Finite Group Databasebeta

← #6849127

Subgroups — #6849127

Order 512.

1495 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37875C211yesmaximal, characteristic, complemented
2#35570C211yesmaximal, characteristic
3#33203C211yesmaximal, characteristic, complemented
4#31758C211yesmaximal, characteristic, complemented
5#31751C211yesmaximal, characteristic, complemented
6#31750C211yesmaximal, characteristic, complemented
7#31748C211yesmaximal, characteristic, complemented
8#31142C211yesmaximal, characteristic, complemented
9#31130C211yesmaximal, characteristic, complemented
10#31127C211yesmaximal, characteristic, complemented
11#31116C211yesmaximal, characteristic, complemented
12#29698C211yesmaximal, characteristic, complemented
13#29692C211yesmaximal, characteristic, complemented
14#29151C211yesmaximal, characteristic, complemented
15#28807C211yesmaximal, characteristic, complemented
16#28792C211yesmaximal, characteristic, complemented
17#28288C211yesmaximal, characteristic, complemented
18#27759C211yesmaximal, characteristic, complemented
19#27751C211yesmaximal, characteristic, complemented
20#27656C211yesmaximal, characteristic, complemented
21#27651C211yesmaximal, characteristic, complemented
22#26244C211yesmaximal, characteristic, complemented
23#26240C211yesmaximal, characteristic, complemented
24#24981C211yesmaximal, characteristic, complemented
25#24965C211yesmaximal, characteristic, complemented
26#24714C211yesmaximal, characteristic, complemented
27#24700C211yesmaximal, characteristic, complemented
28#22800C211yesmaximal, characteristic, complemented
29#21872C211yesmaximal, characteristic, complemented
30#21861C211yesmaximal, characteristic, complemented
31#21623C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#474C2211yescharacteristic
43C2×#433C2211yescharacteristic
44C2×#431C2211yescharacteristic
45#2857C2211yescharacteristic
46#2774—21no—
47#2768—21no—
48#2763—21no—
49#2755—21no—
50#2660C2211yescharacteristic
51#2628C2211yescharacteristic
52#2602—21no—
53#2571C2211yescharacteristic
54#2570C2211yescharacteristic
55#2564—21no—
56#2559—21no—
57#2553—21no—
58#2552C2211yescharacteristic
59#2549—21no—
60#2544C2211yescharacteristic
61#2543—21no—
62#2540C2211yescharacteristic
63#2537C2211yescharacteristic
64#2505—21no—
65#2500—21no—
66#2498—21no—
67#2490C2211yescharacteristic
68#2489C2211yescharacteristic
69#2464—21no—
70#2450—21no—
71#2442C2211yescharacteristic
72#2442C2211yescharacteristic
73#2440C2211yescharacteristic
74#2439C2211yescharacteristic
75#2428C2211yescharacteristic
76#2427C2211yescharacteristic
77#2422—21no—
78#2352C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2331C2211yescharacteristic
81#2326C2211yescharacteristic
82#2323C2211yescharacteristic
83#2317C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2290C2211yescharacteristic
86C2×#382C2211yescharacteristic
87#2275C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2083C2211yescharacteristic
92#2076C2211yescharacteristic
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2026C2211yescharacteristic
125#2025C2211yescharacteristic
126#2024C2211yescharacteristic
127#2023C2211yescharacteristic
128#1992C2211yescharacteristic
129#1991C2211yescharacteristic
130#1991C2211yescharacteristic
131#1991C2211yescharacteristic
132#1989C2211yescharacteristic
133#1988C2211yescharacteristic
134#1987C2211yescharacteristic
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1961C2211yescharacteristic
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1958C2211yescharacteristic
142#1957C2211yescharacteristic
143#1955C2211yescharacteristic
144#1954C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1947C2211yescharacteristic
149#1947C2211yescharacteristic
150#1947C2211yescharacteristic
151#1947C2211yescharacteristic
152#1944C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1942C2211yescharacteristic
156#1935C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1924C2211yescharacteristic
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1843C2211yescharacteristic
177#1836C2211yescharacteristic
178#1834C2211yescharacteristic
179#1825C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1768C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203#540—24no—
204#540—42no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208#529—24no—
209#529—42no—
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#485—42no—
248#484—42no—
249#481—42no—
250#480—42no—
251#478—42no—
252#477—42no—
253#476—24no—
254#474—42no—
255#474—42no—
256#433—42no—
257#431—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—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#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#392—21no—
351#392—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386D411yescharacteristic
404#386D411yescharacteristic
