Finite Group Databasebeta

← C31×#9482 #21466241

Subgroups — C31×#9482 #21466241

Order 7936.

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2484C211yesmaximal, characteristic
2C31×#2313C211yesmaximal, characteristic
3C31×#1826C212yesmaximal
4C31×#1463C211yesmaximal, characteristic
5C31×#1284C212yesmaximal
6C2×C31×#117C2211yescharacteristic
7C22×C4⋊C4×C31C2211yescharacteristic
8C31×#407C2212yes—
9C31×#400C412yescomplemented
10C31×#398C412yescomplemented
11C31×#387—22no—
12C31×#387—24no—
13C31×#385—21no—
14C31×#381—21no—
15C31×#381—21no—
16C31×#381C2211yescharacteristic
17C31×#380—21no—
18C4×C22⋊C4×C31C2212yes—
19C31×#339—24no—
20C31×#324—22no—
21C23×C4×C31D411yescharacteristic
22C23×C4×C31D411yescharacteristic
23C23×C4×C31C2311yescharacteristic
24C2×M16×C31—22no—
25C31×#117—22no—
26C31×#117—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C412yes—
34C2×C4⋊C4×C31D412yes—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—21no—
38C2×C42×C31—21no—
39C2×C42×C31D414yes—
40C31×C22⋊C8—22no—
41C31×C22⋊C8—22no—
42C31×#95—22no—
43C31×#95—24no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—21no—
49C31×#95C2×C412yes—
50C24×C31C2×D411yescharacteristic
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—22no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—24no—
59C22×C4×C31—42no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31C22⋊C412yes—
63C22×C4×C31C22⋊C412yes—
64C22×C4×C31C22×C411yescharacteristic
65C22×C4×C31C2×D412yes—
66C22×C4×C31C2×D411yescharacteristic
67C22×C4×C31#4112yes—
68M16×C31—44no—
69C2×C8×C31—42no—
70C4⋊C4×C31—24no—
71C4⋊C4×C31—24no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—22no—
74C4⋊C4×C31—44no—
75C4⋊C4×C31—82no—
76C22⋊C4×C31—44no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—41no—
79C22⋊C4×C31—41no—
80C42×C31—44no—
81C42×C31—42no—
82#9482C3111yesmaximal, characteristic, direct product factor, Sylow
83C23×C31—22no—
84C23×C31—22no—
85C23×C31—41no—
86C23×C31C2×C22⋊C411yescharacteristic
87C23×C31#12011yescharacteristic
88C23×C31#12311yescharacteristic
89C2×C4×C31—24no—
90C2×C4×C31—22no—
91C2×C4×C31—22no—
92C2×C4×C31—22no—
93C2×C4×C31—22no—
94C2×C4×C31—41no—
95C2×C4×C31—41no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—44no—
103C2×C4×C31—42no—
104C2×C4×C31—44no—
105C2×C4×C31—42no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—44no—
111C2×C4×C31—81no—
112C2×C4×C31C4×D412yes—
113C2×C4×C31#12112yes—
114C8×C31—82no—
115#2484C2×C3111yescharacteristic
116#2313C2×C3111yescharacteristic
117#1826C2×C3112yes—
118#1463C2×C3111yescharacteristic
119#1284C2×C3112yes—
120C22×C31—21no—
121C22×C31—21no—
122C22×C31—21no—
123C22×C31—21no—
124C22×C31—21no—
125C22×C31—21no—
126C22×C31—21no—
127C22×C31—44no—
128C22×C31#38611yescharacteristic
129C22×C31#42112yes—
130C22×C31#45812yes—
131C4×C31—22no—
132C4×C31—22no—
133C4×C31—42no—
134C4×C31—42no—
135C4×C31—84no—
136C4×C31—82no—
137C4×C31—81no—
138C4×C31—81no—
139C2×#117C22×C3111yescharacteristic
140C22×C4⋊C4C22×C3111yescharacteristic
141#407C22×C3112yes—
142#400C4×C3112yescomplemented
143#398C4×C3112yescomplemented
144#387—22no—
145#387—24no—
146#385—21no—
147#381—21no—
148#381—21no—
149#381C22×C3111yescharacteristic
150#380—21no—
151C4×C22⋊C4C22×C3112yes—
152#339—24no—
153#324—22no—
154C2×C31—22no—
155C2×C31—22no—
156C2×C31—41no—
157C2×C31#189011yescharacteristic
158C2×C31#189711yescharacteristic
159C2×C31#191211yescharacteristic
160C23×C4D4×C3111yescharacteristic
161C23×C4D4×C3111yescharacteristic
162C23×C4C23×C3111yescharacteristic
163C2×M16—22no—
164#117—22no—
165#117—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×C4×C3111yescharacteristic
171C2×C4⋊C4C2×C4×C3111yescharacteristic
172C2×C4⋊C4C2×C4×C3112yes—
173C2×C4⋊C4D4×C3112yes—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—21no—
177C2×C42—21no—
178C2×C42D4×C3114yes—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—22no—
182#95—24no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—21no—
188#95C2×C4×C3112yes—
189C31#948211yescharacteristic, direct product factor, Sylow
190C24C2×D4×C3111yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4C22⋊C4×C3112yes—
203C22×C4C22⋊C4×C3112yes—
204C22×C4C22×C4×C3111yescharacteristic
205C22×C4C2×D4×C3112yes—
206C22×C4C2×D4×C3111yescharacteristic
207C22×C4#41×C3112yes—
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—82no—
216C22⋊C4—44no—
217C22⋊C4—42no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C42—44no—
221C42—42no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×C22⋊C4×C3111yescharacteristic
226C23C31×#12011yescharacteristic
227C23C31×#12311yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4C4×D4×C3112yes—
252C2×C4C31×#12112yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22C31×#38611yescharacteristic
263C22C31×#42112yes—
264C22C31×#45812yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—84no—
270C4—82no—
271C4—81no—
272C4—81no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2C31×#189011yescharacteristic
277C2C31×#189711yescharacteristic
278C2C31×#191211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#400C4semidirect
10. C31×#398C4semidirect
82. #9482C31direct (N × H)
142. #400C4×C31semidirect
143. #398C4×C31semidirect
189. C31#9482direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24842
C31×#23132
C31×#18262
C31×#14632
C31×#12842
#948231