Finite Group Databasebeta

← #16846861

Subgroups — #16846861

Order 3968.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11758404C211yesmaximal, characteristic
3C2×#11758398C211yesmaximal, characteristic
4#14520954C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic
6#14520803C211yesmaximal, characteristic
7C31×#340C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊Dic31—21no—
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31C2211yescharacteristic
16C22×C31⋊C8C2211yescharacteristic
17#11758467—22no—
18#11758467—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—21no—
35C2×Dic62Q812yes—
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C4⋊C4×C31D412yes—
43C4⋊Dic31—24no—
44C4⋊Dic31—21no—
45C4⋊Dic31D412yes—
46Dic31⋊C4—24no—
47C4×Dic31—21no—
48C4×Dic31—21no—
49C2×C31⋊C8—21no—
50C2×C31⋊C8—21no—
51C2×C31⋊C8—21no—
52C23×C31C2×D411yescharacteristic
53C2×C4×C31—22no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×Q811yescharacteristic
62C2×C4×C31#4111yescharacteristic
63C2×C4×C31#4111yescharacteristic
64C2×C4×C31#4111yescharacteristic
65C2×Dic31—21no—
66C2×Dic31—21no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—21no—
72C2×Dic31—21no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77Dic62—22no—
78Dic62—22no—
79Dic62—41no—
80Dic62—41no—
81C8×C31—41no—
82C31⋊C8—41no—
83#2026—311nomaximal, Sylow
84C22×C31#12011yescharacteristic
85C22×C31C22⋊Q811yescharacteristic
86C22×C31#12411yescharacteristic
87C22×C31#13511yescharacteristic
88C22×C31#13511yescharacteristic
89C22×C31#13711yescharacteristic
90C22×C31#13711yescharacteristic
91C4×C31—42no—
92C4×C31—81no—
93C4×C31C22⋊Q811yescharacteristic
94C4×C31C22⋊Q811yescharacteristic
95C4×C31#12411yescharacteristic
96C4×C31#12411yescharacteristic
97Dic31—42no—
98Dic31—41no—
99Dic31—41no—
100Dic31—42no—
101C2×#125—311no—
102C2×#103—311no—
103C2×#103—311no—
104#391—311no—
105#340—311no—
106#340D3111yescharacteristic
107#336—311no—
108C2×C31#39311yescharacteristic
109C2×C31#45211yescharacteristic
110C2×C31#45211yescharacteristic
111C2×C31#47911yescharacteristic
112C2×C31#47911yescharacteristic
113C2×C31#48811yescharacteristic
114C2×C31#49111yescharacteristic
115C22×Q8—311no—
116C22×C8—311no—
117C22×C8C2×D3111yescharacteristic
118#125—622no—
119#125—622no—
120C2×C4⋊C4—311no—
121C2×C4⋊C4—621no—
122C2×C4⋊C4—621no—
123C2×C4⋊C4C2×D3111yescharacteristic
124C2×C4⋊C4C2×D3111yescharacteristic
125C2×C42—311no—
126#103—622no—
127#103—622no—
128#95—621no—
129#95—621no—
130C31#202611yescharacteristic, complemented, Sylow
131C2×Q8—312no—
132C2×Q8—621no—
133C2×Q8—621no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—311no—
140C22×C4—311no—
141C22×C4—621no—
142C22×C4—621no—
143C22×C4C22×D3111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—621no—
148C2×C8—621no—
149C2×C8—621no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—312no—
154C4⋊C4—624no—
155C4⋊C4—624no—
156C4⋊C4—621no—
157C4⋊C4D12412yes—
158C42—621no—
159C42—621no—
160C23D4×D3111yescharacteristic
161Q8—622no—
162Q8—622no—
163Q8—1241no—
164Q8—1241no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—621no—
172C2×C4—621no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4—621no—
176C2×C4—621no—
177C2×C4—621no—
178C2×C4—621no—
179C2×C4—1241no—
180C2×C4—1241no—
181C2×C4—1241no—
182C2×C4—1241no—
183C2×C4C2×D12411yescharacteristic
184C2×C4#9249511yescharacteristic
185C2×C4#9249511yescharacteristic
186C2×C4D4×D3111yescharacteristic
187C2×C4#9249711yescharacteristic
188C2×C4Q8×D3111yescharacteristic
189C8—41no—
190C8—1241no—
191C22#1175845911yescharacteristic
192C22#1175846211yescharacteristic
193C22#1175847311yescharacteristic
194C22#1175848911yescharacteristic
195C22#1175849211yescharacteristic
196C22#1175849311yescharacteristic
197C22#1175849511yescharacteristic
198C4—42no—
199C4—81no—
200C4—1241no—
201C4—1241no—
202C4—1242no—
203C4—1242no—
204C4#1175845211yescharacteristic
205C4#1175846211yescharacteristic
206C4#1175847311yescharacteristic
207C4#1175847411yescharacteristic
208C2#1452096211yescharacteristic
209C2#1452121211yescharacteristic
210C2#1452121411yescharacteristic
211C2#1452135511yescharacteristic
212C2#1452135911yescharacteristic
213C2#1452140211yescharacteristic
214C2#1452141611yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#340C2
socle, prime radicalC23×C31C2×D4
hypercenter#340D31
hypocenterC31#2026
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
130. C31#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#117584672
C2×#117584042
C2×#117583982
#145209542
#145208112
#145208032
C31×#3402
#202631