Finite Group Databasebeta

← C31×#23467 #21480226

Subgroups — C31×#23467 #21480226

Order 7936.

1378 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 334 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×#3458C211yesmaximal, characteristic, complemented
2C31×#2280C213yesmaximal
3C31×#2030C214yesmaximal, complemented
4C31×#2029C214yesmaximal
5C31×#1740C213yesmaximal, complemented
6C24×C4×C31C2211yescharacteristic
7C31×#544—26no—
8C31×#543C2214yes—
9C31×#533—26no—
10C2×C31×#117C2213yes—
11C2×C31×#117C2213yes—
12C31×#381C2216yes—
13C31×#380—26no—
14C31×#379C2216yes—
15C4×C22⋊C4×C31—26no—
16C31×#342C22112yes—
17C25×C31C2311yescharacteristic
18C23×C4×C31—23no—
19C23×C4×C31—23no—
20C23×C4×C31—26no—
21C23×C4×C31Q814yescomplemented
22C23×C4×C31C2311yescharacteristic
23C23×C4×C31C2311yescharacteristic
24C31×C4⋊Q8—212no—
25C31×#125—212no—
26C31×C22⋊Q8—224no—
27C4×Q8×C31—28no—
28C31×#117—26no—
29C31×#117—26no—
30C31×#117—212no—
31C2×C4⋊C4×C31—23no—
32C2×C4⋊C4×C31D416yes—
33C2×C22⋊C4×C31—212no—
34C2×C22⋊C4×C31C2316yes—
35C2×C22⋊C4×C31C2316yes—
36C2×C42×C31—23no—
37C2×C42×C31D416yes—
38C31×#95—212no—
39C24×C31—23no—
40C24×C31—23no—
41C24×C31—44no—
42C24×C31C2×Q812yes—
43C24×C31C2411yescharacteristic
44C2×Q8×C31—28no—
45C22×C4×C31—23no—
46C22×C4×C31—23no—
47C22×C4×C31—212no—
48C22×C4×C31—212no—
49C22×C4×C31—26no—
50C22×C4×C31—43no—
51C22×C4×C31—41no—
52C22×C4×C31—46no—
53C22×C4×C31—46no—
54C22×C4×C31C2×D4112yes—
55C22×C4×C31C2×D413yes—
56C22×C4×C31C2×D413yes—
57C22×C4×C31C2×Q812yes—
58C22×C4×C31C2×Q812yes—
59C22×C4×C31#4116yes—
60C4⋊C4×C31—224no—
61C4⋊C4×C31—212no—
62C4⋊C4×C31—46no—
63C22⋊C4×C31—212no—
64C22⋊C4×C31—212no—
65C22⋊C4×C31—424no—
66C42×C31—26no—
67C42×C31—26no—
68C42×C31—46no—
69#23467C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—212no—
71C23×C31—26no—
72C23×C31—44no—
73C23×C31—42no—
74C23×C31—46no—
75C23×C31—412no—
76C23×C31—41no—
77C23×C31—43no—
78C23×C31C22×D413yes—
79C23×C31C22×Q811yescharacteristic
80C23×C31C2×#4113yes—
81Q8×C31—88no—
82C2×C4×C31—212no—
83C2×C4×C31—26no—
84C2×C4×C31—41no—
85C2×C4×C31—43no—
86C2×C4×C31—412no—
87C2×C4×C31—44no—
88C2×C4×C31—412no—
89C2×C4×C31—412no—
90C2×C4×C31—46no—
91C2×C4×C31#12013yes—
92C2×C4×C31#12011yescharacteristic
93C2×C4×C31C22⋊Q816yes—
94C2×C4×C31C22⋊Q816yes—
95C2×C4×C31#12416yes—
96C2×C4×C31#12416yes—
97#3458C2×C3111yescharacteristic, complemented
98#2280C2×C3113yes—
99#2030C2×C3114yescomplemented
100#2029C2×C3114yes—
101#1740C2×C3113yescomplemented
102C22×C31—26no—
103C22×C31—212no—
104C22×C31—41no—
105C22×C31—43no—
106C22×C31—412no—
107C22×C31—46no—
108C22×C31—42no—
109C22×C31—44no—
110C22×C31C2×#12011yescharacteristic
111C22×C31C2×C22⋊Q813yes—
112C22×C31C2×#12413yes—
113C4×C31—42no—
114C4×C31—412no—
115C4×C31—86no—
116C4×C31#39316yes—
117C4×C31#39312yes—
