Finite Group Databasebeta

← C31×#11428 #21468187

Subgroups — C31×#11428 #21468187

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×#1317C214yesmaximal
4C23×Q8×C31C411yescharacteristic
5C2×C31×#117C411yescharacteristic
6C2×C31×#117C2211yescharacteristic
7C31×#431—22no—
8C31×#391—22no—
9C31×#391—22no—
10C31×#381C412yes—
11C31×#381C2212yes—
12C31×#324—22no—
13C31×#323C2214yes—
14C22×Q8×C31—21no—
15C22×Q8×C31—21no—
16C22×Q8×C31—22no—
17C22×Q8×C31—42no—
18C22×Q8×C31—42no—
19C22×Q8×C31C814yescomplemented
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2×C412yes—
22C31×#117—42no—
23C31×#117—42no—
24C2×C4⋊C4×C31—21no—
25C2×C4⋊C4×C31D412yes—
26C2×C22⋊C4×C31C2×C412yes—
27C2×C22⋊C4×C31C2×C411yescharacteristic
28C2×C22⋊C4×C31C2311yescharacteristic
29C2×C42×C31—21no—
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—24no—
39C2×Q8×C31—42no—
40C2×Q8×C31—42no—
41C2×Q8×C31—48no—
42C2×Q8×C31—48no—
43C2×Q8×C31—42no—
44C2×Q8×C31—42no—
45C22×C4×C31—22no—
46C22×C4×C31—22no—
47C22×C4×C31—22no—
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—42no—
51C22×C4×C31—42no—
52C22×C4×C31C22⋊C411yescharacteristic
53C22×C4×C31C22⋊C412yes—
54C22×C4×C31C22⋊C411yescharacteristic
55C22×C4×C31C2×C812yes—
56C22×C4×C31C2×C814yes—
57C22×C4×C31M1612yes—
58C22×C4×C31C2×D412yes—
59C2×C8×C31—44no—
60C4⋊C4×C31—42no—
61C4⋊C4×C31—42no—
62C22⋊C4×C31—41no—
63C22⋊C4×C31—41no—
64C22⋊C4×C31—42no—
65C42×C31—22no—
66C42×C31—22no—
67C42×C31—42no—
68#11428C3111yesmaximal, characteristic, direct product factor, Sylow
69C23×C31—21no—
70C23×C31—21no—
71C23×C31—42no—
72C23×C31C2×C22⋊C411yescharacteristic
73C23×C31C22×C811yescharacteristic
74C23×C31C2×M1611yescharacteristic
75Q8×C31—48no—
76Q8×C31—48no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—24no—
80C2×C4×C31—24no—
81C2×C4×C31—24no—
82C2×C4×C31—22no—
83C2×C4×C31—22no—
84C2×C4×C31—44no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—44no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—44no—
91C2×C4×C31—42no—
92C2×C4×C31C22⋊C812yes—
93C2×C4×C31C22⋊C812yes—
94C2×C4×C31#9912yes—
95C2×C4×C31#10012yes—
96C8×C31—84no—
97#2310C2×C3111yescharacteristic
98#1458C2×C3112yes—
99#1317C2×C3114yes—
100C22×C31—22no—
101C22×C31—21no—
102C22×C31—21no—
103C22×C31—41no—
104C22×C31—41no—
105C22×C31—42no—
106C22×C31—42no—
107C22×C31C2×C22⋊C811yescharacteristic
108C22×C31C2×#9911yescharacteristic
109C22×C31C2×#10011yescharacteristic
110C4×C31—22no—
111C4×C31—42no—
112C4×C31—42no—
113C4×C31—44no—
114C4×C31—82no—
115C4×C31#32314yes—
116C23×Q8C4×C3111yescharacteristic
117C2×#117C4×C3111yescharacteristic
118C2×#117C22×C3111yescharacteristic
119#431—22no—
120#391—22no—
121#391—22no—
122#381C4×C3112yes—
123#381C22×C3112yes—
124#324—22no—
125#323C22×C3114yes—
126C2×C31—21no—
127C2×C31—21no—
128C2×C31—41no—
129C2×C31—41no—
130C2×C31C2×#32311yescharacteristic
131C2×C31#212312yes—
132C22×Q8—21no—
133C22×Q8—21no—
134C22×Q8—22no—
135C22×Q8—42no—
136C22×Q8—42no—
137C22×Q8C8×C3114yescomplemented
138C23×C4C2×C4×C3111yescharacteristic
139C23×C4C2×C4×C3112yes—
140#117—42no—
141#117—42no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4D4×C3112yes—
144C2×C22⋊C4C2×C4×C3112yes—
145C2×C22⋊C4C2×C4×C3111yescharacteristic
146C2×C22⋊C4C23×C3111yescharacteristic
147C2×C42—21no—
148C2×C42D4×C3112yes—
149C4⋊C8—42no—
150C22⋊C8—24no—
151C4×C8—42no—
152#95—24no—
153#95—24no—
154C31#1142811yescharacteristic, direct product factor, Sylow
155C24C22×C4×C3111yescharacteristic
156C2×Q8—24no—
157C2×Q8—24no—
158C2×Q8—48no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4C22⋊C4×C3111yescharacteristic
172C22×C4C22⋊C4×C3112yes—
173C22×C4C22⋊C4×C3111yescharacteristic
174C22×C4C2×C8×C3112yes—
175C22×C4C2×C8×C3114yes—
176C22×C4M16×C3112yes—
177C22×C4C2×D4×C3112yes—
178C2×C8—44no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—42no—
184C42—22no—
185C42—22no—
186C42—42no—
187C23—21no—
188C23—21no—
189C23—42no—
190C23C2×C22⋊C4×C3111yescharacteristic
191C23C22×C8×C3111yescharacteristic
192C23C2×M16×C3111yescharacteristic
193Q8—48no—
194Q8—48no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4C31×C22⋊C812yes—
211C2×C4C31×C22⋊C812yes—
212C2×C4C31×#9912yes—
213C2×C4C31×#10012yes—
214C8—84no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22—42no—
222C22C2×C31×C22⋊C811yescharacteristic
223C22C2×C31×#9911yescharacteristic
224C22C2×C31×#10011yescharacteristic
225C4—22no—
226C4—42no—
227C4—42no—
228C4—44no—
229C4—82no—
230C4C31×#32314yes—
231C2—21no—
232C2—21no—
233C2—41no—
234C2—41no—
235C2C2×C31×#32311yescharacteristic
236C2C31×#212312yes—
subgroupG/H
center, socleC22×C31C2×#99
commutatorC23C22×C8×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C23 ▷ 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
19. C22×Q8×C31C8semidirect
68. #11428C31direct (N × H)
137. C22×Q8C8×C31semidirect
154. C31#11428direct (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×#13172
#1142831