Finite Group Databasebeta

← C31×#10935 #21467694

Subgroups — C31×#10935 #21467694

Order 7936.

2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 302 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×#379C213yesmaximal
2C31×#2273C211yesmaximal, characteristic, complemented
3C2×C31×#342C213yesmaximal, complemented
4C26×C31C2211yescharacteristic
5C22×C22⋊C4×C31—26no—
6C22×C22⋊C4×C31C2213yes—
7C22×C22⋊C4×C31C2213yes—
8C31×#379—26no—
9C31×#379C4112yescomplemented
10C4×C22⋊C4×C31—26no—
11C31×#342—26no—
12C25×C31—23no—
13C25×C31—23no—
14C25×C31—26no—
15C25×C31—48no—
16C25×C31C2×C416yes—
17C25×C31C2311yescharacteristic
18C23×C4×C31—23no—
19C23×C4×C31D416yes—
20C2×C22⋊C4×C31—26no—
21C2×C22⋊C4×C31—26no—
22C2×C22⋊C4×C31—26no—
23C2×C22⋊C4×C31—26no—
24C2×C22⋊C4×C31—23no—
25C2×C22⋊C4×C31—224no—
26C2×C22⋊C4×C31—424no—
27C2×C22⋊C4×C31C2×C416yes—
28C2×C22⋊C4×C31C2×C416yes—
29C2×C22⋊C4×C31D416yes—
30C2×C42×C31—24no—
31C31×#95—24no—
32C24×C31—224no—
33C24×C31—26no—
34C24×C31—212no—
35C24×C31—26no—
36C24×C31—212no—
37C24×C31—424no—
38C24×C31—44no—
39C24×C31—412no—
40C24×C31—424no—
41C24×C31—448no—
42C24×C31—41no—
43C24×C31—46no—
44C24×C31—43no—
45C24×C31—43no—
46C24×C31—42no—
47C24×C31—41no—
48C24×C31C4214yescomplemented
49C24×C31C22×C413yes—
50C24×C31C2×D413yes—
51C24×C31C2×D413yes—
52C24×C31#4116yes—
53C22×C4×C31—26no—
54C22×C4×C31—26no—
55C22×C4×C31—26no—
56C22×C4×C31—412no—
57C22×C4×C31—412no—
58C22×C4×C31—46no—
59C22×C4×C31C22⋊C4112yescomplemented
60C22⋊C4×C31—212no—
61C22⋊C4×C31—212no—
62C22⋊C4×C31—212no—
63C22⋊C4×C31—448no—
64C22⋊C4×C31—43no—
65C22⋊C4×C31—43no—
66C42×C31—84no—
67#10935C3111yesmaximal, characteristic, direct product factor, Sylow
68C23×C31—212no—
69C23×C31—224no—
70C23×C31—248no—
71C23×C31—212no—
72C23×C31—48no—
73C23×C31—46no—
74C23×C31—46no—
75C23×C31—412no—
76C23×C31—412no—
77C23×C31—448no—
78C23×C31—424no—
79C23×C31—424no—
80C23×C31—424no—
81C23×C31—448no—
82C23×C31—424no—
83C23×C31—416no—
84C23×C31—48no—
85C23×C31—46no—
86C23×C31—412no—
87C23×C31—46no—
88C23×C31—48no—
89C23×C31C2×C4211yescharacteristic
90C23×C31C2×C22⋊C413yes—
91C23×C31#11713yes—
92C23×C31C4×D416yes—
93C23×C31C4×D416yes—
94C23×C31#12011yescharacteristic
95C23×C31#12116yes—
96C23×C31#12313yes—
97C23×C31#12413yes—
98C23×C31#12612yes—
99C23×C31#12711yescharacteristic
100C2×C4×C31—212no—
101C2×C4×C31—412no—
102C2×C4×C31—412no—
103C2×C4×C31—412no—
104C2×C4×C31—46no—
105C2×C4×C31—86no—
106C2×C4×C31—812no—
107C2×#379C2×C3113yes—
108#2273C2×C3111yescharacteristic, complemented
109C2×#342C2×C3113yescomplemented
110C22×C31—26no—
111C22×C31—212no—
112C22×C31—26no—
113C22×C31—212no—
114C22×C31—224no—
115C22×C31—41no—
116C22×C31—43no—
117C22×C31—46no—
118C22×C31—43no—
119C22×C31—42no—
120C22×C31—41no—
121C22×C31—424no—
122C22×C31—412no—
123C22×C31—448no—
124C22×C31—424no—
125C22×C31—44no—
126C22×C31C4×C22⋊C413yes—
127C22×C31#38613yes—
128C22×C31#38816yes—
129C22×C31#39013yes—
130C22×C31B(4,𝔽2)14yes—
131C4×C31—412no—
132C4×C31—86no—