118C24×C4C22×C3111yescharacteristic
119#544—26no—
120#543C22×C3114yes—
121#533—26no—
122C2×#117C22×C3113yes—
123C2×#117C22×C3113yes—
124#381C22×C3116yes—
125#380—26no—
126#379C22×C3116yes—
127C4×C22⋊C4—26no—
128#342C22×C31112yes—
129C2×C31—23no—
130C2×C31—23no—
131C2×C31—44no—
132C2×C31C2×#39311yescharacteristic
133C2×C31#302512yes—
134C25C23×C3111yescharacteristic
135C23×C4—23no—
136C23×C4—23no—
137C23×C4—26no—
138C23×C4Q8×C3114yescomplemented
139C23×C4C23×C3111yescharacteristic
140C23×C4C23×C3111yescharacteristic
141C4⋊Q8—212no—
142#125—212no—
143C22⋊Q8—224no—
144C4×Q8—28no—
145#117—26no—
146#117—26no—
147#117—212no—
148C2×C4⋊C4—23no—
149C2×C4⋊C4D4×C3116yes—
150C2×C22⋊C4—212no—
151C2×C22⋊C4C23×C3116yes—
152C2×C22⋊C4C23×C3116yes—
153C2×C42—23no—
154C2×C42D4×C3116yes—
155#95—212no—
156C31#2346711yescharacteristic, direct product factor, Sylow
157C24—23no—
158C24—23no—
159C24—44no—
160C24C2×Q8×C3112yes—
161C24C24×C3111yescharacteristic
162C2×Q8—28no—
163C22×C4—23no—
164C22×C4—23no—
165C22×C4—212no—
166C22×C4—212no—
167C22×C4—26no—
168C22×C4—43no—
169C22×C4—41no—
170C22×C4—46no—
171C22×C4—46no—
172C22×C4C2×D4×C31112yes—
173C22×C4C2×D4×C3113yes—
174C22×C4C2×D4×C3113yes—
175C22×C4C2×Q8×C3112yes—
176C22×C4C2×Q8×C3112yes—
177C22×C4#41×C3116yes—
178C4⋊C4—224no—
179C4⋊C4—212no—
180C4⋊C4—46no—
181C22⋊C4—212no—
182C22⋊C4—212no—
183C22⋊C4—424no—
184C42—26no—
185C42—26no—
186C42—46no—
187C23—212no—
188C23—26no—
189C23—44no—
190C23—42no—
191C23—46no—
192C23—412no—
193C23—41no—
194C23—43no—
195C23C22×D4×C3113yes—
196C23C22×Q8×C3111yescharacteristic
197C23C2×#41×C3113yes—
198Q8—88no—
199C2×C4—212no—
200C2×C4—26no—
201C2×C4—41no—
202C2×C4—43no—
203C2×C4—412no—
204C2×C4—44no—
205C2×C4—412no—
206C2×C4—412no—
207C2×C4—46no—
208C2×C4C31×#12013yes—
209C2×C4C31×#12011yescharacteristic
210C2×C4C31×C22⋊Q816yes—
211C2×C4C31×C22⋊Q816yes—
212C2×C4C31×#12416yes—
213C2×C4C31×#12416yes—
214C22—26no—
215C22—212no—
216C22—41no—
217C22—43no—
218C22—412no—
219C22—46no—
220C22—42no—
221C22—44no—
222C22C2×C31×#12011yescharacteristic
223C22C2×C31×C22⋊Q813yes—
224C22C2×C31×#12413yes—
225C4—42no—
226C4—412no—
227C4—86no—
228C4C31×#39316yes—
229C4C31×#39312yes—
230C2—23no—
231C2—23no—
232C2—44no—
233C2C2×C31×#39311yescharacteristic
234C2C31×#302512yes—
subgroupG/H
centerC2×C4×C31#120
commutator, Frattini, cosocleC24C24×C31
socleC22×C31C2×#120
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3458C2semidirect
3. C31×#2030C2semidirect
5. C31×#1740C2semidirect
21. C23×C4×C31Q8semidirect
69. #23467C31direct (N × H)
97. #3458C2×C31semidirect
99. #2030C2×C31semidirect
101. #1740C2×C31semidirect
138. C23×C4Q8×C31semidirect
156. C31#23467direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34582
C31×#22802
C31×#20302
C31×#20292
C31×#17402
#2346731