Finite Group Databasebeta

← #20245040

Subgroups — #20245040

Order 6016.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689695C211yesmaximal, characteristic
2#15689104C211yesmaximal, characteristic
3#15689095C211yesmaximal, characteristic
4#15688914C211yesmaximal, characteristic, complemented
5#15688913C211yesmaximal, characteristic, complemented
6#15688912C211yesmaximal, characteristic, complemented
7C47×#352C211yesmaximal, characteristic, complemented
8C2×#10625352C2211yescharacteristic
9C22×Dic94C411yescharacteristic, complemented
10M16×D47—21no—
11#13094023—21no—
12#13094010—21no—
13#13094008C411yescharacteristic, complemented
14#13094007C411yescharacteristic, complemented
15#13094005C2211yescharacteristic
16#13094002—21no—
17#13094001—21no—
18#13093980—21no—
19#13093980C411yescharacteristic, complemented
20#13093942—21no—
21#13093941C2211yescharacteristic
22#13093939C2211yescharacteristic
23#13093938—21no—
24#123×C47C2211yescharacteristic
25#100×C47C2211yescharacteristic
26#99×C47C2211yescharacteristic
27C2×D4×C47C2311yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C2×C22⋊D47C2×C411yescharacteristic
30C2×C22⋊D47D411yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C22×Dic47C2×C411yescharacteristic
33C22×Dic47D411yescharacteristic
34#10625352—41no—
35#10625352—41no—
36C2×C4×D47D411yescharacteristic
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—41no—
40C2×Dic94—41no—
41C2×Dic94D411yescharacteristic
42M16×C47—21no—
43C4⋊C4×C47—21no—
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47C2×C411yescharacteristic
47C22⋊Dic47—21no—
48C22⋊Dic47—21no—
49C22⋊Dic47C2×C411yescharacteristic
50(C2×D47)⋊C4—21no—
51(C2×D47)⋊C4—21no—
52C4⋊Dic47—21no—
53Dic47⋊C4—21no—
54Dic47⋊C4—21no—
55Dic47⋊C4—21no—
56Dic47⋊C4—41no—
57C4×Dic47—21no—
58C4×Dic47—41no—
59#10625329—21no—
60#10625324—41no—
61C8×D47—41no—
62C23×C47C22×C411yescharacteristic
63C23×C47C2×D411yescharacteristic
64C22×D47C22⋊C411yescharacteristic
65D4×C47—41no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C2×D411yescharacteristic
71C22⋊D47—41no—
72C22⋊D47—41no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47C22⋊C411yescharacteristic
82C2×Dic47C22⋊C411yescharacteristic
83C2×Dic47C22⋊C411yescharacteristic
84C4×D47—21no—
85C4×D47—21no—
86Dic94—41no—
87Dic94—42no—
88Dic94—41no—
89Dic94—41no—
90C8×C47—41no—
91C47⋊C8—41no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47C2×C22⋊C411yescharacteristic
97C2×D47—21no—
98C2×D47—41no—
99C4×C47—21no—
100C4×C47—41no—
101C4×C47—41no—
102C4×C47—81no—
103Dic47—21no—
104Dic47—21no—
105Dic47—41no—
106Dic47—41no—
107Dic47—81no—
108Dic47#9911yescharacteristic
109Dic47#9911yescharacteristic
110#2123—471nomaximal, Sylow
111C2×C47—21no—
112C2×C47—41no—
113C2×C47—41no—
114C2×C47C2×#9911yescharacteristic
115D47—41no—
116#536—471no—
117#413—471no—
118#410—471no—
119#352—471no—
120#352—471no—
121#352—471no—
122#352D4711yescharacteristic, complemented
123C47#212311yescharacteristic, complemented, Sylow
124C2×#41—471no—
125C22×Q8—471no—
126C2×M16—941no—
127C4⋊Q8—941no—
128#124—941no—
129#123—471no—
130#123—471no—
131#123—471no—
132#123C2×D4711yescharacteristic
133C22⋊Q8—941no—
134C22⋊Q8—941no—
135#117—471no—
136#117—941no—
137#101—941no—
138#100—471no—
139#100C2×D4711yescharacteristic
140#99—471no—
141#99—941no—
142#99C2×D4711yescharacteristic
143#41—1881no—
144#41—1881no—
145C2×Q8—471no—
146C2×Q8—941no—
147C2×Q8—941no—
148C2×Q8—1881no—
149C2×Q8—1881no—
150C2×D4—471no—
151C2×D4—471no—
152C2×D4C22×D4711yescharacteristic
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4C4×D4711yescharacteristic
158M16—21no—
159M16—941no—
160M16—1881no—
161C2×C8—1881no—
162C4⋊C4—21no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—1881no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—471no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C22⋊C4—941no—
175C22⋊C4C4×D4711yescharacteristic
176C42—941no—
177C42—1881no—
178C23—471no—
179C23C2×C4×D4711yescharacteristic
180C23D4×D4711yescharacteristic
181Q8—1881no—
182Q8—1881no—
183Q8—1881no—
184Q8—1882no—
185D4—41no—
186D4—1881no—
187D4—1881no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—471no—
193C2×C4—471no—
194C2×C4—471no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4D4×D4711yescharacteristic
206C8—41no—
207C8—1881no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—941no—
213C22—1881no—
214C22C22⋊C4×D4711yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—471no—
220C4—471no—
221C4—941no—
222C4—941no—
223C4—3761no—
224C4—1881no—
225C4—1881no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—1881no—
230C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#352C2
socleC2×C47C2×#99
hypercenter#352D47
hypocenterC47#2123
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #15688914C2semidirect
5. #15688913C2semidirect
6. #15688912C2semidirect
7. C47×#352C2semidirect
9. C22×Dic94C4semidirect
13. #13094008C4semidirect
14. #13094007C4semidirect
19. #13093980C4semidirect
122. #352D47semidirect
123. C47#2123semidirect