Finite Group Databasebeta

← #355×D47 #20245064

Subgroups — #355×D47 #20245064

Order 6016.

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

normal subgroups only

This group has 260 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
1#124×D47C211yesmaximal, characteristic
2#101×D47C212yesmaximal, complemented
3#15688920C211yesmaximal, characteristic, complemented
4#15688919C212yesmaximal, complemented
5C47×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D47C2211yescharacteristic
7C2×D4×D47C411yescharacteristic
8M16×D47—22no—
9#13094013C2211yescharacteristic
10#13094012C411yescharacteristic
11#13094011C411yescharacteristic
12#13094010—22no—
13C22⋊C4×D47—22no—
14C42×D47C411yescharacteristic
15#13093943C2212yescomplemented
16#13093942—22no—
17#124×C47C2211yescharacteristic
18#101×C47C2212yescomplemented
19C23×D47—21no—
20C2×Q8×C47C2311yescharacteristic
21C2×D4×C47C2×C411yescharacteristic
22C2×C22⋊D47—21no—
23Q8×D47—41no—
24Q8×D47—41no—
25D4×D47—41no—
26D4×D47—41no—
27C2×D188C2×C411yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47C2×C411yescharacteristic
30C2×C4×D47D412yes—
31C2×Dic94C2×C411yescharacteristic
32C2×Dic94D412yes—
33M16×C47—22no—
34C22⋊C4×C47—22no—
35C42×C47C2×C411yescharacteristic
36C22⋊Dic47—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4×Dic47—21no—
40C4×Dic47C2×C411yescharacteristic
41#10625329—22no—
42#10625324—42no—
43C8×D47—42no—
44C23×C47—21no—
45C22×D47—21no—
46C22×D47—44no—
47C22×D47—41no—
48C22×D47—41no—
49C22×D47C22⋊C411yescharacteristic
50Q8×C47—41no—
51D4×C47—41no—
52C2×C4×C47—21no—
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D412yes—
55C22⋊D47—42no—
56C2×Dic47—21no—
57C2×Dic47C22⋊C411yescharacteristic
58C2×Dic47C22⋊C412yes—
59D188—41no—
60C4×D47—22no—
61C4×D47—22no—
62C4×D47—21no—
63C4×D47—21no—
64C4×D47—42no—
65Dic94—41no—
66Dic94—42no—
67C8×C47—42no—
68C47⋊C8—42no—
69C22×C47—42no—
70C22×C47—41no—
71C22×C47C2×C22⋊C411yescharacteristic
72C2×D47—22no—
73C2×D47—42no—
74C2×D47—41no—
75C2×D47—82no—
76C2×D47—82no—
77C2×D47#9911yescharacteristic
78C2×D47#9911yescharacteristic
79C4×C47—22no—
80C4×C47—21no—
81C4×C47—41no—
82Dic47—22no—
83Dic47—21no—
84Dic47—41no—
85C2×#355—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—81no—
88C2×C47C2×#9911yescharacteristic
89D47—21no—
90D47—81no—
91D47#35512yesdirect product factor
92C2×#124—471no—
93C2×#101—472no—
94#355—471no—
95#355—472no—
96#355D4711yescharacteristic, direct product factor
97C47C2×#35511yescharacteristic, complemented, Sylow
98C22×Q8—471no—
99C22×D4—471no—
100C2×M16—942no—
101#124—471no—
102#124—471no—
103#124—471no—
104#124—942no—
105#124C2×D4711yescharacteristic
106C2×C22⋊C4—942no—
107C2×C42—471no—
108#101—472no—
109#101—942no—
110#101C2×D4712yescomplemented
111C24—941no—
112C2×Q8—471no—
113C2×Q8—472no—
114C2×Q8—1881no—
115C2×Q8—1881no—
116C2×Q8C22×D4711yescharacteristic
117C2×D4—471no—
118C2×D4—941no—
119C2×D4—1881no—
120C2×D4—1881no—
121C2×D4C4×D4711yescharacteristic
122C22×C4—471no—
123C22×C4—472no—
124C22×C4—941no—
125M16—22no—
126M16—942no—
127M16—1882no—
128C2×C8—1882no—
129C22⋊C4—22no—
130C22⋊C4—942no—
131C22⋊C4—942no—
132C22⋊C4—942no—
133C42—471no—
134C42—941no—
135C42C4×D4711yescharacteristic
136C23—21no—
137C23—471no—
138C23—941no—
139C23—1881no—
140C23—1881no—
141C23—1884no—
142Q8—41no—
143Q8—1882no—
144Q8—1881no—
145D4—41no—
146D4—1881no—
147D4—1882no—
148C2×C4—21no—
149C2×C4—471no—
150C2×C4—472no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—1882no—
157C2×C4C2×C4×D4711yescharacteristic
158C2×C4D4×D4712yes—
159C8—42no—
160C8—1882no—
161C22—42no—
162C22—41no—
163C22—471no—
164C22—471no—
165C22—942no—
166C22—3762no—
167C22—3762no—
168C22—1882no—
169C22—1881no—
170C22C22⋊C4×D4711yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—941no—
175C4—942no—
176C4—1881no—
177C2—21no—
178C2—81no—
179C2—472no—
180C2—941no—
181C2—3761no—
182C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#355C2
socleC2×C47C2×#99
hypercenter#355D47
hypocenterC47C2×#355
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. #101×D47C2semidirect
3. #15688920C2semidirect
4. #15688919C2semidirect
5. C47×#355C2semidirect
15. #13093943C22semidirect
18. #101×C47C22semidirect
91. D47#355direct (N × H)
96. #355D47direct (N × H)
97. C47C2×#355semidirect
110. #101C2×D47semidirect