Finite Group Databasebeta

← #20255665

Subgroups — #20255665

Order 6016.

374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×Dic94C211yesmaximal, characteristic
2#15689475C211yesmaximal, characteristic, complemented
3#15689464C212yesmaximal, complemented
4#15689405C211yesmaximal, characteristic, complemented
5#15689379C212yesmaximal, complemented
6#15689333C211yesmaximal, characteristic, complemented
7#15689278C212yesmaximal, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9#15689201C211yesmaximal, characteristic
10#15689131C212yesmaximal, complemented
11C47×#556C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13C2×#10625337C2211yescharacteristic
14C2×#10625337C2212yes—
15C2×#10625329C2212yes—
16#13094024C2211yescharacteristic
17#13094023—21no—
18#13094003C2212yes—
19#13094001—22no—
20C4×Dic94C2211yescharacteristic
21D4×Dic47—21no—
22#13093957C2211yescharacteristic
23#13093955C2212yes—
24C4⋊(C47⋊C8)C2211yescharacteristic
25#13093948C2211yescharacteristic
26#13093947C2211yescharacteristic
27#13093947C2212yes—
28#13093947C2212yes—
29#13093947C2212yes—
30#13093947C2212yes—
31C22⋊(C47⋊C8)C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C4⋊Q8×C47C2211yescharacteristic
34#126×C47—22no—
35#124×C47—21no—
36C22⋊Q8×C47C2212yes—
37C4×Q8×C47—21no—
38C4×Q8×C47C2211yescharacteristic
39C4×D4×C47C2211yescharacteristic
40#117×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47D411yescharacteristic
44C22×C4×C47C2312yes—
45C22×Dic47—22no—
46C2×Dic94—24no—
47C2×Dic94—22no—
48C2×Dic94—42no—
49C2×Dic94C2312yes—
50C2×Dic94C2311yescharacteristic
51C4⋊C4×C47—22no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47D411yescharacteristic
55C4⋊C4×C47C2311yescharacteristic
56C4⋊C4×C47C2312yes—
57C22⋊C4×C47—22no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47D412yes—
60C42×C47—22no—
61C42×C47—21no—
62C42×C47C2311yescharacteristic
63C22⋊Dic47—22no—
64#10625337—22no—
65#10625337—42no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71C4×Dic47—21no—
72#10625329—42no—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2312yes—
76C23×C47C2×D412yes—
77Q8×C47—21no—
78Q8×C47—21no—
79Q8×C47—42no—
80D4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—44no—
94Dic94—21no—
95Dic94—22no—
96Dic94—22no—
97Dic94—44no—
98Dic94#4112yes—
99C47⋊C8—21no—
100C47⋊C8—21no—
101C47⋊C8—22no—
102C22×C47—22no—
103C22×C47—22no—
104C22×C47—22no—
105C22×C47C22×D411yescharacteristic
106C4×C47—22no—
107C4×C47—21no—
108C4×C47—41no—
109C4×C47—42no—
110C4×C47—41no—
111C4×C47#13712yes—
112C4×C47C2×#4111yescharacteristic
113C4×C47H(5,𝔽2)11yescharacteristic
114Dic47—22no—
115Dic47—42no—
116Dic47—41no—
117#3328—471nomaximal, Sylow
118C2×C47—42no—
119C2×C47#54611yescharacteristic
120C2×C47C2×#13711yescharacteristic
121C2×C47#57811yescharacteristic
122#556D4711yescharacteristic
123D4×Q8—471no—
124#487—471no—
125#485—472no—
126#475—471no—
127#470—472no—
128#462—471no—
129#451—472no—
130C4×Q16—471no—
131#436—471no—
132#419—472no—
133C47#332811yescharacteristic, complemented, Sylow
134C22×Q8—472no—
135C2×Q16—471no—
136C2×Q16—472no—
137C2×M16—472no—
138C4⋊Q8—471no—
139C4⋊Q8—941no—
140C4⋊Q8C2×D4711yescharacteristic
141#126—22no—
142#124—21no—
143C22⋊Q8—472no—
144C22⋊Q8—942no—
145C22⋊Q8C2×D4712yes—
146C4×Q8—21no—
147C4×Q8—471no—
148C4×Q8C2×D4711yescharacteristic
149C4×D4—941no—
150C4×D4C2×D4711yescharacteristic
151#117C2×D4712yes—
152#107—471no—
153#106—472no—
154C4⋊C8—471no—
155#103—471no—
156#103—471no—
157#103—472no—
158#103—472no—
159#103—472no—
160#103—472no—
161C22⋊C8—472no—
162C4×C8—471no—
163C2×Q8—21no—
164C2×Q8—471no—
165C2×Q8—472no—
166C2×Q8—944no—
167C2×Q8—942no—
168C2×Q8—1882no—
169C2×Q8C22×D4711yescharacteristic
170C2×D4C22⋊D4711yescharacteristic
171C22×C4—942no—
172C22×C4C22×D4712yes—
173Q16—942no—
174Q16—1882no—
175M16—1882no—
176C2×C8—471no—
177C2×C8—471no—
178C2×C8—472no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—471no—
183C4⋊C4—941no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4C22⋊D4711yescharacteristic
188C4⋊C4C22×D4712yes—
189C4⋊C4C22×D4711yescharacteristic
190C22⋊C4—22no—
191C22⋊C4—22no—
192C22⋊C4—942no—
193C22⋊C4C22⋊D4712yes—
194C42—22no—
195C42—21no—
196C42—941no—
197C42C22×D4711yescharacteristic
198C23C2×C22⋊D4712yes—
199Q8—21no—
200Q8—21no—
201Q8—42no—
202Q8—472no—
203Q8—941no—
204Q8—942no—
205Q8—942no—
206Q8—1884no—
207D4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—1884no—
217C2×C4C2×C22⋊D4712yes—
218C2×C4C2×C22⋊D4711yescharacteristic
219C2×C4C2×C22⋊D4711yescharacteristic
220C2×C4C23×D4711yescharacteristic
221C8—941no—
222C8—941no—
223C8—942no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22C22×C22⋊D4711yescharacteristic
228C4—22no—
229C4—21no—
230C4—41no—
231C4—42no—
232C4—41no—
233C4—942no—
234C4—1882no—
235C4—1881no—
236C4#1309405412yes—
237C4#41×D4711yescharacteristic
238C4#1309407011yescharacteristic
239C2—42no—
240C2#1568976111yescharacteristic
241C2C2×#1309405411yescharacteristic
242C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3328
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #15689475C2semidirect
3. #15689464C2semidirect
4. #15689405C2semidirect
5. #15689379C2semidirect
6. #15689333C2semidirect
7. #15689278C2semidirect
8. C4×#10625337C2semidirect
10. #15689131C2semidirect
133. C47#3328semidirect