Finite Group Databasebeta

← #20244588

Subgroups — #20244588

Order 6016.

316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13093957C211yesmaximal, characteristic, complemented
2C2×#13093948C211yesmaximal, characteristic, complemented
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
5#15688983C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C2×C22⋊Q8×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C22⋊Dic47—21no—
13#13093957—22no—
14#13093948—22no—
15#13093948—22no—
16C22⋊(C47⋊C8)—22no—
17C47⋊#95—21no—
18C22×Q8×C47C2211yescharacteristic
19C23×C4×C47C2211yescharacteristic
20C22⋊Q8×C47—22no—
21C22⋊Q8×C47—22no—
22C2×C4⋊C4×C47—21no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—21no—
25C24×C47D411yescharacteristic
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47D412yes—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47D411yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—21no—
43C22×Dic47—21no—
44C4⋊C4×C47—24no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47D412yes—
47C22⋊C4×C47—24no—
48C22⋊Dic47—42no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8D412yes—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—21no—
65C23×C47Q1612yes—
66C23×C47C2×D411yescharacteristic
67Q8×C47—22no—
68Q8×C47—22no—
69Q8×C47—41no—
70Q8×C47—41no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
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—41no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C47⋊C8—22no—
97C47⋊C8—41no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47—22no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47#12011yescharacteristic
106C22×C47#12111yescharacteristic
107C22×C47#12311yescharacteristic
108C22×C47C2×Q1611yescharacteristic
109C22×C47#13511yescharacteristic
110C22×C47AGL(1,ℤ/8)11yescharacteristic
111C22×C47#13711yescharacteristic
112C4×C47—41no—
113C4×C47—42no—
114C4×C47—42no—
115C4×C47#12111yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12311yescharacteristic
118C4×C47#12411yescharacteristic
119Dic47—81no—
120Dic47—81no—
121#2036—471nomaximal, Sylow
122C2×C47—42no—
123C2×C47#39411yescharacteristic
124C2×C47#44911yescharacteristic
125C2×C47#45111yescharacteristic
126C2×C47#46711yescharacteristic
127C2×C47#46811yescharacteristic
128C2×C47#48411yescharacteristic
129C2×C47#48511yescharacteristic
130C2×C22⋊Q8D4711yescharacteristic
131C2×#107—471no—
132C2×#103—471no—
133C2×#103—471no—
134C2×C22⋊C8—471no—
135#380—471no—
136#340—471no—
137C47#203611yescharacteristic, complemented, Sylow
138C22×Q8C2×D4711yescharacteristic
139C23×C4C2×D4711yescharacteristic
140C22×C8—471no—
141C22×C8—471no—
142C22⋊Q8—22no—
143C22⋊Q8—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—21no—
149C2×C22⋊C4—941no—
150#107—942no—
151#103—942no—
152#103—942no—
153C22⋊C8—942no—
154#95—941no—
155C24C22⋊D4711yescharacteristic
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D4712yes—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—941no—
171C22×C4—941no—
172C22×C4C22⋊D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C2×C8—472no—
175C2×C8—941no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—24no—
181C4⋊C4—21no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4C22⋊D4712yes—
187C22⋊C4—24no—
188C22⋊C4—1882no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#1062533712yes—
196C23C2×C22⋊D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1881no—
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—942no—
227C8—1881no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1309399311yescharacteristic
236C22#1309399611yescharacteristic
237C22#1309400511yescharacteristic
238C22C2×#1062533711yescharacteristic
239C22#1309404411yescharacteristic
240C22#1309404911yescharacteristic
241C22#1309405511yescharacteristic
242C4—42no—
243C4—41no—
244C4—42no—
245C4—3761no—
246C4—3761no—
247C4#1309399511yescharacteristic
248C4#1309399611yescharacteristic
249C4#1309400511yescharacteristic
250C4#1309401111yescharacteristic
251C2—42no—
252C2#1568903711yescharacteristic
253C2#1568926811yescharacteristic
254C2#1568927911yescharacteristic
255C2#1568936211yescharacteristic
256C2#1568937111yescharacteristic
257C2#1568945611yescharacteristic
258C2#1568946111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×C22⋊Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊Q8D47
hypocenterC47#2036
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13093957C2semidirect
2. C2×#13093948C2semidirect
3. C2×#13093948C2semidirect
6. #15688885C2semidirect
137. C47#2036semidirect