Finite Group Databasebeta

← #6532448

Subgroups — #6532448

Order 512.

1374 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35117C211yesmaximal, characteristic
2#34328C211yesmaximal, characteristic, complemented
3#29563C211yesmaximal, characteristic
4#29559C211yesmaximal, characteristic, complemented
5#29523C211yesmaximal, characteristic
6#29522C211yesmaximal, characteristic, complemented
7#29451C211yesmaximal, characteristic
8#29446C211yesmaximal, characteristic, complemented
9#29357C211yesmaximal, characteristic, complemented
10#29353C211yesmaximal, characteristic
11#27435C211yesmaximal, characteristic
12#27432C211yesmaximal, characteristic, complemented
13#27205C211yesmaximal, characteristic, complemented
14#27198C211yesmaximal, characteristic
15#27008C211yesmaximal, characteristic, complemented
16#27007C211yesmaximal, characteristic
17#26699C211yesmaximal, characteristic, complemented
18#26696C211yesmaximal, characteristic
19#26455C211yesmaximal, characteristic, complemented
20#26331C211yesmaximal, characteristic
21#26035C211yesmaximal, characteristic, complemented
22#25941C211yesmaximal, characteristic
23#25286C211yesmaximal, characteristic
24#25005C211yesmaximal, characteristic, complemented
25#24641C211yesmaximal, characteristic
26#24344C211yesmaximal, characteristic, complemented
27#22156C211yesmaximal, characteristic
28#22119C211yesmaximal, characteristic, complemented
29C4×#489C211yesmaximal, characteristic
30#21346C211yesmaximal, characteristic, complemented
31#21287C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#441C2211yescharacteristic
37#2863C2211yescharacteristic
38#2862C2211yescharacteristic
39#2861C2211yescharacteristic
40#2860C2211yescharacteristic
41#2650—21no—
42#2637—21no—
43#2592C2211yescharacteristic
44#2581C2211yescharacteristic
45#2550C2211yescharacteristic
46#2545C2211yescharacteristic
47#2532—21no—
48#2529—21no—
49#2515—21no—
50#2465—21no—
51#2453C2211yescharacteristic
52#2452C2211yescharacteristic
53#2447C2211yescharacteristic
54#2446C2211yescharacteristic
55#2371—21no—
56#2371—21no—
57#2370C2211yescharacteristic
58#2370C2211yescharacteristic
59#2365—21no—
60#2365C2211yescharacteristic
61#2356—21no—
62#2356C2211yescharacteristic
63#2356C2211yescharacteristic
64#2355C2211yescharacteristic
65#2355C2211yescharacteristic
66#2336—21no—
67#2336—21no—
68#2334—21no—
69#2332—21no—
70#2327—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#125C2211yescharacteristic
73C4×#125C2211yescharacteristic
74C4×#124C2211yescharacteristic
75#2295C2211yescharacteristic
76#2295C2211yescharacteristic
77#2295C2211yescharacteristic
78#2295C2211yescharacteristic
79#2276—21no—
80C42×Q8C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2097C2211yescharacteristic
84#2092C2211yescharacteristic
85#2088C2211yescharacteristic
86#2086C2211yescharacteristic
87#2074C2211yescharacteristic
88#2074C2211yescharacteristic
89#2074C2211yescharacteristic
90#2073C2211yescharacteristic
91#2068C2211yescharacteristic
92#2067C2211yescharacteristic
93#2066C2211yescharacteristic
94#2066C2211yescharacteristic
95#2059C2211yescharacteristic
96#2059C2211yescharacteristic
97#2059C2211yescharacteristic
98#2058C2211yescharacteristic
99#2056C2211yescharacteristic
100#2055C2211yescharacteristic
101#2043C2211yescharacteristic
102#2042C2211yescharacteristic
103#2026C2211yescharacteristic
104#2026C2211yescharacteristic
105#2026C2211yescharacteristic
106#2026C2211yescharacteristic
107#2026C2211yescharacteristic
108#2025C2211yescharacteristic
109#2025C2211yescharacteristic
110#2024C2211yescharacteristic
111#2016C2211yescharacteristic
112#2015C2211yescharacteristic
113#1993C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1987C2211yescharacteristic
117#1987C2211yescharacteristic
118#1987C2211yescharacteristic
119#1985C2211yescharacteristic
120#1985C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1983C2211yescharacteristic
124#1981C2211yescharacteristic
125#1981C2211yescharacteristic
126#1973C2211yescharacteristic
127#1971C2211yescharacteristic
128#1971C2211yescharacteristic
129#1969C2211yescharacteristic
130#1959C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1941C2211yescharacteristic
137#1940C2211yescharacteristic
138#1940C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1918C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1877C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1836C2211yescharacteristic
188#1805C2211yescharacteristic
189#1803C2211yescharacteristic
190#1776C2211yescharacteristic
191#1767C2211yescharacteristic
192#1767C2211yescharacteristic
193#1767C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1745C2211yescharacteristic
201#1745C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#557—24no—
207#557—24no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#125—21no—
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8D411yescharacteristic
225C2×C4×Q8D411yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233#489—24no—
234#477—24no—
235#464—24no—
236#441—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#395—21no—
299#395—21no—
300#393—21no—
301#393—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#385—21no—
389#385—21no—
