Finite Group Databasebeta

← C131×#7354 #45693238

Subgroups — C131×#7354 #45693238

Order 33536.

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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#1957×C131C211yesmaximal, characteristic
2#1325×C131C212yesmaximal, complemented
3C2×#127×C131C411yescharacteristic
4C2×#102×C131—22no—
5C2×C4×C8×C131C411yescharacteristic
6#384×C131C2211yescharacteristic
7#324×C131—22no—
8C22×D4×C131—21no—
9C22×D4×C131—41no—
10C22×C8×C131—21no—
11#127×C131—21no—
12#127×C131—41no—
13#127×C131C812yescomplemented
14C2×C4⋊C4×C131—41no—
15C2×C4⋊C4×C131D412yes—
16C2×C42×C131C2×C411yescharacteristic
17#102×C131—44no—
18C22⋊C8×C131—42no—
19C4×C8×C131—41no—
20C24×C131—41no—
21C2×D4×C131—22no—
22C2×D4×C131—42no—
23C2×D4×C131—42no—
24C2×D4×C131—42no—
25C2×D4×C131—42no—
26C2×D4×C131—41no—
27C2×D4×C131—82no—
28C2×D4×C131—82no—
29C22×C4×C131—21no—
30C22×C4×C131—22no—
31C22×C4×C131C22⋊C411yescharacteristic
32C2×C8×C131—22no—
33C2×C8×C131—41no—
34C2×C8×C131—41no—
35C2×C8×C131—82no—
36C4⋊C4×C131—42no—
37C4⋊C4×C131—82no—
38C42×C131—21no—
39C42×C131C2×C811yescharacteristic
40C42×C131M1611yescharacteristic
41C23×C131—42no—
42C23×C131—82no—
43C23×C131—82no—
44C23×C131—81no—
45C23×C131—81no—
46C23×C131#9911yescharacteristic
47D4×C131—44no—
48D4×C131—82no—
49D4×C131—84no—
50D4×C131—84no—
51C2×C4×C131—22no—
52C2×C4×C131—22no—
53C2×C4×C131—21no—
54C2×C4×C131—21no—
55C2×C4×C131—21no—
56C2×C4×C131—21no—
57C2×C4×C131—42no—
58C2×C4×C131—82no—
59C2×C4×C131C22⋊C811yescharacteristic
60C2×C4×C131#10011yescharacteristic
61C8×C131—42no—
62C8×C131—162no—
63C22×C131—21no—
64C22×C131—21no—
65C22×C131—84no—
66C22×C131—82no—
67C22×C131—162no—
68C22×C131—161no—
69C22×C131—161no—
70C22×C131#32311yescharacteristic
71C22×C131#35311yescharacteristic
72C22×C131#35511yescharacteristic
73C4×C131—22no—
74C4×C131—22no—
75C4×C131—21no—
76C4×C131—21no—
77C4×C131—82no—
78C2×C131—21no—
79C2×C131—21no—
80C2×C131—162no—
81C2×C131#131811yescharacteristic
82C2×C131#140811yescharacteristic
83C2×C131#141011yescharacteristic
84#7354C13111yesmaximal, characteristic, direct product factor, Sylow
85C131#735411yescharacteristic, direct product factor, Sylow
86#1957C2×C13111yescharacteristic
87#1325C2×C13112yescomplemented
88C2×#127C4×C13111yescharacteristic
89C2×#102—22no—
90C2×C4×C8C4×C13111yescharacteristic
91#384C22×C13111yescharacteristic
92#324—22no—
93C22×D4—21no—
94C22×D4—41no—
95C22×C8—21no—
96#127—21no—
97#127—41no—
98#127C8×C13112yescomplemented
99C2×C4⋊C4—41no—
100C2×C4⋊C4D4×C13112yes—
101C2×C42C2×C4×C13111yescharacteristic
102#102—44no—
103C22⋊C8—42no—
104C4×C8—41no—
105C24—41no—
106C2×D4—22no—
107C2×D4—42no—
108C2×D4—42no—
109C2×D4—42no—
110C2×D4—42no—
111C2×D4—41no—
112C2×D4—82no—
113C2×D4—82no—
114C22×C4—21no—
115C22×C4—22no—
116C22×C4C22⋊C4×C13111yescharacteristic
117C2×C8—22no—
118C2×C8—41no—
119C2×C8—41no—
120C2×C8—82no—
121C4⋊C4—42no—
122C4⋊C4—82no—
123C42—21no—
124C42C2×C8×C13111yescharacteristic
125C42M16×C13111yescharacteristic
126C23—42no—
127C23—82no—
128C23—82no—
129C23—81no—
130C23—81no—
131C23#99×C13111yescharacteristic
132D4—44no—
133D4—82no—
134D4—84no—
135D4—84no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—42no—
143C2×C4—82no—
144C2×C4C22⋊C8×C13111yescharacteristic
145C2×C4#100×C13111yescharacteristic
146C8—42no—
147C8—162no—
148C22—21no—
149C22—21no—
150C22—84no—
151C22—82no—
152C22—162no—
153C22—161no—
154C22—161no—
155C22#323×C13111yescharacteristic
156C22#353×C13111yescharacteristic
157C22#355×C13111yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—21no—
162C4—82no—
163C2—21no—
164C2—21no—
165C2—162no—
166C2#1318×C13111yescharacteristic
167C2#1408×C13111yescharacteristic
168C2#1410×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#353
commutatorC42C2×C8×C131
Frattini, cosocle#384C22×C131
prime radicalC2×#127×C131C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #384×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1325×C131C2semidirect
13. #127×C131C8semidirect
84. #7354C131direct (N × H)
85. C131#7354direct (N × H)
87. #1325C2×C131semidirect
98. #127C8×C131semidirect

Maximal subgroups

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

subgroupindex
#1957×C1312
#1325×C1312
#7354131