Finite Group Databasebeta

← #20256124

Subgroups — #20256124

Order 6016.

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

normal subgroups only

This group has 338 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
1Q8×Dic94C211yesmaximal, characteristic, complemented
2#15689482C212yesmaximal
3#15689473C211yesmaximal, characteristic, complemented
4#15689413C211yesmaximal, characteristic
5#15689408C212yesmaximal, complemented
6#15689342C212yesmaximal
7#15689330C211yesmaximal, characteristic, complemented
8#15689254C211yesmaximal, characteristic, complemented
9#15689228C212yesmaximal, complemented
10C4×#10625335C211yesmaximal, characteristic
11C47×#556C211yesmaximal, characteristic
12C2×#10625337C2212yes—
13C2×#10625335C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094024C2212yes—
16#13094023—21no—
17#13094023—22no—
18Q8×Dic47—21no—
19C4×Dic94C2212yes—
20C4×Dic94C2211yescharacteristic
21#13093955C2212yes—
22#13093955C2211yescharacteristic
23C4⋊(C47⋊C8)C2211yescharacteristic
24C4⋊(C47⋊C8)C2212yes—
25#13093948C2212yes—
26#13093948C2212yes—
27#13093948C2212yes—
28#13093947C2211yescharacteristic
29#13093945C2211yescharacteristic
30#13093945C2212yes—
31#13093935C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C4⋊Q8×C47C2211yescharacteristic
34#126×C47—22no—
35#124×C47C2212yes—
36C22⋊Q8×C47—21no—
37C4×Q8×C47C2212yes—
38C4×Q8×C47C2211yescharacteristic
39C4×D4×C47C2211yescharacteristic
40#117×C47—21no—
41C2×Q8×C47D411yescharacteristic
42C2×Q8×C47C2312yes—
43C2×D4×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C2×Dic94—22no—
46C2×Dic94—21no—
47C2×Dic94C2311yescharacteristic
48C4⋊C4×C47—21no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47D411yescharacteristic
52C4⋊C4×C47D412yes—
53C4⋊C4×C47C2311yescharacteristic
54C22⋊C4×C47—22no—
55C22⋊C4×C47—21no—
56C22⋊C4×C47—22no—
57C42×C47—22no—
58C42×C47C2311yescharacteristic
59C42×C47C2312yes—
60#10625337—24no—
61#10625335—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47—21no—
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2312yes—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68C4×Dic47—22no—
69C4×Dic47—21no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2312yes—
73C23×C47—21no—
74Q8×C47—22no—
75Q8×C47—22no—
76Q8×C47—22no—
77D4×C47—21no—
78D4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—42no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90Dic94—21no—
91Dic94—82no—
92Dic94—81no—
93Dic94#4112yes—
94C47⋊C8—21no—
95C47⋊C8—22no—
96C47⋊C8—21no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47C22×D411yescharacteristic
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—21no—
104C4×C47—42no—
105C4×C47—41no—
106C4×C47#13712yes—
107C4×C47C2×#4111yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—41no—
111Dic47—42no—
112#3369—471nomaximal, Sylow
113C2×C47—81no—
114C2×C47#54811yescharacteristic
115C2×C47C2×#13711yescharacteristic
116C2×C47#57711yescharacteristic
117Q82—471no—
118#556D4711yescharacteristic
119#489—472no—
120#487—471no—
121#476—471no—
122#475—472no—
123#464—472no—
124#462—471no—
125#446—471no—
126#441—472no—
127C4×SD16—471no—
128C47#336911yescharacteristic, complemented, Sylow
129C2×Q16—472no—
130C2×SD16—471no—
131C4⋊Q8—472no—
132C4⋊Q8—471no—
133C4⋊Q8—941no—
134C4⋊Q8—942no—
135C4⋊Q8C2×D4711yescharacteristic
136#126—22no—
137#124C2×D4712yes—
138C22⋊Q8—21no—
139C4×Q8—471no—
140C4×Q8—472no—
141C4×Q8—941no—
142C4×Q8C2×D4712yes—
143C4×Q8C2×D4711yescharacteristic
144C4×D4C2×D4711yescharacteristic
145#117—21no—
146#106—471no—
147#106—472no—
148C4⋊C8—471no—
149C4⋊C8—472no—
150#103—472no—
151#103—472no—
152#103—472no—
153#103—471no—
154#102—471no—
155#102—472no—
156#97—472no—
157C4×C8—471no—
158C2×Q8—471no—
159C2×Q8—942no—
160C2×Q8—941no—
161C2×Q8C22⋊D4711yescharacteristic
162C2×Q8C22×D4712yes—
163C2×D4C22×D4711yescharacteristic
164C22×C4—21no—
165Q16—944no—
166SD16—942no—
167C2×C8—471no—
168C2×C8—471no—
169C2×C8—472no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—21no—
173C4⋊C4—471no—
174C4⋊C4—472no—
175C4⋊C4—942no—
176C4⋊C4—941no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4C22⋊D4711yescharacteristic
180C4⋊C4C22⋊D4712yes—
181C4⋊C4C22×D4711yescharacteristic
182C22⋊C4—22no—
183C22⋊C4—21no—
184C22⋊C4—22no—
185C42—22no—
186C42—942no—
187C42—941no—
188C42C22×D4711yescharacteristic
189C42C22×D4712yes—
190C23—21no—
191Q8—22no—
192Q8—22no—
193Q8—22no—
194Q8—472no—
195Q8—941no—
196Q8—3762no—
197Q8—3761no—
198D4—21no—
199D4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—941no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4C2×C22⋊D4712yes—
207C2×C4C2×C22⋊D4712yes—
208C2×C4C2×C22⋊D4711yescharacteristic
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—941no—
212C8—942no—
213C8—941no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C22×C22⋊D4711yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—42no—
222C4—41no—
223C4—942no—
224C4—1882no—
225C4—1881no—
226C4#1309405412yes—
227C4#41×D4711yescharacteristic
228C4#1309407111yescharacteristic
229C2—81no—
230C2#1568978011yescharacteristic
231C2C2×#1309405411yescharacteristic
232C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3369
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
3. #15689473C2semidirect
5. #15689408C2semidirect
7. #15689330C2semidirect
8. #15689254C2semidirect
9. #15689228C2semidirect
128. C47#3369semidirect