Finite Group Databasebeta

← C31×#8755 #21465514

Subgroups — C31×#8755 #21465514

Order 7936.

398 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2313C211yesmaximal, characteristic
2C31×#1821C212yesmaximal
3C31×#1306C214yesmaximal
4C22×C4⋊C4×C31C2211yescharacteristic
5C31×#407C2214yes—
6C31×#387—24no—
7C31×#381C2212yes—
8C31×#380C412yes—
9C4×C22⋊C4×C31C412yes—
10C31×#343—24no—
11C23×C4×C31C2×C411yescharacteristic
12C23×C4×C31C2×C411yescharacteristic
13C23×C4×C31C2311yescharacteristic
14C2×M16×C31—24no—
15C2×C4⋊C4×C31—24no—
16C2×C4⋊C4×C31—22no—
17C2×C4⋊C4×C31D414yes—
18C2×C22⋊C4×C31C2×C414yes—
19C2×C42×C31—22no—
20C31×C22⋊C8—28no—
21C31×#95—22no—
22C31×#95—22no—
23C31×#95—24no—
24C24×C31C22×C411yescharacteristic
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31—24no—
28C22×C4×C31—42no—
29C22×C4×C31—81no—
30C22×C4×C31—81no—
31C22×C4×C31C22⋊C412yes—
32C22×C4×C31C22⋊C412yes—
33C22×C4×C31C2×D412yes—
34C22×C4×C31#4114yes—
35M16×C31—48no—
36C2×C8×C31—44no—
37C4⋊C4×C31—28no—
38C4⋊C4×C31—82no—
39C22⋊C4×C31—44no—
40C42×C31—82no—
41#8755C3111yesmaximal, characteristic, direct product factor, Sylow
42C23×C31—22no—
43C23×C31—41no—
44C23×C31—41no—
45C23×C31C2×C22⋊C411yescharacteristic
46C23×C31#11712yes—
47C2×C4×C31—24no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—44no—
51C2×C4×C31—42no—
52C2×C4×C31—42no—
53C2×C4×C31—44no—
54C2×C4×C31—44no—
55C2×C4×C31—44no—
56C2×C4×C31—82no—
57C2×C4×C31—82no—
58C2×C4×C31#12314yes—
59C8×C31—84no—
60#2313C2×C3111yescharacteristic
61#1821C2×C3112yes—
62#1306C2×C3114yes—
63C22×C31—21no—
64C22×C31—21no—
65C22×C31—22no—
66C22×C31—22no—
67C22×C31—22no—
68C22×C31—44no—
69C22×C31#38111yescharacteristic
70C22×C31#41012yes—
71C4×C31—24no—
72C4×C31—42no—
73C4×C31—42no—
74C4×C31—84no—
75C22×C4⋊C4C22×C3111yescharacteristic
76#407C22×C3114yes—
77#387—24no—
78#381C22×C3112yes—
79#380C4×C3112yes—
80C4×C22⋊C4C4×C3112yes—
81#343—24no—
82C2×C31—22no—
83C2×C31—42no—
84C2×C31#182011yescharacteristic
85C2×C31#182911yescharacteristic
86C2×C31#183011yescharacteristic
87C23×C4C2×C4×C3111yescharacteristic
88C23×C4C2×C4×C3111yescharacteristic
89C23×C4C23×C3111yescharacteristic
90C2×M16—24no—
91C2×C4⋊C4—24no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4D4×C3114yes—
94C2×C22⋊C4C2×C4×C3114yes—
95C2×C42—22no—
96C22⋊C8—28no—
97#95—22no—
98#95—22no—
99#95—24no—
100C31#875511yescharacteristic, direct product factor, Sylow
101C24C22×C4×C3111yescharacteristic
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—24no—
105C22×C4—42no—
106C22×C4—81no—
107C22×C4—81no—
108C22×C4C22⋊C4×C3112yes—
109C22×C4C22⋊C4×C3112yes—
110C22×C4C2×D4×C3112yes—
111C22×C4#41×C3114yes—
112M16—48no—
113C2×C8—44no—
114C4⋊C4—28no—
115C4⋊C4—82no—
116C22⋊C4—44no—
117C42—82no—
118C23—22no—
119C23—41no—
120C23—41no—
121C23C2×C22⋊C4×C3111yescharacteristic
122C23C31×#11712yes—
123C2×C4—24no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—44no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—44no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4C31×#12314yes—
135C8—84no—
136C22—21no—
137C22—21no—
138C22—22no—
139C22—22no—
140C22—22no—
141C22—44no—
142C22C31×#38111yescharacteristic
143C22C31×#41012yes—
144C4—24no—
145C4—42no—
146C4—42no—
147C4—84no—
148C2—22no—
149C2—42no—
150C2C31×#182011yescharacteristic
151C2C31×#182911yescharacteristic
152C2C31×#183011yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
41. #8755C31direct (N × H)
100. C31#8755direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23132
C31×#18212
C31×#13062
#875531