Finite Group Databasebeta

← #20244538

Subgroups — #20244538

Order 6016.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094015C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3C2×#13093947C211yesmaximal, characteristic
4#15689028C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094015—22no—
11#13094015—22no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093949—22no—
17#13093947—22no—
18C47⋊#95—21no—
19C47⋊#95—21no—
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47D411yescharacteristic
29C22×Dic47D411yescharacteristic
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×Dic94Q812yes—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47D412yes—
43C4⋊Dic47—24no—
44C4⋊Dic47—21no—
45C4⋊Dic47D412yes—
46Dic47⋊C4—24no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C23×C47C2×D411yescharacteristic
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77Dic94—22no—
78Dic94—22no—
79Dic94—41no—
80Dic94—41no—
81C8×C47—41no—
82C47⋊C8—41no—
83C22×C47#12011yescharacteristic
84C22×C47C22⋊Q811yescharacteristic
85C22×C47#12411yescharacteristic
86C22×C47#13511yescharacteristic
87C22×C47#13511yescharacteristic
88C22×C47#13711yescharacteristic
89C22×C47#13711yescharacteristic
90C4×C47—42no—
91C4×C47—81no—
92C4×C47C22⋊Q811yescharacteristic
93C4×C47C22⋊Q811yescharacteristic
94C4×C47#12411yescharacteristic
95C4×C47#12411yescharacteristic
96Dic47—42no—
97Dic47—41no—
98Dic47—41no—
99Dic47—42no—
100#2026—471nomaximal, Sylow
101C2×C47#39311yescharacteristic
102C2×C47#45211yescharacteristic
103C2×C47#45211yescharacteristic
104C2×C47#47911yescharacteristic
105C2×C47#47911yescharacteristic
106C2×C47#48811yescharacteristic
107C2×C47#49111yescharacteristic
108C2×#125—471no—
109C2×#103—471no—
110C2×#103—471no—
111#391—471no—
112#340—471no—
113#340D4711yescharacteristic
114#336—471no—
115C47#202611yescharacteristic, complemented, Sylow
116C22×Q8—471no—
117C22×C8—471no—
118C22×C8C2×D4711yescharacteristic
119#125—942no—
120#125—942no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—941no—
123C2×C4⋊C4—941no—
124C2×C4⋊C4C2×D4711yescharacteristic
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C42—471no—
127#103—942no—
128#103—942no—
129#95—941no—
130#95—941no—
131C2×Q8—472no—
132C2×Q8—941no—
133C2×Q8—941no—
134C2×Q8—941no—
135C2×Q8—941no—
136C2×Q8—941no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—471no—
140C22×C4—471no—
141C22×C4—941no—
142C22×C4—941no—
143C22×C4C22×D4711yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—941no—
148C2×C8—941no—
149C2×C8—941no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—472no—
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—941no—
157C4⋊C4D18812yes—
158C42—941no—
159C42—941no—
160C23D4×D4711yescharacteristic
161Q8—942no—
162Q8—942no—
163Q8—1881no—
164Q8—1881no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—941no—
172C2×C4—941no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—1881no—
180C2×C4—1881no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4C2×D18811yescharacteristic
184C2×C4#1062535011yescharacteristic
185C2×C4#1062535011yescharacteristic
186C2×C4D4×D4711yescharacteristic
187C2×C4#1062535211yescharacteristic
188C2×C4Q8×D4711yescharacteristic
189C8—41no—
190C8—1881no—
191C22#1309399411yescharacteristic
192C22#1309400211yescharacteristic
193C22#1309401011yescharacteristic
194C22#1309404311yescharacteristic
195C22#1309404511yescharacteristic
196C22#1309405311yescharacteristic
197C22#1309405611yescharacteristic
198C4—42no—
199C4—81no—
200C4—1881no—
201C4—1881no—
202C4—1882no—
203C4—1882no—
204C4#1309400211yescharacteristic
205C4#1309400411yescharacteristic
206C4#1309401011yescharacteristic
207C4#1309401211yescharacteristic
208C2#1568903611yescharacteristic
209C2#1568928611yescharacteristic
210C2#1568928811yescharacteristic
211C2#1568942911yescharacteristic
212C2#1568943311yescharacteristic
213C2#1568947611yescharacteristic
214C2#1568949011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2026
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
115. C47#2026semidirect