Finite Group Databasebeta

← #20248626

Subgroups — #20248626

Order 6016.

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

normal subgroups only

This group has 380 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
2#15689062C211yesmaximal, characteristic
3#15689020C212yesmaximal
4#15689018C212yesmaximal
5#15688992C211yesmaximal, characteristic
6#15688987C212yesmaximal
7#15688987C212yesmaximal
8#15688974C212yesmaximal
9C47×#400C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C4×Dic47C2212yes—
18C2×C4×Dic47C2212yes—
19C2×C4×Dic47C2211yescharacteristic
20C47⋊#95C2212yes—
21C47⋊#95C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#95×C47C2212yes—
29#95×C47C2211yescharacteristic
30#95×C47C2212yes—
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C4⋊C4×C47—41no—
41C4⋊C4×C47—41no—
42C4⋊Dic47—41no—
43C4⋊Dic47—41no—
44Dic47⋊C4—24no—
45Dic47⋊C4—24no—
46Dic47⋊C4—24no—
47Dic47⋊C4—24no—
48Dic47⋊C4—42no—
49C4×Dic47—24no—
50C4×Dic47—24no—
51C4×Dic47Q814yes—
52C23×C47C2411yescharacteristic
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47C2×Q812yes—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47C2×Q814yes—
76C2×Dic47#4114yes—
77C2×Dic47#4114yes—
78C22×C47C22×Q811yescharacteristic
79C22×C47C2×#4112yes—
80C22×C47C2×#4112yes—
81C22×C47H(5,𝔽2)11yescharacteristic
82C22×C472−1+411yescharacteristic
83C4×C47—22no—
84C4×C47—42no—
85C4×C47—42no—
86C4×C47—41no—
87C4×C47—41no—
88Dic47—42no—
89Dic47—42no—
90Dic47—42no—
91Dic47#12518yes—
92#2571—471nomaximal, Sylow
93C2×C47C2×#12512yes—
94C2×C47#54411yescharacteristic
95C2×C47#55511yescharacteristic
96C2×C47#55612yes—
97C2×C47#55911yescharacteristic
98#400—471no—
99#400—472no—
100#400D4711yescharacteristic
101#389—472no—
102#389—472no—
103#384—471no—
104#382—472no—
105#382—472no—
106C4×C4⋊C4—472no—
107C47#257111yescharacteristic, complemented, Sylow
108C2×C4⋊C4—472no—
109C2×C4⋊C4—472no—
110C2×C4⋊C4—472no—
111C2×C4⋊C4—472no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4C2×D4711yescharacteristic
116C2×C4⋊C4C2×D4711yescharacteristic
117C2×C42—471no—
118C2×C42—472no—
119C2×C42—472no—
120#95—472no—
121#95—471no—
122#95—472no—
123#95—472no—
124#95—472no—
125#95—472no—
126#95C2×D4712yes—
127#95C2×D4711yescharacteristic
128#95C2×D4712yes—
129C22×C4—472no—
130C22×C4—472no—
131C22×C4—472no—
132C22×C4—472no—
133C22×C4C22×D4712yes—
134C22×C4C22×D4711yescharacteristic
135C22×C4C22×D4712yes—
136C22×C4C22×D4711yescharacteristic
137C22×C4C22×D4711yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—944no—
141C4⋊C4—944no—
142C4⋊C4—944no—
143C4⋊C4—944no—
144C4⋊C4—1882no—
145C4⋊C4—1881no—
146C4⋊C4—1881no—
147C42—474no—
148C42—944no—
149C42—944no—
150C23C23×D4711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—474no—
164C2×C4—474no—
165C2×C4—474no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4Q8×D4712yes—
176C22C2×Q8×D4711yescharacteristic
177C22#41×D4712yes—
178C22#41×D4712yes—
179C22#1309406911yescharacteristic
180C22#1309407111yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—478no—
187C4—1882no—
188C4—1882no—
189C4—1882no—
190C2#125×D4712yes—
191C2#1568975211yescharacteristic
192C2#1568983511yescharacteristic
193C2#1568984012yes—
194C2#1568985711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2571
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
107. C47#2571semidirect