Finite Group Databasebeta

← #20256297

Subgroups — #20256297

Order 6016.

340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic
3#15689531C212yesmaximal, complemented
4#15689526C211yesmaximal, characteristic, complemented
5#15689428C212yesmaximal, complemented
6#15689414C211yesmaximal, characteristic
7#15689402C212yesmaximal
8#15689250C211yesmaximal, characteristic, complemented
9#15689226C212yesmaximal
10C4×#10625336C211yesmaximal, characteristic
11C47×#477C211yesmaximal, characteristic, complemented
12C2×#10625336C2211yescharacteristic
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094023—22no—
16#13094023C2212yes—
17#13094015C2212yes—
18#13094004—21no—
19#13094000—22no—
20Q8×Dic47C2212yes—
21C4×Dic94—21no—
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24#13093986C2212yes—
25C4⋊C4×D47—21no—
26#13093957C2212yes—
27#13093957C2212yes—
28#13093956C2212yes—
29#13093955C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2211yescharacteristic
32#13093946C2212yes—
33#13093944C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#107×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×C4×D47—22no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94D411yescharacteristic
49C2×C8×C47C2312yes—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C4⋊C4×C47C2311yescharacteristic
54C42×C47—21no—
55C42×C47C2311yescharacteristic
56#10625336Q814yescomplemented
57(C2×D47)⋊C4—21no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72C22×D47—21no—
73Q8×C47—21no—
74Q8×C47—81no—
75Q8×C47C2×Q812yes—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47C2×D412yes—
85C2×Dic47C2×D412yes—
86D188—21no—
87D188C2×Q812yes—
88C4×D47—42no—
89C4×D47—82no—
90Dic94—22no—
91Dic94—82no—
92Dic94—81no—
93C8×C47—22no—
94C47⋊C8—21no—
95C47⋊C8C2×Q812yes—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—41no—
100C4×C47—22no—
101C4×C47—21no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47#13712yes—
105C4×C47C22×Q811yescharacteristic
106C4×C472−1+411yescharacteristic
107Dic47—22no—
108Dic47—22no—
109Dic47—41no—
110Dic47—42no—
111#3385—471nomaximal, Sylow
112C2×C47D4×Q811yescharacteristic
113C2×C47C2×#13711yescharacteristic
114C2×C47#57611yescharacteristic
115D47—42no—
116Q82—471no—
117#554—471no—
118#501—472no—
119#500—471no—
120#479—472no—
121#477D4711yescharacteristic, complemented
122#476—471no—
123#474—472no—
124#446—471no—
125#440—472no—
126C4×SD16—471no—
127C47#338511yescharacteristic, complemented, Sylow
128C2×SD16—471no—
129C4⋊Q8—472no—
130C4⋊Q8—471no—
131C4⋊Q8—941no—
132C4⋊Q8—942no—
133C4⋊Q8C2×D4711yescharacteristic
134#125—472no—
135C22⋊Q8—941no—
136C22⋊Q8—942no—
137C4×Q8—471no—
138C4×Q8—472no—
139C4×Q8—941no—
140C4×Q8C2×D4711yescharacteristic
141C4×D4—472no—
142C4×D4—471no—
143C2×C4⋊C4—941no—
144#107—472no—
145#107—472no—
146#107C2×D4712yes—
147#106—472no—
148#106—471no—
149C4⋊C8—472no—
150C4⋊C8C2×D4711yescharacteristic
151#103—471no—
152#103C2×D4712yes—
153#102—472no—
154#102—471no—
155#97—472no—
156C4×C8—471no—
157C2×Q8—21no—
158C2×Q8—471no—
159C2×Q8—942no—
160C2×Q8—941no—
161C2×Q8C22×D4711yescharacteristic
162C2×D4—471no—
163C22×C4—942no—
164C22×C4—941no—
165SD16—474no—
166C2×C8—471no—
167C2×C8—471no—
168C2×C8C22×D4712yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—472no—
174C4⋊C4—471no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4C22×D4711yescharacteristic
181C4⋊C4C22×D4712yes—
182C22⋊C4—942no—
183C22⋊C4—941no—
184C42—21no—
185C42—472no—
186C42—942no—
187C42C22×D4711yescharacteristic
188C23—941no—
189Q8—21no—
190Q8—81no—
191Q8—942no—
192Q8—3761no—
193Q8—3762no—
194Q8Q8×D4712yes—
195D4—472no—
196D4—941no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—472no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—3762no—
205C2×C4—1882no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—22no—
210C8—472no—
211C8—941no—
212C22—942no—
213C22—1881no—
214C22—1881no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—942no—
221C4—942no—
222C4—1881no—
223C4—1882no—
224C4#1309405612yes—
225C4C2×Q8×D4711yescharacteristic
226C4#1309407111yescharacteristic
227C2—1882no—
228C2#1568978611yescharacteristic
229C2C2×#1309405611yescharacteristic
230C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#477C2
socleC22×C47C22×D4
hypercenter#477D47
hypocenterC47#3385
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
3. #15689531C2semidirect
4. #15689526C2semidirect
5. #15689428C2semidirect
8. #15689250C2semidirect
11. C47×#477C2semidirect
56. #10625336Q8semidirect
121. #477D47semidirect
127. C47#3385semidirect