Finite Group Databasebeta

← #7297237

Subgroups — #7297237

Order 512.

1324 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42811C211yesmaximal, characteristic, complemented
2#42495C211yesmaximal, characteristic
3#32832C211yesmaximal, characteristic, complemented
4#32685C211yesmaximal, characteristic, complemented
5#32641C211yesmaximal, characteristic, complemented
6#32604C211yesmaximal, characteristic
7#32581C211yesmaximal, characteristic
8#31991C211yesmaximal, characteristic, complemented
9#31896C211yesmaximal, characteristic, complemented
10#31571C211yesmaximal, characteristic, complemented
11#31484C211yesmaximal, characteristic, complemented
12#31248C211yesmaximal, characteristic
13#31167C211yesmaximal, characteristic
14#30952C211yesmaximal, characteristic, complemented
15#30826C211yesmaximal, characteristic, complemented
16#29591C211yesmaximal, characteristic, complemented
17#29568C211yesmaximal, characteristic
18#29543C211yesmaximal, characteristic
19#29013C211yesmaximal, characteristic, complemented
20#28956C211yesmaximal, characteristic, complemented
21#27449C211yesmaximal, characteristic
22#27201C211yesmaximal, characteristic
23#26845C211yesmaximal, characteristic
24#26481C211yesmaximal, characteristic
25#26376C211yesmaximal, characteristic
26#26182C211yesmaximal, characteristic
27#25842C211yesmaximal, characteristic, complemented
28#25657C211yesmaximal, characteristic, complemented
29#24340C211yesmaximal, characteristic
30#24187C211yesmaximal, characteristic
31#22310C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42#2841—21no—
43#2822—21no—
44#2790—21no—
45#2768—21no—
46#2742—21no—
47#2720—21no—
48#2719—21no—
49#2719—21no—
50#2713—21no—
51#2713—21no—
52#2667—21no—
53#2647C2211yescharacteristic
54#2642C2211yescharacteristic
55#2634—21no—
56#2634—21no—
57#2627—21no—
58#2584C2211yescharacteristic
59#2584C2211yescharacteristic
60#2584C2211yescharacteristic
61#2581—21no—
62#2580C2211yescharacteristic
63#2570C2211yescharacteristic
64#2568C2211yescharacteristic
65#2552C2211yescharacteristic
66#2538C2211yescharacteristic
67#2508C2211yescharacteristic
68#2506C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2453C2211yescharacteristic
72#2453C2211yescharacteristic
73#2451C2211yescharacteristic
74#2451C2211yescharacteristic
75#2446C2211yescharacteristic
76#2446C2211yescharacteristic
77#2446C2211yescharacteristic
78#2446C2211yescharacteristic
79#2442—21no—
80#2399C2211yescharacteristic
81#2357C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2320C2211yescharacteristic
84#2319C2211yescharacteristic
85#2101C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2095C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2072C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2058C2211yescharacteristic
118#2057C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2043C2211yescharacteristic
122#2043C2211yescharacteristic
123#2043C2211yescharacteristic
124#2043C2211yescharacteristic
125#2043C2211yescharacteristic
126#2043C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#1993C2211yescharacteristic
134#1989C2211yescharacteristic
135#1985C2211yescharacteristic
136#1985C2211yescharacteristic
137#1984C2211yescharacteristic
138#1984C2211yescharacteristic
139#1981C2211yescharacteristic
140#1973C2211yescharacteristic
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1956C2211yescharacteristic
144#1944C2211yescharacteristic
145#1943C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1935C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1925C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1918C2211yescharacteristic
171#1917C2211yescharacteristic
172#1917C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1865C2211yescharacteristic
189#1864C2211yescharacteristic
190#1864C2211yescharacteristic
191#1863C2211yescharacteristic
192#1863C2211yescharacteristic
193#1863C2211yescharacteristic
194#1862C2211yescharacteristic
195#1832C2211yescharacteristic
196#1805C2211yescharacteristic
197#1803C2211yescharacteristic
198#1770C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206#557—42no—
207#557—42no—
208#557—42no—
209#557—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C22×C4⋊C4—21no—
239#499—42no—
240#491—42no—
241#479—42no—
242#479—42no—
243#476—42no—
244#461—42no—
245#440—42no—
246C4×SD16—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—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#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398D411yescharacteristic
337#398D411yescharacteristic
338#398D411yescharacteristic
339#398D411yescharacteristic
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#395—21no—
348#395—21no—
349#395D411yescharacteristic
350#395D411yescharacteristic
351#395D411yescharacteristic
