Finite Group Databasebeta

← #20256303

Subgroups — #20256303

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
1#15689853C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic
3#15689531C212yesmaximal, complemented
4#15689429C212yesmaximal, complemented
5#15689415C211yesmaximal, characteristic, complemented
6#15689410C211yesmaximal, characteristic
7#15689402C212yesmaximal
8#15689253C211yesmaximal, characteristic, complemented
9#15689222C212yesmaximal
10C4×#10625325C211yesmaximal, characteristic
11C47×#500C211yesmaximal, characteristic, complemented
12C2×#10625325C2211yescharacteristic
13#13094023—21no—
14#13094023C2212yes—
15#13094022—22no—
16#13094015C2212yes—
17#13094004—21no—
18#13094000—22no—
19C4×Dic94C2211yescharacteristic
20C4×Dic94C2211yescharacteristic
21#13093989—21no—
22#13093989C2212yes—
23C4×D188C2211yescharacteristic
24#13093986C2212yes—
25C4⋊C4×D47—21no—
26#13093957C2212yes—
27#13093956C2211yescharacteristic
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093944C2212yes—
35#13093934C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#107×C47C2212yes—
39#107×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47—21no—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×C4×D47—22no—
46C2×Dic94—22no—
47C2×Dic94D411yescharacteristic
48C2×Dic94C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2312yes—
54C4⋊C4×C47C2312yes—
55C42×C47C2311yescharacteristic
56(C2×D47)⋊C4—21no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47D411yescharacteristic
60C4⋊Dic47C2311yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62Dic47⋊C4—21no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2312yes—
71#10625325Q814yescomplemented
72C22×D47—21no—
73Q8×C47—81no—
74Q8×C47—81no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×D412yes—
85D188—21no—
86D188C2×Q812yes—
87C4×D47—42no—
88C4×D47—82no—
89Dic94—22no—
90Dic94—21no—
91Dic94—82no—
92Dic94C2×Q812yes—
93C8×C47—21no—
94C8×C47C2×Q812yes—
95C47⋊C8—22no—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—41no—
100C4×C47—21no—
101C4×C47—42no—
102C4×C47—42no—
103C4×C47#13712yes—
104C4×C47C22×Q811yescharacteristic
105C4×C472−1+411yescharacteristic
106Dic47—22no—
107Dic47—22no—
108Dic47—22no—
109Dic47—41no—
110Dic47—41no—
111#3385—471nomaximal, Sylow
112C2×C47D4×Q811yescharacteristic
113C2×C47C2×#13711yescharacteristic
114C2×C47#57611yescharacteristic
115D47—42no—
116Q82—471no—
117#554—471no—
118#501—472no—
119#500D4711yescharacteristic, complemented
120#479—472no—
121#477—471no—
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—941no—
131C4⋊Q8—942no—
132C4⋊Q8C2×D4711yescharacteristic
133C4⋊Q8C2×D4711yescharacteristic
134#125—472no—
135C22⋊Q8—941no—
136C22⋊Q8—942no—
137C4×Q8—471no—
138C4×Q8—472no—
139C4×Q8—471no—
140C4×Q8—941no—
141C4×D4—472no—
142C4×D4—471no—
143C2×C4⋊C4—941no—
144#107—472no—
145#107C2×D4712yes—
146#107C2×D4712yes—
147#106—471no—
148#106—472no—
149C4⋊C8—472no—
150C4⋊C8—471no—
151#103—471no—
152#103—472no—
153#102—471no—
154#102—472no—
155#97—472no—
156C4×C8C2×D4711yescharacteristic
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—471no—
160C2×Q8—471no—
161C2×Q8—942no—
162C2×D4—471no—
163C22×C4—942no—
164C22×C4—941no—
165SD16—474no—
166C2×C8—472no—
167C2×C8C22×D4711yescharacteristic
168C2×C8C22×D4711yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—471no—
173C4⋊C4—471no—
174C4⋊C4—471no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4C22×D4712yes—
181C4⋊C4C22×D4712yes—
182C22⋊C4—942no—
183C22⋊C4—941no—
184C42—472no—
185C42—942no—
186C42—941no—
187C42C22×D4711yescharacteristic
188C23—941no—
189Q8—81no—
190Q8—81no—
191Q8—472no—
192Q8—942no—
193Q8—941no—
194Q8—3762no—
195D4—472no—
196D4—941no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—3762no—
205C2×C4—1882no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—21no—
210C8—942no—
211C8Q8×D4712yes—
212C22—942no—
213C22—1881no—
214C22—1881no—
215C22C2×D4×D4711yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—942no—
220C4—942no—
221C4—942no—
222C4—1881no—
223C4—1881no—
224C4#1309405612yes—
225C4C2×Q8×D4711yescharacteristic
226C4#1309407211yescharacteristic
227C2—1882no—
228C2#1568978811yescharacteristic
229C2C2×#1309405611yescharacteristic
230C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#500C2
socleC22×C47C22×D4
hypercenter#500D47
hypocenterC47#3385
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #15689853C2semidirect
3. #15689531C2semidirect
4. #15689429C2semidirect
5. #15689415C2semidirect
8. #15689253C2semidirect
11. C47×#500C2semidirect
71. #10625325Q8semidirect
119. #500D47semidirect
127. C47#3385semidirect