Finite Group Databasebeta

← C107×#1317 #28332000

Subgroups — C107×#1317 #28332000

Order 13696.

150 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 44 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#381×C107C211yesmaximal, characteristic
2#323×C107C212yesmaximal
3C23×C4×C107C411yescharacteristic
4C2×C22⋊C4×C107C411yescharacteristic
5C2×C22⋊C4×C107C2211yescharacteristic
6C22⋊C8×C107—22no—
7#95×C107—22no—
8C24×C107C2×C411yescharacteristic
9C22×C4×C107—21no—
10C22×C4×C107—21no—
11C22×C4×C107—21no—
12C22×C4×C107—41no—
13C22×C4×C107—41no—
14C22×C4×C107C812yescomplemented
15C22×C4×C107D412yes—
16C2×C8×C107—42no—
17C22⋊C4×C107—41no—
18C22⋊C4×C107—41no—
19C23×C107—21no—
20C23×C107—21no—
21C23×C107—42no—
22C23×C107C22⋊C411yescharacteristic
23C23×C107C2×C811yescharacteristic
24C23×C107M1611yescharacteristic
25C2×C4×C107—22no—
26C2×C4×C107—22no—
27C2×C4×C107—42no—
28C2×C4×C107—41no—
29C2×C4×C107—41no—
30C2×C4×C107—42no—
31C2×C4×C107—42no—
32C2×C4×C107—42no—
33C2×C4×C107—41no—
34C8×C107—82no—
35C22×C107—22no—
36C22×C107—21no—
37C22×C107—21no—
38C22×C107—41no—
39C22×C107—41no—
40C22×C107—42no—
41C22×C107—42no—
42C22×C107C22⋊C811yescharacteristic
43C22×C107#9911yescharacteristic
44C22×C107#10011yescharacteristic
45C4×C107—42no—
46C4×C107—42no—
47C4×C107—81no—
48C2×C107—21no—
49C2×C107—21no—
50C2×C107—41no—
51C2×C107—41no—
52C2×C107#32311yescharacteristic
53C2×C107#35212yes—
54#1317C10711yesmaximal, characteristic, direct product factor, Sylow
55C107#131711yescharacteristic, direct product factor, Sylow
56#381C2×C10711yescharacteristic
57#323C2×C10712yes—
58C23×C4C4×C10711yescharacteristic
59C2×C22⋊C4C4×C10711yescharacteristic
60C2×C22⋊C4C22×C10711yescharacteristic
61C22⋊C8—22no—
62#95—22no—
63C24C2×C4×C10711yescharacteristic
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—41no—
68C22×C4—41no—
69C22×C4C8×C10712yescomplemented
70C22×C4D4×C10712yes—
71C2×C8—42no—
72C22⋊C4—41no—
73C22⋊C4—41no—
74C23—21no—
75C23—21no—
76C23—42no—
77C23C22⋊C4×C10711yescharacteristic
78C23C2×C8×C10711yescharacteristic
79C23M16×C10711yescharacteristic
80C2×C4—22no—
81C2×C4—22no—
82C2×C4—42no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—42no—
87C2×C4—42no—
88C2×C4—41no—
89C8—82no—
90C22—22no—
91C22—21no—
92C22—21no—
93C22—41no—
94C22—41no—
95C22—42no—
96C22—42no—
97C22C22⋊C8×C10711yescharacteristic
98C22#99×C10711yescharacteristic
99C22#100×C10711yescharacteristic
100C4—42no—
101C4—42no—
102C4—81no—
103C2—21no—
104C2—21no—
105C2—41no—
106C2—41no—
107C2#323×C10711yescharacteristic
108C2#352×C10712yes—
subgroupG/H
center, socleC22×C107#99
commutatorC23C2×C8×C107
Frattini, cosocleC2×C22⋊C4C22×C107
prime radicalC24×C107C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C2×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
14. C22×C4×C107C8semidirect
54. #1317C107direct (N × H)
55. C107#1317direct (N × H)
69. C22×C4C8×C107semidirect

Maximal subgroups

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

subgroupindex
#381×C1072
#323×C1072
#1317107