Finite Group Databasebeta

← #7078162

Subgroups — #7078162

Order 512.

1520 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45117C211yesmaximal, characteristic, complemented
2#45019C211yesmaximal, characteristic
3#32538C211yesmaximal, characteristic, complemented
4#32538C211yesmaximal, characteristic, complemented
5#32438C211yesmaximal, characteristic, complemented
6#32436C211yesmaximal, characteristic, complemented
7#32076C211yesmaximal, characteristic, complemented
8#32070C211yesmaximal, characteristic, complemented
9#30671C211yesmaximal, characteristic, complemented
10#30662C211yesmaximal, characteristic, complemented
11#28780C211yesmaximal, characteristic, complemented
12#27592C211yesmaximal, characteristic, complemented
13#27591C211yesmaximal, characteristic, complemented
14#27491C211yesmaximal, characteristic, complemented
15#27489C211yesmaximal, characteristic, complemented
16#26570C211yesmaximal, characteristic, complemented
17#26567C211yesmaximal, characteristic, complemented
18#25981C211yesmaximal, characteristic, complemented
19#25968C211yesmaximal, characteristic, complemented
20#25204C211yesmaximal, characteristic, complemented
21#25202C211yesmaximal, characteristic, complemented
22#24884C211yesmaximal, characteristic, complemented
23#24878C211yesmaximal, characteristic
24#24690C211yesmaximal, characteristic, complemented
25#24689C211yesmaximal, characteristic, complemented
26#24264C211yesmaximal, characteristic
27#23541C211yesmaximal, characteristic, complemented
28#22704C211yesmaximal, characteristic, complemented
29#22437C211yesmaximal, characteristic, complemented
30#22066C211yesmaximal, characteristic, complemented
31#21966C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#483C2211yescharacteristic, complemented
35C2×#479C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×#424C2211yescharacteristic
43C2×#419C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2796—21no—
46#2789—21no—
47#2755—21no—
48#2746—21no—
49#2740—21no—
50#2738—21no—
51#2735—21no—
52#2697—21no—
53#2602—21no—
54#2589—21no—
55#2576—21no—
56#2566C2211yescharacteristic
57#2565C2211yescharacteristic, complemented
58#2523—21no—
59#2515—21no—
60#2514C2211yescharacteristic, complemented
61#2514C2211yescharacteristic, complemented
62#2513C2211yescharacteristic
63#2513C2211yescharacteristic
64#2502C2211yescharacteristic, complemented
65#2501C2211yescharacteristic
66#2490C2211yescharacteristic
67#2489C2211yescharacteristic, complemented
68#2482—21no—
69#2471—21no—
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2421C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2418—21no—
75#2409C2211yescharacteristic
76#2408C2211yescharacteristic
77#2395C2211yescharacteristic
78#2361C2211yescharacteristic
79#2360C2211yescharacteristic, complemented
80#2355C2211yescharacteristic, complemented
81#2354C2211yescharacteristic
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic
84Q8×C22⋊C4C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2314C2211yescharacteristic
87#2314C2211yescharacteristic
88#2310C2211yescharacteristic
89#2309C2211yescharacteristic
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2084C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2072C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2036C2211yescharacteristic, complemented
123#2036C2211yescharacteristic, complemented
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1992C2211yescharacteristic, complemented
131#1992C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1924C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1872C2211yescharacteristic, complemented
172#1870C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1850C2211yescharacteristic, complemented
186#1835C2211yescharacteristic, complemented
187#1818C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1808C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#107C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237#483—42no—
238#481—42no—
239#479—42no—
240#478—42no—
241#465—42no—
242#465—42no—
243#440—42no—
244#440—42no—
245C8×D4—24no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262#424—24no—
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#419—42no—
271#418—42no—
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×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#401—21no—
305#401—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400D411yescharacteristic
311#399—21no—
312#399—21no—
313#399—21no—
314#399—21no—
315#399D411yescharacteristic
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397D411yescharacteristic
330#397D411yescharacteristic
331#397D411yescharacteristic
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394D411yescharacteristic
341#394D411yescharacteristic
342#393—21no—
343#392—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
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#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#383—21no—
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445#379—21no—
446#379—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#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—22no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—416no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8#4114yes—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552#125—41no—
553#125—41no—
554#125—41no—
555#125—41no—
556#123—82no—
557#123—82no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562#121—22no—
563#121—41no—
564#121—41no—
565#121—41no—
566#120—82no—
567C4×Q8—22no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—82no—
578#117—22no—
579#117—22no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—82no—
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—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
