Finite Group Databasebeta

← #20241955

Subgroups — #20241955

Order 6016.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13093998C211yesmaximal, characteristic
2C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#15688856C214yesmaximal, complemented
4C47×#380C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic, complemented
6C22×C22⋊D47—21no—
7C22×C47⋊C8—21no—
8#13093998—21no—
9#13093998—21no—
10#13093998C412yescomplemented
11#13093998C2212yes—
12C2×C4⋊Dic47C411yescharacteristic, complemented
13C2×(C2×D47)⋊C4—21no—
14C22⋊(C47⋊C8)—21no—
15C22⋊(C47⋊C8)C2212yescomplemented
16C23×C4×C47C2211yescharacteristic
17C2×C4⋊C4×C47—21no—
18C2×C22⋊C4×C47—21no—
19#95×C47C2212yescomplemented
20C24×C47D411yescharacteristic
21C23×D47—21no—
22C22×C4×C47—22no—
23C22×C4×C47—42no—
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32C2×C22⋊D47—42no—
33C2×C22⋊D47—42no—
34C22×Dic47—21no—
35C2×D188—21no—
36C2×D188—42no—
37C2×D188C2×C412yes—
38C4⋊C4×C47—42no—
39C22⋊C4×C47—42no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42C4⋊Dic47—21no—
43C4⋊Dic47C2×C412yes—
44C2×C47⋊C8—22no—
45C2×C47⋊C8—42no—
46C23×C47—41no—
47C23×C47—41no—
48C23×C47C22⋊C411yescharacteristic
49C23×C47C22⋊C411yescharacteristic
50C23×C47D812yes—
51C23×C47SD1612yes—
52C23×C47C2×D411yescharacteristic
53C22×D47—22no—
54C22×D47—42no—
55C22×D47—42no—
56C22×D47—42no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22⋊C411yescharacteristic
68C2×C4×C47C22×C411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C22⋊D47—44no—
71C22⋊D47—42no—
72C22⋊D47—42no—
73C2×Dic47—22no—
74C2×Dic47—42no—
75D188—42no—
76D188—42no—
77C47⋊C8—42no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47#10212yes—
87C22×C47#10212yes—
88C22×C47C2×C22⋊C411yescharacteristic
89C22×C47C2×D811yescharacteristic
90C22×C47C2×SD1611yescharacteristic
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—42no—
94C2×D47—84no—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—82no—
99C4×C47#9912yes—
100Dic47—42no—
101#1519—471nomaximal, Sylow
102C2×C47—21no—
103C2×C47—22no—
104C2×C47—22no—
105C2×C47—21no—
106C2×C47C2×#9911yescharacteristic
107C2×C47C2×#10211yescharacteristic
108C2×C47#42111yescharacteristic
109D47—82no—
110C2×#121—471no—
111C2×C22⋊C8—471no—
112#380D4711yescharacteristic, complemented
113#327—474no—
114C47#151911yescharacteristic, complemented, Sylow
115C22×D4—471no—
116C22×D4—941no—
117C23×C4C2×D4711yescharacteristic
118C22×C8—941no—
119#121—472no—
120#121—472no—
121#121—941no—
122#121—941no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—471no—
125C2×C22⋊C4—21no—
126C2×C22⋊C4—941no—
127C22⋊C8—472no—
128C22⋊C8—941no—
129#95C2×D4712yescomplemented
130C24—941no—
131C24C22⋊D4711yescharacteristic
132C2×D4—472no—
133C2×D4—942no—
134C2×D4—942no—
135C2×D4—941no—
136C2×D4—1882no—
137C2×D4—1882no—
138C2×D4—1882no—
139C22×C4—22no—
140C22×C4—42no—
141C22×C4—941no—
142C22×C4C4×D4711yescharacteristic
143C22×C4C4×D4711yescharacteristic
144C22×C4D18811yescharacteristic
145C22×C4D18811yescharacteristic
146C22×C4C22⋊D4711yescharacteristic
147C22×C4C22×D4711yescharacteristic
148C2×C8—942no—
149C2×C8—1882no—
150C4⋊C4—42no—
151C4⋊C4—472no—
152C4⋊C4—941no—
153C22⋊C4—42no—
154C22⋊C4—942no—
155C22⋊C4—942no—
156C23—41no—
157C23—41no—
158C23—942no—
159C23—1882no—
160C23—1882no—
161C23—1882no—
162C23(C2×D47)⋊C411yescharacteristic
163C23(C2×D47)⋊C411yescharacteristic
164C23#1062533412yes—
165C23#1062533612yes—
166C23C2×C22⋊D4711yescharacteristic
167D4—1882no—
168D4—1884no—
169D4—1882no—
170D4—1882no—
171D4—1882no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—942no—
182C2×C4—1882no—
183C2×C4(C2×D47)⋊C411yescharacteristic
184C2×C4(C2×D47)⋊C411yescharacteristic
185C2×C4C2×C4×D4711yescharacteristic
186C2×C4C2×D18811yescharacteristic
187C8—1882no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—3764no—
197C22—1882no—
198C22—1882no—
199C22—1882no—
200C22#1309394412yes—
201C22#1309394412yes—
202C22C2×(C2×D47)⋊C411yescharacteristic
203C22C2×#1062533411yescharacteristic
204C22C2×#1062533611yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—82no—
209C4—1882no—
210C4#1309393812yes—
211C2—21no—
212C2—22no—
213C2—22no—
214C2—21no—
215C2—3762no—
216C2C2×#1309393811yescharacteristic
217C2C2×#1309394411yescharacteristic
218C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#380C2
socleC22×C47C2×C22⋊C4
hypercenter#380D47
hypocenterC47#1519
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C47⋊C8)C2semidirect
3. #15688856C2semidirect
4. C47×#380C2semidirect
5. C22×D188C4semidirect
10. #13093998C4semidirect
12. C2×C4⋊Dic47C4semidirect
15. C22⋊(C47⋊C8)C22semidirect
19. #95×C47C22semidirect
112. #380D47semidirect
114. C47#1519semidirect
129. #95C2×D47semidirect