Finite Group Databasebeta

← #19133912

Subgroups — #19133912

Order 5504.

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

normal subgroups only

This group has 208 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#14583294C211yesmaximal, characteristic, complemented
3#14583258C211yesmaximal, characteristic, complemented
4#14582641C211yesmaximal, characteristic, complemented
5#14582639C211yesmaximal, characteristic, complemented
6#14582639C211yesmaximal, characteristic, complemented
7C43×#562C211yesmaximal, characteristic
8C2×#10621885—21no—
9C2×#10621883—21no—
10#13063325C2211yescharacteristic
11#13063258—21no—
12#13063256—21no—
13#13063249—21no—
14#13063246—21no—
15#13063236C2211yescharacteristic
16#13063236C2211yescharacteristic
17#13063236C2211yescharacteristic
18#125×C43C2211yescharacteristic
19#124×C43C2211yescharacteristic
20#124×C43C2211yescharacteristic
21#123×C43—21no—
22#123×C43—21no—
23C22⋊Q8×C43—21no—
24C22⋊Q8×C43—21no—
25#121×C43—21no—
26#121×C43—21no—
27C2×Q8×C43D411yescharacteristic
28C2×Q8×C43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43D411yescharacteristic
32C2×D4×C43D411yescharacteristic
33C22×C4×C43—21no—
34C22×C4×C43—21no—
35C2×Dic86—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
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—
47C22⋊C4×C43—21no—
48C42×C43C2311yescharacteristic
49#10621885—42no—
50#10621883—42no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53C2×C43⋊C8—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C23×C43—21no—
58Q8×C43—41no—
59Q8×C43—41no—
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—81no—
63D4×C43—81no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—81no—
69C2×C4×C43—81no—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×Dic43—41no—
74Dic86—41no—
75Dic86—41no—
76C43⋊C8—22no—
77C43⋊C8—22no—
78C43⋊C8—41no—
79C22×C43—41no—
80C22×C43—41no—
81C22×C43—41no—
82C22×C43—41no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43#12011yescharacteristic
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C43—41no—
90C4×C43—41no—
91C4×C43—41no—
92C4×C43—41no—
93Dic43—81no—
94#1661—431nomaximal, Sylow
95C2×C43—81no—
96C2×C43—81no—
97C2×C43#45311yescharacteristic
98C2×C43#45511yescharacteristic
99C2×C43#45611yescharacteristic
100#562D4311yescharacteristic
101#501—431no—
102#497—431no—
103#489—431no—
104#330—431no—
105#329—431no—
106#329—431no—
107C43#166111yescharacteristic, complemented, Sylow
108C2×Q16—861no—
109C2×SD16—861no—
110C4⋊Q8—431no—
111#125C2×D4311yescharacteristic
112#124C2×D4311yescharacteristic
113#124C2×D4311yescharacteristic
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8—21no—
118#121—21no—
119#121—21no—
120#107—861no—
121#106—861no—
122#103—861no—
123#102—861no—
124#97—431no—
125#97—431no—
126#97—431no—
127C2×Q8—861no—
128C2×Q8C22⋊D4311yescharacteristic
129C2×Q8C22⋊D4311yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D4311yescharacteristic
133C2×D4C22⋊D4311yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—1722no—
137SD16—1722no—
138C2×C8—861no—
139C2×C8—861no—
140C2×C8—861no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4C22⋊D4311yescharacteristic
148C4⋊C4C22⋊D4311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D4311yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—1721no—
161Q8—1721no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—1721no—
173C2×C4C2×C22⋊D4311yescharacteristic
174C2×C4C2×C22⋊D4311yescharacteristic
175C2×C4C2×C22⋊D4311yescharacteristic
176C8—862no—
177C8—862no—
178C8—1721no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#1306329411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—3441no—
194C2—81no—
195C2—81no—
196C2#1458306711yescharacteristic
197C2#1458307711yescharacteristic
198C2#1458308211yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#562C2
socleC22×C43#120
hypercenter#562D43
hypocenterC43#1661
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14583309C2semidirect
2. #14583294C2semidirect
3. #14583258C2semidirect
4. #14582641C2semidirect
5. #14582639C2semidirect
6. #14582639C2semidirect
107. C43#1661semidirect