Finite Group Databasebeta

← #7591051

Subgroups — #7591051

Order 512.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59276C211yesmaximal, characteristic, complemented
2#59272C211yesmaximal, characteristic, complemented
3#32431C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#31933C211yesmaximal, characteristic, complemented
6#31931C211yesmaximal, characteristic, complemented
7#28543C211yesmaximal, characteristic, complemented
8#28029C211yesmaximal, characteristic, complemented
9#28021C211yesmaximal, characteristic, complemented
10#27928C211yesmaximal, characteristic, complemented
11#27798C211yesmaximal, characteristic, complemented
12#27585C211yesmaximal, characteristic, complemented
13#27584C211yesmaximal, characteristic, complemented
14#27517C211yesmaximal, characteristic, complemented
15#27514C211yesmaximal, characteristic, complemented
16#26812C211yesmaximal, characteristic, complemented
17#26811C211yesmaximal, characteristic, complemented
18#26076C211yesmaximal, characteristic, complemented
19#25977C211yesmaximal, characteristic, complemented
20#25966C211yesmaximal, characteristic, complemented
21#25030C211yesmaximal, characteristic, complemented
22#24890C211yesmaximal, characteristic, complemented
23#24885C211yesmaximal, characteristic, complemented
24#24275C211yesmaximal, characteristic
25#23033C211yesmaximal, characteristic, complemented
26#22812C211yesmaximal, characteristic, complemented
27#22662C211yesmaximal, characteristic, complemented
28#22443C211yesmaximal, characteristic, complemented
29#21562C211yesmaximal, characteristic, complemented
30#21236C211yesmaximal, characteristic, complemented
31#20824C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#427C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×C4×M16C2211yescharacteristic
48#2761—21no—
49#2753—21no—
50#2737—21no—
51#2705—21no—
52#2610—21no—
53#2601—21no—
54#2597—21no—
55#2574—21no—
56#2567C2211yescharacteristic, complemented
57#2566C2211yescharacteristic
58#2554—21no—
59#2521—21no—
60#2518—21no—
61#2513C2211yescharacteristic
62#2512C2211yescharacteristic
63#2512C2211yescharacteristic, complemented
64#2512C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2500C2211yescharacteristic, complemented
67#2491C2211yescharacteristic, complemented
68#2490C2211yescharacteristic
69#2480—21no—
70#2442C2211yescharacteristic
71#2439C2211yescharacteristic
72#2423C2211yescharacteristic, complemented
73#2422C2211yescharacteristic
74#2412—21no—
75#2411—21no—
76#2408C2211yescharacteristic
77#2407C2211yescharacteristic
78#2373—21no—
79#2363C2211yescharacteristic
80#2362C2211yescharacteristic, complemented
81#2357C2211yescharacteristic
82#2356C2211yescharacteristic, complemented
83#2354C2211yescharacteristic
84#2352C2211yescharacteristic
85#2342—21no—
86#2341C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88C4×#123C2211yescharacteristic
89#2297C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2285C2211yescharacteristic
92#2285C2211yescharacteristic
93#2097C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic, complemented
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2073C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2071C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic, complemented
112#2065C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2025C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2000C2211yescharacteristic
124#1999C2211yescharacteristic
125#1973C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1948C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1875C2211yescharacteristic
162#1873C2211yescharacteristic, complemented
163#1870C2211yescharacteristic
164#1865C2211yescharacteristic, complemented
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic, complemented
171#1854C2211yescharacteristic, complemented
172#1853C2211yescharacteristic
173#1853C2211yescharacteristic
174#1851C2211yescharacteristic
175#1847C2211yescharacteristic, complemented
176#1846C2211yescharacteristic, complemented
177#1845C2211yescharacteristic, complemented
178#1844C2211yescharacteristic, complemented
179#1834C2211yescharacteristic, complemented
180#1834C2211yescharacteristic, complemented
181#1817C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1807C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1776C2211yescharacteristic, complemented
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1770C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202C8×C22⋊C4C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#123—21no—
222C2×#123D411yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C42C2311yescharacteristic
243#501—42no—
244#482—42no—
245#482—42no—
246#479—42no—
247#474—42no—
248#466—42no—
249#465—24no—
250#440—42no—
251C4×SD16—24no—
252#435—24no—
253#428—42no—
254#427—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#418—42no—
279#417—42no—
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C4×M16—24no—
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#395—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#392—21no—
349#391—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
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#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#376—21no—
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528AGL(1,ℤ/8)—416no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16#4114yes—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—41no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16#4114yes—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#126—44no—
561#126—82no—
562#126—82no—
563#125—41no—
564#125—41no—
565#124—82no—
566#123—42no—
567#123—82no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570#121—22no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#120—82no—
577C4×Q8—22no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—82no—
594#117—82no—
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—21no—
615C2×C4⋊C4—21no—
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×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—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—22no—
