Finite Group Databasebeta

← #20245035

Subgroups — #20245035

Order 6016.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689682C211yesmaximal, characteristic
2C2×#13093939C211yesmaximal, characteristic, complemented
3#15688914C212yesmaximal, complemented
4#15688911C212yesmaximal, complemented
5C2×#100×C47C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C411yescharacteristic, complemented
7#13094007—21no—
8#13094005C411yescharacteristic, complemented
9#13094005C2211yescharacteristic
10#13093996—21no—
11#13093996—21no—
12#13093993—21no—
13#13093992C411yescharacteristic, complemented
14#13093992C2211yescharacteristic
15C2×C22⋊Dic47—21no—
16C2×C22⋊Dic47C411yescharacteristic, complemented
17#13093939—21no—
18#13093939C2212yes—
19C22×D4×C47C2211yescharacteristic
20C2×M16×C47—21no—
21#100×C47—21no—
22#100×C47C2212yes—
23C24×C47C2×C411yescharacteristic
24C24×C47D411yescharacteristic
25C23×D47C2×C411yescharacteristic, complemented
26C2×D4×C47—41no—
27C2×D4×C47—41no—
28C2×D4×C47C2×C411yescharacteristic
29C2×D4×C47D411yescharacteristic
30C2×D4×C47D411yescharacteristic
31C2×D4×C47C2311yescharacteristic
32C22×C4×C47D411yescharacteristic
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C2×C22⋊D47—21no—
36C2×C22⋊D47—21no—
37C2×C22⋊D47—41no—
38C2×C22⋊D47—41no—
39C22×Dic47—21no—
40C22×Dic47—41no—
41C22×Dic47C2×C411yescharacteristic, complemented
42M16×C47—22no—
43M16×C47—41no—
44C2×C8×C47—41no—
45C22⋊Dic47—21no—
46C22⋊Dic47—21no—
47C22⋊Dic47—21no—
48C22⋊Dic47—22no—
49C22⋊Dic47—41no—
50C22⋊Dic47C2×C411yescharacteristic, complemented
51C22⋊Dic47C2×C411yescharacteristic, complemented
52(C2×D47)⋊C4—21no—
53(C2×D47)⋊C4—21no—
54Dic47⋊C4—21no—
55Dic47⋊C4—21no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—21no—
60C23×C47—81no—
61C23×C47—81no—
62C23×C47C22⋊C411yescharacteristic
63C23×C47C22⋊C411yescharacteristic
64C23×C47C22⋊C411yescharacteristic
65C23×C47C22×C411yescharacteristic
66C23×C47C2×D411yescharacteristic
67C22×D47—21no—
68C22×D47—41no—
69C22×D47—81no—
70D4×C47—41no—
71D4×C47—41no—
72D4×C47—41no—
73D4×C47—41no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47C22⋊C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C22⋊D47—42no—
79C22⋊D47—41no—
80C22⋊D47—41no—
81C22⋊D47—81no—
82C22⋊D47—81no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—41no—
87C2×Dic47—42no—
88C2×Dic47—81no—
89C2×Dic47—82no—
90C8×C47—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—81no—
102C22×C47—81no—
103C22×C47—81no—
104C22×C47#9911yescharacteristic
105C22×C47#9911yescharacteristic
106C22×C47C2×C22⋊C411yescharacteristic
107C2×D47—41no—
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—82no—
111C4×C47—21no—
112C4×C47—21no—
113Dic47—41no—
114Dic47—41no—
115Dic47—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×C47C2×#9911yescharacteristic
126D47—81no—
127#534—471no—
128C2×#100D4711yescharacteristic, complemented
129C2×#99—471no—
130#352—472no—
131AΣL(1,𝔽16)—472no—
132C47#212111yescharacteristic, complemented, Sylow
133C22×D4—471no—
134C22×D4C2×D4711yescharacteristic
135C2×M16—21no—
136#123—471no—
137#123—471no—
138#123—941no—
139#121—941no—
140#121—941no—
141#120—471no—
142#120—471no—
143#120—941no—
144C2×C22⋊C4—471no—
145C2×C22⋊C4—941no—
146#100—21no—
147#100C2×D4712yes—
148#99—472no—
149#99—941no—
150C24—471no—
151C24C4×D4711yescharacteristic
152C24D18811yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—941no—
156C2×D4—941no—
157C2×D4—941no—
158C2×D4—941no—
159C2×D4—1881no—
160C2×D4—1881no—
161C2×D4C4×D4711yescharacteristic
162C2×D4D18811yescharacteristic
163C2×D4C22⋊D4711yescharacteristic
164C2×D4C22×D4711yescharacteristic
165C22×C4—471no—
166C22×C4—941no—
167C22×C4—1881no—
168C22×C4C22⋊D4711yescharacteristic
169M16—22no—
170M16—41no—
171C2×C8—41no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C22⋊C4—471no—
175C22⋊C4—471no—
176C22⋊C4—941no—
177C22⋊C4—941no—
178C22⋊C4—941no—
179C22⋊C4—941no—
180C22⋊C4—941no—
181C22⋊C4—942no—
182C22⋊C4—1881no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—941no—
190C23—3761no—
191C23—1881no—
192C23(C2×D47)⋊C411yescharacteristic
193C23(C2×D47)⋊C411yescharacteristic
194C23(C2×D47)⋊C411yescharacteristic
195C23C2×C4×D4711yescharacteristic
196C23C2×D18811yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—3761no—
202D4—3761no—
203D4—1882no—
204D4—1881no—
205D4—1881no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—3762no—
212C2×C4—3761no—
213C2×C4—1882no—
214C2×C4—1881no—
215C2×C4(C2×D47)⋊C411yescharacteristic
216C2×C4C2×C22⋊D4711yescharacteristic
217C8—42no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—3762no—
232C22—1881no—
233C22—1881no—
234C22—1881no—
235C22#1309393811yescharacteristic
236C22#1309393811yescharacteristic
237C22C2×(C2×D47)⋊C411yescharacteristic
238C4—21no—
239C4—21no—
240C4—3762no—
241C4—1881no—
242C4—1881no—
243C4—1881no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—3761no—
252C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC2×#100×C47C2
socleC2×C47C2×#99
hypercenterC2×#100D47
hypocenterC47#2121
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#13093939C2semidirect
3. #15688914C2semidirect
4. #15688911C2semidirect
5. C2×#100×C47C2semidirect
6. C22×C22⋊D47C4semidirect
8. #13094005C4semidirect
13. #13093992C4semidirect
16. C2×C22⋊Dic47C4semidirect
25. C23×D47C2×C4semidirect
41. C22×Dic47C2×C4semidirect
50. C22⋊Dic47C2×C4semidirect
51. C22⋊Dic47C2×C4semidirect
128. C2×#100D47semidirect
132. C47#2121semidirect