Finite Group Databasebeta

← #20256296

Subgroups — #20256296

Order 6016.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689830C211yesmaximal, characteristic
3#15689530C212yesmaximal, complemented
4#15689528C211yesmaximal, characteristic, complemented
5#15689432C212yesmaximal, complemented
6#15689418C211yesmaximal, characteristic, complemented
7#15689413C211yesmaximal, characteristic
8#15689401C212yesmaximal
9#15689253C211yesmaximal, characteristic, complemented
10#15689224C212yesmaximal
11C4×SD16×C47C211yesmaximal, characteristic
12#13094024—21no—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094023—22no—
16#13094023C2212yes—
17#13094015C2212yes—
18#13094003—21no—
19#13094001—22no—
20Q8×Dic47C2212yes—
21C4×Dic94—21no—
22C4×Dic94C2211yescharacteristic
23D4×Dic47C2212yes—
24C2×C4⋊Dic47—21no—
25#13093958C2212yes—
26#13093958C2212yes—
27#13093957C2212yes—
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2212yes—
32#13093945C2212yes—
33#13093934C2212yes—
34C2×SD16×C47C2211yescharacteristic
35C4×Q8×C47C2211yescharacteristic
36C4×D4×C47C2211yescharacteristic
37#106×C47C2211yescharacteristic
38#103×C47C2211yescharacteristic
39#102×C47C2211yescharacteristic
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×Dic47—22no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94D411yescharacteristic
49SD16×C47Q814yescomplemented
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2311yescharacteristic
54C4⋊C4×C47C2311yescharacteristic
55C22⋊C4×C47—21no—
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2312yes—
65C4⋊Dic47C2312yes—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72C23×C47—21no—
73Q8×C47—21no—
74Q8×C47C2×Q812yes—
75D4×C47—21no—
76D4×C47C2×Q812yes—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—42no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—82no—
87C2×Dic47C2×D412yes—
88C2×Dic47C2×D412yes—
89Dic94—22no—
90Dic94—82no—
91Dic94—81no—
92Dic94—81no—
93C8×C47—21no—
94C8×C47C2×Q812yes—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47C22×D411yescharacteristic
100C4×C47—22no—
101C4×C47—21no—
102C4×C47—41no—
103C4×C47—41no—
104C4×C47#13712yes—
105C4×C47C22×Q811yescharacteristic
106C4×C472−1+411yescharacteristic
107Dic47—22no—
108Dic47—22no—
109Dic47—42no—
110Dic47—42no—
111#3385—471nomaximal, Sylow
112C2×C47—42no—
113C2×C47D4×Q811yescharacteristic
114C2×C47C2×#13711yescharacteristic
115C2×C47#57611yescharacteristic
116Q82—471no—
117#554—471no—
118#501—472no—
119#500—471no—
120#479—472no—
121#477—471no—
122#476—471no—
123#474—472no—
124#446—471no—
125#440—472no—
126C4×SD16D4711yescharacteristic
127C47#338511yescharacteristic, complemented, Sylow
128C2×SD16C2×D4711yescharacteristic
129C4⋊Q8—472no—
130C4⋊Q8—471no—
131C4⋊Q8—471no—
132C4⋊Q8—941no—
133C4⋊Q8—942no—
134#125—472no—
135C22⋊Q8—942no—
136C22⋊Q8—941no—
137C4×Q8—471no—
138C4×Q8—472no—
139C4×Q8—941no—
140C4×Q8C2×D4711yescharacteristic
141C4×D4—472no—
142C4×D4C2×D4711yescharacteristic
143C2×C4⋊C4—941no—
144#107—472no—
145#107—472no—
146#107—472no—
147#106—472no—
148#106C2×D4711yescharacteristic
149C4⋊C8—472no—
150C4⋊C8—471no—
151#103—472no—
152#103C2×D4711yescharacteristic
153#102—472no—
154#102C2×D4711yescharacteristic
155#97—472no—
156C4×C8C2×D4711yescharacteristic
157C2×Q8—471no—
158C2×Q8—942no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8C22×D4711yescharacteristic
162C2×D4C22×D4711yescharacteristic
163C22×C4—21no—
164C22×C4—942no—
165SD16Dic9414yescomplemented
166C2×C8—472no—
167C2×C8C22×D4711yescharacteristic
168C2×C8C22×D4711yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—472no—
171C4⋊C4—471no—
172C4⋊C4—472no—
173C4⋊C4—472no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4C22×D4711yescharacteristic
181C4⋊C4C22×D4711yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—942no—
184C42—21no—
185C42—472no—
186C42—942no—
187C42C22×D4711yescharacteristic
188C23—21no—
189Q8—21no—
190Q8—942no—
191Q8—3761no—
192Q8—3761no—
193Q8—3762no—
194Q8C2×Dic9412yes—
195D4—21no—
196D4C2×Dic9412yes—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—472no—
202C2×C4—472no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—3762no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—21no—
210C8—942no—
211C8C2×Dic9412yes—
212C22—22no—
213C22—41no—
214C22—41no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—942no—
221C4—942no—
222C4—1882no—
223C4—1882no—
224C4#1309405312yes—
225C4C22×Dic9411yescharacteristic
226C4#1309407111yescharacteristic
227C2—42no—
228C2D4×Dic9411yescharacteristic
229C2C2×#1309405311yescharacteristic
230C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3385
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
3. #15689530C2semidirect
4. #15689528C2semidirect
5. #15689432C2semidirect
6. #15689418C2semidirect
9. #15689253C2semidirect
49. SD16×C47Q8semidirect
127. C47#3385semidirect
165. SD16Dic94semidirect