Finite Group Databasebeta

← #19140075

Subgroups — #19140075

Order 5504.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13063299C211yesmaximal, characteristic
2#14582838C212yesmaximal, complemented
3#14582816C212yesmaximal, complemented
4#14582789C214yesmaximal, complemented
5#14582778C212yesmaximal, complemented
6#14582778C212yesmaximal, complemented
7C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
9C22×D172C2211yescharacteristic
10C22×C22⋊D43C2212yes—
11#13063299—24no—
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C22⋊Dic43C2212yes—
14C2×(C2×D43)⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2214yes—
16C2×(C2×D43)⋊C4C2214yes—
17C2×C4×Dic43C2212yes—
18C43⋊#95C2214yes—
19C43⋊#95C2214yes—
20C43⋊#95C2212yes—
21C23×C4×C43C2211yescharacteristic
22C23×C4×C43C2211yescharacteristic
23C23×C4×C43C2211yescharacteristic
24C2×C4⋊C4×C43—24no—
25C2×C4⋊C4×C43C2212yes—
26C2×C4⋊C4×C43C2212yes—
27C24×C43C2311yescharacteristic
28C23×D43C2312yes—
29C22×C4×C43—24no—
30C22×C4×C43—22no—
31C22×C4×C43—22no—
32C22×C4×C43—42no—
33C22×C4×C43—42no—
34C22×C4×C43D414yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C2×C22⋊D43—24no—
40C2×C22⋊D43—28no—
41C22×Dic43C2312yes—
42C22×Dic43C2314yes—
43C2×D172—22no—
44C2×D172—42no—
45C4⋊C4×C43—24no—
46C4⋊C4×C43—24no—
47C22⋊Dic43—24no—
48(C2×D43)⋊C4—24no—
49(C2×D43)⋊C4—28no—
50(C2×D43)⋊C4—44no—
51C4⋊Dic43—22no—
52C4×Dic43—42no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43C2×D412yes—
56C23×C43#4114yes—
57C23×C43C2411yescharacteristic
58C22×D43—22no—
59C22×D43—24no—
60C22×D43—24no—
61C22×D43—24no—
62C2×C4×C43—28no—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—24no—
69C2×C4×C43—44no—
70C2×C4×C43—44no—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2×D412yes—
73C2×C4×C43#4114yes—
74C22⋊D43—48no—
75C2×Dic43—22no—
76C2×Dic43—24no—
77C2×Dic43—24no—
78C2×Dic43—24no—
79C2×Dic43—24no—
80D172—44no—
81C22×C43—22no—
82C22×C43—22no—
83C22×C43—28no—
84C22×C43#12414yes—
85C22×C43C22×D411yescharacteristic
86C22×C43C2×#4112yes—
87C22×C43C2×#4112yes—
88C22×C43H(5,𝔽2)12yes—
89C2×D43—42no—
90C2×D43—42no—
91C2×D43—42no—
92C2×D43—48no—
93C4×C43—24no—
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—42no—
97Dic43—42no—
98Dic43—44no—
99#2591—431nomaximal, Sylow
100C2×C43—24no—
101C2×C43#52511yescharacteristic
102C2×C43C2×#12411yescharacteristic
103C2×C43#53411yescharacteristic
104C2×C43#55314yes—
105D43—82no—
106C2×#121—431no—
107C22×C4⋊C4D4311yescharacteristic, complemented
108#400—432no—
109#394—432no—
110#388—434no—
111#386—432no—
112#386—432no—
113C4×C22⋊C4—431no—
114C43#259111yescharacteristic, complemented, Sylow
115C22×D4—432no—
116C22×D4—431no—
117C23×C4C2×D4311yescharacteristic
118C23×C4C2×D4311yescharacteristic
119C23×C4C2×D4311yescharacteristic
120#121—864no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—431no—
123C2×C4⋊C4C2×D4312yes—
124C2×C4⋊C4C2×D4312yes—
125C2×C22⋊C4—432no—
126C2×C22⋊C4—432no—
127C2×C22⋊C4—434no—
128C2×C22⋊C4—434no—
129C2×C42—432no—
130#95—432no—
131#95—434no—
132#95—434no—
133C24—432no—
134C24C22×D4311yescharacteristic
135C2×D4—868no—
136C2×D4—864no—
137C2×D4—862no—
138C2×D4—1722no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—432no—
145C22×C4—434no—
146C22×C4C22⋊D4314yes—
147C22×C4C22×D4312yes—
148C22×C4C22×D4312yes—
149C22×C4C22×D4311yescharacteristic
150C22×C4C22×D4311yescharacteristic
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—862no—
154C22⋊C4—864no—
155C22⋊C4—868no—
156C22⋊C4—864no—
157C22⋊C4—1724no—
158C42—1722no—
159C23—22no—
160C23—22no—
161C23—862no—
162C23—864no—
163C23—864no—
164C23—864no—
165C23#1062190214yes—
166C23C2×C22⋊D4312yes—
167C23C23×D4311yescharacteristic
168D4—1724no—
169D4—1728no—
170C2×C4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—862no—
180C2×C4—864no—
181C2×C4—864no—
182C2×C4—864no—
183C2×C4—864no—
184C2×C4#1062189814yes—
185C2×C4C2×C22⋊D4312yes—
186C2×C4C2×C22⋊D4312yes—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—1728no—
191C22—1722no—
192C22—1722no—
193C22—1722no—
194C22#1306331414yes—
195C22C22×C22⋊D4311yescharacteristic
196C22C2×#1062189812yes—
197C22C2×#1062190212yes—
198C22#1306337012yes—
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—1724no—
204C4—1722no—
205C2—24no—
206C2—3442no—
207C2#1458341011yescharacteristic
208C2C2×#1306331411yescharacteristic
209C2#1458345811yescharacteristic
210C2#1458359714yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC22×C4⋊C4×C43C2
hypercenterC22×C4⋊C4D43
hypocenterC43#2591
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14582838C2semidirect
3. #14582816C2semidirect
4. #14582789C2semidirect
5. #14582778C2semidirect
6. #14582778C2semidirect
7. C4×C22⋊Dic43C2semidirect
8. C22×C4⋊C4×C43C2semidirect
107. C22×C4⋊C4D43semidirect
114. C43#2591semidirect