Finite Group Databasebeta

← C31×#7505 #21464264

Subgroups — C31×#7505 #21464264

Order 7936.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C31×#356C212yesmaximal
2C31×#1960C211yesmaximal, characteristic
3C2×C31×C4⋊Q8C2211yescharacteristic
4C2×C31×#103—22no—
5C2×C31×#101—22no—
6C2×C31×#97C411yescharacteristic
7C31×#382C411yescharacteristic
8C31×#356—22no—
9C31×#356C414yescomplemented
10C22×Q8×C31D412yes—
11C2×M16×C31—42no—
12C22×C8×C31—21no—
13C31×C4⋊Q8—41no—
14C31×C4⋊Q8C2×C412yes—
15C31×C4⋊Q8D411yescharacteristic
16C31×C4⋊Q8Q811yescharacteristic
17C2×C4⋊C4×C31—21no—
18C2×C4⋊C4×C31—41no—
19C2×C42×C31C2×C411yescharacteristic
20C31×#103—44no—
21C31×#101—24no—
22C31×#101—42no—
23C31×#97—41no—
24C31×#95—41no—
25C2×Q8×C31—22no—
26C2×Q8×C31—42no—
27C2×Q8×C31—42no—
28C2×Q8×C31C22⋊C412yes—
29C2×Q8×C31C4⋊C412yes—
30C22×C4×C31—21no—
31C22×C4×C31—22no—
32C22×C4×C31—41no—
33C22×C4×C31C22⋊C411yescharacteristic
34M16×C31—44no—
35M16×C31—82no—
36C2×C8×C31—22no—
37C2×C8×C31—41no—
38C2×C8×C31—41no—
39C2×C8×C31—82no—
40C4⋊C4×C31—42no—
41C4⋊C4×C31—41no—
42C4⋊C4×C31—41no—
43C4⋊C4×C31—42no—
44C42×C31—21no—
45C42×C31C4211yescharacteristic
46C42×C31C4⋊C411yescharacteristic
47#7505C3111yesmaximal, characteristic, direct product factor, Sylow
48C23×C31#9911yescharacteristic
49Q8×C31—42no—
50Q8×C31—42no—
51Q8×C31—82no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—42no—
59C2×C4×C31—42no—
60C2×C4×C31—42no—
61C2×C4×C31—82no—
62C2×C4×C31—81no—
63C2×C4×C31#9511yescharacteristic
64C2×C4×C31#9911yescharacteristic
65C8×C31—42no—
66C8×C31—84no—
67C2×#356C2×C3112yes—
68#1960C2×C3111yescharacteristic
69C22×C31—22no—
70C22×C31#34211yescharacteristic
71C22×C31#35311yescharacteristic
72C22×C31#35411yescharacteristic
73C4×C31—21no—
74C4×C31—21no—
75C4×C31—41no—
76C4×C31—41no—
77C4×C31—42no—
78C4×C31—42no—
79C4×C31—161no—
80C2×C4⋊Q8C22×C3111yescharacteristic
81C2×#103—22no—
82C2×#101—22no—
83C2×#97C4×C3111yescharacteristic
84#382C4×C3111yescharacteristic
85#356—22no—
86#356C4×C3114yescomplemented
87C2×C31—21no—
88C2×C31—21no—
89C2×C31#139311yescharacteristic
90C2×C31#141312yes—
91C22×Q8D4×C3112yes—
92C2×M16—42no—
93C22×C8—21no—
94C4⋊Q8—41no—
95C4⋊Q8C2×C4×C3112yes—
96C4⋊Q8D4×C3111yescharacteristic
97C4⋊Q8Q8×C3111yescharacteristic
98C2×C4⋊C4—21no—
99C2×C4⋊C4—41no—
100C2×C42C2×C4×C3111yescharacteristic
101#103—44no—
102#101—24no—
103#101—42no—
104#97—41no—
105#95—41no—
106C31#750511yescharacteristic, direct product factor, Sylow
107C2×Q8—22no—
108C2×Q8—42no—
109C2×Q8—42no—
110C2×Q8C22⋊C4×C3112yes—
111C2×Q8C4⋊C4×C3112yes—
112C22×C4—21no—
113C22×C4—22no—
114C22×C4—41no—
115C22×C4C22⋊C4×C3111yescharacteristic
116M16—44no—
117M16—82no—
118C2×C8—22no—
119C2×C8—41no—
120C2×C8—41no—
121C2×C8—82no—
122C4⋊C4—42no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C4⋊C4—42no—
126C42—21no—
127C42C42×C3111yescharacteristic
128C42C4⋊C4×C3111yescharacteristic
129C23C31×#9911yescharacteristic
130Q8—42no—
131Q8—42no—
132Q8—82no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—82no—
143C2×C4—81no—
144C2×C4C31×#9511yescharacteristic
145C2×C4C31×#9911yescharacteristic
146C8—42no—
147C8—84no—
148C22—22no—
149C22C31×#34211yescharacteristic
150C22C31×#35311yescharacteristic
151C22C31×#35411yescharacteristic
152C4—21no—
153C4—21no—
154C4—41no—
155C4—41no—
156C4—42no—
157C4—42no—
158C4—161no—
159C2—21no—
160C2—21no—
161C2C31×#139311yescharacteristic
162C2C31×#141312yes—
subgroupG/H
center, socleC22×C31#354
commutatorC42C42×C31
Frattini, cosocleC2×C4⋊Q8C22×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#356C4semidirect
47. #7505C31direct (N × H)
86. #356C4×C31semidirect
106. C31#7505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3562
C31×#19602
#750531