Finite Group Databasebeta

← #20243917

Subgroups — #20243917

Order 6016.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689687C211yesmaximal, characteristic
2#15689597C211yesmaximal, characteristic, complemented
3#15689140C211yesmaximal, characteristic, complemented
4C2×#13093940C211yesmaximal, characteristic, complemented
5#15688880C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094020C412yescomplemented
11#13094013C412yescomplemented
12#13093998—22no—
13#13093992—22no—
14C4×D188—22no—
15#13093986—22no—
16#13093983C2211yescharacteristic
17#13093983C2211yescharacteristic
18C22⋊C4×D47—22no—
19#13093951—22no—
20#13093940—22no—
21C2×#41×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#104×C47—22no—
25C23×D47D412yes—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30C2×Q8×C47C2×C411yescharacteristic, complemented
31C2×D4×C47—21no—
32C2×D4×C47C2×C411yescharacteristic, complemented
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—24no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188C2×C412yes—
41C2×D188D412yes—
42C2×C4×D47—24no—
43M16×C47—21no—
44M16×C47—21no—
45C2×C8×C47—21no—
46C4⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C42×C47D412yescomplemented
49C22⋊Dic47—21no—
50C22⋊Dic47—21no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4×Dic47C2×C412yescomplemented
56C4×Dic47D412yescomplemented
57#10625329—21no—
58#10625329—21no—
59C2×C47⋊C8—21no—
60C23×C47—21no—
61C23×C47C2×D411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—82no—
65C22×D47C22⋊C414yes—
66Q8×C47—21no—
67Q8×C47—21no—
68D4×C47—21no—
69D4×C47—21no—
70D4×C47—41no—
71D4×C47—41no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C22×C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C22⋊D47—84no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85D188—22no—
86D188—22no—
87D188—22no—
88D188—22no—
89C4×D47—84no—
90C8×C47—41no—
91C47⋊C8—41no—
92C22×C47—41no—
93C22×C47—42no—
94C22×C47—41no—
95C22×C47C2×C22⋊C411yescharacteristic
96C22×C47#12011yescharacteristic
97C22×C47#12311yescharacteristic
98C2×D47—24no—
99C2×D47—44no—
100C2×D47—44no—
101C2×D47—82no—
102C4×C47—42no—
103C4×C47—41no—
104C4×C47C4×D411yescharacteristic
105C4×C47C4×D411yescharacteristic
106C4×C47#12111yescharacteristic
107C4×C47#12111yescharacteristic
108Dic47—42no—
109Dic47—42no—
110#1911—471nomaximal, Sylow
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—21no—
114C2×C47—81no—
115C2×C47#38611yescharacteristic
116D47—44no—
117#535—471no—
118#518—471no—
119#421—471no—
120#421D4711yescharacteristic, complemented
121C2×#100—471no—
122H(3,ℤ/4)—471no—
123H(3,ℤ/4)—471no—
124C47#191111yescharacteristic, complemented, Sylow
125C2×#41C2×D4711yescharacteristic
126C22×D4—471no—
127C2×M16—471no—
128C2×M16C2×D4711yescharacteristic
129#127—472no—
130#124—472no—
131#121—942no—
132#120—942no—
133C4×D4—942no—
134C4×D4—942no—
135#117—471no—
136#117—471no—
137#117C2×D4711yescharacteristic
138C2×C22⋊C4—942no—
139#104—22no—
140#104—942no—
141#100—942no—
142C24—472no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C4×D4711yescharacteristic, complemented
148C2×D4—21no—
149C2×D4—472no—
150C2×D4—472no—
151C2×D4—944no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4—941no—
156C2×D4C4×D4711yescharacteristic, complemented
157C22×C4—21no—
158C22×C4—944no—
159C22×C4C22×D4711yescharacteristic
160M16—21no—
161M16—21no—
162M16—941no—
163M16—941no—
164C2×C8—21no—
165C2×C8—941no—
166C4⋊C4—21no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—21no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C42—472no—
175C42—472no—
176C42C22⋊D4712yescomplemented
177C23—21no—
178C23—474no—
179C23—942no—
180C23—942no—
181C23—3762no—
182C23D4×D4711yescharacteristic
183Q8—21no—
184Q8—21no—
185D4—21no—
186D4—21no—
187D4—41no—
188D4—41no—
189D4—942no—
190D4—942no—
191D4—942no—
192D4—942no—
193D4—3764no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—3764no—
201C2×C4C2×C4×D4711yescharacteristic
202C2×C4#1062535011yescharacteristic
203C2×C4D4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4#1062535211yescharacteristic
206C2×C4C2×C22⋊D4711yescharacteristic
207C8—41no—
208C8—1881no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—944no—
213C22—3762no—
214C22—1884no—
215C22—1884no—
216C22C22⋊C4×D4711yescharacteristic
217C22#1309399211yescharacteristic
218C22#1309400611yescharacteristic
219C4—42no—
220C4—41no—
221C4—1882no—
222C4—1882no—
223C4(C22⋊D47)⋊C411yescharacteristic
224C4C4×C22⋊D4711yescharacteristic
225C4#1309399511yescharacteristic
226C4#1309399711yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—81no—
231C2—1884no—
232C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#386
hypercenter#421D47
hypocenterC47#1911
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #15689597C2semidirect
3. #15689140C2semidirect
4. C2×#13093940C2semidirect
5. #15688880C2semidirect
6. #15688879C2semidirect
7. C47×#421C2semidirect
10. #13094020C4semidirect
11. #13094013C4semidirect
30. C2×Q8×C47C2×C4semidirect
32. C2×D4×C47C2×C4semidirect
48. C42×C47D4semidirect
55. C4×Dic47C2×C4semidirect
56. C4×Dic47D4semidirect
120. #421D47semidirect
124. C47#1911semidirect
147. C2×Q8C4×D47semidirect
156. C2×D4C4×D47semidirect
176. C42C22⋊D47semidirect