Finite Group Databasebeta

← #16846851

Subgroups — #16846851

Order 3968.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11758404C211yesmaximal, characteristic
3C2×#11758398C211yesmaximal, characteristic
4#14520954C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic
6#14520803C211yesmaximal, characteristic
7C31×#340C211yesmaximal, characteristic
8C22×Dic62—21no—
9C22×Dic62C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31C2211yescharacteristic
16C22×C31⋊C8C2211yescharacteristic
17#11758465—22no—
18#11758465—22no—
19C31⋊#95—21no—
20C31⋊#95—21no—
21#11758404—22no—
22#11758398—22no—
23C22×C4×C31—21no—
24C22×C4×C31—21no—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31—21no—
27C22×Dic31—21no—
28C22×Dic31D411yescharacteristic
29C22×Dic31D411yescharacteristic
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×Dic62—21no—
33C2×Dic62—21no—
34C2×Dic62—24no—
35C2×Dic62—21no—
36C2×Dic62—42no—
37C2×Dic62—42no—
38C2×Dic62Q812yescomplemented
39C2×C8×C31—21no—
40C2×C8×C31—21no—
41C2×C8×C31—21no—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31D412yes—
46C4⋊Dic31—21no—
47C4⋊Dic31D412yes—
48Dic31⋊C4—24no—
49C4×Dic31—21no—
50C4×Dic31—21no—
51C2×C31⋊C8—21no—
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54C23×C31C2×D411yescharacteristic
55C2×C4×C31—22no—
56C2×C4×C31—41no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×Q811yescharacteristic
64C2×C4×C31#4111yescharacteristic
65C2×C4×C31#4111yescharacteristic
66C2×C4×C31#4111yescharacteristic
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77C2×Dic31SD1612yes—
78C2×Dic31Q1612yes—
79Dic62—22no—
80Dic62—22no—
81Dic62—48no—
82Dic62—41no—
83Dic62—41no—
84C8×C31—41no—
85C31⋊C8—41no—
86#2024—311nomaximal, Sylow
87C22×C31#12011yescharacteristic
88C22×C31C22⋊Q811yescharacteristic
89C22×C31#12411yescharacteristic
90C22×C31C2×SD1611yescharacteristic
91C22×C31C2×Q1611yescharacteristic
92C22×C31AGL(1,ℤ/8)11yescharacteristic
93C22×C31#13711yescharacteristic
94C4×C31—42no—
95C4×C31—81no—
96C4×C31C22⋊Q811yescharacteristic
97C4×C31C22⋊Q811yescharacteristic
98C4×C31#12411yescharacteristic
99C4×C31#12411yescharacteristic
100Dic31—22no—
101Dic31—22no—
102Dic31—42no—
103Dic31—42no—
104C2×C4⋊Q8—311no—
105C2×#103—311no—
106C2×#103—311no—
107#391—311no—
108#340—311no—
109#340D3111yescharacteristic
110#336—311no—
111C2×C31#39311yescharacteristic
112C2×C31#45011yescharacteristic
113C2×C31#45111yescharacteristic
114C2×C31#47511yescharacteristic
115C2×C31#47711yescharacteristic
116C2×C31#48711yescharacteristic
117C2×C31#48911yescharacteristic
118C22×Q8—311no—
119C22×Q8—621no—
120C22×C8—311no—
121C22×C8C2×D3111yescharacteristic
122C4⋊Q8—622no—
123C4⋊Q8—622no—
124C2×C4⋊C4—311no—
125C2×C4⋊C4—621no—
126C2×C4⋊C4C2×D3111yescharacteristic
127C2×C4⋊C4C2×D3111yescharacteristic
128C2×C42—311no—
129#103—622no—
130#103—622no—
131#95—621no—
132#95—621no—
133C31#202411yescharacteristic, complemented, Sylow
134C2×Q8—312no—
135C2×Q8—624no—
136C2×Q8—621no—
137C2×Q8—621no—
138C2×Q8—621no—
139C2×Q8—621no—
140C2×Q8—621no—
141C2×Q8—1242no—
142C2×Q8—1242no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—311no—
146C22×C4—311no—
147C22×C4—621no—
148C22×C4—621no—
149C22×C4C22×D3111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—621no—
154C2×C8—621no—
155C2×C8—621no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—312no—
160C4⋊C4—624no—
161C4⋊C4—621no—
162C4⋊C4D12412yes—
163C42—621no—
164C42—621no—
165C23D4×D3111yescharacteristic
166Q8—622no—
167Q8—622no—
168Q8—1248no—
169Q8—1241no—
170Q8—1241no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—312no—
178C2×C4—312no—
179C2×C4—621no—
180C2×C4—621no—
181C2×C4—621no—
182C2×C4—621no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4—1241no—
186C2×C4—1241no—
187C2×C4—1241no—
188C2×C4—1241no—
189C2×C4C2×D12411yescharacteristic
190C2×C4#9249511yescharacteristic
191C2×C4#9249511yescharacteristic
192C2×C4D4×D3111yescharacteristic
193C2×C4#9249711yescharacteristic
194C2×C4Q8×D3111yescharacteristic
195C8—41no—
196C8—1241no—
197C22#1175845911yescharacteristic
198C22#1175846211yescharacteristic
199C22#1175847311yescharacteristic
200C22#1175848811yescharacteristic
201C22SD16×D3111yescharacteristic
202C22#1175849211yescharacteristic
203C22Q16×D3111yescharacteristic
204C4—42no—
205C4—81no—
206C4—622no—
207C4—622no—
208C4—1242no—
209C4—1242no—
210C4#1175845211yescharacteristic
211C4#1175846211yescharacteristic
212C4#1175847311yescharacteristic
213C4#1175847411yescharacteristic
214C2#1452096211yescharacteristic
215C2#1452120111yescharacteristic
216C2#1452120611yescharacteristic
217C2#1452133311yescharacteristic
218C2#1452134311yescharacteristic
219C2#1452139811yescharacteristic
220C2#1452140711yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#340C2
socle, prime radicalC23×C31C2×D4
hypercenter#340D31
hypocenterC31#2024
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic62Q8semidirect
133. C31#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#117584652
C2×#117584042
C2×#117583982
#145209542
#145208112
#145208032
C31×#3402
#202431