Finite Group Databasebeta

← #20245078

Subgroups — #20245078

Order 6016.

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#15689691C211yesmaximal, characteristic
2#15689106C212yesmaximal, complemented
3#15688920C211yesmaximal, characteristic, complemented
4#15688919C212yesmaximal, complemented
5C47×#355C211yesmaximal, characteristic, complemented
6C2×#10625354C2211yescharacteristic
7C2×D4×D47C411yescharacteristic
8M16×D47—22no—
9#13094021C411yescharacteristic
10#13094020C411yescharacteristic
11#13094013C2211yescharacteristic
12#13093997—22no—
13#13093994—22no—
14#13093981C411yescharacteristic
15#13093943C2212yescomplemented
16#13093940—22no—
17#124×C47C2211yescharacteristic
18#101×C47C2212yescomplemented
19C23×D47—21no—
20C2×Q8×C47C2311yescharacteristic
21C2×D4×C47C2×C411yescharacteristic
22C2×C22⋊D47—22no—
23C2×C22⋊D47—21no—
24#10625354—42no—
25D4×D47—42no—
26C2×D188—22no—
27C2×D188C2×C411yescharacteristic
28C2×D188C2×C411yescharacteristic
29C2×D188D412yes—
30C2×C4×D47C2×C411yescharacteristic
31C2×C4×D47D412yes—
32M16×C47—22no—
33C22⋊C4×C47—22no—
34C42×C47C2×C411yescharacteristic
35(C2×D47)⋊C4—21no—
36(C2×D47)⋊C4—22no—
37Dic47⋊C4—21no—
38C4×Dic47C2×C411yescharacteristic
39#10625329—22no—
40#10625324—42no—
41C8×D47—42no—
42C23×C47—21no—
43C22×D47—21no—
44C22×D47—42no—
45C22×D47—82no—
46C22×D47C22⋊C411yescharacteristic
47C22×D47C22⋊C412yes—
48Q8×C47—41no—
49D4×C47—41no—
50C2×C4×C47—21no—
51C2×C4×C47C22×C411yescharacteristic
52C2×C4×C47C2×D412yes—
53C22⋊D47—42no—
54C22⋊D47—82no—
55C2×Dic47—21no—
56C2×Dic47C22⋊C411yescharacteristic
57D188—41no—
58D188—42no—
59D188—41no—
60D188—82no—
61C4×D47—22no—
62C4×D47—22no—
63C4×D47—22no—
64C8×C47—42no—
65C47⋊C8—42no—
66C22×C47—42no—
67C22×C47—41no—
68C22×C47C2×C22⋊C411yescharacteristic
69C2×D47—21no—
70C2×D47—22no—
71C2×D47—42no—
72C2×D47—41no—
73C2×D47—42no—
74C2×D47—41no—
75C2×D47—84no—
76C4×C47—22no—
77C4×C47—21no—
78C4×C47—41no—
79Dic47—41no—
80Dic47#9912yes—
81#2134—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—81no—
84C2×C47C2×#9911yescharacteristic
85D47—42no—
86D47—41no—
87D47—81no—
88#535—471no—
89#413—472no—
90#355—471no—
91#355—472no—
92#355D4711yescharacteristic, complemented
93C47#213411yescharacteristic, complemented, Sylow
94C2×#41—471no—
95C22×D4—471no—
96C2×M16—942no—
97#127—471no—
98#127—471no—
99#124—471no—
100#124C2×D4711yescharacteristic
101#121—942no—
102#120—942no—
103#117—471no—
104#101—472no—
105#101C2×D4712yescomplemented
106#100—942no—
107C24—941no—
108#41—1882no—
109C2×Q8C22×D4711yescharacteristic
110C2×D4—471no—
111C2×D4—471no—
112C2×D4—472no—
113C2×D4—942no—
114C2×D4—941no—
115C2×D4—942no—
116C2×D4—1882no—
117C2×D4C4×D4711yescharacteristic
118C22×C4—471no—
119C22×C4—472no—
120M16—22no—
121M16—942no—
122M16—1882no—
123C2×C8—1882no—
124C4⋊C4—941no—
125C22⋊C4—22no—
126C22⋊C4—941no—
127C22⋊C4—942no—
128C42—471no—
129C42C4×D4711yescharacteristic
130C23—21no—
131C23—471no—
132C23—472no—
133C23—941no—
134C23—3762no—
135C23—1882no—
136Q8—41no—
137D4—41no—
138D4—3762no—
139D4—3762no—
140D4—1882no—
141D4—1881no—
142D4—1881no—
143D4—1882no—
144C2×C4—21no—
145C2×C4—471no—
146C2×C4—942no—
147C2×C4—942no—
148C2×C4—942no—
149C2×C4—941no—
150C2×C4C2×C4×D4711yescharacteristic
151C2×C4D4×D4712yes—
152C8—42no—
153C8—1882no—
154C22—42no—
155C22—41no—
156C22—941no—
157C22—942no—
158C22—3764no—
159C22—1882no—
160C22—1882no—
161C22—1881no—
162C22—1881no—
163C22C22⋊C4×D4711yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—472no—
168C4—1881no—
169C2—21no—
170C2—81no—
171C2—3761no—
172C2—1881no—
173C2—1882no—
174C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#355C2
socleC2×C47C2×#99
hypercenter#355D47
hypocenterC47#2134
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #15689106C2semidirect
3. #15688920C2semidirect
4. #15688919C2semidirect
5. C47×#355C2semidirect
15. #13093943C22semidirect
18. #101×C47C22semidirect
92. #355D47semidirect
93. C47#2134semidirect
105. #101C2×D47semidirect