Finite Group Databasebeta

← #20256004

Subgroups — #20256004

Order 6016.

342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689843C211yesmaximal, characteristic
2#15689830C211yesmaximal, characteristic
3#15689521C211yesmaximal, characteristic, complemented
4#15689465C212yesmaximal, complemented
5#15689454C212yesmaximal, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689409C211yesmaximal, characteristic, complemented
8#15689381C212yesmaximal, complemented
9C4×Dic188C211yesmaximal, characteristic, complemented
10#15689165C212yesmaximal, complemented
11C47×#436C211yesmaximal, characteristic
12C2×Dic188C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094017—22no—
16#13094015—21no—
17#13094011—21no—
18#13094003C2212yes—
19#13094003C2212yes—
20#13094001—22no—
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23#13093989—21no—
24D4×Dic47—21no—
25#13093983C2212yes—
26C2×C4⋊Dic47C2212yes—
27#13093958C2211yescharacteristic
28#13093958C2212yes—
29#13093956C2212yes—
30#13093956C2212yes—
31#13093956C2212yes—
32#13093949C2211yescharacteristic
33#13093949C2211yescharacteristic
34#13093949C2212yes—
35#13093949C2212yes—
36C2×M16×C47C2212yes—
37C4×D4×C47C2211yescharacteristic
38C4⋊C8×C47C2211yescharacteristic
39C22⋊C8×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×D4×C47D411yescharacteristic
42C22×C4×C47C2312yes—
43C22×Dic47—22no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94C2311yescharacteristic
47C2×Dic94C2311yescharacteristic
48M16×C47—24no—
49C2×C8×C47C2312yes—
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47D411yescharacteristic
53C22⋊C4×C47D412yes—
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47C2312yes—
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—22no—
66Dic47⋊C4—21no—
67Dic47⋊C4—21no—
68Dic47⋊C4—22no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71C4×Dic47—21no—
72Dic188—22no—
73C23×C47C2×D412yes—
74D4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—82no—
88Dic94—21no—
89Dic94—21no—
90Dic94—21no—
91Dic94—21no—
92Dic94—42no—
93Dic94—81no—
94C8×C47—22no—
95C8×C47—21no—
96C8×C47#4112yes—
97C22×C47—22no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47C22×D411yescharacteristic
101C4×C47—22no—
102C4×C47—21no—
103C4×C47#13712yes—
104C4×C47C2×#4111yescharacteristic
105C4×C472−1+411yescharacteristic
106Dic47—41no—
107Dic47—41no—
108Dic47—42no—
109Dic47—42no—
110Dic47—41no—
111Dic47—41no—
112#3356—471nomaximal, Sylow
113C2×C47—42no—
114C2×C47#54711yescharacteristic
115C2×C47C2×#13711yescharacteristic
116C2×C47#57711yescharacteristic
117#556—471no—
118#554—471no—
119#498—471no—
120#485—472no—
121#483—472no—
122#477—471no—
123#475—471no—
124#470—472no—
125C4×Q16—471no—
126#436D4711yescharacteristic
127#428—472no—
128C47#335611yescharacteristic, complemented, Sylow
129C2×Q16—471no—
130C2×M16C2×D4712yes—
131C4⋊Q8—471no—
132C4⋊Q8—471no—
133#126—942no—
134#125—941no—
135#124—941no—
136C22⋊Q8—472no—
137C22⋊Q8—472no—
138C22⋊Q8—942no—
139C4×Q8—471no—
140C4×Q8—471no—
141C4×Q8—941no—
142C4×D4—941no—
143C4×D4C2×D4711yescharacteristic
144#117—472no—
145C2×C4⋊C4—472no—
146#107—471no—
147#107—472no—
148#106—472no—
149#106—472no—
150#106—472no—
151C4⋊C8C2×D4711yescharacteristic
152#103—471no—
153#103—471no—
154#103—472no—
155#103—472no—
156C22⋊C8C2×D4712yes—
157C4×C8C2×D4711yescharacteristic
158C2×Q8—471no—
159C2×Q8—471no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×D4D18811yescharacteristic
163C22×C4—942no—
164C22×C4C22×D4712yes—
165Q16—942no—
166M16—24no—
167C2×C8C22×D4711yescharacteristic
168C2×C8C22×D4712yes—
169C2×C8C22×D4711yescharacteristic
170C4⋊C4—472no—
171C4⋊C4—471no—
172C4⋊C4—472no—
173C4⋊C4—471no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4—941no—
181C4⋊C4D18811yescharacteristic
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4D18812yes—
186C42—942no—
187C42—941no—
188C42—941no—
189C42C22×D4711yescharacteristic
190C23C2×D18812yes—
191Q8—941no—
192Q8—941no—
193Q8—941no—
194Q8—941no—
195Q8—3761no—
196Q8—1882no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—941no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4—3762no—
207C2×C4C2×D18812yes—
208C2×C4C2×D18811yescharacteristic
209C2×C4C2×D18811yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—21no—
213C8#1062535212yes—
214C22—22no—
215C22—22no—
216C22—22no—
217C22C22×D18811yescharacteristic
218C4—22no—
219C4—21no—
220C4—1881no—
221C4—1881no—
222C4—1882no—
223C4—1881no—
224C4—1882no—
225C4—1881no—
226C4#1309405712yes—
227C4C2×#1062535211yescharacteristic
228C4#1309407111yescharacteristic
229C2—42no—
230C2#1568977711yescharacteristic
231C2C2×#1309405711yescharacteristic
232C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3356
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
3. #15689521C2semidirect
4. #15689465C2semidirect
5. #15689454C2semidirect
6. #15689419C2semidirect
7. #15689409C2semidirect
8. #15689381C2semidirect
9. C4×Dic188C2semidirect
10. #15689165C2semidirect
128. C47#3356semidirect