Finite Group Databasebeta

← #20245061

Subgroups — #20245061

Order 6016.

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

normal subgroups only

This group has 238 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#15689693C211yesmaximal, characteristic
2#15689095C212yesmaximal
3#15688918C211yesmaximal, characteristic, complemented
4#15688917C212yesmaximal, complemented
5C47×#354C211yesmaximal, characteristic, complemented
6C2×#10625352C2211yescharacteristic
7C2×Q8×D47C411yescharacteristic, complemented
8#13094024C411yescharacteristic, complemented
9#13094022C411yescharacteristic, complemented
10#13094011C2211yescharacteristic
11#13094006—22no—
12#13094001—22no—
13#13093981C411yescharacteristic, complemented
14#13093980—22no—
15#13093939C2212yes—
16#13093938—22no—
17#124×C47C2211yescharacteristic
18#99×C47C2212yes—
19C2×Q8×C47C2×C411yescharacteristic
20C2×D4×C47C2311yescharacteristic
21C2×C22⋊D47D412yes—
22C22×Dic47D412yes—
23Q8×D47—42no—
24#10625352—42no—
25C2×C4×D47—21no—
26C2×C4×D47C2×C411yescharacteristic
27C2×Dic94—21no—
28C2×Dic94C2×C411yescharacteristic
29C2×Dic94C2×C411yescharacteristic
30C22⋊C4×C47—22no—
31C22⋊C4×C47—22no—
32C42×C47C2×C411yescharacteristic
33C22⋊Dic47—22no—
34C22⋊Dic47—22no—
35(C2×D47)⋊C4—21no—
36C4⋊Dic47—22no—
37Dic47⋊C4—21no—
38Dic47⋊C4—22no—
39Dic47⋊C4—42no—
40C4×Dic47—42no—
41C4×Dic47C2×C411yescharacteristic
42C23×C47C2×D412yes—
43C22×D47C22⋊C411yescharacteristic
44Q8×C47—41no—
45D4×C47—41no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—42no—
49C2×C4×C47C22×C411yescharacteristic
50C22⋊D47—42no—
51C2×Dic47—22no—
52C2×Dic47—22no—
53C2×Dic47—21no—
54C2×Dic47—21no—
55C2×Dic47—42no—
56C2×Dic47C22⋊C412yes—
57C2×Dic47C22⋊C411yescharacteristic
58C4×D47—22no—
59C4×D47—42no—
60Dic94—41no—
61Dic94—42no—
62Dic94—41no—
63C22×C47—22no—
64C22×C47—42no—
65C22×C47C2×C22⋊C411yescharacteristic
66C2×D47—21no—
67C2×D47—41no—
68C4×C47—21no—
69C4×C47—41no—
70C4×C47—41no—
71C4×C47—82no—
72Dic47—22no—
73Dic47—41no—
74Dic47—41no—
75Dic47—82no—
76Dic47#9912yes—
77#2129—471nomaximal, Sylow
78C2×C47—21no—
79C2×C47—42no—
80C2×C47C2×#9911yescharacteristic
81D47—41no—
82#536—471no—
83#410—472no—
84#354—471no—
85#354—472no—
86#354D4711yescharacteristic, complemented
87C47#212911yescharacteristic, complemented, Sylow
88C2×#41—471no—
89C22×Q8—471no—
90C4⋊Q8—471no—
91C4⋊Q8—471no—
92#124—471no—
93#124C2×D4711yescharacteristic
94#123—942no—
95C22⋊Q8—942no—
96#117—471no—
97#117—942no—
98#99—472no—
99#99—942no—
100#99C2×D4712yes—
101#41—1882no—
102C2×Q8—471no—
103C2×Q8—471no—
104C2×Q8—941no—
105C2×Q8—1882no—
106C2×Q8C4×D4711yescharacteristic
107C2×D4—472no—
108C2×D4C22×D4711yescharacteristic
109C22×C4—472no—
110C22×C4—471no—
111C22×C4—941no—
112C4⋊C4—941no—
113C4⋊C4—942no—
114C4⋊C4—942no—
115C4⋊C4—1882no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—941no—
119C22⋊C4—942no—
120C22⋊C4—942no—
121C42—471no—
122C42—1882no—
123C42C4×D4711yescharacteristic
124C23—471no—
125C23D4×D4712yes—
126Q8—41no—
127Q8—1881no—
128Q8—1881no—
129Q8—1882no—
130D4—41no—
131D4—1882no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—471no—
136C2×C4—472no—
137C2×C4—942no—
138C2×C4—942no—
139C2×C4—942no—
140C2×C4—941no—
141C2×C4—941no—
142C2×C4—1882no—
143C2×C4—1882no—
144C2×C4C2×C4×D4711yescharacteristic
145C22—22no—
146C22—42no—
147C22—941no—
148C22—1881no—
149C22C22⋊C4×D4711yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—472no—
155C4—942no—
156C4—3762no—
157C4—1881no—
158C4—1881no—
159C2—21no—
160C2—42no—
161C2—1881no—
162C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#354C2
socleC2×C47C2×#99
hypercenter#354D47
hypocenterC47#2129
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #15688918C2semidirect
4. #15688917C2semidirect
5. C47×#354C2semidirect
7. C2×Q8×D47C4semidirect
8. #13094024C4semidirect
9. #13094022C4semidirect
13. #13093981C4semidirect
86. #354D47semidirect
87. C47#2129semidirect