Finite Group Databasebeta

← C31×#7429 #21464188

Subgroups — C31×#7429 #21464188

Order 7936.

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

normal subgroups only

This group has 196 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×#2026C211yesmaximal, characteristic
2C31×#1394C211yesmaximal, characteristic
3C31×#1319C211yesmaximal, characteristic
4C2×C31×#125C411yescharacteristic
5C2×C31×#103—21no—
6C2×C31×#101—21no—
7C31×#391C2211yescharacteristic
8C31×#340—21no—
9C31×#336C411yescharacteristic
10C31×#324—21no—
11C22×Q8×C31D411yescharacteristic
12C2×M16×C31—41no—
13C22×C8×C31—21no—
14C31×#125—42no—
15C2×C4⋊C4×C31—21no—
16C2×C4⋊C4×C31—41no—
17C2×C4⋊C4×C31D411yescharacteristic
18C2×C42×C31C2×C411yescharacteristic
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—41no—
37C2×C8×C31—41no—
38C2×C8×C31—41no—
39C2×C8×C31—81no—
40C2×C8×C31—81no—
41C4⋊C4×C31—22no—
42C4⋊C4×C31—41no—
43C4⋊C4×C31—41no—
44C4⋊C4×C31—42no—
45C4⋊C4×C31—42no—
46C42×C31—41no—
47#7429C3111yesmaximal, characteristic, direct product factor, Sylow
48C23×C31#9911yescharacteristic
49Q8×C31—41no—
50Q8×C31—41no—
51Q8×C31—81no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
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—42no—
62C2×C4×C31—41no—
63C2×C4×C31—81no—
64C2×C4×C31—81no—
65C2×C4×C31—81no—
66C2×C4×C31#10311yescharacteristic
67C2×C4×C31#10411yescharacteristic
68C8×C31—81no—
69C8×C31—82no—
70C8×C31—161no—
71#2026C2×C3111yescharacteristic
72#1394C2×C3111yescharacteristic
73#1319C2×C3111yescharacteristic
74C22×C31—21no—
75C22×C31—21no—
76C22×C31#32811yescharacteristic
77C22×C31AΣL(1,𝔽16)11yescharacteristic
78C22×C31#35411yescharacteristic
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—41no—
82C4×C31—41no—
83C4×C31—81no—
84C4×C31—82no—
85C4×C31—81no—
86C2×#125C4×C3111yescharacteristic
87C2×#103—21no—
88C2×#101—21no—
89#391C22×C3111yescharacteristic
90#340—21no—
91#336C4×C3111yescharacteristic
92#324—21no—
93C2×C31—21no—
94C2×C31—21no—
95C2×C31#135111yescharacteristic
96C2×C31#141311yescharacteristic
97C2×C31#141411yescharacteristic
98C22×Q8D4×C3111yescharacteristic
99C2×M16—41no—
100C22×C8—21no—
101#125—42no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4D4×C3111yescharacteristic
105C2×C42C2×C4×C3111yescharacteristic
106#103—42no—
107#101—22no—
108#101—41no—
109C22⋊C8—41no—
110#95—41no—
111C31#742911yescharacteristic, direct product factor, Sylow
112C2×Q8—21no—
113C2×Q8—41no—
114C2×Q8—41no—
115C2×Q8SD16×C3111yescharacteristic
116C2×Q8Q16×C3111yescharacteristic
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—41no—
121C22×C4C22⋊C4×C3111yescharacteristic
122M16—42no—
123M16—81no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—81no—
128C2×C8—81no—
129C4⋊C4—22no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C42—41no—
135C23C31×#9911yescharacteristic
136Q8—41no—
137Q8—41no—
138Q8—81no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4C31×#10311yescharacteristic
154C2×C4C31×#10411yescharacteristic
155C8—81no—
156C8—82no—
157C8—161no—
158C22—21no—
159C22—21no—
160C22C31×#32811yescharacteristic
161C22C31×AΣL(1,𝔽16)11yescharacteristic
162C22C31×#35411yescharacteristic
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—81no—
168C4—82no—
169C4—81no—
170C2—21no—
171C2—21no—
172C2C31×#135111yescharacteristic
173C2C31×#141311yescharacteristic
174C2C31×#141411yescharacteristic
subgroupG/H
center, socleC22×C31#354
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
47. #7429C31direct (N × H)
111. C31#7429direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20262
C31×#13942
C31×#13192
#742931