Finite Group Databasebeta

← C31×#11443 #21468202

Subgroups — C31×#11443 #21468202

Order 7936.

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

normal subgroups only

This group has 382 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
1C2×C31×#424C211yesmaximal, characteristic
2C31×#2112C212yesmaximal
3C31×#1323C214yesmaximal, complemented
4C22×M16×C31C411yescharacteristic
5C23×C8×C31C2211yescharacteristic
6C2×C31×#117C411yescharacteristic
7C2×C31×M32—22no—
8C31×#424—22no—
9C31×#424C412yes—
10C31×#424C2212yes—
11C2×C31×C4⋊C8—22no—
12C31×C22⋊C16—22no—
13C31×C22⋊C16C2214yes—
14C23×C4×C31C2×C411yescharacteristic
15C2×M16×C31—21no—
16C2×M16×C31—42no—
17C2×M16×C31C2×C412yes—
18C22×C8×C31—21no—
19C22×C8×C31—42no—
20C22×C8×C31C2×C411yescharacteristic
21C22×C8×C31D412yes—
22C22×C8×C31D412yes—
23C22×C8×C31C2311yescharacteristic
24C31×#117—21no—
25C31×#117—21no—
26C31×#117C812yes—
27C31×#117C2×C412yes—
28C2×C4⋊C4×C31C812yes—
29C2×C22⋊C4×C31—21no—
30C2×C42×C31—21no—
31C31×M32—44no—
32C2×C16×C31—24no—
33C31×C4⋊C8—24no—
34C31×C4⋊C8—24no—
35C24×C31M1611yescharacteristic
36C22×C4×C31—22no—
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31C22⋊C411yescharacteristic
40C22×C4×C31C22⋊C411yescharacteristic
41C22×C4×C31C2×C811yescharacteristic
42C22×C4×C31C2×C811yescharacteristic
43C22×C4×C31M1611yescharacteristic
44C22×C4×C31C22×C411yescharacteristic
45M16×C31—42no—
46M16×C31—42no—
47C2×C8×C31—24no—
48C2×C8×C31—22no—
49C2×C8×C31—41no—
50C2×C8×C31—42no—
51C2×C8×C31—41no—
52C2×C8×C31—42no—
53C2×C8×C31C22⋊C412yes—
54C2×C8×C31C2×D412yes—
55C4⋊C4×C31—22no—
56C4⋊C4×C31C2×C814yes—
57C22⋊C4×C31—22no—
58C22⋊C4×C31—22no—
59C42×C31—22no—
60C42×C31—22no—
61C16×C31—44no—
62#11443C3111yesmaximal, characteristic, direct product factor, Sylow
63C23×C31—22no—
64C23×C31—42no—
65C23×C31C22⋊C811yescharacteristic
66C23×C31C22⋊C811yescharacteristic
67C23×C31C2×M1611yescharacteristic
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—24no—
76C2×C4×C31—44no—
77C2×C4×C31C22⋊C811yescharacteristic
78C2×C4×C31C22⋊C811yescharacteristic
79C2×C4×C31#9912yes—
80C2×C4×C31#10112yes—
81C2×C4×C31C2×C22⋊C411yescharacteristic
82C2×C4×C31C22×C811yescharacteristic
83C8×C31—22no—
84C8×C31—22no—
85C8×C31—42no—
86C2×#424C2×C3111yescharacteristic
87#2112C2×C3112yes—
88#1323C2×C3114yescomplemented
89C22×C31—22no—
90C22×C31—22no—
91C22×C31—22no—
92C22×C31—21no—
93C22×C31—21no—
94C22×C31—44no—
95C22×C31#32412yes—
96C22×C31C2×C22⋊C811yescharacteristic
97C4×C31—21no—
98C4×C31—21no—
99C4×C31—44no—
100C4×C31#32412yes—
101C4×C31C2×#9911yescharacteristic
102C4×C31C2×#10111yescharacteristic
103C22×M16C4×C3111yescharacteristic
104C23×C8C22×C3111yescharacteristic
105C2×#117C4×C3111yescharacteristic
106C2×M32—22no—
107#424—22no—
108#424C4×C3112yes—
109#424C22×C3112yes—
110C2×C4⋊C8—22no—
111C22⋊C16—22no—
112C22⋊C16C22×C3114yes—
113C2×C31—22no—
114C2×C31—41no—
115C2×C31—41no—
116C2×C31C2×#32411yescharacteristic
117C2×C31#211712yes—
118C23×C4C2×C4×C3111yescharacteristic
119C2×M16—21no—
120C2×M16—42no—
121C2×M16C2×C4×C3112yes—
122C22×C8—21no—
123C22×C8—42no—
124C22×C8C2×C4×C3111yescharacteristic
125C22×C8D4×C3112yes—
126C22×C8D4×C3112yes—
127C22×C8C23×C3111yescharacteristic
128#117—21no—
129#117—21no—
130#117C8×C3112yes—
131#117C2×C4×C3112yes—
132C2×C4⋊C4C8×C3112yes—
133C2×C22⋊C4—21no—
134C2×C42—21no—
135M32—44no—
136C2×C16—24no—
137C4⋊C8—24no—
138C4⋊C8—24no—
139C31#1144311yescharacteristic, direct product factor, Sylow
140C24M16×C3111yescharacteristic
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4C22⋊C4×C3111yescharacteristic
145C22×C4C22⋊C4×C3111yescharacteristic
146C22×C4C2×C8×C3111yescharacteristic
147C22×C4C2×C8×C3111yescharacteristic
148C22×C4M16×C3111yescharacteristic
149C22×C4C22×C4×C3111yescharacteristic
150M16—42no—
151M16—42no—
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—42no—
156C2×C8—41no—
157C2×C8—42no—
158C2×C8C22⋊C4×C3112yes—
159C2×C8C2×D4×C3112yes—
160C4⋊C4—22no—
161C4⋊C4C2×C8×C3114yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—22no—
165C42—22no—
166C16—44no—
167C23—22no—
168C23—42no—
169C23C31×C22⋊C811yescharacteristic
170C23C31×C22⋊C811yescharacteristic
171C23C2×M16×C3111yescharacteristic
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—44no—
181C2×C4C31×C22⋊C811yescharacteristic
182C2×C4C31×C22⋊C811yescharacteristic
183C2×C4C31×#9912yes—
184C2×C4C31×#10112yes—
185C2×C4C2×C22⋊C4×C3111yescharacteristic
186C2×C4C22×C8×C3111yescharacteristic
187C8—22no—
188C8—22no—
189C8—42no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—21no—
194C22—21no—
195C22—44no—
196C22C31×#32412yes—
197C22C2×C31×C22⋊C811yescharacteristic
198C4—21no—
199C4—21no—
200C4—44no—
201C4C31×#32412yes—
202C4C2×C31×#9911yescharacteristic
203C4C2×C31×#10111yescharacteristic
204C2—22no—
205C2—41no—
206C2—41no—
207C2C2×C31×#32411yescharacteristic
208C2C31×#211712yes—
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC22×C8C23×C31
socleC22×C31C2×C22⋊C8
prime radicalC24×C31M16
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1323C2semidirect
62. #11443C31direct (N × H)
88. #1323C2×C31semidirect
139. C31#11443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4242
C31×#21122
C31×#13232
#1144331