Finite Group Databasebeta

← #19142298

Subgroups — #19142298

Order 5504.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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#14582838C211yesmaximal, characteristic, complemented
2#14582821C212yesmaximal, complemented
3#14582810C212yesmaximal, complemented
4#14582800C211yesmaximal, characteristic
5#14582786C212yesmaximal, complemented
6#14582777C212yesmaximal
7#14582773C212yesmaximal, complemented
8#14582756C212yesmaximal, complemented
9C43×#395C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C22×C4×D43C2212yes—
12C2×C4⋊Dic43C2212yes—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×C4×Dic43C2211yescharacteristic
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
26C22×Q8×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2212yes—
29#95×C43C2212yes—
30#95×C43C2211yescharacteristic
31C23×D43C2312yes—
32C2×Q8×C43—42no—
33C2×Q8×C43—41no—
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C2×D172—41no—
43C2×D172—41no—
44C2×D172Q814yescomplemented
45C2×C4×D43—24no—
46C2×C4×D43—42no—
47C2×C4×D43—42no—
48C4⋊C4×C43—42no—
49C4⋊C4×C43—41no—
50(C2×D43)⋊C4—24no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4—42no—
53(C2×D43)⋊C4—42no—
54(C2×D43)⋊C4—42no—
55C4⋊Dic43—42no—
56C4⋊Dic43—41no—
57Dic43⋊C4—24no—
58C4×Dic43—41no—
59C23×C43C2411yescharacteristic
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—22no—
66C22×D43C2×Q814yes—
67Q8×C43—44no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43C2×Q812yes—
80C2×C4×C43#4114yes—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90D172—44no—
91C4×D43—48no—
92C22×C43C22×Q811yescharacteristic
93C22×C43C2×#4112yes—
94C22×C43H(5,𝔽2)12yes—
95C22×C43H(5,𝔽2)11yescharacteristic
96C22×C43H(5,𝔽2)11yescharacteristic
97C2×D43—24no—
98C2×D43—24no—
99C2×D43—24no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C2×D43—42no—
104C4×C43—24no—
105C4×C43—22no—
106C4×C43—41no—
107C4×C43—41no—
108C4×C43—42no—
109Dic43—42no—
110Dic43—42no—
111Dic43—42no—
112#2784—431nomaximal, Sylow
113C2×C43#53812yes—
114C2×C43#54311yescharacteristic
115C2×C43#55412yes—
116C2×C43#55511yescharacteristic
117C2×C43#56011yescharacteristic
118D43—44no—
119#400—431no—
120#396—432no—
121#395D4311yescharacteristic, complemented
122#393—432no—
123#390—431no—
124#387—432no—
125#386—432no—
126#385—432no—
127#380—432no—
128C43#278411yescharacteristic, complemented, Sylow
129C22×Q8C2×D4311yescharacteristic
130C22×D4—431no—
131C23×C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—431no—
135C2×C4⋊C4C2×D4312yes—
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—431no—
143#95—431no—
144#95—432no—
145#95—432no—
146#95—432no—
147#95—432no—
148#95C2×D4311yescharacteristic
149#95C2×D4312yes—
150C24—432no—
151C2×Q8—42no—
152C2×Q8—41no—
153C2×D4—434no—
154C2×D4—1721no—
155C2×D4—1721no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4—864no—
160C22×C4—1722no—
161C22×C4—1722no—
162C22×C4C22×D4312yes—
163C22×C4C22×D4311yescharacteristic
164C22×C4C22×D4311yescharacteristic
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4312yes—
167C4⋊C4—42no—
168C4⋊C4—41no—
169C4⋊C4—864no—
170C4⋊C4—1722no—
171C4⋊C4—1721no—
172C22⋊C4—864no—
173C22⋊C4—1722no—
174C22⋊C4—1722no—
175C22⋊C4—1722no—
176C22⋊C4—1722no—
177C42—1721no—
178C23—434no—
179C23—862no—
180C23—862no—
181C23—862no—
182C23—862no—
183C23—862no—
184C23—862no—
185C23C23×D4311yescharacteristic
186Q8—44no—
187D4—1724no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—21no—
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×C4—862no—
208C2×C4—1728no—
209C2×C4Q8×D4312yes—
210C2×C4#1062190214yes—
211C22—864no—
212C22—864no—
213C22—864no—
214C22—1722no—
215C22—1722no—
216C22—1722no—
217C22—1722no—
218C22C2×Q8×D4311yescharacteristic
219C22C2×#1062190212yes—
220C22#1306337012yes—
221C22#1306337011yescharacteristic
222C22#1306337111yescharacteristic
223C4—24no—
224C4—22no—
225C4—41no—
226C4—42no—
227C4—41no—
228C4—1722no—
229C4—1722no—
230C4—1722no—
231C2—1724no—
232C2#1458348912yes—
233C2#1458352411yescharacteristic
234C2#1458361012yes—
235C2#1458361511yescharacteristic
236C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2784
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #14582838C2semidirect
2. #14582821C2semidirect
3. #14582810C2semidirect
5. #14582786C2semidirect
7. #14582773C2semidirect
8. #14582756C2semidirect
9. C43×#395C2semidirect
44. C2×D172Q8semidirect
121. #395D43semidirect
128. C43#2784semidirect