Finite Group Databasebeta

← #7038604

Subgroups — #7038604

Order 512.

1492 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59271C211yesmaximal, characteristic, complemented
2#40169C211yesmaximal, characteristic
3#32450C211yesmaximal, characteristic, complemented
4#32307C211yesmaximal, characteristic, complemented
5#31655C211yesmaximal, characteristic, complemented
6#31130C211yesmaximal, characteristic, complemented
7#31065C211yesmaximal, characteristic
8#31012C211yesmaximal, characteristic, complemented
9#30783C211yesmaximal, characteristic, complemented
10#30423C211yesmaximal, characteristic, complemented
11#28884C211yesmaximal, characteristic, complemented
12#28859C211yesmaximal, characteristic, complemented
13#28537C211yesmaximal, characteristic, complemented
14#28361C211yesmaximal, characteristic, complemented
15#28315C211yesmaximal, characteristic, complemented
16#28026C211yesmaximal, characteristic, complemented
17#27894C211yesmaximal, characteristic, complemented
18#27806C211yesmaximal, characteristic, complemented
19#27510C211yesmaximal, characteristic, complemented
20#27238C211yesmaximal, characteristic, complemented
21#27225C211yesmaximal, characteristic, complemented
22#27087C211yesmaximal, characteristic, complemented
23#26809C211yesmaximal, characteristic, complemented
24#25157C211yesmaximal, characteristic, complemented
25#25028C211yesmaximal, characteristic, complemented
26#24878C211yesmaximal, characteristic
27#23760C211yesmaximal, characteristic, complemented
28#23304C211yesmaximal, characteristic, complemented
29#23103C211yesmaximal, characteristic, complemented
30#22884C211yesmaximal, characteristic, complemented
31#22047C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#484C2211yescharacteristic, complemented
34C2×#481C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#451C2211yescharacteristic, complemented
41C2×#448C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×#418C2211yescharacteristic
47#2850C2211yescharacteristic
48#2779—21no—
49#2762—21no—
50#2754—21no—
51#2749—21no—
52#2735—21no—
53#2697—21no—
54#2636—21no—
55#2569—21no—
56#2566C2211yescharacteristic
57#2565C2211yescharacteristic, complemented
58#2538C2211yescharacteristic
59#2532—21no—
60#2520—21no—
61#2518—21no—
62#2514C2211yescharacteristic, complemented
63#2512C2211yescharacteristic
64#2511C2211yescharacteristic, complemented
65#2510—21no—
66#2499C2211yescharacteristic
67#2498—21no—
68#2495C2211yescharacteristic
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic
71#2489C2211yescharacteristic
72#2480—21no—
73#2448C2211yescharacteristic
74#2442C2211yescharacteristic, complemented
75#2435C2211yescharacteristic
76#2427C2211yescharacteristic
77#2423C2211yescharacteristic
78#2409C2211yescharacteristic
79#2408C2211yescharacteristic
80#2367C2211yescharacteristic
81#2362C2211yescharacteristic
82#2356C2211yescharacteristic, complemented
83#2352C2211yescharacteristic
84#2343—21no—
85Q8×C22⋊C4C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2321—21no—
88C4×#123C2211yescharacteristic
89C4×#121C2211yescharacteristic
90C2×#391C2211yescharacteristic, complemented
91#2285C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2085C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2026C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2001C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1971C2211yescharacteristic, complemented
139#1971C2211yescharacteristic, complemented
140#1969C2211yescharacteristic, complemented
141#1968C2211yescharacteristic
142#1959C2211yescharacteristic
143#1959C2211yescharacteristic
144#1958C2211yescharacteristic
145#1955C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1923C2211yescharacteristic, complemented
164#1923C2211yescharacteristic, complemented
165#1920C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1894C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1874C2211yescharacteristic
178#1870C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1805C2211yescharacteristic, complemented
189#1787C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123D411yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C22⋊C4—21no—
236C22×C42C2311yescharacteristic
237#499—42no—
238#485—42no—
239#484—42no—
240#481—42no—
241#479—42no—
242#478—42no—
243#470—42no—
244#464—24no—
245#451—42no—
246#450—24no—
247#450—42no—
248#448—24no—
249#448—42no—
250C4×SD16—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268#418—42no—
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×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#401—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#392—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
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#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388D411yescharacteristic
391#388D411yescharacteristic
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#387—21no—
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386D411yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385D411yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#383—21no—
426#383—21no—
427#382—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381D411yescharacteristic
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376—21no—
465C2×#95—21no—
466C2×#95—21no—
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×Q16—22no—
525C2×Q16—22no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16#4114yes—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553#126—82no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#124—22no—
559#124—41no—
560#124—41no—
