Finite Group Databasebeta

← C2×#484×C157 #34097448

Subgroups — C2×#484×C157 #34097448

Order 20096.

460 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 216 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×C157C211yesmaximal, characteristic
2C22×C4⋊C4×C157C211yesmaximal, characteristic
3#484×C157C218yesmaximal, direct product factor
4C2×#107×C157C212yesmaximal, complemented
5C2×#103×C157C212yesmaximal, complemented
6C2×C22⋊C8×C157C211yesmaximal, characteristic
7C22×Q8×C157C2211yescharacteristic
8C23×C4×C157—21no—
9C23×C4×C157C2211yescharacteristic
10C22×C8×C157C2212yes—
11C22⋊Q8×C157—22no—
12C22⋊Q8×C157C2214yes—
13C2×C4⋊C4×C157—22no—
14C2×C4⋊C4×C157—21no—
15C2×C4⋊C4×C157—21no—
16C2×C4⋊C4×C157C2212yes—
17C2×C4⋊C4×C157C2211yescharacteristic
18C2×C4⋊C4×C157C2214yes—
19C2×C22⋊C4×C157—21no—
20#107×C157C2218yescomplemented
21#103×C157C2218yescomplemented
22C22⋊C8×C157C2214yes—
23C24×C157D411yescharacteristic
24C2×Q8×C157—21no—
25C2×Q8×C157—24no—
26C2×Q8×C157C2312yes—
27C22×C4×C157—24no—
28C22×C4×C157—24no—
29C22×C4×C157—21no—
30C22×C4×C157—21no—
31C22×C4×C157—22no—
32C22×C4×C157—44no—
33C22×C4×C157D412yes—
34C22×C4×C157D411yescharacteristic
35C22×C4×C157C2312yes—
36C22×C4×C157C2311yescharacteristic
37C2×C8×C157—24no—
38C2×C8×C157C2314yes—
39C4⋊C4×C157—24no—
40C4⋊C4×C157—22no—
41C4⋊C4×C157—24no—
42C4⋊C4×C157—21no—
43C4⋊C4×C157C2314yes—
44C4⋊C4×C157C2312yes—
45C22⋊C4×C157—24no—
46C23×C157—22no—
47C23×C157—22no—
48C23×C157Q1614yes—
49C23×C157C2×D412yes—
50C23×C157C2×D411yescharacteristic
51Q8×C157—24no—
52Q8×C157—42no—
53C2×C4×C157—22no—
54C2×C4×C157—24no—
55C2×C4×C157—24no—
56C2×C4×C157—22no—
57C2×C4×C157—22no—
58C2×C4×C157—24no—
59C2×C4×C157—48no—
60C2×C4×C157—42no—
61C2×C4×C157—42no—
62C2×C4×C157—44no—
63C2×C4×C157C2×D412yes—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157#4114yes—
66C2×C4×C157C2411yescharacteristic
67C8×C157—24no—
68C22×C157—22no—
69C22×C157—22no—
70C22×C157—28no—
71C22×C157#12312yes—
72C22×C157C2×Q1614yes—
73C22×C157C2×Q1612yes—
74C22×C157AGL(1,ℤ/8)12yes—
75C22×C157C22×D411yescharacteristic
76C4×C157—22no—
77C4×C157—42no—
78C4×C157—42no—
79C4×C157—44no—
80C4×C157#12312yes—
81C4×C157C2×#4112yes—
82C2×C157—24no—
83C2×C157#48414yesdirect product factor
84C2×C157C2×#12311yescharacteristic
85C2×C157C22×Q1611yescharacteristic
86C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
87C157C2×#48411yescharacteristic, direct product factor, Sylow
88C2×#484C15711yesmaximal, characteristic, direct product factor, Sylow
89C2×C22⋊Q8C2×C15711yescharacteristic
90C22×C4⋊C4C2×C15711yescharacteristic
91#484C2×C15718yesdirect product factor
92C2×#107C2×C15712yescomplemented
93C2×#103C2×C15712yescomplemented
94C2×C22⋊C8C2×C15711yescharacteristic
95C22×Q8C22×C15711yescharacteristic
96C23×C4—21no—
97C23×C4C22×C15711yescharacteristic
98C22×C8C22×C15712yes—
99C22⋊Q8—22no—
100C22⋊Q8C22×C15714yes—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4C22×C15712yes—
105C2×C4⋊C4C22×C15714yes—
106C2×C4⋊C4C22×C15711yescharacteristic
107C2×C22⋊C4—21no—
108#107C22×C15718yescomplemented
109#103C22×C15718yescomplemented
110C22⋊C8C22×C15714yes—
111C24D4×C15711yescharacteristic
112C2×Q8—21no—
113C2×Q8—24no—
114C2×Q8C23×C15712yes—
115C22×C4—24no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—24no—
119C22×C4—22no—
120C22×C4—44no—
121C22×C4D4×C15711yescharacteristic
122C22×C4D4×C15712yes—
123C22×C4C23×C15712yes—
124C22×C4C23×C15711yescharacteristic
125C2×C8—24no—
126C2×C8C23×C15714yes—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—24no—
130C4⋊C4—21no—
131C4⋊C4C23×C15714yes—
132C4⋊C4C23×C15712yes—
133C22⋊C4—24no—
134C23—22no—
135C23—22no—
136C23Q16×C15714yes—
137C23C2×D4×C15712yes—
138C23C2×D4×C15711yescharacteristic
139Q8—24no—
140Q8—42no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—48no—
148C2×C4—42no—
149C2×C4—44no—
150C2×C4—42no—
151C2×C4C2×D4×C15712yes—
152C2×C4C2×D4×C15711yescharacteristic
153C2×C4#41×C15714yes—
154C2×C4C24×C15711yescharacteristic
155C8—24no—
156C22—28no—
157C22—22no—
158C22—22no—
159C22#123×C15712yes—
160C22C2×Q16×C15714yes—
161C22C2×Q16×C15712yes—
162C22AGL(1,ℤ/8)×C15712yes—
163C22C22×D4×C15711yescharacteristic
164C4—22no—
165C4—42no—
166C4—44no—
167C4—42no—
168C4#123×C15712yes—
169C4C2×#41×C15712yes—
170C2—24no—
171C2#484×C15714yesdirect product factor
172C2C2×#123×C15711yescharacteristic
173C2C22×Q16×C15711yescharacteristic
174C2C2×AGL(1,ℤ/8)×C15711yescharacteristic
subgroupG/H
center, socleC23×C157C2×D4
commutator, Frattini, cosocleC2×C4C24×C157
prime radicalC24×C157D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C157 ◁ C23×C4×C157 ◁ G

Complements

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

NH ≅ G/Ntype
3. #484×C157C2direct (N × H)
4. C2×#107×C157C2semidirect
5. C2×#103×C157C2semidirect
20. #107×C157C22semidirect
21. #103×C157C22semidirect
83. C2×C157#484direct (N × H)
87. C157C2×#484direct (N × H)
88. C2×#484C157direct (N × H)
91. #484C2×C157direct (N × H)
92. C2×#107C2×C157semidirect
93. C2×#103C2×C157semidirect
108. #107C22×C157semidirect
109. #103C22×C157semidirect
171. C2#484×C157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1572
C22×C4⋊C4×C1572
#484×C1572
C2×#107×C1572
C2×#103×C1572
C2×C22⋊C8×C1572
C2×#484157