Finite Group Databasebeta

← #28384416

Subgroups — #28384416

Order 14272.

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#20297352C212yesmaximal, complemented
2#20297351C214yesmaximal, complemented
3#20297350C214yesmaximal, complemented
4#20297349C216yesmaximal, complemented
5C2×#16813170C216yesmaximal, complemented
6#41×D223C218yesmaximal, complemented
7C2×#41×C223C211yesmaximal, characteristic, complemented
8#16813171C2218yescomplemented
9#16813170C22112yescomplemented
10#16813170C2214yescomplemented
11#16813170C22112yescomplemented
12#16813170C22112yescomplemented
13#16813169C22124yescomplemented
14C2×Dic446C2216yescomplemented
15Q8×D223C2218yescomplemented
16C2×D892C2216yescomplemented
17C2×C22⋊D223C22112yescomplemented
18D4×D223C22124yescomplemented
19C2×C4×D223C22112yescomplemented
20#41×C223C2214yescomplemented
21#41×C223C2214yescomplemented
22C2×Q8×C223C2211yescharacteristic, complemented
23C2×D4×C223C2213yescomplemented
24C22×C4×C223C2213yescomplemented
25C22×D223C23112yes—
26Dic446C23112yes—
27Dic446C2314yes—
28D892C23112yes—
29D892C2314yes—
30C22⋊D223C23124yes—
31C22⋊D223C2318yes—
32C2×Dic223C23112yes—
33C4×D223C2318yes—
34C4×D223C23124yes—
35C23×C223C2313yes—
36Q8×C223C2314yes—
37D4×C223C23112yes—
38C2×C4×C223C2311yescharacteristic
39C2×C4×C223C2313yes—
40C2×C4×C223C2316yes—
41C2×C4×C223C2316yes—
42C22×C223—43no—
43C22×C223C2411yescharacteristic
44C22×C223C2416yes—
45C2×D223—412no—
46C2×D223C2418yes—
47C4×C223C2411yescharacteristic
48C4×C223C2416yes—
49C4×C223C2411yescharacteristic
50Dic223C2418yes—
51C2×C223—26no—
52C2×C223—21no—
53C2×C223C2511yescharacteristic
54D223—28no—
55C223#58511yescharacteristic, complemented, Sylow
56#585—2231nomaximal, Sylow
572−1+4—2234no—
582−1+4—2232no—
59H(5,𝔽2)—2234no—
60H(5,𝔽2)—2236no—
61C2×#41—2238no—
62C2×#41—2236no—
63C2×#41D22311yescharacteristic, complemented
64#41—2238no—
65#41—22324no—
66#41—22312no—
67#41—2234no—
68#41—22312no—
69#41—22312no—
70#41C2×D22314yescomplemented
71#41C2×D22314yescomplemented
72C2×Q8—2238no—
73C2×Q8—2236no—
74C2×Q8C2×D22311yescharacteristic, complemented
75C2×D4—22312no—
76C2×D4—22324no—
77C2×D4—2236no—
78C2×D4C2×D22313yescomplemented
79C22×C4—22312no—
80C22×C4C2×D22313yescomplemented
81C23—22312no—
82C23C22×D22313yes—
83Q8—22312no—
84Q8—2234no—
85Q8C22×D22314yes—
86D4—22324no—
87D4—2238no—
88D4—22312no—
89D4—2234no—
90D4C22×D223112yes—
91C2×C4—22312no—
92C2×C4—22324no—
93C2×C4—2238no—
94C2×C4C22×D22316yes—
95C2×C4C22×D22313yes—
96C2×C4C22×D22316yes—
97C2×C4C22×D22311yescharacteristic
98C22—43no—
99C22—89212no—
100C22—2238no—
101C22C23×D22316yes—
102C22C23×D22311yescharacteristic
103C4—2238no—
104C4C23×D22316yes—
105C4C23×D22311yescharacteristic
106C4C23×D22311yescharacteristic
107C2—21no—
108C2—26no—
109C2—4468no—
110C2C24×D22311yescharacteristic
subgroupG/H
centerC4C23×D223
commutator, socle, cosocleC2×C223C25
FrattiniC2C24×D223
FittingC2×#41×C223C2
hypercenterC2×#41D223
hypocenterC223#585
LCSG ▷ C2×C223 ▷ C223
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20297352C2semidirect
2. #20297351C2semidirect
3. #20297350C2semidirect
4. #20297349C2semidirect
5. C2×#16813170C2semidirect
6. #41×D223C2semidirect
7. C2×#41×C223C2semidirect
8. #16813171C22semidirect
9. #16813170C22semidirect
10. #16813170C22semidirect
11. #16813170C22semidirect
12. #16813170C22semidirect
13. #16813169C22semidirect
14. C2×Dic446C22semidirect
15. Q8×D223C22semidirect
16. C2×D892C22semidirect
17. C2×C22⋊D223C22semidirect
18. D4×D223C22semidirect
19. C2×C4×D223C22semidirect
20. #41×C223C22semidirect
21. #41×C223C22semidirect
22. C2×Q8×C223C22semidirect
23. C2×D4×C223C22semidirect
24. C22×C4×C223C22semidirect
55. C223#585semidirect
63. C2×#41D223semidirect
70. #41C2×D223semidirect
71. #41C2×D223semidirect
74. C2×Q8C2×D223semidirect
78. C2×D4C2×D223semidirect
80. C22×C4C2×D223semidirect

Maximal subgroups

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

subgroupindex
#202973522
#202973512
#202973502
#202973492
C2×#168131702
#41×D2232
C2×#41×C2232
#585223