Finite Group Databasebeta

← #20244577

Subgroups — #20244577

Order 6016.

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

normal subgroups only

This group has 368 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×#13093998C211yesmaximal, characteristic
2C2×#13093955C211yesmaximal, characteristic, complemented
3C2×#13093944C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic, complemented
5C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#380C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C22⋊D47—21no—
10C22×C47⋊C8C2211yescharacteristic
11C22×C47⋊C8C2211yescharacteristic
12#13093998—22no—
13#13093998—22no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×(C2×D47)⋊C4—21no—
16#13093955—22no—
17#13093944—22no—
18#13093944—22no—
19C22⋊(C47⋊C8)—22no—
20C23×C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C22⋊C4×C47—21no—
24#95×C47—21no—
25C24×C47D411yescharacteristic
26C23×D47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—24no—
38C2×C22⋊D47—42no—
39C2×C22⋊D47—42no—
40C22×Dic47—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188D412yes—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C22⋊C4×C47—42no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—21no—
54C4⋊Dic47D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8D412yescomplemented
61C23×C47—21no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—21no—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47SD1612yes—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—41no—
71C22×D47—41no—
72C22×D47—41no—
73C22×D47—41no—
74C22×D47—41no—
75C22×D47—41no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—41no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C2×C4×C47#4111yescharacteristic
94C2×C4×C47#4111yescharacteristic
95C22⋊D47—48no—
96C2×Dic47—22no—
97C2×Dic47—41no—
98C2×Dic47—41no—
99D188—22no—
100D188—22no—
101D188—41no—
102D188—41no—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47#12011yescharacteristic
113C22×C47#12111yescharacteristic
114C22×C47#12311yescharacteristic
115C22×C47C2×SD1611yescharacteristic
116C22×C47#13511yescharacteristic
117C22×C47AGL(1,ℤ/8)11yescharacteristic
118C22×C47AGL(1,ℤ/8)11yescharacteristic
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—42no—
122C2×D47—81no—
123C2×D47—81no—
124C2×D47—81no—
125C2×D47—81no—
126C4×C47—41no—
127C4×C47—81no—
128C4×C47—81no—
129C4×C47#12111yescharacteristic
130C4×C47#12111yescharacteristic
131C4×C47#12311yescharacteristic
132C4×C47#12411yescharacteristic
133Dic47—42no—
134#2034—471nomaximal, Sylow
135C2×C47—42no—
136C2×C47#39411yescharacteristic
137C2×C47#44911yescharacteristic
138C2×C47#45011yescharacteristic
139C2×C47#46511yescharacteristic
140C2×C47#46911yescharacteristic
141C2×C47#48111yescharacteristic
142C2×C47#48211yescharacteristic
143D47—82no—
144C2×#121—471no—
145C2×#106—471no—
146C2×#102—471no—
147C2×#102—471no—
148C2×C22⋊C8—471no—
149#380D4711yescharacteristic, complemented
150#340—471no—
151C47#203411yescharacteristic, complemented, Sylow
152C22×D4—471no—
153C22×D4—941no—
154C23×C4C2×D4711yescharacteristic
155C22×C8—471no—
156C22×C8—471no—
157#121—942no—
158#121—942no—
159C2×C4⋊C4—471no—
160C2×C4⋊C4C2×D4711yescharacteristic
161C2×C4⋊C4C2×D4711yescharacteristic
162C2×C22⋊C4—21no—
163C2×C22⋊C4—941no—
164#106—942no—
165#102—942no—
166#102—942no—
167C22⋊C8—942no—
168#95—21no—
169C24—941no—
170C24C22⋊D4711yescharacteristic
171C2×D4—472no—
172C2×D4—944no—
173C2×D4—941no—
174C2×D4—941no—
175C2×D4—941no—
176C2×D4—941no—
177C2×D4—941no—
178C2×D4—1882no—
179C2×D4—1882no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—941no—
189C22×C4C22⋊D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C2×C8—472no—
192C2×C8—941no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8—941no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—472no—
202C4⋊C4—941no—
203C22⋊C4—42no—
204C22⋊C4—944no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—942no—
212C23—1881no—
213C23—1881no—
214C23—1881no—
215C23—1881no—
216C23—1881no—
217C23—1881no—
218C23#1062533612yes—
219C23C2×C22⋊D4711yescharacteristic
220D4—942no—
221D4—942no—
222D4—1888no—
223D4—1881no—
224D4—1881no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—942no—
239C2×C4—1881no—
240C2×C4—1881no—
241C2×C4#1062535011yescharacteristic
242C2×C4#1062535011yescharacteristic
243C2×C4D4×D4711yescharacteristic
244C2×C4D4×D4711yescharacteristic
245C2×C4D4×D4711yescharacteristic
246C2×C4#1062535211yescharacteristic
247C8—942no—
248C8—1881no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—3761no—
257C22—3761no—
258C22—3761no—
259C22—3761no—
260C22—1882no—
261C22—1882no—
262C22—1882no—
263C22#1309399211yescharacteristic
264C22#1309399611yescharacteristic
265C22#1309400711yescharacteristic
266C22C2×#1062533611yescharacteristic
267C22#1309404411yescharacteristic
268C22#1309404911yescharacteristic
269C22#1309405011yescharacteristic
270C4—41no—
271C4—81no—
272C4—81no—
273C4—1882no—
274C4#1309399711yescharacteristic
275C4#1309399711yescharacteristic
276C4#1309400611yescharacteristic
277C4#1309401011yescharacteristic
278C2—42no—
279C2—3762no—
280C2#1568903811yescharacteristic
281C2#1568926611yescharacteristic
282C2#1568927311yescharacteristic
283C2#1568935411yescharacteristic
284C2#1568937411yescharacteristic
285C2#1568944111yescharacteristic
286C2#1568944711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#380C2
socleC23×C47C2×D4
hypercenter#380D47
hypocenterC47#2034
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#13093955C2semidirect
3. C2×#13093944C2semidirect
4. C2×#13093944C2semidirect
5. C2×C22⋊(C47⋊C8)C2semidirect
6. #15688885C2semidirect
7. C47×#380C2semidirect
60. C2×C47⋊C8D4semidirect
149. #380D47semidirect
151. C47#2034semidirect