Finite Group Databasebeta

← C31×#7353 #21464112

Subgroups — C31×#7353 #21464112

Order 7936.

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

normal subgroups only

This group has 204 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×#1960C211yesmaximal, characteristic
2C31×#1324C212yesmaximal
3C2×C31×C4⋊Q8C411yescharacteristic
4C2×C31×#103—22no—
5C2×C31×#97C411yescharacteristic
6C31×#382C2211yescharacteristic
7C31×#324—22no—
8C22×Q8×C31—21no—
9C22×C8×C31—21no—
10C31×C4⋊Q8—21no—
11C31×C4⋊Q8—41no—
12C31×C4⋊Q8C812yescomplemented
13C2×C4⋊C4×C31—41no—
14C2×C4⋊C4×C31D412yes—
15C2×C42×C31C2×C411yescharacteristic
16C31×#103—44no—
17C31×C22⋊C8—42no—
18C31×#97—41no—
19C31×#95—41no—
20C2×Q8×C31—22no—
21C2×Q8×C31—42no—
22C2×Q8×C31—42no—
23C2×Q8×C31—41no—
24C22×C4×C31—21no—
25C22×C4×C31—22no—
26C22×C4×C31—41no—
27C22×C4×C31C22⋊C411yescharacteristic
28C2×C8×C31—22no—
29C2×C8×C31—41no—
30C2×C8×C31—41no—
31C2×C8×C31—82no—
32C4⋊C4×C31—42no—
33C4⋊C4×C31—42no—
34C4⋊C4×C31—42no—
35C42×C31—21no—
36C42×C31C2×C811yescharacteristic
37C42×C31M1611yescharacteristic
38#7353C3111yesmaximal, characteristic, direct product factor, Sylow
39C23×C31#9911yescharacteristic
40Q8×C31—44no—
41Q8×C31—82no—
42C2×C4×C31—21no—
43C2×C4×C31—21no—
44C2×C4×C31—21no—
45C2×C4×C31—21no—
46C2×C4×C31—42no—
47C2×C4×C31—42no—
48C2×C4×C31—42no—
49C2×C4×C31—81no—
50C2×C4×C31—81no—
51C2×C4×C31—82no—
52C2×C4×C31C22⋊C811yescharacteristic
53C2×C4×C31#10011yescharacteristic
54C8×C31—42no—
55C8×C31—162no—
56#1960C2×C3111yescharacteristic
57#1324C2×C3112yes—
58C22×C31—22no—
59C22×C31#32311yescharacteristic
60C22×C31#35311yescharacteristic
61C22×C31#35511yescharacteristic
62C4×C31—21no—
63C4×C31—21no—
64C4×C31—41no—
65C4×C31—41no—
66C4×C31—82no—
67C4×C31—82no—
68C2×C4⋊Q8C4×C3111yescharacteristic
69C2×#103—22no—
70C2×#97C4×C3111yescharacteristic
71#382C22×C3111yescharacteristic
72#324—22no—
73C2×C31—21no—
74C2×C31—21no—
75C2×C31#131811yescharacteristic
76C2×C31#140712yes—
77C22×Q8—21no—
78C22×C8—21no—
79C4⋊Q8—21no—
80C4⋊Q8—41no—
81C4⋊Q8C8×C3112yescomplemented
82C2×C4⋊C4—41no—
83C2×C4⋊C4D4×C3112yes—
84C2×C42C2×C4×C3111yescharacteristic
85#103—44no—
86C22⋊C8—42no—
87#97—41no—
88#95—41no—
89C31#735311yescharacteristic, direct product factor, Sylow
90C2×Q8—22no—
91C2×Q8—42no—
92C2×Q8—42no—
93C2×Q8—41no—
94C22×C4—21no—
95C22×C4—22no—
96C22×C4—41no—
97C22×C4C22⋊C4×C3111yescharacteristic
98C2×C8—22no—
99C2×C8—41no—
100C2×C8—41no—
101C2×C8—82no—
102C4⋊C4—42no—
103C4⋊C4—42no—
104C4⋊C4—42no—
105C42—21no—
106C42C2×C8×C3111yescharacteristic
107C42M16×C3111yescharacteristic
108C23C31×#9911yescharacteristic
109Q8—44no—
110Q8—82no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—81no—
119C2×C4—81no—
120C2×C4—82no—
121C2×C4C31×C22⋊C811yescharacteristic
122C2×C4C31×#10011yescharacteristic
123C8—42no—
124C8—162no—
125C22—22no—
126C22C31×#32311yescharacteristic
127C22C31×#35311yescharacteristic
128C22C31×#35511yescharacteristic
129C4—21no—
130C4—21no—
131C4—41no—
132C4—41no—
133C4—82no—
134C4—82no—
135C2—21no—
136C2—21no—
137C2C31×#131811yescharacteristic
138C2C31×#140712yes—
subgroupG/H
center, socleC22×C31#353
commutatorC42C2×C8×C31
Frattini, cosocle#382C22×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#382 ◁ G

Complements

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

NH ≅ G/Ntype
12. C31×C4⋊Q8C8semidirect
38. #7353C31direct (N × H)
81. C4⋊Q8C8×C31semidirect
89. C31#7353direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19602
C31×#13242
#735331