Finite Group Databasebeta

← C31×#17114 #21473873

Subgroups — C31×#17114 #21473873

Order 7936.

1222 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C216yesmaximal
2C31×#1444C211yesmaximal, characteristic
3C31×#1444C213yesmaximal
4C31×#1443C212yesmaximal
5C31×#1442C213yesmaximal
6C22×C4⋊C4×C31C2213yes—
7C22×C4⋊C4×C31C2216yes—
8C22×C4⋊C4×C31C2213yes—
9C22×C4⋊C4×C31C2211yescharacteristic
10C31×#398—224no—
11C2×C31×#95C2216yes—
12C2×C31×#95C2216yes—
13C2×C31×#95C2213yes—
14C2×C31×#95C2213yes—
15C2×C31×#95C2213yes—
16C2×C31×#95C2211yescharacteristic
17C23×C4×C31C2312yes—
18C23×C4×C31C2313yes—
19C23×C4×C31C2316yes—
20C23×C4×C31C2313yes—
21C23×C4×C31C2311yescharacteristic
22C2×C4⋊C4×C31—212no—
23C2×C4⋊C4×C31—212no—
24C2×C4⋊C4×C31—212no—
25C2×C4⋊C4×C31—212no—
26C2×C4⋊C4×C31—43no—
27C2×C4⋊C4×C31—43no—
28C2×C4⋊C4×C31—46no—
29C2×C4⋊C4×C31—43no—
30C31×#95—212no—
31C31×#95—212no—
32C31×#95—26no—
33C31×#95—43no—
34C31×#95D4112yes—
35C31×#95Q814yes—
36C24×C31C2411yescharacteristic
37C22×C4×C31—26no—
38C22×C4×C31—26no—
39C22×C4×C31—26no—
40C22×C4×C31—26no—
41C22×C4×C31—23no—
42C22×C4×C31—23no—
43C22×C4×C31—23no—
44C22×C4×C31—26no—
45C22×C4×C31—26no—
46C22×C4×C31—26no—
47C22×C4×C31—26no—
48C22×C4×C31—23no—
49C22×C4×C31—23no—
50C22×C4×C31—23no—
51C22×C4×C31—26no—
52C22×C4×C31—26no—
53C22×C4×C31—26no—
54C22×C4×C31—26no—
55C22×C4×C31—22no—
56C22×C4×C31C2×D4112yes—
57C22×C4×C31C2×D416yes—
58C22×C4×C31C2×Q816yes—
59C22×C4×C31#4112yes—
60C4⋊C4×C31—412no—
61C4⋊C4×C31—412no—
62C4⋊C4×C31—424no—
63C4⋊C4×C31—44no—
64#17114C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31C22×D413yes—
66C23×C31C22×Q811yescharacteristic
67C23×C31C2×#4111yescharacteristic
68C23×C31H(5,𝔽2)13yes—
69C23×C312−1+413yes—
70C23×C312−1+413yes—
71C23×C312−1+411yescharacteristic
72C2×C4×C31—212no—
73C2×C4×C31—26no—
74C2×C4×C31—26no—
75C2×C4×C31—26no—
76C2×C4×C31—212no—
77C2×C4×C31—212no—
78C2×C4×C31—212no—
79C2×C4×C31—212no—
80C2×C4×C31—46no—
81C2×C4×C31—46no—
82C2×C4×C31—46no—
83C2×C4×C31—46no—
84C2×C4×C31—43no—
85C2×C4×C31—43no—
86C2×C4×C31—46no—
87C2×C4×C31—41no—
88C2×C4×C31—43no—
89C2×C4×C31—43no—
90C2×C4×C31—43no—
91C2×C4×C31—46no—
92C2×C4×C31—46no—
93C2×C4×C31—46no—
94C2×C4×C31—42no—
95C2×#398C2×C3116yes—
96#1444C2×C3111yescharacteristic
97#1444C2×C3113yes—
98#1443C2×C3112yes—
99#1442C2×C3113yes—
100C22×C31#53616yes—
101C22×C31#53713yes—
102C22×C31#53913yes—
103C22×C31#54413yes—
104C22×C31D4213yes—
105C22×C31#54713yes—
106C22×C31D4×Q813yes—
107C22×C31#55711yescharacteristic
108C22×C31#56011yescharacteristic
109C22×C31#56313yes—
110C22×C31#56313yes—
111C22×C31#56413yes—
112C4×C31—42no—
113C4×C31—46no—
114C4×C31—46no—
115C4×C31—412no—
116C4×C31—82no—
