Finite Group Databasebeta

← C31×#7402 #21464161

Subgroups — C31×#7402 #21464161

Order 7936.

334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2011C211yesmaximal, characteristic
2C31×#1393C211yesmaximal, characteristic, complemented
3C31×#1318C211yesmaximal, characteristic, complemented
4C22×D8×C31—21no—
5C2×C31×#127C411yescharacteristic, complemented
6C2×C31×#102—21no—
7C2×C31×#99—21no—
8C31×#390C2211yescharacteristic
9C31×#336C411yescharacteristic, complemented
10C31×#324—21no—
11C22×D4×C31—21no—
12C22×D4×C31—41no—
13C22×D4×C31D411yescharacteristic
14C2×D8×C31—42no—
15C2×D8×C31—42no—
16C2×D8×C31—41no—
17C2×D8×C31—41no—
18C22×C8×C31—21no—
19C31×#127—42no—
20C2×C4⋊C4×C31D411yescharacteristic
21C2×C22⋊C4×C31—41no—
22C2×C22⋊C4×C31—41no—
23C2×C42×C31C2×C411yescharacteristic
24C31×#102—42no—
25C31×#99—22no—
26C31×#99—41no—
27C31×C22⋊C8—41no—
28C24×C31—21no—
29C24×C31—41no—
30C2×D4×C31—22no—
31C2×D4×C31—21no—
32C2×D4×C31—41no—
33C2×D4×C31—41no—
34C2×D4×C31—41no—
35C2×D4×C31—41no—
36C2×D4×C31—41no—
37C2×D4×C31—42no—
38C2×D4×C31—42no—
39C2×D4×C31—41no—
40C2×D4×C31—41no—
41C2×D4×C31—82no—
42C2×D4×C31—82no—
43C2×D4×C31D811yescharacteristic
44C2×D4×C31SD1611yescharacteristic
45C22×C4×C31—21no—
46C22×C4×C31—21no—
47C22×C4×C31—81no—
48C22×C4×C31C22⋊C411yescharacteristic
49D8×C31—44no—
50D8×C31—44no—
51C2×C8×C31—22no—
52C2×C8×C31—41no—
53C2×C8×C31—41no—
54C2×C8×C31—81no—
55C4⋊C4×C31—41no—
56C22⋊C4×C31—42no—
57C22⋊C4×C31—82no—
58C22⋊C4×C31—81no—
59C42×C31—41no—
60#7402C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—21no—
62C23×C31—21no—
63C23×C31—41no—
64C23×C31—41no—
65C23×C31—42no—
66C23×C31—81no—
67C23×C31—81no—
68C23×C31—82no—
69C23×C31—82no—
70C23×C31—81no—
71C23×C31—81no—
72C23×C31#9911yescharacteristic
73D4×C31—41no—
74D4×C31—41no—
75D4×C31—42no—
76D4×C31—42no—
77D4×C31—81no—
78D4×C31—81no—
79D4×C31—81no—
80D4×C31—84no—
81D4×C31—84no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—22no—
85C2×C4×C31—41no—
86C2×C4×C31—41no—
87C2×C4×C31—41no—
88C2×C4×C31—81no—
89C2×C4×C31—82no—
90C2×C4×C31—161no—
91C2×C4×C31—161no—
92C2×C4×C31#10211yescharacteristic
93C2×C4×C31#10411yescharacteristic
94C8×C31—42no—
95C8×C31—161no—
96#2011C2×C3111yescharacteristic
97#1393C2×C3111yescharacteristic, complemented
98#1318C2×C3111yescharacteristic, complemented
99C22×C31—21no—
100C22×C31—21no—
101C22×C31—41no—
102C22×C31—41no—
103C22×C31—81no—
104C22×C31—81no—
105C22×C31—84no—
106C22×C31—81no—
107C22×C31—81no—
108C22×C31—82no—
109C22×C31—161no—
110C22×C31—162no—
111C22×C31—161no—
112C22×C31—161no—
113C22×C31#32711yescharacteristic
114C22×C31AΣL(1,𝔽16)11yescharacteristic
115C22×C31#35311yescharacteristic
116C4×C31—21no—
117C4×C31—21no—
118C4×C31—42no—
119C4×C31—81no—
120C4×C31—162no—
121C22×D8—21no—
122C2×#127C4×C3111yescharacteristic, complemented
123C2×#102—21no—
124C2×#99—21no—
125#390C22×C3111yescharacteristic
126#336C4×C3111yescharacteristic, complemented
127#324—21no—
128C2×C31—21no—
129C2×C31—21no—
130C2×C31—81no—
131C2×C31—81no—
132C2×C31—162no—
133C2×C31#134311yescharacteristic
134C2×C31#140611yescharacteristic
135C2×C31#140811yescharacteristic
136C22×D4—21no—
137C22×D4—41no—
138C22×D4D4×C3111yescharacteristic
139C2×D8—42no—
140C2×D8—42no—
141C2×D8—41no—
142C2×D8—41no—
143C22×C8—21no—
144#127—42no—
145C2×C4⋊C4D4×C3111yescharacteristic
146C2×C22⋊C4—41no—
147C2×C22⋊C4—41no—
148C2×C42C2×C4×C3111yescharacteristic
149#102—42no—
150#99—22no—
151#99—41no—
152C22⋊C8—41no—
153C31#740211yescharacteristic, direct product factor, Sylow
154C24—21no—
155C24—41no—
156C2×D4—22no—
157C2×D4—21no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—42no—
164C2×D4—42no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—82no—
168C2×D4—82no—
169C2×D4D8×C3111yescharacteristic
170C2×D4SD16×C3111yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—81no—
174C22×C4C22⋊C4×C3111yescharacteristic
175D8—44no—
176D8—44no—
177C2×C8—22no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—81no—
181C4⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—82no—
184C22⋊C4—81no—
185C42—41no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—42no—
191C23—81no—
192C23—81no—
193C23—82no—
194C23—82no—
195C23—81no—
196C23—81no—
197C23C31×#9911yescharacteristic
198D4—41no—
199D4—41no—
200D4—42no—
201D4—42no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—84no—
206D4—84no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—81no—
214C2×C4—82no—
215C2×C4—161no—
216C2×C4—161no—
217C2×C4C31×#10211yescharacteristic
218C2×C4C31×#10411yescharacteristic
219C8—42no—
220C8—161no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—84no—
228C22—81no—
229C22—81no—
230C22—82no—
231C22—161no—
232C22—162no—
233C22—161no—
234C22—161no—
235C22C31×#32711yescharacteristic
236C22C31×AΣL(1,𝔽16)11yescharacteristic
237C22C31×#35311yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—81no—
242C4—162no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—81no—
247C2—162no—
248C2C31×#134311yescharacteristic
249C2C31×#140611yescharacteristic
250C2C31×#140811yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC2×C42C2×C4×C31
Frattini, cosocle#390C22×C31
prime radicalC31×#2011C2
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#390 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1393C2semidirect
3. C31×#1318C2semidirect
5. C2×C31×#127C4semidirect
9. C31×#336C4semidirect
60. #7402C31direct (N × H)
97. #1393C2×C31semidirect
98. #1318C2×C31semidirect
122. C2×#127C4×C31semidirect
126. #336C4×C31semidirect
153. C31#7402direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20112
C31×#13932
C31×#13182
#740231