Finite Group Databasebeta

← C31×#7319 #21464078

Subgroups — C31×#7319 #21464078

Order 7936.

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

normal subgroups only

This group has 456 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×#1785C212yesmaximal
2C31×#1782C211yesmaximal, characteristic
3C22×#41×C31C2211yescharacteristic
4C2×C31×#101—22no—
5C2×C31×#100—22no—
6C2×C31×#99—22no—
7C31×#407C414yescomplemented
8C31×#381C412yes—
9C2×#41×C31—42no—
10C2×#41×C31—44no—
11C22×Q8×C31D411yescharacteristic
12C22×D4×C31D412yes—
13C22×D4×C31Q811yescharacteristic
14C23×C4×C31C2×C412yes—
15C23×C4×C31C2×C411yescharacteristic
16C2×M16×C31—24no—
17C2×C22⋊C4×C31—22no—
18C31×#101—44no—
19C31×#100—44no—
20C31×#99—44no—
21C31×C22⋊C8—44no—
22C31×#95—42no—
23C24×C31C22⋊C411yescharacteristic
24C24×C31C4⋊C412yes—
25#41×C31—416no—
26C2×Q8×C31—24no—
27C2×Q8×C31—41no—
28C2×D4×C31—24no—
29C2×D4×C31—24no—
30C2×D4×C31—42no—
31C2×D4×C31—41no—
32C2×D4×C31—42no—
33C22×C4×C31—22no—
34C22×C4×C31—24no—
35C22×C4×C31—42no—
36C22×C4×C31—42no—
37C22×C4×C31—42no—
38C22×C4×C31—42no—
39C22×C4×C31C4211yescharacteristic
40C22×C4×C31C22⋊C412yes—
41C22×C4×C31C4⋊C411yescharacteristic
42M16×C31—44no—
43M16×C31—44no—
44C2×C8×C31—44no—
45C22⋊C4×C31—44no—
46#7319C3111yesmaximal, characteristic, direct product factor, Sylow
47C23×C31—22no—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31—22no—
51C23×C31—81no—
52C23×C31—82no—
53C23×C31#9511yescharacteristic
54C23×C31#9912yes—
55Q8×C31—44no—
56D4×C31—48no—
57D4×C31—44no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—21no—
61C2×C4×C31—22no—
62C2×C4×C31—21no—
63C2×C4×C31—22no—
64C2×C4×C31—48no—
65C2×C4×C31—44no—
66C2×C4×C31—82no—
67C2×C4×C31—84no—
68C2×C4×C31#9914yes—
69C8×C31—84no—
70#1785C2×C3112yes—
71#1782C2×C3111yescharacteristic
72C22×C31—22no—
73C22×C31—41no—
74C22×C31—42no—
75C22×C31—44no—
76C22×C31—42no—
77C22×C31—82no—
78C22×C31—82no—
79C22×C31—82no—
80C22×C31#34211yescharacteristic
81C22×C31#34212yes—
82C4×C31—24no—
83C4×C31—41no—
84C4×C31—41no—
85C4×C31—162no—
86C22×#41C22×C3111yescharacteristic
87C2×#101—22no—
88C2×#100—22no—
89C2×#99—22no—
90#407C4×C3114yescomplemented
91#381C4×C3112yes—
92C2×C31—21no—
93C2×C31—22no—
94C2×C31—42no—
95C2×C31—82no—
96C2×C31#130411yescharacteristic
97C2×#41—42no—
98C2×#41—44no—
99C22×Q8D4×C3111yescharacteristic
100C22×D4D4×C3112yes—
101C22×D4Q8×C3111yescharacteristic
102C23×C4C2×C4×C3112yes—
103C23×C4C2×C4×C3111yescharacteristic
104C2×M16—24no—
105C2×C22⋊C4—22no—
106#101—44no—
107#100—44no—
108#99—44no—
109C22⋊C8—44no—
110#95—42no—
111C31#731911yescharacteristic, direct product factor, Sylow
112C24C22⋊C4×C3111yescharacteristic
113C24C4⋊C4×C3112yes—
114#41—416no—
115C2×Q8—24no—
116C2×Q8—41no—
117C2×D4—24no—
118C2×D4—24no—
119C2×D4—42no—
120C2×D4—41no—
121C2×D4—42no—
122C22×C4—22no—
123C22×C4—24no—
124C22×C4—42no—
125C22×C4—42no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4C42×C3111yescharacteristic
129C22×C4C22⋊C4×C3112yes—
130C22×C4C4⋊C4×C3111yescharacteristic
131M16—44no—
132M16—44no—
133C2×C8—44no—
134C22⋊C4—44no—
135C23—22no—
136C23—22no—
137C23—22no—
138C23—22no—
139C23—81no—
140C23—82no—
141C23C31×#9511yescharacteristic
142C23C31×#9912yes—
143Q8—44no—
144D4—48no—
145D4—44no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—48no—
153C2×C4—44no—
154C2×C4—82no—
155C2×C4—84no—
156C2×C4C31×#9914yes—
157C8—84no—
158C22—22no—
159C22—41no—
160C22—42no—
161C22—44no—
162C22—42no—
163C22—82no—
164C22—82no—
165C22—82no—
166C22C31×#34211yescharacteristic
167C22C31×#34212yes—
168C4—24no—
169C4—41no—
170C4—41no—
171C4—162no—
172C2—21no—
173C2—22no—
174C2—42no—
175C2—82no—
176C2C31×#130411yescharacteristic
subgroupG/H
center, socleC2×C31#1304
commutatorC22×C4C42×C31
Frattini, cosocleC22×#41C22×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
7. C31×#407C4semidirect
46. #7319C31direct (N × H)
90. #407C4×C31semidirect
111. C31#7319direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17852
C31×#17822
#731931