Finite Group Databasebeta

← #19146877

Subgroups — #19146877

Order 5504.

374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583623C211yesmaximal, characteristic
2#14583564C211yesmaximal, characteristic
3#14583239C212yesmaximal, complemented
4#14583181C211yesmaximal, characteristic, complemented
5#14583156C212yesmaximal, complemented
6#14583106C211yesmaximal, characteristic, complemented
7#14583056C212yesmaximal, complemented
8C4×Dic172C211yesmaximal, characteristic, complemented
9#14582978C211yesmaximal, characteristic
10#14582906C212yesmaximal, complemented
11C43×#487C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2212yes—
13C2×Dic172C2211yescharacteristic
14C2×#10621885C2212yes—
15C2×#10621872C2212yes—
16#13063324—21no—
17#13063320—22no—
18#13063314—21no—
19#13063305C2212yes—
20#13063303—22no—
21#13063301C2212yes—
22Q8×Dic43—21no—
23C4×Dic86C2211yescharacteristic
24C4×Dic86C2211yescharacteristic
25C4×D172C2211yescharacteristic
26#13063287—21no—
27#13063283C2212yes—
28#13063259C2211yescharacteristic
29#13063256C2212yes—
30C4⋊(C43⋊C8)C2211yescharacteristic
31#13063250C2211yescharacteristic
32#13063250C2211yescharacteristic
33#13063249C2212yes—
34#13063248C2212yes—
35(C2×D43)⋊C8C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#103×C43C2212yes—
39#103×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43C2312yes—
43Q8×D43—24no—
44Q8×D43—42no—
45C2×D172D411yescharacteristic
46C2×C4×D43—22no—
47C2×C4×D43C2312yes—
48C2×Dic86—22no—
49C2×Dic86C2311yescharacteristic
50C2×Dic86C2311yescharacteristic
51C2×C8×C43C2311yescharacteristic
52C2×C8×C43C2311yescharacteristic
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43C2312yes—
57C42×C43C2311yescharacteristic
58#10621885—42no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4D412yes—
63C4⋊Dic43—22no—
64C4⋊Dic43D411yescharacteristic
65C4⋊Dic43C2311yescharacteristic
66C4⋊Dic43C2311yescharacteristic
67Dic43⋊C4—21no—
68Dic43⋊C4—21no—
69Dic43⋊C4—22no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72C4×Dic43—22no—
73C2×C43⋊C8C2312yes—
74Dic172—22no—
75#10621872—42no—
76C22×D43C2×D412yes—
77Q8×C43—22no—
78Q8×C43—22no—
79Q8×C43—42no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2411yescharacteristic
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43C2×D412yes—
90D172—22no—
91C4×D43—22no—
92C4×D43—22no—
93C4×D43—44no—
94Dic86—21no—
95Dic86—21no—
96Dic86—21no—
97Dic86—44no—
98Dic86#4112yes—
99C8×C43—21no—
100C8×C43—21no—
101C43⋊C8—22no—
102C22×C43C22×D411yescharacteristic
103C2×D43—22no—
104C2×D43—22no—
105C2×D43—22no—
106C4×C43—21no—
107C4×C43—42no—
108C4×C43—42no—
109C4×C43#13712yes—
110C4×C43C2×#4111yescharacteristic
111C4×C43H(5,𝔽2)11yescharacteristic
112Dic43—22no—
113Dic43—22no—
114Dic43—41no—
115Dic43—41no—
116Dic43—41no—
117#3328—431nomaximal, Sylow
118C2×C43#54611yescharacteristic
119C2×C43C2×#13711yescharacteristic
120C2×C43#57811yescharacteristic
121D43—42no—
122#556—431no—
123D4×Q8—431no—
124#487D4311yescharacteristic, complemented
125#485—432no—
126#475—431no—
127#470—432no—
128#462—431no—
129#451—432no—
130C4×Q16—431no—
131#436—431no—
132#419—432no—
133C43#332811yescharacteristic, complemented, Sylow
134C22×Q8—432no—
135C2×Q16—432no—
136C2×Q16—431no—
137C2×M16—432no—
138C4⋊Q8—861no—
139C4⋊Q8C2×D4311yescharacteristic
140C4⋊Q8C2×D4311yescharacteristic
141#126—862no—
142#124—861no—
143C22⋊Q8—432no—
144C22⋊Q8—432no—
145C22⋊Q8—862no—
146C4×Q8—431no—
147C4×Q8—431no—
148C4×Q8—861no—
149C4×D4—431no—
150C4×D4—861no—
151#117—432no—
152#107—431no—
153#106—432no—
154C4⋊C8—431no—
155#103—432no—
156#103—431no—
157#103—431no—
158#103—432no—
159#103C2×D4312yes—
160#103C2×D4312yes—
161C22⋊C8—432no—
162C4×C8C2×D4311yescharacteristic
163C2×Q8—21no—
164C2×Q8—431no—
165C2×Q8—431no—
166C2×Q8—862no—
167C2×Q8—864no—
168C2×Q8—1722no—
169C2×Q8C22×D4312yes—
170C2×D4—431no—
171C22×C4—432no—
172C22×C4—862no—
173Q16—862no—
174Q16—1722no—
175M16—1722no—
176C2×C8—432no—
177C2×C8C22×D4311yescharacteristic
178C2×C8C22×D4311yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—431no—
183C4⋊C4—431no—
184C4⋊C4—431no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4—861no—
188C4⋊C4—861no—
189C4⋊C4C22×D4312yes—
190C22⋊C4—432no—
191C22⋊C4—862no—
192C22⋊C4—862no—
193C22⋊C4—862no—
194C42—862no—
195C42—861no—
196C42—861no—
197C42C22×D4311yescharacteristic
198C23—432no—
199Q8—22no—
200Q8—22no—
201Q8—42no—
202Q8—432no—
203Q8—861no—
204Q8—861no—
205Q8—861no—
206Q8—1724no—
207D4—862no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—432no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—861no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—1724no—
218C2×C4D4×D4311yescharacteristic
219C2×C4D4×D4311yescharacteristic
220C2×C4C23×D4311yescharacteristic
221C8—21no—
222C8—21no—
223C8—862no—
224C22—862no—
225C22—862no—
226C22—862no—
227C22C2×D4×D4311yescharacteristic
228C4—21no—
229C4—42no—
230C4—42no—
231C4—862no—
232C4—862no—
233C4—1721no—
234C4—1721no—
235C4—1721no—
236C4#1306335412yes—
237C4#41×D4311yescharacteristic
238C4#1306337111yescharacteristic
239C2—1722no—
240C2#1458354211yescharacteristic
241C2C2×#1306335411yescharacteristic
242C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3328
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14583239C2semidirect
4. #14583181C2semidirect
5. #14583156C2semidirect
6. #14583106C2semidirect
7. #14583056C2semidirect
8. C4×Dic172C2semidirect
10. #14582906C2semidirect
11. C43×#487C2semidirect
124. #487D43semidirect
133. C43#3328semidirect