Finite Group Databasebeta

← C31×#11434 #21468193

Subgroups — C31×#11434 #21468193

Order 7936.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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×#1458C212yesmaximal
3C31×#1319C214yesmaximal, complemented
4C23×Q8×C31C411yescharacteristic
5C2×C31×#117C411yescharacteristic
6C2×C31×#117C2211yescharacteristic
7C31×#431—22no—
8C31×#391—22no—
9C31×#391C412yes—
10C31×#391C2212yes—
11C31×#381—22no—
12C31×#324C2214yes—
13C31×#323—22no—
14C22×Q8×C31—21no—
15C22×Q8×C31—22no—
16C22×Q8×C31—42no—
17C22×Q8×C31—42no—
18C22×Q8×C31C814yescomplemented
19C22×Q8×C31C2×C412yes—
20C23×C4×C31—21no—
21C23×C4×C31C2×C411yescharacteristic
22C31×#117—42no—
23C31×#117—42no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31C2×C411yescharacteristic
26C2×C4⋊C4×C31C2311yescharacteristic
27C2×C22⋊C4×C31—21no—
28C2×C22⋊C4×C31D412yes—
29C2×C42×C31C2×C412yes—
30C2×C42×C31D412yes—
31C31×C4⋊C8—42no—
32C31×C22⋊C8—24no—
33C4×C8×C31—42no—
34C31×#95—24no—
35C31×#95—24no—
36C24×C31C22⋊C411yescharacteristic
37C2×Q8×C31—24no—
38C2×Q8×C31—22no—
39C2×Q8×C31—48no—
40C2×Q8×C31—48no—
41C2×Q8×C31—42no—
42C2×Q8×C31—42no—
43C2×Q8×C31—42no—
44C2×Q8×C31—42no—
45C2×Q8×C31C2×C814yes—
46C22×C4×C31—22no—
47C22×C4×C31—22no—
48C22×C4×C31—24no—
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—42no—
52C22×C4×C31—42no—
53C22×C4×C31C22⋊C412yes—
54C22×C4×C31C22⋊C411yescharacteristic
55C22×C4×C31C2×C812yes—
56C22×C4×C31M1612yes—
57C22×C4×C31C22×C411yescharacteristic
58C22×C4×C31C2×D412yes—
59C2×C8×C31—44no—
60C4⋊C4×C31—41no—
61C4⋊C4×C31—41no—
62C4⋊C4×C31—42no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—42no—
65C42×C31—22no—
66C42×C31—22no—
67C42×C31—42no—
68#11434C3111yesmaximal, characteristic, direct product factor, Sylow
69C23×C31—21no—
70C23×C31—21no—
71C23×C31—41no—
72C23×C31—41no—
73C23×C31C22⋊C812yes—
74C23×C31C2×C22⋊C411yescharacteristic
75Q8×C31—44no—
76Q8×C31—44no—
77Q8×C31—48no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—24no—
81C2×C4×C31—24no—
82C2×C4×C31—24no—
83C2×C4×C31—22no—
84C2×C4×C31—22no—
85C2×C4×C31—48no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31C22⋊C812yes—
94C2×C4×C31#9912yes—
95C2×C4×C31#10012yes—
96C2×C4×C31C22×C811yescharacteristic
97C2×C4×C31C2×M1611yescharacteristic
98C8×C31—84no—
99#2310C2×C3111yescharacteristic
100#1458C2×C3112yes—
101#1319C2×C3114yescomplemented
102C22×C31—21no—
103C22×C31—21no—
104C22×C31—22no—
105C22×C31—42no—
106C22×C31—42no—
107C22×C31—41no—
108C22×C31—41no—
109C22×C31C2×C22⋊C811yescharacteristic
110C22×C31C2×#9911yescharacteristic
111C22×C31C2×#10011yescharacteristic
112C4×C31—21no—
113C4×C31—21no—
114C4×C31—42no—
115C4×C31—42no—
116C4×C31—44no—
117C4×C31—82no—
118C4×C31#32314yes—
119C23×Q8C4×C3111yescharacteristic
120C2×#117C4×C3111yescharacteristic
121C2×#117C22×C3111yescharacteristic
122#431—22no—
123#391—22no—
124#391C4×C3112yes—
125#391C22×C3112yes—
126#381—22no—
127#324C22×C3114yes—
128#323—22no—
129C2×C31—21no—
130C2×C31—21no—
131C2×C31—42no—
132C2×C31C2×#32311yescharacteristic
133C2×C31#212911yescharacteristic
134C2×C31#213511yescharacteristic
135C22×Q8—21no—
136C22×Q8—22no—
137C22×Q8—42no—
138C22×Q8—42no—
139C22×Q8C8×C3114yescomplemented
140C22×Q8C2×C4×C3112yes—
141C23×C4—21no—
142C23×C4C2×C4×C3111yescharacteristic
143#117—42no—
144#117—42no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4C2×C4×C3111yescharacteristic
147C2×C4⋊C4C23×C3111yescharacteristic
148C2×C22⋊C4—21no—
149C2×C22⋊C4D4×C3112yes—
150C2×C42C2×C4×C3112yes—
151C2×C42D4×C3112yes—
152C4⋊C8—42no—
153C22⋊C8—24no—
154C4×C8—42no—
155#95—24no—
156#95—24no—
157C31#1143411yescharacteristic, direct product factor, Sylow
158C24C22⋊C4×C3111yescharacteristic
159C2×Q8—24no—
160C2×Q8—22no—
161C2×Q8—48no—
162C2×Q8—48no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8C2×C8×C3114yes—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4C22⋊C4×C3112yes—
176C22×C4C22⋊C4×C3111yescharacteristic
177C22×C4C2×C8×C3112yes—
178C22×C4M16×C3112yes—
179C22×C4C22×C4×C3111yescharacteristic
180C22×C4C2×D4×C3112yes—
181C2×C8—44no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42—22no—
188C42—22no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23C31×C22⋊C812yes—
195C23C2×C22⋊C4×C3111yescharacteristic
196Q8—44no—
197Q8—44no—
198Q8—48no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—48no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4C31×C22⋊C812yes—
215C2×C4C31×#9912yes—
216C2×C4C31×#10012yes—
217C2×C4C22×C8×C3111yescharacteristic
218C2×C4C2×M16×C3111yescharacteristic
219C8—84no—
220C22—21no—
221C22—21no—
222C22—22no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22C2×C31×C22⋊C811yescharacteristic
228C22C2×C31×#9911yescharacteristic
229C22C2×C31×#10011yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—44no—
235C4—82no—
236C4C31×#32314yes—
237C2—21no—
238C2—21no—
239C2—42no—
240C2C2×C31×#32311yescharacteristic
241C2C31×#212911yescharacteristic
242C2C31×#213511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C2×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
18. C22×Q8×C31C8semidirect
68. #11434C31direct (N × H)
101. #1319C2×C31semidirect
139. C22×Q8C8×C31semidirect
157. C31#11434direct (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×#14582
C31×#13192
#1143431