Finite Group Databasebeta

← C107×#3080 #28333763

Subgroups — C107×#3080 #28333763

Order 13696.

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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×#125×C107C211yesmaximal, characteristic, complemented
2C4×#41×C107C211yesmaximal, characteristic
3#479×C107C214yesmaximal, complemented
4#478×C107C214yesmaximal, complemented
5#428×C107C212yesmaximal, complemented
6#423×C107C211yesmaximal, characteristic, complemented
7#417×C107C212yesmaximal
8C2×#41×C107C2211yescharacteristic
9C2×M16×C107C2212yes—
10#125×C107—21no—
11#125×C107—21no—
12#125×C107C2214yes—
13C4×Q8×C107C2212yes—
14C4×D4×C107—22no—
15C4×D4×C107C2212yes—
16#117×C107—21no—
17#117×C107C2211yescharacteristic
18C2×C4⋊C4×C107—22no—
19C2×C4⋊C4×C107C2212yes—
20C2×C42×C107—21no—
21C2×C42×C107C2211yescharacteristic
22#107×C107C2214yes—
23#106×C107C2214yes—
24C4⋊C8×C107C2214yes—
25#103×C107C2214yes—
26#102×C107C2214yes—
27#41×C107—22no—
28#41×C107Q814yes—
29C2×Q8×C107C2311yescharacteristic
30C2×D4×C107—21no—
31C2×D4×C107C2311yescharacteristic
32C22×C4×C107—21no—
33C22×C4×C107—22no—
34C22×C4×C107—22no—
35C22×C4×C107D412yes—
36C22×C4×C107C2311yescharacteristic
37M16×C107—24no—
38C2×C8×C107C2314yes—
39C4⋊C4×C107—24no—
40C4⋊C4×C107—24no—
41C4⋊C4×C107—22no—
42C4⋊C4×C107—22no—
43C4⋊C4×C107C2314yes—
44C4⋊C4×C107C2312yes—
45C22⋊C4×C107—21no—
46C22⋊C4×C107—22no—
47C42×C107—21no—
48C42×C107—22no—
49C42×C107D411yescharacteristic
50C42×C107D411yescharacteristic
51C42×C107C2312yes—
52C23×C107—21no—
53C23×C107C2×D411yescharacteristic
54Q8×C107—21no—
55Q8×C107C2×Q812yes—
56D4×C107—24no—
57D4×C107—21no—
58D4×C107C2×Q812yes—
59C2×C4×C107—21no—
60C2×C4×C107—24no—
61C2×C4×C107—22no—
62C2×C4×C107—24no—
63C2×C4×C107—42no—
64C2×C4×C107—44no—
65C2×C4×C107—44no—
66C2×C4×C107C2×D412yes—
67C2×C4×C107C2×D412yes—
68C2×C4×C107C2×D411yescharacteristic
69C2×C4×C107C2×Q812yes—
70C2×C4×C107#4112yes—
71C2×C4×C107C2411yescharacteristic
72C8×C107—24no—
73C22×C107—22no—
74C22×C107—22no—
75C22×C107—42no—
76C22×C107C22⋊Q812yes—
77C22×C107C22×D411yescharacteristic
78C4×C107—22no—
79C4×C107—22no—
80C4×C107—22no—
81C4×C107—42no—
82C4×C107—44no—
83C4×C107C22⋊Q812yes—
84C4×C107C22×Q811yescharacteristic
85C4×C107C2×#4111yescharacteristic
86C2×C107—22no—
87C2×C107—42no—
88C2×C107C2×C22⋊Q811yescharacteristic
89C2×C107#57512yes—
90#3080C10711yesmaximal, characteristic, direct product factor, Sylow
91C107#308011yescharacteristic, direct product factor, Sylow
92C2×#125C2×C10711yescharacteristic, complemented
93C4×#41C2×C10711yescharacteristic
94#479C2×C10714yescomplemented
95#478C2×C10714yescomplemented
96#428C2×C10712yescomplemented
97#423C2×C10711yescharacteristic, complemented
98#417C2×C10712yes—
99C2×#41C22×C10711yescharacteristic
100C2×M16C22×C10712yes—
101#125—21no—
102#125—21no—
103#125C22×C10714yes—
104C4×Q8C22×C10712yes—
105C4×D4—22no—
106C4×D4C22×C10712yes—
107#117—21no—
108#117C22×C10711yescharacteristic
109C2×C4⋊C4—22no—
110C2×C4⋊C4C22×C10712yes—
111C2×C42—21no—
112C2×C42C22×C10711yescharacteristic
113#107C22×C10714yes—
114#106C22×C10714yes—
115C4⋊C8C22×C10714yes—
116#103C22×C10714yes—
117#102C22×C10714yes—
118#41—22no—
119#41Q8×C10714yes—
120C2×Q8C23×C10711yescharacteristic
121C2×D4—21no—
122C2×D4C23×C10711yescharacteristic
123C22×C4—21no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4D4×C10712yes—
127C22×C4C23×C10711yescharacteristic
128M16—24no—
129C2×C8C23×C10714yes—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4C23×C10714yes—
135C4⋊C4C23×C10712yes—
136C22⋊C4—21no—
137C22⋊C4—22no—
138C42—21no—
139C42—22no—
140C42D4×C10711yescharacteristic
141C42D4×C10711yescharacteristic
142C42C23×C10712yes—
143C23—21no—
144C23C2×D4×C10711yescharacteristic
145Q8—21no—
146Q8C2×Q8×C10712yes—
147D4—24no—
148D4—21no—
149D4C2×Q8×C10712yes—
150C2×C4—21no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—44no—
157C2×C4C2×D4×C10712yes—
158C2×C4C2×D4×C10712yes—
159C2×C4C2×D4×C10711yescharacteristic
160C2×C4C2×Q8×C10712yes—
161C2×C4#41×C10712yes—
162C2×C4C24×C10711yescharacteristic
163C8—24no—
164C22—22no—
165C22—22no—
166C22—42no—
167C22C22⋊Q8×C10712yes—
168C22C22×D4×C10711yescharacteristic
169C4—22no—
170C4—22no—
171C4—22no—
172C4—42no—
173C4—44no—
174C4C22⋊Q8×C10712yes—
175C4C22×Q8×C10711yescharacteristic
176C4C2×#41×C10711yescharacteristic
177C2—22no—
178C2—42no—
179C2C2×C22⋊Q8×C10711yescharacteristic
180C2#575×C10712yes—
subgroupG/H
center, socleC22×C107C22×D4
commutator, Frattini, cosocleC2×C4C24×C107
prime radicalC2×#41×C107C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#125×C107C2semidirect
3. #479×C107C2semidirect
4. #478×C107C2semidirect
5. #428×C107C2semidirect
6. #423×C107C2semidirect
90. #3080C107direct (N × H)
91. C107#3080direct (N × H)
92. C2×#125C2×C107semidirect
94. #479C2×C107semidirect
95. #478C2×C107semidirect
96. #428C2×C107semidirect
97. #423C2×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1072
C4×#41×C1072
#479×C1072
#478×C1072
#428×C1072
#423×C1072
#417×C1072
#3080107