Finite Group Databasebeta

← #16846678

Subgroups — #16846678

Order 3968.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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×#11758467C211yesmaximal, characteristic
2C2×#11758403C211yesmaximal, characteristic
3#14520918C211yesmaximal, characteristic
4#14520812C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic
6#14520811C211yesmaximal, characteristic
7C31×#340C211yesmaximal, characteristic
8C22×C8×C31C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊Dic31—21no—
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15C2×Dic31⋊C4—21no—
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19#11758467—22no—
20#11758467C414yescomplemented
21#11758403—22no—
22C22×C4×C31—21no—
23C22×C4×C31—21no—
24C22×C4×C31C2311yescharacteristic
25C22×Dic31—21no—
26C22×Dic31—21no—
27C22×Dic31D411yescharacteristic
28C22×Dic31D411yescharacteristic
29C2×C8×C31—21no—
30C2×C8×C31—21no—
31C2×C8×C31Q812yes—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31C2×C412yes—
36C4⋊Dic31—21no—
37C4⋊Dic31—24no—
38C4⋊Dic31—21no—
39C4⋊Dic31—21no—
40C4⋊Dic31C2×C412yes—
41Dic31⋊C4—24no—
42Dic31⋊C4—42no—
43Dic31⋊C4—42no—
44C4×Dic31C2×C412yes—
45C4×Dic31D412yes—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C2×C31⋊C8Q812yes—
49C23×C31C2×D411yescharacteristic
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×Q811yescharacteristic
59C2×C4×C31C2×Q811yescharacteristic
60C2×C4×C31#4111yescharacteristic
61C2×C4×C31#4111yescharacteristic
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—21no—
66C2×Dic31—22no—
67C2×Dic31—41no—
68C2×Dic31—41no—
69C2×Dic31—41no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31C22⋊C412yes—
73C2×Dic31C22⋊C412yes—
74C8×C31—22no—
75C31⋊C8—22no—
76#1992—311nomaximal, Sylow
77C22×C31C2×C22⋊C411yescharacteristic
78C22×C31#12411yescharacteristic
79C22×C31C4⋊Q811yescharacteristic
80C22×C31AGL(1,ℤ/8)11yescharacteristic
81C22×C31AGL(1,ℤ/8)11yescharacteristic
82C22×C31#13711yescharacteristic
83C22×C31#13711yescharacteristic
84C4×C31—42no—
85C4×C31—81no—
86C4×C31C4×Q811yescharacteristic
87C4×C31C4×Q811yescharacteristic
88C4×C31C22⋊Q811yescharacteristic
89C4×C31C22⋊Q811yescharacteristic
90Dic31—22no—
91Dic31—22no—
92Dic31—42no—
93Dic31—81no—
94C2×#125—311no—
95C2×#97—311no—
96#384—311no—
97#340—311no—
98#340—311no—
99#340—311no—
100#340D3111yescharacteristic
101C2×C31#39111yescharacteristic
102C2×C31#41711yescharacteristic
103C2×C31#41711yescharacteristic
104C2×C31#49011yescharacteristic
105C2×C31#49111yescharacteristic
106C2×C31#50111yescharacteristic
107C2×C31#50111yescharacteristic
108C22×C8—311no—
109C22×C8C2×D3111yescharacteristic
110#125—314no—
111#125—622no—
112C2×C4⋊C4—311no—
113C2×C4⋊C4—311no—
114C2×C4⋊C4—621no—
115C2×C4⋊C4—621no—
116C2×C4⋊C4—621no—
117C2×C4⋊C4—621no—
118C2×C4⋊C4C2×D3111yescharacteristic
119C2×C4⋊C4C2×D3111yescharacteristic
120C2×C42—311no—
121#97—622no—
122C31#199211yescharacteristic, complemented, Sylow
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—311no—
126C22×C4—311no—
127C22×C4—621no—
128C22×C4—621no—
129C22×C4C22×D3111yescharacteristic
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—312no—
133C2×C8—621no—
134C2×C8—621no—
135C2×C8Dic6212yes—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—312no—
140C4⋊C4—624no—
141C4⋊C4—624no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—1242no—
146C4⋊C4—1242no—
147C4⋊C4C4×D3112yes—
148C42—312no—
149C42—312no—
150C23D4×D3111yescharacteristic
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—312no—
158C2×C4—312no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—621no—
162C2×C4—621no—
163C2×C4—622no—
164C2×C4—1241no—
165C2×C4—1241no—
166C2×C4—1241no—
167C2×C4—1241no—
168C2×C4—1241no—
169C2×C4C2×Dic6211yescharacteristic
170C2×C4C2×C4×D3111yescharacteristic
171C2×C4#9249511yescharacteristic
172C2×C4D4×D3111yescharacteristic
173C2×C4#9249711yescharacteristic
174C2×C4Q8×D3111yescharacteristic
175C8—22no—
176C8—622no—
177C22C22⋊C4×D3111yescharacteristic
178C22#1175846211yescharacteristic
179C22#1175846511yescharacteristic
180C22#1175848811yescharacteristic
181C22#1175849111yescharacteristic
182C22#1175849211yescharacteristic
183C22#1175849511yescharacteristic
184C4—42no—
185C4—81no—
186C4—622no—
187C4—622no—
188C4—1242no—
189C4—2481no—
190C4C4×Dic6211yescharacteristic
191C4#1175845511yescharacteristic
192C4#1175846411yescharacteristic
193C4#1175847311yescharacteristic
194C2#1452095311yescharacteristic
195C2#1452104711yescharacteristic
196C2#1452104911yescharacteristic
197C2#1452141211yescharacteristic
198C2#1452141611yescharacteristic
199C2#1452145611yescharacteristic
200C2#1452145711yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#340C2
socle, prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#340D31
hypocenterC31#1992
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
20. #11758467C4semidirect
122. C31#1992semidirect

Maximal subgroups

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

subgroupindex
C2×#117584672
C2×#117584032
#145209182
#145208122
#145208112
C31×#3402
#199231