Finite Group Databasebeta

← C31×#11521 #21468280

Subgroups — C31×#11521 #21468280

Order 7936.

330 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2920C211yesmaximal, characteristic
2C31×#2165C212yesmaximal, complemented
3C31×#1327C212yesmaximal, complemented
4C31×#1320C212yesmaximal
5C22×C42×C31C411yescharacteristic
6C31×#432—22no—
7C31×#431—22no—
8C31×#423C411yescharacteristic
9C31×#423C2211yescharacteristic
10C31×#407C411yescharacteristic
11C31×#407C2211yescharacteristic
12C4×M16×C31C411yescharacteristic
13C4×M16×C31C2211yescharacteristic
14C31×#364—22no—
15C31×#349C2214yes—
16C31×#347—22no—
17C23×C4×C31—21no—
18C23×C4×C31C2×C411yescharacteristic
19C2×M16×C31C2×C411yescharacteristic
20C2×M16×C31C2×C411yescharacteristic
21C2×M16×C31C2×C411yescharacteristic
22C2×M16×C31C2311yescharacteristic
23C2×C42×C31—21no—
24C2×C42×C31—21no—
25C2×C42×C31—21no—
26C2×C42×C31—21no—
27C2×C42×C31—21no—
28C2×C42×C31C2×C411yescharacteristic
29C2×C42×C31C2×C411yescharacteristic
30C31×M32—24no—
31C31×C4⋊C8—22no—
32C31×C4⋊C8—22no—
33C31×C22⋊C8—22no—
34C31×C22⋊C8—22no—
35C31×#97—21no—
36C31×#97D412yes—
37C4×C8×C31—21no—
38C4×C8×C31D412yes—
39C24×C31M1611yescharacteristic
40C22×C4×C31—21no—
41C22×C4×C31—21no—
42C22×C4×C31—21no—
43C22×C4×C31—21no—
44C22×C4×C31—21no—
45C22×C4×C31—21no—
46C22×C4×C31—21no—
47C22×C4×C31—21no—
48C22×C4×C31—44no—
49C22×C4×C31—41no—
50C22×C4×C31—41no—
51C22×C4×C31M1611yescharacteristic
52C22×C4×C31C22×C411yescharacteristic
53M16×C31—41no—
54M16×C31—41no—
55M16×C31—41no—
56M16×C31—41no—
57C2×C8×C31—21no—
58C2×C8×C31—21no—
59C2×C8×C31C22⋊C412yes—
60C2×C8×C31C2×D412yes—
61C42×C31—21no—
62C42×C31—21no—
63C42×C31—21no—
64C42×C31—21no—
65C42×C31—21no—
66C42×C31—21no—
67C42×C31C22⋊C411yescharacteristic
68C42×C31C22⋊C411yescharacteristic
69C42×C31M1611yescharacteristic
70C42×C31M1611yescharacteristic
71C16×C31—44no—
72#11521C3111yesmaximal, characteristic, direct product factor, Sylow
73C23×C31—21no—
74C23×C31—42no—
75C23×C31—41no—
76C23×C31C2×M1611yescharacteristic
77C2×C4×C31—24no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31C2×C22⋊C411yescharacteristic
95C2×C4×C31C2×M1611yescharacteristic
96C8×C31—22no—
97C8×C31—22no—
98C8×C31—41no—
99C8×C31—41no—
100#2920C2×C3111yescharacteristic
101#2165C2×C3112yescomplemented
102#1327C2×C3112yescomplemented
103#1320C2×C3112yes—
104C22×C31—22no—
105C22×C31—21no—
106C22×C31—41no—
107C22×C31—41no—
108C22×C31—42no—
109C22×C31—42no—
110C22×C31—41no—
111C22×C31#40711yescharacteristic
112C4×C31—22no—
113C4×C31—22no—
114C4×C31—21no—
115C4×C31—41no—
116C4×C31—41no—
117C4×C31—41no—
118C4×C31#41011yescharacteristic
119C4×C31#41311yescharacteristic
120C22×C42C4×C3111yescharacteristic
121#432—22no—
122#431—22no—
123#423C4×C3111yescharacteristic
124#423C22×C3111yescharacteristic
125#407C4×C3111yescharacteristic
126#407C22×C3111yescharacteristic
127C4×M16C4×C3111yescharacteristic
128C4×M16C22×C3111yescharacteristic
129#364—22no—
130#349C22×C3114yes—
131#347—22no—
132C2×C31—21no—
133C2×C31—42no—
134C2×C31—41no—
135C2×C31#146411yescharacteristic
136C23×C4—21no—
137C23×C4C2×C4×C3111yescharacteristic
138C2×M16C2×C4×C3111yescharacteristic
139C2×M16C2×C4×C3111yescharacteristic
140C2×M16C2×C4×C3111yescharacteristic
141C2×M16C23×C3111yescharacteristic
142C2×C42—21no—
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—21no—
147C2×C42C2×C4×C3111yescharacteristic
148C2×C42C2×C4×C3111yescharacteristic
149M32—24no—
150C4⋊C8—22no—
151C4⋊C8—22no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154#97—21no—
155#97D4×C3112yes—
156C4×C8—21no—
157C4×C8D4×C3112yes—
158C31#1152111yescharacteristic, direct product factor, Sylow
159C24M16×C3111yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—44no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4M16×C3111yescharacteristic
172C22×C4C22×C4×C3111yescharacteristic
173M16—41no—
174M16—41no—
175M16—41no—
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8C22⋊C4×C3112yes—
180C2×C8C2×D4×C3112yes—
181C42—21no—
182C42—21no—
183C42—21no—
184C42—21no—
185C42—21no—
186C42—21no—
187C42C22⋊C4×C3111yescharacteristic
188C42C22⋊C4×C3111yescharacteristic
189C42M16×C3111yescharacteristic
190C42M16×C3111yescharacteristic
191C16—44no—
192C23—21no—
193C23—42no—
194C23—41no—
195C23C2×M16×C3111yescharacteristic
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4C2×C22⋊C4×C3111yescharacteristic
214C2×C4C2×M16×C3111yescharacteristic
215C8—22no—
216C8—22no—
217C8—41no—
218C8—41no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22C31×#40711yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4C31×#41011yescharacteristic
234C4C31×#41311yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2C31×#146411yescharacteristic
subgroupG/H
centerC4×C31#410
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×M16C23×C31
socleC2×C31#1464
prime radicalC24×C31M16
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C42×C31 ◁ C4×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2165C2semidirect
3. C31×#1327C2semidirect
72. #11521C31direct (N × H)
101. #2165C2×C31semidirect
102. #1327C2×C31semidirect
158. C31#11521direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29202
C31×#21652
C31×#13272
C31×#13202
#1152131