Finite Group Databasebeta

← #19133144

Subgroups — #19133144

Order 5504.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#14583451C211yesmaximal, characteristic
2#14582953C211yesmaximal, characteristic
3#14582766C211yesmaximal, characteristic
4#14582637C211yesmaximal, characteristic
5#14582636C211yesmaximal, characteristic
6#14582635C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic
8#13063324C411yescharacteristic, complemented
9#13063323C411yescharacteristic, complemented
10#13063315—21no—
11#13063304C2211yescharacteristic
12#13063302—21no—
13Q8×Dic43C411yescharacteristic, complemented
14#13063290—21no—
15#13063290C411yescharacteristic, complemented
16#13063281—21no—
17C2×C4×Dic43C2211yescharacteristic
18Dic43⋊C8—21no—
19C22⋊(C43⋊C8)C2211yescharacteristic
20#13063235—21no—
21C43⋊#95—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×Q8×C43C2×C411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C22×Dic43—21no—
31C22×Dic43D411yescharacteristic
32C22×Dic43D411yescharacteristic
33C2×Dic86—21no—
34C2×Dic86C2×C411yescharacteristic
35C2×C8×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43C2×C411yescharacteristic
38C22⋊C4×C43—21no—
39C22⋊Dic43—21no—
40C4⋊Dic43—21no—
41C4⋊Dic43C2×C411yescharacteristic
42Dic43⋊C4—21no—
43Dic43⋊C4—21no—
44Dic43⋊C4—21no—
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47C4×Dic43—21no—
48C4×Dic43—21no—
49C4×Dic43C2×C411yescharacteristic
50C4×Dic43C2×C411yescharacteristic
51C4×Dic43D411yescharacteristic
52C4×Dic43D411yescharacteristic
53C2×C43⋊C8—21no—
54C23×C43C2×D411yescharacteristic
55Q8×C43—41no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43C22×C411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×Dic43—21no—
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—41no—
69C2×Dic43—41no—
70C2×Dic43—41no—
71C2×Dic43—41no—
72C2×Dic43C22⋊C411yescharacteristic
73C2×Dic43C22⋊C411yescharacteristic
74C2×Dic43C22⋊C411yescharacteristic
75C2×Dic43C22⋊C411yescharacteristic
76Dic86—42no—
77Dic86—41no—
78C8×C43—41no—
79C43⋊C8—41no—
80C22×C43—21no—
81C22×C43—21no—
82C22×C43C2×C22⋊C411yescharacteristic
83C22×C43#13711yescharacteristic
84C22×C43#13711yescharacteristic
85C4×C43—21no—
86C4×C43—21no—
87C4×C43—41no—
88C4×C43—41no—
89C4×C43—81no—
90Dic43—21no—
91Dic43—21no—
92Dic43—21no—
93Dic43—21no—
94Dic43—41no—
95Dic43—41no—
96Dic43—81no—
97#1515—431nomaximal, Sylow
98C2×C43—21no—
99C2×C43—21no—
100C2×C43#41011yescharacteristic
101C2×C43#41911yescharacteristic
102C2×C43#42111yescharacteristic
103#533—431no—
104#432—431no—
105#383—431no—
106#328—431no—
107#328—431no—
108#328—431no—
109#328D4311yescharacteristic
110C43#151511yescharacteristic, complemented, Sylow
111C4⋊Q8—431no—
112C4⋊Q8—431no—
113#125—861no—
114C22⋊Q8—431no—
115C22⋊Q8—861no—
116C22⋊Q8C2×D4311yescharacteristic
117C4×Q8—431no—
118C4×Q8—431no—
119C4×Q8—861no—
120#117—861no—
121C2×C42—431no—
122C4⋊C8—861no—
123C22⋊C8—431no—
124C22⋊C8C2×D4311yescharacteristic
125#97—861no—
126#95—431no—
127#95—861no—
128#95—861no—
129#95C2×D4311yescharacteristic
130C2×Q8—431no—
131C2×Q8—861no—
132C2×Q8C4×D4311yescharacteristic
133C22×C4—21no—
134C22×C4—431no—
135C22×C4—431no—
136C22×C4—861no—
137C22×C4C22×D4311yescharacteristic
138C2×C8—21no—
139C2×C8—861no—
140C4⋊C4—21no—
141C4⋊C4—431no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4—861no—
148C4⋊C4C4×D4311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—861no—
151C42—431no—
152C42—431no—
153C42—431no—
154C42—431no—
155C42—861no—
156C42—861no—
157C23D4×D4311yescharacteristic
158Q8—41no—
159Q8—1721no—
160Q8—1722no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—431no—
168C2×C4—431no—
169C2×C4—431no—
170C2×C4—431no—
171C2×C4—861no—
172C2×C4—861no—
173C2×C4—861no—
174C2×C4—861no—
175C2×C4—1721no—
176C2×C4—1721no—
177C2×C4—1721no—
178C2×C4—1721no—
179C2×C4C2×C4×D4311yescharacteristic
180C2×C4D4×D4311yescharacteristic
181C8—41no—
182C8—1721no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D4311yescharacteristic
186C22#1306335411yescharacteristic
187C22#1306335711yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—861no—
194C4—861no—
195C4—861no—
196C4—861no—
197C4—3441no—
198C4—1721no—
199C4—1721no—
200C2—21no—
201C2—21no—
202C2#1458287111yescharacteristic
203C2#1458290611yescharacteristic
204C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43C2×C22⋊C4
hypercenter#328D43
hypocenterC43#1515
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #13063324C4semidirect
9. #13063323C4semidirect
13. Q8×Dic43C4semidirect
15. #13063290C4semidirect
110. C43#1515semidirect