Finite Group Databasebeta

← #20243644

Subgroups — #20243644

Order 6016.

298 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q8×Dic47C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4#15689022C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9Q8×Dic47—22no—
10Q8×Dic47—22no—
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4×Dic47—21no—
16C2×C4×Dic47C2211yescharacteristic
17#13093958—22no—
18#13093948—22no—
19C47⋊#95—21no—
20C22×Q8×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#103×C47C414yescomplemented
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47C2×C412yes—
28C2×Q8×C47D412yes—
29C2×Q8×C47Q812yes—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47—21no—
35C22×Dic47D411yescharacteristic
36C22×Dic47D411yescharacteristic
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47C2×C412yes—
40C4⋊C4×C47—21no—
41C4⋊C4×C47C2×C412yes—
42C4⋊Dic47—24no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—42no—
47C4⋊Dic47D412yes—
48C4×Dic47—24no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55Q8×C47—22no—
56Q8×C47—22no—
57Q8×C47—22no—
58Q8×C47C4⋊C414yescomplemented
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×Q811yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—22no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47Q1612yes—
83C8×C47—22no—
84C47⋊C8—41no—
85C22×C47C4×D411yescharacteristic
86C22×C47#12011yescharacteristic
87C22×C47C22⋊Q811yescharacteristic
88C22×C47C2×Q1611yescharacteristic
89C22×C47#13511yescharacteristic
90C22×C47AGL(1,ℤ/8)11yescharacteristic
91C22×C47#13711yescharacteristic
92C4×C47—24no—
93C4×C47—42no—
94C4×C47C2×C4⋊C411yescharacteristic
95C4×C47C4×D411yescharacteristic
96C4×C47C22⋊Q811yescharacteristic
97C4×C47#12311yescharacteristic
98Dic47—22no—
99Dic47—41no—
100Dic47—42no—
101Dic47—81no—
102#1863—471nomaximal, Sylow
103C2×C47#38511yescharacteristic
104C2×C47C4×Q1611yescharacteristic
105C2×C47#44011yescharacteristic
106C2×C47#44911yescharacteristic
107C2×C47#45111yescharacteristic
108C2×C47#47711yescharacteristic
109C2×C47#47911yescharacteristic
110C2×C4×Q8—471no—
111C2×#107—471no—
112C2×#103—471no—
113C2×#103D4711yescharacteristic
114#389—471no—
115#340—471no—
116#336—471no—
117C47#186311yescharacteristic, complemented, Sylow
118C22×Q8C2×D4711yescharacteristic
119C22×C8—471no—
120C22×C8C2×D4711yescharacteristic
121C4×Q8—942no—
122C4×Q8—942no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—941no—
126C2×C4⋊C4—941no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C42—471no—
129C2×C42—941no—
130#107—942no—
131#103—942no—
132#103Dic4714yescomplemented
133#95—941no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8Dic9412yes—
138C2×Q8D18812yes—
139C2×Q8C2×Dic4712yes—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—941no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—941no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8C2×Dic4712yes—
153C4⋊C4—21no—
154C4⋊C4—472no—
155C4⋊C4—944no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C4⋊C4—1882no—
160C4⋊C4C2×Dic4712yes—
161C42—944no—
162C42—941no—
163C42—941no—
164C23D4×D4711yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—22no—
168Q8C4⋊Dic4714yescomplemented
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—472no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—942no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4C2×Dic9411yescharacteristic
188C2×C4C2×D18811yescharacteristic
189C2×C4D4×D4711yescharacteristic
190C2×C4#1062535211yescharacteristic
191C2×C4#1062535211yescharacteristic
192C2×C4C22×Dic4711yescharacteristic
193C8—22no—
194C8—1881no—
195C22D4×Dic4711yescharacteristic
196C22#1309399411yescharacteristic
197C22#1309400111yescharacteristic
198C22Q16×D4711yescharacteristic
199C22#1309404711yescharacteristic
200C22#1309405111yescharacteristic
201C22#1309405311yescharacteristic
202C4—24no—
203C4—42no—
204C4—942no—
205C4—3761no—
206C4—1881no—
207C4—1882no—
208C4C2×C4⋊Dic4711yescharacteristic
209C4D4×Dic4711yescharacteristic
210C4#1309400111yescharacteristic
211C4#1309400811yescharacteristic
212C2#1568899811yescharacteristic
213C2Q16×Dic4711yescharacteristic
214C2#1568922411yescharacteristic
215C2#1568927111yescharacteristic
216C2#1568928011yescharacteristic
217C2#1568941611yescharacteristic
218C2#1568943211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1863
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
23. #103×C47C4semidirect
58. Q8×C47C4⋊C4semidirect
117. C47#1863semidirect
132. #103Dic47semidirect
168. Q8C4⋊Dic47semidirect