Finite Group Databasebeta

← #20243959

Subgroups — #20243959

Order 6016.

230 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13093957C211yesmaximal, characteristic
2#15689021C211yesmaximal, characteristic
3#15688885C211yesmaximal, characteristic
4#15688885C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C4×C4⋊C4×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093957C414yescomplemented
14C47⋊#95—21no—
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C4⋊C4×C47C2211yescharacteristic
17C2×C42×C47—21no—
18C2×C42×C47C2211yescharacteristic
19#95×C47—21no—
20C22×C4×C47—21no—
21C22×C4×C47—21no—
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C4⋊C4×C47—21no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47C2×C412yes—
30C4⋊C4×C47Q812yes—
31C42×C47—21no—
32C42×C47—21no—
33C42×C47—42no—
34C4⋊Dic47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47C2×C412yes—
38Dic47⋊C4—42no—
39C2×C47⋊C8—21no—
40C2×C47⋊C8—21no—
41C2×C47⋊C8—21no—
42C2×C47⋊C8—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8C2×C412yes—
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—22no—
49C2×C4×C47—22no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47D812yes—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C47⋊C8—22no—
71C47⋊C8—41no—
72C22×C47C4×D411yescharacteristic
73C22×C47C22⋊Q811yescharacteristic
74C22×C47#12311yescharacteristic
75C22×C47C2×D811yescharacteristic
76C22×C47#13511yescharacteristic
77C22×C47#13711yescharacteristic
78C22×C47#13711yescharacteristic
79C4×C47—22no—
80C4×C47—42no—
81C4×C47—42no—
82C4×C47—41no—
83C4×C47#11711yescharacteristic
84C4×C47C4×Q811yescharacteristic
85C4×C47#12511yescharacteristic
86C4×C47#12611yescharacteristic
87Dic47—42no—
88Dic47—81no—
89#1918—471nomaximal, Sylow
90C2×C47#38711yescharacteristic
91C2×C47C4×D811yescharacteristic
92C2×C47#44111yescharacteristic
93C2×C47#47411yescharacteristic
94C2×C47#47911yescharacteristic
95C2×C47#48011yescharacteristic
96C2×C47#48511yescharacteristic
97C2×#107—471no—
98#389—471no—
99C4×C4⋊C4D4711yescharacteristic
100#340—471no—
101#340—471no—
102#340—471no—
103#336—471no—
104C47#191811yescharacteristic, complemented, Sylow
105C22×C8—471no—
106C22×C8—471no—
107C2×C4⋊C4—471no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—941no—
110C2×C4⋊C4C2×D4711yescharacteristic
111C2×C4⋊C4C2×D4711yescharacteristic
112C2×C42—21no—
113C2×C42C2×D4711yescharacteristic
114#107—474no—
115#95—21no—
116#95—941no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—941no—
120C22×C4—941no—
121C22×C4C22⋊D4711yescharacteristic
122C22×C4C22⋊D4711yescharacteristic
123C22×C4C22×D4711yescharacteristic
124C2×C8—472no—
125C2×C8—941no—
126C2×C8—941no—
127C2×C8—941no—
128C2×C8—941no—
129C2×C8—941no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—472no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—1882no—
137C4⋊C4Dic9412yes—
138C4⋊C4C4×D4712yes—
139C42—21no—
140C42—21no—
141C42—42no—
142C23C2×C22⋊D4711yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—942no—
155C2×C4—1881no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4#1062533412yes—
161C2×C4C2×Dic9411yescharacteristic
162C2×C4C2×C4×D4711yescharacteristic
163C2×C4#1062535011yescharacteristic
164C2×C4#1062535011yescharacteristic
165C2×C4#1062535011yescharacteristic
166C2×C4#1062535011yescharacteristic
167C8—942no—
168C8—1881no—
169C22C4×C22⋊D4711yescharacteristic
170C22#1309400311yescharacteristic
171C22#1309400711yescharacteristic
172C22C2×#1062533411yescharacteristic
173C22#1309404411yescharacteristic
174C22#1309405411yescharacteristic
175C22#1309405511yescharacteristic
176C4—22no—
177C4—42no—
178C4—42no—
179C4—41no—
180C4—3761no—
181C4—1882no—
182C4#1309398111yescharacteristic
183C4C4×Dic9411yescharacteristic
184C4#1309401611yescharacteristic
185C4#1309401811yescharacteristic
186C2#1568900711yescharacteristic
187C2C4×#1062533411yescharacteristic
188C2#1568922811yescharacteristic
189C2#1568940311yescharacteristic
190C2#1568943011yescharacteristic
191C2#1568943611yescharacteristic
192C2#1568946411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×C4⋊C4×C47C2
socleC23×C47C2×D4
hypercenterC4×C4⋊C4D47
hypocenterC47#1918
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #13093957C4semidirect
104. C47#1918semidirect