Finite Group Databasebeta

← #20252856

Subgroups — #20252856

Order 6016.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094054C212yesmaximal, complemented
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3#15689342C214yesmaximal, complemented
4#15689330C212yesmaximal, complemented
5#15689320C212yesmaximal, complemented
6#15689147C211yesmaximal, characteristic, complemented
7#15689124C212yesmaximal, complemented
8C47×#532C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10#13094054—28no—
11C2×#10625337C2214yes—
12C2×#10625335C2214yes—
13C2×#10625329C2212yes—
14C4×Dic94—21no—
15C4×Dic94—21no—
16C4×Dic94C2212yes—
17C4×Dic94C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4—21no—
20C2×C4×Dic47—21no—
21C4⋊(C47⋊C8)C2212yes—
22C4⋊(C47⋊C8)C2212yes—
23#13093948C2214yes—
24#13093945C2214yes—
25C2×#41×C47C2212yes—
26C4⋊Q8×C47C2211yescharacteristic
27#127×C47C2211yescharacteristic
28#124×C47C2212yes—
29#121×C47—21no—
30#121×C47—21no—
31C4×D4×C47—21no—
32C4×D4×C47—21no—
33C2×C42×C47C2211yescharacteristic
34#41×C47—24no—
35#41×C47—24no—
36C2×Q8×C47C2312yes—
37C2×D4×C47—22no—
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47C2312yes—
41C22×C4×C47—22no—
42C22×C4×C47D411yescharacteristic
43C22×C4×C47D411yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C2×Dic94—21no—
48C2×Dic94—22no—
49C2×Dic94D414yescomplemented
50C2×Dic94C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C22⋊C4×C47—22no—
54C22⋊C4×C47—22no—
55C42×C47D411yescharacteristic
56C42×C47D411yescharacteristic
57C42×C47C2311yescharacteristic
58C42×C47C2311yescharacteristic
59#10625337—28no—
60#10625335—28no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65C4×Dic47—22no—
66C4×Dic47—22no—
67#10625329—24no—
68C2×C47⋊C8C2314yes—
69C23×C47—22no—
70C23×C47C2×D411yescharacteristic
71Q8×C47—22no—
72Q8×C47—22no—
73D4×C47—22no—
74D4×C47—22no—
75D4×C47—42no—
76D4×C47—44no—
77D4×C47—42no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—41no—
81C2×C4×C47—44no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4112yes—
89C2×C4×C47C2411yescharacteristic
90C2×Dic47—24no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—42no—
94Dic94—24no—
95Dic94—22no—
96Dic94C2×D414yes—
97C47⋊C8—24no—
98C22×C47—21no—
99C22×C47—21no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47#12112yes—
104C22×C47C22×D411yescharacteristic
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—42no—
109C4×C47#12112yes—
110C4×C47#13712yescomplemented
111C4×C47C22×D411yescharacteristic
112C4×C47C2×#4111yescharacteristic
113Dic47—24no—
114Dic47—42no—
115#3037—471nomaximal, Sylow
116C2×C47—22no—
117C2×C47—82no—
118C2×C47C2×#12111yescharacteristic
119C2×C47C2×#13711yescharacteristic
120C2×C47#57511yescharacteristic
121C2×#137—472no—
122#532D4711yescharacteristic
123C2×C4×Q8—471no—
124#464—474no—
125#462—472no—
126#460—472no—
127#423—471no—
128#417—472no—
129C47#303711yescharacteristic, complemented, Sylow
130C2×#41C2×D4712yes—
131C22×Q8—471no—
132#137—948no—
133C2×Q16—474no—
134C2×SD16—474no—
135C2×M16—472no—
136C4⋊Q8C2×D4711yescharacteristic
137#127C2×D4711yescharacteristic
138#124C2×D4712yes—
139#121—21no—
140#121—21no—
141C4×Q8—472no—
142C4×Q8—472no—
143C4×Q8—941no—
144C4×Q8—941no—
145C4×D4—21no—
146C4×D4—21no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—941no—
149C2×C42—941no—
150C2×C42C2×D4711yescharacteristic
151C4⋊C8—472no—
152C4⋊C8—472no—
153#103—474no—
154#102—474no—
155#41—24no—
156#41—24no—
157C2×Q8—474no—
158C2×Q8—472no—
159C2×Q8—942no—
160C2×Q8—941no—
161C2×Q8C22×D4712yes—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D4712yes—
166C22×C4—22no—
167C22×C4—941no—
168C22×C4—941no—
169C22×C4C22⋊D4711yescharacteristic
170C22×C4C22⋊D4711yescharacteristic
171C22×C4C22×D4711yescharacteristic
172Q16—948no—
173SD16—948no—
174M16—944no—
175C2×C8—474no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—472no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C42—942no—
185C42—942no—
186C42C22⋊D4711yescharacteristic
187C42C22⋊D4711yescharacteristic
188C42C22×D4711yescharacteristic
189C42C22×D4711yescharacteristic
190C23—22no—
191C23C2×C22⋊D4711yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—474no—
195Q8—944no—
196Q8—942no—
197D4—22no—
198D4—22no—
199D4—42no—
200D4—44no—
201D4—42no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—44no—
206C2×C4—944no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—1882no—
210C2×C4D4×D4712yes—
211C2×C4#1062535212yes—
212C2×C4C2×C22⋊D4711yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C2×C4C2×C22⋊D4711yescharacteristic
216C2×C4C2×C22⋊D4711yescharacteristic
217C2×C4C23×D4711yescharacteristic
218C8—944no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1309399512yes—
225C22C22×C22⋊D4711yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—42no—
230C4—944no—
231C4—1882no—
232C4#1309399512yes—
233C4#1309405412yescomplemented
234C4C2×D4×D4711yescharacteristic
235C4C2×#1062535211yescharacteristic
236C2—22no—
237C2—82no—
238C2C2×#1309399511yescharacteristic
239C2C2×#1309405411yescharacteristic
240C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3037
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×C4×Dic94C2semidirect
3. #15689342C2semidirect
4. #15689330C2semidirect
5. #15689320C2semidirect
6. #15689147C2semidirect
7. #15689124C2semidirect
49. C2×Dic94D4semidirect
110. C4×C47#137semidirect
129. C47#3037semidirect
233. C4#13094054semidirect