Finite Group Databasebeta

← #19133560

Subgroups — #19133560

Order 5504.

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

normal subgroups only

This group has 244 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#14583496C211yesmaximal, characteristic
2#14583057C211yesmaximal, characteristic, complemented
3#14583040C211yesmaximal, characteristic
4#14582819C211yesmaximal, characteristic, complemented
5#14582637C211yesmaximal, characteristic, complemented
6#14582634C211yesmaximal, characteristic
7C43×#324C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic
9C2×Dic172—21no—
10C2×#10621873—21no—
11#13063320—21no—
12#13063315—21no—
13#13063310—21no—
14#13063308—21no—
15#13063304C2211yescharacteristic
16#13063303—21no—
17#13063299C2211yescharacteristic
18C4×C22⋊D43—21no—
19C2×Dic43⋊C4—21no—
20#13063250—21no—
21#13063250—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26C22⋊C8×C43C2211yescharacteristic
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C22×Dic43—21no—
33C2×D172D411yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86—21no—
36C2×Dic86—21no—
37C2×Dic86—42no—
38C2×Dic86D411yescharacteristic
39C2×C8×C43—21no—
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43—21no—
43C22⋊Dic43—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—42no—
55C4×Dic43—21no—
56Dic172—42no—
57#10621873—42no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—41no—
69C22⋊D43—41no—
70C2×Dic43—22no—
71C2×Dic43—22no—
72C2×Dic43—21no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79D172—41no—
80C4×D43—81no—
81Dic86—22no—
82Dic86—22no—
83Dic86—41no—
84Dic86—41no—
85Dic86—41no—
86C8×C43—41no—
87C8×C43—41no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43#12011yescharacteristic
91C22×C43#13511yescharacteristic
92C22×C43#13711yescharacteristic
93C2×D43—41no—
94C2×D43—41no—
95C2×D43—41no—
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—41no—
99C4×C43—41no—
100Dic43—42no—
101Dic43—41no—
102Dic43—41no—
103Dic43—42no—
104Dic43—41no—
105#1603—431nomaximal, Sylow
106C2×C43—21no—
107C2×C43—21no—
108C2×C43#45211yescharacteristic
109C2×C43#45611yescharacteristic
110C2×C43B(4,𝔽2)11yescharacteristic
111D43—81no—
112#539—431no—
113#451—431no—
114#448—431no—
115#395—431no—
116#328—431no—
117#327—431no—
118#324D4311yescharacteristic, complemented
119C43#160311yescharacteristic, complemented, Sylow
120C22×Q8—431no—
121C2×Q16—861no—
122C2×SD16—861no—
123#126—861no—
124#125—861no—
125#123—861no—
126#123—861no—
127C22⋊Q8—431no—
128C22⋊Q8—861no—
129#121—431no—
130C4×D4—861no—
131C2×C4⋊C4—861no—
132C2×C4⋊C4C2×D4311yescharacteristic
133#103—861no—
134#103—861no—
135C22⋊C8C2×D4311yescharacteristic
136C22⋊C8C2×D4311yescharacteristic
137#95—431no—
138#95—861no—
139C2×Q8—431no—
140C2×Q8—861no—
141C2×Q8—861no—
142C2×Q8—1722no—
143C2×D4—431no—
144C2×D4—861no—
145C22×C4—861no—
146C22×C4—861no—
147C22×C4—861no—
148C22×C4D17211yescharacteristic
149C22×C4D17211yescharacteristic
150C22×C4C22×D4311yescharacteristic
151Q16—1722no—
152SD16—1722no—
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—431no—
158C4⋊C4—431no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—861no—
163C4⋊C4—1722no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C42—861no—
170C23—861no—
171C23C2×D17211yescharacteristic
172Q8—862no—
173Q8—862no—
174Q8—1721no—
175Q8—1721no—
176Q8—1721no—
177D4—1721no—
178D4—1721no—
179D4—1721no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—3441no—
192C2×C4—1721no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4D4×D4311yescharacteristic
197C2×C4D4×D4311yescharacteristic
198C8—41no—
199C8—41no—
200C22—21no—
201C22—21no—
202C22—1721no—
203C22—1721no—
204C22—1721no—
205C22#1306329511yescharacteristic
206C22#1306334711yescharacteristic
207C22#1306335811yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—1722no—
213C4—1721no—
214C4—1721no—
215C4—1721no—
216C4—1722no—
217C2—21no—
218C2—21no—
219C2—3441no—
220C2#1458306311yescharacteristic
221C2#1458308411yescharacteristic
222C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#324C2
socleC22×C43#120
hypercenter#324D43
hypocenterC43#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14583057C2semidirect
4. #14582819C2semidirect
5. #14582637C2semidirect
7. C43×#324C2semidirect
118. #324D43semidirect
119. C43#1603semidirect