Finite Group Databasebeta

← #20244624

Subgroups — #20244624

Order 6016.

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

normal subgroups only

This group has 318 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×#13093948C211yesmaximal, characteristic, complemented
2C2×#13093948C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4C2×#13093945C211yesmaximal, characteristic
5#15689021C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C2×#124×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093948—22no—
14#13093948—22no—
15#13093945—22no—
16#13093945—22no—
17C47⋊#95—21no—
18C22×Q8×C47C2211yescharacteristic
19C22×D4×C47C2211yescharacteristic
20#124×C47—22no—
21#124×C47—22no—
22C2×C22⋊C4×C47—21no—
23C2×C22⋊C4×C47—21no—
24C2×C42×C47C2211yescharacteristic
25C24×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47D412yes—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47D412yes—
38C22×C4×C47—21no—
39C22×C4×C47D411yescharacteristic
40C22×C4×C47D411yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22⋊C4×C47—24no—
45C22⋊C4×C47—24no—
46C42×C47—21no—
47C42×C47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47D412yes—
52Dic47⋊C4—42no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47—22no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47—41no—
63C23×C47—41no—
64C23×C47—41no—
65C23×C47—41no—
66C23×C47C2×D411yescharacteristic
67Q8×C47—22no—
68Q8×C47—22no—
69Q8×C47—41no—
70Q8×C47—41no—
71D4×C47—22no—
72D4×C47—22no—
73D4×C47—41no—
74D4×C47—41no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C47⋊C8—41no—
97C47⋊C8—41no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—81no—
102C22×C47—81no—
103C22×C47—81no—
104C22×C47—81no—
105C22×C47#12011yescharacteristic
106C22×C47#12111yescharacteristic
107C22×C47#12411yescharacteristic
108C22×C47#13511yescharacteristic
109C22×C47#13511yescharacteristic
110C22×C47AGL(1,ℤ/8)11yescharacteristic
111C22×C47#13711yescharacteristic
112C4×C47—42no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47#12111yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12311yescharacteristic
118C4×C47#12311yescharacteristic
119Dic47—42no—
120Dic47—81no—
121#2042—471nomaximal, Sylow
122C2×C47—82no—
123C2×C47#39411yescharacteristic
124C2×C47#44911yescharacteristic
125C2×C47#45211yescharacteristic
126C2×C47#46311yescharacteristic
127C2×C47#46411yescharacteristic
128C2×C47#48811yescharacteristic
129C2×C47#48911yescharacteristic
130C2×#124D4711yescharacteristic
131C2×#103—471no—
132C2×#103—471no—
133C2×#102—471no—
134C2×#102—471no—
135#389—471no—
136#336—471no—
137C47#204211yescharacteristic, complemented, Sylow
138C22×Q8C2×D4711yescharacteristic
139C22×D4C2×D4711yescharacteristic
140C22×C8—471no—
141C22×C8—471no—
142#124—22no—
143#124—22no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—941no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42C2×D4711yescharacteristic
150#103—942no—
151#103—942no—
152#102—942no—
153#102—942no—
154#95—941no—
155C24—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D4712yes—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D4712yes—
168C22×C4—21no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4C22⋊D4711yescharacteristic
172C22×C4C22⋊D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C2×C8—941no—
175C2×C8—941no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—472no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—1882no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C42—21no—
188C42—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—942no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1881no—
220C2×C4D4×D4711yescharacteristic
221C2×C4#1062535211yescharacteristic
222C2×C4#1062535211yescharacteristic
223C2×C4#1062535211yescharacteristic
224C2×C4C2×C22⋊D4711yescharacteristic
225C2×C4C2×C22⋊D4711yescharacteristic
226C8—1881no—
227C8—1881no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1309399311yescharacteristic
236C22#1309399511yescharacteristic
237C22#1309401111yescharacteristic
238C22#1309404411yescharacteristic
239C22#1309404411yescharacteristic
240C22#1309404911yescharacteristic
241C22#1309405411yescharacteristic
242C4—41no—
243C4—41no—
244C4—42no—
245C4—3761no—
246C4—1882no—
247C4#1309399611yescharacteristic
248C4#1309399611yescharacteristic
249C4#1309400511yescharacteristic
250C4#1309400511yescharacteristic
251C2—82no—
252C2#1568903711yescharacteristic
253C2#1568926811yescharacteristic
254C2#1568928511yescharacteristic
255C2#1568933511yescharacteristic
256C2#1568934211yescharacteristic
257C2#1568947711yescharacteristic
258C2#1568948211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#124×C47C2
socleC23×C47C2×D4
hypercenterC2×#124D47
hypocenterC47#2042
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13093948C2semidirect
2. C2×#13093948C2semidirect
5. #15689021C2semidirect
6. #15688878C2semidirect
137. C47#2042semidirect