Finite Group Databasebeta

← #20245081

Subgroups — #20245081

Order 6016.

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

normal subgroups only

This group has 230 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#15689698C211yesmaximal, characteristic
2#15689106C212yesmaximal
3#15688922C211yesmaximal, characteristic, complemented
4#15688921C212yesmaximal, complemented
5C47×#356C211yesmaximal, characteristic, complemented
6C2×#10625354C2211yescharacteristic
7C2×Q8×D47C411yescharacteristic
8M16×D47—22no—
9#13094022C2211yescharacteristic
10#13094013C411yescharacteristic
11#13094012C411yescharacteristic
12#13094009—22no—
13#13094002—22no—
14#13093981C411yescharacteristic
15#13093943C2212yes—
16#13093940—22no—
17C4⋊Q8×C47C2211yescharacteristic
18#101×C47C2212yes—
19C2×Q8×C47C2×C411yescharacteristic
20C2×Q8×C47C2311yescharacteristic
21#10625354—42no—
22Q8×D47—42no—
23C2×D188C2×C411yescharacteristic
24C2×D188D412yes—
25C2×C4×D47—21no—
26C2×C4×D47C2×C411yescharacteristic
27C2×C4×D47D412yes—
28C2×Dic94—21no—
29C2×Dic94C2×C411yescharacteristic
30M16×C47—22no—
31C4⋊C4×C47—22no—
32C42×C47C2×C411yescharacteristic
33(C2×D47)⋊C4—21no—
34(C2×D47)⋊C4—22no—
35(C2×D47)⋊C4—22no—
36Dic47⋊C4—22no—
37Dic47⋊C4—21no—
38C4×Dic47C2×C411yescharacteristic
39#10625329—22no—
40#10625324—42no—
41C8×D47—42no—
42C22×D47C22⋊C412yes—
43C22×D47C22⋊C411yescharacteristic
44Q8×C47—41no—
45Q8×C47—41no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D412yes—
50C2×Dic47—21no—
51C2×Dic47—21no—
52C2×Dic47C22⋊C411yescharacteristic
53D188—41no—
54D188—42no—
55C4×D47—22no—
56C4×D47—22no—
57C4×D47—22no—
58C4×D47—42no—
59Dic94—42no—
60Dic94—41no—
61C8×C47—42no—
62C47⋊C8—42no—
63C22×C47C2×C22⋊C411yescharacteristic
64C2×D47—21no—
65C2×D47—22no—
66C2×D47—42no—
67C2×D47—41no—
68C4×C47—22no—
69C4×C47—21no—
70C4×C47—41no—
71C4×C47—41no—
72Dic47—41no—
73Dic47—41no—
74Dic47#9912yes—
75#2135—471nomaximal, Sylow
76C2×C47—21no—
77C2×C47C2×#9911yescharacteristic
78D47—41no—
79D47—42no—
80#536—471no—
81#413—472no—
82#356—471no—
83#356—472no—
84#356D4711yescharacteristic, complemented
85C47#213511yescharacteristic, complemented, Sylow
86C2×#41—471no—
87C22×Q8—471no—
88C2×M16—942no—
89C4⋊Q8—471no—
90C4⋊Q8C2×D4711yescharacteristic
91#124—471no—
92#124—471no—
93#123—942no—
94C22⋊Q8—942no—
95#117—471no—
96#101—472no—
97#101C2×D4712yes—
98#100—942no—
99#41—1882no—
100C2×Q8—471no—
101C2×Q8—941no—
102C2×Q8—1882no—
103C2×Q8C4×D4711yescharacteristic
104C2×Q8C22×D4711yescharacteristic
105C2×D4—471no—
106C2×D4—472no—
107C22×C4—471no—
108C22×C4—472no—
109C22×C4—941no—
110M16—22no—
111M16—942no—
112M16—1882no—
113C2×C8—1882no—
114C4⋊C4—22no—
115C4⋊C4—941no—
116C4⋊C4—942no—
117C22⋊C4—941no—
118C22⋊C4—942no—
119C22⋊C4—942no—
120C42—471no—
121C42C4×D4711yescharacteristic
122C23—472no—
123C23—471no—
124Q8—41no—
125Q8—41no—
126Q8—1881no—
127Q8—1882no—
128D4—1882no—
129D4—1881no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—471no—
133C2×C4—942no—
134C2×C4—942no—
135C2×C4—942no—
136C2×C4—941no—
137C2×C4—941no—
138C2×C4—1882no—
139C2×C4C2×C4×D4711yescharacteristic
140C2×C4D4×D4712yes—
141C8—42no—
142C8—1882no—
143C22—941no—
144C22—942no—
145C22—1882no—
146C22—1881no—
147C22C22⋊C4×D4711yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—472no—
153C4—1881no—
154C4—1881no—
155C2—21no—
156C2—1881no—
157C2—1882no—
158C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#356C2
socleC2×C47C2×#99
hypercenter#356D47
hypocenterC47#2135
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #15688922C2semidirect
4. #15688921C2semidirect
5. C47×#356C2semidirect
84. #356D47semidirect
85. C47#2135semidirect