Finite Group Databasebeta

← #20244528

Subgroups — #20244528

Order 6016.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13094023C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3C2×#13093947C211yesmaximal, characteristic
4#15689028C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94—21no—
9C22×Dic94C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13094023—22no—
12#13094023—22no—
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—24no—
35C2×Dic94—21no—
36C2×Dic94—42no—
37C2×Dic94—42no—
38C2×Dic94Q812yescomplemented
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47D412yes—
46C4⋊Dic47—21no—
47C4⋊Dic47D412yes—
48Dic47⋊C4—24no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55C2×C4×C47—22no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×Q811yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47SD1612yes—
78C2×Dic47Q1612yes—
79Dic94—22no—
80Dic94—22no—
81Dic94—48no—
82Dic94—41no—
83Dic94—41no—
84C8×C47—41no—
85C47⋊C8—41no—
86C22×C47#12011yescharacteristic
87C22×C47C22⋊Q811yescharacteristic
88C22×C47#12411yescharacteristic
89C22×C47C2×SD1611yescharacteristic
90C22×C47C2×Q1611yescharacteristic
91C22×C47AGL(1,ℤ/8)11yescharacteristic
92C22×C47#13711yescharacteristic
93C4×C47—42no—
94C4×C47—81no—
95C4×C47C22⋊Q811yescharacteristic
96C4×C47C22⋊Q811yescharacteristic
97C4×C47#12411yescharacteristic
98C4×C47#12411yescharacteristic
99Dic47—22no—
100Dic47—22no—
101Dic47—42no—
102Dic47—42no—
103#2024—471nomaximal, Sylow
104C2×C47#39311yescharacteristic
105C2×C47#45011yescharacteristic
106C2×C47#45111yescharacteristic
107C2×C47#47511yescharacteristic
108C2×C47#47711yescharacteristic
109C2×C47#48711yescharacteristic
110C2×C47#48911yescharacteristic
111C2×C4⋊Q8—471no—
112C2×#103—471no—
113C2×#103—471no—
114#391—471no—
115#340—471no—
116#340D4711yescharacteristic
117#336—471no—
118C47#202411yescharacteristic, complemented, Sylow
119C22×Q8—471no—
120C22×Q8—941no—
121C22×C8—471no—
122C22×C8C2×D4711yescharacteristic
123C4⋊Q8—942no—
124C4⋊Q8—942no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—941no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C42—471no—
130#103—942no—
131#103—942no—
132#95—941no—
133#95—941no—
134C2×Q8—472no—
135C2×Q8—944no—
136C2×Q8—941no—
137C2×Q8—941no—
138C2×Q8—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—1882no—
142C2×Q8—1882no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—471no—
146C22×C4—471no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4C22×D4711yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—941no—
154C2×C8—941no—
155C2×C8—941no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—472no—
160C4⋊C4—944no—
161C4⋊C4—941no—
162C4⋊C4D18812yes—
163C42—941no—
164C42—941no—
165C23D4×D4711yescharacteristic
166Q8—942no—
167Q8—942no—
168Q8—1888no—
169Q8—1881no—
170Q8—1881no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—472no—
178C2×C4—472no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4—1881no—
189C2×C4C2×D18811yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4#1062535011yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4#1062535211yescharacteristic
194C2×C4Q8×D4711yescharacteristic
195C8—41no—
196C8—1881no—
197C22#1309399411yescharacteristic
198C22#1309400211yescharacteristic
199C22#1309401011yescharacteristic
200C22SD16×D4711yescharacteristic
201C22Q16×D4711yescharacteristic
202C22#1309404811yescharacteristic
203C22#1309405311yescharacteristic
204C4—42no—
205C4—81no—
206C4—942no—
207C4—942no—
208C4—1882no—
209C4—1882no—
210C4#1309400211yescharacteristic
211C4#1309400411yescharacteristic
212C4#1309401011yescharacteristic
213C4#1309401211yescharacteristic
214C2#1568903611yescharacteristic
215C2#1568927511yescharacteristic
216C2#1568928011yescharacteristic
217C2#1568940711yescharacteristic
218C2#1568941711yescharacteristic
219C2#1568947211yescharacteristic
220C2#1568948111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2024
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
38. C2×Dic94Q8semidirect
118. C47#2024semidirect