Finite Group Databasebeta

← #20242018

Subgroups — #20242018

Order 6016.

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

normal subgroups only

This group has 200 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#15689658C211yesmaximal, characteristic
2#15689178C211yesmaximal, characteristic, complemented
3#15689178C211yesmaximal, characteristic, complemented
4#15688865C211yesmaximal, characteristic, complemented
5#15688862C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#330C211yesmaximal, characteristic, complemented
8#13094019—21no—
9#13094012C2211yescharacteristic
10#13094009—21no—
11#13094004C411yescharacteristic
12#13093999C411yescharacteristic
13#13093989C411yescharacteristic
14#13093986—21no—
15#13093986C411yescharacteristic
16#13093982—21no—
17C42×D47C2211yescharacteristic
18Dic47⋊C8—21no—
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22#13093935C2211yescharacteristic
23#13093935C2211yescharacteristic
24#125×C47C2211yescharacteristic
25#97×C47C2211yescharacteristic
26#97×C47C2211yescharacteristic
27C2×D188—21no—
28C2×D188C2×C411yescharacteristic
29C2×C4×D47—21no—
30C2×C4×D47C2×C411yescharacteristic
31C2×C4×D47D411yescharacteristic
32C2×C4×D47D411yescharacteristic
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C411yescharacteristic
39C4⋊C4×C47C2×C411yescharacteristic
40C42×C47C2311yescharacteristic
41(C2×D47)⋊C4—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—
48C4×Dic47—21no—
49C4×Dic47C2×C411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C22×D47—21no—
55C22×D47C22⋊C411yescharacteristic
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×Dic47—21no—
62C2×Dic47C22⋊C411yescharacteristic
63C2×Dic47C22⋊C411yescharacteristic
64C2×Dic47C22⋊C411yescharacteristic
65D188—41no—
66D188—42no—
67C4×D47—41no—
68C4×D47—41no—
69C4×D47—41no—
70C4×D47—42no—
71Dic94—41no—
72C8×C47—41no—
73C8×C47—41no—
74C47⋊C8—41no—
75C47⋊C8—41no—
76C22×C47C2×C22⋊C411yescharacteristic
77C2×D47—21no—
78C2×D47—21no—
79C2×D47—21no—
80C2×D47—41no—
81C2×D47—41no—
82C2×D47—41no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47—41no—
88Dic47—21no—
89Dic47—21no—
90Dic47—21no—
91Dic47—41no—
92#1535—471nomaximal, Sylow
93C2×C47#41311yescharacteristic
94C2×C47#42111yescharacteristic
95C2×C47#42111yescharacteristic
96D47—41no—
97D47—81no—
98#529—471no—
99#432—471no—
100#432—471no—
101#330—471no—
102#330D4711yescharacteristic, complemented
103#329—471no—
104#329—471no—
105C47#153511yescharacteristic, complemented, Sylow
106#126—941no—
107#125C2×D4711yescharacteristic
108#124—471no—
109#123—941no—
110C22⋊Q8—471no—
111#121—471no—
112C4×Q8—471no—
113C4×D4—471no—
114C4×D4—941no—
115#117—941no—
116C2×C42—471no—
117C4⋊C8—941no—
118C4⋊C8—941no—
119C22⋊C8—941no—
120C22⋊C8—941no—
121#97—471no—
122#97—471no—
123#97C2×D4711yescharacteristic
124#97C2×D4711yescharacteristic
125C2×Q8—471no—
126C2×D4—471no—
127C2×D4—941no—
128C22×C4—471no—
129C22×C4—471no—
130C22×C4—471no—
131C22×C4—941no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—941no—
135C2×C8—941no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4C4×D4711yescharacteristic
141C4⋊C4C4×D4711yescharacteristic
142C22⋊C4—941no—
143C22⋊C4—941no—
144C22⋊C4—941no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C42—471no—
148C42—471no—
149C42—471no—
150C42—941no—
151C42C22×D4711yescharacteristic
152C23—471no—
153C23—941no—
154Q8—1881no—
155D4—1881no—
156D4—1882no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—471no—
160C2×C4—471no—
161C2×C4—471no—
162C2×C4—941no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4—1882no—
167C2×C4C2×C4×D4711yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C8—41no—
171C8—41no—
172C8—1881no—
173C8—1881no—
174C22—941no—
175C22—941no—
176C22—941no—
177C22—1881no—
178C22—1881no—
179C22—1881no—
180C22C22⋊C4×D4711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—941no—
187C4—941no—
188C4—941no—
189C4—1881no—
190C2—3761no—
191C2—1881no—
192C2#1568910611yescharacteristic
193C2#1568913811yescharacteristic
194C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#330C2
socleC22×C47C2×C22⋊C4
hypercenter#330D47
hypocenterC47#1535
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #15689178C2semidirect
3. #15689178C2semidirect
4. #15688865C2semidirect
5. #15688862C2semidirect
6. #15688862C2semidirect
7. C47×#330C2semidirect
102. #330D47semidirect
105. C47#1535semidirect