Finite Group Databasebeta

← #19145497

Subgroups — #19145497

Order 5504.

402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583477C212yesmaximal, complemented
2#14583235C212yesmaximal, complemented
3#14583213C212yesmaximal, complemented
4#14583145C212yesmaximal, complemented
5#14583140C211yesmaximal, characteristic, complemented
6#14583135C211yesmaximal, characteristic, complemented
7#14583063C212yesmaximal, complemented
8#14583046C212yesmaximal, complemented
9C43×#408C211yesmaximal, characteristic, complemented
10C2×#10621898C2212yes—
11C2×Dic172C2211yescharacteristic
12C2×#10621873C2212yes—
13C2×D344C2211yescharacteristic
14#13063304C2212yes—
15#13063304C2212yes—
16#13063301—22no—
17#13063299C2212yes—
18#13063299C2212yes—
19#13063297—22no—
20#13063297—22no—
21#13063296—22no—
22C2×C4⋊Dic43C2212yes—
23#13063259C2211yescharacteristic
24#13063259C2211yescharacteristic
25#13063259C2212yes—
26#13063250C2212yes—
27#13063250C2212yes—
28#13063247C2212yes—
29#13063247C2212yes—
30C2×#41×C43C2211yescharacteristic
31C2×M16×C43C2211yescharacteristic
32C22×C8×C43C2211yescharacteristic
33C22⋊C8×C43C2212yes—
34C22⋊C8×C43C2212yes—
35#41×C43—41no—
36#41×C43—41no—
37C2×Q8×C43D411yescharacteristic
38C2×D4×C43D412yes—
39C2×D4×C43D411yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—22no—
43C2×C22⋊D43—22no—
44C2×C22⋊D43—22no—
45C22×Dic43—22no—
46#10621898—42no—
47#10621898—42no—
48C2×D172C2312yes—
49C2×C4×D43—22no—
50C2×Dic86C2312yes—
51M16×C43—41no—
52C2×C8×C43—41no—
53C2×C8×C43C2311yescharacteristic
54C2×C8×C43C2311yescharacteristic
55C2×C8×C43C2312yes—
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—22no—
61C4⋊Dic43C2312yes—
62C4⋊Dic43C2312yes—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic172—41no—
66D344—41no—
67#10621873—42no—
68C23×C43C2×D411yescharacteristic
69C23×C43C2×D412yes—
70C22×D43—22no—
71Q8×C43—41no—
72D4×C43—42no—
73D4×C43—41no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—44no—
82C22⋊D43—82no—
83C22⋊D43—82no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—82no—
88D172—22no—
89D172—22no—
90C4×D43—44no—
91Dic86—22no—
92Dic86—22no—
93C8×C43—22no—
94C8×C43—21no—
95C8×C43—21no—
96C22×C43—22no—
97C22×C43—21no—
98C22×C43—22no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—22no—
102C22×C43C22×D411yescharacteristic
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C4×C43—22no—
107C4×C43—21no—
108C4×C43H(5,𝔽2)11yescharacteristic
109C4×C43H(5,𝔽2)11yescharacteristic
110Dic43—42no—
111Dic43—42no—
112Dic43—42no—
113#3203—431nomaximal, Sylow
114C2×C43—42no—
115C2×C43—41no—
116C2×C43#53411yescharacteristic
117C2×C43#57611yescharacteristic
118C2×C43#57811yescharacteristic
119D43—82no—
120#537—432no—
121#484—432no—
122#480—432no—
123#468—432no—
124#467—431no—
125#466—431no—
126#452—432no—
127#449—432no—
128#408D4311yescharacteristic, complemented
129C43#320311yescharacteristic, complemented, Sylow
130C2×#41—432no—
131C2×#41C2×D4311yescharacteristic
132C2×Q16—431no—
133C2×SD16—432no—
134C2×D8—431no—
135C2×M16C2×D4311yescharacteristic
136C22×C8C2×D4311yescharacteristic
137C22⋊Q8—432no—
138C22⋊Q8—432no—
139C22⋊Q8—862no—
140#121—432no—
141#121—432no—
142#121—862no—
143#121—862no—
144#121—862no—
145C2×C4⋊C4—432no—
146#107—431no—
147#107—431no—
148#107—432no—
149#103—432no—
150#103—432no—
151#102—432no—
152#102—432no—
153C22⋊C8C2×D4312yes—
154C22⋊C8C2×D4312yes—
155#41—41no—
156#41—41no—
157#41—1722no—
158#41—1722no—
159C2×Q8—432no—
160C2×Q8D17211yescharacteristic
161C2×D4—432no—
162C2×D4—862no—
163C2×D4—862no—
164C2×D4—862no—
165C2×D4D17211yescharacteristic
166C2×D4D17212yes—
167C22×C4—862no—
168C22×C4—862no—
169C22×C4C22×D4312yes—
170C22×C4C22×D4311yescharacteristic
171Q16—1721no—
172SD16—1722no—
173D8—1721no—
174M16—41no—
175C2×C8—41no—
176C2×C8C22×D4311yescharacteristic
177C2×C8C22×D4312yes—
178C2×C8C22×D4311yescharacteristic
179C4⋊C4—432no—
180C4⋊C4—432no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—862no—
188C23—862no—
189C23C2×D17211yescharacteristic
190C23C2×D17212yes—
191Q8—41no—
192Q8—862no—
193Q8—862no—
194D4—42no—
195D4—41no—
196D4—862no—
197D4—862no—
198D4—3442no—
199D4—3442no—
200D4—1724no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—3442no—
209C2×C4—1724no—
210C2×C4C2×D17211yescharacteristic
211C2×C4C2×D17212yes—
212C2×C4C23×D4311yescharacteristic
213C8—21no—
214C8—21no—
215C8—22no—
216C22—22no—
217C22—21no—
218C22—21no—
219C22—22no—
220C22—22no—
221C22—21no—
222C22—1722no—
223C22—1722no—
224C22—1722no—
225C22C22×D17211yescharacteristic
226C4—22no—
227C4—21no—
228C4—1722no—
229C4—1722no—
230C4—1722no—
231C4#1306337011yescharacteristic
232C4#1306337011yescharacteristic
233C2—42no—
234C2—41no—
235C2—3442no—
236C2#1458346111yescharacteristic
237C2#1458370411yescharacteristic
238C2#1458371611yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#408C2
socleC22×C43C22×D4
hypercenter#408D43
hypocenterC43#3203
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14583477C2semidirect
2. #14583235C2semidirect
3. #14583213C2semidirect
4. #14583145C2semidirect
5. #14583140C2semidirect
6. #14583135C2semidirect
7. #14583063C2semidirect
8. #14583046C2semidirect
9. C43×#408C2semidirect
128. #408D43semidirect
129. C43#3203semidirect