117C22×C4⋊C4C22×C3113yes—
118C22×C4⋊C4C22×C3116yes—
119C22×C4⋊C4C22×C3113yes—
120C22×C4⋊C4C22×C3111yescharacteristic
121#398—224no—
122C2×#95C22×C3116yes—
123C2×#95C22×C3116yes—
124C2×#95C22×C3113yes—
125C2×#95C22×C3113yes—
126C2×#95C22×C3113yes—
127C2×#95C22×C3111yescharacteristic
128C2×C31#267511yescharacteristic
129C2×C31#267713yes—
130C2×C31#268013yes—
131C2×C31#272613yes—
132C2×C31#282213yes—
133C2×C31#283411yescharacteristic
134C2×C31#284311yescharacteristic
135C23×C4C23×C3112yes—
136C23×C4C23×C3113yes—
137C23×C4C23×C3116yes—
138C23×C4C23×C3113yes—
139C23×C4C23×C3111yescharacteristic
140C2×C4⋊C4—212no—
141C2×C4⋊C4—212no—
142C2×C4⋊C4—212no—
143C2×C4⋊C4—212no—
144C2×C4⋊C4—43no—
145C2×C4⋊C4—43no—
146C2×C4⋊C4—46no—
147C2×C4⋊C4—43no—
148#95—212no—
149#95—212no—
150#95—26no—
151#95—43no—
152#95D4×C31112yes—
153#95Q8×C3114yes—
154C31#1711411yescharacteristic, direct product factor, Sylow
155C24C24×C3111yescharacteristic
156C22×C4—26no—
157C22×C4—26no—
158C22×C4—26no—
159C22×C4—26no—
160C22×C4—23no—
161C22×C4—23no—
162C22×C4—23no—
163C22×C4—26no—
164C22×C4—26no—
165C22×C4—26no—
166C22×C4—26no—
167C22×C4—23no—
168C22×C4—23no—
169C22×C4—23no—
170C22×C4—26no—
171C22×C4—26no—
172C22×C4—26no—
173C22×C4—26no—
174C22×C4—22no—
175C22×C4C2×D4×C31112yes—
176C22×C4C2×D4×C3116yes—
177C22×C4C2×Q8×C3116yes—
178C22×C4#41×C3112yes—
179C4⋊C4—412no—
180C4⋊C4—412no—
181C4⋊C4—424no—
182C4⋊C4—44no—
183C23C22×D4×C3113yes—
184C23C22×Q8×C3111yescharacteristic
185C23C2×#41×C3111yescharacteristic
186C23C31×H(5,𝔽2)13yes—
187C23C31×2−1+413yes—
188C23C31×2−1+413yes—
189C23C31×2−1+411yescharacteristic
190C2×C4—212no—
191C2×C4—26no—
192C2×C4—26no—
193C2×C4—26no—
194C2×C4—212no—
195C2×C4—212no—
196C2×C4—212no—
197C2×C4—212no—
198C2×C4—46no—
199C2×C4—46no—
200C2×C4—46no—
201C2×C4—46no—
202C2×C4—43no—
203C2×C4—43no—
204C2×C4—46no—
205C2×C4—41no—
206C2×C4—43no—
207C2×C4—43no—
208C2×C4—43no—
209C2×C4—46no—
210C2×C4—46no—
211C2×C4—46no—
212C2×C4—42no—
213C22C31×#53616yes—
214C22C31×#53713yes—
215C22C31×#53913yes—
216C22C31×#54413yes—
217C22D42×C3113yes—
218C22C31×#54713yes—
219C22D4×Q8×C3113yes—
220C22C31×#55711yescharacteristic
221C22C31×#56011yescharacteristic
222C22C31×#56313yes—
223C22C31×#56313yes—
224C22C31×#56413yes—
225C4—42no—
226C4—46no—
227C4—46no—
228C4—412no—
229C4—82no—
230C2C31×#267511yescharacteristic
231C2C31×#267713yes—
232C2C31×#268013yes—
233C2C31×#272613yes—
234C2C31×#282213yes—
235C2C31×#283411yescharacteristic
236C2C31×#284311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
64. #17114C31direct (N × H)
154. C31#17114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C31×#14442
C31×#14432
C31×#14422
#1711431