Finite Group Databasebeta

← C31×#14673 #21471432

Subgroups — C31×#14673 #21471432

Order 7936.

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 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×#379C212yesmaximal
2C2×C31×#379C211yesmaximal, characteristic
3C31×#1439C2112yesmaximal, complemented
4C26×C31C2211yescharacteristic
5C22×C4⋊C4×C31C2214yescomplemented
6C22×C22⋊C4×C31C22112yes—
7C22×C22⋊C4×C31C2216yes—
8C31×#379—28no—
9C31×#379C418yescomplemented
10C2×C31×#95C22112yescomplemented
11C25×C31—46no—
12C25×C31—46no—
13C25×C31C2×C414yes—
14C25×C31D414yes—
15C25×C31Q814yes—
16C25×C31C2313yes—
17C23×C4×C31C2318yes—
18C23×C4×C31C2314yes—
19C2×C4⋊C4×C31—412no—
20C2×C22⋊C4×C31—224no—
21C2×C22⋊C4×C31—46no—
22C2×C22⋊C4×C31—46no—
23C2×C22⋊C4×C31—412no—
24C2×C22⋊C4×C31—412no—
25C2×C22⋊C4×C31C2×C4124yes—
26C31×#95—412no—
27C24×C31—26no—
28C24×C31—26no—
29C24×C31—212no—
30C24×C31—212no—
31C24×C31—424no—
32C24×C31—424no—
33C24×C31—412no—
34C24×C31—412no—
35C24×C31—448no—
36C24×C31—416no—
37C24×C31C4⋊C4116yescomplemented
38C24×C31C22×C416yes—
39C24×C31C2×D416yes—
40C24×C31C2×Q816yes—
41C24×C31C2411yescharacteristic
42C22×C4×C31—212no—
43C22×C4×C31—212no—
44C22×C4×C31—28no—
45C22×C4×C31—224no—
46C22×C4×C31—224no—
47C22×C4×C31C22×C418yes—
48C4⋊C4×C31—416no—
49C22⋊C4×C31—424no—
50C22⋊C4×C31—448no—
51#14673C3111yesmaximal, characteristic, direct product factor, Sylow
52C23×C31—212no—
53C23×C31—224no—
54C23×C31—224no—
55C23×C31—212no—
56C23×C31—26no—
57C23×C31—212no—
58C23×C31—26no—
59C23×C31—212no—
60C23×C31—448no—
61C23×C31—416no—
62C23×C31—448no—
63C23×C31—464no—
64C23×C31—464no—
65C23×C31—424no—
66C23×C31—412no—
67C23×C31—412no—
68C23×C31C2×C4⋊C4112yes—
69C23×C31C23×C411yescharacteristic
70C23×C31C22×D411yescharacteristic
71C23×C31C22×Q811yescharacteristic
72C23×C31H(5,𝔽2)16yes—
73C23×C31H(5,𝔽2)16yes—
74C2×C4×C31—224no—
75C2×C4×C31—412no—
76C2×C4×C31—44no—
77C2×C4×C31—424no—
78C2×C4×C31—424no—
79C2×C4×C31—48no—
80C2×#379C2×C3112yes—
81C2×#379C2×C3111yescharacteristic
82#1439C2×C31112yescomplemented
83C22×C31—212no—
84C22×C31—224no—
85C22×C31—464no—
86C22×C31—46no—
87C22×C31—46no—
88C22×C31—412no—
89C22×C31—424no—
90C22×C31—424no—
91C22×C31C22×C4⋊C411yescharacteristic
92C22×C31#51816yes—
93C22×C31#53416yes—
94C22×C31#54313yes—
95C22×C31#54313yes—
96C22×C31#560112yes—
97C22×C31H(3,𝔽4)14yes—
98C4×C31—48no—
99C4×C31—88no—
100C26C22×C3111yescharacteristic
101C22×C4⋊C4C22×C3114yescomplemented
102C22×C22⋊C4C22×C31112yes—
103C22×C22⋊C4C22×C3116yes—
104#379—28no—
105#379C4×C3118yescomplemented
106C2×#95C22×C31112yescomplemented
107C2×C31—412no—
108C2×C31#231513yes—
109C2×C31#237514yes—
110C2×C31#281214yes—
111C2×C31#284011yescharacteristic
112C2×C31#284213yes—
113C25—46no—
114C25—46no—
115C25C2×C4×C3114yes—
116C25D4×C3114yes—
117C25Q8×C3114yes—
118C25C23×C3113yes—
119C23×C4C23×C3118yes—
120C23×C4C23×C3114yes—
121C2×C4⋊C4—412no—
122C2×C22⋊C4—224no—
123C2×C22⋊C4—46no—
124C2×C22⋊C4—46no—
125C2×C22⋊C4—412no—
126C2×C22⋊C4—412no—
127C2×C22⋊C4C2×C4×C31124yes—
128#95—412no—
129C31#1467311yescharacteristic, direct product factor, Sylow
130C24—26no—
131C24—26no—
132C24—212no—
133C24—212no—
134C24—424no—
135C24—424no—
136C24—412no—
137C24—412no—
138C24—448no—
139C24—416no—
140C24C4⋊C4×C31116yescomplemented
141C24C22×C4×C3116yes—
142C24C2×D4×C3116yes—
143C24C2×Q8×C3116yes—
144C24C24×C3111yescharacteristic
145C22×C4—212no—
146C22×C4—212no—
147C22×C4—28no—
148C22×C4—224no—
149C22×C4—224no—
150C22×C4C22×C4×C3118yes—
151C4⋊C4—416no—
152C22⋊C4—424no—
153C22⋊C4—448no—
154C23—212no—
155C23—224no—
156C23—224no—
157C23—212no—
158C23—26no—
159C23—212no—
160C23—26no—
161C23—212no—
162C23—448no—
163C23—416no—
164C23—448no—
165C23—464no—
166C23—464no—
167C23—424no—
168C23—412no—
169C23—412no—
170C23C2×C4⋊C4×C31112yes—
171C23C23×C4×C3111yescharacteristic
172C23C22×D4×C3111yescharacteristic
173C23C22×Q8×C3111yescharacteristic
174C23C31×H(5,𝔽2)16yes—
175C23C31×H(5,𝔽2)16yes—
176C2×C4—224no—
177C2×C4—412no—
178C2×C4—44no—
179C2×C4—424no—
180C2×C4—424no—
181C2×C4—48no—
182C22—212no—
183C22—224no—
184C22—464no—
185C22—46no—
186C22—46no—
187C22—412no—
188C22—424no—
189C22—424no—
190C22C22×C4⋊C4×C3111yescharacteristic
191C22C31×#51816yes—
192C22C31×#53416yes—
193C22C31×#54313yes—
194C22C31×#54313yes—
195C22C31×#560112yes—
196C22C31×H(3,𝔽4)14yes—
197C4—48no—
198C4—88no—
199C2—412no—
200C2C31×#231513yes—
201C2C31×#237514yes—
202C2C31×#281214yes—
203C2C31×#284011yescharacteristic
204C2C31×#284213yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1439C2semidirect
5. C22×C4⋊C4×C31C22semidirect
9. C31×#379C4semidirect
10. C2×C31×#95C22semidirect
37. C24×C31C4⋊C4semidirect
51. #14673C31direct (N × H)
82. #1439C2×C31semidirect
101. C22×C4⋊C4C22×C31semidirect
105. #379C4×C31semidirect
106. C2×#95C22×C31semidirect
129. C31#14673direct (N × H)
140. C24C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3792
C31×#14392
#1467331