Finite Group Databasebeta

← #16846140

Subgroups — #16846140

Order 3968.

432 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 129 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×#11758420C212yesmaximal, complemented
3#14520909C211yesmaximal, characteristic, complemented
4#14520811C212yesmaximal, complemented
5C2×C31×#121C211yesmaximal, characteristic
6C22×D4×C31—21no—
7C22×D4×C31C2211yescharacteristic
8C23×C4×C31C2211yescharacteristic
9C31×#121—22no—
10C31×#121C414yescomplemented
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31—21no—
13C2×C22⋊Dic31—21no—
14C2×C4⋊Dic31C2212yes—
15C22×C31⋊C8—22no—
16C22×C31⋊C8—24no—
17C22×C31⋊C8C2212yes—
18#11758420—24no—
19C31⋊#95—21no—
20C24×C31—21no—
21C24×C31D411yescharacteristic
22C2×D4×C31—24no—
23C2×D4×C31—22no—
24C2×D4×C31—21no—
25C2×D4×C31—22no—
26C2×D4×C31—42no—
27C2×D4×C31—42no—
28C2×D4×C31C2×C412yes—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—21no—
32C22×C4×C31C2×C412yes—
33C22×C4×C31D411yescharacteristic
34C22×C4×C31D412yes—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31—22no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31C2×C412yes—
39C22⋊C4×C31—24no—
40C22⋊Dic31—42no—
41C4⋊Dic31—22no—
42C4⋊Dic31—22no—
43C2×C31⋊C8—28no—
44C2×C31⋊C8—22no—
45C2×C31⋊C8—22no—
46C2×C31⋊C8D414yescomplemented
47C23×C31—22no—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31—42no—
51C23×C31—41no—
52C23×C31—41no—
53C23×C31—42no—
54C23×C31C22⋊C412yes—
55C23×C31D812yes—
56C23×C31SD1612yes—
57C23×C31C2×D411yescharacteristic
58D4×C31—24no—
59D4×C31—48no—
60D4×C31—41no—
61D4×C31—41no—
62C2×C4×C31—22no—
63C2×C4×C31—24no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31C22⋊C412yes—
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D412yes—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4112yes—
74C2×Dic31—42no—
75C2×Dic31—42no—
76C2×Dic31—42no—
77C31⋊C8—24no—
78#1893—311nomaximal, Sylow
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—24no—
82C22×C31—24no—
83C22×C31—42no—
84C22×C31—42no—
85C22×C31—42no—
86C22×C31—82no—
87C22×C31—82no—
88C22×C31#10214yescomplemented
89C22×C31C2×C22⋊C411yescharacteristic
90C22×C31#12112yes—
91C22×C31C2×D811yescharacteristic
92C22×C31C2×SD1611yescharacteristic
93C22×C31#13512yes—
94C4×C31—22no—
95C4×C31—42no—
96C4×C31C4×D412yes—
97C4×C31#12011yescharacteristic
98C4×C31#12311yescharacteristic
99Dic31—82no—
100C23×C8—311no—
101C2×#121D3111yescharacteristic
102C2×#102—312no—
103#380—311no—
104#340—312no—
105C2×C31—24no—
106C2×C31—82no—
107C2×C31#38611yescharacteristic
108C2×C31C2×#10211yescharacteristic
109C2×C31#41611yescharacteristic
110C2×C31#46512yes—
111C2×C31#46612yes—
112C22×D4—21no—
113C22×D4C2×D3111yescharacteristic
114C23×C4C2×D3111yescharacteristic
115C22×C8—312no—
116C22×C8—624no—
117C22×C8—622no—
118#121—22no—
119#121Dic3114yescomplemented
120C2×C4⋊C4—312no—
121C2×C4⋊C4C2×D3111yescharacteristic
122C2×C22⋊C4—21no—
123C2×C22⋊C4—621no—
124#102—624no—
125#95—621no—
126C31#189311yescharacteristic, complemented, Sylow
127C24—21no—
128C24C22⋊D3111yescharacteristic
129C2×D4—24no—
130C2×D4—22no—
131C2×D4—22no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—42no—
135C2×D4C2×Dic3112yes—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—622no—
140C22×C4C2×Dic3112yes—
141C22×C4C22⋊D3111yescharacteristic
142C22×C4C22⋊D3112yes—
143C22×C4C22×D3111yescharacteristic
144C2×C8—314no—
145C2×C8—628no—
146C2×C8—622no—
147C2×C8—622no—
148C4⋊C4—21no—
149C4⋊C4—622no—
150C4⋊C4—622no—
151C4⋊C4C2×Dic3112yes—
152C22⋊C4—24no—
153C22⋊C4—1242no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—42no—
160C23—42no—
161C23#9247912yes—
162C23#9248012yes—
163C23C22⋊Dic3112yes—
164C23C2×C22⋊D3111yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—1242no—
177C2×C4—1242no—
178C2×C4—1242no—
179C2×C4C22⋊Dic3112yes—
180C2×C4D4×D3112yes—
181C2×C4#9249712yes—
182C2×C4C22×Dic3111yescharacteristic
183C2×C4C2×C22⋊D3111yescharacteristic
184C8—624no—
185C22—22no—
186C22—24no—
187C22—24no—
188C22—22no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#1175842014yescomplemented
195C22C2×#9247911yescharacteristic
196C22C2×#9248011yescharacteristic
197C22#1175851612yes—
198C22#1175852712yes—
199C22C2×C22⋊Dic3111yescharacteristic
200C4—22no—
201C4—42no—
202C4—2482no—
203C4D4×Dic3112yes—
204C4#1175851211yescharacteristic
205C4#1175851411yescharacteristic
206C2—24no—
207C2—82no—
208C2#1452092911yescharacteristic
209C2C2×#1175842011yescharacteristic
210C2#1452104511yescharacteristic
211C2#1452127612yes—
212C2#1452128312yes—
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC2×C31×#121C2
socleC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC2×#121D31
hypocenterC31#1893
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×C31⋊C8C2semidirect
2. C2×#11758420C2semidirect
3. #14520909C2semidirect
4. #14520811C2semidirect
10. C31×#121C4semidirect
46. C2×C31⋊C8D4semidirect
88. C22×C31#102semidirect
119. #121Dic31semidirect
126. C31#1893semidirect
194. C22#11758420semidirect

Maximal subgroups

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

subgroupindex
C23×C31⋊C82
C2×#117584202
#145209092
#145208112
C2×C31×#1212
#189331