352#395D411yescharacteristic
353#393—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#382—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451#376C2311yescharacteristic
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#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2×D411yescharacteristic
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—44no—
526#125—22no—
527#125—41no—
528#125—41no—
529#125—41no—
530#125—41no—
531#125—41no—
532#125—41no—
533#125—41no—
534#125—44no—
535#125—44no—
536#125—44no—
537#125—44no—
538#125—44no—
539#125—82no—
540C22⋊Q8—82no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—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⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—82no—
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—41no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#102—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#102—41no—
704#97—41no—
705#97—41no—
706#97—41no—
707C4×C8—22no—
708C4×C8—41no—
709C4×C8—41no—
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#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
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
767#95C2×D411yescharacteristic
768C24—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
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—41no—
788C2×Q8—41no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8H(5,𝔽2)12yes—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D42−1+412yes—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—24no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
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×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
841SD16—44no—
842SD16—44no—
843SD16—82no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C82−1+412yes—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—22no—
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—41no—
894C4⋊C4—41no—
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—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
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⋊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⋊C4H(5,𝔽2)12yes—
947C4⋊C42−1+412yes—
948C22⋊C4—24no—
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—
959C42—24no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C23—22no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23C23×D411yescharacteristic
990Q8—22no—
991Q8—22no—
992Q8—44no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—82no—
1004Q8—84no—
1005D4—22no—
1006D4—22no—
1007D4—41no—
1008D4—41no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
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—21no—
1033C2×C4—22no—
1034C2×C4—22no—
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—22no—
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—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—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—84no—
1096C2×C4—162no—
1097C2×C4—162no—
1098C2×C4#57712yes—
1099C2×C4C2×H(5,𝔽2)11yescharacteristic
1100C2×C4C2×H(5,𝔽2)11yescharacteristic
1101C2×C4C2×2−1+411yescharacteristic
1102C2×C4C2×2−1+411yescharacteristic
1103C2×C4C2×2−1+411yescharacteristic
1104C2×C4#58511yescharacteristic
1105C8—22no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22#348411yescharacteristic
1121C22#348611yescharacteristic
1122C22#349711yescharacteristic
1123C22C2×#57711yescharacteristic
1124C22#358411yescharacteristic
1125C22#358611yescharacteristic
1126C22#358611yescharacteristic
1127C4—22no—
1128C4—41no—
1129C4—42no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—42no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4#353511yescharacteristic
1157C4#353811yescharacteristic
1158C4#354411yescharacteristic
1159C4#354711yescharacteristic
1160C2—82no—
1161C2#4779511yescharacteristic
1162C2#6161111yescharacteristic
1163C2#6162611yescharacteristic
1164C2#6184811yescharacteristic
1165C2#6186211yescharacteristic
1166C2#6237811yescharacteristic
1167C2#6238811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42811C2semidirect
3. #32832C2semidirect
4. #32685C2semidirect
5. #32641C2semidirect
8. #31991C2semidirect
9. #31896C2semidirect
10. #31571C2semidirect
11. #31484C2semidirect
14. #30952C2semidirect
15. #30826C2semidirect
16. #29591C2semidirect
19. #29013C2semidirect
20. #28956C2semidirect
27. #25842C2semidirect
28. #25657C2semidirect
31. #22310C2semidirect

Maximal subgroups

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

subgroupindex
#428112
#424952
#328322
#326852
#326412
#326042
#325812
#319912
#318962
#315712
#314842
#312482
#311672
#309522
#308262
#295912
#295682
#295432
#290132
#289562
#274492
#272012
#268452
#264812
#263762
#261822
#258422
#256572
#243402
#241872
#223102