Finite Group Databasebeta

← C31×#7340 #21464099

Subgroups — C31×#7340 #21464099

Order 7936.

452 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C31×#1783C211yesmaximal, characteristic
2C31×#1320C212yesmaximal, complemented
3C23×D4×C31C411yescharacteristic
4C2×C31×#100—22no—
5C31×#407C411yescharacteristic
6C31×#407C2211yescharacteristic
7C31×#349—22no—
8C25×C31C812yes—
9C22×D4×C31—21no—
10C22×D4×C31—21no—
11C22×D4×C31—41no—
12C22×D4×C31—41no—
13C22×D4×C31—44no—
14C23×C4×C31C2×C411yescharacteristic
15C2×M16×C31—21no—
16C2×M16×C31D412yes—
17C31×M32—42no—
18C31×#100—44no—
19C31×C22⋊C8—41no—
20C31×C22⋊C8—41no—
21C24×C31—22no—
22C24×C31—42no—
23C24×C31—44no—
24C24×C31—84no—
25C24×C31C2×C811yescharacteristic
26C2×D4×C31—24no—
27C2×D4×C31—42no—
28C2×D4×C31—42no—
29C2×D4×C31—44no—
30C2×D4×C31—48no—
31C2×D4×C31—44no—
32C2×D4×C31—44no—
33C2×D4×C31—41no—
34C2×D4×C31—41no—
35C22×C4×C31—21no—
36C22×C4×C31—21no—
37C22×C4×C31—42no—
38C22×C4×C31C22⋊C411yescharacteristic
39C22×C4×C31M1611yescharacteristic
40M16×C31—42no—
41M16×C31—42no—
42C2×C8×C31—22no—
43C2×C8×C31—41no—
44C16×C31—82no—
45#7340C3111yesmaximal, characteristic, direct product factor, Sylow
46C23×C31—21no—
47C23×C31—24no—
48C23×C31—41no—
49C23×C31—42no—
50C23×C31—42no—
51C23×C31—44no—
52C23×C31—44no—
53C23×C31—42no—
54C23×C31—84no—
55C23×C31—84no—
56C23×C31—88no—
57C23×C31—84no—
58C23×C31—88no—
59C23×C31C22⋊C811yescharacteristic
60D4×C31—44no—
61D4×C31—48no—
62D4×C31—44no—
63C2×C4×C31—22no—
64C2×C4×C31—21no—
65C2×C4×C31—42no—
66C2×C4×C31—42no—
67C2×C4×C31—41no—
68C2×C4×C31#9911yescharacteristic
69C2×C4×C31#10011yescharacteristic
70C8×C31—42no—
71C8×C31—81no—
72#1783C2×C3111yescharacteristic
73#1320C2×C3112yescomplemented
74C22×C31—22no—
75C22×C31—21no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31—42no—
79C22×C31—42no—
80C22×C31—41no—
81C22×C31—44no—
82C22×C31—84no—
83C22×C31—84no—
84C22×C31—88no—
85C22×C31—84no—
86C22×C31—88no—
87C22×C31#32311yescharacteristic
88C4×C31—21no—
89C4×C31—41no—
90C4×C31AΣL(1,𝔽16)12yes—
91C23×D4C4×C3111yescharacteristic
92C2×#100—22no—
93#407C4×C3111yescharacteristic
94#407C22×C3111yescharacteristic
95#349—22no—
96C2×C31—21no—
97C2×C31—42no—
98C2×C31—41no—
99C2×C31—84no—
100C2×C31#131611yescharacteristic
101C25C8×C3112yes—
102C22×D4—21no—
103C22×D4—21no—
104C22×D4—41no—
105C22×D4—41no—
106C22×D4—44no—
107C23×C4C2×C4×C3111yescharacteristic
108C2×M16—21no—
109C2×M16D4×C3112yes—
110M32—42no—
111#100—44no—
112C22⋊C8—41no—
113C22⋊C8—41no—
114C31#734011yescharacteristic, direct product factor, Sylow
115C24—22no—
116C24—42no—
117C24—44no—
118C24—84no—
119C24C2×C8×C3111yescharacteristic
120C2×D4—24no—
121C2×D4—42no—
122C2×D4—42no—
123C2×D4—44no—
124C2×D4—48no—
125C2×D4—44no—
126C2×D4—44no—
127C2×D4—41no—
128C2×D4—41no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—42no—
132C22×C4C22⋊C4×C3111yescharacteristic
133C22×C4M16×C3111yescharacteristic
134M16—42no—
135M16—42no—
136C2×C8—22no—
137C2×C8—41no—
138C16—82no—
139C23—21no—
140C23—24no—
141C23—41no—
142C23—42no—
143C23—42no—
144C23—44no—
145C23—44no—
146C23—42no—
147C23—84no—
148C23—84no—
149C23—88no—
150C23—84no—
151C23—88no—
152C23C31×C22⋊C811yescharacteristic
153D4—44no—
154D4—48no—
155D4—44no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4C31×#9911yescharacteristic
162C2×C4C31×#10011yescharacteristic
163C8—42no—
164C8—81no—
165C22—22no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—41no—
172C22—44no—
173C22—84no—
174C22—84no—
175C22—88no—
176C22—84no—
177C22—88no—
178C22C31×#32311yescharacteristic
179C4—21no—
180C4—41no—
181C4C31×AΣL(1,𝔽16)12yes—
182C2—21no—
183C2—42no—
184C2—41no—
185C2—84no—
186C2C31×#131611yescharacteristic
subgroupG/H
center, socleC2×C31#1316
commutatorC24C2×C8×C31
Frattini, cosocle#407C22×C31
prime radicalC23×D4×C31C4
LCSG ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#407 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1320C2semidirect
45. #7340C31direct (N × H)
73. #1320C2×C31semidirect
114. C31#7340direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17832
C31×#13202
#734031