Finite Group Databasebeta

← #20256421

Subgroups — #20256421

Order 6016.

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

normal subgroups only

This group has 350 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#15689852C211yesmaximal, characteristic, complemented
2#15689846C211yesmaximal, characteristic
3#15689517C212yesmaximal
4#15689503C211yesmaximal, characteristic, complemented
5#15689346C212yesmaximal
6#15689334C211yesmaximal, characteristic, complemented
7#15689334C212yesmaximal, complemented
8#15689329C211yesmaximal, characteristic
9#15689231C212yesmaximal, complemented
10C4×#10625325C211yesmaximal, characteristic
11C47×#446C211yesmaximal, characteristic, complemented
12C2×Dic188C2212yes—
13C2×Dic188C2212yes—
14C2×Dic188C2212yes—
15C2×#10625325C2211yescharacteristic
16C2×#10625325C2212yes—
17#13094024C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094024C2212yes—
20#13094019—22no—
21#13094015—21no—
22#13094015—22no—
23#13094012C2212yes—
24#13094000—21no—
25Q8×Dic47—21no—
26C4×Dic94C2212yes—
27C4×Dic94C2212yes—
28C4×Dic94C2211yescharacteristic
29C4×D188C2211yescharacteristic
30#13093982—21no—
31#13093956C2211yescharacteristic
32#13093949C2212yes—
33#13093949C2212yes—
34#13093949C2211yescharacteristic
35#13093946C2211yescharacteristic
36C4×Q8×C47C2211yescharacteristic
37C4⋊C8×C47C2211yescharacteristic
38C4⋊C8×C47C2212yes—
39#97×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47D411yescharacteristic
42C2×D188C2311yescharacteristic
43C2×C4×D47—21no—
44C2×Dic94C2312yes—
45C2×Dic94C2311yescharacteristic
46C2×Dic94C2312yes—
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2312yes—
49C2×C8×C47C2311yescharacteristic
50C4⋊C4×C47D411yescharacteristic
51C4⋊C4×C47D412yes—
52C42×C47C2311yescharacteristic
53C42×C47C2312yes—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—21no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—21no—
58C4⋊Dic47—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71Dic188—24no—
72Dic188—42no—
73Dic188—42no—
74#10625325—22no—
75#10625325—42no—
76C22×D47—21no—
77Q8×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88D188—21no—
89D188—21no—
90C4×D47—42no—
91Dic94—21no—
92Dic94—22no—
93Dic94—22no—
94Dic94—22no—
95Dic94—22no—
96Dic94—21no—
97C8×C47—22no—
98C8×C47—21no—
99C8×C47#4112yes—
100C22×C47C22×D411yescharacteristic
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—41no—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—21no—
107C4×C47#13712yes—
108C4×C47C2×#4111yescharacteristic
109C4×C47H(5,𝔽2)11yescharacteristic
110Dic47—41no—
111Dic47—42no—
112Dic47—42no—
113Dic47—41no—
114Dic47—41no—
115#3398—471nomaximal, Sylow
116C2×C47#55011yescharacteristic
117C2×C47C2×#13711yescharacteristic
118C2×C47#57811yescharacteristic
119D47—81no—
120#557—471no—
121#556—471no—
122#497—472no—
123#494—471no—
124#464—472no—
125#462—472no—
126#462—471no—
127#461—471no—
128#446D4711yescharacteristic, complemented
129#441—472no—
130C4×SD16—471no—
131C47#339811yescharacteristic, complemented, Sylow
132C2×Q16—472no—
133C2×Q16—472no—
134C2×Q16—472no—
135C2×SD16—471no—
136C2×SD16—472no—
137C4⋊Q8—471no—
138C4⋊Q8—471no—
139C4⋊Q8—472no—
140#126—942no—
141#125—941no—
142#125—942no—
143#124—472no—
144C22⋊Q8—941no—
145C4×Q8—472no—
146C4×Q8—471no—
147C4×Q8—472no—
148C4×Q8—941no—
149C4×Q8C2×D4711yescharacteristic
150C4×D4—471no—
151#117—941no—
152#106—471no—
153C4⋊C8C2×D4711yescharacteristic
154C4⋊C8C2×D4712yes—
155#103—471no—
156#103—472no—
157#103—472no—
158#102—471no—
159#97C2×D4712yes—
160C4×C8C2×D4711yescharacteristic
161C2×Q8—472no—
162C2×Q8—471no—
163C2×Q8—472no—
164C2×Q8D18811yescharacteristic
165C2×D4—471no—
166C22×C4—941no—
167Q16—944no—
168Q16—1882no—
169Q16—1882no—
170SD16—942no—
171SD16—1882no—
172C2×C8C22×D4711yescharacteristic
173C2×C8C22×D4712yes—
174C2×C8C22×D4711yescharacteristic
175C4⋊C4—471no—
176C4⋊C4—471no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4—941no—
181C4⋊C4—942no—
182C4⋊C4—941no—
183C4⋊C4—942no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4D18811yescharacteristic
187C4⋊C4D18812yes—
188C22⋊C4—942no—
189C22⋊C4—941no—
190C22⋊C4—942no—
191C42—942no—
192C42—942no—
193C42—941no—
194C42C22×D4711yescharacteristic
195C42C22×D4712yes—
196C23—941no—
197Q8—22no—
198Q8—941no—
199Q8—942no—
200Q8—942no—
201Q8—942no—
202Q8—942no—
203Q8—941no—
204D4—941no—
205D4—941no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—942no—
209C2×C4—941no—
210C2×C4—942no—
211C2×C4—1882no—
212C2×C4C2×D18812yes—
213C2×C4C2×D18812yes—
214C2×C4C2×D18811yescharacteristic
215C2×C4C2×D18811yescharacteristic
216C2×C4C23×D4711yescharacteristic
217C8—22no—
218C8—21no—
219C8#1062535412yes—
220C22—1881no—
221C22—1881no—
222C22—1881no—
223C22C22×D18811yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—1882no—
228C4—1881no—
229C4—1882no—
230C4—1881no—
231C4—1881no—
232C4#1309405712yes—
233C4C2×#1062535411yescharacteristic
234C4#1309407011yescharacteristic
235C2—3761no—
236C2#1568979511yescharacteristic
237C2C2×#1309405711yescharacteristic
238C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3398
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #15689852C2semidirect
4. #15689503C2semidirect
6. #15689334C2semidirect
7. #15689334C2semidirect
9. #15689231C2semidirect
11. C47×#446C2semidirect
128. #446D47semidirect
131. C47#3398semidirect