Finite Group Databasebeta

← #19133920

Subgroups — #19133920

Order 5504.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14583643C211yesmaximal, characteristic
2#14583268C211yesmaximal, characteristic, complemented
3#14583259C211yesmaximal, characteristic, complemented
4#14583258C211yesmaximal, characteristic, complemented
5#14582640C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#329C211yesmaximal, characteristic, complemented
8#13063325C2211yescharacteristic
9#13063317C2211yescharacteristic
10#13063313C2211yescharacteristic
11#13063309—21no—
12#13063307—21no—
13#13063302—21no—
14#13063301—21no—
15#13063298—21no—
16#13063297—21no—
17#13063250—21no—
18#13063250—21no—
19#13063250—21no—
20#13063249—21no—
21#13063247—21no—
22#13063246—21no—
23#13063236C2211yescharacteristic
24#124×C43C2211yescharacteristic
25#97×C43C2211yescharacteristic
26#97×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C2×C22⋊D43—21no—
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C2×D172D411yescharacteristic
33C2×C4×D43—21no—
34C2×Dic86—21no—
35C2×Dic86D411yescharacteristic
36C2×C8×C43—21no—
37C2×C8×C43—21no—
38C22⋊C4×C43—21no—
39C22⋊C4×C43—21no—
40C42×C43C2311yescharacteristic
41C22⋊Dic43—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53C2×C43⋊C8—21no—
54C23×C43—21no—
55C22×D43—21no—
56Q8×C43—41no—
57D4×C43—41no—
58C2×C4×C43—21no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C22⋊D43—81no—
63C22⋊D43—81no—
64C2×Dic43—21no—
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—41no—
68C2×Dic43—81no—
69D172—41no—
70C4×D43—81no—
71Dic86—41no—
72Dic86—42no—
73C8×C43—41no—
74C8×C43—41no—
75C43⋊C8—41no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43—41no—
79C22×C43#12011yescharacteristic
80C2×D43—41no—
81C2×D43—41no—
82C2×D43—41no—
83C4×C43—21no—
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—41no—
87Dic43—41no—
88Dic43—41no—
89Dic43—41no—
90Dic43—81no—
91#1662—431nomaximal, Sylow
92C2×C43—81no—
93C2×C43#45411yescharacteristic
94C2×C43#45511yescharacteristic
95C2×C43#45511yescharacteristic
96D43—81no—
97#562—431no—
98#491—431no—
99#489—431no—
100#489—431no—
101#330—431no—
102#329—431no—
103#329D4311yescharacteristic, complemented
104C43#166211yescharacteristic, complemented, Sylow
105C4⋊Q8—431no—
106#125—431no—
107#124—431no—
108#124C2×D4311yescharacteristic
109#123—861no—
110#123—861no—
111C22⋊Q8—861no—
112C22⋊Q8—861no—
113#121—861no—
114#121—861no—
115#103—861no—
116#103—861no—
117#103—861no—
118#103—861no—
119#102—861no—
120#102—861no—
121#97—431no—
122#97C2×D4311yescharacteristic
123#97C2×D4311yescharacteristic
124C2×Q8—431no—
125C2×Q8—861no—
126C2×Q8D17211yescharacteristic
127C2×D4—431no—
128C2×D4—861no—
129C2×D4—861no—
130C2×D4D17211yescharacteristic
131C22×C4—861no—
132C22×C4—861no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—861no—
136C4⋊C4—431no—
137C4⋊C4—431no—
138C4⋊C4—861no—
139C4⋊C4—861no—
140C4⋊C4—861no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—861no—
147C22⋊C4—861no—
148C22⋊C4—861no—
149C22⋊C4—861no—
150C42C22×D4311yescharacteristic
151C23—21no—
152C23—861no—
153Q8—41no—
154Q8—1722no—
155Q8—1721no—
156D4—41no—
157D4—3441no—
158D4—3441no—
159D4—1721no—
160C2×C4—21no—
161C2×C4—861no—
162C2×C4—861no—
163C2×C4—861no—
164C2×C4—3441no—
165C2×C4—3441no—
166C2×C4—1721no—
167C2×C4C2×D17211yescharacteristic
168C2×C4D4×D4311yescharacteristic
169C2×C4D4×D4311yescharacteristic
170C8—41no—
171C8—41no—
172C8—1721no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1721no—
177C22—1721no—
178C22—1721no—
179C22#1306329511yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—3441no—
185C4—1721no—
186C4—1721no—
187C4—1721no—
188C2—81no—
189C2—3441no—
190C2#1458307311yescharacteristic
191C2#1458307811yescharacteristic
192C2#1458307911yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#329C2
socleC22×C43#120
hypercenter#329D43
hypocenterC43#1662
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14583268C2semidirect
3. #14583259C2semidirect
4. #14583258C2semidirect
5. #14582640C2semidirect
6. #14582638C2semidirect
7. C43×#329C2semidirect
103. #329D43semidirect
104. C43#1662semidirect