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⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
631C2×C22⋊C4—21no—
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—82no—
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×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
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×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
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#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738#97—41no—
739#97—41no—
740C4×C8—22no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#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#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—81no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—42no—
814C2×Q8—44no—
815C2×Q8—44no—
816C2×Q8—42no—
817C2×Q8—81no—
818C2×Q8—82no—
819C2×Q8—82no—
820C2×Q8H(5,𝔽2)12yes—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—41no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4H(5,𝔽2)12yes—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
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—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
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×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
901C22×C42−1+412yes—
902C22×C4C2511yescharacteristic
903SD16—28no—
904SD16—44no—
905SD16—44no—
906SD16—44no—
907M16—82no—
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—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—44no—
931C2×C8—82no—
932C2×C8C2×#4112yes—
933C2×C8C2×#4112yes—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
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—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
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⋊C4—81no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—41no—
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—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—84no—
1074C23—84no—
1075C23—162no—
1076C23—162no—
1077C23—162no—
1078C23—162no—
1079C23—162no—
1080C23#54712yes—
1081C23#57712yes—
1082C23C23×D411yescharacteristic
1083Q8—22no—
1084Q8—22no—
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—84no—
1092D4—22no—
1093D4—22no—
1094D4—44no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—84no—
1102D4—84no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
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—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
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—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—84no—
1190C2×C4—84no—
1191C2×C4—162no—
1192C2×C4—162no—
1193C2×C4—162no—
1194C2×C4#54712yes—
1195C2×C4C22×#4111yescharacteristic
1196C2×C4C2×H(5,𝔽2)11yescharacteristic
1197C2×C4C2×H(5,𝔽2)11yescharacteristic
1198C2×C4C2×2−1+411yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—22no—
1202C8—22no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—168no—
1238C22C2×#54711yescharacteristic
1239C22#348811yescharacteristic
1240C22#348811yescharacteristic
1241C22C2×#57711yescharacteristic
1242C22#358411yescharacteristic
1243C22#358511yescharacteristic
1244C22#358611yescharacteristic
1245C4—22no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—42no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4#349011yescharacteristic
1272C4#351011yescharacteristic
1273C4#353511yescharacteristic
1274C4#353511yescharacteristic
1275C2—42no—
1276C2—42no—
1277C2—82no—
1278C2—161no—
1279C2#4395911yescharacteristic
1280C2#6126311yescharacteristic
1281C2#6129111yescharacteristic
1282C2#6200811yescharacteristic
1283C2#6200911yescharacteristic
1284C2#6202711yescharacteristic
1285C2#6203011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45117C2semidirect
3. #32538C2semidirect
4. #32538C2semidirect
5. #32438C2semidirect
6. #32436C2semidirect
7. #32076C2semidirect
8. #32070C2semidirect
9. #30671C2semidirect
10. #30662C2semidirect
11. #28780C2semidirect
12. #27592C2semidirect
13. #27591C2semidirect
14. #27491C2semidirect
15. #27489C2semidirect
16. #26570C2semidirect
17. #26567C2semidirect
18. #25981C2semidirect
19. #25968C2semidirect
20. #25204C2semidirect
21. #25202C2semidirect
22. #24884C2semidirect
24. #24690C2semidirect
25. #24689C2semidirect
27. #23541C2semidirect
28. #22704C2semidirect
29. #22437C2semidirect
30. #22066C2semidirect
31. #21966C2semidirect
34. C2×#483C22semidirect
35. C2×#479C22semidirect
57. #2565C22semidirect
60. #2514C22semidirect
61. #2514C22semidirect
64. #2502C22semidirect
67. #2489C22semidirect
72. #2421C22semidirect
79. #2360C22semidirect
80. #2355C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2095C22semidirect
98. #2084C22semidirect
99. #2084C22semidirect
100. #2074C22semidirect
102. #2072C22semidirect
103. #2072C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
122. #2036C22semidirect
123. #2036C22semidirect
126. #2026C22semidirect
130. #1992C22semidirect
131. #1992C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1948C22semidirect
143. #1948C22semidirect
144. #1947C22semidirect
145. #1947C22semidirect
146. #1943C22semidirect
147. #1943C22semidirect
148. #1940C22semidirect
149. #1940C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
162. #1924C22semidirect
163. #1924C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
171. #1872C22semidirect
173. #1865C22semidirect
175. #1863C22semidirect
181. #1852C22semidirect
182. #1852C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
186. #1835C22semidirect
192. #1807C22semidirect
193. #1803C22semidirect
199. C4×#107C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#451172
#450192
#325382
#324382
#324362
#320762
#320702
#306712
#306622
#287802
#275922
#275912
#274912
#274892
#265702
#265672
#259812
#259682
#252042
#252022
#248842
#248782
#246902
#246892
#242642
#235412
#227042
#224372
#220662
#219662