Finite Group Databasebeta

← #16846871

Subgroups — #16846871

Order 3968.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#14521677C211yesmaximal, characteristic
2#14521059C211yesmaximal, characteristic
3#14521057C211yesmaximal, characteristic
4#14520955C211yesmaximal, characteristic
5#14520817C211yesmaximal, characteristic
6#14520809C211yesmaximal, characteristic
7C31×#339C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C31×#117C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12#11758503C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×#92474C2211yescharacteristic
15#11758467—21no—
16#11758465—21no—
17#11758455—22no—
18#11758447—21no—
19#11758446—21no—
20C31⋊#95—22no—
21#11758404—21no—
22#11758404—21no—
23#11758398—21no—
24#11758398—21no—
25C22×C4×C31—21no—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—21no—
28C22×Dic31D412yes—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×Dic62—21no—
33C2×Dic62—21no—
34C2×Dic62—22no—
35C2×Dic62Q812yescomplemented
36M16×C31—21no—
37M16×C31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31D411yescharacteristic
40C4⋊C4×C31D411yescharacteristic
41C22⋊C4×C31—21no—
42C42×C31—21no—
43C42×C31—21no—
44C42×C31—21no—
45C22⋊Dic31—21no—
46C4⋊Dic31—22no—
47C4⋊Dic31—21no—
48C4⋊Dic31—21no—
49C4⋊Dic31D411yescharacteristic
50C4⋊Dic31D411yescharacteristic
51Dic31⋊C4—22no—
52Dic31⋊C4—22no—
53C4×Dic31—21no—
54#92474—21no—
55#92474—21no—
56C2×C31⋊C8—21no—
57C23×C31C2×D411yescharacteristic
58C2×C4×C31—22no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×Q811yescharacteristic
66C2×C4×C31#4111yescharacteristic
67C2×C4×C31#4111yescharacteristic
68C2×C4×C31#4111yescharacteristic
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31—42no—
76Dic62—22no—
77Dic62—22no—
78Dic62—41no—
79Dic62—41no—
80Dic62—82no—
81C8×C31—41no—
82C31⋊C8—41no—
83#2028—311nomaximal, Sylow
84C22×C31—21no—
85C22×C31—21no—
86C22×C31#12011yescharacteristic
87C22×C31C22⋊Q811yescharacteristic
88C22×C31#12411yescharacteristic
89C4×C31—42no—
90C4×C31—41no—
91C4×C31—41no—
92C4×C31C22⋊Q811yescharacteristic
93C4×C31C22⋊Q811yescharacteristic
94C4×C31#12411yescharacteristic
95C4×C31#12411yescharacteristic
96Dic31—42no—
97Dic31—41no—
98Dic31—42no—
99Dic31—41no—
100#544—311no—
101#419—311no—
102#419—311no—
103#391—311no—
104#343—311no—
105#339—311no—
106#339D3111yescharacteristic
107C2×C31—21no—
108C2×C31—21no—
109C2×C31#39311yescharacteristic
110C2×C31#45511yescharacteristic
111C2×C31#45611yescharacteristic
112C22×Q8—311no—
113C2×M16—311no—
114C2×M16C2×D3111yescharacteristic
115C4⋊Q8—621no—
116C4⋊Q8—621no—
117#125—621no—
118#125—621no—
119C22⋊Q8—622no—
120#117—311no—
121#117C2×D3111yescharacteristic
122C2×C4⋊C4—311no—
123C2×C42C2×D3111yescharacteristic
124#103—621no—
125#103—621no—
126#103—621no—
127#103—621no—
128#95—622no—
129C31#202811yescharacteristic, complemented, Sylow
130C2×Q8—312no—
131C2×Q8—622no—
132C2×Q8—621no—
133C2×Q8—621no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C22×C4—21no—
138C22×C4—312no—
139C22×C4—621no—
140C22×C4C22×D3111yescharacteristic
141M16—21no—
142M16—21no—
143M16—621no—
144M16—621no—
145C2×C8—21no—
146C2×C8—621no—
147C4⋊C4—311no—
148C4⋊C4—311no—
149C4⋊C4—622no—
150C4⋊C4—622no—
151C4⋊C4—622no—
152C4⋊C4—621no—
153C4⋊C4—621no—
154C4⋊C4D12411yescharacteristic
155C4⋊C4D12411yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—621no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—621no—
162C23D4×D3111yescharacteristic
163Q8—622no—
164Q8—622no—
165Q8—1241no—
166Q8—1241no—
167Q8—2482no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—621no—
174C2×C4—621no—
175C2×C4—622no—
176C2×C4—622no—
177C2×C4—1241no—
178C2×C4—1241no—
179C2×C4—1242no—
180C2×C4C2×D12411yescharacteristic
181C2×C4#9249511yescharacteristic
182C2×C4#9249511yescharacteristic
183C2×C4D4×D3111yescharacteristic
184C2×C4#9249711yescharacteristic
185C2×C4Q8×D3111yescharacteristic
186C8—41no—
187C8—1241no—
188C22—21no—
189C22—21no—
190C22#1175845911yescharacteristic
191C22#1175846211yescharacteristic
192C22#1175847311yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1242no—
197C4—1242no—
198C4—1241no—
199C4—1241no—
200C4#1175845211yescharacteristic
201C4#1175846211yescharacteristic
202C4#1175847311yescharacteristic
203C4#1175847411yescharacteristic
204C2—21no—
205C2—21no—
206C2#1452096211yescharacteristic
207C2#1452122811yescharacteristic
208C2#1452123311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#339D31
hypocenterC31#2028
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
35. C2×Dic62Q8semidirect
129. C31#2028semidirect

Maximal subgroups

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

subgroupindex
#145216772
#145210592
#145210572
#145209552
#145208172
#145208092
C31×#3392
#202831