Finite Group Databasebeta

← #19140272

Subgroups — #19140272

Order 5504.

540 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063282C212yesmaximal, complemented
2#14582829C211yesmaximal, characteristic, complemented
3#14582821C212yesmaximal, complemented
4#14582816C211yesmaximal, characteristic
5#14582791C212yesmaximal, complemented
6#14582784C212yesmaximal, complemented
7#14582777C212yesmaximal
8#14582773C212yesmaximal, complemented
9C43×#382C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C22×C4×D43C2212yes—
12#13063282—28no—
13C2×C4⋊Dic43C2212yes—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×C4×Dic43C2212yes—
23C43⋊#95C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C42×C43C2211yescharacteristic
30#95×C43C2212yes—
31#95×C43C2212yes—
32C23×D43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C2×D172—24no—
42C2×D172—41no—
43C2×C4×D43—24no—
44C2×C4×D43—24no—
45C2×C4×D43—24no—
46C4⋊C4×C43—41no—
47C4⋊C4×C43—41no—
48C42×C43D414yescomplemented
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—24no—
51(C2×D43)⋊C4—24no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—42no—
54C4⋊Dic43—24no—
55C4⋊Dic43—41no—
56Dic43⋊C4—24no—
57Dic43⋊C4—24no—
58C4×Dic43—24no—
59C23×C43C2411yescharacteristic
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—22no—
66C22×D43#4114yes—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43C2×D414yes—
79C2×C4×C43C2×D412yes—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43#4114yes—
89D172—44no—
90C4×D43—216no—
91C22×C43C22×D411yescharacteristic
92C22×C43C2×#4112yes—
93C22×C43C2×#4112yes—
94C22×C43H(5,𝔽2)11yescharacteristic
95C22×C432−1+411yescharacteristic
96C2×D43—24no—
97C2×D43—24no—
98C2×D43—24no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C4×C43—24no—
104C4×C43—22no—
105C4×C43—41no—
106C4×C43—41no—
107C4×C43—42no—
108Dic43—24no—
109Dic43—42no—
110Dic43—42no—
111#2609—431nomaximal, Sylow
112C2×C43#52512yes—
113C2×C43#53711yescharacteristic
114C2×C43#55111yescharacteristic
115C2×C43#55212yes—
116C2×C43#55511yescharacteristic
117D43—44no—
118C2×#117—432no—
119#398—431no—
120#396—432no—
121#394—431no—
122#388—432no—
123#387—432no—
124#386—432no—
125#385—432no—
126#382D4311yescharacteristic, complemented
127C43#260911yescharacteristic, complemented, Sylow
128C22×D4—431no—
129C23×C4—432no—
130#117—868no—
131C2×C4⋊C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—431no—
135C2×C4⋊C4C2×D4311yescharacteristic
136C2×C4⋊C4C2×D4311yescharacteristic
137C2×C22⋊C4—432no—
138C2×C22⋊C4—432no—
139C2×C22⋊C4—432no—
140C2×C22⋊C4—432no—
141C2×C22⋊C4—432no—
142C2×C42—432no—
143C2×C42C2×D4311yescharacteristic
144#95—431no—
145#95—432no—
146#95—431no—
147#95—432no—
148#95C2×D4312yes—
149#95C2×D4312yes—
150C24—432no—
151C2×D4—864no—
152C2×D4—1721no—
153C22×C4—432no—
154C22×C4—432no—
155C22×C4—432no—
156C22×C4—864no—
157C22×C4—864no—
158C22×C4—864no—
159C22×C4C22×D4311yescharacteristic
160C22×C4C22×D4311yescharacteristic
161C22×C4C22×D4312yes—
162C22×C4C22×D4312yes—
163C22×C4C22×D4311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—864no—
167C4⋊C4—864no—
168C4⋊C4—864no—
169C4⋊C4—1721no—
170C22⋊C4—864no—
171C22⋊C4—864no—
172C22⋊C4—864no—
173C22⋊C4—864no—
174C22⋊C4—1722no—
175C42—864no—
176C42D17214yescomplemented
177C23—434no—
178C23—862no—
179C23—862no—
180C23—862no—
181C23—862no—
182C23—862no—
183C23—862no—
184C23C23×D4311yescharacteristic
185D4—1724no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—434no—
198C2×C4—8616no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4C2×D17214yes—
208C2×C4C2×D17212yes—
209C22—864no—
210C22—864no—
211C22—864no—
212C22—1722no—
213C22—1722no—
214C22—1722no—
215C22—1722no—
216C22C22×D17211yescharacteristic
217C22#41×D4312yes—
218C22#41×D4312yes—
219C22#1306337011yescharacteristic
220C22#1306337311yescharacteristic
221C4—24no—
222C4—22no—
223C4—41no—
224C4—41no—
225C4—42no—
226C4—864no—
227C4—1722no—
228C4—1722no—
229C2—1724no—
230C2#1458341112yes—
231C2#1458348011yescharacteristic
232C2#1458357911yescharacteristic
233C2#1458358112yes—
234C2#1458361111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#382C2
hypercenter#382D43
hypocenterC43#2609
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#13063282C2semidirect
2. #14582829C2semidirect
3. #14582821C2semidirect
5. #14582791C2semidirect
6. #14582784C2semidirect
8. #14582773C2semidirect
9. C43×#382C2semidirect
48. C42×C43D4semidirect
126. #382D43semidirect
127. C43#2609semidirect
176. C42D172semidirect