Finite Group Databasebeta

← #19137191

Subgroups — #19137191

Order 5504.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×C22⋊Dic43C211yesmaximal, characteristic
2#14582793C214yesmaximal, complemented
3#14582787C214yesmaximal, complemented
4#14582757C212yesmaximal, complemented
5#14582755C211yesmaximal, characteristic
6C22⋊C4×Dic43C212yesmaximal, complemented
7C43×#379C211yesmaximal, characteristic
8C23×Dic43C2211yescharacteristic
9C23×Dic43C2211yescharacteristic
10C2×Dic43⋊C4C2214yescomplemented
11C2×C22⋊Dic43C418yescomplemented
12C2×C22⋊Dic43C2212yes—
13C2×C22⋊Dic43C2212yes—
14C2×C22⋊Dic43C2212yes—
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2212yes—
17C2×C4×Dic43C2214yescomplemented
18C43⋊#95C2214yescomplemented
19C43⋊#95C2214yescomplemented
20C25×C43C2211yescharacteristic
21C2×C22⋊C4×C43C2212yes—
22C2×C22⋊C4×C43C2212yes—
23C2×C22⋊C4×C43C2212yes—
24C24×C43—24no—
25C24×C43—42no—
26C24×C43—42no—
27C24×C43C2×C414yes—
28C24×C43C2311yescharacteristic
29C24×C43C2311yescharacteristic
30C24×C43C2311yescharacteristic
31C22×C4×C43C2314yes—
32C22×Dic43—42no—
33C22×Dic43—42no—
34C22×Dic43C2×C414yes—
35C22×Dic43C2×C414yes—
36C22×Dic43C2314yes—
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22⋊C4×C43—24no—
40C22⋊C4×C43—42no—
41C22⋊C4×C43—42no—
42C22⋊Dic43—24no—
43C22⋊Dic43—42no—
44C22⋊Dic43—42no—
45C22⋊Dic43C2×C418yes—
46C22⋊Dic43C2×C418yes—
47Dic43⋊C4—44no—
48C4×Dic43—44no—
49C23×C43—22no—
50C23×C43—22no—
51C23×C43—28no—
52C23×C43—22no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43—22no—
56C23×C43—22no—
57C23×C43—22no—
58C23×C43—44no—
59C23×C43—44no—
60C23×C43—416no—
61C23×C43C22×C412yes—
62C23×C43C22×C412yes—
63C23×C43C22×C412yes—
64C23×C43#4114yes—
65C23×C43C2411yescharacteristic
66C2×C4×C43—24no—
67C2×C4×C43—24no—
68C2×C4×C43—24no—
69C2×Dic43—24no—
70C2×Dic43—24no—
71C2×Dic43—24no—
72C2×Dic43—24no—
73C2×Dic43—24no—
74C2×Dic43—44no—
75C2×Dic43—44no—
76C2×Dic43C22×C414yes—
77C2×Dic43C22×C414yes—
78C22×C43—22no—
79C22×C43—22no—
80C22×C43—28no—
81C22×C43—22no—
82C22×C43—22no—
83C22×C43—22no—
84C22×C43—22no—
85C22×C43—22no—
86C22×C43—22no—
87C22×C43—416no—
88C22×C43—44no—
89C22×C43—44no—
90C22×C43#11714yes—
91C22×C43C23×C411yescharacteristic
92C22×C43C2×#4112yes—
93C22×C43H(5,𝔽2)12yes—
94C22×C43H(5,𝔽2)12yes—
95C4×C43—44no—
96Dic43—24no—
97Dic43—24no—
98Dic43—44no—
99#2312—431nomaximal, Sylow
100C2×C43—24no—
101C2×C43—42no—
102C2×C43—42no—
103C2×C43C2×#11711yescharacteristic
104C2×C43#51811yescharacteristic
105C2×C43#51811yescharacteristic
106C2×C43#53814yes—
107C22×C22⋊C4—431no—
108#388—434no—
109#388—434no—
110#380—432no—
111#379—431no—
112#379D4311yescharacteristic
113C4×C22⋊C4—432no—
114C43#231211yescharacteristic, complemented, Sylow
115C25C2×D4311yescharacteristic
116C23×C4—431no—
117C23×C4—431no—
118C2×C4⋊C4—434no—
119C2×C22⋊C4—432no—
120C2×C22⋊C4—432no—
121C2×C22⋊C4—438no—
122C2×C22⋊C4—432no—
123C2×C22⋊C4—432no—
124C2×C22⋊C4—432no—
125C2×C22⋊C4C2×D4312yes—
126C2×C22⋊C4C2×D4312yes—
127C2×C22⋊C4C2×D4312yes—
128C2×C42—434no—
129#95—434no—
130#95—434no—
131C24—24no—
132C24—42no—
133C24—42no—
134C24C4×D4314yes—
135C24C22×D4311yescharacteristic
136C24C22×D4311yescharacteristic
137C24C22×D4311yescharacteristic
138C22×C4—432no—
139C22×C4—432no—
140C22×C4—434no—
141C22×C4—434no—
142C22×C4—434no—
143C22×C4—1722no—
144C22×C4—1722no—
145C22×C4C22×D4314yes—
146C4⋊C4—1724no—
147C22⋊C4—24no—
148C22⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4—438no—
151C22⋊C4—438no—
152C22⋊C4—864no—
153C22⋊C4—1722no—
154C22⋊C4—1722no—
155C42—1724no—
156C23—22no—
157C23—22no—
158C23—28no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—416no—
168C23C2×C4×D4312yes—
169C23C2×C4×D4312yes—
170C23C2×C4×D4312yes—
171C23#1062190014yes—
172C23C23×D4311yescharacteristic
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—434no—
177C2×C4—434no—
178C2×C4—864no—
179C2×C4—864no—
180C2×C4—864no—
181C2×C4—864no—
182C2×C4—864no—
183C2×C4—1724no—
184C2×C4—1724no—
185C22—22no—
186C22—22no—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—416no—
195C22—44no—
196C22—44no—
197C22#1306328114yes—
198C22C22×C4×D4311yescharacteristic
199C22C2×#1062190012yes—
200C22#1306337012yes—
201C22#1306337012yes—
202C4—44no—
203C4—864no—
204C4—864no—
205C4—1724no—
206C2—24no—
207C2—42no—
208C2—42no—
209C2C2×#1306328111yescharacteristic
210C2#1458337211yescharacteristic
211C2#1458337211yescharacteristic
212C2#1458348414yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#379C2
socleC23×C43C24
hypercenter#379D43
hypocenterC43#2312
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #14582793C2semidirect
3. #14582787C2semidirect
4. #14582757C2semidirect
6. C22⋊C4×Dic43C2semidirect
10. C2×Dic43⋊C4C22semidirect
11. C2×C22⋊Dic43C4semidirect
17. C2×C4×Dic43C22semidirect
18. C43⋊#95C22semidirect
19. C43⋊#95C22semidirect
114. C43#2312semidirect