Finite Group Databasebeta

← C31×#7437 #21464196

Subgroups — C31×#7437 #21464196

Order 7936.

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

normal subgroups only

This group has 194 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×#2096C211yesmaximal, characteristic
2C31×#1394C211yesmaximal, characteristic
3C31×#1319C211yesmaximal, characteristic
4C2×C31×#106—21no—
5C2×C31×#103—21no—
6C2×C31×#101—21no—
7C31×#391C2211yescharacteristic
8C31×#384C411yescharacteristic
9C31×#336C411yescharacteristic
10C31×#324—21no—
11C22×Q8×C31D411yescharacteristic
12C2×M16×C31—41no—
13C22×C8×C31—21no—
14C2×C4⋊C4×C31—21no—
15C2×C4⋊C4×C31—41no—
16C2×C4⋊C4×C31D411yescharacteristic
17C2×C42×C31C2×C411yescharacteristic
18C31×#106—42no—
19C31×#103—42no—
20C31×#101—22no—
21C31×#101—41no—
22C31×C22⋊C8—41no—
23C31×#95—41no—
24C2×Q8×C31—21no—
25C2×Q8×C31—41no—
26C2×Q8×C31—41no—
27C2×Q8×C31SD1611yescharacteristic
28C2×Q8×C31Q1611yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—41no—
33C22×C4×C31C22⋊C411yescharacteristic
34M16×C31—42no—
35M16×C31—81no—
36C2×C8×C31—22no—
37C2×C8×C31—41no—
38C2×C8×C31—41no—
39C2×C8×C31—81no—
40C2×C8×C31—81no—
41C4⋊C4×C31—41no—
42C4⋊C4×C31—41no—
43C4⋊C4×C31—41no—
44C4⋊C4×C31—82no—
45C42×C31—41no—
46#7437C3111yesmaximal, characteristic, direct product factor, Sylow
47C23×C31#9911yescharacteristic
48Q8×C31—41no—
49Q8×C31—41no—
50Q8×C31—81no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—22no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—41no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31—81no—
62C2×C4×C31—82no—
63C2×C4×C31—81no—
64C2×C4×C31#10311yescharacteristic
65C2×C4×C31#10411yescharacteristic
66C8×C31—42no—
67C8×C31—82no—
68C8×C31—161no—
69#2096C2×C3111yescharacteristic
70#1394C2×C3111yescharacteristic
71#1319C2×C3111yescharacteristic
72C22×C31—21no—
73C22×C31—21no—
74C22×C31#32811yescharacteristic
75C22×C31#35211yescharacteristic
76C22×C31#35311yescharacteristic
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—42no—
80C4×C31—41no—
81C4×C31—41no—
82C4×C31—81no—
83C4×C31—161no—
84C2×#106—21no—
85C2×#103—21no—
86C2×#101—21no—
87#391C22×C3111yescharacteristic
88#384C4×C3111yescharacteristic
89#336C4×C3111yescharacteristic
90#324—21no—
91C2×C31—21no—
92C2×C31—21no—
93C2×C31#135211yescharacteristic
94C2×C31#140711yescharacteristic
95C2×C31#141011yescharacteristic
96C22×Q8D4×C3111yescharacteristic
97C2×M16—41no—
98C22×C8—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4D4×C3111yescharacteristic
102C2×C42C2×C4×C3111yescharacteristic
103#106—42no—
104#103—42no—
105#101—22no—
106#101—41no—
107C22⋊C8—41no—
108#95—41no—
109C31#743711yescharacteristic, direct product factor, Sylow
110C2×Q8—21no—
111C2×Q8—41no—
112C2×Q8—41no—
113C2×Q8SD16×C3111yescharacteristic
114C2×Q8Q16×C3111yescharacteristic
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4C22⋊C4×C3111yescharacteristic
120M16—42no—
121M16—81no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—81no—
126C2×C8—81no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—82no—
131C42—41no—
132C23C31×#9911yescharacteristic
133Q8—41no—
134Q8—41no—
135Q8—81no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—82no—
148C2×C4—81no—
149C2×C4C31×#10311yescharacteristic
150C2×C4C31×#10411yescharacteristic
151C8—42no—
152C8—82no—
153C8—161no—
154C22—21no—
155C22—21no—
156C22C31×#32811yescharacteristic
157C22C31×#35211yescharacteristic
158C22C31×#35311yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—161no—
166C2—21no—
167C2—21no—
168C2C31×#135211yescharacteristic
169C2C31×#140711yescharacteristic
170C2C31×#141011yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC2×C42C2×C4×C31
Frattini, cosocle#391C22×C31
prime radicalC23×C31#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#391 ◁ G

Complements

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

NH ≅ G/Ntype
46. #7437C31direct (N × H)
109. C31#7437direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20962
C31×#13942
C31×#13192
#743731