Finite Group Databasebeta

← C31×#7507 #21464266

Subgroups — C31×#7507 #21464266

Order 7936.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2132C212yesmaximal
2C31×#1963C211yesmaximal, characteristic
3C31×#532C2211yescharacteristic
4C31×#423C411yescharacteristic
5C2×C31×#104—22no—
6C31×#413—22no—
7C31×#376C411yescharacteristic
8C31×#356—22no—
9C31×#355C414yescomplemented
10C2×#41×C31D412yes—
11C2×M16×C31—21no—
12C2×M16×C31—42no—
13C31×C4⋊Q8D411yescharacteristic
14C31×#127Q811yescharacteristic
15C31×#124C2×C412yes—
16C31×#121—41no—
17C4×D4×C31—41no—
18C2×C42×C31—21no—
19C2×C42×C31C2×C411yescharacteristic
20C31×C4⋊C8—41no—
21C31×#104—44no—
22C31×#101—24no—
23C31×#100—42no—
24C31×#95—41no—
25#41×C31—42no—
26#41×C31—42no—
27C2×Q8×C31C22⋊C412yes—
28C2×D4×C31—22no—
29C2×D4×C31—41no—
30C2×D4×C31C4⋊C412yes—
31C22×C4×C31—21no—
32C22×C4×C31—22no—
33C22×C4×C31—41no—
34C22×C4×C31C22⋊C411yescharacteristic
35M16×C31—44no—
36M16×C31—42no—
37M16×C31—82no—
38C2×C8×C31—41no—
39C2×C8×C31—82no—
40C4⋊C4×C31—41no—
41C22⋊C4×C31—42no—
42C42×C31—21no—
43C42×C31—22no—
44C42×C31—41no—
45C42×C31C4211yescharacteristic
46C42×C31C4⋊C411yescharacteristic
47#7507C3111yesmaximal, characteristic, direct product factor, Sylow
48C23×C31—22no—
49C23×C31#9911yescharacteristic
50Q8×C31—42no—
51D4×C31—42no—
52D4×C31—82no—
53D4×C31—82no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—22no—
59C2×C4×C31—42no—
60C2×C4×C31—42no—
61C2×C4×C31—42no—
62C2×C4×C31—81no—
63C2×C4×C31—82no—
64C2×C4×C31#9511yescharacteristic
65C2×C4×C31#9911yescharacteristic
66C8×C31—84no—
67C8×C31—81no—
68#2132C2×C3112yes—
69#1963C2×C3111yescharacteristic
70C22×C31—21no—
71C22×C31—41no—
72C22×C31—42no—
73C22×C31—82no—
74C22×C31#34211yescharacteristic
75C4×C31—21no—
76C4×C31—41no—
77C4×C31—41no—
78C4×C31—42no—
79C4×C31—82no—
80C4×C31#35311yescharacteristic
81C4×C31#35411yescharacteristic
82#532C22×C3111yescharacteristic
83#423C4×C3111yescharacteristic
84C2×#104—22no—
85#413—22no—
86#376C4×C3111yescharacteristic
87#356—22no—
88#355C4×C3114yescomplemented
89C2×C31—21no—
90C2×C31—41no—
91C2×C31—82no—
92C2×C31#139311yescharacteristic
93C2×#41D4×C3112yes—
94C2×M16—21no—
95C2×M16—42no—
96C4⋊Q8D4×C3111yescharacteristic
97#127Q8×C3111yescharacteristic
98#124C2×C4×C3112yes—
99#121—41no—
100C4×D4—41no—
101C2×C42—21no—
102C2×C42C2×C4×C3111yescharacteristic
103C4⋊C8—41no—
104#104—44no—
105#101—24no—
106#100—42no—
107#95—41no—
108C31#750711yescharacteristic, direct product factor, Sylow
109#41—42no—
110#41—42no—
111C2×Q8C22⋊C4×C3112yes—
112C2×D4—22no—
113C2×D4—41no—
114C2×D4C4⋊C4×C3112yes—
115C22×C4—21no—
116C22×C4—22no—
117C22×C4—41no—
118C22×C4C22⋊C4×C3111yescharacteristic
119M16—44no—
120M16—42no—
121M16—82no—
122C2×C8—41no—
123C2×C8—82no—
124C4⋊C4—41no—
125C22⋊C4—42no—
126C42—21no—
127C42—22no—
128C42—41no—
129C42C42×C3111yescharacteristic
130C42C4⋊C4×C3111yescharacteristic
131C23—22no—
132C23C31×#9911yescharacteristic
133Q8—42no—
134D4—42no—
135D4—82no—
136D4—82no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—81no—
146C2×C4—82no—
147C2×C4C31×#9511yescharacteristic
148C2×C4C31×#9911yescharacteristic
149C8—84no—
150C8—81no—
151C22—21no—
152C22—41no—
153C22—42no—
154C22—82no—
155C22C31×#34211yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—42no—
160C4—82no—
161C4C31×#35311yescharacteristic
162C4C31×#35411yescharacteristic
163C2—21no—
164C2—41no—
165C2—82no—
166C2C31×#139311yescharacteristic
subgroupG/H
centerC4×C31#353
commutatorC42C42×C31
Frattini, cosocle#532C22×C31
socleC2×C31#1393
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#355C4semidirect
47. #7507C31direct (N × H)
88. #355C4×C31semidirect
108. C31#7507direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#21322
C31×#19632
#750731