Finite Group Databasebeta

← C31×#7348 #21464107

Subgroups — C31×#7348 #21464107

Order 7936.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1820C211yesmaximal, characteristic
2C31×#1317C212yesmaximal
3C2×C31×#117C411yescharacteristic
4C31×#381C411yescharacteristic
5C31×#381C2211yescharacteristic
6C31×#342—22no—
7C31×#323—22no—
8C23×C4×C31C2×C411yescharacteristic
9C31×#117—41no—
10C31×#117—41no—
11C2×C4⋊C4×C31—21no—
12C2×C22⋊C4×C31—21no—
13C2×C22⋊C4×C31—21no—
14C2×C22⋊C4×C31D412yes—
15C2×C42×C31C812yescomplemented
16C31×C22⋊C8—42no—
17C31×#95—41no—
18C31×#95—41no—
19C24×C31C22⋊C411yescharacteristic
20C22×C4×C31—21no—
21C22×C4×C31—21no—
22C22×C4×C31—22no—
23C22×C4×C31—22no—
24C22×C4×C31—42no—
25C22×C4×C31—41no—
26C22×C4×C31C2×C811yescharacteristic
27C22×C4×C31M1611yescharacteristic
28C2×C8×C31—82no—
29C4⋊C4×C31—42no—
30C22⋊C4×C31—41no—
31C22⋊C4×C31—41no—
32C22⋊C4×C31—42no—
33C22⋊C4×C31—42no—
34C42×C31—42no—
35#7348C3111yesmaximal, characteristic, direct product factor, Sylow
36C23×C31—22no—
37C23×C31—81no—
38C23×C31C22⋊C811yescharacteristic
39C23×C31#9911yescharacteristic
40C23×C31#10011yescharacteristic
41C2×C4×C31—21no—
42C2×C4×C31—21no—
43C2×C4×C31—42no—
44C2×C4×C31—42no—
45C2×C4×C31—41no—
46C2×C4×C31—41no—
47C2×C4×C31—42no—
48C2×C4×C31—42no—
49C2×C4×C31—82no—
50C2×C4×C31—82no—
51C2×C4×C31—81no—
52C2×C4×C31—82no—
53C8×C31—162no—
54#1820C2×C3111yescharacteristic
55#1317C2×C3112yes—
56C22×C31—21no—
57C22×C31—21no—
58C22×C31—41no—
59C22×C31—41no—
60C22×C31—41no—
61C22×C31—82no—
62C22×C31#32311yescharacteristic
63C22×C31#35212yes—
64C4×C31—41no—
65C4×C31—41no—
66C4×C31—82no—
67C4×C31—82no—
68C4×C31—161no—
69C2×#117C4×C3111yescharacteristic
70#381C4×C3111yescharacteristic
71#381C22×C3111yescharacteristic
72#342—22no—
73#323—22no—
74C2×C31—21no—
75C2×C31—22no—
76C2×C31—41no—
77C2×C31—41no—
78C2×C31#131711yescharacteristic
79C23×C4C2×C4×C3111yescharacteristic
80#117—41no—
81#117—41no—
82C2×C4⋊C4—21no—
83C2×C22⋊C4—21no—
84C2×C22⋊C4—21no—
85C2×C22⋊C4D4×C3112yes—
86C2×C42C8×C3112yescomplemented
87C22⋊C8—42no—
88#95—41no—
89#95—41no—
90C31#734811yescharacteristic, direct product factor, Sylow
91C24C22⋊C4×C3111yescharacteristic
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—42no—
97C22×C4—41no—
98C22×C4C2×C8×C3111yescharacteristic
99C22×C4M16×C3111yescharacteristic
100C2×C8—82no—
101C4⋊C4—42no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C22⋊C4—42no—
105C22⋊C4—42no—
106C42—42no—
107C23—22no—
108C23—81no—
109C23C31×C22⋊C811yescharacteristic
110C23C31×#9911yescharacteristic
111C23C31×#10011yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—82no—
121C2×C4—82no—
122C2×C4—81no—
123C2×C4—82no—
124C8—162no—
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22C31×#32311yescharacteristic
132C22C31×#35212yes—
133C4—41no—
134C4—41no—
135C4—82no—
136C4—82no—
137C4—161no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2C31×#131711yescharacteristic
subgroupG/H
center, socleC2×C31#1317
commutatorC22×C4C2×C8×C31
Frattini, cosocle#381C22×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C24×C31 ◁ C31×#381 ◁ G

Complements

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

NH ≅ G/Ntype
15. C2×C42×C31C8semidirect
35. #7348C31direct (N × H)
86. C2×C42C8×C31semidirect
90. C31#7348direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18202
C31×#13172
#734831