Finite Group Databasebeta

← C31×#7734 #21464493

Subgroups — C31×#7734 #21464493

Order 7936.

872 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 872 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2679C211yesmaximal, characteristic, complemented
2C31×#2011C213yesmaximal, complemented
3C31×#1270C213yesmaximal, complemented
4C22×D8×C31—23no—
5C2×C31×#127C2211yescharacteristic, complemented
6C2×C31×#120—23no—
7C2×C31×#102—23no—
8C31×#394—23no—
9C31×#390C2213yes—
10C31×#336C2213yescomplemented
11C25×C31—21no—
12C22×D4×C31—23no—
13C22×D4×C31—23no—
14C22×D4×C31D413yes—
15C2×D8×C31—46no—
16C2×D8×C31—46no—
17C2×D8×C31—46no—
18C22×C8×C31—23no—
19C31×#127—42no—
20C31×#120—46no—
21C31×#120—46no—
22C2×C4⋊C4×C31D413yes—
23C2×C22⋊C4×C31—23no—
24C2×C22⋊C4×C31—26no—
25C2×C42×C31C2311yescharacteristic
26C31×#102—46no—
27C31×#95—21no—
28C24×C31—23no—
29C24×C31—46no—
30C24×C31—41no—
31C24×C31—83no—
32C24×C31—81no—
33C2×D4×C31—26no—
34C2×D4×C31—23no—
35C2×D4×C31—43no—
36C2×D4×C31—43no—
37C2×D4×C31—43no—
38C2×D4×C31—43no—
39C2×D4×C31—43no—
40C2×D4×C31—412no—
41C2×D4×C31—43no—
42C2×D4×C31—43no—
43C2×D4×C31—83no—
44C2×D4×C31D816yescomplemented
45C22×C4×C31—23no—
46C22×C4×C31C2×D413yes—
47D8×C31—424no—
48C2×C8×C31—26no—
49C2×C8×C31—43no—
50C2×C8×C31—43no—
51C4⋊C4×C31—43no—
52C22⋊C4×C31—46no—
53C22⋊C4×C31—46no—
54C22⋊C4×C31—46no—
55C42×C31—41no—
56#7734C3111yesmaximal, characteristic, direct product factor, Sylow
57C23×C31—26no—
58C23×C31—46no—
59C23×C31—43no—
60C23×C31—46no—
61C23×C31—43no—
62C23×C31—42no—
63C23×C31—812no—
64C23×C31—812no—
65C23×C31—84no—
66C23×C31—83no—
67C23×C31—83no—
68C23×C31#12011yescharacteristic
69D4×C31—46no—
70D4×C31—46no—
71D4×C31—46no—
72D4×C31—83no—
73D4×C31—83no—
74D4×C31—83no—
75D4×C31—812no—
76C2×C4×C31—23no—
77C2×C4×C31—23no—
78C2×C4×C31—46no—
79C2×C4×C31—43no—
80C2×C4×C31C2×D813yes—
81C2×C4×C31AGL(1,ℤ/8)13yes—
82C8×C31—46no—
83#2679C2×C3111yescharacteristic, complemented
84#2011C2×C3113yescomplemented
85#1270C2×C3113yescomplemented
86C22×C31—46no—
87C22×C31—412no—
88C22×C31—816no—
89C22×C31—86no—
90C22×C31—83no—
91C22×C31—83no—
92C22×C31—86no—
93C22×C31—163no—
94C22×C31—161no—
95C22×C31#44713yes—
96C22×C31#45313yes—
97C22×C31B(4,𝔽2)11yescharacteristic
98C4×C31—23no—
99C4×C31—23no—
100C4×C31—83no—
101C22×D8—23no—
102C2×#127C22×C3111yescharacteristic, complemented
103C2×#120—23no—
104C2×#102—23no—
105#394—23no—
106#390C22×C3113yes—
107#336C22×C3113yescomplemented
108C2×C31—86no—
109C2×C31—162no—
110C2×C31#159513yes—
111C2×C31#161913yes—
112C2×C31#165511yescharacteristic
113C25—21no—
114C22×D4—23no—
115C22×D4—23no—
116C22×D4D4×C3113yes—
117C2×D8—46no—
118C2×D8—46no—
119C2×D8—46no—
120C22×C8—23no—
121#127—42no—
122#120—46no—
123#120—46no—
124C2×C4⋊C4D4×C3113yes—
125C2×C22⋊C4—23no—
126C2×C22⋊C4—26no—
127C2×C42C23×C3111yescharacteristic
128#102—46no—
129#95—21no—
130C31#773411yescharacteristic, direct product factor, Sylow
131C24—23no—
132C24—46no—
133C24—41no—
134C24—83no—
135C24—81no—
136C2×D4—26no—
137C2×D4—23no—
138C2×D4—43no—
139C2×D4—43no—
140C2×D4—43no—
141C2×D4—43no—
142C2×D4—43no—
143C2×D4—412no—
144C2×D4—43no—
145C2×D4—43no—
146C2×D4—83no—
147C2×D4D8×C3116yescomplemented
148C22×C4—23no—
149C22×C4C2×D4×C3113yes—
150D8—424no—
151C2×C8—26no—
152C2×C8—43no—
153C2×C8—43no—
154C4⋊C4—43no—
155C22⋊C4—46no—
156C22⋊C4—46no—
157C22⋊C4—46no—
158C42—41no—
159C23—26no—
160C23—46no—
161C23—43no—
162C23—46no—
163C23—43no—
164C23—42no—
165C23—812no—
166C23—812no—
167C23—84no—
168C23—83no—
169C23—83no—
170C23C31×#12011yescharacteristic
171D4—46no—
172D4—46no—
173D4—46no—
174D4—83no—
175D4—83no—
176D4—83no—
177D4—812no—
178C2×C4—23no—
179C2×C4—23no—
180C2×C4—46no—
181C2×C4—43no—
182C2×C4C2×D8×C3113yes—
183C2×C4C31×AGL(1,ℤ/8)13yes—
184C8—46no—
185C22—46no—
186C22—412no—
187C22—816no—
188C22—86no—
189C22—83no—
190C22—83no—
191C22—86no—
192C22—163no—
193C22—161no—
194C22C31×#44713yes—
195C22C31×#45313yes—
196C22C31×B(4,𝔽2)11yescharacteristic
197C4—23no—
198C4—23no—
199C4—83no—
200C2—86no—
201C2—162no—
202C2C31×#159513yes—
203C2C31×#161913yes—
204C2C31×#165511yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2679C2semidirect
2. C31×#2011C2semidirect
3. C31×#1270C2semidirect
5. C2×C31×#127C22semidirect
10. C31×#336C22semidirect
44. C2×D4×C31D8semidirect
56. #7734C31direct (N × H)
83. #2679C2×C31semidirect
84. #2011C2×C31semidirect
85. #1270C2×C31semidirect
102. C2×#127C22×C31semidirect
107. #336C22×C31semidirect
130. C31#7734direct (N × H)
147. C2×D4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#26792
C31×#20112
C31×#12702
#773431