Finite Group Databasebeta

← #19145717

Subgroups — #19145717

Order 5504.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583450C211yesmaximal, characteristic
2C4⋊Q8×D43C211yesmaximal, characteristic, complemented
3#14583302C211yesmaximal, characteristic, complemented
4#14583247C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583214C214yesmaximal, complemented
7#14583178C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic, complemented
9C43×#500C211yesmaximal, characteristic, complemented
10C2×#10621902—21no—
11C2×Q8×D43—21no—
12#13063325C2211yescharacteristic
13#13063324—21no—
14#13063324C2212yes—
15#13063323—21no—
16#13063322C2211yescharacteristic
17#13063314—21no—
18#13063300—21no—
19#13063300C2212yes—
20#13063287—21no—
21#13063287C2212yes—
22C4⋊C4×D43—21no—
23C4⋊C4×D43C2212yes—
24C42×D43C2211yescharacteristic
25#13063258C2214yes—
26Dic43⋊C8C2212yes—
27#13063247C2214yes—
28#13063245C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#107×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43—21no—
37#10621902—44no—
38Q8×D43—44no—
39C2×D172—21no—
40C2×D172—21no—
41C2×D172—22no—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×C4×D43—22no—
45C2×C4×D43D411yescharacteristic
46C2×C4×D43D411yescharacteristic
47C2×C4×D43C2311yescharacteristic
48C2×Dic86—21no—
49C2×Dic86—22no—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C4⋊C4×C43C2312yes—
55C42×C43C2311yescharacteristic
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—21no—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43D411yescharacteristic
63C4×Dic43D411yescharacteristic
64C4×Dic43C2311yescharacteristic
65C2×C43⋊C8C2312yes—
66C22×D43—22no—
67C22×D43C2×D411yescharacteristic
68Q8×C43—42no—
69Q8×C43—42no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2411yescharacteristic
75C2×Dic43—22no—
76C2×Dic43C2×D411yescharacteristic
77C2×Dic43C2×D411yescharacteristic
78C2×Dic43C2×D411yescharacteristic
79D172—24no—
80D172—44no—
81D172—42no—
82D172—42no—
83C4×D43—22no—
84C4×D43—22no—
85C4×D43—44no—
86C4×D43—44no—
87C4×D43D814yes—
88Dic86—42no—
89Dic86—44no—
90C8×C43—22no—
91C43⋊C8—22no—
92C22×C43C22×D411yescharacteristic
93C2×D43—21no—
94C2×D43—21no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43C2×D812yes—
99C4×C43—42no—
100C4×C43—42no—
101C4×C43C2×D812yes—
102C4×C43#13712yes—
103C4×C432−1+412yes—
104Dic43—21no—
105Dic43—21no—
106Dic43—42no—
107Dic43C2×D812yes—
108#3226—431nomaximal, Sylow
109C2×C43#53611yescharacteristic
110C2×C43C22×D811yescharacteristic
111C2×C43C2×#13711yescharacteristic
112D43—22no—
113D43—82no—
114#532—431no—
115C2×C4⋊Q8—431no—
116#500—431no—
117#500D4311yescharacteristic, complemented
118#486—431no—
119#486—431no—
120#480—434no—
121#474—434no—
122#431—431no—
123C43#322611yescharacteristic, complemented, Sylow
124C2×#41—861no—
125C22×Q8—861no—
126C4⋊Q8—432no—
127C4⋊Q8—431no—
128C4⋊Q8—861no—
129C4⋊Q8—861no—
130C4⋊Q8C2×D4311yescharacteristic
131C4⋊Q8C2×D4311yescharacteristic
132#127—431no—
133#124—861no—
134#121—432no—
135#121—861no—
136C4×D4—432no—
137C4×D4—861no—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—861no—
140C2×C42—431no—
141#107—434no—
142#107C2×D4314yes—
143C4⋊C8—432no—
144#102—434no—
145#102—434no—
146C22⋊C8—432no—
147C4×C8—431no—
148C4×C8C2×D4311yescharacteristic
149#41—1724no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—862no—
153C2×Q8—861no—
154C2×Q8—1724no—
155C2×D4—432no—
156C2×D4—862no—
157C2×D4—861no—
158C2×D4—861no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—862no—
163C22×C4—862no—
164C2×C8—432no—
165C2×C8C22×D4312yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—432no—
169C4⋊C4—862no—
170C4⋊C4—862no—
171C4⋊C4—861no—
172C4⋊C4C22×D4312yes—
173C4⋊C4C22×D4312yes—
174C22⋊C4—862no—
175C22⋊C4—862no—
176C42—431no—
177C42—431no—
178C42—431no—
179C42C22×D4311yescharacteristic
180C23—431no—
181C23—862no—
182Q8—42no—
183Q8—42no—
184Q8—1724no—
185Q8—1722no—
186D4—864no—
187D4—1724no—
188D4—1722no—
189D4—1722no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—431no—
193C2×C4—434no—
194C2×C4—431no—
195C2×C4—431no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—1724no—
200C2×C4—1724no—
201C2×C4D4×D4311yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C2×C4C23×D4311yescharacteristic
204C8—22no—
205C8—862no—
206C22—432no—
207C22—861no—
208C22—861no—
209C22—1722no—
210C22—1722no—
211C22—1722no—
212C22C2×D4×D4311yescharacteristic
213C4—42no—
214C4—42no—
215C4—432no—
216C4—861no—
217C4—861no—
218C4—1722no—
219C4D8×D4312yes—
220C4#1306335712yes—
221C4#1306337312yes—
222C2—862no—
223C2—3442no—
224C2#1458347411yescharacteristic
225C2C2×D8×D4311yescharacteristic
226C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#500C2
socleC22×C43C22×D4
hypercenter#500D43
hypocenterC43#3226
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D43C2semidirect
3. #14583302C2semidirect
4. #14583247C2semidirect
5. #14583246C2semidirect
6. #14583214C2semidirect
7. #14583178C2semidirect
8. #14582950C2semidirect
9. C43×#500C2semidirect
117. #500D43semidirect
123. C43#3226semidirect