561#124—41no—
562#123—42no—
563C22⋊Q8—22no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571#121—22no—
572#121—41no—
573#121—41no—
574#121—41no—
575#120—44no—
576C4×Q8—22no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—82no—
589#117—44no—
590#117—41no—
591#117—41no—
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—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
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×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⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—82no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#106—22no—
699#106—22no—
700#106—22no—
701#106—41no—
702#106—41no—
703#106—41no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—41no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742#97—41no—
743#97—41no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—41no—
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#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—42no—
803C24—42no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24C22×D411yescharacteristic
810C24C22×D411yescharacteristic
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—42no—
829C2×Q8—42no—
830C2×Q8—81no—
831C2×Q8—82no—
832C2×Q8—82no—
833C2×Q8—82no—
834C2×Q8—82no—
835C2×Q8C2×#4112yes—
836C2×D4—22no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—42no—
851C2×D4—44no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—82no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4C2×#4112yes—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C2511yescharacteristic
921Q16—82no—
922Q16—82no—
923SD16—44no—
924SD16—82no—
925SD16—82no—
926SD16—82no—
927M16—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C2×#4112yes—
950C2×C8H(5,𝔽2)12yes—
951C2×C8H(5,𝔽2)12yes—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C22⋊C4—22no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—41no—
1051C42—41no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—84no—
1089C23—84no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23—162no—
1094C23—162no—
1095C23#57512yes—
1096C23C23×D411yescharacteristic
1097Q8—22no—
1098Q8—22no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—84no—
1110D4—22no—
1111D4—22no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—82no—
1119D4—84no—
1120D4—84no—
1121D4—162no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—44no—
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—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—82no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—22no—
1222C8—22no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—41no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—168no—
1257C22D4×#4111yescharacteristic
1258C22#348511yescharacteristic
1259C22#349811yescharacteristic
1260C22C2×#57511yescharacteristic
1261C22#358511yescharacteristic
1262C22#358611yescharacteristic
1263C22#358611yescharacteristic
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#350511yescharacteristic
1291C4#351411yescharacteristic
1292C4#354511yescharacteristic
1293C4#356011yescharacteristic
1294C2—42no—
1295C2—81no—
1296C2—82no—
1297C2—161no—
1298C2#4350211yescharacteristic
1299C2#6145611yescharacteristic
1300C2#6151411yescharacteristic
1301C2#6171611yescharacteristic
1302C2#6178011yescharacteristic
1303C2#6244611yescharacteristic
1304C2#6245011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59271C2semidirect
3. #32450C2semidirect
4. #32307C2semidirect
5. #31655C2semidirect
6. #31130C2semidirect
8. #31012C2semidirect
9. #30783C2semidirect
10. #30423C2semidirect
11. #28884C2semidirect
12. #28859C2semidirect
13. #28537C2semidirect
14. #28361C2semidirect
15. #28315C2semidirect
16. #28026C2semidirect
17. #27894C2semidirect
18. #27806C2semidirect
19. #27510C2semidirect
20. #27238C2semidirect
21. #27225C2semidirect
22. #27087C2semidirect
23. #26809C2semidirect
24. #25157C2semidirect
25. #25028C2semidirect
27. #23760C2semidirect
28. #23304C2semidirect
29. #23103C2semidirect
30. #22884C2semidirect
31. #22047C2semidirect
32. C2×#499C22semidirect
33. C2×#484C22semidirect
36. C2×#479C22semidirect
40. C2×#451C22semidirect
57. #2565C22semidirect
62. #2514C22semidirect
64. #2511C22semidirect
74. #2442C22semidirect
82. #2356C22semidirect
85. Q8×C22⋊C4C22semidirect
90. C2×#391C22semidirect
91. #2285C22semidirect
92. #2100C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2096C22semidirect
99. #2085C22semidirect
100. #2083C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
105. #2072C22semidirect
107. #2068C22semidirect
109. #2066C22semidirect
110. #2059C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
125. #2026C22semidirect
126. #2026C22semidirect
138. #1971C22semidirect
139. #1971C22semidirect
140. #1969C22semidirect
146. #1949C22semidirect
147. #1947C22semidirect
148. #1942C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
163. #1923C22semidirect
164. #1923C22semidirect
165. #1920C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
179. #1863C22semidirect
183. #1852C22semidirect
184. #1847C22semidirect
185. #1847C22semidirect
186. #1836C22semidirect
188. #1805C22semidirect
189. #1787C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. #1770C22semidirect
194. #1770C22semidirect
195. #1763C22semidirect
198. C4×#103C22semidirect
201. #1749C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#592712
#401692
#324502
#323072
#316552
#311302
#310652
#310122
#307832
#304232
#288842
#288592
#285372
#283612
#283152
#280262
#278942
#278062
#275102
#272382
#272252
#270872
#268092
#251572
#250282
#248782
#237602
#233042
#231032
#228842
#220472