Finite Group Databasebeta

← C31×#8101 #21464860

Subgroups — C31×#8101 #21464860

Order 7936.

2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 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
1C2×C31×#379C213yesmaximal
2C31×#1304C214yesmaximal, complemented
3C26×C31C2211yescharacteristic
4C22×C22⋊C4×C31—26no—
5C22×C22⋊C4×C31C416yescomplemented
6C31×#379—26no—
7C31×#379C416yescomplemented
8C31×#379C2216yes—
9C25×C31—412no—
10C25×C31C2×C413yes—
11C25×C31C2×C413yes—
12C25×C31D416yes—
13C25×C31Q812yes—
14C25×C31C2311yescharacteristic
15C23×C4×C31—26no—
16C2×C22⋊C4×C31—212no—
17C2×C22⋊C4×C31—26no—
18C2×C22⋊C4×C31—212no—
19C2×C22⋊C4×C31—424no—
20C2×C22⋊C4×C31—412no—
21C2×C22⋊C4×C31C2×C4112yescomplemented
22C24×C31—212no—
23C24×C31—224no—
24C24×C31—412no—
25C24×C31—412no—
26C24×C31—46no—
27C24×C31—412no—
28C24×C31—412no—
29C24×C31—412no—
30C24×C31—46no—
31C24×C31—464no—
32C24×C31C4213yes—
33C24×C31C4211yescharacteristic
34C24×C31C22⋊C413yes—
35C24×C31C22⋊C416yes—
36C24×C31C22⋊C413yes—
37C24×C31C4⋊C416yes—
38C24×C31C4⋊C416yes—
39C24×C31C22×C413yes—
40C24×C31C2×D413yes—
41C24×C31C2×Q811yescharacteristic
42C22×C4×C31—212no—
43C22×C4×C31—424no—
44C22×C4×C31—412no—
45C22⋊C4×C31—424no—
46C22⋊C4×C31—424no—
47C22⋊C4×C31—412no—
48C22⋊C4×C31—412no—
49#8101C3111yesmaximal, characteristic, direct product factor, Sylow
50C23×C31—212no—
51C23×C31—26no—
52C23×C31—212no—
53C23×C31—212no—
54C23×C31—212no—
55C23×C31—212no—
56C23×C31—212no—
57C23×C31—26no—
58C23×C31—212no—
59C23×C31—212no—
60C23×C31—43no—
61C23×C31—43no—
62C23×C31—46no—
63C23×C31—46no—
64C23×C31—46no—
65C23×C31—46no—
66C23×C31—46no—
67C23×C31—46no—
68C23×C31—43no—
69C23×C31—43no—
70C23×C31—448no—
71C23×C31—496no—
72C23×C31—448no—
73C23×C31—432no—
74C23×C31—416no—
75C23×C31#9512yes—
76C23×C31#9516yes—
77C23×C31#99112yes—
78C23×C31C2×C4211yescharacteristic
79C23×C31C2×C22⋊C413yes—
80C23×C31C2×C4⋊C413yes—
81C2×C4×C31—424no—
82C2×C4×C31—412no—
83C2×C4×C31—824no—
84C2×#379C2×C3113yes—
85#1304C2×C3114yescomplemented
86C22×C31—224no—
87C22×C31—26no—
88C22×C31—26no—
89C22×C31—26no—
90C22×C31—26no—
91C22×C31—23no—
92C22×C31—23no—
93C22×C31—26no—
94C22×C31—412no—
95C22×C31—412no—
96C22×C31—424no—
97C22×C31—412no—
98C22×C31—424no—
99C22×C31—412no—
100C22×C31—424no—
101C22×C31—44no—
102C22×C31—44no—
103C22×C31#342112yes—
104C22×C31C2×#9511yescharacteristic
105C22×C31C2×#9916yes—
106C4×C31—812no—
107C26C22×C3111yescharacteristic
108C22×C22⋊C4—26no—
109C22×C22⋊C4C4×C3116yescomplemented
110#379—26no—
111#379C4×C3116yescomplemented
112#379C22×C3116yes—
113C2×C31—26no—
114C2×C31—212no—
115C2×C31—42no—
116C2×C31—41no—
117C2×C31—43no—
118C2×C31C2×#34213yes—
119C25—412no—
120C25C2×C4×C3113yes—
121C25C2×C4×C3113yes—
122C25D4×C3116yes—
123C25Q8×C3112yes—
124C25C23×C3111yescharacteristic
125C23×C4—26no—
126C2×C22⋊C4—212no—
127C2×C22⋊C4—26no—
128C2×C22⋊C4—212no—
129C2×C22⋊C4—424no—
130C2×C22⋊C4—412no—
131C2×C22⋊C4C2×C4×C31112yescomplemented
132C31#810111yescharacteristic, direct product factor, Sylow
133C24—212no—
134C24—224no—
135C24—412no—
136C24—46no—
137C24—412no—
138C24—412no—
139C24—412no—
140C24—412no—
141C24—46no—
142C24—464no—
143C24C42×C3113yes—
144C24C42×C3111yescharacteristic
145C24C22⋊C4×C3113yes—
146C24C22⋊C4×C3116yes—
147C24C22⋊C4×C3113yes—
148C24C4⋊C4×C3116yes—
149C24C4⋊C4×C3116yes—
150C24C22×C4×C3113yes—
151C24C2×D4×C3113yes—
152C24C2×Q8×C3111yescharacteristic
153C22×C4—212no—
154C22×C4—424no—
155C22×C4—412no—
156C22⋊C4—424no—
157C22⋊C4—424no—
158C22⋊C4—412no—
159C22⋊C4—412no—
160C23—26no—
161C23—212no—
162C23—26no—
163C23—212no—
164C23—212no—
165C23—212no—
166C23—212no—
167C23—212no—
168C23—212no—
169C23—212no—
170C23—43no—
171C23—43no—
172C23—46no—
173C23—46no—
174C23—46no—
175C23—46no—
176C23—46no—
177C23—46no—
178C23—43no—
179C23—43no—
180C23—448no—
181C23—496no—
182C23—448no—
183C23—432no—
184C23—416no—
185C23C31×#9512yes—
186C23C31×#9516yes—
187C23C31×#99112yes—
188C23C2×C42×C3111yescharacteristic
189C23C2×C22⋊C4×C3113yes—
190C23C2×C4⋊C4×C3113yes—
191C2×C4—424no—
192C2×C4—412no—
193C2×C4—824no—
194C22—224no—
195C22—26no—
196C22—26no—
197C22—26no—
198C22—26no—
199C22—23no—
200C22—23no—
201C22—26no—
202C22—412no—
203C22—412no—
204C22—424no—
205C22—412no—
206C22—424no—
207C22—412no—
208C22—424no—
209C22—44no—
210C22—44no—
211C22C31×#342112yes—
212C22C2×C31×#9511yescharacteristic
213C22C2×C31×#9916yes—
214C4—812no—
215C2—26no—
216C2—212no—
217C2—42no—
218C2—41no—
219C2—43no—
220C2C2×C31×#34213yes—
subgroupG/H
center, socleC22×C31C2×#95
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C26×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1304C2semidirect
5. C22×C22⋊C4×C31C4semidirect
7. C31×#379C4semidirect
21. C2×C22⋊C4×C31C2×C4semidirect
49. #8101C31direct (N × H)
85. #1304C2×C31semidirect
109. C22×C22⋊C4C4×C31semidirect
111. #379C4×C31semidirect
131. C2×C22⋊C4C2×C4×C31semidirect
132. C31#8101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3792
C31×#13042
#810131