Finite Group Databasebeta

← #19136279

Subgroups — #19136279

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#14583450C211yesmaximal, characteristic
2#14582882C212yesmaximal, complemented
3#14582698C211yesmaximal, characteristic, complemented
4#14582695C212yesmaximal, complemented
5C43×#356C211yesmaximal, characteristic, complemented
6C2×#10621902C411yescharacteristic
7C2×#10621902C2211yescharacteristic
8M16×D43—22no—
9#13063322C411yescharacteristic
10#13063314C411yescharacteristic
11#13063314C2211yescharacteristic
12#13063300—22no—
13#13063287—22no—
14C42×D43C411yescharacteristic
15#13063244C2212yes—
16#13063241—22no—
17C4⋊Q8×C43C2211yescharacteristic
18#101×C43C2212yes—
19C2×Q8×C43C2×C411yescharacteristic
20C2×Q8×C43C2311yescharacteristic
21#10621902—41no—
22#10621902—41no—
23#10621902—41no—
24#10621902—41no—
25C2×D172—22no—
26C2×D172—21no—
27C2×D172C2×C411yescharacteristic
28C2×D172C2×C411yescharacteristic
29C2×D172D412yes—
30C2×C4×D43—21no—
31C2×C4×D43—21no—
32C2×C4×D43C2×C411yescharacteristic
33C2×C4×D43D412yes—
34M16×C43—22no—
35C4⋊C4×C43—22no—
36C42×C43C2×C411yescharacteristic
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—22no—
39C4×Dic43—21no—
40C4×Dic43C2×C411yescharacteristic
41#10621877—22no—
42#10621872—42no—
43C8×D43—42no—
44C22×D43—21no—
45C22×D43C22⋊C412yes—
46C22×D43C22⋊C411yescharacteristic
47Q8×C43—41no—
48Q8×C43—41no—
49C2×C4×C43—21no—
50C2×C4×C43—21no—
51C2×C4×C43C22×C411yescharacteristic
52C2×C4×C43C2×D412yes—
53C2×Dic43—21no—
54C2×Dic43C22⋊C411yescharacteristic
55D172—41no—
56D172—42no—
57D172—41no—
58D172—44no—
59D172—42no—
60C4×D43—22no—
61C4×D43—22no—
62C4×D43—21no—
63C4×D43—21no—
64C4×D43—42no—
65C4×D43—41no—
66C4×D43—41no—
67C8×C43—42no—
68C43⋊C8—42no—
69C22×C43C2×C22⋊C411yescharacteristic
70C2×D43—22no—
71C2×D43—21no—
72C2×D43—41no—
73C2×D43—42no—
74C2×D43—42no—
75C2×D43—41no—
76C4×C43—22no—
77C4×C43—22no—
78C4×C43—21no—
79C4×C43—41no—
80Dic43—41no—
81Dic43#9911yescharacteristic
82Dic43#9911yescharacteristic
83#2132—431nomaximal, Sylow
84C2×C43—21no—
85C2×C43C2×#9911yescharacteristic
86D43—42no—
87D43—41no—
88D43—81no—
89#532—431no—
90#413—432no—
91#356—431no—
92#356D4311yescharacteristic, complemented
93#355—432no—
94C43#213211yescharacteristic, complemented, Sylow
95C2×#41—431no—
96C2×#41—431no—
97C2×M16—862no—
98C4⋊Q8C2×D4311yescharacteristic
99#127—431no—
100#124—431no—
101#124—431no—
102#121—862no—
103C4×D4—862no—
104C2×C42—431no—
105#101—432no—
106#101C2×D4312yes—
107#100—862no—
108#41—1721no—
109#41—1721no—
110#41—1721no—
111#41—1721no—
112C2×Q8C4×D4311yescharacteristic
113C2×Q8C22×D4311yescharacteristic
114C2×D4—431no—
115C2×D4—431no—
116C2×D4—432no—
117C2×D4—862no—
118C2×D4—861no—
119C22×C4—431no—
120C22×C4—432no—
121C22×C4—861no—
122C22×C4—861no—
123M16—22no—
124M16—862no—
125M16—1722no—
126C2×C8—1722no—
127C4⋊C4—22no—
128C22⋊C4—862no—
129C22⋊C4—862no—
130C42—431no—
131C42—861no—
132C42C4×D4311yescharacteristic
133C23—432no—
134C23—431no—
135C23—861no—
136Q8—41no—
137Q8—41no—
138D4—1722no—
139D4—1721no—
140D4—1721no—
141D4—1724no—
142D4—1722no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—431no—
146C2×C4—862no—
147C2×C4—862no—
148C2×C4—861no—
149C2×C4—861no—
150C2×C4—861no—
151C2×C4—1722no—
152C2×C4—1721no—
153C2×C4—1721no—
154C2×C4C2×C4×D4311yescharacteristic
155C2×C4D4×D4312yes—
156C8—42no—
157C8—1722no—
158C22—861no—
159C22—862no—
160C22—1722no—
161C22—1721no—
162C22—1722no—
163C22—1721no—
164C22C22⋊C4×D4311yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—431no—
170C4—431no—
171C4—1721no—
172C2—21no—
173C2—3441no—
174C2—1721no—
175C2—1722no—
176C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#356C2
socleC2×C43C2×#99
hypercenter#356D43
hypocenterC43#2132
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #14582882C2semidirect
3. #14582698C2semidirect
4. #14582695C2semidirect
5. C43×#356C2semidirect
92. #356D43semidirect
94. C43#2132semidirect