Finite Group Databasebeta

← #20243642

Subgroups — #20243642

Order 6016.

298 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 113 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
2C2×#13093948C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4#15689021C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C2×C4×Q8×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093957—22no—
14#13093948—22no—
15#13093948C414yescomplemented
16C47⋊#95—21no—
17C22×Q8×C47C2211yescharacteristic
18C4×Q8×C47—22no—
19C4×Q8×C47—22no—
20C2×C4⋊C4×C47—21no—
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C42×C47—21no—
23C2×C42×C47C2211yescharacteristic
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×C47D411yescharacteristic
33C22×C4×C47D411yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—21no—
36C22×Dic47—21no—
37C4⋊C4×C47—24no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47D412yes—
40C42×C47—24no—
41C42×C47—21no—
42C42×C47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47C2×C412yes—
47Dic47⋊C4—42no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8C2×C412yes—
54C23×C47C2×D411yescharacteristic
55Q8×C47—22no—
56Q8×C47—22no—
57Q8×C47—22no—
58Q8×C47C4⋊C414yescomplemented
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47Q1612yes—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×Q811yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C47⋊C8—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—22no—
94C4×C47—41no—
95C4×C47—42no—
96C4×C47C2×C4⋊C411yescharacteristic
97C4×C47C4×D411yescharacteristic
98C4×C47C22⋊Q811yescharacteristic
99C4×C47#12311yescharacteristic
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×Q8D4711yescharacteristic
111C2×#107—471no—
112C2×#103—471no—
113C2×#103—471no—
114#389—471no—
115#340—471no—
116#336—471no—
117C47#186311yescharacteristic, complemented, Sylow
118C22×Q8C2×D4711yescharacteristic
119C22×C8—471no—
120C22×C8—471no—
121C4×Q8—22no—
122C4×Q8—22no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—941no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C42—21no—
129C2×C42C2×D4711yescharacteristic
130#107—942no—
131#103—474no—
132#103—942no—
133#95—941no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8Dic9412yes—
138C2×Q8C4×D4712yes—
139C2×Q8C22⋊D4712yes—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4C22⋊D4711yescharacteristic
145C22×C4C22⋊D4711yescharacteristic
146C22×C4C22×D4711yescharacteristic
147C2×C8—472no—
148C2×C8—941no—
149C2×C8—941no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8—941no—
153C4⋊C4—24no—
154C4⋊C4—21no—
155C4⋊C4—472no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C4⋊C4—1882no—
160C4⋊C4C22⋊D4712yes—
161C42—24no—
162C42—21no—
163C42—21no—
164C23C2×C22⋊D4711yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—22no—
168Q8Dic47⋊C414yescomplemented
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—942no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4#1062533712yes—
187C2×C4C2×Dic9411yescharacteristic
188C2×C4C2×C4×D4711yescharacteristic
189C2×C4#1062535011yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4C2×C22⋊D4711yescharacteristic
192C2×C4C2×C22⋊D4711yescharacteristic
193C8—942no—
194C8—1881no—
195C22C4×C22⋊D4711yescharacteristic
196C22#1309399311yescharacteristic
197C22#1309400311yescharacteristic
198C22C2×#1062533711yescharacteristic
199C22#1309404411yescharacteristic
200C22#1309404911yescharacteristic
201C22#1309405511yescharacteristic
202C4—24no—
203C4—22no—
204C4—41no—
205C4—42no—
206C4—3761no—
207C4—1882no—
208C4C2×Dic47⋊C411yescharacteristic
209C4C4×C22⋊D4711yescharacteristic
210C4#1309400311yescharacteristic
211C4#1309400711yescharacteristic
212C2#1568899611yescharacteristic
213C2C4×#1062533711yescharacteristic
214C2#1568922111yescharacteristic
215C2#1568926811yescharacteristic
216C2#1568927911yescharacteristic
217C2#1568941811yescharacteristic
218C2#1568943011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C4×Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×Q8D47
hypocenterC47#1863
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
15. #13093948C4semidirect
58. Q8×C47C4⋊C4semidirect
117. C47#1863semidirect
168. Q8Dic47⋊C4semidirect