Finite Group Databasebeta

← #46831011

Subgroups — #46831011

Order 34624.

810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31772676C212yesmaximal, complemented
2#31772675C214yesmaximal, complemented
3#31772674C214yesmaximal, complemented
4#31772673C216yesmaximal, complemented
5C2×#22575836C216yesmaximal, complemented
6#41×D541C218yesmaximal, complemented
7C2×#41×C541C211yesmaximal, characteristic, complemented
8#22575837C2218yescomplemented
9#22575836C22112yescomplemented
10#22575836C22112yescomplemented
11#22575836C22112yescomplemented
12#22575836C2214yescomplemented
13#22575835C22124yescomplemented
14C2×Dic1082C2216yescomplemented
15Q8×D541C2218yescomplemented
16C2×D2164C2216yescomplemented
17C2×C22⋊D541C22112yescomplemented
18D4×D541C22124yescomplemented
19C2×C4×D541C22112yescomplemented
20#41×C541C2214yescomplemented
21#41×C541C2214yescomplemented
22C2×Q8×C541C2211yescharacteristic, complemented
23C2×D4×C541C2213yescomplemented
24C22×C4×C541C2213yescomplemented
25C22×D541C23112yes—
26Dic1082C23112yes—
27Dic1082C2314yes—
28D2164C23112yes—
29D2164C2314yes—
30C22⋊D541C23124yes—
31C22⋊D541C2318yes—
32C2×Dic541C23112yes—
33C4×D541C2318yes—
34C4×D541C23124yes—
35C23×C541C2313yes—
36Q8×C541C2314yes—
37D4×C541C23112yes—
38C2×C4×C541C2311yescharacteristic
39C2×C4×C541C2313yes—
40C2×C4×C541C2316yes—
41C2×C4×C541C2316yes—
42C22×C541—43no—
43C22×C541C2411yescharacteristic
44C22×C541C2416yes—
45C2×D541—412no—
46C2×D541C2418yes—
47C4×C541C2416yes—
48C4×C541C2411yescharacteristic
49C4×C541C2411yescharacteristic
50Dic541C2418yes—
51C2×C541—26no—
52C2×C541—21no—
53C2×C541C2511yescharacteristic
54D541—28no—
55C541#58511yescharacteristic, complemented, Sylow
56#585—5411nomaximal, Sylow
572−1+4—5414no—
582−1+4—5412no—
59H(5,𝔽2)—5414no—
60H(5,𝔽2)—5416no—
61C2×#41—5418no—
62C2×#41—5416no—
63C2×#41D54111yescharacteristic, complemented
64#41—5418no—
65#41—54124no—
66#41—54112no—
67#41—5414no—
68#41—54112no—
69#41—54112no—
70#41C2×D54114yescomplemented
71#41C2×D54114yescomplemented
72C2×Q8—5418no—
73C2×Q8—5416no—
74C2×Q8C2×D54111yescharacteristic, complemented
75C2×D4—54112no—
76C2×D4—54124no—
77C2×D4—5416no—
78C2×D4C2×D54113yescomplemented
79C22×C4—54112no—
80C22×C4C2×D54113yescomplemented
81C23—54112no—
82C23C22×D54113yes—
83Q8—54112no—
84Q8—5414no—
85Q8C22×D54114yes—
86D4—54124no—
87D4—5418no—
88D4—54112no—
89D4—5414no—
90D4C22×D541112yes—
91C2×C4—54112no—
92C2×C4—54124no—
93C2×C4—5418no—
94C2×C4C22×D54116yes—
95C2×C4C22×D54113yes—
96C2×C4C22×D54116yes—
97C2×C4C22×D54111yescharacteristic
98C22—43no—
99C22—5418no—
100C22—216412no—
101C22C23×D54116yes—
102C22C23×D54111yescharacteristic
103C4—5418no—
104C4C23×D54116yes—
105C4C23×D54111yescharacteristic
106C4C23×D54111yescharacteristic
107C2—21no—
108C2—26no—
109C2—10828no—
110C2C24×D54111yescharacteristic
subgroupG/H
centerC4C23×D541
commutator, socle, cosocleC2×C541C25
FrattiniC2C24×D541
FittingC2×#41×C541C2
hypercenterC2×#41D541
hypocenterC541#585
LCSG ▷ C2×C541 ▷ C541
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #31772676C2semidirect
2. #31772675C2semidirect
3. #31772674C2semidirect
4. #31772673C2semidirect
5. C2×#22575836C2semidirect
6. #41×D541C2semidirect
7. C2×#41×C541C2semidirect
8. #22575837C22semidirect
9. #22575836C22semidirect
10. #22575836C22semidirect
11. #22575836C22semidirect
12. #22575836C22semidirect
13. #22575835C22semidirect
14. C2×Dic1082C22semidirect
15. Q8×D541C22semidirect
16. C2×D2164C22semidirect
17. C2×C22⋊D541C22semidirect
18. D4×D541C22semidirect
19. C2×C4×D541C22semidirect
20. #41×C541C22semidirect
21. #41×C541C22semidirect
22. C2×Q8×C541C22semidirect
23. C2×D4×C541C22semidirect
24. C22×C4×C541C22semidirect
55. C541#585semidirect
63. C2×#41D541semidirect
70. #41C2×D541semidirect
71. #41C2×D541semidirect
74. C2×Q8C2×D541semidirect
78. C2×D4C2×D541semidirect
80. C22×C4C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726762
#317726752
#317726742
#317726732
C2×#225758362
#41×D5412
C2×#41×C5412
#585541