Finite Group Databasebeta

← #19133593

Subgroups — #19133593

Order 5504.

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

normal subgroups only

This group has 216 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#14583494C211yesmaximal, characteristic
2#14583230C211yesmaximal, characteristic, complemented
3#14583210C211yesmaximal, characteristic
4#14582831C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic
8#13063318—21no—
9#13063315—21no—
10#13063306—21no—
11#13063306—21no—
12#13063304C2211yescharacteristic
13#13063302—21no—
14D4×Dic43—21no—
15C2×C4⋊Dic43—21no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18#13063258—21no—
19#13063257—21no—
20#13063250—21no—
21#13063246—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C22×Dic43—21no—
32C22×Dic43—21no—
33C22×Dic43D411yescharacteristic
34C22×Dic43D411yescharacteristic
35C2×Dic86D411yescharacteristic
36C2×C8×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C22⋊C4×C43—21no—
39C22⋊Dic43—21no—
40C22⋊Dic43—21no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43—42no—
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C23×C43—21no—
56C23×C43C2×D411yescharacteristic
57D4×C43—41no—
58D4×C43—41no—
59D4×C43—41no—
60C2×C4×C43—22no—
61C2×C4×C43—21no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—21no—
71C2×Dic43—21no—
72C2×Dic43—21no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43—81no—
78Dic86—41no—
79C8×C43—41no—
80C43⋊C8—41no—
81C22×C43—21no—
82C22×C43—21no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43#12011yescharacteristic
87C22×C43#13511yescharacteristic
88C22×C43AGL(1,ℤ/8)11yescharacteristic
89C4×C43—21no—
90C4×C43—21no—
91C4×C43—42no—
92C4×C43—41no—
93Dic43—41no—
94Dic43—41no—
95Dic43—41no—
96Dic43—41no—
97Dic43—81no—
98#1609—431nomaximal, Sylow
99C2×C43—21no—
100C2×C43—21no—
101C2×C43—81no—
102C2×C43#44911yescharacteristic
103C2×C43#45611yescharacteristic
104C2×C43#45811yescharacteristic
105#539—431no—
106#483—431no—
107#480—431no—
108#398—431no—
109#328—431no—
110#327D4311yescharacteristic
111#324—431no—
112C43#160911yescharacteristic, complemented, Sylow
113#126—861no—
114#125—861no—
115#123—861no—
116#123—861no—
117C22⋊Q8—431no—
118C22⋊Q8—861no—
119#121C2×D4311yescharacteristic
120C4×D4—861no—
121C2×C4⋊C4—431no—
122C2×C4⋊C4—431no—
123C2×C4⋊C4—861no—
124#107—861no—
125#106—861no—
126#103—861no—
127#102—861no—
128C22⋊C8—431no—
129C22⋊C8C2×D4311yescharacteristic
130#95—861no—
131#95C2×D4311yescharacteristic
132C2×Q8—431no—
133C2×D4—21no—
134C2×D4D17211yescharacteristic
135C22×C4—21no—
136C22×C4—431no—
137C22×C4—431no—
138C22×C4—861no—
139C22×C4—861no—
140C22×C4C22×D4311yescharacteristic
141C2×C8—21no—
142C2×C8—861no—
143C4⋊C4—431no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4—861no—
148C4⋊C4—861no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4—1722no—
153C4⋊C4D17211yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—861no—
156C22⋊C4—861no—
157C22⋊C4—861no—
158C22⋊C4—861no—
159C42—861no—
160C23—21no—
161C23D4×D4311yescharacteristic
162Q8—1721no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—861no—
172C2×C4—861no—
173C2×C4—861no—
174C2×C4—861no—
175C2×C4—861no—
176C2×C4—861no—
177C2×C4—3441no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4—1721no—
181C2×C4—1721no—
182C2×C4C2×D17211yescharacteristic
183C2×C4D4×D4311yescharacteristic
184C8—41no—
185C8—1721no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1306329511yescharacteristic
192C22#1306334611yescharacteristic
193C22#1306334911yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—3441no—
199C4—1721no—
200C4—1721no—
201C4—1721no—
202C4—1721no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1458304511yescharacteristic
207C2#1458308311yescharacteristic
208C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1609
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14583230C2semidirect
4. #14582831C2semidirect
5. #14582635C2semidirect
6. #14582624C2semidirect
112. C43#1609semidirect