133C26C22×C3111yescharacteristic
134C22×C22⋊C4—26no—
135C22×C22⋊C4C22×C3113yes—
136C22×C22⋊C4C22×C3113yes—
137#379—26no—
138#379C4×C31112yescomplemented
139C4×C22⋊C4—26no—
140#342—26no—
141C2×C31—23no—
142C2×C31—23no—
143C2×C31—26no—
144C2×C31—48no—
145C2×C31#143711yescharacteristic
146C2×C31#188916yes—
147C25—23no—
148C25—23no—
149C25—26no—
150C25—48no—
151C25C2×C4×C3116yes—
152C25C23×C3111yescharacteristic
153C23×C4—23no—
154C23×C4D4×C3116yes—
155C2×C22⋊C4—26no—
156C2×C22⋊C4—26no—
157C2×C22⋊C4—26no—
158C2×C22⋊C4—26no—
159C2×C22⋊C4—23no—
160C2×C22⋊C4—224no—
161C2×C22⋊C4—424no—
162C2×C22⋊C4C2×C4×C3116yes—
163C2×C22⋊C4C2×C4×C3116yes—
164C2×C22⋊C4D4×C3116yes—
165C2×C42—24no—
166#95—24no—
167C31#1093511yescharacteristic, direct product factor, Sylow
168C24—224no—
169C24—26no—
170C24—212no—
171C24—26no—
172C24—212no—
173C24—424no—
174C24—44no—
175C24—412no—
176C24—424no—
177C24—448no—
178C24—41no—
179C24—46no—
180C24—43no—
181C24—43no—
182C24—42no—
183C24—41no—
184C24C42×C3114yescomplemented
185C24C22×C4×C3113yes—
186C24C2×D4×C3113yes—
187C24C2×D4×C3113yes—
188C24#41×C3116yes—
189C22×C4—26no—
190C22×C4—26no—
191C22×C4—26no—
192C22×C4—412no—
193C22×C4—412no—
194C22×C4—46no—
195C22×C4C22⋊C4×C31112yescomplemented
196C22⋊C4—212no—
197C22⋊C4—212no—
198C22⋊C4—212no—
199C22⋊C4—448no—
200C22⋊C4—43no—
201C22⋊C4—43no—
202C42—84no—
203C23—212no—
204C23—224no—
205C23—248no—
206C23—212no—
207C23—48no—
208C23—46no—
209C23—46no—
210C23—412no—
211C23—412no—
212C23—448no—
213C23—424no—
214C23—424no—
215C23—424no—
216C23—448no—
217C23—424no—
218C23—416no—
219C23—48no—
220C23—48no—
221C23—46no—
222C23—412no—
223C23—46no—
224C23C2×C42×C3111yescharacteristic
225C23C2×C22⋊C4×C3113yes—
226C23C31×#11713yes—
227C23C4×D4×C3116yes—
228C23C4×D4×C3116yes—
229C23C31×#12011yescharacteristic
230C23C31×#12116yes—
231C23C31×#12313yes—
232C23C31×#12413yes—
233C23C31×#12612yes—
234C23C31×#12711yescharacteristic
235C2×C4—212no—
236C2×C4—412no—
237C2×C4—412no—
238C2×C4—412no—
239C2×C4—46no—
240C2×C4—86no—
241C2×C4—812no—
242C22—26no—
243C22—212no—
244C22—26no—
245C22—212no—
246C22—224no—
247C22—41no—
248C22—43no—
249C22—46no—
250C22—43no—
251C22—42no—
252C22—41no—
253C22—424no—
254C22—412no—
255C22—448no—
256C22—424no—
257C22—44no—
258C22C4×C22⋊C4×C3113yes—
259C22C31×#38613yes—
260C22C31×#38816yes—
261C22C31×#39013yes—
262C22C31×B(4,𝔽2)14yes—
263C4—412no—
264C4—86no—
265C2—23no—
266C2—23no—
267C2—26no—
268C2—48no—
269C2C31×#143711yescharacteristic
270C2C31×#188916yes—
subgroupG/H
center, socleC23×C31#120
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2273C2semidirect
3. C2×C31×#342C2semidirect
9. C31×#379C4semidirect
48. C24×C31C42semidirect
59. C22×C4×C31C22⋊C4semidirect
67. #10935C31direct (N × H)
108. #2273C2×C31semidirect
109. C2×#342C2×C31semidirect
138. #379C4×C31semidirect
167. C31#10935direct (N × H)
184. C24C42×C31semidirect
195. C22×C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3792
C31×#22732
C2×C31×#3422
#1093531