Finite Group Databasebeta

← C31×#7214 #21463973

Subgroups — C31×#7214 #21463973

Order 7936.

290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 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×#1820C211yesmaximal, characteristic
2C31×#1750C211yesmaximal, characteristic
3C31×#1464C211yesmaximal, characteristic
4C2×C31×#117C2211yescharacteristic
5C31×#432—21no—
6C2×C31×C22⋊C8—21no—
7C2×C31×#97C411yescharacteristic, complemented
8C2×C4×C8×C31C411yescharacteristic, complemented
9C31×#381—21no—
10C31×#342—21no—
11C31×#342C412yes—
12C31×#336—21no—
13C31×#324C412yescomplemented
14C31×#323—21no—
15C23×C4×C31D411yescharacteristic
16C22×C8×C31—21no—
17C22×C8×C31—21no—
18C31×#117—41no—
19C31×#117—41no—
20C2×C4⋊C4×C31C2×C411yescharacteristic
21C2×C4⋊C4×C31Q811yescharacteristic
22C2×C22⋊C4×C31—22no—
23C2×C22⋊C4×C31C2×C411yescharacteristic
24C2×C22⋊C4×C31D411yescharacteristic
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31D411yescharacteristic
27C31×C4⋊C8—41no—
28C31×C22⋊C8—24no—
29C31×C22⋊C8—22no—
30C31×#97—41no—
31C31×#97—41no—
32C4×C8×C31—41no—
33C31×#95—41no—
34C31×#95—41no—
35C24×C31C22⋊C411yescharacteristic
36C22×C4×C31—22no—
37C22×C4×C31—21no—
38C22×C4×C31—21no—
39C22×C4×C31—41no—
40C22×C4×C31—42no—
41C22×C4×C31C4211yescharacteristic
42C22×C4×C31C22⋊C411yescharacteristic
43C22×C4×C31C22⋊C411yescharacteristic
44C22×C4×C31C4⋊C411yescharacteristic
45C22×C4×C31C4⋊C411yescharacteristic
46C22×C4×C31C4⋊C411yescharacteristic
47C2×C8×C31—22no—
48C2×C8×C31—22no—
49C2×C8×C31—41no—
50C2×C8×C31—41no—
51C2×C8×C31—41no—
52C2×C8×C31—41no—
53C2×C8×C31—42no—
54C4⋊C4×C31—41no—
55C4⋊C4×C31—41no—
56C22⋊C4×C31—41no—
57C22⋊C4×C31—41no—
58C22⋊C4×C31—42no—
59C22⋊C4×C31—42no—
60C42×C31—21no—
61C42×C31—21no—
62C42×C31—21no—
63C42×C31—21no—
64#7214C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31—21no—
66C23×C31—21no—
67C23×C31—41no—
68C23×C31—41no—
69C23×C31#9511yescharacteristic
70C23×C31#10412yes—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—42no—
81C2×C4×C31—42no—
82C2×C4×C31—41no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×C4×C31—41no—
86C2×C4×C31—82no—
87C2×C4×C31—82no—
88C2×C4×C31—82no—
89C2×C4×C31#9911yescharacteristic
90C2×C4×C31#9911yescharacteristic
91C8×C31—42no—
92C8×C31—42no—
93C8×C31—82no—
94#1820C2×C3111yescharacteristic
95#1750C2×C3111yescharacteristic
96#1464C2×C3111yescharacteristic
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—22no—
100C22×C31—42no—
101C22×C31—41no—
102C22×C31—41no—
103C22×C31—81no—
104C22×C31H(3,ℤ/4)11yescharacteristic
105C22×C31#33911yescharacteristic
106C22×C31#34211yescharacteristic
107C4×C31—21no—
108C4×C31—21no—
109C4×C31—41no—
110C4×C31—41no—
111C4×C31—41no—
112C4×C31—41no—
113C4×C31—41no—
114C4×C31—162no—
115C2×#117C22×C3111yescharacteristic
116#432—21no—
117C2×C22⋊C8—21no—
118C2×#97C4×C3111yescharacteristic, complemented
119C2×C4×C8C4×C3111yescharacteristic, complemented
120#381—21no—
121#342—21no—
122#342C4×C3112yes—
123#336—21no—
124#324C4×C3112yescomplemented
125#323—21no—
126C2×C31—21no—
127C2×C31—21no—
128C2×C31—42no—
129C2×C31#128411yescharacteristic
130C2×C31#139111yescharacteristic
131C2×C31#139511yescharacteristic
132C23×C4D4×C3111yescharacteristic
133C22×C8—21no—
134C22×C8—21no—
135#117—41no—
136#117—41no—
137C2×C4⋊C4C2×C4×C3111yescharacteristic
138C2×C4⋊C4Q8×C3111yescharacteristic
139C2×C22⋊C4—22no—
140C2×C22⋊C4C2×C4×C3111yescharacteristic
141C2×C22⋊C4D4×C3111yescharacteristic
142C2×C42C2×C4×C3111yescharacteristic
143C2×C42D4×C3111yescharacteristic
144C4⋊C8—41no—
145C22⋊C8—24no—
146C22⋊C8—22no—
147#97—41no—
148#97—41no—
149C4×C8—41no—
150#95—41no—
151#95—41no—
152C31#721411yescharacteristic, direct product factor, Sylow
153C24C22⋊C4×C3111yescharacteristic
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—42no—
159C22×C4C42×C3111yescharacteristic
160C22×C4C22⋊C4×C3111yescharacteristic
161C22×C4C22⋊C4×C3111yescharacteristic
162C22×C4C4⋊C4×C3111yescharacteristic
163C22×C4C4⋊C4×C3111yescharacteristic
164C22×C4C4⋊C4×C3111yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—42no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C22⋊C4—41no—
175C22⋊C4—41no—
176C22⋊C4—42no—
177C22⋊C4—42no—
178C42—21no—
179C42—21no—
180C42—21no—
181C42—21no—
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23C31×#9511yescharacteristic
187C23C31×#10412yes—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—82no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4C31×#9911yescharacteristic
207C2×C4C31×#9911yescharacteristic
208C8—42no—
209C8—42no—
210C8—82no—
211C22—21no—
212C22—21no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22C31×H(3,ℤ/4)11yescharacteristic
219C22C31×#33911yescharacteristic
220C22C31×#34211yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—162no—
229C2—21no—
230C2—21no—
231C2—42no—
232C2C31×#128411yescharacteristic
233C2C31×#139111yescharacteristic
234C2C31×#139511yescharacteristic
subgroupG/H
center, socleC22×C31#342
commutatorC22×C4C42×C31
Frattini, cosocleC2×#117C22×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C31×#97C4semidirect
8. C2×C4×C8×C31C4semidirect
13. C31×#324C4semidirect
64. #7214C31direct (N × H)
118. C2×#97C4×C31semidirect
119. C2×C4×C8C4×C31semidirect
124. #324C4×C31semidirect
152. C31#7214direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18202
C31×#17502
C31×#14642
#721431