Finite Group Databasebeta

← C31×#7308 #21464067

Subgroups — C31×#7308 #21464067

Order 7936.

518 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 86 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×#1784C212yesmaximal
2C31×#1446C211yesmaximal, characteristic
3C23×Q8×C31C2211yescharacteristic
4C2×C31×#101—22no—
5C2×C31×#101C414yescomplemented
6C31×#407—22no—
7C2×C31×#95—22no—
8C2×C31×#95C412yes—
9C22×Q8×C31—42no—
10C22×Q8×C31—44no—
11C22×Q8×C31C2×C412yes—
12C22×Q8×C31D411yescharacteristic
13C22×Q8×C31Q811yescharacteristic
14C23×C4×C31—22no—
15C23×C4×C31C2×C411yescharacteristic
16C23×C4×C31D412yes—
17C2×M16×C31—24no—
18C31×#101—44no—
19C31×#101—44no—
20C31×C22⋊C8—44no—
21C31×#95—44no—
22C31×#95—42no—
23C24×C31C22⋊C411yescharacteristic
24C2×Q8×C31—24no—
25C2×Q8×C31—24no—
26C2×Q8×C31—42no—
27C2×Q8×C31—42no—
28C2×Q8×C31—41no—
29C2×Q8×C31—42no—
30C2×Q8×C31—41no—
31C2×Q8×C31—416no—
32C22×C4×C31—22no—
33C22×C4×C31—24no—
34C22×C4×C31—24no—
35C22×C4×C31—24no—
36C22×C4×C31—42no—
37C22×C4×C31—42no—
38C22×C4×C31—44no—
39C22×C4×C31—42no—
40C22×C4×C31—44no—
41C22×C4×C31—42no—
42C22×C4×C31C4211yescharacteristic
43C22×C4×C31C22⋊C412yes—
44C22×C4×C31C4⋊C411yescharacteristic
45C22×C4×C31C4⋊C412yes—
46M16×C31—44no—
47M16×C31—44no—
48C2×C8×C31—44no—
49#7308C3111yesmaximal, characteristic, direct product factor, Sylow
50C23×C31—22no—
51C23×C31—22no—
52C23×C31—22no—
53C23×C31#9511yescharacteristic
54C23×C31#9912yes—
55Q8×C31—44no—
56Q8×C31—48no—
57Q8×C31—44no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31—21no—
65C2×C4×C31—21no—
66C2×C4×C31—22no—
67C2×C4×C31—48no—
68C2×C4×C31—44no—
69C2×C4×C31—48no—
70C2×C4×C31—44no—
71C2×C4×C31—84no—
72C2×C4×C31—82no—
73C2×C4×C31—82no—
74C2×C4×C31#9914yes—
75C8×C31—84no—
76#1784C2×C3112yes—
77#1446C2×C3111yescharacteristic
78C22×C31—24no—
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—22no—
82C22×C31—22no—
83C22×C31—22no—
84C22×C31#34212yes—
85C22×C31#34211yescharacteristic
86C22×C31#35512yes—
87C22×C31#35612yes—
88C4×C31—24no—
89C4×C31—42no—
90C4×C31—41no—
91C4×C31—41no—
92C4×C31—84no—
93C23×Q8C22×C3111yescharacteristic
94C2×#101—22no—
95C2×#101C4×C3114yescomplemented
96#407—22no—
97C2×#95—22no—
98C2×#95C4×C3112yes—
99C2×C31—22no—
100C2×C31—22no—
101C2×C31—22no—
102C2×C31#130411yescharacteristic
103C2×C31#139412yes—
104C22×Q8—42no—
105C22×Q8—44no—
106C22×Q8C2×C4×C3112yes—
107C22×Q8D4×C3111yescharacteristic
108C22×Q8Q8×C3111yescharacteristic
109C23×C4—22no—
110C23×C4C2×C4×C3111yescharacteristic
111C23×C4D4×C3112yes—
112C2×M16—24no—
113#101—44no—
114#101—44no—
115C22⋊C8—44no—
116#95—42no—
117#95—44no—
118C31#730811yescharacteristic, direct product factor, Sylow
119C24C22⋊C4×C3111yescharacteristic
120C2×Q8—24no—
121C2×Q8—24no—
122C2×Q8—42no—
123C2×Q8—42no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—42no—
127C2×Q8—416no—
128C22×C4—22no—
129C22×C4—24no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—42no—
133C22×C4—42no—
134C22×C4—44no—
135C22×C4—42no—
136C22×C4—44no—
137C22×C4—42no—
138C22×C4C42×C3111yescharacteristic
139C22×C4C22⋊C4×C3112yes—
140C22×C4C4⋊C4×C3111yescharacteristic
141C22×C4C4⋊C4×C3112yes—
142M16—44no—
143M16—44no—
144C2×C8—44no—
145C23—22no—
146C23—22no—
147C23—22no—
148C23C31×#9511yescharacteristic
149C23C31×#9912yes—
150Q8—44no—
151Q8—48no—
152Q8—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—48no—
163C2×C4—44no—
164C2×C4—48no—
165C2×C4—44no—
166C2×C4—84no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4C31×#9914yes—
170C8—84no—
171C22—24no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22C31×#34212yes—
178C22C31×#34211yescharacteristic
179C22C31×#35512yes—
180C22C31×#35612yes—
181C4—24no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—84no—
186C2—22no—
187C2—22no—
188C2—22no—
189C2C31×#130411yescharacteristic
190C2C31×#139412yes—
subgroupG/H
center, socleC22×C31#342
commutatorC22×C4C42×C31
Frattini, cosocleC23×Q8C22×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C23×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C31×#101C4semidirect
49. #7308C31direct (N × H)
95. C2×#101C4×C31semidirect
118. C31#7308direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17842
C31×#14462
#730831