Finite Group Databasebeta

← #20241756

Subgroups — #20241756

Order 6016.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#13094019C211yesmaximal, characteristic
2#15689177C211yesmaximal, characteristic, complemented
3#15689173C211yesmaximal, characteristic, complemented
4#15688849C211yesmaximal, characteristic, complemented
5#15688846C211yesmaximal, characteristic
6#15688846C211yesmaximal, characteristic
7C47×#324C211yesmaximal, characteristic, complemented
8#13094019—21no—
9#13094019—21no—
10#13094019—21no—
11#13094019—21no—
12C2×C4⋊Dic47C411yescharacteristic
13C2×Dic47⋊C4C411yescharacteristic
14C2×(C2×D47)⋊C4C411yescharacteristic
15C2×(C2×D47)⋊C4C411yescharacteristic
16C2×(C2×D47)⋊C4C2211yescharacteristic
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—21no—
19Dic47⋊C8—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22#13093934—21no—
23C8×Dic47—21no—
24C2×C4⋊C4×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26C22⋊C8×C47C2211yescharacteristic
27C23×D47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C22×Dic47C2×C411yescharacteristic
33C22×Dic47C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47D411yescharacteristic
49C4×Dic47D411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C22×C411yescharacteristic
55C22×D47—21no—
56C22×D47—21no—
57C22×D47—21no—
58C22×D47—41no—
59C22×D47—41no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C2×Dic47C22⋊C411yescharacteristic
76C2×Dic47C22⋊C411yescharacteristic
77C8×C47—41no—
78C8×C47—41no—
79C47⋊C8—41no—
80C47⋊C8—41no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47#13111yescharacteristic
85C22×C47#13111yescharacteristic
86C2×D47—41no—
87C2×D47—41no—
88C2×D47—41no—
89C2×D47—81no—
90C2×D47—81no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—41no—
94C4×C47—41no—
95Dic47—21no—
96Dic47—21no—
97Dic47—21no—
98Dic47—21no—
99Dic47—41no—
100#1473—471nomaximal, Sylow
101C2×C47—21no—
102C2×C47—21no—
103C2×C47#40811yescharacteristic
104C2×C47#41011yescharacteristic
105C2×C47#41311yescharacteristic
106D47—81no—
107C2×#126—471no—
108#432—471no—
109#431—471no—
110#324—471no—
111#324D4711yescharacteristic, complemented
112#323—471no—
113#323—471no—
114C47#147311yescharacteristic, complemented, Sylow
115#126—941no—
116#126—941no—
117#126—941no—
118#126—941no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—471no—
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C22⋊C4—471no—
123C2×C22⋊C4—471no—
124C2×C22⋊C4—471no—
125C2×C42—471no—
126C4⋊C8—941no—
127C4⋊C8—941no—
128C22⋊C8—471no—
129C22⋊C8—471no—
130C22⋊C8C2×D4711yescharacteristic
131C22⋊C8C2×D4711yescharacteristic
132#97—941no—
133C4×C8—941no—
134C24—471no—
135C22×C4—471no—
136C22×C4—471no—
137C22×C4—471no—
138C22×C4C4×D4711yescharacteristic
139C22×C4C4×D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—941no—
144C2×C8—941no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C22⋊C4—941no—
152C22⋊C4—941no—
153C22⋊C4—941no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C42—471no—
158C42—471no—
159C42—471no—
160C42—471no—
161C23—941no—
162C23—941no—
163C23—941no—
164C23—1881no—
165C23—1881no—
166C23C2×C4×D4711yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—471no—
174C2×C4—471no—
175C2×C4—471no—
176C2×C4—471no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—1881no—
181C2×C4—1881no—
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C8—41no—
185C8—41no—
186C8—1881no—
187C8—1881no—
188C22—21no—
189C22—21no—
190C22—3761no—
191C22—3761no—
192C22—1881no—
193C22—1881no—
194C22—1881no—
195C22C22⋊C4×D4711yescharacteristic
196C22#1309403011yescharacteristic
197C22#1309403211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—941no—
203C4—941no—
204C4—941no—
205C4—941no—
206C4—1881no—
207C2—21no—
208C2—21no—
209C2—3761no—
210C2#1568908811yescharacteristic
211C2#1568909511yescharacteristic
212C2#1568910611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1473
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #15689177C2semidirect
3. #15689173C2semidirect
4. #15688849C2semidirect
7. C47×#324C2semidirect
111. #324D47semidirect
114. C47#1473semidirect