Finite Group Databasebeta

← C31×#8732 #21465491

Subgroups — C31×#8732 #21465491

Order 7936.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2298C211yesmaximal, characteristic
2C31×#1458C212yesmaximal
3C31×#1276C212yesmaximal, complemented
4C31×#1274C212yesmaximal, complemented
5C2×C31×#117C2211yescharacteristic
6C31×#431C2214yes—
7C31×#388—22no—
8C31×#387—22no—
9C4×C4⋊C4×C31C412yes—
10C4×C22⋊C4×C31C412yes—
11C31×#376C2211yescharacteristic
12C43×C31C2211yescharacteristic
13C31×#324—22no—
14C31×#323—22no—
15C23×C4×C31C2×C411yescharacteristic
16C31×#117—22no—
17C31×#117—22no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31D412yes—
20C2×C22⋊C4×C31—22no—
21C2×C22⋊C4×C31D412yes—
22C2×C42×C31—22no—
23C2×C42×C31C2×C412yes—
24C2×C42×C31C2×C412yes—
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31C2311yescharacteristic
27C31×C4⋊C8—24no—
28C31×C22⋊C8—24no—
29C4×C8×C31—24no—
30C31×#95—22no—
31C31×#95—22no—
32C31×#95—22no—
33C24×C31C22⋊C411yescharacteristic
34C22×C4×C31—22no—
35C22×C4×C31—21no—
36C22×C4×C31—21no—
37C22×C4×C31—24no—
38C22×C4×C31—22no—
39C22×C4×C31C22⋊C411yescharacteristic
40C22×C4×C31C22⋊C412yes—
41C22×C4×C31C22×C411yescharacteristic
42C22×C4×C31C2×D412yes—
43C2×C8×C31—44no—
44C4⋊C4×C31—24no—
45C4⋊C4×C31—44no—
46C22⋊C4×C31—24no—
47C22⋊C4×C31—44no—
48C42×C31—21no—
49C42×C31—21no—
50C42×C31—24no—
51C42×C31—24no—
52C42×C31—44no—
53C42×C31#4112yes—
54C42×C31#4112yes—
55#8732C3111yesmaximal, characteristic, direct product factor, Sylow
56C23×C31—21no—
57C23×C31—22no—
58C23×C31—42no—
59C23×C31C2×C22⋊C411yescharacteristic
60C2×C4×C31—24no—
61C2×C4×C31—22no—
62C2×C4×C31—21no—
63C2×C4×C31—22no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31—42no—
67C2×C4×C31—42no—
68C2×C4×C31—42no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31#11711yescharacteristic
74C2×C4×C31#11711yescharacteristic
75C2×C4×C31#12314yes—
76C2×C4×C31#13114yes—
77C8×C31—84no—
78#2298C2×C3111yescharacteristic
79#1458C2×C3112yes—
80#1276C2×C3112yescomplemented
81#1274C2×C3112yescomplemented
82C22×C31—22no—
83C22×C31—41no—
84C22×C31—42no—
85C22×C31—82no—
86C22×C31#38111yescharacteristic
87C22×C31#40812yes—
88C4×C31—24no—
89C4×C31—44no—
90C4×C31—41no—
91C4×C31—42no—
92C4×C31—82no—
93C4×C31#43312yes—
94C4×C31#43312yes—
95C2×#117C22×C3111yescharacteristic
96#431C22×C3114yes—
97#388—22no—
98#387—22no—
99C4×C4⋊C4C4×C3112yes—
100C4×C22⋊C4C4×C3112yes—
101#376C22×C3111yescharacteristic
102C43C22×C3111yescharacteristic
103#324—22no—
104#323—22no—
105C2×C31—22no—
106C2×C31—81no—
107C2×C31#181811yescharacteristic
108C2×C31#182712yes—
109C23×C4C2×C4×C3111yescharacteristic
110#117—22no—
111#117—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4D4×C3112yes—
114C2×C22⋊C4—22no—
115C2×C22⋊C4D4×C3112yes—
116C2×C42—22no—
117C2×C42C2×C4×C3112yes—
118C2×C42C2×C4×C3112yes—
119C2×C42C2×C4×C3111yescharacteristic
120C2×C42C23×C3111yescharacteristic
121C4⋊C8—24no—
122C22⋊C8—24no—
123C4×C8—24no—
124#95—22no—
125#95—22no—
126#95—22no—
127C31#873211yescharacteristic, direct product factor, Sylow
128C24C22⋊C4×C3111yescharacteristic
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4C22⋊C4×C3111yescharacteristic
135C22×C4C22⋊C4×C3112yes—
136C22×C4C22×C4×C3111yescharacteristic
137C22×C4C2×D4×C3112yes—
138C2×C8—44no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C22⋊C4—24no—
142C22⋊C4—44no—
143C42—21no—
144C42—21no—
145C42—24no—
146C42—24no—
147C42—44no—
148C42#41×C3112yes—
149C42#41×C3112yes—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊C4×C3111yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4C31×#11711yescharacteristic
168C2×C4C31×#11711yescharacteristic
169C2×C4C31×#12314yes—
170C2×C4C31×#13114yes—
171C8—84no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22C31×#38111yescharacteristic
177C22C31×#40812yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4C31×#43312yes—
184C4C31×#43312yes—
185C2—22no—
186C2—81no—
187C2C31×#181811yescharacteristic
188C2C31×#182712yes—
subgroupG/H
centerC2×C4×C31#117
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#381
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C31×#376 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1276C2semidirect
4. C31×#1274C2semidirect
55. #8732C31direct (N × H)
80. #1276C2×C31semidirect
81. #1274C2×C31semidirect
127. C31#8732direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22982
C31×#14582
C31×#12762
C31×#12742
#873231