Finite Group Databasebeta

← #16854086

Subgroups — #16854086

Order 3968.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×#11758465C211yesmaximal, characteristic
2C2×#11758521C211yesmaximal, characteristic
3#14520956C211yesmaximal, characteristic
4#14520955C211yesmaximal, characteristic
5#14520954C211yesmaximal, characteristic
6#14520953C214yesmaximal
7#14520913C214yesmaximal
8C42×Dic31C211yesmaximal, characteristic
9C31×#391C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C22×Dic62C2212yes—
12C22×Dic62C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C42×C31C2211yescharacteristic
15#11758521—24no—
16C2×C4⋊Dic31C2211yescharacteristic
17C2×Dic31⋊C4C2212yes—
18C2×Dic31⋊C4C2212yes—
19C2×Dic31⋊C4C2212yes—
20C2×C4×Dic31C2212yes—
21C2×C4×Dic31C2211yescharacteristic
22C2×C4×Dic31C2211yescharacteristic
23C2×C4×Dic31C2212yes—
24#11758465—24no—
25C31×#95C2214yes—
26C31⋊#95C2214yes—
27C31⋊#95C2214yes—
28C31⋊#95C2214yes—
29C2×Q8×C31—22no—
30C2×Q8×C31—22no—
31C2×Q8×C31—22no—
32C22×C4×C31C2312yes—
33C22×C4×C31C2312yes—
34C22×C4×C31C2312yes—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31C2312yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2311yescharacteristic
40C22×Dic31C2311yescharacteristic
41C2×Dic62—22no—
42C2×Dic62—22no—
43C2×Dic62—22no—
44C2×Dic62—24no—
45C2×Dic62—28no—
46C4⋊C4×C31—22no—
47C42×C31—22no—
48C4⋊Dic31—22no—
49Dic31⋊C4—24no—
50Dic31⋊C4—24no—
51Dic31⋊C4—24no—
52C4×Dic31—22no—
53C4×Dic31—24no—
54C4×Dic31D414yes—
55C4×Dic31Q818yescomplemented
56C23×C31C2411yescharacteristic
57Q8×C31—44no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—24no—
63C2×C4×C31—22no—
64C2×C4×C31—22no—
65C2×C4×C31C2×D412yes—
66C2×C4×C31C2×Q814yes—
67C2×C4×C31#4112yes—
68C2×C4×C31#4112yes—
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—24no—
76C2×Dic31C2×D412yes—
77C2×Dic31C2×D412yes—
78C2×Dic31C2×Q814yes—
79C2×Dic31C2×Q814yes—
80C2×Dic31#4114yes—
81Dic62—44no—
82Dic62—48no—
83#2862—311nomaximal, Sylow
84C22×C31C22×D411yescharacteristic
85C22×C31C22×Q812yes—
86C22×C31C2×#4111yescharacteristic
87C22×C31C2×#4111yescharacteristic
88C22×C31C2×#4112yes—
89C4×C31—24no—
90C4×C31—42no—
91C4×C31—42no—
92C4×C31#12414yes—
93Dic31—24no—
94Dic31—42no—
95Dic31—42no—
96Dic31#12414yes—
97Dic31C4⋊Q814yes—
98C2×C4⋊Q8—311no—
99C2×C4⋊Q8—311no—
100#391—311no—
101#391—311no—
102#391—311no—
103#391—314no—
104#391D3111yescharacteristic
105#382—314no—
106C43—311no—
107C2×C31C2×#12411yescharacteristic
108C2×C31C2×#12411yescharacteristic
109C2×C31C2×C4⋊Q811yescharacteristic
110C2×C31#53312yes—
111C2×C31#53312yes—
112C22×Q8—312no—
113C22×Q8—311no—
114C22×Q8C2×D3111yescharacteristic
115C4⋊Q8—624no—
116C4⋊Q8—624no—
117C2×C4⋊C4—312no—
118C2×C4⋊C4—312no—
119C2×C4⋊C4—312no—
120C2×C4⋊C4—311no—
121C2×C4⋊C4C2×D3111yescharacteristic
122C2×C42—311no—
123C2×C42—312no—
124C2×C42—312no—
125C2×C42—311no—
126C2×C42C2×D3111yescharacteristic
127#95—314no—
128#95—314no—
129#95—314no—
130#95C2×D3114yes—
131C31#286211yescharacteristic, complemented, Sylow
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—624no—
136C2×Q8—628no—
137C2×Q8—622no—
138C2×Q8—622no—
139C2×Q8—622no—
140C22×C4—311no—
141C22×C4—311no—
142C22×C4—312no—
143C22×C4—312no—
144C22×C4—312no—
145C22×C4C22×D3112yes—
146C22×C4C22×D3112yes—
147C22×C4C22×D3112yes—
148C22×C4C22×D3111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—624no—
151C4⋊C4—624no—
152C4⋊C4—624no—
153C4⋊C4—622no—
154C42—22no—
155C42—314no—
156C42—318no—
157C42—624no—
158C42—622no—
159C23C23×D3111yescharacteristic
160Q8—44no—
161Q8—1248no—
162Q8—1244no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—312no—
171C2×C4—312no—
172C2×C4—314no—
173C2×C4—314no—
174C2×C4—314no—
175C2×C4—622no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4—622no—
179C2×C4—622no—
180C2×C4—622no—
181C2×C4—624no—
182C2×C4#9249512yes—
183C2×C4D4×D3112yes—
184C2×C4#9249712yes—
185C2×C4Q8×D3114yes—
186C22C2×#9249511yescharacteristic
187C22C2×D4×D3111yescharacteristic
188C22C2×#9249711yescharacteristic
189C22C2×Q8×D3112yes—
190C22#41×D3112yes—
191C4—24no—
192C4—42no—
193C4—42no—
194C4—314no—
195C4—314no—
196C4—624no—
197C4—1242no—
198C4—1242no—
199C4#1175846214yes—
200C2#124×D3111yescharacteristic
201C2C2×#1175846211yescharacteristic
202C2C4⋊Q8×D3111yescharacteristic
203C2#1452160112yes—
204C2#1452160312yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, prime radical, cosocleC23×C31C24
FittingC31×#391C2
hypercenter#391D31
hypocenterC31#2862
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
55. C4×Dic31Q8semidirect
131. C31#2862semidirect

Maximal subgroups

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

subgroupindex
C2×#117584652
C2×#117585212
#145209562
#145209552
#145209542
#145209532
#145209132
C42×Dic312
C31×#3912
#286231