Finite Group Databasebeta

← #19133932

Subgroups — #19133932

Order 5504.

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

normal subgroups only

This group has 184 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#14583649C211yesmaximal, characteristic
2#14583308C211yesmaximal, characteristic, complemented
3#14583268C211yesmaximal, characteristic, complemented
4#14583258C211yesmaximal, characteristic
5#14582640C211yesmaximal, characteristic, complemented
6#14582640C211yesmaximal, characteristic, complemented
7C43×#329C211yesmaximal, characteristic
8#13063325C2211yescharacteristic
9#13063323—21no—
10#13063318—21no—
11#13063318—21no—
12#13063317C2211yescharacteristic
13#13063317C2211yescharacteristic
14#13063306—21no—
15#13063302—21no—
16#13063302—21no—
17#13063259—21no—
18#13063257—21no—
19#13063250—21no—
20#13063250—21no—
21#13063249—21no—
22#13063246—21no—
23#13063236C2211yescharacteristic
24#124×C43C2211yescharacteristic
25#97×C43C2211yescharacteristic
26#97×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C22×Dic43—21no—
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×C8×C43—21no—
33C2×C8×C43—21no—
34C22⋊C4×C43—21no—
35C22⋊C4×C43—21no—
36C42×C43C2311yescharacteristic
37C22⋊Dic43—21no—
38C22⋊Dic43—21no—
39C22⋊Dic43—21no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43D411yescharacteristic
43C4⋊Dic43D411yescharacteristic
44C4⋊Dic43D411yescharacteristic
45C4⋊Dic43D411yescharacteristic
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C2×C43⋊C8—21no—
54C23×C43—21no—
55Q8×C43—41no—
56D4×C43—41no—
57C2×C4×C43—21no—
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×Dic43—21no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65C2×Dic43—41no—
66C2×Dic43—81no—
67Dic86—42no—
68Dic86—81no—
69C8×C43—22no—
70C8×C43—41no—
71C43⋊C8—41no—
72C22×C43—41no—
73C22×C43—41no—
74C22×C43—41no—
75C22×C43#12011yescharacteristic
76C4×C43—21no—
77C4×C43—21no—
78C4×C43—21no—
79C4×C43—41no—
80Dic43—41no—
81Dic43—41no—
82Dic43—41no—
83Dic43—41no—
84Dic43—81no—
85#1664—431nomaximal, Sylow
86C2×C43—81no—
87C2×C43#45411yescharacteristic
88C2×C43#45511yescharacteristic
89C2×C43#45611yescharacteristic
90#563—431no—
91#501—431no—
92#491—431no—
93#489—431no—
94#330—431no—
95#330—431no—
96#329D4311yescharacteristic
97C43#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—431no—
99C4⋊Q8—861no—
100#126—861no—
101#126—861no—
102#125—431no—
103#125—431no—
104#124C2×D4311yescharacteristic
105#123—861no—
106C22⋊Q8—861no—
107C22⋊Q8—861no—
108#107—861no—
109#106—861no—
110#103—861no—
111#103—861no—
112#103—861no—
113#102—861no—
114#97—431no—
115#97C2×D4311yescharacteristic
116#97C2×D4311yescharacteristic
117C2×Q8—861no—
118C2×Q8—861no—
119C2×Q8D17211yescharacteristic
120C2×D4D17211yescharacteristic
121C22×C4—861no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—861no—
125C4⋊C4—431no—
126C4⋊C4—431no—
127C4⋊C4—431no—
128C4⋊C4—431no—
129C4⋊C4—861no—
130C4⋊C4—861no—
131C4⋊C4—861no—
132C4⋊C4—861no—
133C4⋊C4—861no—
134C4⋊C4—861no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—861no—
140C22⋊C4—861no—
141C22⋊C4—861no—
142C42—861no—
143C42C22×D4311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—3441no—
147Q8—1722no—
148D4—41no—
149C2×C4—21no—
150C2×C4—861no—
151C2×C4—861no—
152C2×C4—861no—
153C2×C4—861no—
154C2×C4—3441no—
155C2×C4—1721no—
156C2×C4C2×D17211yescharacteristic
157C2×C4D4×D4311yescharacteristic
158C2×C4D4×D4311yescharacteristic
159C8—22no—
160C8—41no—
161C8—1721no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1306329511yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—3441no—
171C4—1721no—
172C4—1721no—
173C4—1721no—
174C4—1721no—
175C2—81no—
176C2#1458307311yescharacteristic
177C2#1458307911yescharacteristic
178C2#1458308311yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#329C2
socleC22×C43#120
hypercenter#329D43
hypocenterC43#1664
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. #14583308C2semidirect
3. #14583268C2semidirect
5. #14582640C2semidirect
6. #14582640C2semidirect
97. C43#1664semidirect