Finite Group Databasebeta

← #20249558

Subgroups — #20249558

Order 6016.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689065C212yesmaximal, complemented
2#15689046C212yesmaximal
3#15689044C212yesmaximal, complemented
4#15689035C212yesmaximal
5#15689029C212yesmaximal, complemented
6#15689007C212yesmaximal, complemented
7#15688986C211yesmaximal, characteristic
8#15688983C211yesmaximal, characteristic
9C4×C22⋊C4×C47C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47C2211yescharacteristic
17C2×C22⋊Dic47C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2211yescharacteristic
20C47⋊#95C2211yescharacteristic
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C23×C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C42×C47C2212yes—
29#95×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic
31C24×C47C2311yescharacteristic
32C22×C4×C47—42no—
33C22×C4×C47Q814yescomplemented
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C2×Dic94—24no—
43C2×Dic94—42no—
44C2×Dic94—42no—
45C22⋊C4×C47—24no—
46C42×C47—42no—
47C22⋊Dic47—42no—
48C22⋊Dic47—41no—
49C22⋊Dic47—41no—
50C4⋊Dic47—42no—
51C4⋊Dic47—42no—
52Dic47⋊C4—24no—
53Dic47⋊C4—42no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47—22no—
57C23×C47—21no—
58C23×C47C2×Q812yes—
59C23×C47C2411yescharacteristic
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—44no—
68C2×C4×C47C2×Q812yes—
69C2×C4×C47C2×Q812yes—
70C2×C4×C47#4114yes—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83Dic94—48no—
84C22×C47—22no—
85C22×C47—22no—
86C22×C47—22no—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47C22×Q811yescharacteristic
90C22×C47C2×#4112yes—
91C22×C47H(5,𝔽2)12yes—
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C472−1+411yescharacteristic
94C4×C47—24no—
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—42no—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101Dic47—42no—
102#2665—471nomaximal, Sylow
103C2×C47—42no—
104C2×C47#53311yescharacteristic
105C2×C47#53812yes—
106C2×C47#54212yes—
107C2×C47#54311yescharacteristic
108C2×C47#54411yescharacteristic
109#400—472no—
110#396—472no—
111#395—472no—
112#393—472no—
113#391—472no—
114#387—472no—
115#381—471no—
116#380—471no—
117C4×C22⋊C4D4711yescharacteristic
118C47#266511yescharacteristic, complemented, Sylow
119C22×Q8—472no—
120C23×C4C2×D4711yescharacteristic
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C22⋊C4—471no—
126C2×C22⋊C4—471no—
127C2×C22⋊C4—472no—
128C2×C22⋊C4C2×D4712yes—
129C2×C42C2×D4712yes—
130#95—472no—
131#95—471no—
132#95—471no—
133#95—472no—
134#95—472no—
135#95—472no—
136#95—472no—
137#95—472no—
138#95C2×D4711yescharacteristic
139#95C2×D4711yescharacteristic
140C24C22×D4711yescharacteristic
141C2×Q8—944no—
142C2×Q8—1882no—
143C2×Q8—1882no—
144C22×C4—42no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4—472no—
149C22×C4Dic9414yescomplemented
150C22×C4C22×D4712yes—
151C22×C4C22×D4711yescharacteristic
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4712yes—
154C4⋊C4—944no—
155C4⋊C4—1882no—
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C22⋊C4—24no—
159C22⋊C4—1882no—
160C22⋊C4—1881no—
161C22⋊C4—1881no—
162C42—42no—
163C23—22no—
164C23—22no—
165C23—21no—
166C23—21no—
167C23C2×Dic9412yes—
168C23C23×D4711yescharacteristic
169Q8—1888no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—44no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4C2×Dic9412yes—
191C2×C4C2×Dic9412yes—
192C2×C4#1062535014yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×Dic9411yescharacteristic
199C22C2×#1062535012yes—
200C22#1309406912yes—
201C22#1309407011yescharacteristic
202C22#1309407111yescharacteristic
203C4—22no—
204C4—22no—
205C4—24no—
206C4—42no—
207C4—1882no—
208C4—1882no—
209C4—1882no—
210C4—1882no—
211C2—42no—
212C2#1568968011yescharacteristic
213C2#1568970612yes—
214C2#1568973812yes—
215C2#1568974911yescharacteristic
216C2#1568975111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2665
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
3. #15689044C2semidirect
5. #15689029C2semidirect
6. #15689007C2semidirect
33. C22×C4×C47Q8semidirect
118. C47#2665semidirect
149. C22×C4Dic94semidirect