Finite Group Databasebeta

← C31×#7650 #21464409

Subgroups — C31×#7650 #21464409

Order 7936.

384 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C4×C31×#125C211yesmaximal, characteristic
2C31×#1839C212yesmaximal
3C31×#1271C214yesmaximal
4C2×C31×#125C411yescharacteristic
5C31×#389C2212yes—
6C31×#387—22no—
7C31×#382C411yescharacteristic
8C4×C4⋊C4×C31—22no—
9C4×C4⋊C4×C31C412yes—
10C43×C31C2211yescharacteristic
11C31×#336—22no—
12C31×#336—22no—
13C31×#336C2214yes—
14C22×C8×C31—24no—
15C31×#125—24no—
16C2×C4⋊C4×C31—22no—
17C2×C4⋊C4×C31—22no—
18C2×C4⋊C4×C31C2×C412yes—
19C2×C4⋊C4×C31C2×C412yes—
20C2×C42×C31—22no—
21C2×C42×C31C2×C411yescharacteristic
22C2×C42×C31C2×C411yescharacteristic
23C2×C42×C31D412yes—
24C2×C42×C31D412yes—
25C2×C42×C31C2311yescharacteristic
26C31×#95—22no—
27C31×#95—22no—
28C31×#95—22no—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31C22⋊C411yescharacteristic
32C22×C4×C31C22⋊C412yes—
33C22×C4×C31C22⋊C411yescharacteristic
34C22×C4×C31C22×C411yescharacteristic
35C22×C4×C31C2×D412yes—
36C2×C8×C31—44no—
37C2×C8×C31—44no—
38C2×C8×C31—44no—
39C4⋊C4×C31—28no—
40C4⋊C4×C31—22no—
41C4⋊C4×C31—42no—
42C4⋊C4×C31—44no—
43C4⋊C4×C31M1614yes—
44C42×C31—22no—
45C42×C31—22no—
46C42×C31—24no—
47C42×C31—42no—
48C42×C31—41no—
49C42×C31—44no—
50#7650C3111yesmaximal, characteristic, direct product factor, Sylow
51C23×C31C2×C22⋊C411yescharacteristic
52C2×C4×C31—21no—
53C2×C4×C31—22no—
54C2×C4×C31—21no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—24no—
59C2×C4×C31—21no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31—42no—
67C2×C4×C31—42no—
68C2×C4×C31#10112yes—
69C2×C4×C31C2×M1612yes—
70C2×C4×C31#13514yes—
71C8×C31—84no—
72C4×#125C2×C3111yescharacteristic
73#1839C2×C3112yes—
74#1271C2×C3114yes—
75C22×C31#40711yescharacteristic
76C22×C31#41011yescharacteristic
77C22×C31C2×#10111yescharacteristic
78C22×C31#41612yes—
79C22×C31#42112yes—
80C4×C31—22no—
81C4×C31—24no—
82C4×C31—22no—
83C4×C31—41no—
84C4×C31—42no—
85C4×C31—44no—
86C4×C31—82no—
87C2×#125C4×C3111yescharacteristic
88#389C22×C3112yes—
89#387—22no—
90#382C4×C3111yescharacteristic
91C4×C4⋊C4—22no—
92C4×C4⋊C4C4×C3112yes—
93C43C22×C3111yescharacteristic
94#336—22no—
95#336—22no—
96#336C22×C3114yes—
97C2×C31#146711yescharacteristic
98C2×C31#148812yes—
99C2×C31#152112yes—
100C2×C31#153411yescharacteristic
101C2×C31#154411yescharacteristic
102C22×C8—24no—
103#125—24no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4C2×C4×C3112yes—
107C2×C4⋊C4C2×C4×C3112yes—
108C2×C42—22no—
109C2×C42C2×C4×C3111yescharacteristic
110C2×C42C2×C4×C3111yescharacteristic
111C2×C42D4×C3112yes—
112C2×C42D4×C3112yes—
113C2×C42C23×C3111yescharacteristic
114#95—22no—
115#95—22no—
116#95—22no—
117C31#765011yescharacteristic, direct product factor, Sylow
118C22×C4—22no—
119C22×C4—22no—
120C22×C4C22⋊C4×C3111yescharacteristic
121C22×C4C22⋊C4×C3112yes—
122C22×C4C22⋊C4×C3111yescharacteristic
123C22×C4C22×C4×C3111yescharacteristic
124C22×C4C2×D4×C3112yes—
125C2×C8—44no—
126C2×C8—44no—
127C2×C8—44no—
128C4⋊C4—28no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—44no—
132C4⋊C4M16×C3114yes—
133C42—22no—
134C42—22no—
135C42—24no—
136C42—42no—
137C42—41no—
138C42—44no—
139C23C2×C22⋊C4×C3111yescharacteristic
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4C31×#10112yes—
157C2×C4C2×M16×C3112yes—
158C2×C4C31×#13514yes—
159C8—84no—
160C22C31×#40711yescharacteristic
161C22C31×#41011yescharacteristic
162C22C2×C31×#10111yescharacteristic
163C22C31×#41612yes—
164C22C31×#42112yes—
165C4—22no—
166C4—24no—
167C4—22no—
168C4—41no—
169C4—42no—
170C4—44no—
171C4—82no—
172C2C31×#146711yescharacteristic
173C2C31×#148812yes—
174C2C31×#152112yes—
175C2C31×#153411yescharacteristic
176C2C31×#154411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
50. #7650C31direct (N × H)
117. C31#7650direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1252
C31×#18392
C31×#12712
#765031