Finite Group Databasebeta

← #20244760

Subgroups — #20244760

Order 6016.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13093956C211yesmaximal, characteristic, complemented
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15689026C211yesmaximal, characteristic
5#15689019C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×C22⋊Dic47—21no—
13C2×C22⋊Dic47—21no—
14C2×C4×Dic47C2211yescharacteristic
15#13093956—22no—
16Dic47⋊C8—22no—
17#13093945—22no—
18C47⋊#95—21no—
19C22×D4×C47C2211yescharacteristic
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22#102×C47—22no—
23C24×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47Q812yes—
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33C22×Dic47—21no—
34C22×Dic47D411yescharacteristic
35C22×Dic47D411yescharacteristic
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47D412yes—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C22⋊Dic47—42no—
42C22⋊Dic47—42no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47D412yes—
47Dic47⋊C4—42no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47—41no—
59C23×C47—41no—
60C23×C47C2×D411yescharacteristic
61D4×C47—22no—
62D4×C47—22no—
63D4×C47—41no—
64D4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×Q811yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—22no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47SD1612yes—
86C8×C47—22no—
87C47⋊C8—41no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47—81no—
94C22×C47—81no—
95C22×C47#12111yescharacteristic
96C22×C47#12111yescharacteristic
97C22×C47C22⋊Q811yescharacteristic
98C22×C47C2×SD1611yescharacteristic
99C22×C47#13511yescharacteristic
100C22×C47AGL(1,ℤ/8)11yescharacteristic
101C22×C47AGL(1,ℤ/8)11yescharacteristic
102C4×C47—81no—
103C4×C47#12111yescharacteristic
104C4×C47C22⋊Q811yescharacteristic
105C4×C47C22⋊Q811yescharacteristic
106C4×C47#12611yescharacteristic
107Dic47—22no—
108Dic47—42no—
109Dic47—41no—
110Dic47—81no—
111#2065—471nomaximal, Sylow
112C2×C47—82no—
113C2×C47#39611yescharacteristic
114C2×C47#46011yescharacteristic
115C2×C47#46311yescharacteristic
116C2×C47#46511yescharacteristic
117C2×C47#46911yescharacteristic
118C2×C47#47611yescharacteristic
119C2×C47#47811yescharacteristic
120C2×#106—471no—
121C2×C4⋊C8—471no—
122C2×#102—471no—
123C2×#102D4711yescharacteristic
124#390—471no—
125#389—471no—
126#340—471no—
127C47#206511yescharacteristic, complemented, Sylow
128C22×D4C2×D4711yescharacteristic
129C22×C8—471no—
130C22×C8C2×D4711yescharacteristic
131C2×C4⋊C4—471no—
132C2×C4⋊C4—471no—
133C2×C4⋊C4—941no—
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C22⋊C4—941no—
136C2×C22⋊C4—941no—
137C2×C42—471no—
138#106—942no—
139C4⋊C8—942no—
140#102—22no—
141#102—942no—
142#95—941no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic9412yes—
150C22×C4—21no—
151C22×C4—471no—
152C22×C4—471no—
153C22×C4—941no—
154C22×C4—941no—
155C22×C4C22×D4711yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—941no—
159C2×C8—941no—
160C2×C8—941no—
161C2×C8C22⋊D4712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—1882no—
169C22⋊C4—1882no—
170C22⋊C4—1882no—
171C42—941no—
172C42—941no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D4711yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—472no—
189C2×C4—941no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4—1881no—
200C2×C4C2×Dic9411yescharacteristic
201C2×C4#1062535011yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4#1062535211yescharacteristic
204C2×C4#1062535211yescharacteristic
205C2×C4C2×C22⋊D4711yescharacteristic
206C8—22no—
207C8—1881no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1309399511yescharacteristic
216C22#1309399711yescharacteristic
217C22#1309400111yescharacteristic
218C22SD16×D4711yescharacteristic
219C22#1309404511yescharacteristic
220C22#1309404811yescharacteristic
221C22#1309404811yescharacteristic
222C4—81no—
223C4—942no—
224C4—3761no—
225C4—1882no—
226C4—1881no—
227C4#1309399611yescharacteristic
228C4#1309400111yescharacteristic
229C4#1309400311yescharacteristic
230C4#1309401711yescharacteristic
231C2—82no—
232C2#1568904611yescharacteristic
233C2#1568932211yescharacteristic
234C2#1568933711yescharacteristic
235C2#1568934911yescharacteristic
236C2#1568937311yescharacteristic
237C2#1568941111yescharacteristic
238C2#1568942511yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2065
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13093956C2semidirect
2. C2×Dic47⋊C8C2semidirect
5. #15689019C2semidirect
6. #15688885C2semidirect
127. C47#2065semidirect