Finite Group Databasebeta

← #20243623

Subgroups — #20243623

Order 6016.

286 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 97 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#15689606C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic, complemented
3#15689124C211yesmaximal, characteristic
4#15688989C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9Q8×Dic47—21no—
10D4×Dic47—21no—
11D4×Dic47—22no—
12#13093983—21no—
13#13093983C2211yescharacteristic
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17#13093958—21no—
18#13093956—21no—
19#13093948—21no—
20#13093945—21no—
21C47⋊#95—22no—
22C2×#41×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C42×C47C2211yescharacteristic
25#104×C47C414yescomplemented
26#41×C47—21no—
27#41×C47—21no—
28#41×C47C2×C412yes—
29#41×C47Q812yes—
30C2×Q8×C47D411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C22×Dic47—21no—
38C22×Dic47D412yes—
39M16×C47—21no—
40M16×C47C2×C412yescomplemented
41C2×C8×C47—21no—
42C42×C47—21no—
43C42×C47C2×C412yescomplemented
44C22⋊Dic47—22no—
45C22⋊Dic47—21no—
46C4⋊Dic47—22no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47D411yescharacteristic
52C4⋊Dic47D411yescharacteristic
53C4×Dic47—22no—
54C4×Dic47—21no—
55#10625329—21no—
56#10625329—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47C2×D411yescharacteristic
60Q8×C47—21no—
61Q8×C47C4⋊C412yes—
62D4×C47—22no—
63D4×C47—22no—
64D4×C47—21no—
65D4×C47C4⋊C412yes—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×Q811yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×Dic47—21no—
79C2×Dic47—22no—
80C2×Dic47—21no—
81C2×Dic47—42no—
82C2×Dic47—42no—
83C2×Dic47—41no—
84C2×Dic47—82no—
85C8×C47—22no—
86C47⋊C8—41no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—22no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47C4×D411yescharacteristic
93C22×C47#12011yescharacteristic
94C22×C47C22⋊Q811yescharacteristic
95C4×C47—22no—
96C4×C47—42no—
97C4×C47C2×C4⋊C411yescharacteristic
98C4×C47C4×D411yescharacteristic
99C4×C47C22⋊Q811yescharacteristic
100C4×C47#12311yescharacteristic
101Dic47—41no—
102Dic47—42no—
103Dic47—41no—
104Dic47—81no—
105#1860—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—42no—
109C2×C47#38511yescharacteristic
110C2×C47#45411yescharacteristic
111C2×C47#45511yescharacteristic
112#520—471no—
113#428—471no—
114C2×#104D4711yescharacteristic
115#417—471no—
116#382—471no—
117#343—471no—
118#339—471no—
119C47#186011yescharacteristic, complemented, Sylow
120C2×#41C2×D4711yescharacteristic
121C2×M16—471no—
122C2×M16C2×D4711yescharacteristic
123C4×Q8—941no—
124C4×D4—942no—
125C4×D4—941no—
126#117—471no—
127#117—941no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—941no—
131C2×C42C2×D4711yescharacteristic
132#107—941no—
133#106—941no—
134#104Dic4714yescomplemented
135#103—941no—
136#102—941no—
137#95—942no—
138#41—21no—
139#41—21no—
140#41Dic9412yes—
141#41C2×Dic4712yes—
142C2×Q8D18811yescharacteristic
143C2×D4—21no—
144C2×D4D18811yescharacteristic
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—472no—
148C22×C4—942no—
149C22×C4—941no—
150C22×C4C22×D4711yescharacteristic
151M16—21no—
152M16—941no—
153M16—941no—
154M16C2×Dic4712yescomplemented
155C2×C8—21no—
156C2×C8—941no—
157C4⋊C4—471no—
158C4⋊C4—471no—
159C4⋊C4—942no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C22⋊C4—942no—
165C22⋊C4—941no—
166C42—21no—
167C42—942no—
168C42—941no—
169C42C2×Dic4712yescomplemented
170C23—21no—
171C23D4×D4711yescharacteristic
172Q8—21no—
173Q8C4⋊Dic4712yes—
174D4—22no—
175D4—22no—
176D4—21no—
177D4C4⋊Dic4712yes—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—941no—
185C2×C4—941no—
186C2×C4—942no—
187C2×C4—3762no—
188C2×C4—1882no—
189C2×C4—1881no—
190C2×C4—1882no—
191C2×C4C2×Dic9411yescharacteristic
192C2×C4C2×D18811yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4#1062535211yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C22×Dic4711yescharacteristic
197C8—22no—
198C8—1881no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—41no—
203C22—41no—
204C22D4×Dic4711yescharacteristic
205C22#1309399411yescharacteristic
206C22#1309400111yescharacteristic
207C4—22no—
208C4—42no—
209C4—3761no—
210C4—1881no—
211C4—1881no—
212C4—1882no—
213C4C2×C4⋊Dic4711yescharacteristic
214C4D4×Dic4711yescharacteristic
215C4#1309400111yescharacteristic
216C4#1309400811yescharacteristic
217C2—21no—
218C2—21no—
219C2—42no—
220C2#1568899811yescharacteristic
221C2#1568929711yescharacteristic
222C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#1860
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #15689165C2semidirect
4. #15688989C2semidirect
5. #15688891C2semidirect
6. #15688883C2semidirect
25. #104×C47C4semidirect
40. M16×C47C2×C4semidirect
43. C42×C47C2×C4semidirect
119. C47#1860semidirect
134. #104Dic47semidirect
154. M16C2×Dic47semidirect
169. C42C2×Dic47semidirect