Finite Group Databasebeta

← #19136285

Subgroups — #19136285

Order 5504.

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

normal subgroups only

This group has 262 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#14583467C211yesmaximal, characteristic
2#14582882C212yesmaximal, complemented
3#14582696C211yesmaximal, characteristic, complemented
4#14582695C212yesmaximal, complemented
5C43×#355C211yesmaximal, characteristic, complemented
6C2×#10621902C2211yescharacteristic
7C2×D4×D43C411yescharacteristic
8M16×D43—22no—
9#13063322C411yescharacteristic
10#13063321C411yescharacteristic
11#13063314C2211yescharacteristic
12#13063298—22no—
13#13063295—22no—
14#13063282C411yescharacteristic
15#13063244C2212yescomplemented
16#13063241—22no—
17#124×C43C2211yescharacteristic
18#101×C43C2212yescomplemented
19C23×D43—21no—
20C2×Q8×C43C2311yescharacteristic
21C2×D4×C43C2×C411yescharacteristic
22C2×C22⋊D43—21no—
23C2×C22⋊D43—22no—
24#10621902—42no—
25D4×D43—42no—
26C2×D172—22no—
27C2×D172C2×C411yescharacteristic
28C2×D172C2×C411yescharacteristic
29C2×D172D412yes—
30C2×C4×D43C2×C411yescharacteristic
31C2×C4×D43D412yes—
32M16×C43—22no—
33C22⋊C4×C43—22no—
34C42×C43C2×C411yescharacteristic
35(C2×D43)⋊C4—22no—
36(C2×D43)⋊C4—21no—
37Dic43⋊C4—21no—
38C4×Dic43C2×C411yescharacteristic
39#10621877—22no—
40#10621872—42no—
41C8×D43—42no—
42C23×C43—21no—
43C22×D43—21no—
44C22×D43—42no—
45C22×D43—82no—
46C22×D43C22⋊C411yescharacteristic
47C22×D43C22⋊C412yes—
48Q8×C43—41no—
49D4×C43—41no—
50C2×C4×C43—21no—
51C2×C4×C43C22×C411yescharacteristic
52C2×C4×C43C2×D412yes—
53C22⋊D43—42no—
54C22⋊D43—82no—
55C2×Dic43—21no—
56C2×Dic43C22⋊C411yescharacteristic
57D172—41no—
58D172—42no—
59D172—41no—
60D172—82no—
61C4×D43—22no—
62C4×D43—22no—
63C4×D43—22no—
64C8×C43—42no—
65C43⋊C8—42no—
66C22×C43—42no—
67C22×C43—41no—
68C22×C43C2×C22⋊C411yescharacteristic
69C2×D43—21no—
70C2×D43—22no—
71C2×D43—41no—
72C2×D43—42no—
73C2×D43—42no—
74C2×D43—41no—
75C2×D43—84no—
76C4×C43—22no—
77C4×C43—21no—
78C4×C43—41no—
79Dic43—41no—
80Dic43#9912yes—
81#2134—431nomaximal, Sylow
82C2×C43—21no—
83C2×C43—81no—
84C2×C43C2×#9911yescharacteristic
85D43—42no—
86D43—41no—
87D43—81no—
88#535—431no—
89#413—432no—
90#355—431no—
91#355—432no—
92#355D4311yescharacteristic, complemented
93C43#213411yescharacteristic, complemented, Sylow
94C2×#41—431no—
95C22×D4—431no—
96C2×M16—862no—
97#127—431no—
98#127—431no—
99#124—431no—
100#124C2×D4311yescharacteristic
101#121—862no—
102#120—862no—
103#117—431no—
104#101—432no—
105#101C2×D4312yescomplemented
106#100—862no—
107C24—861no—
108#41—1722no—
109C2×Q8C22×D4311yescharacteristic
110C2×D4—431no—
111C2×D4—431no—
112C2×D4—432no—
113C2×D4—862no—
114C2×D4—861no—
115C2×D4—862no—
116C2×D4—1722no—
117C2×D4C4×D4311yescharacteristic
118C22×C4—431no—
119C22×C4—432no—
120M16—22no—
121M16—862no—
122M16—1722no—
123C2×C8—1722no—
124C4⋊C4—861no—
125C22⋊C4—22no—
126C22⋊C4—861no—
127C22⋊C4—862no—
128C42—431no—
129C42C4×D4311yescharacteristic
130C23—21no—
131C23—431no—
132C23—432no—
133C23—861no—
134C23—3442no—
135C23—1722no—
136Q8—41no—
137D4—41no—
138D4—3442no—
139D4—3442no—
140D4—1722no—
141D4—1721no—
142D4—1721no—
143D4—1722no—
144C2×C4—21no—
145C2×C4—431no—
146C2×C4—862no—
147C2×C4—862no—
148C2×C4—862no—
149C2×C4—861no—
150C2×C4C2×C4×D4311yescharacteristic
151C2×C4D4×D4312yes—
152C8—42no—
153C8—1722no—
154C22—42no—
155C22—41no—
156C22—861no—
157C22—862no—
158C22—3444no—
159C22—1722no—
160C22—1722no—
161C22—1721no—
162C22—1721no—
163C22C22⋊C4×D4311yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—432no—
168C4—1721no—
169C2—21no—
170C2—81no—
171C2—3441no—
172C2—1721no—
173C2—1722no—
174C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#355C2
socleC2×C43C2×#99
hypercenter#355D43
hypocenterC43#2134
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #14582882C2semidirect
3. #14582696C2semidirect
4. #14582695C2semidirect
5. C43×#355C2semidirect
15. #13063244C22semidirect
18. #101×C43C22semidirect
92. #355D43semidirect
93. C43#2134semidirect
105. #101C2×D43semidirect