Finite Group Databasebeta

← #16846870

Subgroups — #16846870

Order 3968.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521058C211yesmaximal, characteristic
3#14520956C211yesmaximal, characteristic
4#14520817C211yesmaximal, characteristic
5#14520810C211yesmaximal, characteristic
6#14520808C211yesmaximal, characteristic
7C31×#419C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C31×#117C2211yescharacteristic
11#11758503C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4×Dic31C2211yescharacteristic
14C2×#92474C2211yescharacteristic
15#11758467—21no—
16#11758465—21no—
17#11758455—22no—
18#11758447—21no—
19#11758446—21no—
20C31×#103—21no—
21C31×#103—21no—
22#11758423—21no—
23#11758423—21no—
24C31⋊#95—22no—
25C2×Q8×C31—21no—
26C2×Q8×C31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31Q812yescomplemented
31C22×C4×C31—21no—
32C22×C4×C31C2311yescharacteristic
33C22×Dic31—21no—
34C22×Dic31D412yes—
35C2×Dic62—22no—
36M16×C31—21no—
37M16×C31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31D411yescharacteristic
40C4⋊C4×C31D411yescharacteristic
41C22⋊C4×C31—21no—
42C42×C31—21no—
43C22⋊Dic31—21no—
44C4⋊Dic31—22no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31D411yescharacteristic
48C4⋊Dic31D411yescharacteristic
49Dic31⋊C4—22no—
50Dic31⋊C4—22no—
51C4×Dic31—21no—
52C4×Dic31—21no—
53C4×Dic31—21no—
54#92474—21no—
55#92474—21no—
56C2×C31⋊C8—21no—
57C23×C31C2×D411yescharacteristic
58Q8×C31—22no—
59Q8×C31—22no—
60Q8×C31—41no—
61Q8×C31—41no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—22no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×Q811yescharacteristic
70C2×C4×C31#4111yescharacteristic
71C2×C4×C31#4111yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×Dic31—22no—
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—22no—
77C2×Dic31—41no—
78C2×Dic31—41no—
79C2×Dic31—42no—
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#419D3111yescharacteristic
103#391—311no—
104#343—311no—
105#339—311no—
106#339—311no—
107C2×C31—21no—
108C2×C31—21no—
109C2×C31#39311yescharacteristic
110C2×C31#45511yescharacteristic
111C2×C31#45611yescharacteristic
112C22×Q8C2×D3111yescharacteristic
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×C42—311no—
124#103—21no—
125#103—21no—
126#103—621no—
127#103—621no—
128#95—622no—
129C31#202811yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—622no—
136C2×Q8Dic6212yescomplemented
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⋊C4C22⋊D3111yescharacteristic
155C4⋊C4C22⋊D3111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—621no—
158C42—21no—
159C42—621no—
160C42—621no—
161C42—621no—
162C23D4×D3111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—2482no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—622no—
174C2×C4—621no—
175C2×C4—621no—
176C2×C4—622no—
177C2×C4—1241no—
178C2×C4—1241no—
179C2×C4—1242no—
180C2×C4C2×Dic6211yescharacteristic
181C2×C4#9249511yescharacteristic
182C2×C4D4×D3111yescharacteristic
183C2×C4#9249711yescharacteristic
184C2×C4#9249711yescharacteristic
185C2×C4C2×C22⋊D3111yescharacteristic
186C8—41no—
187C8—1241no—
188C22—21no—
189C22—21no—
190C22#1175845511yescharacteristic
191C22#1175846211yescharacteristic
192C22#1175851411yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1242no—
197C4—1242no—
198C4—1241no—
199C4—1241no—
200C4#1175845511yescharacteristic
201C4#1175846211yescharacteristic
202C4#1175850111yescharacteristic
203C4#1175851311yescharacteristic
204C2—21no—
205C2—21no—
206C2#1452096111yescharacteristic
207C2#1452122511yescharacteristic
208C2#1452123011yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#419C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#419D31
hypocenterC31#2028
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C31Q8semidirect
129. C31#2028semidirect
136. C2×Q8Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216772
#145210582
#145209562
#145208172
#145208102
#145208082
C31×#4192
#202831