Finite Group Databasebeta

← C31×#8225 #21464984

Subgroups — C31×#8225 #21464984

Order 7936.

444 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 178 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×#125C211yesmaximal, characteristic
2C31×#1745C212yesmaximal
3C2×C31×#330C212yesmaximal
4C31×#1295C212yesmaximal
5C2×C31×#125C2211yescharacteristic
6C2×C31×#97C2214yes—
7C31×#389C412yes—
8C31×#387—22no—
9C31×#382C2211yescharacteristic
10C4×C4⋊C4×C31—22no—
11C4×C4⋊C4×C31C412yes—
12C43×C31C2211yescharacteristic
13C31×#336—22no—
14C31×#336—22no—
15C31×#330C418yescomplemented
16C22×C8×C31—24no—
17C31×#125—22no—
18C31×#125C2×C414yes—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—22no—
21C2×C4⋊C4×C31C2×C412yes—
22C2×C4⋊C4×C31C2×C412yes—
23C2×C42×C31—22no—
24C2×C42×C31C2×C411yescharacteristic
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31D412yes—
27C2×C42×C31D412yes—
28C2×C42×C31C2311yescharacteristic
29C31×#97—24no—
30C31×#97C2×C418yes—
31C31×#95—22no—
32C31×#95—22no—
33C31×#95—22no—
34C22×C4×C31—22no—
35C22×C4×C31—22no—
36C22×C4×C31C22⋊C411yescharacteristic
37C22×C4×C31C22⋊C412yes—
38C22×C4×C31C22⋊C411yescharacteristic
39C22×C4×C31C22×C411yescharacteristic
40C22×C4×C31C2×D412yes—
41C2×C8×C31—28no—
42C2×C8×C31—44no—
43C2×C8×C31—44no—
44C4⋊C4×C31—22no—
45C4⋊C4×C31—28no—
46C4⋊C4×C31—44no—
47C4⋊C4×C31—42no—
48C4⋊C4×C31C4214yes—
49C42×C31—22no—
50C42×C31—41no—
51C42×C31—42no—
52C42×C31—42no—
53C42×C31—44no—
54C42×C31C22×C412yes—
55C42×C31#4112yes—
56#8225C3111yesmaximal, characteristic, direct product factor, Sylow
57C23×C31C2×C22⋊C411yescharacteristic
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—22no—
63C2×C4×C31—24no—
64C2×C4×C31—21no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31#10112yes—
75C2×C4×C31C2×C4211yescharacteristic
76C2×C4×C31#11711yescharacteristic
77C2×C4×C31C4×D414yes—
78C8×C31—48no—
79C4×#125C2×C3111yescharacteristic
80#1745C2×C3112yes—
81C2×#330C2×C3112yes—
82#1295C2×C3112yes—
83C22×C31C4×C22⋊C411yescharacteristic
84C22×C31C2×#10111yescharacteristic
85C22×C31#41311yescharacteristic
86C22×C31#42112yes—
87C22×C31#42112yes—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31—24no—
91C4×C31—22no—
92C4×C31—41no—
93C4×C31—44no—
94C4×C31—42no—
95C4×C31—82no—
96C2×#125C22×C3111yescharacteristic
97C2×#97C22×C3114yes—
98#389C4×C3112yes—
99#387—22no—
100#382C22×C3111yescharacteristic
101C4×C4⋊C4—22no—
102C4×C4⋊C4C4×C3112yes—
103C43C22×C3111yescharacteristic
104#336—22no—
105#336—22no—
106#330C4×C3118yescomplemented
107C2×C31#153411yescharacteristic
108C2×C31#153512yes—
109C2×C31#153711yescharacteristic
110C2×C31C4×#10111yescharacteristic
111C2×C31#175912yes—
112C22×C8—24no—
113#125—22no—
114#125C2×C4×C3114yes—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×C4×C3112yes—
118C2×C4⋊C4C2×C4×C3112yes—
119C2×C42—22no—
120C2×C42C2×C4×C3111yescharacteristic
121C2×C42C2×C4×C3111yescharacteristic
122C2×C42D4×C3112yes—
123C2×C42D4×C3112yes—
124C2×C42C23×C3111yescharacteristic
125#97—24no—
126#97C2×C4×C3118yes—
127#95—22no—
128#95—22no—
129#95—22no—
130C31#822511yescharacteristic, direct product factor, Sylow
131C22×C4—22no—
132C22×C4—22no—
133C22×C4C22⋊C4×C3111yescharacteristic
134C22×C4C22⋊C4×C3112yes—
135C22×C4C22⋊C4×C3111yescharacteristic
136C22×C4C22×C4×C3111yescharacteristic
137C22×C4C2×D4×C3112yes—
138C2×C8—28no—
139C2×C8—44no—
140C2×C8—44no—
141C4⋊C4—22no—
142C4⋊C4—28no—
143C4⋊C4—42no—
144C4⋊C4—44no—
145C4⋊C4C42×C3114yes—
146C42—22no—
147C42—41no—
148C42—42no—
149C42—42no—
150C42—44no—
151C42C22×C4×C3112yes—
152C42#41×C3112yes—
153C23C2×C22⋊C4×C3111yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4C31×#10112yes—
171C2×C4C2×C42×C3111yescharacteristic
172C2×C4C31×#11711yescharacteristic
173C2×C4C4×D4×C3114yes—
174C8—48no—
175C22C4×C22⋊C4×C3111yescharacteristic
176C22C2×C31×#10111yescharacteristic
177C22C31×#41311yescharacteristic
178C22C31×#42112yes—
179C22C31×#42112yes—
180C4—21no—
181C4—21no—
182C4—24no—
183C4—22no—
184C4—44no—
185C4—42no—
186C4—41no—
187C4—82no—
188C2C31×#153411yescharacteristic
189C2C31×#153512yes—
190C2C31×#153711yescharacteristic
191C2C4×C31×#10111yescharacteristic
192C2C31×#175912yes—
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
15. C31×#330C4semidirect
56. #8225C31direct (N × H)
106. #330C4×C31semidirect
130. C31#8225direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1252
C31×#17452
C2×C31×#3302
C31×#12952
#822531