390#384C2311yescharacteristic
391#383—21no—
392#383—21no—
393#383—21no—
394#382—21no—
395#382—21no—
396#382—21no—
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#381—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4D411yescharacteristic
416C4×C4⋊C4D411yescharacteristic
417C4×C4⋊C4D411yescharacteristic
418C4×C4⋊C4D411yescharacteristic
419C4×C4⋊C4D411yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435#376—21no—
436#376—21no—
437#376—21no—
438#376—21no—
439#376—21no—
440#376—21no—
441C43C2311yescharacteristic
442C43C2311yescharacteristic
443C43C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2×D411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C4⋊Q8—28no—
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515C4⋊Q8#4114yes—
516#126—44no—
517#125—28no—
518#125—28no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—22no—
523#125—41no—
524#125—41no—
525#124—22no—
526#124—22no—
527#124—41no—
528#124—41no—
529C22⋊Q8—44no—
530C4×Q8—28no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—42no—
541C4×Q8—42no—
542C4×Q8—44no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—44no—
546C4×Q8#4114yes—
547C4×D4—41no—
548C4×D4—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—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⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
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×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×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
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×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#107—22no—
647#107—22no—
648#107—22no—
649#107—41no—
650#106—22no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#97—22no—
688#97—22no—
689#97—22no—
690#97—41no—
691#97—41no—
692#97—41no—
693C4×C8—41no—
694C4×C8—41no—
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#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753C24—21no—
754C2×Q8—22no—
755C2×Q8—24no—
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—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—41no—
774C2×Q8—41no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8C2×#4112yes—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C22×C4—21no—
788C22×C4—21no—
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—42no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C2511yescharacteristic
820Q16—44no—
821Q16—82no—
822SD16—82no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
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×C82−1+412yes—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
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—41no—
884C4⋊C4—41no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4C2×#4112yes—
907C4⋊C4C2×#4112yes—
908C4⋊C4C2×#4112yes—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—22no—
926C42—22no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—41no—
940C42—41no—
941C42—41no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42C2×#4112yes—
962C42C2×#4112yes—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23C23×D411yescharacteristic
971Q8—22no—
972Q8—22no—
973Q8—44no—
974Q8—48no—
975Q8—41no—
976Q8—41no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—162no—
986D4—41no—
987D4—41no—
988D4—41no—
989D4—41no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—162no—
1074C2×C4#52512yes—
1075C2×C4#52512yes—
1076C2×C4#57512yes—
1077C2×C4#57512yes—
1078C2×C4C22×#4111yescharacteristic
1079C2×C4C22×#4111yescharacteristic
1080C2×C4C2×2−1+411yescharacteristic
1081C2×C4#58511yescharacteristic
1082C2×C4#58511yescharacteristic
1083C2×C4#58511yescharacteristic
1084C8—22no—
1085C8—41no—
1086C8—41no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22C2×#52511yescharacteristic
1100C22#349711yescharacteristic
1101C22#350011yescharacteristic
1102C22C2×#57511yescharacteristic
1103C22C2×#57511yescharacteristic
1104C22#358611yescharacteristic
1105C22#358611yescharacteristic
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—42no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—41no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4#349511yescharacteristic
1136C4#351011yescharacteristic
1137C4#351811yescharacteristic
1138C4#352411yescharacteristic
1139C2—161no—
1140C2#3567511yescharacteristic
1141C2#6055911yescharacteristic
1142C2#6057711yescharacteristic
1143C2#6239911yescharacteristic
1144C2#6239911yescharacteristic
1145C2#6257911yescharacteristic
1146C2#6258511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34328C2semidirect
4. #29559C2semidirect
6. #29522C2semidirect
8. #29446C2semidirect
9. #29357C2semidirect
12. #27432C2semidirect
13. #27205C2semidirect
15. #27008C2semidirect
17. #26699C2semidirect
19. #26455C2semidirect
21. #26035C2semidirect
24. #25005C2semidirect
26. #24344C2semidirect
28. #22119C2semidirect
30. #21346C2semidirect
31. #21287C2semidirect

Maximal subgroups

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

subgroupindex
#351172
#343282
#295632
#295592
#295232
#295222
#294512
#294462
#293572
#293532
#274352
#274322
#272052
#271982
#270082
#270072
#266992
#266962
#264552
#263312
#260352
#259412
#252862
#250052
#246412
#243442
#221562
#221192
C4×#4892
#213462
#212872