Finite Group Databasebeta

← #20245034

Subgroups — #20245034

Order 6016.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13093941C211yesmaximal, characteristic, complemented
2C2×#13093939C211yesmaximal, characteristic, complemented
3#15688913C212yesmaximal, complemented
4#15688910C212yesmaximal, complemented
5C47×#534C211yesmaximal, characteristic
6C2×#10625329—21no—
7C2×C22⋊Dic47—21no—
8#13093941—21no—
9#13093941C2212yes—
10#13093939—21no—
11#13093939C2212yes—
12C22×D4×C47C411yescharacteristic, complemented
13C22×D4×C47C2211yescharacteristic
14#123×C47—21no—
15#123×C47C411yescharacteristic, complemented
16#123×C47C2211yescharacteristic
17#121×C47—21no—
18#121×C47—21no—
19#120×C47—21no—
20#120×C47C411yescharacteristic, complemented
21#120×C47C2211yescharacteristic
22C2×C22⋊C4×C47C411yescharacteristic, complemented
23C24×C47C2×C411yescharacteristic
24C24×C47C2×C411yescharacteristic, complemented
25C24×C47D411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—41no—
31C2×D4×C47—41no—
32C2×D4×C47—41no—
33C2×D4×C47—41no—
34C2×D4×C47C2×C411yescharacteristic
35C2×D4×C47D411yescharacteristic
36C2×D4×C47D411yescharacteristic
37C2×D4×C47C2311yescharacteristic
38C22×C4×C47—21no—
39C22×C4×C47C2×C411yescharacteristic, complemented
40C22×C4×C47D411yescharacteristic
41C22×Dic47—41no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47C2×C411yescharacteristic, complemented
50C22⋊C4×C47C2×C411yescharacteristic, complemented
51C22⋊Dic47—22no—
52C22⋊Dic47—41no—
53#10625329—22no—
54#10625329—41no—
55C2×C47⋊C8—41no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—41no—
62C23×C47—81no—
63C23×C47—81no—
64C23×C47—81no—
65C23×C47C22⋊C411yescharacteristic
66C23×C47C22⋊C411yescharacteristic
67C23×C47C22⋊C411yescharacteristic
68C23×C47C22×C411yescharacteristic
69C23×C47C2×D411yescharacteristic
70D4×C47—41no—
71D4×C47—41no—
72D4×C47—41no—
73D4×C47—41no—
74D4×C47—42no—
75D4×C47—41no—
76D4×C47—41no—
77D4×C47—81no—
78D4×C47—81no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—41no—
85C2×C4×C47—81no—
86C2×C4×C47C22⋊C411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×Dic47—42no—
89C2×Dic47—82no—
90C47⋊C8—42no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—42no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—81no—
105C22×C47—81no—
106C22×C47—81no—
107C22×C47—82no—
108C22×C47#9911yescharacteristic
109C22×C47#9911yescharacteristic
110C22×C47C2×C22⋊C411yescharacteristic
111C4×C47—21no—
112C4×C47—21no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47—41no—
116Dic47—82no—
117#2121—471nomaximal, Sylow
118C2×C47—21no—
119C2×C47—21no—
120C2×C47—21no—
121C2×C47—41no—
122C2×C47—41no—
123C2×C47—41no—
124C2×C47—41no—
125C2×C47—81no—
126C2×C47C2×#9911yescharacteristic
127#534D4711yescharacteristic
128C2×#100—471no—
129C2×#99—471no—
130#352—472no—
131AΣL(1,𝔽16)—472no—
132C47#212111yescharacteristic, complemented, Sylow
133C22×D4Dic4711yescharacteristic, complemented
134C22×D4C2×D4711yescharacteristic
135C2×M16—941no—
136#123—21no—
137#123Dic4711yescharacteristic, complemented
138#123C2×D4711yescharacteristic
139#121—21no—
140#121—21no—
141#120—21no—
142#120Dic4711yescharacteristic, complemented
143#120C2×D4711yescharacteristic
144C2×C22⋊C4—941no—
145C2×C22⋊C4Dic4711yescharacteristic, complemented
146#100—472no—
147#100—941no—
148#99—472no—
149#99—941no—
150C24C2×Dic4711yescharacteristic
151C24C2×Dic4711yescharacteristic, complemented
152C24C22⋊D4711yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4C2×Dic4711yescharacteristic
162C2×D4C22⋊D4711yescharacteristic
163C2×D4C22⋊D4711yescharacteristic
164C2×D4C22×D4711yescharacteristic
165C22×C4—21no—
166C22×C4—1881no—
167C22×C4C2×Dic4711yescharacteristic, complemented
168C22×C4C22⋊D4711yescharacteristic
169M16—942no—
170M16—1881no—
171C2×C8—1881no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—942no—
180C22⋊C4—1881no—
181C22⋊C4C2×Dic4711yescharacteristic, complemented
182C22⋊C4C2×Dic4711yescharacteristic, complemented
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—81no—
190C23—81no—
191C23—81no—
192C23C22⋊Dic4711yescharacteristic
193C23C22⋊Dic4711yescharacteristic
194C23C22⋊Dic4711yescharacteristic
195C23C22×Dic4711yescharacteristic
196C23C2×C22⋊D4711yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—42no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—81no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—3762no—
214C2×C4—1882no—
215C2×C4C22⋊Dic4711yescharacteristic
216C2×C4C2×C22⋊D4711yescharacteristic
217C8—1882no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—82no—
235C22#1309393911yescharacteristic
236C22#1309393911yescharacteristic
237C22C2×C22⋊Dic4711yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—3762no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2C2×#1309393911yescharacteristic
subgroupG/H
centerC2C2×#13093939
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#534C2
socleC2×C47C2×#99
hypercenter#534D47
hypocenterC47#2121
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#13093941C2semidirect
2. C2×#13093939C2semidirect
3. #15688913C2semidirect
4. #15688910C2semidirect
12. C22×D4×C47C4semidirect
15. #123×C47C4semidirect
20. #120×C47C4semidirect
22. C2×C22⋊C4×C47C4semidirect
24. C24×C47C2×C4semidirect
39. C22×C4×C47C2×C4semidirect
49. C22⋊C4×C47C2×C4semidirect
50. C22⋊C4×C47C2×C4semidirect
132. C47#2121semidirect
133. C22×D4Dic47semidirect
137. #123Dic47semidirect
142. #120Dic47semidirect
145. C2×C22⋊C4Dic47semidirect
151. C24C2×Dic47semidirect
167. C22×C4C2×Dic47semidirect
181. C22⋊C4C2×Dic47semidirect
182. C22⋊C4C2×Dic47semidirect