Finite Group Databasebeta

← #16849001

Subgroups — #16849001

Order 3968.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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×Q8×Dic31C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic
3#14520982C212yesmaximal
4#14520981C211yesmaximal, characteristic
5#14520979C211yesmaximal, characteristic
6#14520970C212yesmaximal
7#14520968C211yesmaximal, characteristic
8C4⋊C4×Dic31C212yesmaximal
9#14520900C212yesmaximal
10#14520894C211yesmaximal, characteristic
11C31×#395C211yesmaximal, characteristic
12C22×Q8×C31C2211yescharacteristic
13C22×Dic62C2211yescharacteristic
14C2×C4⋊C4×C31C2212yes—
15C2×C4⋊C4×C31C2211yescharacteristic
16Q8×Dic31—24no—
17C2×C4⋊Dic31C2212yes—
18C2×C4⋊Dic31C2212yes—
19C2×C4⋊Dic31C2211yescharacteristic
20C2×Dic31⋊C4C2212yes—
21C2×Dic31⋊C4C2212yes—
22C2×Dic31⋊C4C2211yescharacteristic
23C2×Dic31⋊C4C2211yescharacteristic
24C2×C4×Dic31C2211yescharacteristic
25C2×C4×Dic31C2212yes—
26C2×C4×Dic31C2211yescharacteristic
27C2×C4×Dic31C2211yescharacteristic
28C2×C4×Dic31C2212yes—
29#11758464—24no—
30C31×#95C2211yescharacteristic
31C31×#95C2212yes—
32C31⋊#95C2211yescharacteristic
33C31⋊#95C2212yes—
34C31⋊#95C2212yes—
35C31⋊#95C2212yes—
36C31⋊#95C2212yes—
37C2×Q8×C31—22no—
38C2×Q8×C31—24no—
39C22×C4×C31C2311yescharacteristic
40C22×C4×C31C2311yescharacteristic
41C22×C4×C31C2312yes—
42C22×C4×C31C2312yes—
43C22×C4×C31C2311yescharacteristic
44C22×Dic31C2311yescharacteristic
45C22×Dic31C2312yes—
46C22×Dic31C2311yescharacteristic
47C22×Dic31C2312yes—
48C22×Dic31C2311yescharacteristic
49C22×Dic31C2311yescharacteristic
50C2×Dic62—22no—
51C2×Dic62—22no—
52C2×Dic62—22no—
53C4⋊C4×C31—22no—
54C4⋊C4×C31—24no—
55C4⋊Dic31—22no—
56C4⋊Dic31—24no—
57C4⋊Dic31—24no—
58Dic31⋊C4—22no—
59Dic31⋊C4—24no—
60Dic31⋊C4—24no—
61Dic31⋊C4—22no—
62C4×Dic31—22no—
63C4×Dic31—22no—
64C4×Dic31—24no—
65C4×Dic31D414yes—
66C4×Dic31Q818yescomplemented
67C23×C31C2411yescharacteristic
68Q8×C31—28no—
69C2×C4×C31—22no—
70C2×C4×C31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—21no—
77C2×C4×C31—22no—
78C2×C4×C31C2×D412yes—
79C2×C4×C31C2×Q814yes—
80C2×C4×C31#4114yes—
81C2×C4×C31#4112yes—
82C2×Dic31—21no—
83C2×Dic31—22no—
84C2×Dic31—22no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—21no—
88C2×Dic31—21no—
89C2×Dic31—22no—
90C2×Dic31—22no—
91C2×Dic31—22no—
92C2×Dic31—22no—
93C2×Dic31C2×D412yes—
94C2×Dic31C2×D412yes—
95C2×Dic31C2×Q814yes—
96C2×Dic31C2×Q814yes—
97C2×Dic31#4112yes—
98Dic62—28no—
99#2399—311nomaximal, Sylow
100C22×C31C22×D411yescharacteristic
101C22×C31C22×Q812yes—
102C22×C31C2×#4112yes—
103C22×C31C2×#4111yescharacteristic
104C22×C31C2×#4111yescharacteristic
105C4×C31—22no—
106C4×C31—22no—
107C4×C31—24no—
108C4×C31—24no—
109C4×C31—41no—
110Dic31—22no—
111Dic31—22no—
112Dic31—24no—
