Finite Group Databasebeta

← C31×#7432 #21464191

Subgroups — C31×#7432 #21464191

Order 7936.

210 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2091C211yesmaximal, characteristic
2C31×#1320C211yesmaximal, characteristic
3C31×#1297C211yesmaximal, characteristic
4C31×#430—21no—
5C31×#430C411yescharacteristic, complemented
6C31×#407—21no—
7C31×#407C2211yescharacteristic
8C4×C22⋊C4×C31—21no—
9C31×#349—21no—
10C31×#338C411yescharacteristic, complemented
11C23×C4×C31D411yescharacteristic
12C2×M16×C31—21no—
13C2×M16×C31—21no—
14C2×M16×C31C2×C411yescharacteristic
15C2×M16×C31D411yescharacteristic
16C2×C22⋊C4×C31—41no—
17C2×C42×C31—41no—
18C31×M32—41no—
19C31×#108—42no—
20C31×#108—41no—
21C31×C22⋊C8—41no—
22C31×C22⋊C8—42no—
23C31×#95—22no—
24C24×C31SD1611yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31—41no—
28C22×C4×C31—41no—
29C22×C4×C31—42no—
30C22×C4×C31C22⋊C411yescharacteristic
31C22×C4×C31Q1611yescharacteristic
32M16×C31—41no—
33M16×C31—41no—
34M16×C31—41no—
35M16×C31—41no—
36M16×C31—41no—
37M16×C31—41no—
38C2×C8×C31—22no—
39C2×C8×C31—21no—
40C2×C8×C31—21no—
41C2×C8×C31—41no—
42C22⋊C4×C31—44no—
43C42×C31—81no—
44C42×C31—81no—
45C16×C31—81no—
46#7432C3111yesmaximal, characteristic, direct product factor, Sylow
47C23×C31—21no—
48C23×C31—42no—
49C23×C31—41no—
50C23×C31#10311yescharacteristic
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31—44no—
58C2×C4×C31—81no—
59C2×C4×C31—82no—
60C2×C4×C31—82no—
61C2×C4×C31#9911yescharacteristic
62C2×C4×C31#10411yescharacteristic
63C8×C31—42no—
64C8×C31—41no—
65C8×C31—41no—
66C8×C31—81no—
67#2091C2×C3111yescharacteristic
68#1320C2×C3111yescharacteristic
69#1297C2×C3111yescharacteristic
70C22×C31—22no—
71C22×C31—21no—
72C22×C31—41no—
73C22×C31—41no—
74C22×C31—42no—
75C22×C31—41no—
76C22×C31—81no—
77C22×C31#32811yescharacteristic
78C4×C31—21no—
79C4×C31—41no—
80C4×C31—84no—
81C4×C31#35211yescharacteristic
82C4×C31#35311yescharacteristic
83#430—21no—
84#430C4×C3111yescharacteristic, complemented
85#407—21no—
86#407C22×C3111yescharacteristic
87C4×C22⋊C4—21no—
88#349—21no—
89#338C4×C3111yescharacteristic, complemented
90C2×C31—21no—
91C2×C31—42no—
92C2×C31—41no—
93C2×C31#135211yescharacteristic
94C23×C4D4×C3111yescharacteristic
95C2×M16—21no—
96C2×M16—21no—
97C2×M16C2×C4×C3111yescharacteristic
98C2×M16D4×C3111yescharacteristic
99C2×C22⋊C4—41no—
100C2×C42—41no—
101M32—41no—
102#108—41no—
103#108—42no—
104C22⋊C8—41no—
105C22⋊C8—42no—
106#95—22no—
107C31#743211yescharacteristic, direct product factor, Sylow
108C24SD16×C3111yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—41no—
112C22×C4—41no—
113C22×C4—42no—
114C22×C4C22⋊C4×C3111yescharacteristic
115C22×C4Q16×C3111yescharacteristic
116M16—41no—
117M16—41no—
118M16—41no—
119M16—41no—
120M16—41no—
121M16—41no—
122C2×C8—22no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—41no—
126C22⋊C4—44no—
127C42—81no—
128C42—81no—
129C16—81no—
130C23—21no—
131C23—42no—
132C23—41no—
133C23C31×#10311yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—44no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4C31×#9911yescharacteristic
145C2×C4C31×#10411yescharacteristic
146C8—42no—
147C8—41no—
148C8—41no—
149C8—81no—
150C22—22no—
151C22—21no—
152C22—41no—
153C22—41no—
154C22—42no—
155C22—41no—
156C22—81no—
157C22C31×#32811yescharacteristic
158C4—21no—
159C4—41no—
160C4—84no—
161C4C31×#35211yescharacteristic
162C4C31×#35311yescharacteristic
163C2—21no—
164C2—42no—
165C2—41no—
166C2C31×#135211yescharacteristic
subgroupG/H
centerC4×C31#353
commutatorC2×M16C2×C4×C31
Frattini, cosocle#407C22×C31
socleC2×C31#1352
prime radicalC24×C31SD16
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#407 ◁ G

Complements

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

NH ≅ G/Ntype
5. C31×#430C4semidirect
10. C31×#338C4semidirect
46. #7432C31direct (N × H)
84. #430C4×C31semidirect
89. #338C4×C31semidirect
107. C31#7432direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20912
C31×#13202
C31×#12972
#743231