Finite Group Databasebeta

← C31×#8722 #21465481

Subgroups — C31×#8722 #21465481

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×#384C412yes—
9C31×#382C2212yes—
10C31×#380—22no—
11C4×C4⋊C4×C31—22no—
12C31×#336—22no—
13C23×C4×C31C2×C411yescharacteristic
14C23×C4×C31D412yes—
15C22×C8×C31—24no—
16C31×#117—44no—
17C2×C4⋊C4×C31—22no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31C2×C414yes—
20C2×C22⋊C4×C31—22no—
21C2×C42×C31—24no—
22C2×C42×C31—22no—
23C2×C42×C31C2×C411yescharacteristic
24C2×C42×C31D412yes—
25C2×C42×C31C2311yescharacteristic
26C31×C22⋊C8—28no—
27C31×#97—28no—
28C31×#95—24no—
29C24×C31C22⋊C411yescharacteristic
30C22×C4×C31—22no—
31C22×C4×C31—22no—
32C22×C4×C31—22no—
33C22×C4×C31—24no—
34C22×C4×C31—24no—
35C22×C4×C31—24no—
36C22×C4×C31—42no—
37C22×C4×C31C22⋊C411yescharacteristic
38C22×C4×C31C22⋊C412yes—
39C22×C4×C31C22×C411yescharacteristic
40C22×C4×C31C2×D412yes—
41C2×C8×C31—28no—
42C2×C8×C31—44no—
43C2×C8×C31—44no—
44C4⋊C4×C31—44no—
45C4⋊C4×C31—44no—
46C4⋊C4×C31—44no—
47C22⋊C4×C31—44no—
48C42×C31—22no—
49C42×C31—24no—
50C42×C31—44no—
51C42×C31#4114yes—
52#8722C3111yesmaximal, characteristic, direct product factor, Sylow
53C23×C31—21no—
54C23×C31—21no—
55C23×C31—22no—
56C23×C31—22no—
57C23×C31#10012yes—
58C23×C31C2×C22⋊C411yescharacteristic
59C2×C4×C31—28no—
60C2×C4×C31—21no—
61C2×C4×C31—22no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—21no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—48no—
69C2×C4×C31—44no—
70C2×C4×C31—44no—
71C2×C4×C31—44no—
72C2×C4×C31#10112yes—
73C2×C4×C31#10414yes—
74C2×C4×C31#11712yes—
75C2×C4×C31#12314yes—
76C8×C31—48no—
77#2285C2×C3111yescharacteristic
78#1749C2×C3112yes—
79#1295C2×C3114yescomplemented
80C22×C31—22no—
81C22×C31—24no—
82C22×C31—41no—
83C22×C31—42no—
84C22×C31—41no—
85C22×C31#38111yescharacteristic
86C22×C31C2×#10011yescharacteristic
87C22×C31C2×#10111yescharacteristic
88C22×C31C2×#10412yes—
89C22×C31#42112yes—
90C4×C31—22no—
91C4×C31—22no—
92C4×C31—24no—
93C4×C31—24no—
94C4×C31—84no—
95C2×#117C4×C3112yes—
96C22×C42C22×C3111yescharacteristic
97C2×C22⋊C8—22no—
98C2×#97C22×C3114yes—
99#384C4×C3112yes—
100#382C22×C3112yes—
101#380—22no—
102C4×C4⋊C4—22no—
103#336—22no—
104C2×C31—42no—
105C2×C31#152611yescharacteristic
106C2×C31#153012yes—
107C2×C31#153711yescharacteristic
108C2×C31#182111yescharacteristic
109C2×C31#182612yes—
110C23×C4C2×C4×C3111yescharacteristic
111C23×C4D4×C3112yes—
112C22×C8—24no—
113#117—44no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4C2×C4×C3114yes—
117C2×C22⋊C4—22no—
118C2×C42—24no—
119C2×C42—22no—
120C2×C42C2×C4×C3111yescharacteristic
121C2×C42D4×C3112yes—
122C2×C42C23×C3111yescharacteristic
123C22⋊C8—28no—
124#97—28no—
125#95—24no—
126C31#872211yescharacteristic, direct product factor, Sylow
127C24C22⋊C4×C3111yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—42no—
135C22×C4C22⋊C4×C3111yescharacteristic
136C22×C4C22⋊C4×C3112yes—
137C22×C4C22×C4×C3111yescharacteristic
138C22×C4C2×D4×C3112yes—
139C2×C8—28no—
140C2×C8—44no—
141C2×C8—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C22⋊C4—44no—
146C42—22no—
147C42—24no—
148C42—44no—
149C42#41×C3114yes—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23C31×#10012yes—
155C23C2×C22⋊C4×C3111yescharacteristic
156C2×C4—28no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4C31×#10112yes—
170C2×C4C31×#10414yes—
171C2×C4C31×#11712yes—
172C2×C4C31×#12314yes—
173C8—48no—
174C22—22no—
175C22—24no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22C31×#38111yescharacteristic
180C22C2×C31×#10011yescharacteristic
181C22C2×C31×#10111yescharacteristic
182C22C2×C31×#10412yes—
183C22C31×#42112yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—24no—
188C4—84no—
189C2—42no—
190C2C31×#152611yescharacteristic
191C2C31×#153012yes—
192C2C31×#153711yescharacteristic
193C2C31×#182111yescharacteristic
194C2C31×#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
52. #8722C31direct (N × H)
79. #1295C2×C31semidirect
126. C31#8722direct (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
#872231