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385D411yescharacteristic
415#385D411yescharacteristic
416#384—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376C2311yescharacteristic
456C2×#95—21no—
457C2×#95—21no—
458C2×#95—21no—
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#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528#127—22no—
529#127—41no—
530#126—44no—
531#125—22no—
532#125—22no—
533#125—41no—
534#125—41no—
535#125—41no—
536#125—41no—
537#124—22no—
538#124—22no—
539#124—22no—
540#124—41no—
541#123—44no—
542#123—44no—
543#123—44no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—82no—
549C22⋊Q8—82no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—22no—
554#121—44no—
555#121—44no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—82no—
561#121—82no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—41no—
573C4×D4—44no—
574C4×D4—82no—
575C4×D4—82no—
576C4×D4#4114yes—
577#117—22no—
578#117—22no—
579#117—44no—
580#117—41no—
581#117—41no—
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—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—22no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#102—22no—
714#102—22no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—22no—
738#97—41no—
739C4×C8—22no—
740C4×C8—41no—
741C4×C8—41no—
742C4×C8—41no—
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#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—42no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—41no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4C2×#4112yes—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C2511yescharacteristic
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4C2×#4112yes—
987C4⋊C4H(5,𝔽2)12yes—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C42—22no—
1022C42—22no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42C2×#4112yes—
1037C42H(5,𝔽2)12yes—
1038C422−1+412yes—
1039C422−1+412yes—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23#57612yes—
1068C23C23×D411yescharacteristic
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—162no—
1074Q8—162no—
1075D4—22no—
1076D4—22no—
1077D4—44no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—84no—
1085D4—84no—
1086D4—162no—
1087D4—162no—
1088D4—162no—
1089D4—162no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—44no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—82no—
1174C2×C4—84no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4—162no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4#53612yes—
1182C2×C4#53612yes—
1183C2×C4#54612yes—
1184C2×C4#54612yes—
1185C2×C4C22×#4111yescharacteristic
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4C2×2−1+411yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4#58511yescharacteristic
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22—42no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—41no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22C2×#53611yescharacteristic
1228C22C2×#54611yescharacteristic
1229C22#348811yescharacteristic
1230C22C2×#57611yescharacteristic
1231C22#358411yescharacteristic
1232C22#358411yescharacteristic
1233C22#358611yescharacteristic
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—41no—
1247C4—41no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4#350711yescharacteristic
1261C4#351111yescharacteristic
1262C4#354711yescharacteristic
1263C4#354811yescharacteristic
1264C2—42no—
1265C2—81no—
1266C2—82no—
1267C2—161no—
1268C2#3947011yescharacteristic
1269C2#6087111yescharacteristic
1270C2#6088211yescharacteristic
1271C2#6117111yescharacteristic
1272C2#6118811yescharacteristic
1273C2#6205011yescharacteristic
1274C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35570C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37875C2semidirect
3. #33203C2semidirect
4. #31758C2semidirect
5. #31751C2semidirect
6. #31750C2semidirect
7. #31748C2semidirect
8. #31142C2semidirect
9. #31130C2semidirect
10. #31127C2semidirect
11. #31116C2semidirect
12. #29698C2semidirect
13. #29692C2semidirect
14. #29151C2semidirect
15. #28807C2semidirect
16. #28792C2semidirect
17. #28288C2semidirect
18. #27759C2semidirect
19. #27751C2semidirect
20. #27656C2semidirect
21. #27651C2semidirect
22. #26244C2semidirect
23. #26240C2semidirect
24. #24981C2semidirect
25. #24965C2semidirect
26. #24714C2semidirect
27. #24700C2semidirect
28. #22800C2semidirect
29. #21872C2semidirect
30. #21861C2semidirect
31. #21623C2semidirect

Maximal subgroups

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

subgroupindex
#378752
#355702
#332032
#317582
#317512
#317502
#317482
#311422
#311302
#311272
#311162
#296982
#296922
#291512
#288072
#287922
#282882
#277592
#277512
#276562
#276512
#262442
#262402
#249812
#249652
#247142
#247002
#228002
#218722
#218612
#216232