Finite Group Databasebeta

← #19133749

Subgroups — #19133749

Order 5504.

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

normal subgroups only

This group has 234 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#14583554C211yesmaximal, characteristic
2#14583250C211yesmaximal, characteristic, complemented
3#14583190C211yesmaximal, characteristic, complemented
4#14583189C211yesmaximal, characteristic, complemented
5#14582646C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621898—21no—
9#13063325C2211yescharacteristic
10#13063325C2211yescharacteristic
11#13063307—22no—
12#13063304—21no—
13#13063296—21no—
14C4×D172C2211yescharacteristic
15C4⋊C4×D43—21no—
16#13063257—21no—
17#13063256—21no—
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063250—22no—
20#13063247—21no—
21#13063246—21no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×D4×C43D411yescharacteristic
26C22×C4×C43—21no—
27C2×C22⋊D43—22no—
28#10621898—42no—
29#10621898—42no—
30C2×D172D411yescharacteristic
31C2×C4×D43—22no—
32C2×C4×D43—21no—
33C2×Dic86—21no—
34C2×Dic86—21no—
35C2×C8×C43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C22⋊C4×C43—21no—
39C42×C43C2311yescharacteristic
40C22⋊Dic43—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43D412yes—
46C4⋊Dic43D411yescharacteristic
47Dic43⋊C4—22no—
48C2×C43⋊C8—21no—
49C23×C43—21no—
50C22×D43—21no—
51D4×C43—21no—
52D4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C22⋊D43—44no—
60C2×Dic43—21no—
61C2×Dic43—22no—
62C2×Dic43—41no—
63D172—21no—
64D172SD1612yes—
65C4×D43—44no—
66C4×D43—41no—
67C4×D43—41no—
68Dic86—41no—
69Dic86—41no—
70Dic86—42no—
71C8×C43—41no—
72C8×C43—41no—
73C43⋊C8—41no—
74C22×C43—41no—
75C22×C43—41no—
76C22×C43—41no—
77C22×C43#12011yescharacteristic
78C2×D43—22no—
79C2×D43—41no—
80C2×D43—41no—
81C4×C43—21no—
82C4×C43—41no—
83C4×C43C2×SD1611yescharacteristic
84C4×C43#13511yescharacteristic
85C4×C43AGL(1,ℤ/8)11yescharacteristic
86C4×C43#13711yescharacteristic
87Dic43—42no—
88Dic43—41no—
89Dic43—81no—
90#1635—431nomaximal, Sylow
91C2×C43—81no—
92C2×C43#45011yescharacteristic
93C2×C43#45211yescharacteristic
94C2×C43#45411yescharacteristic
95D43—42no—
96#547—431no—
97#487—431no—
98#476—431no—
99#476—431no—
100#332—431no—
101D4⋊C8—431no—
102D4⋊C8D4311yescharacteristic, complemented
103C43#163511yescharacteristic, complemented, Sylow
104C2×#41—861no—
105C4⋊Q8—431no—
106C4⋊Q8—431no—
107#123—862no—
108C22⋊Q8—861no—
109#121—861no—
110C4×D4—431no—
111C4×D4C2×D4311yescharacteristic
112C2×C4⋊C4—861no—
113#106—861no—
114#106—861no—
115C4⋊C8—431no—
116C4⋊C8C2×D4311yescharacteristic
117#103—862no—
118#102—861no—
119#102—861no—
120C4×C8C2×D4311yescharacteristic
121#41—1722no—
122#41—1722no—
123C2×Q8—861no—
124C2×Q8—861no—
125C2×D4—431no—
126C2×D4—862no—
127C2×D4D17211yescharacteristic
128C22×C4—21no—
129C22×C4—862no—
130C22×C4—861no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—861no—
134C4⋊C4—432no—
135C4⋊C4—431no—
136C4⋊C4—862no—
137C4⋊C4—861no—
138C4⋊C4—861no—
139C4⋊C4—861no—
140C4⋊C4D17211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—862no—
143C22⋊C4—861no—
144C42C22×D4311yescharacteristic
145C23—21no—
146C23—861no—
147Q8—1722no—
148Q8—1721no—
149Q8—1721no—
150D4—21no—
151D4—21no—
152D4—432no—
153D4—861no—
154D4—1724no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—861no—
159C2×C4—862no—
160C2×C4—1724no—
161C2×C4—1721no—
162C2×C4—1721no—
163C2×C4—1721no—
164C2×C4C2×D17211yescharacteristic
165C2×C4D4×D4311yescharacteristic
166C2×C4D4×D4311yescharacteristic
167C8—41no—
168C8—41no—
169C8—1721no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—862no—
174C22—1721no—
175C22—1721no—
176C22#1306329511yescharacteristic
177C4—21no—
178C4—41no—
179C4—3441no—
180C4—1722no—
181C4—1721no—
182C4SD16×D4311yescharacteristic
183C4#1306334711yescharacteristic
184C4#1306334911yescharacteristic
185C4#1306335811yescharacteristic
186C2—81no—
187C2—1722no—
188C2#1458305111yescharacteristic
189C2#1458306311yescharacteristic
190C2#1458307311yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1635
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14583250C2semidirect
3. #14583190C2semidirect
4. #14583189C2semidirect
5. #14582646C2semidirect
6. #14582628C2semidirect
7. C43×D4⋊C8C2semidirect
102. D4⋊C8D43semidirect
103. C43#1635semidirect