Finite Group Databasebeta

← #20245075

Subgroups — #20245075

Order 6016.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689697C211yesmaximal, characteristic
2C2×#13093943C211yesmaximal, characteristic, complemented
3#15688921C212yesmaximal, complemented
4#15688919C212yesmaximal, complemented
5C2×#101×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic
7C2×#10625329—21no—
8#13094022C411yescharacteristic
9#13094022C2211yescharacteristic
10#13094013C411yescharacteristic
11#13094013C2211yescharacteristic
12#13094007—21no—
13#13094007—21no—
14#13094000—21no—
15#13094000—21no—
16#13093983C411yescharacteristic
17#13093943—21no—
18#13093943C2212yes—
19C22×Q8×C47C2211yescharacteristic
20C2×M16×C47—21no—
21#101×C47—21no—
22#101×C47C2212yes—
23C2×Q8×C47—41no—
24C2×Q8×C47—41no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×Q8×C47D411yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C2×Q8×C47C2311yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C2×C22⋊D47—21no—
33#10625350—41no—
34#10625350—41no—
35C2×D188C2×C411yescharacteristic
36C2×C4×D47—21no—
37C2×Dic94C2×C411yescharacteristic
38M16×C47—22no—
39M16×C47—41no—
40C2×C8×C47—41no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46C4⋊Dic47—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47C2×C411yescharacteristic
53#10625329—22no—
54#10625329—41no—
55C2×C47⋊C8—41no—
56C23×C47C22⋊C411yescharacteristic
57C22×D47—21no—
58Q8×C47—41no—
59Q8×C47—41no—
60Q8×C47—41no—
61Q8×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22⋊C411yescharacteristic
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C22⋊D47—41no—
75C22⋊D47—41no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79D188—41no—
80C4×D47—42no—
81Dic94—41no—
82C8×C47—42no—
83C47⋊C8—42no—
84C22×C47—41no—
85C22×C47#9911yescharacteristic
86C22×C47#9911yescharacteristic
87C22×C47C2×C22⋊C411yescharacteristic
88C2×D47—42no—
89C2×D47—41no—
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—21no—
96Dic47—41no—
97Dic47—41no—
98Dic47—41no—
99#2133—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47—21no—
103C2×C47C2×#9911yescharacteristic
104D47—81no—
105#536—471no—
106C2×#101—471no—
107C2×#101D4711yescharacteristic, complemented
108#356—472no—
109#355—472no—
110C47#213311yescharacteristic, complemented, Sylow
111C2×#41—471no—
112C22×Q8C2×D4711yescharacteristic
113C2×M16—21no—
114C2×M16—941no—
115C4⋊Q8—471no—
116C4⋊Q8—471no—
117#124—471no—
118#124—471no—
119#123—941no—
120#123—941no—
121C22⋊Q8—941no—
122C22⋊Q8—941no—
123#117—471no—
124#101—21no—
125#101—472no—
126#101—941no—
127#101C2×D4712yes—
128#41—1881no—
129#41—1881no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—471no—
133C2×Q8C4×D4711yescharacteristic
134C2×Q8D18811yescharacteristic
135C2×Q8C22⋊D4711yescharacteristic
136C2×Q8C22×D4711yescharacteristic
137C2×D4—471no—
138C2×D4—941no—
139C22×C4—941no—
140C22×C4C4×D4711yescharacteristic
141C22×C4D18811yescharacteristic
142C22×C4C22⋊D4711yescharacteristic
143M16—22no—
144M16—41no—
145M16—942no—
146M16—1881no—
147C2×C8—41no—
148C2×C8—1881no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C22⋊C4—941no—
159C42—471no—
160C42—471no—
161C23—941no—
162C23(C2×D47)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—1881no—
168D4—1881no—
169D4—1881no—
170D4—1881no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—1882no—
181C2×C4(C2×D47)⋊C411yescharacteristic
182C2×C4(C2×D47)⋊C411yescharacteristic
183C2×C4(C2×D47)⋊C411yescharacteristic
184C2×C4C2×C4×D4711yescharacteristic
185C2×C4C2×D18811yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C8—42no—
188C8—1882no—
189C22—41no—
190C22—1882no—
191C22—1881no—
192C22#1309393811yescharacteristic
193C22#1309393811yescharacteristic
194C22C2×(C2×D47)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—1881no—
202C4—1881no—
203C4—1881no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—3761no—
208C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC2×#101×C47C2
socleC2×C47C2×#99
hypercenterC2×#101D47
hypocenterC47#2133
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#13093943C2semidirect
3. #15688921C2semidirect
4. #15688919C2semidirect
5. C2×#101×C47C2semidirect
107. C2×#101D47semidirect
110. C47#2133semidirect