Finite Group Databasebeta

← #20243738

Subgroups — #20243738

Order 6016.

438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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×D4×Dic47C211yesmaximal, characteristic, complemented
2C2×#13093945C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4#15689026C211yesmaximal, characteristic, complemented
5#15688886C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C22×D8×C47C211yesmaximal, characteristic
8C23×Dic47—21no—
9C22×C47⋊C8C2211yescharacteristic
10D4×Dic47—22no—
11D4×Dic47—22no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C22⋊Dic47—21no—
15C2×C22⋊Dic47—21no—
16C2×C22⋊Dic47—21no—
17C2×C4×Dic47C2211yescharacteristic
18#13093945—22no—
19#13093945—22no—
20C22×D4×C47C2211yescharacteristic
21C22×D4×C47C2211yescharacteristic
22C2×D8×C47—22no—
23C2×D8×C47—22no—
24C2×D8×C47C414yescomplemented
25C22×C8×C47C2211yescharacteristic
26C24×C47—21no—
27C24×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47C2×C412yes—
37C2×D4×C47C2×C412yescomplemented
38C2×D4×C47D412yes—
39C2×D4×C47D412yes—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—24no—
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22×Dic47—42no—
45C22×Dic47—42no—
46C22×Dic47D411yescharacteristic
47C22×Dic47D411yescharacteristic
48D8×C47—28no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C2×C8×C47C2×C412yescomplemented
52C22⋊Dic47—24no—
53C22⋊Dic47—42no—
54C22⋊Dic47—42no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47D412yes—
59C4×Dic47—21no—
60C4×Dic47—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47—41no—
72C23×C47—41no—
73C23×C47—41no—
74C23×C47—41no—
75C23×C47—41no—
76C23×C47—41no—
77C23×C47—41no—
78C23×C47C2×D411yescharacteristic
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—22no—
82D4×C47—22no—
83D4×C47—22no—
84D4×C47—41no—
85D4×C47—41no—
86D4×C47C22⋊C414yescomplemented
87C2×C4×C47C22×C411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—48no—
100C2×Dic47—41no—
101C2×Dic47—41no—
102C2×Dic47—41no—
103C2×Dic47—41no—
104C2×Dic47—41no—
105C2×Dic47D812yescomplemented
106C8×C47—22no—
107C47⋊C8—41no—
108C22×C47—24no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—81no—
119C22×C47—81no—
120C22×C47—81no—
121C22×C47—81no—
122C22×C47C4×D411yescharacteristic
123C22×C47#12011yescharacteristic
124C22×C47#12111yescharacteristic
125C22×C47C2×D811yescharacteristic
126C22×C47#13511yescharacteristic
127C22×C47AGL(1,ℤ/8)11yescharacteristic
128C22×C47AGL(1,ℤ/8)11yescharacteristic
129C4×C47C2×C22⋊C411yescharacteristic
130C4×C47C4×D411yescharacteristic
131C4×C47#12111yescharacteristic
132C4×C47#12311yescharacteristic
133Dic47—22no—
134Dic47—42no—
135Dic47—41no—
136Dic47—81no—
137#1879—471nomaximal, Sylow
138C2×C47—44no—
139C2×C47—82no—
140C2×C47#38611yescharacteristic
141C2×C47C4×D811yescharacteristic
142C2×C47#44211yescharacteristic
143C2×C47#44711yescharacteristic
144C2×C47#44911yescharacteristic
145C2×C47#45911yescharacteristic
146C2×C47#46311yescharacteristic
147C22×D8D4711yescharacteristic
148C2×C4×D4—471no—
149C2×#102—471no—
150C2×#102—471no—
151#390—471no—
152#340—471no—
153#336—471no—
154C47#187911yescharacteristic, complemented, Sylow
155C22×D4C2×D4711yescharacteristic
156C22×D4C2×D4711yescharacteristic
157C23×C4—941no—
158C2×D8—22no—
159C2×D8—22no—
160C2×D8Dic4714yescomplemented
161C22×C8—471no—
162C22×C8C2×D4711yescharacteristic
163C4×D4—942no—
164C4×D4—942no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—471no—
167C2×C22⋊C4—941no—
168C2×C22⋊C4—941no—
169C2×C22⋊C4—941no—
170C2×C42—471no—
171#102—942no—
172#102—942no—
173C24—21no—
174C24—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4C2×Dic4712yes—
184C2×D4C2×Dic4712yescomplemented
185C2×D4C22⋊D4712yes—
186C2×D4C22⋊D4712yes—
187C22×C4—471no—
188C22×C4—471no—
189C22×C4—944no—
190C22×C4—941no—
191C22×C4—941no—
192C22×C4—1882no—
193C22×C4—1882no—
194C22×C4C22×D4711yescharacteristic
195D8—28no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—941no—
199C2×C8—941no—
200C2×C8—941no—
201C2×C8C2×Dic4712yescomplemented
202C4⋊C4—472no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C22⋊C4—944no—
207C22⋊C4—1882no—
208C22⋊C4—1882no—
209C42—941no—
210C42—941no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—41no—
220C23—41no—
221C23—41no—
222C23—41no—
223C23—41no—
224C23—41no—
225C23D4×D4711yescharacteristic
226D4—22no—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4C22⋊Dic4714yescomplemented
234C2×C4—472no—
235C2×C4—941no—
236C2×C4—941no—
237C2×C4—941no—
238C2×C4—942no—
239C2×C4—941no—
240C2×C4—941no—
241C2×C4—1888no—
242C2×C4—1881no—
243C2×C4—1881no—
244C2×C4—1881no—
245C2×C4—1881no—
246C2×C4—1881no—
247C2×C4D4×D4711yescharacteristic
248C2×C4#1062535211yescharacteristic
249C2×C4#1062535211yescharacteristic
250C2×C4C22×Dic4711yescharacteristic
251C2×C4C2×C22⋊D4711yescharacteristic
252C2×C4C2×C22⋊D4711yescharacteristic
253C8—22no—
254C8—1881no—
255C22—24no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—81no—
269C22D4×Dic4711yescharacteristic
270C22#1309399211yescharacteristic
271C22#1309399611yescharacteristic
272C22D8×D4711yescharacteristic
273C22#1309404311yescharacteristic
274C22#1309404811yescharacteristic
275C22#1309404811yescharacteristic
276C4—942no—
277C4—3761no—
278C4—1882no—
279C4—1881no—
280C4C2×C22⋊Dic4711yescharacteristic
281C4D4×Dic4711yescharacteristic
282C4#1309399611yescharacteristic
283C4#1309400511yescharacteristic
284C2—44no—
285C2—82no—
286C2#1568900311yescharacteristic
287C2D8×Dic4711yescharacteristic
288C2#1568923511yescharacteristic
289C2#1568925511yescharacteristic
290C2#1568926511yescharacteristic
291C2#1568931611yescharacteristic
292C2#1568933611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×D8×C47C2
socleC23×C47C2×D4
hypercenterC22×D8D47
hypocenterC47#1879
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic47C2semidirect
2. C2×#13093945C2semidirect
3. C2×#13093945C2semidirect
4. #15689026C2semidirect
5. #15688886C2semidirect
6. #15688877C2semidirect
24. C2×D8×C47C4semidirect
37. C2×D4×C47C2×C4semidirect
51. C2×C8×C47C2×C4semidirect
86. D4×C47C22⋊C4semidirect
105. C2×Dic47D8semidirect
154. C47#1879semidirect
160. C2×D8Dic47semidirect
184. C2×D4C2×Dic47semidirect
201. C2×C8C2×Dic47semidirect
233. D4C22⋊Dic47semidirect