Finite Group Databasebeta

← #20254524

Subgroups — #20254524

Order 6016.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689673C211yesmaximal, characteristic
2#15689526C211yesmaximal, characteristic, complemented
3#15689519C211yesmaximal, characteristic, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689447C214yesmaximal, complemented
7#15689420C214yesmaximal, complemented
8#15689176C211yesmaximal, characteristic, complemented
9C47×#533C211yesmaximal, characteristic, complemented
10C2×#10625350—21no—
11#13094024C2211yescharacteristic
12#13094021C2211yescharacteristic
13#13094012—21no—
14#13093998—21no—
15#13093998C2212yes—
16C4×D188—21no—
17C4×D188C2212yes—
18#13093957C2214yes—
19#13093955C2214yes—
20C4⋊(C47⋊C8)C2212yes—
21#13093944C2214yes—
22#13093944C2214yes—
23C22⋊(C47⋊C8)C2212yes—
24C4×C47⋊C8C2211yescharacteristic
25C4×C47⋊C8C2211yescharacteristic
26C4⋊Q8×C47C2211yescharacteristic
27C4⋊Q8×C47C2211yescharacteristic
28#125×C47C2212yes—
29C22⋊Q8×C47—21no—
30C22⋊Q8×C47—21no—
31C4×Q8×C47—21no—
32C4×Q8×C47—21no—
33#117×C47C2212yes—
34C2×C42×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37C22×C4×C47D411yescharacteristic
38C22×C4×C47D411yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—22no—
41#10625350—44no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2312yes—
45C2×C4×D47—22no—
46C2×Dic94—21no—
47C4⋊C4×C47—22no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2312yes—
52C4⋊C4×C47C2312yes—
53C22⋊C4×C47—22no—
54C42×C47—22no—
55C42×C47D411yescharacteristic
56C42×C47D411yescharacteristic
57C42×C47C2311yescharacteristic
58C42×C47C2311yescharacteristic
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63C2×C47⋊C8C2312yes—
64C2×C47⋊C8C2312yes—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67Q8×C47—42no—
68Q8×C47—42no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C22⋊D47—44no—
81C2×Dic47—22no—
82D188—24no—
83D188—42no—
84D188—42no—
85C4×D47—44no—
86Dic94—42no—
87C47⋊C8—22no—
88C47⋊C8—22no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47C22×D411yescharacteristic
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—42no—
100C4×C47—42no—
101C4×C47#13512yes—
102C4×C47AGL(1,ℤ/8)12yes—
103C4×C472−1+412yes—
104Dic47—42no—
105#3228—471nomaximal, Sylow
106C2×C47—41no—
107C2×C47#53611yescharacteristic
108C2×C47C2×#13511yescharacteristic
109C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
110D47—82no—
111#533D4711yescharacteristic, complemented
112#532—471no—
113#500—471no—
114#498—471no—
115#486—471no—
116#486—471no—
117#482—474no—
118#478—474no—
119#431—471no—
120C47#322811yescharacteristic, complemented, Sylow
121C2×#41—941no—
122C4⋊Q8—471no—
123C4⋊Q8C2×D4711yescharacteristic
124C4⋊Q8C2×D4711yescharacteristic
125#127—471no—
126#125C2×D4712yes—
127#124—941no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130#121—472no—
131#121—941no—
132C4×Q8—21no—
133C4×Q8—21no—
134C4×D4—472no—
135C4×D4—941no—
136#117C2×D4712yes—
137C2×C42C2×D4711yescharacteristic
138#107—474no—
139#106—474no—
140C4⋊C8—472no—
141#102—474no—
142#102—474no—
143C22⋊C8—472no—
144C4×C8—471no—
145C4×C8—471no—
146#41—1884no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—941no—
150C2×D4—472no—
151C2×D4—942no—
152C2×D4—941no—
153C2×D4—941no—
154C22×C4—942no—
155C22×C4C22⋊D4711yescharacteristic
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22×D4711yescharacteristic
158C2×C8—472no—
159C2×C8—472no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—941no—
166C4⋊C4C22×D4712yes—
167C4⋊C4C22×D4712yes—
168C22⋊C4—22no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C42—22no—
172C42C22⋊D4711yescharacteristic
173C42C22⋊D4711yescharacteristic
174C42C22×D4711yescharacteristic
175C42C22×D4711yescharacteristic
176C23—942no—
177C23C2×C22⋊D4711yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—1882no—
181D4—944no—
182D4—1884no—
183D4—1882no—
184D4—1882no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—942no—
191C2×C4—1884no—
192C2×C4C2×C22⋊D4711yescharacteristic
193C2×C4C2×C22⋊D4711yescharacteristic
194C2×C4C2×C22⋊D4711yescharacteristic
195C2×C4C2×C22⋊D4711yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C23×D4711yescharacteristic
198C8—942no—
199C8—942no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C22×C22⋊D4711yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—1882no—
213C4#1309404412yes—
214C4#1309404912yes—
215C4#1309407212yes—
216C2—41no—
217C2—3762no—
218C2#1568969711yescharacteristic
219C2C2×#1309404411yescharacteristic
220C2C2×#1309404911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3228
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #15689526C2semidirect
3. #15689519C2semidirect
4. #15689471C2semidirect
5. #15689471C2semidirect
6. #15689447C2semidirect
7. #15689420C2semidirect
8. #15689176C2semidirect
9. C47×#533C2semidirect
111. #533D47semidirect
120. C47#3228semidirect