Finite Group Databasebeta

← #19133670

Subgroups — #19133670

Order 5504.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583609C211yesmaximal, characteristic, complemented
2#14583272C211yesmaximal, characteristic, complemented
3#14583099C211yesmaximal, characteristic, complemented
4#14583095C211yesmaximal, characteristic
5#14582647C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621873—22no—
9C2×#10621884—21no—
10C2×D344—21no—
11#13063325C2211yescharacteristic
12#13063322C2211yescharacteristic
13#13063317—21no—
14#13063303—22no—
15#13063301—21no—
16C4×D172—21no—
17C4×D172C2211yescharacteristic
18C4⋊C4×D43—21no—
19C4⋊(C43⋊C8)C2211yescharacteristic
20#13063247—21no—
21#13063245—21no—
22C4×Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43D411yescharacteristic
26C2×D172—21no—
27C2×D172—21no—
28C2×D172—21no—
29C2×D172D411yescharacteristic
30C2×C4×D43—21no—
31C2×C4×D43—22no—
32C2×Dic86D412yes—
33C2×C8×C43—21no—
34C2×C8×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43D411yescharacteristic
37C42×C43—21no—
38C42×C43C2311yescharacteristic
39#10621884—42no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43D411yescharacteristic
45Dic43⋊C4—22no—
46Dic43⋊C4—22no—
47C2×C43⋊C8—21no—
48D344—42no—
49#10621873—44no—
50C22×D43—21no—
51C22×D43—41no—
52Q8×C43—21no—
53Q8×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×Dic43—21no—
60C2×Dic43—22no—
61D172—21no—
62D172—42no—
63D172—41no—
64D172—41no—
65D172—41no—
66D172—41no—
67D172SD1612yescomplemented
68C4×D43—41no—
69C4×D43—41no—
70C4×D43—82no—
71Dic86—42no—
72C8×C43—22no—
73C8×C43—41no—
74C43⋊C8—41no—
75C22×C43#12011yescharacteristic
76C2×D43—22no—
77C2×D43—41no—
78C2×D43—41no—
79C2×D43—81no—
80C2×D43—81no—
81C2×D43—81no—
82C4×C43—21no—
83C4×C43—41no—
84C4×C43—41no—
85C4×C43C2×SD1611yescharacteristic
86C4×C43#13511yescharacteristic
87C4×C43AGL(1,ℤ/8)11yescharacteristic
88C4×C43#13711yescharacteristic
89Dic43—41no—
90Dic43—42no—
91#1622—431nomaximal, Sylow
92C2×C43#44811yescharacteristic
93C2×C43#44911yescharacteristic
94C2×C43#45311yescharacteristic
95D43—42no—
96D43—161no—
97#554—431no—
98#492—431no—
99#460—431no—
100#459—431no—
101#333—431no—
102Q8⋊C8D4311yescharacteristic, complemented
103D4⋊C8—431no—
104C43#162211yescharacteristic, complemented, Sylow
105C2×SD16—862no—
106C2×SD16—861no—
107C2×D8—861no—
108C4⋊Q8—431no—
109#127—431no—
110#125—861no—
111C22⋊Q8—862no—
112C22⋊Q8—861no—
113C4×Q8C2×D4311yescharacteristic
114C4×D4—431no—
115C4×D4—861no—
116C2×C4⋊C4—861no—
117C4⋊C8—431no—
118C4⋊C8C2×D4311yescharacteristic
119#102—861no—
120#102—861no—
121C4×C8C2×D4311yescharacteristic
122C2×Q8—432no—
123C2×Q8D17211yescharacteristic
124C2×D4—431no—
125C2×D4—861no—
126C2×D4—861no—
127C2×D4—861no—
128C22×C4—862no—
129C22×C4—861no—
130SD16—1724no—
131SD16—1722no—
132D8—1722no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—861no—
136C4⋊C4—21no—
137C4⋊C4—431no—
138C4⋊C4—862no—
139C4⋊C4—862no—
140C4⋊C4—861no—
141C4⋊C4—861no—
142C4⋊C4D17211yescharacteristic
143C22⋊C4—862no—
144C22⋊C4—861no—
145C42—21no—
146C42C22×D4311yescharacteristic
147C23—861no—
148C23—1721no—
149Q8—21no—
150Q8—21no—
151Q8—1722no—
152D4—432no—
153D4—861no—
154D4—1722no—
155D4—1721no—
156D4—1721no—
157D4—1721no—
158D4—1721no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—861no—
162C2×C4—862no—
163C2×C4—3442no—
164C2×C4—1721no—
165C2×C4—1721no—
166C2×C4C2×D17211yescharacteristic
167C2×C4D4×D4311yescharacteristic
168C2×C4D4×D4311yescharacteristic
169C8—22no—
170C8—41no—
171C8—1721no—
172C22—862no—
173C22—3441no—
174C22—3441no—
175C22—3441no—
176C22—1721no—
177C22—1721no—
178C22#1306329511yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—1721no—
183C4—1722no—
184C4SD16×D4311yescharacteristic
185C4#1306334711yescharacteristic
186C4#1306335311yescharacteristic
187C4#1306335711yescharacteristic
188C2—1722no—
189C2—6881no—
190C2#1458303911yescharacteristic
191C2#1458304611yescharacteristic
192C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×Q8⋊C8C2
socleC22×C43#120
hypercenterQ8⋊C8D43
hypocenterC43#1622
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14583609C2semidirect
2. #14583272C2semidirect
3. #14583099C2semidirect
5. #14582647C2semidirect
6. #14582628C2semidirect
7. C43×Q8⋊C8C2semidirect
67. D172SD16semidirect
102. Q8⋊C8D43semidirect
104. C43#1622semidirect