Finite Group Databasebeta

← #20254620

Subgroups — #20254620

Order 6016.

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

normal subgroups only

This group has 362 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
1C2×#13094024C211yesmaximal, characteristic, complemented
2#15689657C211yesmaximal, characteristic
3#15689532C212yesmaximal, complemented
4#15689483C212yesmaximal, complemented
5#15689459C212yesmaximal, complemented
6#15689442C212yesmaximal
7#15689409C212yesmaximal, complemented
8#15689404C212yesmaximal, complemented
9C47×#432C211yesmaximal, characteristic, complemented
10C22×Dic94—21no—
11#13094024—21no—
12#13094024—21no—
13#13094024C2212yes—
14#13094024C2212yes—
15#13094018—21no—
16#13094016C2211yescharacteristic
17#13094012C2211yescharacteristic
18#13094007—21no—
19#13094003C2211yescharacteristic
20#13093998C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×D188C2211yescharacteristic
23C4×C22⋊D47—21no—
24#13093981—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2212yes—
27#13093958C2214yes—
28#13093956C2214yes—
29#13093949C2214yes—
30#13093946C2214yes—
31C2×C42×C47C2211yescharacteristic
32C4⋊C8×C47C2212yes—
33C22⋊C8×C47C2212yes—
34#97×C47C2212yes—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—21no—
39C22×Dic47—22no—
40C2×D188C2311yescharacteristic
41C2×C4×D47—21no—
42C2×Dic94—22no—
43C2×Dic94—22no—
44C2×Dic94—44no—
45C2×Dic94C2311yescharacteristic
46C2×C8×C47C2314yes—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51C22⋊Dic47—21no—
52(C2×D47)⋊C4—21no—
53(C2×D47)⋊C4—21no—
54(C2×D47)⋊C4—21no—
55(C2×D47)⋊C4—21no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47C2314yes—
60C4⋊Dic47C2311yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62Dic47⋊C4—21no—
63Dic47⋊C4—21no—
64Dic47⋊C4—21no—
65Dic47⋊C4—21no—
66C4×Dic47—21no—
67C23×C47C2×D411yescharacteristic
68C22×D47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—42no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—24no—
83C2×Dic47—44no—
84D188—22no—
85C4×D47—42no—
86Dic94—22no—
87Dic94—44no—
88Dic94—44no—
89C8×C47—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#13712yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—41no—
95C2×D47—41no—
96C2×D47—41no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47AGL(1,ℤ/8)12yes—
102C4×C472−1+412yes—
103Dic47—41no—
104Dic47—44no—
105Dic47—41no—
106Dic47—41no—
107#3239—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#53611yescharacteristic
110C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—81no—
113C2×C4⋊Q8—471no—
114#529—471no—
115#501—472no—
116#489—472no—
117#484—472no—
118#481—472no—
119#475—472no—
120#474—472no—
121#432D4711yescharacteristic, complemented
122C47#323911yescharacteristic, complemented, Sylow
123C22×Q8—941no—
124C4⋊Q8—472no—
125C4⋊Q8—472no—
126C4⋊Q8—941no—
127C4⋊Q8—941no—
128#126—941no—
129#125—471no—
130#124—471no—
131#123—941no—
132C22⋊Q8—471no—
133#121—471no—
134C4×Q8—471no—
135C4×D4—471no—
136C4×D4—941no—
137#117—941no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—941no—
140C2×C42C2×D4711yescharacteristic
141#107—474no—
142#106—474no—
143C4⋊C8C2×D4712yes—
144#103—474no—
145#102—474no—
146C22⋊C8C2×D4712yes—
147#97C2×D4712yes—
148C2×Q8—471no—
149C2×Q8—942no—
150C2×Q8—942no—
151C2×Q8—1884no—
152C2×D4—471no—
153C2×D4—941no—
154C22×C4—942no—
155C22×C4—941no—
156C22×C4D18811yescharacteristic
157C22×C4D18811yescharacteristic
158C22×C4C22×D4711yescharacteristic
159C2×C8C22×D4714yes—
160C4⋊C4—474no—
161C4⋊C4—471no—
162C4⋊C4—471no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C22⋊C4—941no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C22⋊C4—941no—
175C42—941no—
176C42D18811yescharacteristic
177C42D18811yescharacteristic
178C42C22×D4711yescharacteristic
179C42C22×D4711yescharacteristic
180C23—941no—
181C23C2×D18811yescharacteristic
182Q8—942no—
183Q8—1884no—
184Q8—1884no—
185D4—942no—
186D4—1882no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—944no—
194C2×C4—1884no—
195C2×C4—1882no—
196C2×C4C2×D18811yescharacteristic
197C2×C4C2×D18811yescharacteristic
198C2×C4C2×D18811yescharacteristic
199C2×C4C2×D18811yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—1881no—
206C22—1881no—
207C22—1881no—
208C22#1309405712yes—
209C22C22×D18811yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—1884no—
215C4—1881no—
216C4—1881no—
217C4—1881no—
218C4#1309405212yes—
219C4#1309407112yes—
220C2—22no—
221C2—3761no—
222C2#1568969911yescharacteristic
223C2C2×#1309405211yescharacteristic
224C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3239
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
3. #15689532C2semidirect
4. #15689483C2semidirect
5. #15689459C2semidirect
7. #15689409C2semidirect
8. #15689404C2semidirect
9. C47×#432C2semidirect
121. #432D47semidirect
122. C47#3239semidirect