Finite Group Databasebeta

← C107×#1318 #28332001

Subgroups — C107×#1318 #28332001

Order 13696.

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

normal subgroups only

This group has 170 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#390×C107C211yesmaximal, characteristic
2#324×C107C212yesmaximal, complemented
3C22×D4×C107C411yescharacteristic
4C2×C4⋊C4×C107C2211yescharacteristic
5C2×C22⋊C4×C107—22no—
6C2×C42×C107C411yescharacteristic
7C22⋊C8×C107—22no—
8C24×C107—21no—
9C2×D4×C107—21no—
10C2×D4×C107—41no—
11C2×D4×C107—41no—
12C2×D4×C107C812yescomplemented
13C22×C4×C107—21no—
14C22×C4×C107C2×C411yescharacteristic
15C22×C4×C107D412yes—
16C2×C8×C107—42no—
17C4⋊C4×C107—41no—
18C22⋊C4×C107—44no—
19C42×C107—41no—
20C23×C107—22no—
21C23×C107—42no—
22C23×C107—42no—
23C23×C107—41no—
24C23×C107—41no—
25C23×C107C22⋊C411yescharacteristic
26D4×C107—42no—
27D4×C107—42no—
28C2×C4×C107—21no—
29C2×C4×C107—21no—
30C2×C4×C107—22no—
31C2×C4×C107—22no—
32C2×C4×C107—41no—
33C2×C4×C107—41no—
34C2×C4×C107—42no—
35C2×C4×C107C2×C811yescharacteristic
36C2×C4×C107M1611yescharacteristic
37C8×C107—82no—
38C22×C107—21no—
39C22×C107—21no—
40C22×C107—44no—
41C22×C107—42no—
42C22×C107—82no—
43C22×C107—81no—
44C22×C107—81no—
45C22×C107C22⋊C811yescharacteristic
46C22×C107#9911yescharacteristic
47C22×C107#10011yescharacteristic
48C4×C107—21no—
49C4×C107—21no—
50C4×C107—42no—
51C4×C107—42no—
52C2×C107—21no—
53C2×C107—21no—
54C2×C107—82no—
55C2×C107#32311yescharacteristic
56C2×C107#35311yescharacteristic
57C2×C107#35511yescharacteristic
58#1318C10711yesmaximal, characteristic, direct product factor, Sylow
59C107#131811yescharacteristic, direct product factor, Sylow
60#390C2×C10711yescharacteristic
61#324C2×C10712yescomplemented
62C22×D4C4×C10711yescharacteristic
63C2×C4⋊C4C22×C10711yescharacteristic
64C2×C22⋊C4—22no—
65C2×C42C4×C10711yescharacteristic
66C22⋊C8—22no—
67C24—21no—
68C2×D4—21no—
69C2×D4—41no—
70C2×D4—41no—
71C2×D4C8×C10712yescomplemented
72C22×C4—21no—
73C22×C4C2×C4×C10711yescharacteristic
74C22×C4D4×C10712yes—
75C2×C8—42no—
76C4⋊C4—41no—
77C22⋊C4—44no—
78C42—41no—
79C23—22no—
80C23—42no—
81C23—42no—
82C23—41no—
83C23—41no—
84C23C22⋊C4×C10711yescharacteristic
85D4—42no—
86D4—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—42no—
94C2×C4C2×C8×C10711yescharacteristic
95C2×C4M16×C10711yescharacteristic
96C8—82no—
97C22—21no—
98C22—21no—
99C22—44no—
100C22—42no—
101C22—82no—
102C22—81no—
103C22—81no—
104C22C22⋊C8×C10711yescharacteristic
105C22#99×C10711yescharacteristic
106C22#100×C10711yescharacteristic
107C4—21no—
108C4—21no—
109C4—42no—
110C4—42no—
111C2—21no—
112C2—21no—
113C2—82no—
114C2#323×C10711yescharacteristic
115C2#353×C10711yescharacteristic
116C2#355×C10711yescharacteristic
subgroupG/H
center, socleC22×C107#99
commutatorC2×C4C2×C8×C107
Frattini, cosocleC2×C4⋊C4C22×C107
prime radicalC22×D4×C107C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C2×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. #324×C107C2semidirect
12. C2×D4×C107C8semidirect
58. #1318C107direct (N × H)
59. C107#1318direct (N × H)
61. #324C2×C107semidirect
71. C2×D4C8×C107semidirect

Maximal subgroups

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

subgroupindex
#390×C1072
#324×C1072
#1318107