Finite Group Databasebeta

← C31×#7646 #21464405

Subgroups — C31×#7646 #21464405

Order 7936.

490 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2296C211yesmaximal, characteristic
2C31×#1817C212yesmaximal
3C31×#1271C214yesmaximal, complemented
4C2×C31×#117C411yescharacteristic
5C2×C31×#117C411yescharacteristic
6C22×C42×C31C2211yescharacteristic
7C2×C31×C22⋊C8—22no—
8C31×#389C412yes—
9C31×#389C2212yes—
10C31×#385—22no—
11C4×C4⋊C4×C31—22no—
12C31×#336—22no—
13C31×#336C2214yes—
14C23×C4×C31C2×C411yescharacteristic
15C23×C4×C31D412yes—
16C22×C8×C31—24no—
17C31×#117—24no—
18C31×#117—42no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—22no—
21C2×C4⋊C4×C31C2×C412yes—
22C2×C4⋊C4×C31C2×C412yes—
23C2×C22⋊C4×C31—21no—
24C2×C22⋊C4×C31—21no—
25C2×C42×C31—21no—
26C2×C42×C31—21no—
27C2×C42×C31—42no—
28C2×C42×C31C2×C411yescharacteristic
29C2×C42×C31D412yes—
30C2×C42×C31C2311yescharacteristic
31C31×C22⋊C8—44no—
32C31×#95—22no—
33C31×#95—22no—
34C24×C31C22⋊C411yescharacteristic
35C22×C4×C31—22no—
36C22×C4×C31—22no—
37C22×C4×C31—22no—
38C22×C4×C31—24no—
39C22×C4×C31—22no—
40C22×C4×C31—24no—
41C22×C4×C31—22no—
42C22×C4×C31—42no—
43C22×C4×C31C22⋊C412yes—
44C22×C4×C31C22⋊C411yescharacteristic
45C22×C4×C31C22×C411yescharacteristic
46C22×C4×C31C2×D412yes—
47C2×C8×C31—44no—
48C2×C8×C31—44no—
49C2×C8×C31—44no—
50C4⋊C4×C31—22no—
51C4⋊C4×C31—44no—
52C4⋊C4×C31—42no—
53C4⋊C4×C31—44no—
54C4⋊C4×C31M1614yes—
55C22⋊C4×C31—24no—
56C22⋊C4×C31—42no—
57C42×C31—24no—
58C42×C31—41no—
59C42×C31—42no—
60C42×C31—41no—
61C42×C31—42no—
62#7646C3111yesmaximal, characteristic, direct product factor, Sylow
63C23×C31—21no—
64C23×C31—21no—
65C23×C31—22no—
66C23×C31—22no—
67C23×C31#9912yes—
68C23×C31C2×C22⋊C411yescharacteristic
69C2×C4×C31—28no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—22no—
74C2×C4×C31—21no—
75C2×C4×C31—22no—
76C2×C4×C31—24no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—48no—
81C2×C4×C31—42no—
82C2×C4×C31—42no—
83C2×C4×C31—42no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31#10112yes—
87C2×C4×C31C2×M1612yes—
88C2×C4×C31#13514yes—
89C8×C31—84no—
90#2296C2×C3111yescharacteristic
91#1817C2×C3112yes—
92#1271C2×C3114yescomplemented
93C22×C31—22no—
94C22×C31—24no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31—42no—
98C22×C31#40711yescharacteristic
99C22×C31C2×#9911yescharacteristic
100C22×C31C2×#10111yescharacteristic
101C22×C31#41612yes—
102C22×C31#42112yes—
103C4×C31—22no—
104C4×C31—22no—
105C4×C31—24no—
106C4×C31—44no—
107C4×C31—42no—
108C4×C31—82no—
109C2×#117C4×C3111yescharacteristic
110C2×#117C4×C3111yescharacteristic
111C22×C42C22×C3111yescharacteristic
112C2×C22⋊C8—22no—
113#389C4×C3112yes—
114#389C22×C3112yes—
115#385—22no—
116C4×C4⋊C4—22no—
117#336—22no—
118#336C22×C3114yes—
119C2×C31—42no—
120C2×C31#146311yescharacteristic
121C2×C31#148812yes—
122C2×C31#151612yes—
123C2×C31#153711yescharacteristic
124C2×C31#154411yescharacteristic
125C23×C4C2×C4×C3111yescharacteristic
126C23×C4D4×C3112yes—
127C22×C8—24no—
128#117—24no—
129#117—42no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4C2×C4×C3112yes—
133C2×C4⋊C4C2×C4×C3112yes—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—21no—
136C2×C42—21no—
137C2×C42—21no—
138C2×C42—42no—
139C2×C42C2×C4×C3111yescharacteristic
140C2×C42D4×C3112yes—
141C2×C42C23×C3111yescharacteristic
142C22⋊C8—44no—
143#95—22no—
144#95—22no—
145C31#764611yescharacteristic, direct product factor, Sylow
146C24C22⋊C4×C3111yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4C22⋊C4×C3112yes—
156C22×C4C22⋊C4×C3111yescharacteristic
157C22×C4C22×C4×C3111yescharacteristic
158C22×C4C2×D4×C3112yes—
159C2×C8—44no—
160C2×C8—44no—
161C2×C8—44no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—44no—
166C4⋊C4M16×C3114yes—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C42—24no—
170C42—41no—
171C42—42no—
172C42—41no—
173C42—42no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23C31×#9912yes—
179C23C2×C22⋊C4×C3111yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—48no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4C31×#10112yes—
198C2×C4C2×M16×C3112yes—
199C2×C4C31×#13514yes—
200C8—84no—
201C22—22no—
202C22—24no—
203C22—41no—
204C22—42no—
205C22—41no—
206C22C31×#40711yescharacteristic
207C22C2×C31×#9911yescharacteristic
208C22C2×C31×#10111yescharacteristic
209C22C31×#41612yes—
210C22C31×#42112yes—
211C4—22no—
212C4—22no—
213C4—24no—
214C4—44no—
215C4—42no—
216C4—82no—
217C2—42no—
218C2C31×#146311yescharacteristic
219C2C31×#148812yes—
220C2C31×#151612yes—
221C2C31×#153711yescharacteristic
222C2C31×#154411yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1271C2semidirect
62. #7646C31direct (N × H)
92. #1271C2×C31semidirect
145. C31#7646direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22962
C31×#18172
C31×#12712
#764631