113Dic31—41no—
114Dic31—42no—
115Dic31C4⋊Q814yes—
116C2×C4×Q8—311no—
117C2×C4×Q8—311no—
118#398—311no—
119#398—312no—
120#398—311no—
121#395—311no—
122#395—312no—
123#395D3111yescharacteristic
124C4×C4⋊C4—312no—
125C4×C4⋊C4—312no—
126#376—311no—
127C2×C31#52511yescharacteristic
128C2×C31#52511yescharacteristic
129C2×C31C2×C4⋊Q811yescharacteristic
130C2×C31#53312yes—
131C2×C31#53312yes—
132C22×Q8—311no—
133C22×Q8C2×D3111yescharacteristic
134C4×Q8—624no—
135C4×Q8—624no—
136C2×C4⋊C4—311no—
137C2×C4⋊C4—312no—
138C2×C4⋊C4—311no—
139C2×C4⋊C4—311no—
140C2×C4⋊C4—312no—
141C2×C4⋊C4—312no—
142C2×C4⋊C4—312no—
143C2×C4⋊C4C2×D3111yescharacteristic
144C2×C4⋊C4C2×D3112yes—
145C2×C42—311no—
146C2×C42—312no—
147C2×C42—311no—
148C2×C42—312no—
149C2×C42—311no—
150#95—311no—
151#95—312no—
152#95—312no—
153#95—312no—
154#95—312no—
155#95C2×D3111yescharacteristic
156#95C2×D3112yes—
157C31#239911yescharacteristic, complemented, Sylow
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—622no—
161C2×Q8—622no—
162C2×Q8—622no—
163C22×C4—311no—
164C22×C4—312no—
165C22×C4—311no—
166C22×C4—311no—
167C22×C4—311no—
168C22×C4—312no—
169C22×C4C22×D3111yescharacteristic
170C22×C4C22×D3111yescharacteristic
171C22×C4C22×D3112yes—
172C22×C4C22×D3112yes—
173C22×C4C22×D3111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—622no—
177C4⋊C4—624no—
178C4⋊C4—624no—
179C4⋊C4—622no—
180C4⋊C4—622no—
181C4⋊C4—624no—
182C4⋊C4—624no—
183C42—314no—
184C42—318no—
185C42—622no—
186C42—624no—
187C42—622no—
188C23C23×D3111yescharacteristic
189Q8—28no—
190Q8—628no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—312no—
201C2×C4—314no—
202C2×C4—312no—
203C2×C4—314no—
204C2×C4—312no—
205C2×C4—621no—
206C2×C4—622no—
207C2×C4—622no—
208C2×C4—621no—
209C2×C4—621no—
210C2×C4—621no—
211C2×C4—621no—
212C2×C4—622no—
213C2×C4—622no—
214C2×C4—622no—
215C2×C4—622no—
216C2×C4D4×D3112yes—
217C2×C4#9249714yes—
218C2×C4Q8×D3114yes—
219C2×C4#9249912yes—
220C22C2×D4×D3111yescharacteristic
221C22C2×#9249712yes—
222C22C2×Q8×D3112yes—
223C22C2×#9249911yescharacteristic
224C22#41×D3111yescharacteristic
225C4—24no—
226C4—22no—
227C4—24no—
228C4—22no—
229C4—41no—
230C4—314no—
231C4—624no—
232C4—622no—
233C4—622no—
234C4—1241no—
235C4—1242no—
236C2#1452155511yescharacteristic
237C2#1452156211yescharacteristic
238C2C4⋊Q8×D3111yescharacteristic
239C2#1452160112yes—
240C2#1452160412yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, prime radical, cosocleC23×C31C24
FittingC31×#395C2
hypercenter#395D31
hypocenterC31#2399
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
66. C4×Dic31Q8semidirect
157. C31#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic312
C2×#117584642
#145209822
#145209812
#145209792
#145209702
#145209682
C4⋊C4×Dic312
#145209002
#145208942
C31×#3952
#239931