C43—21no—
455C43—21no—
456C43C2311yescharacteristic
457C43C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527#125—28no—
528#124—22no—
529#124—22no—
530C22⋊Q8—28no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537#121—41no—
538#121—41no—
539C4×Q8—28no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—82no—
553C4×Q8#4114yes—
554C4×Q8#4114yes—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—82no—
558#117—28no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117—82no—
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—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—22no—
634C2×C42—22no—
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×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#107—22no—
665#107—22no—
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—41no—
675#106—41no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8#4114yes—
679C4⋊C8#4114yes—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—41no—
703#102—41no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708#97—22no—
709#97—22no—
710#97—22no—
711#97—22no—
712#97—22no—
713#97—22no—
714#97—41no—
715#97—41no—
716C4×C8—22no—
717C4×C8—22no—
718C4×C8—41no—
719C4×C8—41no—
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#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C24C22×D411yescharacteristic
776C2×Q8—24no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8C2×#4112yes—
799C2×Q8C2×#4112yes—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—42no—
807C2×D4—81no—
808C2×D4—81no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
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—41no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C2511yescharacteristic
853Q16—44no—
854Q16—44no—
855SD16—44no—
856SD16—44no—
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×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8C2×#4112yes—
878C2×C8C2×#4112yes—
879C2×C8C2×#4112yes—
880C2×C8C2×#4112yes—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
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—41no—
913C4⋊C4—41no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4C2×#4112yes—
936C4⋊C4C2×#4112yes—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
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—24no—
963C42—24no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—41no—
973C42—41no—
974C42—41no—
975C42—41no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42C2×#4112yes—
994C42C2×#4112yes—
995C42C2×#4112yes—
996C42C2×#4112yes—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23C23×D411yescharacteristic
1012Q8—22no—
1013Q8—22no—
1014Q8—22no—
1015Q8—22no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—84no—
1025Q8—84no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—84no—
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—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—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—44no—
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—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—82no—
1117C2×C4—84no—
1118C2×C4#52512yes—
1119C2×C4#52512yes—
1120C2×C4#53212yes—
1121C2×C4#53212yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C22×#4111yescharacteristic
1124C2×C4C22×#4111yescharacteristic
1125C2×C4C22×#4111yescharacteristic
1126C2×C4#58511yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—22no—
1129C8—22no—
1130C8—22no—
1131C8—22no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—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—
1150C22C2×#52511yescharacteristic
1151C22C2×#53211yescharacteristic
1152C22#344911yescharacteristic
1153C22#358511yescharacteristic
1154C22#358611yescharacteristic
1155C22#358611yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—42no—
1169C4—42no—
1170C4—41no—
1171C4—41no—
1172C4—42no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4#347511yescharacteristic
1186C4#347511yescharacteristic
1187C4#348011yescharacteristic
1188C4#348011yescharacteristic
1189C2—81no—
1190C2—161no—
1191C2#3491111yescharacteristic
1192C2#6056611yescharacteristic
1193C2#6056711yescharacteristic
1194C2#6069711yescharacteristic
1195C2#6069911yescharacteristic
1196C2#6097311yescharacteristic
1197C2#6097511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34085C2semidirect
3. #29526C2semidirect
4. #29524C2semidirect
5. #29509C2semidirect
6. #29508C2semidirect
8. #29487C2semidirect
10. #29470C2semidirect
11. #29362C2semidirect
12. #29325C2semidirect
13. #29138C2semidirect
14. #28396C2semidirect
15. #24718C2semidirect
16. #24714C2semidirect
19. #23765C2semidirect
21. #23577C2semidirect
23. #21616C2semidirect
24. #21615C2semidirect
25. #21508C2semidirect
26. #21508C2semidirect
27. #21288C2semidirect
28. #21288C2semidirect
29. #21287C2semidirect
30. #21287C2semidirect
31. #20465C2semidirect

Maximal subgroups

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

subgroupindex
#346192
#340852
#295262
#295242
#295092
#295082
#294912
#294872
#294742
#294702
#293622
#293252
#291382
#283962
#247182
#247142
#246692
#246652
#237652
#237642
#235772
#235742
#216162
#216152
#215082
#212882
#212872
#204652