Finite Group Databasebeta

← C31×#11510 #21468269

Subgroups — C31×#11510 #21468269

Order 7936.

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

normal subgroups only

This group has 510 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×#2310C211yesmaximal, characteristic
2C31×#1464C212yesmaximal
3C31×#1319C214yesmaximal, complemented
4C23×Q8×C31C411yescharacteristic
5C2×C31×#117C411yescharacteristic
6C2×C31×#117C2211yescharacteristic
7C31×#432—22no—
8C31×#391—22no—
9C31×#391C412yes—
10C31×#391C2212yes—
11C31×#381—22no—
12C31×#324C2214yes—
13C31×#323—22no—
14C22×Q8×C31—24no—
15C22×Q8×C31—21no—
16C22×Q8×C31—42no—
17C22×Q8×C31—42no—
18C22×Q8×C31C2×C412yes—
19C23×C4×C31—21no—
20C23×C4×C31C2×C411yescharacteristic
21C31×#117—42no—
22C31×#117—42no—
23C2×C4⋊C4×C31—21no—
24C2×C4⋊C4×C31C2×C411yescharacteristic
25C2×C4⋊C4×C31C2311yescharacteristic
26C2×C22⋊C4×C31—21no—
27C2×C22⋊C4×C31D412yes—
28C2×C42×C31C2×C412yes—
29C2×C42×C31D412yes—
30C31×C4⋊C8—42no—
31C31×C22⋊C8—24no—
32C31×#97—42no—
33C31×#95—24no—
34C31×#95—24no—
35C24×C31C22⋊C411yescharacteristic
36C2×Q8×C31—24no—
37C2×Q8×C31—22no—
38C2×Q8×C31—416no—
39C2×Q8×C31—42no—
40C2×Q8×C31—42no—
41C2×Q8×C31—42no—
42C2×Q8×C31—42no—
43C2×Q8×C31M1614yes—
44C22×C4×C31—22no—
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—42no—
52C22×C4×C31C22⋊C412yes—
53C22×C4×C31C22⋊C411yescharacteristic
54C22×C4×C31C22×C411yescharacteristic
55C22×C4×C31C2×D412yes—
56C2×C8×C31—44no—
57C4⋊C4×C31—41no—
58C4⋊C4×C31—41no—
59C4⋊C4×C31—42no—
60C22⋊C4×C31—42no—
61C22⋊C4×C31—42no—
62C42×C31—22no—
63C42×C31—22no—
64C42×C31—42no—
65#11510C3111yesmaximal, characteristic, direct product factor, Sylow
66C23×C31—21no—
67C23×C31—21no—
68C23×C31—41no—
69C23×C31—41no—
70C23×C31#10012yes—
71C23×C31C2×C22⋊C411yescharacteristic
72Q8×C31—44no—
73Q8×C31—48no—
74Q8×C31—44no—
75C2×C4×C31—28no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—24no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—48no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31#9912yes—
92C2×C4×C31C2×M1612yes—
93C8×C31—84no—
94#2310C2×C3111yescharacteristic
95#1464C2×C3112yes—
96#1319C2×C3114yescomplemented
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—22no—
100C22×C31—42no—
101C22×C31—42no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31#40711yescharacteristic
105C22×C31C2×#9911yescharacteristic
106C22×C31C2×#10011yescharacteristic
107C4×C31—22no—
108C4×C31—22no—
109C4×C31—42no—
110C4×C31—42no—
111C4×C31—44no—
112C4×C31—82no—
113C23×Q8C4×C3111yescharacteristic
114C2×#117C4×C3111yescharacteristic
115C2×#117C22×C3111yescharacteristic
116#432—22no—
117#391—22no—
118#391C4×C3112yes—
119#391C22×C3112yes—
120#381—22no—
121#324C22×C3114yes—
122#323—22no—
123C2×C31—21no—
124C2×C31—21no—
125C2×C31—42no—
126C2×C31#146211yescharacteristic
127C2×C31#212911yescharacteristic
128C2×C31#213511yescharacteristic
129C22×Q8—24no—
130C22×Q8—21no—
131C22×Q8—42no—
132C22×Q8—42no—
133C22×Q8C2×C4×C3112yes—
134C23×C4—21no—
135C23×C4C2×C4×C3111yescharacteristic
136#117—42no—
137#117—42no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×C4×C3111yescharacteristic
140C2×C4⋊C4C23×C3111yescharacteristic
141C2×C22⋊C4—21no—
142C2×C22⋊C4D4×C3112yes—
143C2×C42C2×C4×C3112yes—
144C2×C42D4×C3112yes—
145C4⋊C8—42no—
146C22⋊C8—24no—
147#97—42no—
148#95—24no—
149#95—24no—
150C31#1151011yescharacteristic, direct product factor, Sylow
151C24C22⋊C4×C3111yescharacteristic
152C2×Q8—24no—
153C2×Q8—22no—
154C2×Q8—416no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8M16×C3114yes—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4C22⋊C4×C3111yescharacteristic
169C22×C4C22⋊C4×C3112yes—
170C22×C4C22×C4×C3111yescharacteristic
171C22×C4C2×D4×C3112yes—
172C2×C8—44no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C22⋊C4—42no—
177C22⋊C4—42no—
178C42—22no—
179C42—22no—
180C42—42no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C31×#10012yes—
186C23C2×C22⋊C4×C3111yescharacteristic
187Q8—44no—
188Q8—48no—
189Q8—44no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—48no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4C31×#9912yes—
207C2×C4C2×M16×C3112yes—
208C8—84no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22C31×#40711yescharacteristic
217C22C2×C31×#9911yescharacteristic
218C22C2×C31×#10011yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—44no—
224C4—82no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2C31×#146211yescharacteristic
229C2C31×#212911yescharacteristic
230C2C31×#213511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×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
3. C31×#1319C2semidirect
65. #11510C31direct (N × H)
96. #1319C2×C31semidirect
150. C31#11510direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23102
C31×#14642
C31×#13192
#1151031