Finite Group Databasebeta

← C31×#9406 #21466165

Subgroups — C31×#9406 #21466165

Order 7936.

554 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2983C211yesmaximal, characteristic, complemented
2C31×#2548C211yesmaximal, characteristic
3C31×#1801C211yesmaximal, characteristic, complemented
4C31×#1545C212yesmaximal
5C31×#1303C212yesmaximal, complemented
6C2×C31×#127C2211yescharacteristic
7C2×C31×#124—21no—
8C2×C4×Q8×C31C2211yescharacteristic
9C31×#446—24no—
10C31×#432—22no—
11C31×#431C2212yes—
12C31×#423C2212yes—
13C2×C31×#101—21no—
14C31×#394C414yes—
15C31×#390—21no—
16C31×#390—22no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#331—24no—
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31—21no—
22C22×D4×C31—21no—
23C22×D4×C31C2×C412yes—
24C2×M16×C31—22no—
25C31×#127—22no—
26C31×#127—22no—
27C31×#124—44no—
28C4×Q8×C31—22no—
29C4×Q8×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C412yes—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31—24no—
35C2×C42×C31—21no—
36C2×C42×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×C4⋊C8—24no—
39C31×C4⋊C8—22no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8D414yes—
42C31×#101—42no—
43C31×C22⋊C8—22no—
44C31×#97—24no—
45C4×C8×C31—22no—
46C31×#95C2×C412yes—
47C24×C31—22no—
48C2×Q8×C31—22no—
49C2×Q8×C31—21no—
50C2×Q8×C31—22no—
51C2×Q8×C31—21no—
52C2×D4×C31—24no—
53C2×D4×C31—44no—
54C2×D4×C31—41no—
55C2×D4×C31—42no—
56C2×D4×C31—41no—
57C2×D4×C31—42no—
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31—82no—
61C22×C4×C31—22no—
62C22×C4×C31C22⋊C412yes—
63C22×C4×C31C22⋊C412yes—
64C22×C4×C31C22×C411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66C22×C4×C31C2×D411yescharacteristic
67M16×C31—42no—
68M16×C31—42no—
69C2×C8×C31—24no—
70C2×C8×C31—42no—
71C4⋊C4×C31—24no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—42no—
74C22⋊C4×C31—48no—
75C22⋊C4×C31—84no—
76C42×C31—22no—
77C42×C31—22no—
78C42×C31—42no—
79C42×C31C2×D412yes—
80C42×C31#4112yes—
81#9406C3111yesmaximal, characteristic, direct product factor, Sylow
82C23×C31—44no—
83C23×C31—44no—
84C23×C31—42no—
85C23×C31—42no—
86C23×C31—42no—
87C23×C31C2×C22⋊C411yescharacteristic
88Q8×C31—42no—
89Q8×C31—42no—
90D4×C31—84no—
91D4×C31—82no—
92D4×C31—82no—
93D4×C31—82no—
94D4×C31—82no—
95C2×C4×C31—22no—
96C2×C4×C31—22no—
97C2×C4×C31—22no—
98C2×C4×C31—22no—
99C2×C4×C31—22no—
100C2×C4×C31—41no—
101C2×C4×C31—42no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31C4×D412yes—
106C2×C4×C31#12011yescharacteristic
107C2×C4×C31#12112yes—
108C2×C4×C31#12311yescharacteristic
109C2×C4×C31AGL(1,ℤ/8)12yes—
110C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C31#13711yescharacteristic
112C8×C31—44no—
113C8×C31—82no—
114#2983C2×C3111yescharacteristic, complemented
115#2548C2×C3111yescharacteristic
116#1801C2×C3111yescharacteristic, complemented
117#1545C2×C3112yes—
118#1303C2×C3112yescomplemented
119C22×C31—21no—
120C22×C31—21no—
121C22×C31—84no—
122C22×C31—84no—
123C22×C31—82no—
124C22×C31—82no—
125C22×C31—82no—
126C22×C31#38611yescharacteristic
127C22×C31#41711yescharacteristic
128C22×C31#41811yescharacteristic
