Finite Group Databasebeta

← #37566080

Subgroups — #37566080

Order 24256.

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#27131379C212yesmaximal, complemented
2#27131378C214yesmaximal, complemented
3#27131377C214yesmaximal, complemented
4#27131376C216yesmaximal, complemented
5C2×#20258606C216yesmaximal, complemented
6#41×D379C218yesmaximal, complemented
7C2×#41×C379C211yesmaximal, characteristic, complemented
8#20258607C2218yescomplemented
9#20258606C22112yescomplemented
10#20258606C2214yescomplemented
11#20258606C22112yescomplemented
12#20258606C22112yescomplemented
13#20258605C22124yescomplemented
14C2×Dic758C2216yescomplemented
15Q8×D379C2218yescomplemented
16C2×D1516C2216yescomplemented
17C2×C22⋊D379C22112yescomplemented
18D4×D379C22124yescomplemented
19C2×C4×D379C22112yescomplemented
20#41×C379C2214yescomplemented
21#41×C379C2214yescomplemented
22C2×Q8×C379C2211yescharacteristic, complemented
23C2×D4×C379C2213yescomplemented
24C22×C4×C379C2213yescomplemented
25C22×D379C23112yes—
26Dic758C23112yes—
27Dic758C2314yes—
28D1516C23112yes—
29D1516C2314yes—
30C22⋊D379C23124yes—
31C22⋊D379C2318yes—
32C2×Dic379C23112yes—
33C4×D379C2318yes—
34C4×D379C23124yes—
35C23×C379C2313yes—
36Q8×C379C2314yes—
37D4×C379C23112yes—
38C2×C4×C379C2311yescharacteristic
39C2×C4×C379C2313yes—
40C2×C4×C379C2316yes—
41C2×C4×C379C2316yes—
42C22×C379—43no—
43C22×C379C2411yescharacteristic
44C22×C379C2416yes—
45C2×D379—412no—
46C2×D379C2418yes—
47C4×C379C2411yescharacteristic
48C4×C379C2416yes—
49C4×C379C2411yescharacteristic
50Dic379C2418yes—
51C2×C379—26no—
52C2×C379—21no—
53C2×C379C2511yescharacteristic
54D379—28no—
55C379#58511yescharacteristic, complemented, Sylow
56#585—3791nomaximal, Sylow
572−1+4—3794no—
582−1+4—3792no—
59H(5,𝔽2)—3794no—
60H(5,𝔽2)—3796no—
61C2×#41—3798no—
62C2×#41—3796no—
63C2×#41D37911yescharacteristic, complemented
64#41—3798no—
65#41—37924no—
66#41—37912no—
67#41—3794no—
68#41—37912no—
69#41—37912no—
70#41C2×D37914yescomplemented
71#41C2×D37914yescomplemented
72C2×Q8—3798no—
73C2×Q8—3796no—
74C2×Q8C2×D37911yescharacteristic, complemented
75C2×D4—37912no—
76C2×D4—37924no—
77C2×D4—3796no—
78C2×D4C2×D37913yescomplemented
79C22×C4—37912no—
80C22×C4C2×D37913yescomplemented
81C23—37912no—
82C23C22×D37913yes—
83Q8—37912no—
84Q8—3794no—
85Q8C22×D37914yes—
86D4—37924no—
87D4—3798no—
88D4—37912no—
89D4—3794no—
90D4C22×D379112yes—
91C2×C4—37912no—
92C2×C4—37924no—
93C2×C4—3798no—
94C2×C4C22×D37916yes—
95C2×C4C22×D37913yes—
96C2×C4C22×D37916yes—
97C2×C4C22×D37911yescharacteristic
98C22—43no—
99C22—3798no—
100C22—151612no—
101C22C23×D37916yes—
102C22C23×D37911yescharacteristic
103C4—3798no—
104C4C23×D37916yes—
105C4C23×D37911yescharacteristic
106C4C23×D37911yescharacteristic
107C2—21no—
108C2—26no—
109C2—7588no—
110C2C24×D37911yescharacteristic
subgroupG/H
centerC4C23×D379
commutator, socle, cosocleC2×C379C25
FrattiniC2C24×D379
FittingC2×#41×C379C2
hypercenterC2×#41D379
hypocenterC379#585
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #27131379C2semidirect
2. #27131378C2semidirect
3. #27131377C2semidirect
4. #27131376C2semidirect
5. C2×#20258606C2semidirect
6. #41×D379C2semidirect
7. C2×#41×C379C2semidirect
8. #20258607C22semidirect
9. #20258606C22semidirect
10. #20258606C22semidirect
11. #20258606C22semidirect
12. #20258606C22semidirect
13. #20258605C22semidirect
14. C2×Dic758C22semidirect
15. Q8×D379C22semidirect
16. C2×D1516C22semidirect
17. C2×C22⋊D379C22semidirect
18. D4×D379C22semidirect
19. C2×C4×D379C22semidirect
20. #41×C379C22semidirect
21. #41×C379C22semidirect
22. C2×Q8×C379C22semidirect
23. C2×D4×C379C22semidirect
24. C22×C4×C379C22semidirect
55. C379#585semidirect
63. C2×#41D379semidirect
70. #41C2×D379semidirect
71. #41C2×D379semidirect
74. C2×Q8C2×D379semidirect
78. C2×D4C2×D379semidirect
80. C22×C4C2×D379semidirect

Maximal subgroups

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

subgroupindex
#271313792
#271313782
#271313772
#271313762
C2×#202586062
#41×D3792
C2×#41×C3792
#585379