Finite Group Databasebeta

← C31×#8721 #21465480

Subgroups — C31×#8721 #21465480

Order 7936.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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×#1749C212yesmaximal
3C31×#1295C214yesmaximal, complemented
4C2×C31×#117C412yes—
5C22×C42×C31C2211yescharacteristic
6C2×C31×C22⋊C8—22no—
7C2×C31×#97C2214yes—
8C31×#384C411yescharacteristic
9C31×#384C411yescharacteristic
10C31×#382C2212yes—
11C31×#380—22no—
12C4×C4⋊C4×C31—22no—
13C31×#336—22no—
14C23×C4×C31C2×C411yescharacteristic
15C23×C4×C31D412yes—
16C22×C8×C31—24no—
17C31×#117—44no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31C2×C412yes—
21C2×C4⋊C4×C31C2×C412yes—
22C2×C22⋊C4×C31—22no—
23C2×C42×C31—24no—
24C2×C42×C31—22no—
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31D412yes—
27C2×C42×C31C2311yescharacteristic
28C31×C22⋊C8—28no—
29C31×#97—28no—
30C31×#95—24no—
31C24×C31C22⋊C411yescharacteristic
32C22×C4×C31—22no—
33C22×C4×C31—22no—
34C22×C4×C31—22no—
35C22×C4×C31—24no—
36C22×C4×C31—24no—
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31—42no—
40C22×C4×C31C22⋊C411yescharacteristic
41C22×C4×C31C22⋊C412yes—
42C22×C4×C31C22×C411yescharacteristic
43C22×C4×C31C2×D412yes—
44C2×C8×C31—28no—
45C2×C8×C31—44no—
46C2×C8×C31—44no—
47C4⋊C4×C31—44no—
48C4⋊C4×C31—42no—
49C4⋊C4×C31—42no—
50C4⋊C4×C31—44no—
51C22⋊C4×C31—44no—
52C42×C31—22no—
53C42×C31—24no—
54C42×C31—44no—
55C42×C31#4114yes—
56#8721C3111yesmaximal, characteristic, direct product factor, Sylow
57C23×C31—21no—
58C23×C31—21no—
59C23×C31—22no—
60C23×C31—22no—
61C23×C31#10112yes—
62C23×C31C2×C22⋊C411yescharacteristic
63C2×C4×C31—28no—
64C2×C4×C31—21no—
65C2×C4×C31—22no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—48no—
73C2×C4×C31—42no—
74C2×C4×C31—42no—
75C2×C4×C31—44no—
76C2×C4×C31—44no—
77C2×C4×C31#10012yes—
78C2×C4×C31#10414yes—
79C2×C4×C31#11712yes—
80C2×C4×C31#12314yes—
81C8×C31—48no—
82#2285C2×C3111yescharacteristic
83#1749C2×C3112yes—
84#1295C2×C3114yescomplemented
85C22×C31—22no—
86C22×C31—24no—
87C22×C31—41no—
88C22×C31—42no—
89C22×C31—41no—
90C22×C31#38111yescharacteristic
91C22×C31C2×#10011yescharacteristic
92C22×C31C2×#10111yescharacteristic
93C22×C31C2×#10412yes—
94C22×C31#42112yes—
95C4×C31—22no—
96C4×C31—22no—
97C4×C31—24no—
98C4×C31—24no—
99C4×C31—82no—
100C4×C31—82no—
101C2×#117C4×C3112yes—
102C22×C42C22×C3111yescharacteristic
103C2×C22⋊C8—22no—
104C2×#97C22×C3114yes—
105#384C4×C3111yescharacteristic
106#384C4×C3111yescharacteristic
107#382C22×C3112yes—
108#380—22no—
109C4×C4⋊C4—22no—
110#336—22no—
111C2×C31—42no—
112C2×C31#152511yescharacteristic
113C2×C31#153112yes—
114C2×C31#153611yescharacteristic
115C2×C31#182111yescharacteristic
116C2×C31#182612yes—
117C23×C4C2×C4×C3111yescharacteristic
118C23×C4D4×C3112yes—
119C22×C8—24no—
120#117—44no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4C2×C4×C3112yes—
124C2×C4⋊C4C2×C4×C3112yes—
125C2×C22⋊C4—22no—
126C2×C42—24no—
127C2×C42—22no—
128C2×C42C2×C4×C3111yescharacteristic
129C2×C42D4×C3112yes—
130C2×C42C23×C3111yescharacteristic
131C22⋊C8—28no—
132#97—28no—
133#95—24no—
134C31#872111yescharacteristic, direct product factor, Sylow
135C24C22⋊C4×C3111yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4C22⋊C4×C3111yescharacteristic
145C22×C4C22⋊C4×C3112yes—
146C22×C4C22×C4×C3111yescharacteristic
147C22×C4C2×D4×C3112yes—
148C2×C8—28no—
149C2×C8—44no—
150C2×C8—44no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C22⋊C4—44no—
156C42—22no—
157C42—24no—
158C42—44no—
159C42#41×C3114yes—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23C31×#10112yes—
165C23C2×C22⋊C4×C3111yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4C31×#10012yes—
181C2×C4C31×#10414yes—
182C2×C4C31×#11712yes—
183C2×C4C31×#12314yes—
184C8—48no—
185C22—22no—
186C22—24no—
187C22—42no—
188C22—41no—
189C22—41no—
190C22C31×#38111yescharacteristic
191C22C2×C31×#10011yescharacteristic
192C22C2×C31×#10111yescharacteristic
193C22C2×C31×#10412yes—
194C22C31×#42112yes—
195C4—22no—
196C4—22no—
197C4—24no—
198C4—24no—
199C4—82no—
200C4—82no—
201C2—42no—
202C2C31×#152511yescharacteristic
203C2C31×#153112yes—
204C2C31×#153611yescharacteristic
205C2C31×#182111yescharacteristic
206C2C31×#182612yes—
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×#1295C2semidirect
56. #8721C31direct (N × H)
84. #1295C2×C31semidirect
134. C31#8721direct (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×#17492
C31×#12952
#872131