Finite Group Databasebeta

← C31×#2133 #16842066

Subgroups — C31×#2133 #16842066

Order 3968.

230 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 84 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×#536C211yesmaximal, characteristic
2C2×C31×#101C212yesmaximal, complemented
3C31×#356C212yesmaximal, complemented
4C31×#355C212yesmaximal, complemented
5C2×#41×C31C411yescharacteristic
6C22×Q8×C31C2211yescharacteristic
7C2×M16×C31—22no—
8C31×C4⋊Q8C411yescharacteristic
9C31×C4⋊Q8C2211yescharacteristic
10C31×#124C411yescharacteristic
11C31×#124C2211yescharacteristic
12C31×#123—22no—
13C31×C22⋊Q8—22no—
14C31×#117C411yescharacteristic
15C31×#101—22no—
16C31×#101C2214yes—
17#41×C31—42no—
18C2×Q8×C31—42no—
19C2×Q8×C31C2×C411yescharacteristic
20C2×Q8×C31C2×C411yescharacteristic
21C2×Q8×C31D412yes—
22C2×Q8×C31C2311yescharacteristic
23C2×D4×C31—21no—
24C2×D4×C31C2×C411yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D412yes—
28M16×C31—24no—
29M16×C31—42no—
30C2×C8×C31—42no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31—22no—
33C4⋊C4×C31—22no—
34C22⋊C4×C31—21no—
35C22⋊C4×C31—22no—
36C22⋊C4×C31—22no—
37C42×C31C2×C411yescharacteristic
38C42×C31C2×C411yescharacteristic
39C23×C31—21no—
40C23×C31C22⋊C411yescharacteristic
41Q8×C31—41no—
42Q8×C31—42no—
43Q8×C31—41no—
44Q8×C31—41no—
45D4×C31—41no—
46D4×C31—42no—
47C2×C4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—42no—
54C2×C4×C31C22⋊C412yes—
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D412yes—
58C8×C31—44no—
59#2133C3111yesmaximal, characteristic, direct product factor, Sylow
60C22×C31—41no—
61C22×C31—42no—
62C22×C31—41no—
63C22×C31#9912yes—
64C22×C31C2×C22⋊C411yescharacteristic
65C4×C31—22no—
66C4×C31—21no—
67C4×C31—22no—
68C4×C31—21no—
69C4×C31—41no—
70C4×C31—41no—
71C4×C31—41no—
72#536C2×C3111yescharacteristic
73C2×#101C2×C3112yescomplemented
74#356C2×C3112yescomplemented
75#355C2×C3112yescomplemented
76C2×C31—21no—
77C2×C31—22no—
78C2×C31—81no—
79C2×C31C2×#9911yescharacteristic
80C2×#41C4×C3111yescharacteristic
81C22×Q8C22×C3111yescharacteristic
82C2×M16—22no—
83C4⋊Q8C4×C3111yescharacteristic
84C4⋊Q8C22×C3111yescharacteristic
85#124C4×C3111yescharacteristic
86#124C22×C3111yescharacteristic
87#123—22no—
88C22⋊Q8—22no—
89#117C4×C3111yescharacteristic
90#101—22no—
91#101C22×C3114yes—
92C31#213311yescharacteristic, direct product factor, Sylow
93#41—42no—
94C2×Q8—42no—
95C2×Q8C2×C4×C3111yescharacteristic
96C2×Q8C2×C4×C3111yescharacteristic
97C2×Q8D4×C3112yes—
98C2×Q8C23×C3111yescharacteristic
99C2×D4—21no—
100C2×D4C2×C4×C3111yescharacteristic
101C22×C4—21no—
102C22×C4C2×C4×C3111yescharacteristic
103C22×C4D4×C3112yes—
104M16—24no—
105M16—42no—
106C2×C8—42no—
107C4⋊C4—21no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C22⋊C4—21no—
111C22⋊C4—22no—
112C22⋊C4—22no—
113C42C2×C4×C3111yescharacteristic
114C42C2×C4×C3111yescharacteristic
115C23—21no—
116C23C22⋊C4×C3111yescharacteristic
117Q8—41no—
118Q8—42no—
119Q8—41no—
120Q8—41no—
121D4—41no—
122D4—42no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—42no—
130C2×C4C22⋊C4×C3112yes—
131C2×C4C22⋊C4×C3111yescharacteristic
132C2×C4C22×C4×C3111yescharacteristic
133C2×C4C2×D4×C3112yes—
134C8—44no—
135C22—41no—
136C22—42no—
137C22—41no—
138C22C31×#9912yes—
139C22C2×C22⋊C4×C3111yescharacteristic
140C4—22no—
141C4—21no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—41no—
146C4—41no—
147C2—21no—
148C2—22no—
149C2—81no—
150C2C2×C31×#9911yescharacteristic
subgroupG/H
center, socleC2×C31C2×#99
commutatorC2×C4C22×C4×C31
Frattini, cosocleC2×Q8C23×C31
prime radicalC2×#41×C31C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#101C2semidirect
3. C31×#356C2semidirect
4. C31×#355C2semidirect
59. #2133C31direct (N × H)
73. C2×#101C2×C31semidirect
74. #356C2×C31semidirect
75. #355C2×C31semidirect
92. C31#2133direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5362
C2×C31×#1012
C31×#3562
C31×#3552
#213331