Finite Group Databasebeta

← #19133929

Subgroups — #19133929

Order 5504.

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

normal subgroups only

This group has 184 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#14583309C211yesmaximal, characteristic, complemented
2#14583269C211yesmaximal, characteristic, complemented
3#14583258C211yesmaximal, characteristic
4#14582641C211yesmaximal, characteristic, complemented
5#14582641C211yesmaximal, characteristic, complemented
6#14582639C211yesmaximal, characteristic
7C43×#563C211yesmaximal, characteristic
8#13063325C2211yescharacteristic
9#13063258—21no—
10#13063256—21no—
11#13063249—21no—
12#13063248—21no—
13#13063248—21no—
14#13063246—21no—
15#13063236C2211yescharacteristic
16#13063236C2211yescharacteristic
17#13063236C2211yescharacteristic
18C4⋊Q8×C43—21no—
19#126×C43—21no—
20#126×C43—21no—
21#125×C43C2211yescharacteristic
22#125×C43C2211yescharacteristic
23#124×C43C2211yescharacteristic
24#123×C43—21no—
25C22⋊Q8×C43—21no—
26C22⋊Q8×C43—21no—
27C2×Q8×C43—21no—
28C2×Q8×C43D411yescharacteristic
29C2×D4×C43D411yescharacteristic
30C22×C4×C43—21no—
31C2×Dic86—21no—
32C4⋊C4×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43D411yescharacteristic
39C4⋊C4×C43D411yescharacteristic
40C4⋊C4×C43D411yescharacteristic
41C4⋊C4×C43D411yescharacteristic
42C22⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊C4×C43—21no—
46C22⋊C4×C43—21no—
47C42×C43—21no—
48C42×C43C2311yescharacteristic
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C2×C43⋊C8—21no—
52C2×C43⋊C8—21no—
53C2×C43⋊C8—21no—
54C23×C43—21no—
55Q8×C43—41no—
56Q8×C43—81no—
57D4×C43—41no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—81no—
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×Dic43—41no—
68Dic86—42no—
69C43⋊C8—22no—
70C43⋊C8—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—
80C4×C43—41no—
81C4×C43—41no—
82C4×C43—41no—
83C4×C43—41no—
84Dic43—81no—
85#1664—431nomaximal, Sylow
86C2×C43—81no—
87C2×C43#45411yescharacteristic
88C2×C43#45511yescharacteristic
89C2×C43#45611yescharacteristic
90#563D4311yescharacteristic
91#501—431no—
92#491—431no—
93#489—431no—
94#330—431no—
95#330—431no—
96#329—431no—
97C43#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—21no—
99C4⋊Q8—431no—
100#126—21no—
101#126—21no—
102#125C2×D4311yescharacteristic
103#125C2×D4311yescharacteristic
104#124C2×D4311yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—861no—
109#106—861no—
110#103—861no—
111#103—861no—
112#103—861no—
113#102—861no—
114#97—431no—
115#97—431no—
116#97—431no—
117C2×Q8—21no—
118C2×Q8—861no—
119C2×Q8C22⋊D4311yescharacteristic
120C2×D4C22⋊D4311yescharacteristic
121C22×C4—21no—
122C2×C8—861no—
123C2×C8—861no—
124C2×C8—861no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—861no—
132C4⋊C4—861no—
133C4⋊C4C22⋊D4311yescharacteristic
134C4⋊C4C22⋊D4311yescharacteristic
135C4⋊C4C22⋊D4311yescharacteristic
136C4⋊C4C22⋊D4311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D4311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—1722no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—1721no—
156C2×C4C2×C22⋊D4311yescharacteristic
157C2×C4C2×C22⋊D4311yescharacteristic
158C2×C4C2×C22⋊D4311yescharacteristic
159C8—862no—
160C8—1721no—
161C8—1721no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1306329411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—3441no—
175C2—81no—
176C2#1458307211yescharacteristic
177C2#1458307711yescharacteristic
178C2#1458308211yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#563C2
socleC22×C43#120
hypercenter#563D43
hypocenterC43#1664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14583309C2semidirect
2. #14583269C2semidirect
4. #14582641C2semidirect
5. #14582641C2semidirect
97. C43#1664semidirect