Finite Group Databasebeta

← C31×#7354 #21464113

Subgroups — C31×#7354 #21464113

Order 7936.

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1957C211yesmaximal, characteristic
2C31×#1325C212yesmaximal, complemented
3C2×C31×#127C411yescharacteristic
4C2×C31×#102—22no—
5C2×C4×C8×C31C411yescharacteristic
6C31×#384C2211yescharacteristic
7C31×#324—22no—
8C22×D4×C31—21no—
9C22×D4×C31—41no—
10C22×C8×C31—21no—
11C31×#127—21no—
12C31×#127—41no—
13C31×#127C812yescomplemented
14C2×C4⋊C4×C31—41no—
15C2×C4⋊C4×C31D412yes—
16C2×C42×C31C2×C411yescharacteristic
17C31×#102—44no—
18C31×C22⋊C8—42no—
19C4×C8×C31—41no—
20C24×C31—41no—
21C2×D4×C31—22no—
22C2×D4×C31—42no—
23C2×D4×C31—42no—
24C2×D4×C31—42no—
25C2×D4×C31—42no—
26C2×D4×C31—41no—
27C2×D4×C31—82no—
28C2×D4×C31—82no—
29C22×C4×C31—21no—
30C22×C4×C31—22no—
31C22×C4×C31C22⋊C411yescharacteristic
32C2×C8×C31—22no—
33C2×C8×C31—41no—
34C2×C8×C31—41no—
35C2×C8×C31—82no—
36C4⋊C4×C31—42no—
37C4⋊C4×C31—82no—
38C42×C31—21no—
39C42×C31C2×C811yescharacteristic
40C42×C31M1611yescharacteristic
41#7354C3111yesmaximal, characteristic, direct product factor, Sylow
42C23×C31—42no—
43C23×C31—82no—
44C23×C31—82no—
45C23×C31—81no—
46C23×C31—81no—
47C23×C31#9911yescharacteristic
48D4×C31—44no—
49D4×C31—82no—
50D4×C31—84no—
51D4×C31—84no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—42no—
59C2×C4×C31—82no—
60C2×C4×C31C22⋊C811yescharacteristic
61C2×C4×C31#10011yescharacteristic
62C8×C31—42no—
63C8×C31—162no—
64#1957C2×C3111yescharacteristic
65#1325C2×C3112yescomplemented
66C22×C31—21no—
67C22×C31—21no—
68C22×C31—84no—
69C22×C31—82no—
70C22×C31—162no—
71C22×C31—161no—
72C22×C31—161no—
73C22×C31#32311yescharacteristic
74C22×C31#35311yescharacteristic
75C22×C31#35511yescharacteristic
76C4×C31—22no—
77C4×C31—22no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31—82no—
81C2×#127C4×C3111yescharacteristic
82C2×#102—22no—
83C2×C4×C8C4×C3111yescharacteristic
84#384C22×C3111yescharacteristic
85#324—22no—
86C2×C31—21no—
87C2×C31—21no—
88C2×C31—162no—
89C2×C31#131811yescharacteristic
90C2×C31#140811yescharacteristic
91C2×C31#141011yescharacteristic
92C22×D4—21no—
93C22×D4—41no—
94C22×C8—21no—
95#127—21no—
96#127—41no—
97#127C8×C3112yescomplemented
98C2×C4⋊C4—41no—
99C2×C4⋊C4D4×C3112yes—
100C2×C42C2×C4×C3111yescharacteristic
101#102—44no—
102C22⋊C8—42no—
103C4×C8—41no—
104C31#735411yescharacteristic, direct product factor, Sylow
105C24—41no—
106C2×D4—22no—
107C2×D4—42no—
108C2×D4—42no—
109C2×D4—42no—
110C2×D4—42no—
111C2×D4—41no—
112C2×D4—82no—
113C2×D4—82no—
114C22×C4—21no—
115C22×C4—22no—
116C22×C4C22⋊C4×C3111yescharacteristic
117C2×C8—22no—
118C2×C8—41no—
119C2×C8—41no—
120C2×C8—82no—
121C4⋊C4—42no—
122C4⋊C4—82no—
123C42—21no—
124C42C2×C8×C3111yescharacteristic
125C42M16×C3111yescharacteristic
126C23—42no—
127C23—82no—
128C23—82no—
129C23—81no—
130C23—81no—
131C23C31×#9911yescharacteristic
132D4—44no—
133D4—82no—
134D4—84no—
135D4—84no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—42no—
143C2×C4—82no—
144C2×C4C31×C22⋊C811yescharacteristic
145C2×C4C31×#10011yescharacteristic
146C8—42no—
147C8—162no—
148C22—21no—
149C22—21no—
150C22—84no—
151C22—82no—
152C22—162no—
153C22—161no—
154C22—161no—
155C22C31×#32311yescharacteristic
156C22C31×#35311yescharacteristic
157C22C31×#35511yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—21no—
162C4—82no—
163C2—21no—
164C2—21no—
165C2—162no—
166C2C31×#131811yescharacteristic
167C2C31×#140811yescharacteristic
168C2C31×#141011yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C2×C8×C31
Frattini, cosocle#384C22×C31
prime radicalC2×C31×#127C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#384 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1325C2semidirect
13. C31×#127C8semidirect
41. #7354C31direct (N × H)
65. #1325C2×C31semidirect
97. #127C8×C31semidirect
104. C31#7354direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19572
C31×#13252
#735431