129C4×C31—21no—
130C4×C31—22no—
131C4×C31—42no—
132C4×C31—42no—
133C4×C31—82no—
134C4×C31#45412yes—
135C4×C31#46812yes—
136C4×C31#46912yes—
137C2×#127C22×C3111yescharacteristic
138C2×#124—21no—
139C2×C4×Q8C22×C3111yescharacteristic
140#446—24no—
141#432—22no—
142#431C22×C3112yes—
143#423C22×C3112yes—
144C2×#101—21no—
145#394C4×C3114yes—
146#390—21no—
147#390—22no—
148C4×C4⋊C4C22×C3111yescharacteristic
149#343—21no—
150#331—24no—
151C2×C31—21no—
152C2×C31—21no—
153C2×C31—162no—
154C2×C31#188811yescharacteristic
155C2×C31#189511yescharacteristic
156C2×C31#191411yescharacteristic
157C22×Q8D4×C3111yescharacteristic
158C22×D4—21no—
159C22×D4—21no—
160C22×D4C2×C4×C3112yes—
161C2×M16—22no—
162#127—22no—
163#127—22no—
164#124—44no—
165C4×Q8—22no—
166C4×Q8—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×C4×C3112yes—
169C2×C4⋊C4D4×C3111yescharacteristic
170C2×C22⋊C4—24no—
171C2×C22⋊C4—24no—
172C2×C42—21no—
173C2×C42D4×C3112yes—
174C2×C42C23×C3111yescharacteristic
175C4⋊C8—24no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8D4×C3114yes—
179#101—42no—
180C22⋊C8—22no—
181#97—24no—
182C4×C8—22no—
183#95C2×C4×C3112yes—
184C31#940611yescharacteristic, direct product factor, Sylow
185C24—22no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×D4—24no—
191C2×D4—44no—
192C2×D4—41no—
193C2×D4—42no—
194C2×D4—41no—
195C2×D4—42no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—82no—
199C22×C4—22no—
200C22×C4C22⋊C4×C3112yes—
201C22×C4C22⋊C4×C3112yes—
202C22×C4C22×C4×C3111yescharacteristic
203C22×C4C2×D4×C3111yescharacteristic
204C22×C4C2×D4×C3111yescharacteristic
205M16—42no—
206M16—42no—
207C2×C8—24no—
208C2×C8—42no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—42no—
212C22⋊C4—48no—
213C22⋊C4—84no—
214C42—22no—
215C42—22no—
216C42—42no—
217C42C2×D4×C3112yes—
218C42#41×C3112yes—
219C23—44no—
220C23—44no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23C2×C22⋊C4×C3111yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—84no—
228D4—82no—
229D4—82no—
230D4—82no—
231D4—82no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4C4×D4×C3112yes—
243C2×C4C31×#12011yescharacteristic
244C2×C4C31×#12112yes—
245C2×C4C31×#12311yescharacteristic
246C2×C4C31×AGL(1,ℤ/8)12yes—
247C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
248C2×C4C31×#13711yescharacteristic
249C8—44no—
250C8—82no—
251C22—21no—
252C22—21no—
253C22—84no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22C31×#38611yescharacteristic
259C22C31×#41711yescharacteristic
260C22C31×#41811yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4C31×#45412yes—
267C4C31×#46812yes—
268C4C31×#46912yes—
269C2—21no—
270C2—21no—
271C2—162no—
272C2C31×#188811yescharacteristic
273C2C31×#189511yescharacteristic
274C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2983C2semidirect
3. C31×#1801C2semidirect
5. C31×#1303C2semidirect
81. #9406C31direct (N × H)
114. #2983C2×C31semidirect
116. #1801C2×C31semidirect
118. #1303C2×C31semidirect
184. C31#9406direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29832
C31×#25482
C31×#18012
C31×#15452
C31×#13032
#940631