Finite Group Databasebeta

← C31×#11500 #21468259

Subgroups — C31×#11500 #21468259

Order 7936.

706 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 118 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×#381C211yesmaximal, characteristic
2C31×#1462C212yesmaximal
3C31×#1317C214yesmaximal, complemented
4C24×C4×C31C411yescharacteristic
5C22×C22⋊C4×C31C411yescharacteristic
6C22×C22⋊C4×C31C2211yescharacteristic
7C31×#407—22no—
8C31×#381—22no—
9C31×#381C412yes—
10C31×#381C2212yes—
11C2×C31×#95—22no—
12C31×#323—22no—
13C31×#323C2214yes—
14C25×C31C2×C411yescharacteristic
15C23×C4×C31—21no—
16C23×C4×C31—21no—
17C23×C4×C31—24no—
18C23×C4×C31—21no—
19C23×C4×C31—42no—
20C23×C4×C31—42no—
21C23×C4×C31C2×C412yes—
22C23×C4×C31D412yes—
23C2×M16×C31—42no—
24C2×C22⋊C4×C31—21no—
25C2×C22⋊C4×C31—42no—
26C2×C22⋊C4×C31—42no—
27C2×C22⋊C4×C31C2×C412yes—
28C2×C22⋊C4×C31C2×C411yescharacteristic
29C2×C22⋊C4×C31D412yes—
30C2×C22⋊C4×C31C2311yescharacteristic
31C31×C22⋊C8—24no—
32C31×C22⋊C8—42no—
33C31×#95—24no—
34C31×#95—24no—
35C24×C31—22no—
36C24×C31—22no—
37C24×C31—22no—
38C24×C31—44no—
39C24×C31C22⋊C411yescharacteristic
40C24×C31C22⋊C411yescharacteristic
41C24×C31C22×C411yescharacteristic
42C22×C4×C31—24no—
43C22×C4×C31—24no—
44C22×C4×C31—22no—
45C22×C4×C31—22no—
46C22×C4×C31—22no—
47C22×C4×C31—22no—
48C22×C4×C31—22no—
49C22×C4×C31—416no—
50C22×C4×C31—42no—
51C22×C4×C31—42no—
52C22×C4×C31—42no—
53C22×C4×C31—42no—
54C22×C4×C31—42no—
55C22×C4×C31—42no—
56C22×C4×C31—44no—
57C22×C4×C31—42no—
58C22×C4×C31—44no—
59C22×C4×C31C22⋊C412yes—
60C22×C4×C31M1614yescomplemented
61C22×C4×C31C2×D412yes—
62M16×C31—84no—
63C2×C8×C31—44no—
64C22⋊C4×C31—41no—
65C22⋊C4×C31—42no—
66C22⋊C4×C31—41no—
67C22⋊C4×C31—42no—
68C22⋊C4×C31—42no—
69#11500C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—24no—
71C23×C31—21no—
72C23×C31—21no—
73C23×C31—28no—
74C23×C31—21no—
75C23×C31—21no—
76C23×C31—21no—
77C23×C31—21no—
78C23×C31—42no—
79C23×C31—42no—
80C23×C31—48no—
81C23×C31—48no—
82C23×C31—44no—
83C23×C31—44no—
84C23×C31#9912yes—
85C23×C31#10012yes—
86C23×C31C2×C22⋊C411yescharacteristic
87C23×C31C2×M1612yes—
88C2×C4×C31—24no—
89C2×C4×C31—22no—
90C2×C4×C31—22no—
91C2×C4×C31—48no—
92C2×C4×C31—48no—
93C2×C4×C31—44no—
94C2×C4×C31—44no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—44no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—44no—
101C2×C4×C31—42no—
102C2×C4×C31—82no—
103C2×C4×C31—84no—
104C8×C31—84no—
105C2×#381C2×C3111yescharacteristic
106#1462C2×C3112yes—
107#1317C2×C3114yescomplemented
108C22×C31—24no—
109C22×C31—24no—
110C22×C31—22no—
111C22×C31—22no—
112C22×C31—22no—
113C22×C31—22no—
114C22×C31—22no—
115C22×C31—42no—
116C22×C31—42no—
117C22×C31—42no—
118C22×C31—416no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—42no—
122C22×C31#35214yes—
123C22×C31#40711yescharacteristic
124C22×C31C2×#9911yescharacteristic
125C22×C31C2×#10011yescharacteristic
126C4×C31—42no—
127C4×C31—42no—
128C4×C31—44no—
129C4×C31—82no—
130C24×C4C4×C3111yescharacteristic
131C22×C22⋊C4C4×C3111yescharacteristic
132C22×C22⋊C4C22×C3111yescharacteristic
133#407—22no—
134#381—22no—
135#381C4×C3112yes—
136#381C22×C3112yes—
137C2×#95—22no—
138#323—22no—
139#323C22×C3114yes—
140C2×C31—21no—
141C2×C31—24no—
142C2×C31—21no—
143C2×C31—42no—
144C2×C31—42no—
145C2×C31#146211yescharacteristic
146C2×C31C2×#35212yes—
147C25C2×C4×C3111yescharacteristic
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—24no—
151C23×C4—21no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4C2×C4×C3112yes—
155C23×C4D4×C3112yes—
156C2×M16—42no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—42no—
159C2×C22⋊C4—42no—
160C2×C22⋊C4C2×C4×C3112yes—
161C2×C22⋊C4C2×C4×C3111yescharacteristic
162C2×C22⋊C4D4×C3112yes—
163C2×C22⋊C4C23×C3111yescharacteristic
164C22⋊C8—24no—
165C22⋊C8—42no—
166#95—24no—
167#95—24no—
168C31#1150011yescharacteristic, direct product factor, Sylow
169C24—22no—
170C24—22no—
171C24—22no—
172C24—44no—
173C24C22⋊C4×C3111yescharacteristic
174C24C22⋊C4×C3111yescharacteristic
175C24C22×C4×C3111yescharacteristic
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—416no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—44no—
191C22×C4—42no—
192C22×C4—44no—
193C22×C4C22⋊C4×C3112yes—
194C22×C4M16×C3114yescomplemented
195C22×C4C2×D4×C3112yes—
196M16—84no—
197C2×C8—44no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C23—21no—
204C23—21no—
205C23—24no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23C31×#9912yes—
218C23C31×#10012yes—
219C23C2×C22⋊C4×C3111yescharacteristic
220C23C2×M16×C3112yes—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—48no—
225C2×C4—48no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C8—84no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—416no—
250C22—42no—
251C22—42no—
252C22C31×#35214yes—
253C22C31×#40711yescharacteristic
254C22C2×C31×#9911yescharacteristic
255C22C2×C31×#10011yescharacteristic
256C4—42no—
257C4—42no—
258C4—44no—
259C4—82no—
260C2—21no—
261C2—21no—
262C2—24no—
263C2—42no—
264C2—42no—
265C2C31×#146211yescharacteristic
266C2C2×C31×#35212yes—
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1317C2semidirect
60. C22×C4×C31M16semidirect
69. #11500C31direct (N × H)
107. #1317C2×C31semidirect
168. C31#11500direct (N × H)
194. C22×C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3812
C31×#14622
C31×#13172
#1150031