688C2×C42—22no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—22no—
708#107—22no—
709#107—22no—
710#107—22no—
711#107—22no—
712#107—41no—
713#107—41no—
714#107—41no—
715#106—22no—
716#106—22no—
717#106—22no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727C4⋊C8—22no—
728C4⋊C8—22no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—41no—
759#97—22no—
760#97—22no—
761#97—22no—
762#97—22no—
763C4×C8—22no—
764C4×C8—22no—
765C4×C8—22no—
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#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—44no—
818#41—82no—
819#41—82no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8C2×#4112yes—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
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—44no—
848C2×D4—44no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—82no—
857C2×D4—82no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4C2×#4112yes—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—22no—
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—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
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×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C2×#4112yes—
923C22×C42−1+412yes—
924C22×C4C2511yescharacteristic
925SD16—28no—
926SD16—44no—
927D8—44no—
928D8—44no—
929M16—28no—
930M16—44no—
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×C8—21no—
950C2×C8—44no—
951C2×C8C2×#4112yes—
952C2×C8C2×#4112yes—
953C2×C8C2×#4112yes—
954C2×C8H(5,𝔽2)12yes—
955C2×C8H(5,𝔽2)12yes—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
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—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
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—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
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—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C42—22no—
1056C42—22no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—84no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23#54712yes—
1120C23C23×D411yescharacteristic
1121Q8—22no—
1122Q8—22no—
1123Q8—41no—
1124Q8—41no—
1125Q8—162no—
1126D4—22no—
1127D4—22no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—84no—
1139D4—82no—
1140D4—84no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—44no—
1183C2×C4—44no—
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—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—84no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4#54712yes—
1231C2×C4#57512yes—
1232C2×C4#57712yes—
1233C2×C4C22×#4111yescharacteristic
1234C2×C4C22×#4111yescharacteristic
1235C2×C4C2×H(5,𝔽2)11yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×2−1+411yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8#55114yes—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—41no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—168no—
1283C22C2×#54711yescharacteristic
1284C22D4×#4111yescharacteristic
1285C22#349811yescharacteristic
1286C22C2×#57511yescharacteristic
1287C22C2×#57711yescharacteristic
1288C22#358511yescharacteristic
1289C22#358511yescharacteristic
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4C2×#55111yescharacteristic
1316C4#349411yescharacteristic
1317C4#352011yescharacteristic
1318C4#356111yescharacteristic
1319C2—42no—
1320C2—81no—
1321C2—82no—
1322C2—161no—
1323C2—161no—
1324C2#5927311yescharacteristic
1325C2#6125511yescharacteristic
1326C2#6127211yescharacteristic
1327C2#6145911yescharacteristic
1328C2#6154311yescharacteristic
1329C2#6242711yescharacteristic
1330C2#6244311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24275C2
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. #59276C2semidirect
2. #59272C2semidirect
3. #32431C2semidirect
4. #32430C2semidirect
5. #31933C2semidirect
6. #31931C2semidirect
7. #28543C2semidirect
8. #28029C2semidirect
9. #28021C2semidirect
10. #27928C2semidirect
11. #27798C2semidirect
12. #27585C2semidirect
13. #27584C2semidirect
14. #27517C2semidirect
15. #27514C2semidirect
16. #26812C2semidirect
17. #26811C2semidirect
18. #26076C2semidirect
19. #25977C2semidirect
20. #25966C2semidirect
21. #25030C2semidirect
22. #24890C2semidirect
23. #24885C2semidirect
25. #23033C2semidirect
26. #22812C2semidirect
27. #22662C2semidirect
28. #22443C2semidirect
29. #21562C2semidirect
30. #21236C2semidirect
31. #20824C2semidirect
33. C2×#501C22semidirect
35. C2×#482C22semidirect
36. C2×#479C22semidirect
44. C2×#427C22semidirect
56. #2567C22semidirect
63. #2512C22semidirect
64. #2512C22semidirect
66. #2500C22semidirect
67. #2491C22semidirect
72. #2423C22semidirect
80. #2362C22semidirect
82. #2356C22semidirect
93. #2097C22semidirect
94. #2095C22semidirect
97. #2094C22semidirect
100. #2092C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
103. #2073C22semidirect
104. #2072C22semidirect
108. #2071C22semidirect
111. #2065C22semidirect
112. #2065C22semidirect
113. #2059C22semidirect
114. #2058C22semidirect
117. #2035C22semidirect
119. #2034C22semidirect
121. #2025C22semidirect
137. #1949C22semidirect
138. #1948C22semidirect
139. #1944C22semidirect
140. #1941C22semidirect
141. #1927C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
150. #1926C22semidirect
151. #1925C22semidirect
152. #1925C22semidirect
153. #1924C22semidirect
154. #1923C22semidirect
155. #1917C22semidirect
156. #1916C22semidirect
162. #1873C22semidirect
164. #1865C22semidirect
165. #1865C22semidirect
170. #1854C22semidirect
171. #1854C22semidirect
175. #1847C22semidirect
176. #1846C22semidirect
177. #1845C22semidirect
178. #1844C22semidirect
179. #1834C22semidirect
180. #1834C22semidirect
186. #1807C22semidirect
187. #1805C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1776C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
199. #1770C22semidirect
201. #1752C22semidirect
202. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592762
#592722
#324312
#324302
#319332
#319312
#285432
#280292
#280212
#279282
#277982
#275852
#275842
#275172
#275142
#268122
#268112
#260762
#259772
#259662
#250302
#248902
#248852
#242752
#230332
#228122
#226622
#224432
#215622
#212362
#208242