Finite Group Databasebeta

← #20243717

Subgroups — #20243717

Order 6016.

324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13094031C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic, complemented
3C2×#13093951C211yesmaximal, characteristic, complemented
4#15689090C211yesmaximal, characteristic, complemented
5#15688888C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#135×C47C211yesmaximal, characteristic
8#13094031—22no—
9#13094031—22no—
10C2×#10625329—21no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8—21no—
14C22×C47⋊C8C2211yescharacteristic
15C2×C4×Dic47C2211yescharacteristic
16#13093951—22no—
17#13093951—22no—
18C22⋊(C47⋊C8)—21no—
19C22⋊(C47⋊C8)—21no—
20C2×#41×C47C2211yescharacteristic
21C2×#41×C47C2211yescharacteristic
22#135×C47—22no—
23#135×C47—22no—
24C2×Q16×C47C411yescharacteristic, complemented
25C2×SD16×C47C411yescharacteristic, complemented
26C2×SD16×C47C411yescharacteristic, complemented
27C2×D8×C47C411yescharacteristic, complemented
28C22×C8×C47C2211yescharacteristic
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32#41×C47—21no—
33#41×C47—21no—
34#41×C47—21no—
35#41×C47D412yes—
36#41×C47D412yes—
37C2×Q8×C47C2×C411yescharacteristic
38C2×Q8×C47C2×C411yescharacteristic
39C2×D4×C47—21no—
40C2×D4×C47—21no—
41C2×D4×C47C2×C411yescharacteristic
42C2×D4×C47C2×C411yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C22×Dic47—21no—
47Q16×C47—22no—
48SD16×C47—22no—
49SD16×C47—22no—
50D8×C47—22no—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47C2×C411yescharacteristic
54C2×C8×C47C2×C411yescharacteristic
55C4×Dic47—21no—
56C4×Dic47—21no—
57#10625329—24no—
58#10625329—21no—
59#10625329—21no—
60#10625329—21no—
61#10625329D412yes—
62C2×C47⋊C8—24no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8—21no—
65C2×C47⋊C8—21no—
66C2×C47⋊C8—21no—
67C2×C47⋊C8D411yescharacteristic
68C2×C47⋊C8D411yescharacteristic
69C23×C47—21no—
70C23×C47—21no—
71C23×C47#4111yescharacteristic
72Q8×C47—21no—
73Q8×C47—21no—
74Q8×C47—21no—
75Q8×C47C22⋊C412yes—
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—21no—
79D4×C47—21no—
80D4×C47—21no—
81D4×C47—41no—
82D4×C47—41no—
83D4×C47C22⋊C412yes—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47C22×C411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47#4111yescharacteristic
96C2×Dic47—22no—
97C2×Dic47—41no—
98C2×Dic47—41no—
99C8×C47—21no—
100C8×C47—21no—
101C47⋊C8—21no—
102C47⋊C8—22no—
103C47⋊C8—21no—
104C47⋊C8—41no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47C4×D411yescharacteristic
114C22×C47#12111yescharacteristic
115C22×C47#12311yescharacteristic
116C4×C47—22no—
117C4×C47—41no—
118C4×C47C2×C22⋊C411yescharacteristic
119C4×C47C4×D411yescharacteristic
120C4×C47#12011yescharacteristic
121C4×C47#12111yescharacteristic
122Dic47—42no—
123#1876—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—42no—
127C2×C47—81no—
128C2×C47#38611yescharacteristic
129C2×C47#44311yescharacteristic
130C2×C47#44411yescharacteristic
131C2×#135D4711yescharacteristic
132C2×#131—471no—
133C2×#104—471no—
134C2×#104—471no—
135#408—471no—
136#341—471no—
137#336—471no—
138C47#187611yescharacteristic, complemented, Sylow
139C2×#41C2×D4711yescharacteristic
140C2×#41C2×D4711yescharacteristic
141#135—22no—
142#135—22no—
143C2×Q16Dic4711yescharacteristic, complemented
144C2×SD16Dic4711yescharacteristic, complemented
145C2×SD16Dic4711yescharacteristic, complemented
146C2×D8Dic4711yescharacteristic, complemented
147#131—942no—
148#131—942no—
149C2×M16—471no—
150C2×M16—471no—
151C2×M16—941no—
152C22×C8—471no—
153C22×C8—941no—
154C22×C8C2×D4711yescharacteristic
155C2×C42—471no—
156#104—942no—
157#104—942no—
158C22⋊C8—941no—
159C22⋊C8—941no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166#41C22⋊D4712yes—
167#41C22⋊D4712yes—
168C2×Q8C2×Dic4711yescharacteristic
169C2×Q8C2×Dic4711yescharacteristic
170C2×D4—21no—
171C2×D4—21no—
172C2×D4C2×Dic4711yescharacteristic
173C2×D4C2×Dic4711yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—22no—
179SD16—22no—
180SD16—22no—
181D8—22no—
182M16—472no—
183M16—944no—
184M16—941no—
185M16—941no—
186M16—941no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—471no—
190C2×C8—471no—
191C2×C8—944no—
192C2×C8—941no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8C2×Dic4711yescharacteristic
197C2×C8C2×Dic4711yescharacteristic
198C42—941no—
199C42—941no—
200C23—21no—
201C23—21no—
202C23#1062535211yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—21no—
206Q8C22⋊Dic4712yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—21no—
211D4—21no—
212D4—41no—
213D4—41no—
214D4C22⋊Dic4712yes—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—942no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4D4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4#1062535211yescharacteristic
227C2×C4C22×Dic4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C8—21no—
231C8—21no—
232C8—941no—
233C8—941no—
234C8—942no—
235C8—1881no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22D4×Dic4711yescharacteristic
245C22#1309399611yescharacteristic
246C22#1309400511yescharacteristic
247C4—22no—
248C4—41no—
249C4—1882no—
250C4C2×C22⋊Dic4711yescharacteristic
251C4D4×Dic4711yescharacteristic
252C4#1309399211yescharacteristic
253C4#1309399611yescharacteristic
254C2—21no—
255C2—21no—
256C2—42no—
257C2—81no—
258C2#1568900311yescharacteristic
259C2#1568924011yescharacteristic
260C2#1568924511yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#135×C47C2
socleC22×C47C4×D4
hypercenterC2×#135D47
hypocenterC47#1876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094031C2semidirect
2. C2×#13093951C2semidirect
3. C2×#13093951C2semidirect
4. #15689090C2semidirect
5. #15688888C2semidirect
6. #15688877C2semidirect
24. C2×Q16×C47C4semidirect
25. C2×SD16×C47C4semidirect
26. C2×SD16×C47C4semidirect
27. C2×D8×C47C4semidirect
138. C47#1876semidirect
143. C2×Q16Dic47semidirect
144. C2×SD16Dic47semidirect
145. C2×SD16Dic47semidirect
146. C2×D8Dic47semidirect