Finite Group Databasebeta

← C31×#8541 #21465300

Subgroups — C31×#8541 #21465300

Order 7936.

2618 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 2618 conjugacy classes of subgroups — too many to draw. Only its 174 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
1C22×C31×#120C211yesmaximal, characteristic
2C31×#1781C216yesmaximal, complemented
3C26×C31C411yescharacteristic, complemented
4C23×D4×C31C2213yes—
5C2×C31×#120—212no—
6C22×C22⋊C4×C31C413yescomplemented
7C2×C31×#99—212no—
8C31×#379C2214yescomplemented
9C25×C31—26no—
10C25×C31—412no—
11C25×C31C2×C413yes—
12C25×C31C2311yescharacteristic
13C22×D4×C31—212no—
14C22×D4×C31—412no—
15C22×D4×C31D4112yes—
16C23×C4×C31C2×C413yes—
17C31×#120—232no—
18C2×C22⋊C4×C31—26no—
19C2×C22⋊C4×C31—212no—
20C2×C22⋊C4×C31—212no—
21C31×#99—424no—
22C24×C31—212no—
23C24×C31—26no—
24C24×C31—28no—
25C24×C31—46no—
26C24×C31—448no—
27C24×C31—412no—
28C24×C31—412no—
29C24×C31—464no—
30C24×C31—412no—
31C24×C31C22⋊C416yes—
32C24×C31C22×C411yescharacteristic
33C24×C31C2×D416yes—
34C2×D4×C31—224no—
35C2×D4×C31—224no—
36C2×D4×C31—412no—
37C2×D4×C31—448no—
38C22×C4×C31—26no—
39C22×C4×C31—46no—
40C22×C4×C31—44no—
41C22×C4×C31C22⋊C416yes—
42C22⋊C4×C31—224no—
43C22⋊C4×C31—424no—
44#8541C3111yesmaximal, characteristic, direct product factor, Sylow
45C23×C31—26no—
46C23×C31—224no—
47C23×C31—26no—
48C23×C31—26no—
49C23×C31—212no—
50C23×C31—412no—
51C23×C31—412no—
52C23×C31—448no—
53C23×C31—412no—
54C23×C31—448no—
55C23×C31—496no—
56C23×C31—496no—
57C23×C31—412no—
58C23×C31—88no—
59C23×C31#99112yescomplemented
60C23×C31C2×C22⋊C413yes—
61C23×C31#12014yes—
62D4×C31—448no—
63C2×C4×C31—26no—
64C2×C4×C31—212no—
65C2×C4×C31—412no—
66C2×C4×C31—812no—
67C22×#120C2×C3111yescharacteristic
68#1781C2×C3116yescomplemented
69C22×C31—28no—
70C22×C31—26no—
71C22×C31—212no—
72C22×C31—212no—
73C22×C31—412no—
74C22×C31—448no—
75C22×C31—412no—
76C22×C31—464no—
77C22×C31—412no—
78C22×C31—812no—
79C22×C31#37911yescharacteristic
80C22×C31C2×#9916yes—
81C4×C31—46no—
82C4×C31—164no—
83C26C4×C3111yescharacteristic, complemented
84C23×D4C22×C3113yes—
85C2×#120—212no—
86C22×C22⋊C4C4×C3113yescomplemented
87C2×#99—212no—
88#379C22×C3114yescomplemented
89C2×C31—26no—
90C2×C31—44no—
91C2×C31—412no—
92C2×C31#178113yes—
93C25—26no—
94C25—412no—
95C25C2×C4×C3113yes—
96C25C23×C3111yescharacteristic
97C22×D4—212no—
98C22×D4—412no—
99C22×D4D4×C31112yes—
100C23×C4C2×C4×C3113yes—
101#120—232no—
102C2×C22⋊C4—26no—
103C2×C22⋊C4—212no—
104C2×C22⋊C4—212no—
105#99—424no—
106C31#854111yescharacteristic, direct product factor, Sylow
107C24—212no—
108C24—26no—
109C24—28no—
110C24—46no—
111C24—412no—
112C24—448no—
113C24—412no—
114C24—464no—
115C24—412no—
116C24C22⋊C4×C3116yes—
117C24C22×C4×C3111yescharacteristic
118C24C2×D4×C3116yes—
119C2×D4—224no—
120C2×D4—224no—
121C2×D4—412no—
122C2×D4—448no—
123C22×C4—26no—
124C22×C4—46no—
125C22×C4—44no—
126C22×C4C22⋊C4×C3116yes—
127C22⋊C4—224no—
128C22⋊C4—424no—
129C23—26no—
130C23—224no—
131C23—26no—
132C23—26no—
133C23—212no—
134C23—412no—
135C23—412no—
136C23—448no—
137C23—412no—
138C23—448no—
139C23—496no—
140C23—496no—
141C23—412no—
142C23—88no—
143C23C31×#99112yescomplemented
144C23C2×C22⋊C4×C3113yes—
145C23C31×#12014yes—
146D4—448no—
147C2×C4—212no—
148C2×C4—26no—
149C2×C4—412no—
150C2×C4—812no—
151C22—28no—
152C22—26no—
153C22—212no—
154C22—212no—
155C22—412no—
156C22—448no—
157C22—412no—
158C22—464no—
159C22—412no—
160C22—812no—
161C22C31×#37911yescharacteristic
162C22C2×C31×#9916yes—
163C4—46no—
164C4—164no—
165C2—26no—
166C2—44no—
167C2—412no—
168C2C31×#178113yes—
subgroupG/H
center, socleC22×C31#379
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC22×C31×#120C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1781C2semidirect
3. C26×C31C4semidirect
6. C22×C22⋊C4×C31C4semidirect
8. C31×#379C22semidirect
44. #8541C31direct (N × H)
59. C23×C31#99semidirect
68. #1781C2×C31semidirect
83. C26C4×C31semidirect
86. C22×C22⋊C4C4×C31semidirect
88. #379C22×C31semidirect
106. C31#8541direct (N × H)
143. C23C31×#99semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C31×#17812
#854131