Finite Group Databasebeta

← C31×#2027 #16841960

Subgroups — C31×#2027 #16841960

Order 3968.

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

normal subgroups only

This group has 282 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×#544C211yesmaximal, characteristic, complemented
2C31×#418C212yesmaximal
3C31×#390C211yesmaximal, characteristic
4C31×#343C211yesmaximal, characteristic, complemented
5C31×#339C212yesmaximal, complemented
6C22×D4×C31C2211yescharacteristic
7C2×M16×C31C2212yes—
8C31×C4⋊Q8—22no—
9C31×#125—22no—
10C31×C22⋊Q8—22no—
11C31×#117C2212yes—
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31—22no—
14C2×C42×C31C2211yescharacteristic
15C31×#102—22no—
16C31×#102—22no—
17C24×C31—21no—
18C2×Q8×C31—22no—
19C2×D4×C31—22no—
20C2×D4×C31—22no—
21C2×D4×C31—21no—
22C2×D4×C31Q812yescomplemented
23C22×C4×C31—21no—
24C22×C4×C31D412yes—
25C22×C4×C31C2311yescharacteristic
26M16×C31—22no—
27M16×C31—22no—
28C2×C8×C31—22no—
29C4⋊C4×C31—22no—
30C4⋊C4×C31—24no—
31C4⋊C4×C31—22no—
32C4⋊C4×C31D412yes—
33C4⋊C4×C31D412yes—
34C22⋊C4×C31—22no—
35C22⋊C4×C31—44no—
36C42×C31—22no—
37C42×C31—22no—
38C23×C31—22no—
39C23×C31—42no—
40C23×C31—42no—
41C23×C31—41no—
42C23×C31—41no—
43C23×C31C2×D411yescharacteristic
44Q8×C31—82no—
45D4×C31—24no—
46D4×C31—42no—
47C2×C4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—42no—
54C2×C4×C31C2×D412yes—
55C2×C4×C31C2×Q811yescharacteristic
56C2×C4×C31#4112yes—
57C2×C4×C31#4111yescharacteristic
58C8×C31—42no—
59#2027C3111yesmaximal, characteristic, direct product factor, Sylow
60C22×C31—21no—
61C22×C31—21no—
62C22×C31—44no—
63C22×C31—42no—
64C22×C31—82no—
65C22×C31—81no—
66C22×C31—81no—
67C22×C31#12011yescharacteristic
68C22×C31C22⋊Q811yescharacteristic
69C22×C31#12411yescharacteristic
70C4×C31—42no—
71C4×C31—42no—
72C4×C31—42no—
73C4×C31—42no—
74C4×C31C22⋊Q812yes—
75C4×C31#12412yes—
76#544C2×C3111yescharacteristic, complemented
77#418C2×C3112yes—
78#390C2×C3111yescharacteristic
79#343C2×C3111yescharacteristic, complemented
80#339C2×C3112yescomplemented
81C2×C31—21no—
82C2×C31—21no—
83C2×C31—82no—
84C2×C31#39311yescharacteristic
85C2×C31#45311yescharacteristic
86C2×C31#45411yescharacteristic
87C22×D4C22×C3111yescharacteristic
88C2×M16C22×C3112yes—
89C4⋊Q8—22no—
90#125—22no—
91C22⋊Q8—22no—
92#117C22×C3112yes—
93C2×C4⋊C4C22×C3111yescharacteristic
94C2×C22⋊C4—22no—
95C2×C42C22×C3111yescharacteristic
96#102—22no—
97#102—22no—
98C31#202711yescharacteristic, direct product factor, Sylow
99C24—21no—
100C2×Q8—22no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4Q8×C3112yescomplemented
105C22×C4—21no—
106C22×C4D4×C3112yes—
107C22×C4C23×C3111yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4D4×C3112yes—
115C4⋊C4D4×C3112yes—
116C22⋊C4—22no—
117C22⋊C4—44no—
118C42—22no—
119C42—22no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×D4×C3111yescharacteristic
126Q8—82no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4C2×D4×C3112yes—
137C2×C4C2×Q8×C3111yescharacteristic
138C2×C4#41×C3112yes—
139C2×C4#41×C3111yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22C31×#12011yescharacteristic
149C22C31×C22⋊Q811yescharacteristic
150C22C31×#12411yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—42no—
155C4C31×C22⋊Q812yes—
156C4C31×#12412yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2C31×#39311yescharacteristic
161C2C31×#45311yescharacteristic
162C2C31×#45411yescharacteristic
subgroupG/H
center, socleC22×C31#120
commutator, Frattini, cosocleC22×C4C23×C31
prime radicalC22×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#544C2semidirect
4. C31×#343C2semidirect
5. C31×#339C2semidirect
22. C2×D4×C31Q8semidirect
59. #2027C31direct (N × H)
76. #544C2×C31semidirect
79. #343C2×C31semidirect
80. #339C2×C31semidirect
98. C31#2027direct (N × H)
104. C2×D4Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#5442
C31×#4182
C31×#3902
C31×#3432
C31×#3392
#202731