Finite Group Databasebeta

← C31×#7637 #21464396

Subgroups — C31×#7637 #21464396

Order 7936.

636 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C4×C31×#127C211yesmaximal, characteristic
2C31×#1745C212yesmaximal, complemented
3C31×#1270C214yesmaximal, complemented
4C2×C31×#127C411yescharacteristic
5C2×C4×D4×C31—22no—
6C2×C4×D4×C31C412yes—
7C2×C31×#97—22no—
8C31×#390—22no—
9C31×#390C2212yes—
10C31×#384C411yescharacteristic
11C43×C31C2211yescharacteristic
12C31×#336—22no—
13C31×#336C2214yes—
14C22×D4×C31—22no—
15C22×D4×C31C2×C412yes—
16C23×C4×C31—22no—
17C22×C8×C31—24no—
18C31×#127—24no—
19C4×D4×C31—48no—
20C4×D4×C31—44no—
21C2×C4⋊C4×C31—22no—
22C2×C4⋊C4×C31C2×C412yes—
23C2×C22⋊C4×C31—22no—
24C2×C22⋊C4×C31—24no—
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31C2×C411yescharacteristic
27C2×C42×C31D412yes—
28C2×C42×C31D412yes—
29C2×C42×C31C2311yescharacteristic
30C31×#97—28no—
31C24×C31—22no—
32C2×D4×C31—28no—
33C2×D4×C31—22no—
34C2×D4×C31—44no—
35C2×D4×C31—42no—
36C2×D4×C31—42no—
37C2×D4×C31—44no—
38C2×D4×C31M1614yes—
39C22×C4×C31—22no—
40C22×C4×C31—48no—
41C22×C4×C31—44no—
42C22×C4×C31C22⋊C411yescharacteristic
43C22×C4×C31C22⋊C411yescharacteristic
44C22×C4×C31C22⋊C412yes—
45C22×C4×C31C22×C411yescharacteristic
46C22×C4×C31C2×D412yes—
47C2×C8×C31—28no—
48C2×C8×C31—44no—
49C2×C8×C31—44no—
50C4⋊C4×C31—44no—
51C4⋊C4×C31—42no—
52C22⋊C4×C31—44no—
53C22⋊C4×C31—48no—
54C42×C31—22no—
55C42×C31—24no—
56C42×C31—22no—
57C42×C31—24no—
58C42×C31—41no—
59#7637C3111yesmaximal, characteristic, direct product factor, Sylow
60C23×C31—24no—
61C23×C31—42no—
62C23×C31—42no—
63C23×C31—44no—
64C23×C31—44no—
65C23×C31C2×C22⋊C411yescharacteristic
66D4×C31—44no—
67D4×C31—44no—
68D4×C31—416no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—21no—
77C2×C4×C31—22no—
78C2×C4×C31—42no—
79C2×C4×C31—44no—
80C2×C4×C31—88no—
81C2×C4×C31#10012yes—
82C2×C4×C31#10414yes—
83C2×C4×C31C2×M1612yes—
84C2×C4×C31AGL(1,ℤ/8)14yes—
85C8×C31—48no—
86C4×#127C2×C3111yescharacteristic
87#1745C2×C3112yescomplemented
88#1270C2×C3114yescomplemented
89C22×C31—44no—
90C22×C31—48no—
91C22×C31—82no—
92C22×C31—84no—
93C22×C31—82no—
94C22×C31#40711yescharacteristic
95C22×C31#41011yescharacteristic
96C22×C31C2×#10011yescharacteristic
97C22×C31#41812yes—
98C22×C31C2×#10412yes—
99C4×C31—22no—
100C4×C31—22no—
101C4×C31—24no—
102C4×C31—24no—
103C4×C31—41no—
104C4×C31—82no—
105C2×#127C4×C3111yescharacteristic
106C2×C4×D4—22no—
107C2×C4×D4C4×C3112yes—
108C2×#97—22no—
109#390—22no—
110#390C22×C3112yes—
111#384C4×C3111yescharacteristic
112C43C22×C3111yescharacteristic
113#336—22no—
114#336C22×C3114yes—
115C2×C31—84no—
116C2×C31#146611yescharacteristic
117C2×C31#149012yes—
118C2×C31#150512yes—
119C2×C31#152511yescharacteristic
120C2×C31#155511yescharacteristic
121C22×D4—22no—
122C22×D4C2×C4×C3112yes—
123C23×C4—22no—
124C22×C8—24no—
125#127—24no—
126C4×D4—48no—
127C4×D4—44no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4C2×C4×C3112yes—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—24no—
132C2×C42C2×C4×C3111yescharacteristic
133C2×C42C2×C4×C3111yescharacteristic
134C2×C42D4×C3112yes—
135C2×C42D4×C3112yes—
136C2×C42C23×C3111yescharacteristic
137#97—28no—
138C31#763711yescharacteristic, direct product factor, Sylow
139C24—22no—
140C2×D4—28no—
141C2×D4—22no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—44no—
145C2×D4—44no—
146C2×D4M16×C3114yes—
147C22×C4—22no—
148C22×C4—48no—
149C22×C4—44no—
150C22×C4C22⋊C4×C3111yescharacteristic
151C22×C4C22⋊C4×C3111yescharacteristic
152C22×C4C22⋊C4×C3112yes—
153C22×C4C22×C4×C3111yescharacteristic
154C22×C4C2×D4×C3112yes—
155C2×C8—28no—
156C2×C8—44no—
157C2×C8—44no—
158C4⋊C4—42no—
159C4⋊C4—44no—
160C22⋊C4—44no—
161C22⋊C4—48no—
162C42—22no—
163C42—24no—
164C42—22no—
165C42—24no—
166C42—41no—
167C23—24no—
168C23—42no—
169C23—42no—
170C23—44no—
171C23—44no—
172C23C2×C22⋊C4×C3111yescharacteristic
173D4—44no—
174D4—44no—
175D4—416no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—44no—
187C2×C4—88no—
188C2×C4C31×#10012yes—
189C2×C4C31×#10414yes—
190C2×C4C2×M16×C3112yes—
191C2×C4C31×AGL(1,ℤ/8)14yes—
192C8—48no—
193C22—44no—
194C22—48no—
195C22—82no—
196C22—84no—
197C22—82no—
198C22C31×#40711yescharacteristic
199C22C31×#41011yescharacteristic
200C22C2×C31×#10011yescharacteristic
201C22C31×#41812yes—
202C22C2×C31×#10412yes—
203C4—22no—
204C4—22no—
205C4—24no—
206C4—24no—
207C4—41no—
208C4—82no—
209C2—84no—
210C2C31×#146611yescharacteristic
211C2C31×#149012yes—
212C2C31×#150512yes—
213C2C31×#152511yescharacteristic
214C2C31×#155511yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1745C2semidirect
3. C31×#1270C2semidirect
59. #7637C31direct (N × H)
87. #1745C2×C31semidirect
88. #1270C2×C31semidirect
138. C31#7637direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1272
C31×#17452
C31×#12702
#763731