Finite Group Databasebeta

← #20243715

Subgroups — #20243715

Order 6016.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094044C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic, complemented
4#15689089C211yesmaximal, characteristic, complemented
5#15688887C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#131×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094044—22no—
10#13094044—22no—
11C2×#10625337C411yescharacteristic, complemented
12C2×#10625335C411yescharacteristic, complemented
13C2×#10625336C411yescharacteristic, complemented
14C2×#10625334C411yescharacteristic, complemented
15C2×#10625329C2211yescharacteristic
16C22×C47⋊C8C2211yescharacteristic
17C2×C4×Dic47C2211yescharacteristic
18#13093951—22no—
19#13093950—22no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22C2×#41×C47C2211yescharacteristic
23#131×C47—22no—
24#131×C47—22no—
25C2×M16×C47—21no—
26C2×M16×C47C2211yescharacteristic
27C22×C8×C47—21no—
28C22×C8×C47C2211yescharacteristic
29#41×C47—21no—
30#41×C47—21no—
31#41×C47D412yes—
32#41×C47D412yes—
33C2×Q8×C47C2×C411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47C2×C411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—21no—
39C22×Dic47—21no—
40#10625350—21no—
41#10625350—21no—
42#10625350—21no—
43#10625350—21no—
44C2×D188C2×C411yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94C2×C411yescharacteristic
47M16×C47—24no—
48M16×C47—21no—
49M16×C47D412yes—
50C2×C8×C47—24no—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47—21no—
54C2×C8×C47D411yescharacteristic
55C2×C8×C47D411yescharacteristic
56#10625337—22no—
57#10625336—22no—
58#10625335—22no—
59#10625334—22no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62#10625329—21no—
63#10625329—21no—
64C2×C47⋊C8—21no—
65C2×C47⋊C8—21no—
66C2×C47⋊C8—21no—
67C2×C47⋊C8C2×C411yescharacteristic
68C2×C47⋊C8C2×C411yescharacteristic
69C23×C47—21no—
70C23×C47#4111yescharacteristic
71C22×D47—21no—
72Q8×C47—21no—
73Q8×C47C22⋊C412yes—
74D4×C47—22no—
75D4×C47—22no—
76D4×C47—21no—
77D4×C47C22⋊C412yes—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C22×C411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C22⋊D47—41no—
88C22⋊D47—41no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93D188—21no—
94D188—21no—
95C4×D47—41no—
96C4×D47—41no—
97Dic94—21no—
98Dic94—21no—
99C8×C47—21no—
100C8×C47—22no—
101C8×C47—21no—
102C47⋊C8—21no—
103C47⋊C8—21no—
104C47⋊C8—41no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47C4×D411yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47#12311yescharacteristic
113C2×D47—41no—
114C2×D47—41no—
115C2×D47—41no—
116C4×C47—22no—
117C4×C47C2×C22⋊C411yescharacteristic
118C4×C47C4×D411yescharacteristic
119C4×C47#12011yescharacteristic
120C4×C47#12111yescharacteristic
121Dic47—42no—
122Dic47—41no—
123#1876—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—42no—
127C2×C47#38611yescharacteristic
128C2×C47#44311yescharacteristic
129C2×C47#44411yescharacteristic
130D47—81no—
131C2×#135—471no—
132C2×#131D4711yescharacteristic, complemented
133C2×#104—471no—
134C2×#104—471no—
135#408—471no—
136#341—471no—
137#336—471no—
138C47#187611yescharacteristic, complemented, Sylow
139C2×#41—471no—
140C2×#41C2×D4711yescharacteristic
141#135—942no—
142#135—942no—
143C2×Q16—471no—
144C2×SD16—471no—
145C2×SD16—471no—
146C2×D8—471no—
147#131—22no—
148#131—22no—
149C2×M16—21no—
150C2×M16—471no—
151C2×M16C2×D4711yescharacteristic
152C22×C8—21no—
153C22×C8—471no—
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—941no—
163#41—941no—
164#41—941no—
165#41—941no—
166#41D18812yes—
167#41C22⋊D4712yes—
168C2×Q8—471no—
169C2×Q8C4×D4711yescharacteristic
170C2×D4—21no—
171C2×D4—471no—
172C2×D4—941no—
173C2×D4C4×D4711yescharacteristic
174C22×C4—21no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—24no—
183M16—21no—
184M16—941no—
185M16—941no—
186M16C22⋊D4712yes—
187C2×C8—24no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—471no—
192C2×C8—471no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8C22⋊D4711yescharacteristic
197C2×C8C22⋊D4711yescharacteristic
198C42—941no—
199C42—941no—
200C23—21no—
201C23—941no—
202C23#1062535011yescharacteristic
203Q8—21no—
204Q8—941no—
205Q8—941no—
206Q8(C2×D47)⋊C412yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—941no—
211D4—941no—
212D4—1881no—
213D4—1881no—
214D4(C2×D47)⋊C412yes—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—1881no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4C2×C4×D4711yescharacteristic
225C2×C4C2×D18811yescharacteristic
226C2×C4#1062535011yescharacteristic
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C8—21no—
231C8—22no—
232C8—21no—
233C8—941no—
234C8—941no—
235C8—1881no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—1881no—
242C22—1881no—
243C22—1881no—
244C22C4×C22⋊D4711yescharacteristic
245C22#1309399811yescharacteristic
246C22#1309400711yescharacteristic
247C4—22no—
248C4—1882no—
249C4—1881no—
250C4C2×(C2×D47)⋊C411yescharacteristic
251C4C4×C22⋊D4711yescharacteristic
252C4#1309399311yescharacteristic
253C4#1309399811yescharacteristic
254C2—21no—
255C2—21no—
256C2—42no—
257C2—3761no—
258C2#1568900211yescharacteristic
259C2#1568923811yescharacteristic
260C2#1568924311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#131×C47C2
socleC22×C47C4×D4
hypercenterC2×#131D47
hypocenterC47#1876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. C2×#13093951C2semidirect
3. C2×#13093950C2semidirect
4. #15689089C2semidirect
5. #15688887C2semidirect
6. #15688877C2semidirect
7. C2×#131×C47C2semidirect
11. C2×#10625337C4semidirect
12. C2×#10625335C4semidirect
13. C2×#10625336C4semidirect
14. C2×#10625334C4semidirect
132. C2×#131D47semidirect
138. C47#1876semidirect