Finite Group Databasebeta

← #19133797

Subgroups — #19133797

Order 5504.

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

normal subgroups only

This group has 250 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#14583570C211yesmaximal, characteristic
2#14583246C211yesmaximal, characteristic, complemented
3#14583185C211yesmaximal, characteristic, complemented
4#14583104C211yesmaximal, characteristic, complemented
5#14582642C211yesmaximal, characteristic, complemented
6#14582631C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621898—21no—
9C2×#10621883—21no—
10#13063325C2211yescharacteristic
11#13063322C2211yescharacteristic
12#13063321—21no—
13#13063299—21no—
14#13063298—22no—
15C4×Dic86C2211yescharacteristic
16#13063287—21no—
17#13063257—21no—
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063250—21no—
20#13063248—21no—
21#13063247—22no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×D4×C43D411yescharacteristic
26C22×C4×C43—21no—
27C2×C22⋊D43—22no—
28C2×C22⋊D43—22no—
29#10621898—42no—
30#10621898—42no—
31C2×D172—21no—
32C2×D172—21no—
33C2×D172D412yes—
34C2×C4×D43—22no—
35C2×Dic86—21no—
36C2×Dic86D411yescharacteristic
37C2×C8×C43—21no—
38C2×C8×C43—21no—
39C4⋊C4×C43D411yescharacteristic
40C22⋊C4×C43—21no—
41C42×C43C2311yescharacteristic
42#10621883—42no—
43(C2×D43)⋊C4—22no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43D411yescharacteristic
47Dic43⋊C4—21no—
48C4×Dic43—21no—
49C2×C43⋊C8—21no—
50C23×C43—21no—
51C22×D43—22no—
52D4×C43—21no—
53D4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C22⋊D43—44no—
61C22⋊D43—82no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—41no—
65D172—42no—
66D172—41no—
67D172—41no—
68D172—41no—
69D172—41no—
70C4×D43—44no—
71Dic86—21no—
72Dic86—41no—
73Dic86—41no—
74Dic86SD1612yescomplemented
75C8×C43—41no—
76C8×C43—41no—
77C43⋊C8—41no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43—41no—
81C22×C43#12011yescharacteristic
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—42no—
85C4×C43—21no—
86C4×C43—41no—
87C4×C43C2×SD1611yescharacteristic
88C4×C43#13511yescharacteristic
89C4×C43AGL(1,ℤ/8)11yescharacteristic
90C4×C43AGL(1,ℤ/8)11yescharacteristic
91Dic43—22no—
92Dic43—41no—
93Dic43—81no—
94#1642—431nomaximal, Sylow
95C2×C43—81no—
96C2×C43#44911yescharacteristic
97C2×C43#45011yescharacteristic
98C2×C43#45511yescharacteristic
99D43—82no—
100#550—431no—
101#486—431no—
102#475—431no—
103#461—431no—
104#331—431no—
105Q8⋊C8—431no—
106D4⋊C8D4311yescharacteristic, complemented
107C43#164211yescharacteristic, complemented, Sylow
108C2×#41—861no—
109C2×SD16—861no—
110C4⋊Q8—431no—
111#127—431no—
112#127—861no—
113#121—862no—
114#121—861no—
115C4×Q8—431no—
116C4×D4—861no—
117C4×D4C2×D4311yescharacteristic
118#106—861no—
119C4⋊C8—431no—
120C4⋊C8C2×D4311yescharacteristic
121#103—861no—
122#103—861no—
123#102—862no—
124C4×C8C2×D4311yescharacteristic
125#41—1722no—
126#41—1722no—
127C2×Q8—431no—
128C2×Q8—861no—
129C2×D4—432no—
130C2×D4—862no—
131C2×D4—862no—
132C2×D4—861no—
133C2×D4—861no—
134C2×D4D17211yescharacteristic
135C22×C4—21no—
136C22×C4—862no—
137SD16—1722no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—861no—
141C4⋊C4—431no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4D17211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—862no—
148C42—861no—
149C42C22×D4311yescharacteristic
150C23—21no—
151C23—862no—
152Q8—432no—
153Q8—861no—
154Q8—1721no—
155Q8—1721no—
156D4—21no—
157D4—21no—
158D4—3442no—
159D4—1722no—
160D4—1724no—
161D4—1721no—
162D4—1721no—
163D4—1721no—
164D4—1721no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—861no—
169C2×C4—861no—
170C2×C4—1724no—
171C2×C4—1721no—
172C2×C4C2×D17211yescharacteristic
173C2×C4D4×D4311yescharacteristic
174C2×C4D4×D4311yescharacteristic
175C8—41no—
176C8—41no—
177C8—1721no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1722no—
182C22—1722no—
183C22—1722no—
184C22#1306329511yescharacteristic
185C4—21no—
186C4—41no—
187C4—862no—
188C4—3441no—
189C4—1721no—
190C4SD16×D4311yescharacteristic
191C4#1306334711yescharacteristic
192C4#1306334911yescharacteristic
193C4#1306335311yescharacteristic
194C2—81no—
195C2—3442no—
196C2#1458304611yescharacteristic
197C2#1458305111yescharacteristic
198C2#1458307811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1642
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. #14583246C2semidirect
3. #14583185C2semidirect
4. #14583104C2semidirect
5. #14582642C2semidirect
6. #14582631C2semidirect
7. C43×D4⋊C8C2semidirect
74. Dic86SD16semidirect
106. D4⋊C8D43semidirect
107. C43#1642semidirect