Finite Group Databasebeta

← C31×#8728 #21465487

Subgroups — C31×#8728 #21465487

Order 7936.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2285C211yesmaximal, characteristic
2C31×#1797C212yesmaximal
3C31×#1296C212yesmaximal, complemented
4C31×#1296C212yesmaximal, complemented
5C2×C31×#117C412yes—
6C22×C42×C31C2211yescharacteristic
7C2×C31×C4⋊C8C2214yes—
8C2×C31×C22⋊C8—22no—
9C31×#384C2211yescharacteristic
10C31×#384C2211yescharacteristic
11C31×#382C412yes—
12C31×#380—22no—
13C4×C4⋊C4×C31—22no—
14C31×#336—22no—
15C23×C4×C31C2×C411yescharacteristic
16C23×C4×C31D412yes—
17C22×C8×C31—24no—
18C31×#117—44no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—22no—
21C2×C4⋊C4×C31C2×C412yes—
22C2×C4⋊C4×C31C2×C412yes—
23C2×C22⋊C4×C31—22no—
24C2×C42×C31—24no—
25C2×C42×C31—22no—
26C2×C42×C31C2×C411yescharacteristic
27C2×C42×C31D412yes—
28C2×C42×C31C2311yescharacteristic
29C31×C4⋊C8—28no—
30C31×C22⋊C8—44no—
31C31×#95—24no—
32C24×C31C22⋊C411yescharacteristic
33C22×C4×C31—22no—
34C22×C4×C31—22no—
35C22×C4×C31—22no—
36C22×C4×C31—24no—
37C22×C4×C31—24no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31—22no—
41C22×C4×C31—22no—
42C22×C4×C31C22⋊C412yes—
43C22×C4×C31C22⋊C411yescharacteristic
44C22×C4×C31C22×C411yescharacteristic
45C22×C4×C31C2×D412yes—
46C2×C8×C31—44no—
47C2×C8×C31—44no—
48C2×C8×C31—44no—
49C4⋊C4×C31—42no—
50C4⋊C4×C31—42no—
51C4⋊C4×C31—44no—
52C4⋊C4×C31—42no—
53C4⋊C4×C31—42no—
54C22⋊C4×C31—44no—
55C42×C31—22no—
56C42×C31—24no—
57C42×C31—44no—
58C42×C31#4114yes—
59#8728C3111yesmaximal, characteristic, direct product factor, Sylow
60C23×C31—21no—
61C23×C31—21no—
62C23×C31—22no—
63C23×C31—22no—
64C23×C31#10112yes—
65C23×C31C2×C22⋊C411yescharacteristic
66C2×C4×C31—28no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—44no—
75C2×C4×C31—44no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—44no—
79C2×C4×C31—44no—
80C2×C4×C31#10012yes—
81C2×C4×C31#11712yes—
82C2×C4×C31#12314yes—
83C2×C4×C31#13514yes—
84C2×C4×C31AGL(1,ℤ/8)12yes—
85C2×C4×C31#13712yes—
86C8×C31—84no—
87#2285C2×C3111yescharacteristic
88#1797C2×C3112yes—
89#1296C2×C3112yescomplemented
90#1296C2×C3112yescomplemented
91C22×C31—24no—
92C22×C31—22no—
93C22×C31—41no—
94C22×C31—41no—
95C22×C31—42no—
96C22×C31#38111yescharacteristic
97C22×C31C2×#10011yescharacteristic
98C22×C31C2×#10111yescharacteristic
99C22×C31#41612yes—
100C22×C31#41712yes—
101C4×C31—22no—
102C4×C31—22no—
103C4×C31—42no—
104C4×C31—82no—
105C4×C31—82no—
106C4×C31#48214yes—
107C4×C31#48514yes—
108C2×#117C4×C3112yes—
109C22×C42C22×C3111yescharacteristic
110C2×C4⋊C8C22×C3114yes—
111C2×C22⋊C8—22no—
112#384C22×C3111yescharacteristic
113#384C22×C3111yescharacteristic
114#382C4×C3112yes—
115#380—22no—
116C4×C4⋊C4—22no—
117#336—22no—
118C2×C31—42no—
119C2×C31#154311yescharacteristic
120C2×C31#155212yes—
121C2×C31#156011yescharacteristic
122C2×C31#182111yescharacteristic
123C2×C31#182512yes—
124C23×C4C2×C4×C3111yescharacteristic
125C23×C4D4×C3112yes—
126C22×C8—24no—
127#117—44no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4C2×C4×C3112yes—
131C2×C4⋊C4C2×C4×C3112yes—
132C2×C22⋊C4—22no—
133C2×C42—24no—
134C2×C42—22no—
135C2×C42C2×C4×C3111yescharacteristic
136C2×C42D4×C3112yes—
137C2×C42C23×C3111yescharacteristic
138C4⋊C8—28no—
139C22⋊C8—44no—
140#95—24no—
141C31#872811yescharacteristic, direct product factor, Sylow
142C24C22⋊C4×C3111yescharacteristic
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4—24no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4C22⋊C4×C3112yes—
153C22×C4C22⋊C4×C3111yescharacteristic
154C22×C4C22×C4×C3111yescharacteristic
155C22×C4C2×D4×C3112yes—
156C2×C8—44no—
157C2×C8—44no—
158C2×C8—44no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C22⋊C4—44no—
165C42—22no—
166C42—24no—
167C42—44no—
168C42#41×C3114yes—
169C23—21no—
170C23—22no—
171C23—22no—
172C23—21no—
173C23C31×#10112yes—
174C23C2×C22⋊C4×C3111yescharacteristic
175C2×C4—28no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—44no—
189C2×C4C31×#10012yes—
190C2×C4C31×#11712yes—
191C2×C4C31×#12314yes—
192C2×C4C31×#13514yes—
193C2×C4C31×AGL(1,ℤ/8)12yes—
194C2×C4C31×#13712yes—
195C8—84no—
196C22—24no—
197C22—22no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22C31×#38111yescharacteristic
202C22C2×C31×#10011yescharacteristic
203C22C2×C31×#10111yescharacteristic
204C22C31×#41612yes—
205C22C31×#41712yes—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—82no—
210C4—82no—
211C4C31×#48214yes—
212C4C31×#48514yes—
213C2—42no—
214C2C31×#154311yescharacteristic
215C2C31×#155212yes—
216C2C31×#156011yescharacteristic
217C2C31×#182111yescharacteristic
218C2C31×#182512yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1296C2semidirect
4. C31×#1296C2semidirect
59. #8728C31direct (N × H)
89. #1296C2×C31semidirect
90. #1296C2×C31semidirect
141. C31#8728direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22852
C31×#17972
C31×#12962
#872831