Finite Group Databasebeta

← C31×#7355 #21464114

Subgroups — C31×#7355 #21464114

Order 7936.

216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1956C211yesmaximal, characteristic
2C31×#1325C212yesmaximal
3C2×C31×C4⋊Q8C411yescharacteristic
4C2×C31×#103—22no—
5C2×C4×C8×C31C411yescharacteristic
6C31×#384C2211yescharacteristic
7C31×#324—22no—
8C22×Q8×C31—21no—
9C22×C8×C31—21no—
10C31×C4⋊Q8—21no—
11C31×C4⋊Q8—41no—
12C31×C4⋊Q8C812yescomplemented
13C2×C4⋊C4×C31—41no—
14C2×C4⋊C4×C31—41no—
15C2×C4⋊C4×C31D412yes—
16C2×C42×C31C2×C411yescharacteristic
17C31×#103—44no—
18C31×C22⋊C8—42no—
19C4×C8×C31—41no—
20C2×Q8×C31—22no—
21C2×Q8×C31—42no—
22C2×Q8×C31—42no—
23C2×Q8×C31—41no—
24C22×C4×C31—21no—
25C22×C4×C31—22no—
26C22×C4×C31—41no—
27C22×C4×C31C22⋊C411yescharacteristic
28C2×C8×C31—22no—
29C2×C8×C31—41no—
30C2×C8×C31—41no—
31C2×C8×C31—82no—
32C4⋊C4×C31—42no—
33C4⋊C4×C31—42no—
34C4⋊C4×C31—42no—
35C4⋊C4×C31—82no—
36C42×C31—21no—
37C42×C31C2×C811yescharacteristic
38C42×C31M1611yescharacteristic
39#7355C3111yesmaximal, characteristic, direct product factor, Sylow
40C23×C31#9911yescharacteristic
41Q8×C31—44no—
42Q8×C31—82no—
43C2×C4×C31—22no—
44C2×C4×C31—22no—
45C2×C4×C31—21no—
46C2×C4×C31—21no—
47C2×C4×C31—21no—
48C2×C4×C31—21no—
49C2×C4×C31—42no—
50C2×C4×C31—42no—
51C2×C4×C31—81no—
52C2×C4×C31—81no—
53C2×C4×C31—82no—
54C2×C4×C31C22⋊C811yescharacteristic
55C2×C4×C31#10011yescharacteristic
56C8×C31—42no—
57C8×C31—162no—
58#1956C2×C3111yescharacteristic
59#1325C2×C3112yes—
60C22×C31—21no—
61C22×C31—21no—
62C22×C31#32311yescharacteristic
63C22×C31#35311yescharacteristic
64C22×C31#35511yescharacteristic
65C4×C31—22no—
66C4×C31—22no—
67C4×C31—21no—
68C4×C31—21no—
69C4×C31—82no—
70C4×C31—82no—
71C2×C4⋊Q8C4×C3111yescharacteristic
72C2×#103—22no—
73C2×C4×C8C4×C3111yescharacteristic
74#384C22×C3111yescharacteristic
75#324—22no—
76C2×C31—21no—
77C2×C31—21no—
78C2×C31#131811yescharacteristic
79C2×C31#140911yescharacteristic
80C2×C31#141111yescharacteristic
81C22×Q8—21no—
82C22×C8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—41no—
85C4⋊Q8C8×C3112yescomplemented
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4D4×C3112yes—
89C2×C42C2×C4×C3111yescharacteristic
90#103—44no—
91C22⋊C8—42no—
92C4×C8—41no—
93C31#735511yescharacteristic, direct product factor, Sylow
94C2×Q8—22no—
95C2×Q8—42no—
96C2×Q8—42no—
97C2×Q8—41no—
98C22×C4—21no—
99C22×C4—22no—
100C22×C4—41no—
101C22×C4C22⋊C4×C3111yescharacteristic
102C2×C8—22no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—82no—
106C4⋊C4—42no—
107C4⋊C4—42no—
108C4⋊C4—42no—
109C4⋊C4—82no—
110C42—21no—
111C42C2×C8×C3111yescharacteristic
112C42M16×C3111yescharacteristic
113C23C31×#9911yescharacteristic
114Q8—44no—
115Q8—82no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—42no—
123C2×C4—42no—
124C2×C4—81no—
125C2×C4—81no—
126C2×C4—82no—
127C2×C4C31×C22⋊C811yescharacteristic
128C2×C4C31×#10011yescharacteristic
129C8—42no—
130C8—162no—
131C22—21no—
132C22—21no—
133C22C31×#32311yescharacteristic
134C22C31×#35311yescharacteristic
135C22C31×#35511yescharacteristic
136C4—22no—
137C4—22no—
138C4—21no—
139C4—21no—
140C4—82no—
141C4—82no—
142C2—21no—
143C2—21no—
144C2C31×#131811yescharacteristic
145C2C31×#140911yescharacteristic
146C2C31×#141111yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C2×C8×C31
Frattini, cosocle#384C22×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#384 ◁ G

Complements

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

NH ≅ G/Ntype
12. C31×C4⋊Q8C8semidirect
39. #7355C31direct (N × H)
85. C4⋊Q8C8×C31semidirect
93. C31#7355direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19562
C31×#13252
#735531