Finite Group Databasebeta

← C31×#7315 #21464074

Subgroups — C31×#7315 #21464074

Order 7936.

432 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 74 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×#1784C211yesmaximal, characteristic
3C23×Q8×C31C2211yescharacteristic
4C2×C31×#101—22no—
5C2×C31×#101—22no—
6C2×C31×#101C414yes—
7C31×#407—22no—
8C31×#407C412yes—
9C22×Q8×C31—42no—
10C22×Q8×C31—44no—
11C22×Q8×C31C2×C412yes—
12C22×Q8×C31D412yes—
13C23×C4×C31C2×C411yescharacteristic
14C23×C4×C31D411yescharacteristic
15C23×C4×C31Q811yescharacteristic
16C2×M16×C31—24no—
17C2×M16×C31—22no—
18C31×#101—44no—
19C31×#101—44no—
20C31×#101—44no—
21C31×C22⋊C8—44no—
22C31×C22⋊C8—42no—
23C24×C31C4⋊C411yescharacteristic
24C2×Q8×C31—24no—
25C2×Q8×C31—24no—
26C2×Q8×C31—24no—
27C2×Q8×C31—42no—
28C2×Q8×C31—42no—
29C2×Q8×C31—42no—
30C2×Q8×C31—416no—
31C22×C4×C31—22no—
32C22×C4×C31—24no—
33C22×C4×C31—42no—
34C22×C4×C31—41no—
35C22×C4×C31—42no—
36C22×C4×C31—41no—
37C22×C4×C31C4211yescharacteristic
38C22×C4×C31C22⋊C411yescharacteristic
39C22×C4×C31C22⋊C412yes—
40C22×C4×C31C4⋊C412yes—
41M16×C31—44no—
42M16×C31—44no—
43M16×C31—44no—
44C2×C8×C31—44no—
45C2×C8×C31—42no—
46#7315C3111yesmaximal, characteristic, direct product factor, Sylow
47C23×C31—21no—
48C23×C31—22no—
49C23×C31—42no—
50C23×C31#9511yescharacteristic
51Q8×C31—48no—
52Q8×C31—48no—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—21no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—44no—
62C2×C4×C31—44no—
63C2×C4×C31—44no—
64C2×C4×C31#9912yes—
65C2×C4×C31#9914yes—
66C8×C31—84no—
67C8×C31—82no—
68#1784C2×C3112yes—
69#1784C2×C3111yescharacteristic
70C22×C31—22no—
71C22×C31—24no—
72C22×C31—41no—
73C22×C31—41no—
74C22×C31—42no—
75C22×C31—41no—
76C22×C31#34212yes—
77C22×C31#34211yescharacteristic
78C4×C31—24no—
79C4×C31—22no—
80C4×C31—41no—
81C4×C31—42no—
82C23×Q8C22×C3111yescharacteristic
83C2×#101—22no—
84C2×#101—22no—
85C2×#101C4×C3114yes—
86#407—22no—
87#407C4×C3112yes—
88C2×C31—22no—
89C2×C31—21no—
90C2×C31—42no—
91C2×C31#130411yescharacteristic
92C22×Q8—42no—
93C22×Q8—44no—
94C22×Q8C2×C4×C3112yes—
95C22×Q8D4×C3112yes—
96C23×C4C2×C4×C3111yescharacteristic
97C23×C4D4×C3111yescharacteristic
98C23×C4Q8×C3111yescharacteristic
99C2×M16—24no—
100C2×M16—22no—
101#101—44no—
102#101—44no—
103#101—44no—
104C22⋊C8—44no—
105C22⋊C8—42no—
106C31#731511yescharacteristic, direct product factor, Sylow
107C24C4⋊C4×C3111yescharacteristic
108C2×Q8—24no—
109C2×Q8—24no—
110C2×Q8—24no—
111C2×Q8—42no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8—416no—
115C22×C4—22no—
116C22×C4—24no—
117C22×C4—42no—
118C22×C4—41no—
119C22×C4—42no—
120C22×C4—41no—
121C22×C4C42×C3111yescharacteristic
122C22×C4C22⋊C4×C3111yescharacteristic
123C22×C4C22⋊C4×C3112yes—
124C22×C4C4⋊C4×C3112yes—
125M16—44no—
126M16—44no—
127M16—44no—
128C2×C8—44no—
129C2×C8—42no—
130C23—21no—
131C23—22no—
132C23—42no—
133C23C31×#9511yescharacteristic
134Q8—48no—
135Q8—48no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—44no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4C31×#9912yes—
148C2×C4C31×#9914yes—
149C8—84no—
150C8—82no—
151C22—22no—
152C22—24no—
153C22—41no—
154C22—41no—
155C22—42no—
156C22—41no—
157C22C31×#34212yes—
158C22C31×#34211yescharacteristic
159C4—24no—
160C4—22no—
161C4—41no—
162C4—42no—
163C2—22no—
164C2—21no—
165C2—42no—
166C2C31×#130411yescharacteristic
subgroupG/H
center, socleC2×C31#1304
commutatorC22×C4C42×C31
Frattini, cosocleC23×Q8C22×C31
prime radicalC24×C31C4⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C23×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
46. #7315C31direct (N × H)
106. C31#7315direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17842
#731531