Finite Group Databasebeta

← #16846137

Subgroups — #16846137

Order 3968.

432 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C23×C31⋊C8C211yesmaximal, characteristic, complemented
2C2×#11758507C211yesmaximal, characteristic
3C2×#11758397C212yesmaximal, complemented
4#14520811C212yesmaximal, complemented
5C31×#380C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31—21no—
8C22×D124C2211yescharacteristic
9C2×C4⋊C4×C31C2212yes—
10C2×C22⋊C4×C31—21no—
11#11758507—22no—
12#11758507C414yescomplemented
13C2×(C2×D31)⋊C4—21no—
14C2×C4⋊Dic31C2211yescharacteristic
15C22×C31⋊C8—22no—
16C22×C31⋊C8—24no—
17C22×C31⋊C8C2212yes—
18C31×#95—21no—
19#11758397—24no—
20C24×C31D411yescharacteristic
21C23×D31—21no—
22C22×C4×C31—22no—
23C22×C4×C31—22no—
24C22×C4×C31—22no—
25C22×C4×C31C2×C412yes—
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D412yes—
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—24no—
30C2×C22⋊D31—42no—
31C2×C22⋊D31—42no—
32C22×Dic31—21no—
33C2×D124—22no—
34C2×D124—22no—
35C2×D124—21no—
36C2×D124C2×C412yes—
37C4⋊C4×C31—22no—
38C4⋊C4×C31—22no—
39C22⋊C4×C31—42no—
40(C2×D31)⋊C4—24no—
41C4⋊Dic31—21no—
42C4⋊Dic31C2×C412yes—
43C2×C31⋊C8—28no—
44C2×C31⋊C8—22no—
45C2×C31⋊C8—22no—
46C2×C31⋊C8D414yescomplemented
47C23×C31—22no—
48C23×C31—22no—
49C23×C31C22⋊C412yes—
50C23×C31D812yes—
51C23×C31SD1612yes—
52C23×C31C2×D411yescharacteristic
53C22×D31—22no—
54C22×D31—42no—
55C22×D31—41no—
56C22×D31—41no—
57C22×D31—42no—
58C2×C4×C31—22no—
59C2×C4×C31—24no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—42no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31C22⋊C412yes—
66C2×C4×C31C22×C411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D412yes—
69C2×C4×C31#4112yes—
70C22⋊D31—48no—
71C2×Dic31—22no—
72C2×Dic31—41no—
73C2×Dic31—41no—
74D124—24no—
75D124—41no—
76D124—41no—
77C31⋊C8—24no—
78#1893—311nomaximal, Sylow
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—24no—
82C22×C31—24no—
83C22×C31#10214yescomplemented
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31#12112yes—
86C22×C31C2×D811yescharacteristic
87C22×C31C2×SD1611yescharacteristic
88C22×C31#13512yes—
89C2×D31—42no—
90C2×D31—42no—
91C2×D31—42no—
92C2×D31—82no—
93C2×D31—82no—
94C4×C31—22no—
95C4×C31—82no—
96C4×C31C4×D412yes—
97C4×C31#12011yescharacteristic
98C4×C31#12311yescharacteristic
99Dic31—42no—
100C23×C8—311no—
101C2×#121—311no—
102C2×#102—312no—
103#380D3111yescharacteristic, complemented
104#340—312no—
105C2×C31—24no—
106C2×C31#38611yescharacteristic
107C2×C31C2×#10211yescharacteristic
108C2×C31#41611yescharacteristic
109C2×C31#46512yes—
110C2×C31#46612yes—
111D31—82no—
112C22×D4—311no—
113C22×D4—621no—
114C23×C4C2×D3111yescharacteristic
115C22×C8—312no—
116C22×C8—624no—
117C22×C8—622no—
118#121—314no—
119#121—622no—
120C2×C4⋊C4—311no—
121C2×C4⋊C4C2×D3112yes—
122C2×C22⋊C4—21no—
123C2×C22⋊C4—621no—
124#102—624no—
125#95—21no—
126C31#189311yescharacteristic, complemented, Sylow
127C24—621no—
128C24C22⋊D3111yescharacteristic
129C2×D4—312no—
130C2×D4—624no—
131C2×D4—621no—
132C2×D4—622no—
133C2×D4—622no—
134C2×D4—1242no—
135C2×D4—1242no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—621no—
140C22×C4C4×D3112yes—
141C22×C4D12412yes—
142C22×C4C22⋊D3111yescharacteristic
143C22×C4C22×D3111yescharacteristic
144C2×C8—314no—
145C2×C8—628no—
146C2×C8—622no—
147C2×C8—622no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—312no—
151C4⋊C4—621no—
152C22⋊C4—42no—
153C22⋊C4—624no—
154C23—22no—
155C23—22no—
156C23—622no—
157C23—1241no—
158C23—1242no—
159C23—1241no—
160C23—1242no—
161C23(C2×D31)⋊C412yes—
162C23#9247912yes—
163C23#9248112yes—
164C23C2×C22⋊D3111yescharacteristic
165D4—624no—
166D4—1248no—
167D4—1241no—
168D4—1241no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—622no—
177C2×C4—1241no—
178C2×C4—1241no—
179C2×C4(C2×D31)⋊C412yes—
180C2×C4C2×C4×D3111yescharacteristic
181C2×C4C2×D12411yescharacteristic
182C2×C4D4×D3112yes—
183C2×C4#9249712yes—
184C8—624no—
185C22—22no—
186C22—24no—
187C22—24no—
188C22—22no—
189C22—1242no—
190C22—1242no—
191C22—1242no—
192C22—2482no—
193C22—2482no—
194C22#1175839714yescomplemented
195C22C2×(C2×D31)⋊C411yescharacteristic
196C22C2×#9247911yescharacteristic
197C22#1175851612yes—
198C22C2×#9248111yescharacteristic
199C22#1175852712yes—
200C4—22no—
201C4—82no—
202C4—1242no—
203C4(C22⋊D31)⋊C412yes—
204C4#1175845911yescharacteristic
205C4#1175846311yescharacteristic
206C2—24no—
207C2—2482no—
208C2#1452092611yescharacteristic
209C2C2×#1175839711yescharacteristic
210C2#1452104311yescharacteristic
211C2#1452128012yes—
212C2#1452128312yes—
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#380C2
socleC23×C31C2×D4
prime radicalC2×#11758507C2
cosocleC22×C4×C31C23
hypercenter#380D31
hypocenterC31#1893
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C23×C31⋊C8C2semidirect
3. C2×#11758397C2semidirect
4. #14520811C2semidirect
5. C31×#380C2semidirect
12. #11758507C4semidirect
46. C2×C31⋊C8D4semidirect
83. C22×C31#102semidirect
103. #380D31semidirect
126. C31#1893semidirect
194. C22#11758397semidirect

Maximal subgroups

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

subgroupindex
C23×C31⋊C82
C2×#117585072
C2×#117583972
#145208112
C31×#3802
#189331