Finite Group Databasebeta

← #30682774

Subgroups — #30682774

Order 16832.

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#22554518C212yesmaximal, complemented
2#22554517C214yesmaximal, complemented
3#22554516C214yesmaximal, complemented
4#22554515C216yesmaximal, complemented
5C2×#16862376C216yesmaximal, complemented
6#41×D263C218yesmaximal, complemented
7C2×#41×C263C211yesmaximal, characteristic, complemented
8#16862377C2218yescomplemented
9#16862376C22112yescomplemented
10#16862376C2214yescomplemented
11#16862376C22112yescomplemented
12#16862376C22112yescomplemented
13#16862375C22124yescomplemented
14C2×Dic526C2216yescomplemented
15Q8×D263C2218yescomplemented
16C2×D1052C2216yescomplemented
17C2×C22⋊D263C22112yescomplemented
18D4×D263C22124yescomplemented
19C2×C4×D263C22112yescomplemented
20#41×C263C2214yescomplemented
21#41×C263C2214yescomplemented
22C2×Q8×C263C2211yescharacteristic, complemented
23C2×D4×C263C2213yescomplemented
24C22×C4×C263C2213yescomplemented
25C22×D263C23112yes—
26Dic526C23112yes—
27Dic526C2314yes—
28D1052C23112yes—
29D1052C2314yes—
30C22⋊D263C23124yes—
31C22⋊D263C2318yes—
32C2×Dic263C23112yes—
33C4×D263C2318yes—
34C4×D263C23124yes—
35C23×C263C2313yes—
36Q8×C263C2314yes—
37D4×C263C23112yes—
38C2×C4×C263C2311yescharacteristic
39C2×C4×C263C2313yes—
40C2×C4×C263C2316yes—
41C2×C4×C263C2316yes—
42C22×C263—43no—
43C22×C263C2411yescharacteristic
44C22×C263C2416yes—
45C2×D263—412no—
46C2×D263C2418yes—
47C4×C263C2411yescharacteristic
48C4×C263C2416yes—
49C4×C263C2411yescharacteristic
50Dic263C2418yes—
51C2×C263—26no—
52C2×C263—21no—
53C2×C263C2511yescharacteristic
54D263—28no—
55C263#58511yescharacteristic, complemented, Sylow
56#585—2631nomaximal, Sylow
572−1+4—2634no—
582−1+4—2632no—
59H(5,𝔽2)—2634no—
60H(5,𝔽2)—2636no—
61C2×#41—2638no—
62C2×#41—2636no—
63C2×#41D26311yescharacteristic, complemented
64#41—2638no—
65#41—26324no—
66#41—26312no—
67#41—2634no—
68#41—26312no—
69#41—26312no—
70#41C2×D26314yescomplemented
71#41C2×D26314yescomplemented
72C2×Q8—2638no—
73C2×Q8—2636no—
74C2×Q8C2×D26311yescharacteristic, complemented
75C2×D4—26312no—
76C2×D4—26324no—
77C2×D4—2636no—
78C2×D4C2×D26313yescomplemented
79C22×C4—26312no—
80C22×C4C2×D26313yescomplemented
81C23—26312no—
82C23C22×D26313yes—
83Q8—26312no—
84Q8—2634no—
85Q8C22×D26314yes—
86D4—26324no—
87D4—2638no—
88D4—26312no—
89D4—2634no—
90D4C22×D263112yes—
91C2×C4—26312no—
92C2×C4—26324no—
93C2×C4—2638no—
94C2×C4C22×D26316yes—
95C2×C4C22×D26313yes—
96C2×C4C22×D26316yes—
97C2×C4C22×D26311yescharacteristic
98C22—43no—
99C22—2638no—
100C22—105212no—
101C22C23×D26316yes—
102C22C23×D26311yescharacteristic
103C4—2638no—
104C4C23×D26316yes—
105C4C23×D26311yescharacteristic
106C4C23×D26311yescharacteristic
107C2—21no—
108C2—26no—
109C2—5268no—
110C2C24×D26311yescharacteristic
subgroupG/H
centerC4C23×D263
commutator, socle, cosocleC2×C263C25
FrattiniC2C24×D263
FittingC2×#41×C263C2
hypercenterC2×#41D263
hypocenterC263#585
LCSG ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #22554518C2semidirect
2. #22554517C2semidirect
3. #22554516C2semidirect
4. #22554515C2semidirect
5. C2×#16862376C2semidirect
6. #41×D263C2semidirect
7. C2×#41×C263C2semidirect
8. #16862377C22semidirect
9. #16862376C22semidirect
10. #16862376C22semidirect
11. #16862376C22semidirect
12. #16862376C22semidirect
13. #16862375C22semidirect
14. C2×Dic526C22semidirect
15. Q8×D263C22semidirect
16. C2×D1052C22semidirect
17. C2×C22⋊D263C22semidirect
18. D4×D263C22semidirect
19. C2×C4×D263C22semidirect
20. #41×C263C22semidirect
21. #41×C263C22semidirect
22. C2×Q8×C263C22semidirect
23. C2×D4×C263C22semidirect
24. C22×C4×C263C22semidirect
55. C263#585semidirect
63. C2×#41D263semidirect
70. #41C2×D263semidirect
71. #41C2×D263semidirect
74. C2×Q8C2×D263semidirect
78. C2×D4C2×D263semidirect
80. C22×C4C2×D263semidirect

Maximal subgroups

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

subgroupindex
#225545182
#225545172
#225545162
#225545152
C2×#168623762
#41×D2632
C2×#41×C2632
#585263