Finite Group Databasebeta

← C31×#11519 #21468278

Subgroups — C31×#11519 #21468278

Order 7936.

542 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2315C211yesmaximal, characteristic
2C31×#1462C212yesmaximal
3C31×#1326C214yesmaximal, complemented
4C22×C22⋊C4×C31C411yescharacteristic
5C22×C22⋊C4×C31C411yescharacteristic
6C22×C22⋊C4×C31C2211yescharacteristic
7C31×#407—22no—
8C31×#385—22no—
9C31×#385C412yes—
10C31×#385C2212yes—
11C31×#380—22no—
12C31×#323—22no—
13C31×#323C2214yes—
14C25×C31C2×C411yescharacteristic
15C23×C4×C31—21no—
16C23×C4×C31C2×C412yes—
17C23×C4×C31D412yes—
18C2×M16×C31—42no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—22no—
21C2×C22⋊C4×C31—21no—
22C2×C22⋊C4×C31—24no—
23C2×C22⋊C4×C31—21no—
24C2×C22⋊C4×C31—21no—
25C2×C22⋊C4×C31—41no—
26C2×C22⋊C4×C31—41no—
27C2×C22⋊C4×C31—41no—
28C2×C22⋊C4×C31—41no—
29C2×C22⋊C4×C31C2×C412yes—
30C2×C22⋊C4×C31C2×C411yescharacteristic
31C2×C22⋊C4×C31D412yes—
32C2×C22⋊C4×C31C2311yescharacteristic
33C31×C22⋊C8—24no—
34C31×C22⋊C8—42no—
35C31×#95—22no—
36C31×#95—22no—
37C24×C31—21no—
38C24×C31—21no—
39C24×C31—22no—
40C24×C31—22no—
41C24×C31—82no—
42C24×C31C22⋊C411yescharacteristic
43C24×C31C22⋊C411yescharacteristic
44C24×C31C22×C411yescharacteristic
45C22×C4×C31—22no—
46C22×C4×C31—22no—
47C22×C4×C31—24no—
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—42no—
51C22×C4×C31—82no—
52C22×C4×C31—82no—
53C22×C4×C31—82no—
54C22×C4×C31C22⋊C412yes—
55C22×C4×C31C2×D412yes—
56M16×C31—84no—
57C2×C8×C31—44no—
58C4⋊C4×C31—82no—
59C4⋊C4×C31—82no—
60C22⋊C4×C31—24no—
61C22⋊C4×C31—22no—
62C22⋊C4×C31—41no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—41no—
65C22⋊C4×C31—42no—
66C22⋊C4×C31—41no—
67C22⋊C4×C31—41no—
68C22⋊C4×C31M1614yescomplemented
69#11519C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31—24no—
71C23×C31—24no—
72C23×C31—21no—
73C23×C31—21no—
74C23×C31—21no—
75C23×C31—21no—
76C23×C31—21no—
77C23×C31—21no—
78C23×C31—42no—
79C23×C31—42no—
80C23×C31—42no—
81C23×C31—82no—
82C23×C31—82no—
83C23×C31—84no—
84C23×C31—84no—
85C23×C31#9911yescharacteristic
86C23×C31#9911yescharacteristic
87C23×C31#10112yes—
88C23×C31C2×C22⋊C411yescharacteristic
89C23×C31C2×M1612yes—
90C2×C4×C31—24no—
91C2×C4×C31—22no—
92C2×C4×C31—22no—
93C2×C4×C31—42no—
94C2×C4×C31—42no—
95C2×C4×C31—44no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—82no—
102C2×C4×C31—84no—
103C2×C4×C31—84no—
104C8×C31—84no—
105#2315C2×C3111yescharacteristic
106#1462C2×C3112yes—
107#1326C2×C3114yescomplemented
108C22×C31—22no—
109C22×C31—22no—
110C22×C31—22no—
111C22×C31—21no—
112C22×C31—21no—
113C22×C31—22no—
114C22×C31—22no—
115C22×C31—42no—
116C22×C31—42no—
117C22×C31—42no—
118C22×C31—42no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—42no—
122C22×C31—42no—
123C22×C31—84no—
124C22×C31—84no—
125C22×C31#40711yescharacteristic
126C22×C31C2×#9911yescharacteristic
127C22×C31C2×#10111yescharacteristic
128C4×C31—44no—
129C4×C31—42no—
130C4×C31—42no—
131C4×C31—82no—
132C22×C22⋊C4C4×C3111yescharacteristic
133C22×C22⋊C4C4×C3111yescharacteristic
134C22×C22⋊C4C22×C3111yescharacteristic
135#407—22no—
136#385—22no—
137#385C4×C3112yes—
138#385C22×C3112yes—
139#380—22no—
140#323—22no—
141#323C22×C3114yes—
142C2×C31—21no—
143C2×C31—21no—
144C2×C31—41no—
145C2×C31—41no—
146C2×C31—42no—
147C2×C31—42no—
148C2×C31#146311yescharacteristic
149C2×C31#212112yes—
150C25C2×C4×C3111yescharacteristic
151C23×C4—21no—
152C23×C4C2×C4×C3112yes—
153C23×C4D4×C3112yes—
154C2×M16—42no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—24no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—41no—
162C2×C22⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4C2×C4×C3112yes—
166C2×C22⋊C4C2×C4×C3111yescharacteristic
167C2×C22⋊C4D4×C3112yes—
168C2×C22⋊C4C23×C3111yescharacteristic
169C22⋊C8—24no—
170C22⋊C8—42no—
171#95—22no—
172#95—22no—
173C31#1151911yescharacteristic, direct product factor, Sylow
174C24—21no—
175C24—21no—
176C24—22no—
177C24—22no—
178C24—82no—
179C24C22⋊C4×C3111yescharacteristic
180C24C22⋊C4×C3111yescharacteristic
181C24C22×C4×C3111yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—82no—
189C22×C4—82no—
190C22×C4—82no—
191C22×C4C22⋊C4×C3112yes—
192C22×C4C2×D4×C3112yes—
193M16—84no—
194C2×C8—44no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C22⋊C4—24no—
198C22⋊C4—22no—
199C22⋊C4—41no—
200C22⋊C4—42no—
201C22⋊C4—41no—
202C22⋊C4—42no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4M16×C3114yescomplemented
206C23—24no—
207C23—24no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—42no—
215C23—42no—
216C23—42no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23C31×#9911yescharacteristic
222C23C31×#9911yescharacteristic
223C23C31×#10112yes—
224C23C2×C22⋊C4×C3111yescharacteristic
225C23C2×M16×C3112yes—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—84no—
239C2×C4—84no—
240C8—84no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—22no—
247C22—22no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—84no—
257C22—84no—
258C22C31×#40711yescharacteristic
259C22C2×C31×#9911yescharacteristic
260C22C2×C31×#10111yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—41no—
268C2—41no—
269C2—42no—
270C2—42no—
271C2C31×#146311yescharacteristic
272C2C31×#212112yes—
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×#1326C2semidirect
68. C22⋊C4×C31M16semidirect
69. #11519C31direct (N × H)
107. #1326C2×C31semidirect
173. C31#11519direct (N × H)
205. C22⋊C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23152
C31×#14622
C31×#13262
#1151931