Finite Group Databasebeta

← C107×#3189 #28333872

Subgroups — C107×#3189 #28333872

Order 13696.

416 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 188 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
1C2×C22⋊Q8×C107C212yesmaximal
2#484×C107C214yesmaximal, complemented
3#467×C107C214yesmaximal, complemented
4#451×C107C214yesmaximal, complemented
5C2×C22⋊C8×C107C211yesmaximal, characteristic
6C22×Q8×C107C2212yes—
7C23×C4×C107C2211yescharacteristic
8C2×Q16×C107C2214yescomplemented
9C22×C8×C107C2212yes—
10C22⋊Q8×C107—22no—
11C22⋊Q8×C107—22no—
12C22⋊Q8×C107C2214yes—
13C22⋊Q8×C107C2214yes—
14C2×C4⋊C4×C107—22no—
15C2×C4⋊C4×C107C2212yes—
16C2×C22⋊C4×C107—22no—
17#107×C107C2214yescomplemented
18#103×C107C2218yescomplemented
19C22⋊C8×C107C2214yes—
20C24×C107D411yescharacteristic
21C2×Q8×C107—22no—
22C2×Q8×C107—44no—
23C2×Q8×C107C2314yes—
24C22×C4×C107—22no—
25C22×C4×C107—22no—
26C22×C4×C107—42no—
27C22×C4×C107D412yes—
28C22×C4×C107D411yescharacteristic
29C22×C4×C107C2312yes—
30C22×C4×C107C2311yescharacteristic
31Q16×C107—44no—
32C2×C8×C107—42no—
33C2×C8×C107C2314yes—
34C4⋊C4×C107—24no—
35C4⋊C4×C107—24no—
36C4⋊C4×C107—22no—
37C4⋊C4×C107C2314yes—
38C22⋊C4×C107—24no—
39C22⋊C4×C107—24no—
40C23×C107—41no—
41C23×C107—41no—
42C23×C107Q1614yescomplemented
43C23×C107C2×D411yescharacteristic
44C23×C107C2×D412yes—
45Q8×C107—28no—
46Q8×C107—44no—
47C2×C4×C107—22no—
48C2×C4×C107—24no—
49C2×C4×C107—24no—
50C2×C4×C107—24no—
51C2×C4×C107—42no—
52C2×C4×C107—41no—
53C2×C4×C107—44no—
54C2×C4×C107—44no—
55C2×C4×C107C2×D411yescharacteristic
56C2×C4×C107C2×D412yes—
57C2×C4×C107C2411yescharacteristic
58C8×C107—24no—
59C22×C107—22no—
60C22×C107—21no—
61C22×C107—22no—
62C22×C107—21no—
63C22×C107—44no—
64C22×C107C2×Q1612yes—
65C22×C107C2×Q1614yes—
66C22×C107C22×D411yescharacteristic
67C4×C107—21no—
68C4×C107—22no—
69C4×C107—44no—
70C4×C107—44no—
71C4×C107H(5,𝔽2)12yes—
72C2×C107—24no—
73C2×C107—22no—
74C2×C107#53411yescharacteristic
75C2×C107C22×Q1611yescharacteristic
76C2×C107#57511yescharacteristic
77#3189C10711yesmaximal, characteristic, direct product factor, Sylow
78C107#318911yescharacteristic, direct product factor, Sylow
79C2×C22⋊Q8C2×C10712yes—
80#484C2×C10714yescomplemented
81#467C2×C10714yescomplemented
82#451C2×C10714yescomplemented
83C2×C22⋊C8C2×C10711yescharacteristic
84C22×Q8C22×C10712yes—
85C23×C4C22×C10711yescharacteristic
86C2×Q16C22×C10714yescomplemented
87C22×C8C22×C10712yes—
88C22⋊Q8—22no—
89C22⋊Q8—22no—
90C22⋊Q8C22×C10714yes—
91C22⋊Q8C22×C10714yes—
92C2×C4⋊C4—22no—
93C2×C4⋊C4C22×C10712yes—
94C2×C22⋊C4—22no—
95#107C22×C10714yescomplemented
96#103C22×C10718yescomplemented
97C22⋊C8C22×C10714yes—
98C24D4×C10711yescharacteristic
99C2×Q8—22no—
100C2×Q8—44no—
101C2×Q8C23×C10714yes—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—42no—
105C22×C4D4×C10712yes—
106C22×C4D4×C10711yescharacteristic
107C22×C4C23×C10712yes—
108C22×C4C23×C10711yescharacteristic
109Q16—44no—
110C2×C8—42no—
111C2×C8C23×C10714yes—
112C4⋊C4—24no—
113C4⋊C4—24no—
114C4⋊C4—22no—
115C4⋊C4C23×C10714yes—
116C22⋊C4—24no—
117C22⋊C4—24no—
118C23—41no—
119C23—41no—
120C23Q16×C10714yescomplemented
121C23C2×D4×C10711yescharacteristic
122C23C2×D4×C10712yes—
123Q8—28no—
124Q8—44no—
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—24no—
129C2×C4—41no—
130C2×C4—42no—
131C2×C4—44no—
132C2×C4—44no—
133C2×C4C2×D4×C10711yescharacteristic
134C2×C4C2×D4×C10712yes—
135C2×C4C24×C10711yescharacteristic
136C8—24no—
137C22—22no—
138C22—21no—
139C22—22no—
140C22—21no—
141C22—44no—
142C22C2×Q16×C10712yes—
143C22C2×Q16×C10714yes—
144C22C22×D4×C10711yescharacteristic
145C4—22no—
146C4—21no—
147C4—44no—
148C4—44no—
149C4H(5,𝔽2)×C10712yes—
150C2—24no—
151C2—22no—
152C2#534×C10711yescharacteristic
153C2C22×Q16×C10711yescharacteristic
154C2#575×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C22×D4
commutator, Frattini, cosocleC2×C4C24×C107
prime radicalC24×C107D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. #484×C107C2semidirect
3. #467×C107C2semidirect
4. #451×C107C2semidirect
8. C2×Q16×C107C22semidirect
17. #107×C107C22semidirect
18. #103×C107C22semidirect
42. C23×C107Q16semidirect
77. #3189C107direct (N × H)
78. C107#3189direct (N × H)
80. #484C2×C107semidirect
81. #467C2×C107semidirect
82. #451C2×C107semidirect
86. C2×Q16C22×C107semidirect
95. #107C22×C107semidirect
96. #103C22×C107semidirect
120. C23Q16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1072
#484×C1072
#467×C1072
#451×C1072
C2×C22⋊C8×C1072
#3189107