Finite Group Databasebeta

← #19133625

Subgroups — #19133625

Order 5504.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583498C211yesmaximal, characteristic
2#14583217C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic, complemented
4#14582636C211yesmaximal, characteristic, complemented
5#14582634C211yesmaximal, characteristic
6#14582624C211yesmaximal, characteristic, complemented
7C43×#484C211yesmaximal, characteristic, complemented
8#13063320—21no—
9#13063316—21no—
10#13063310—21no—
11#13063309—21no—
12#13063301—21no—
13#13063299C2211yescharacteristic
14(C22⋊D43)⋊C4—21no—
15C2×Dic43⋊C4C2211yescharacteristic
16#13063256—21no—
17#13063245—21no—
18C22⋊(C43⋊C8)C2211yescharacteristic
19C43⋊#95—21no—
20C43⋊#95—21no—
21C43⋊#95C2211yescharacteristic
22C22⋊Q8×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24#107×C43—21no—
25#103×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33C22×Dic43D411yescharacteristic
34C2×D172D411yescharacteristic
35C2×C4×D43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43D411yescharacteristic
41C22⋊C4×C43—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48C4⋊Dic43D411yescharacteristic
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C2×C43⋊C8—21no—
54C23×C43C2×D411yescharacteristic
55C22×D43—21no—
56Q8×C43—41no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—41no—
60C2×C4×C43—42no—
61C2×C4×C43—41no—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C22⋊D43—41no—
65C22⋊D43—41no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—21no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75D172—41no—
76C4×D43—81no—
77C8×C43—41no—
78C43⋊C8—41no—
79C22×C43—21no—
80C22×C43—21no—
81C22×C43#12011yescharacteristic
82C22×C43#13511yescharacteristic
83C22×C43#13711yescharacteristic
84C2×D43—41no—
85C2×D43—41no—
86C2×D43—41no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C43—41no—
90C4×C43—41no—
91C4×C43—81no—
92Dic43—41no—
93Dic43—41no—
94Dic43—41no—
95Dic43—81no—
96#1615—431nomaximal, Sylow
97C2×C43—21no—
98C2×C43—21no—
99C2×C43#45211yescharacteristic
100C2×C43#45411yescharacteristic
101C2×C43#45811yescharacteristic
102D43—81no—
103#539—431no—
104#484D4311yescharacteristic, complemented
105#481—431no—
106#400—431no—
107#328—431no—
108#327—431no—
109#324—431no—
110C43#161511yescharacteristic, complemented, Sylow
111#126—861no—
112#125—861no—
113#123—861no—
114#123—861no—
115C22⋊Q8—861no—
116C22⋊Q8C2×D4311yescharacteristic
117#121—431no—
118C4×D4—861no—
119C2×C4⋊C4—431no—
120C2×C4⋊C4C2×D4311yescharacteristic
121#107—21no—
122#106—861no—
123#103—21no—
124#102—861no—
125C22⋊C8—431no—
126C22⋊C8C2×D4311yescharacteristic
127#95—431no—
128#95—861no—
129#95—861no—
130C2×Q8C22⋊D4311yescharacteristic
131C2×D4—431no—
132C2×D4—861no—
133C22×C4—21no—
134C22×C4—431no—
135C22×C4—431no—
136C22×C4—861no—
137C22×C4—861no—
138C22×C4C22×D4311yescharacteristic
139C2×C8—21no—
140C2×C8—861no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—431no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4—861no—
148C4⋊C4—861no—
149C4⋊C4—861no—
150C4⋊C4C22⋊D4311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—861no—
153C22⋊C4—861no—
154C22⋊C4—861no—
155C22⋊C4—861no—
156C42—861no—
157C23—861no—
158C23D4×D4311yescharacteristic
159Q8—41no—
160D4—1721no—
161D4—1721no—
162D4—1721no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—861no—
169C2×C4—861no—
170C2×C4—861no—
171C2×C4—861no—
172C2×C4—861no—
173C2×C4—3441no—
174C2×C4—1721no—
175C2×C4—1721no—
176C2×C4—1721no—
177C2×C4—1721no—
178C2×C4D4×D4311yescharacteristic
179C2×C4C2×C22⋊D4311yescharacteristic
180C8—41no—
181C8—1721no—
182C22—21no—
183C22—21no—
184C22—1721no—
185C22—1721no—
186C22—1721no—
187C22#1306329311yescharacteristic
188C22#1306334811yescharacteristic
189C22#1306335711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—3441no—
196C4—1721no—
197C4—1721no—
198C4—1721no—
199C2—21no—
200C2—21no—
201C2—3441no—
202C2#1458306011yescharacteristic
203C2#1458307011yescharacteristic
204C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#484C2
socleC22×C43#120
hypercenter#484D43
hypocenterC43#1615
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #14582837C2semidirect
4. #14582636C2semidirect
6. #14582624C2semidirect
7. C43×#484C2semidirect
104. #484D43semidirect
110. C43#1615semidirect