Finite Group Databasebeta

← C151×#7222 #50312147

Subgroups — C151×#7222 #50312147

Order 38656.

214 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 94 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#2163×C151C211yesmaximal, characteristic
2#1834×C151C211yesmaximal, characteristic
3#1568×C151C211yesmaximal, characteristic
4#432×C151—21no—
5C2×C4×C8×C151C2211yescharacteristic
6#384×C151—21no—
7C4⋊C16×C151—21no—
8C22⋊C16×C151—21no—
9#346×C151C412yescomplemented
10#340×C151—21no—
11#340×C151C412yes—
12#335×C151C412yescomplemented
13#334×C151—21no—
14C22×C8×C151C2×C411yescharacteristic
15C22×C8×C151D411yescharacteristic
16C2×C4⋊C4×C151—22no—
17C2×C4⋊C4×C151—41no—
18C2×C4⋊C4×C151—41no—
19C2×C42×C151D411yescharacteristic
20C2×C16×C151—22no—
21C4⋊C8×C151—22no—
22C22⋊C8×C151—41no—
23#97×C151—41no—
24C4×C8×C151C2×C411yescharacteristic
25C4×C8×C151C2×C411yescharacteristic
26C4×C8×C151D411yescharacteristic
27C4×C8×C151Q811yescharacteristic
28C22×C4×C151—42no—
29C22×C4×C151C22⋊C411yescharacteristic
30C22×C4×C151D811yescharacteristic
31C22×C4×C151SD1611yescharacteristic
32C2×C8×C151—41no—
33C2×C8×C151—41no—
34C2×C8×C151—42no—
35C2×C8×C151C4211yescharacteristic
36C2×C8×C151C22⋊C411yescharacteristic
37C2×C8×C151C4⋊C411yescharacteristic
38C2×C8×C151C4⋊C411yescharacteristic
39C4⋊C4×C151—42no—
40C4⋊C4×C151—42no—
41C4⋊C4×C151—82no—
42C4⋊C4×C151—82no—
43C42×C151C22⋊C411yescharacteristic
44C42×C151C4⋊C411yescharacteristic
45C42×C151SD1611yescharacteristic
46C42×C151Q1611yescharacteristic
47C16×C151—42no—
48C23×C151#10211yescharacteristic
49C2×C4×C151—21no—
50C2×C4×C151—21no—
51C2×C4×C151—21no—
52C2×C4×C151—21no—
53C2×C4×C151—22no—
54C2×C4×C151—82no—
55C2×C4×C151—82no—
56C2×C4×C151—82no—
57C2×C4×C151#9511yescharacteristic
58C2×C4×C151#10211yescharacteristic
59C2×C4×C151#10311yescharacteristic
60C2×C4×C151#10311yescharacteristic
61C2×C4×C151#10611yescharacteristic
62C2×C4×C151#10711yescharacteristic
63C8×C151—21no—
64C8×C151—21no—
65C8×C151—21no—
66C8×C151—21no—
67C8×C151—82no—
68C22×C151—21no—
69C22×C151—21no—
70C22×C151#34011yescharacteristic
71C22×C151#36111yescharacteristic
72C22×C151#36211yescharacteristic
73C4×C151—21no—
74C4×C151—21no—
75C4×C151—21no—
76C4×C151—21no—
77C4×C151—162no—
78C4×C151H(3,ℤ/4)11yescharacteristic
79C4×C151#34411yescharacteristic
80C4×C151#36012yes—
81C2×C151—21no—
82C2×C151—21no—
83C2×C151#128611yescharacteristic
84C2×C151#138611yescharacteristic
85C2×C151#138711yescharacteristic
86#7222C15111yesmaximal, characteristic, direct product factor, Sylow
87C151#722211yescharacteristic, direct product factor, Sylow
88#2163C2×C15111yescharacteristic
89#1834C2×C15111yescharacteristic
90#1568C2×C15111yescharacteristic
91#432—21no—
92C2×C4×C8C22×C15111yescharacteristic
93#384—21no—
94C4⋊C16—21no—
95C22⋊C16—21no—
96#346C4×C15112yescomplemented
97#340—21no—
98#340C4×C15112yes—
99#335C4×C15112yescomplemented
100#334—21no—
101C22×C8C2×C4×C15111yescharacteristic
102C22×C8D4×C15111yescharacteristic
103C2×C4⋊C4—22no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42D4×C15111yescharacteristic
107C2×C16—22no—
108C4⋊C8—22no—
109C22⋊C8—41no—
110#97—41no—
111C4×C8C2×C4×C15111yescharacteristic
112C4×C8C2×C4×C15111yescharacteristic
113C4×C8D4×C15111yescharacteristic
114C4×C8Q8×C15111yescharacteristic
115C22×C4—42no—
116C22×C4C22⋊C4×C15111yescharacteristic
117C22×C4D8×C15111yescharacteristic
118C22×C4SD16×C15111yescharacteristic
119C2×C8—41no—
120C2×C8—41no—
121C2×C8—42no—
122C2×C8C42×C15111yescharacteristic
123C2×C8C22⋊C4×C15111yescharacteristic
124C2×C8C4⋊C4×C15111yescharacteristic
125C2×C8C4⋊C4×C15111yescharacteristic
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—82no—
129C4⋊C4—82no—
130C42C22⋊C4×C15111yescharacteristic
131C42C4⋊C4×C15111yescharacteristic
132C42SD16×C15111yescharacteristic
133C42Q16×C15111yescharacteristic
134C16—42no—
135C23#102×C15111yescharacteristic
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—82no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4#95×C15111yescharacteristic
145C2×C4#102×C15111yescharacteristic
146C2×C4#103×C15111yescharacteristic
147C2×C4#103×C15111yescharacteristic
148C2×C4#106×C15111yescharacteristic
149C2×C4#107×C15111yescharacteristic
150C8—21no—
151C8—21no—
152C8—21no—
153C8—21no—
154C8—82no—
155C22—21no—
156C22—21no—
157C22#340×C15111yescharacteristic
158C22#361×C15111yescharacteristic
159C22#362×C15111yescharacteristic
160C4—21no—
161C4—21no—
162C4—21no—
163C4—21no—
164C4—162no—
165C4H(3,ℤ/4)×C15111yescharacteristic
166C4#344×C15111yescharacteristic
167C4#360×C15112yes—
168C2—21no—
169C2—21no—
170C2#1286×C15111yescharacteristic
171C2#1386×C15111yescharacteristic
172C2#1387×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#340
commutatorC2×C8C42×C151
Frattini, cosocleC2×C4×C8C22×C151
prime radicalC23×C151#102
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
9. #346×C151C4semidirect
12. #335×C151C4semidirect
86. #7222C151direct (N × H)
87. C151#7222direct (N × H)
96. #346C4×C151semidirect
99. #335C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2163×C1512
#1834×C1512
#1568×C1512
#7222151