Finite Group Databasebeta

← #19147452

Subgroups — #19147452

Order 5504.

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

normal subgroups only

This group has 370 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#14583629C211yesmaximal, characteristic, complemented
2#14583564C211yesmaximal, characteristic
3#14583296C212yesmaximal, complemented
4#14583188C212yesmaximal
5#14583186C211yesmaximal, characteristic
6#14583183C212yesmaximal, complemented
7#14583181C211yesmaximal, characteristic, complemented
8C8×Dic86C211yesmaximal, characteristic, complemented
9C4×#10621873C211yesmaximal, characteristic
10#14582986C212yesmaximal
11C43×#498C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13C2×#10621873C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063324C2212yes—
17#13063323—22no—
18#13063303—22no—
19#13063301—21no—
20C4×Dic86C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22#13063290—21no—
23#13063290C2212yes—
24C4×D172C2211yescharacteristic
25#13063287C2212yes—
26#13063257C2211yescharacteristic
27#13063256C2212yes—
28#13063256C2212yes—
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063248C2212yes—
33#13063247C2211yescharacteristic
34#13063245C2212yes—
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#106×C43C2212yes—
39#106×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43—21no—
43Q8×D43—44no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×C4×D43—22no—
47C2×Dic86—22no—
48C2×Dic86—22no—
49C2×Dic86D411yescharacteristic
50C2×Dic86C2311yescharacteristic
51C2×C8×C43C2311yescharacteristic
52C2×C8×C43C2311yescharacteristic
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C4⋊C4×C43C2312yes—
56C4⋊C4×C43C2312yes—
57C42×C43C2311yescharacteristic
58(C2×D43)⋊C4—21no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43D411yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4D412yes—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2312yes—
72#10621873Q814yescomplemented
73C22×D43—21no—
74Q8×C43—42no—
75Q8×C43—81no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43C2×D412yes—
85C2×Dic43C2×D412yes—
86D172—21no—
87D172C2×Q812yes—
88C4×D43—42no—
89C4×D43—44no—
90Dic86—21no—
91Dic86—44no—
92Dic86—82no—
93Dic86SD1614yescomplemented
94Dic86C2×Q812yescomplemented
95C8×C43—21no—
96C8×C43C2×Q812yescomplemented
97C43⋊C8—22no—
98C22×C43C22×D411yescharacteristic
99C2×D43—22no—
100C2×D43—41no—
101C2×D43—41no—
102C4×C43—21no—
103C4×C43—42no—
104C4×C43—42no—
105C4×C43C2×SD1612yes—
106C4×C43C22×Q811yescharacteristic
107C4×C432−1+411yescharacteristic
108Dic43—22no—
109Dic43—22no—
110Dic43—41no—
111Dic43—41no—
112Dic43C2×SD1614yes—
113Q8×SD16—431nomaximal, Sylow
114C2×C43D4×Q811yescharacteristic
115C2×C43C22×SD1611yescharacteristic
116C2×C43#57711yescharacteristic
117D43—42no—
118Q82—431no—
119D4×Q8—431no—
120#498—432no—
121#498D4311yescharacteristic, complemented
122#476—431no—
123#476—432no—
124#475—431no—
125#475—432no—
126C8×Q8—431no—
127C4×SD16—432no—
128C4×SD16—431no—
129C43Q8×SD1611yescharacteristic, complemented, Sylow
130C22×Q8—861no—
131C2×SD16—431no—
132C4⋊Q8—432no—
133C4⋊Q8—432no—
134C4⋊Q8—861no—
135C4⋊Q8—862no—
136C4⋊Q8C2×D4311yescharacteristic
137C4⋊Q8C2×D4311yescharacteristic
138C22⋊Q8—862no—
139C22⋊Q8—861no—
140C4×Q8—431no—
141C4×Q8—432no—
142C4×Q8—431no—
143C4×Q8—861no—
144C4×D4—432no—
145C4×D4—431no—
146#106—431no—
147#106—432no—
148#106—432no—
149#106C2×D4312yes—
150#106C2×D4312yes—
151C4⋊C8—432no—
152C4⋊C8—431no—
153#103—431no—
154#103—432no—
155#102—431no—
156#102—432no—
157C4×C8—432no—
158C4×C8C2×D4311yescharacteristic
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×Q8—862no—
164C2×Q8—862no—
165C2×Q8—1724no—
166C2×D4—431no—
167C22×C4—862no—
168C22×C4—861no—
169SD16—434no—
170C2×C8—432no—
171C2×C8C22×D4311yescharacteristic
172C2×C8C22×D4311yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—432no—
176C4⋊C4—431no—
177C4⋊C4—431no—
178C4⋊C4—431no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—861no—
183C4⋊C4C22×D4312yes—
184C4⋊C4C22×D4312yes—
185C22⋊C4—862no—
186C22⋊C4—861no—
187C42—432no—
188C42—862no—
189C42—861no—
190C42C22×D4311yescharacteristic
191C23—861no—
192Q8—42no—
193Q8—81no—
194Q8—434no—
195Q8—432no—
196Q8—861no—
197Q8—3442no—
198Q8—1724no—
199D4—432no—
200D4—861no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—432no—
204C2×C4—432no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—1724no—
209C2×C4—1722no—
210C2×C4D4×D4311yescharacteristic
211C2×C4D4×D4311yescharacteristic
212C2×C4C23×D4311yescharacteristic
213C8—21no—
214C8—862no—
215C8Q8×D4312yescomplemented
216C22—862no—
217C22—1721no—
218C22—1721no—
219C22C2×D4×D4311yescharacteristic
220C4—21no—
221C4—42no—
222C4—42no—
223C4—434no—
224C4—862no—
225C4—862no—
226C4—1721no—
227C4—1721no—
228C4SD16×D4312yes—
229C4C2×Q8×D4311yescharacteristic
230C4#1306337311yescharacteristic
231C2—1722no—
232C2#1458356411yescharacteristic
233C2C2×SD16×D4311yescharacteristic
234C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#498C2
socleC22×C43C22×D4
hypercenter#498D43
hypocenterC43Q8×SD16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #14583629C2semidirect
3. #14583296C2semidirect
6. #14583183C2semidirect
7. #14583181C2semidirect
8. C8×Dic86C2semidirect
11. C43×#498C2semidirect
72. #10621873Q8semidirect
93. Dic86SD16semidirect
94. Dic86C2×Q8semidirect
96. C8×C43C2×Q8semidirect
121. #498D43semidirect
129. C43Q8×SD16semidirect
215. C8Q8×D43semidirect