Finite Group Databasebeta

← C31×#3080 #16843013

Subgroups — C31×#3080 #16843013

Order 3968.

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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×#125C211yesmaximal, characteristic, complemented
2C4×#41×C31C211yesmaximal, characteristic
3C31×#479C214yesmaximal, complemented
4C31×#478C214yesmaximal, complemented
5C31×#428C212yesmaximal, complemented
6C31×#423C211yesmaximal, characteristic, complemented
7C31×#417C212yesmaximal
8C2×#41×C31C2211yescharacteristic
9C2×M16×C31C2212yes—
10C31×#125—21no—
11C31×#125—21no—
12C31×#125C2214yes—
13C4×Q8×C31C2212yes—
14C4×D4×C31—22no—
15C4×D4×C31C2212yes—
16C31×#117—21no—
17C31×#117C2211yescharacteristic
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31C2212yes—
20C2×C42×C31—21no—
21C2×C42×C31C2211yescharacteristic
22C31×#107C2214yes—
23C31×#106C2214yes—
24C31×C4⋊C8C2214yes—
25C31×#103C2214yes—
26C31×#102C2214yes—
27#41×C31—22no—
28#41×C31Q814yes—
29C2×Q8×C31C2311yescharacteristic
30C2×D4×C31—21no—
31C2×D4×C31C2311yescharacteristic
32C22×C4×C31—21no—
33C22×C4×C31—22no—
34C22×C4×C31—22no—
35C22×C4×C31D412yes—
36C22×C4×C31C2311yescharacteristic
37M16×C31—24no—
38C2×C8×C31C2314yes—
39C4⋊C4×C31—24no—
40C4⋊C4×C31—24no—
41C4⋊C4×C31—22no—
42C4⋊C4×C31—22no—
43C4⋊C4×C31C2314yes—
44C4⋊C4×C31C2312yes—
45C22⋊C4×C31—21no—
46C22⋊C4×C31—22no—
47C42×C31—21no—
48C42×C31—22no—
49C42×C31D411yescharacteristic
50C42×C31D411yescharacteristic
51C42×C31C2312yes—
52C23×C31—21no—
53C23×C31C2×D411yescharacteristic
54Q8×C31—21no—
55Q8×C31C2×Q812yes—
56D4×C31—24no—
57D4×C31—21no—
58D4×C31C2×Q812yes—
59C2×C4×C31—21no—
60C2×C4×C31—24no—
61C2×C4×C31—22no—
62C2×C4×C31—24no—
63C2×C4×C31—42no—
64C2×C4×C31—44no—
65C2×C4×C31—44no—
66C2×C4×C31C2×D412yes—
67C2×C4×C31C2×D412yes—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×Q812yes—
70C2×C4×C31#4112yes—
71C2×C4×C31C2411yescharacteristic
72C8×C31—24no—
73#3080C3111yesmaximal, characteristic, direct product factor, Sylow
74C22×C31—22no—
75C22×C31—22no—
76C22×C31—42no—
77C22×C31C22⋊Q812yes—
78C22×C31C22×D411yescharacteristic
79C4×C31—22no—
80C4×C31—22no—
81C4×C31—22no—
82C4×C31—42no—
83C4×C31—44no—
84C4×C31C22⋊Q812yes—
85C4×C31C22×Q811yescharacteristic
86C4×C31C2×#4111yescharacteristic
87C2×#125C2×C3111yescharacteristic, complemented
88C4×#41C2×C3111yescharacteristic
89#479C2×C3114yescomplemented
90#478C2×C3114yescomplemented
91#428C2×C3112yescomplemented
92#423C2×C3111yescharacteristic, complemented
93#417C2×C3112yes—
94C2×C31—22no—
95C2×C31—42no—
96C2×C31C2×C22⋊Q811yescharacteristic
97C2×C31#57512yes—
98C2×#41C22×C3111yescharacteristic
99C2×M16C22×C3112yes—
100#125—21no—
101#125—21no—
102#125C22×C3114yes—
103C4×Q8C22×C3112yes—
104C4×D4—22no—
105C4×D4C22×C3112yes—
106#117—21no—
107#117C22×C3111yescharacteristic
108C2×C4⋊C4—22no—
109C2×C4⋊C4C22×C3112yes—
110C2×C42—21no—
111C2×C42C22×C3111yescharacteristic
112#107C22×C3114yes—
113#106C22×C3114yes—
114C4⋊C8C22×C3114yes—
115#103C22×C3114yes—
116#102C22×C3114yes—
117C31#308011yescharacteristic, direct product factor, Sylow
118#41—22no—
119#41Q8×C3114yes—
120C2×Q8C23×C3111yescharacteristic
121C2×D4—21no—
122C2×D4C23×C3111yescharacteristic
123C22×C4—21no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4D4×C3112yes—
127C22×C4C23×C3111yescharacteristic
128M16—24no—
129C2×C8C23×C3114yes—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4C23×C3114yes—
135C4⋊C4C23×C3112yes—
136C22⋊C4—21no—
137C22⋊C4—22no—
138C42—21no—
139C42—22no—
140C42D4×C3111yescharacteristic
141C42D4×C3111yescharacteristic
142C42C23×C3112yes—
143C23—21no—
144C23C2×D4×C3111yescharacteristic
145Q8—21no—
146Q8C2×Q8×C3112yes—
147D4—24no—
148D4—21no—
149D4C2×Q8×C3112yes—
150C2×C4—21no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—44no—
157C2×C4C2×D4×C3112yes—
158C2×C4C2×D4×C3112yes—
159C2×C4C2×D4×C3111yescharacteristic
160C2×C4C2×Q8×C3112yes—
161C2×C4#41×C3112yes—
162C2×C4C24×C3111yescharacteristic
163C8—24no—
164C22—22no—
165C22—22no—
166C22—42no—
167C22C31×C22⋊Q812yes—
168C22C22×D4×C3111yescharacteristic
169C4—22no—
170C4—22no—
171C4—22no—
172C4—42no—
173C4—44no—
174C4C31×C22⋊Q812yes—
175C4C22×Q8×C3111yescharacteristic
176C4C2×#41×C3111yescharacteristic
177C2—22no—
178C2—42no—
179C2C2×C31×C22⋊Q811yescharacteristic
180C2C31×#57512yes—
subgroupG/H
center, socleC22×C31C22×D4
commutator, Frattini, cosocleC2×C4C24×C31
prime radicalC2×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#125C2semidirect
3. C31×#479C2semidirect
4. C31×#478C2semidirect
5. C31×#428C2semidirect
6. C31×#423C2semidirect
73. #3080C31direct (N × H)
87. C2×#125C2×C31semidirect
89. #479C2×C31semidirect
90. #478C2×C31semidirect
91. #428C2×C31semidirect
92. #423C2×C31semidirect
117. C31#3080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#1252
C4×#41×C312
C31×#4792
C31×#4782
C31×#4282
C31×#4232
C31×#4172
#308031