Finite Group Databasebeta

← #20243877

Subgroups — #20243877

Order 6016.

346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689598C211yesmaximal, characteristic, complemented
2#15689140C211yesmaximal, characteristic, complemented
3#15689128C211yesmaximal, characteristic, complemented
4#15689097C211yesmaximal, characteristic, complemented
5#15688894C211yesmaximal, characteristic, complemented
6#15688880C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9D4×Dic47—22no—
10D4×Dic47—22no—
11#13093983C2211yescharacteristic
12#13093983C2211yescharacteristic
13#13093983C2211yescharacteristic
14C2×C22⋊Dic47—22no—
15#13093951—22no—
16#13093945—22no—
17#13093939—22no—
18C2×#41×C47C2211yescharacteristic
19C22×D4×C47C2211yescharacteristic
20AGL(1,ℤ/8)×C47—22no—
21AGL(1,ℤ/8)×C47—22no—
22C2×SD16×C47C412yescomplemented
23C2×D8×C47C412yescomplemented
24C2×M16×C47C2211yescharacteristic
25C24×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30C2×Q8×C47C2×C411yescharacteristic, complemented
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47C2×C412yes—
36C2×D4×C47C2×C411yescharacteristic, complemented
37C2×D4×C47D412yes—
38C2×D4×C47D412yes—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—24no—
42SD16×C47—24no—
43D8×C47—24no—
44M16×C47—21no—
45M16×C47—21no—
46C2×C8×C47C2×C412yescomplemented
47C22⋊Dic47—24no—
48C22⋊Dic47—21no—
49C22⋊Dic47—21no—
50C22⋊Dic47D412yes—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4×Dic47—21no—
55C4×Dic47—21no—
56C4×Dic47D412yes—
57#10625329—21no—
58#10625329—21no—
59C2×C47⋊C8—21no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—21no—
64C23×C47—82no—
65C23×C47C2×D411yescharacteristic
66Q8×C47—21no—
67Q8×C47—21no—
68D4×C47—21no—
69D4×C47—22no—
70D4×C47—21no—
71D4×C47—22no—
72D4×C47—22no—
73D4×C47—41no—
74D4×C47—41no—
75D4×C47C22⋊C414yes—
76C2×C4×C47—21no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47C22×C411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—41no—
88C2×Dic47—84no—
89C8×C47—22no—
90C47⋊C8—41no—
91C22×C47—24no—
92C22×C47—41no—
93C22×C47—44no—
94C22×C47—41no—
95C22×C47—82no—
96C22×C47—82no—
97C22×C47—81no—
98C22×C47C4×D411yescharacteristic
99C22×C47#12011yescharacteristic
100C22×C47#12111yescharacteristic
101C4×C47—41no—
102C4×C47C2×C22⋊C411yescharacteristic
103C4×C47C4×D411yescharacteristic
104C4×C47#12111yescharacteristic
105C4×C47#12311yescharacteristic
106Dic47—42no—
107Dic47—42no—
108Dic47—81no—
109#1904—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—44no—
114C2×C47—81no—
115C2×C47#38611yescharacteristic
116C2×AGL(1,ℤ/8)D4711yescharacteristic
117#518—471no—
118#421—471no—
119#418—471no—
120#410—471no—
121#344—471no—
122H(3,ℤ/4)—471no—
123C47#190411yescharacteristic, complemented, Sylow
124C2×#41C2×D4711yescharacteristic
125C22×D4C2×D4711yescharacteristic
126AGL(1,ℤ/8)—22no—
127AGL(1,ℤ/8)—22no—
128C2×SD16Dic4712yescomplemented
129C2×D8Dic4712yescomplemented
130C2×M16—471no—
131C2×M16C2×D4711yescharacteristic
132C4×D4—942no—
133C4×D4—942no—
134#117—471no—
135#117—471no—
136#117—471no—
137C2×C22⋊C4—942no—
138#104—942no—
139#102—942no—
140#99—942no—
141C24—21no—
142#41—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146C2×Q8C2×Dic4711yescharacteristic, complemented
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4C2×Dic4712yes—
152C2×D4C2×Dic4711yescharacteristic, complemented
153C2×D4C22⋊D4712yes—
154C2×D4C22⋊D4712yes—
155C22×C4—21no—
156C22×C4—944no—
157C22×C4C22×D4711yescharacteristic
158SD16—24no—
159D8—24no—
160M16—21no—
161M16—21no—
162M16—941no—
163M16—941no—
164C2×C8—941no—
165C2×C8C2×Dic4712yescomplemented
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—472no—
170C22⋊C4—944no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C42—472no—
174C42—941no—
175C42—941no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—21no—
180C23—82no—
181C23D4×D4711yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—22no—
186D4—21no—
187D4—22no—
188D4—22no—
189D4—41no—
190D4—41no—
191D4C22⋊Dic4714yes—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—3764no—
198C2×C4—1881no—
199C2×C4D4×D4711yescharacteristic
200C2×C4#1062535211yescharacteristic
201C2×C4#1062535211yescharacteristic
202C2×C4C22×Dic4711yescharacteristic
203C2×C4C2×C22⋊D4711yescharacteristic
204C2×C4C2×C22⋊D4711yescharacteristic
205C8—22no—
206C8—1881no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—41no—
211C22—82no—
212C22—82no—
213C22—81no—
214C22D4×Dic4711yescharacteristic
215C22#1309399211yescharacteristic
216C22#1309399611yescharacteristic
217C4—41no—
218C4—3761no—
219C4—1882no—
220C4—1882no—
221C4C2×C22⋊Dic4711yescharacteristic
222C4D4×Dic4711yescharacteristic
223C4#1309399611yescharacteristic
224C4#1309400511yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—81no—
230C2#1568900311yescharacteristic
subgroupG/H
centerC2#15689003
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC2×C47#386
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15689598C2semidirect
2. #15689140C2semidirect
3. #15689128C2semidirect
4. #15689097C2semidirect
5. #15688894C2semidirect
6. #15688880C2semidirect
22. C2×SD16×C47C4semidirect
23. C2×D8×C47C4semidirect
30. C2×Q8×C47C2×C4semidirect
36. C2×D4×C47C2×C4semidirect
46. C2×C8×C47C2×C4semidirect
123. C47#1904semidirect
128. C2×SD16Dic47semidirect
129. C2×D8Dic47semidirect
146. C2×Q8C2×Dic47semidirect
152. C2×D4C2×Dic47semidirect
165. C2×C8C2×Dic47semidirect