Finite Group Databasebeta

← #356×D47 #20245067

Subgroups — #356×D47 #20245067

Order 6016.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C4⋊Q8×D47C211yesmaximal, characteristic
2#101×D47C212yesmaximal
3#15688922C211yesmaximal, characteristic, complemented
4#15688921C212yesmaximal, complemented
5C47×#356C211yesmaximal, characteristic, complemented
6C2×Q8×D47C411yescharacteristic
7C2×Q8×D47C2211yescharacteristic
8M16×D47—22no—
9#13094024C411yescharacteristic
10#13094023—22no—
11#13094022C411yescharacteristic
12#13094022C2211yescharacteristic
13C4⋊C4×D47—22no—
14C42×D47C411yescharacteristic
15#13093943C2212yes—
16#13093942—22no—
17C4⋊Q8×C47C2211yescharacteristic
18#101×C47C2212yes—
19C2×Q8×C47C2×C411yescharacteristic
20C2×Q8×C47C2311yescharacteristic
21Q8×D47—41no—
22Q8×D47—41no—
23Q8×D47—41no—
24Q8×D47—41no—
25C2×C4×D47—21no—
26C2×C4×D47—21no—
27C2×C4×D47C2×C411yescharacteristic
28C2×C4×D47D412yes—
29C2×Dic94—21no—
30C2×Dic94C2×C411yescharacteristic
31C2×Dic94C2×C411yescharacteristic
32C2×Dic94D412yes—
33M16×C47—22no—
34C4⋊C4×C47—22no—
35C42×C47C2×C411yescharacteristic
36C4⋊Dic47—22no—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47—21no—
40C4×Dic47C2×C411yescharacteristic
41#10625329—22no—
42#10625324—42no—
43C8×D47—42no—
44C22×D47C22⋊C411yescharacteristic
45Q8×C47—41no—
46Q8×C47—41no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C2×D412yes—
51C2×Dic47—21no—
52C2×Dic47—21no—
53C2×Dic47C22⋊C411yescharacteristic
54C2×Dic47C22⋊C412yes—
55C4×D47—24no—
56C4×D47—22no—
57C4×D47—22no—
58C4×D47—21no—
59C4×D47—21no—
60C4×D47—41no—
61C4×D47—41no—
62Dic94—41no—
63Dic94—42no—
64Dic94—42no—
65Dic94—41no—
66C8×C47—42no—
67C47⋊C8—42no—
68C22×C47C2×C22⋊C411yescharacteristic
69C2×D47—22no—
70C2×D47#9911yescharacteristic
71C2×D47#9911yescharacteristic
72C4×C47—22no—
73C4×C47—22no—
74C4×C47—21no—
75C4×C47—41no—
76Dic47—22no—
77Dic47—21no—
78Dic47—22no—
79Dic47—41no—
80C2×#356—471nomaximal, Sylow
81C2×C47—21no—
82C2×C47C2×#9911yescharacteristic
83D47—21no—
84D47#35612yesdirect product factor
85C2×C4⋊Q8—471no—
86C2×#101—472no—
87#356—471no—
88#356—472no—
89#356D4711yescharacteristic, direct product factor
90C47C2×#35611yescharacteristic, complemented, Sylow
91C22×Q8—471no—
92C22×Q8—471no—
93C2×M16—942no—
94C4⋊Q8—471no—
95C4⋊Q8—471no—
96C4⋊Q8—471no—
97C4⋊Q8—942no—
98C4⋊Q8C2×D4711yescharacteristic
99C2×C4⋊C4—942no—
100C2×C42—471no—
101#101—472no—
102#101—942no—
103#101C2×D4712yes—
104C2×Q8—471no—
105C2×Q8—472no—
106C2×Q8—471no—
107C2×Q8—941no—
108C2×Q8—1881no—
109C2×Q8—1881no—
110C2×Q8—1881no—
111C2×Q8—1881no—
112C2×Q8C4×D4711yescharacteristic
113C2×Q8C22×D4711yescharacteristic
114C22×C4—471no—
115C22×C4—472no—
116C22×C4—941no—
117C22×C4—941no—
118M16—22no—
119M16—942no—
120M16—1882no—
121C2×C8—1882no—
122C4⋊C4—22no—
123C4⋊C4—942no—
124C4⋊C4—942no—
125C4⋊C4—942no—
126C42—471no—
127C42—941no—
128C42C4×D4711yescharacteristic
129C23—471no—
130Q8—41no—
131Q8—41no—
132Q8—1882no—
133Q8—1881no—
134Q8—1881no—
135Q8—1882no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—471no—
139C2×C4—472no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4—941no—
143C2×C4—941no—
144C2×C4—944no—
145C2×C4—941no—
146C2×C4—941no—
147C2×C4—1881no—
148C2×C4—1881no—
149C2×C4C2×C4×D4711yescharacteristic
150C2×C4D4×D4712yes—
151C8—42no—
152C8—1882no—
153C22—471no—
154C22—471no—
155C22—942no—
156C22C22⋊C4×D4711yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—942no—
162C4—941no—
163C4—942no—
164C4—1881no—
165C2—21no—
166C2—472no—
167C2—941no—
168C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#356C2
socleC2×C47C2×#99
hypercenter#356D47
hypocenterC47C2×#356
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. D47#356direct (N × H)
89. #356D47direct (N × H)
90. C47C2×#356semidirect