Finite Group Databasebeta

← #20243495

Subgroups — #20243495

Order 6016.

296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689596C211yesmaximal, characteristic
2C2×#13093938C211yesmaximal, characteristic
3C2×#13093938C211yesmaximal, characteristic
4#15688890C211yesmaximal, characteristic, complemented
5#15688889C211yesmaximal, characteristic, complemented
6#15688889C211yesmaximal, characteristic, complemented
7C47×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C4×C22⋊D47—22no—
10(C22⋊D47)⋊C4—22no—
11#13093980C412yescomplemented
12C2×C22⋊Dic47C2211yescharacteristic
13C2×C22⋊Dic47C2211yescharacteristic
14C2×C22⋊Dic47C2211yescharacteristic
15C22⋊C4×D47C412yescomplemented
16#13093938—22no—
17#13093938—22no—
18C2×C22⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47C2211yescharacteristic
20C2×C22⋊C4×C47C2211yescharacteristic
21C24×C47C2311yescharacteristic
22C23×D47C2×C411yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C2×C22⋊D47—21no—
27C2×C22⋊D47—21no—
28C2×C22⋊D47—21no—
29C2×C22⋊D47—21no—
30C2×C22⋊D47D412yes—
31C2×C22⋊D47D412yes—
32C22×Dic47—21no—
33C22×Dic47—21no—
34C22×Dic47—21no—
35C22×Dic47C2×C411yescharacteristic
36C2×C4×D47—22no—
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C22⋊C4×C47C2×C412yes—
43C22⋊Dic47—21no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46C22⋊Dic47—21no—
47C22⋊Dic47—21no—
48C22⋊Dic47C2×C412yes—
49(C2×D47)⋊C4—22no—
50Dic47⋊C4—22no—
51C4×Dic47—22no—
52C23×C47—81no—
53C23×C47C22×C411yescharacteristic
54C23×C47C2×D411yescharacteristic
55C23×C47C2×D411yescharacteristic
56C23×C47#4111yescharacteristic
57C23×C47#4111yescharacteristic
58C23×C47#4111yescharacteristic
59C23×C47#4111yescharacteristic
60C22×D47—21no—
61C22×D47—21no—
62C22×D47—81no—
63C22×D47C22⋊C412yes—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—81no—
68C2×C4×C47—81no—
69C2×C4×C47—81no—
70C22⋊D47—22no—
71C22⋊D47—22no—
72C22⋊D47—22no—
73C22⋊D47—22no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—22no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—81no—
80C2×Dic47—81no—
81C2×Dic47—81no—
82C2×Dic47C22⋊C412yes—
83C4×D47—82no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47—41no—
89C22×C47—41no—
90C22×C47—41no—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47#11711yescharacteristic
93C22×C47#11711yescharacteristic
94C22×C47#12311yescharacteristic
95C22×C47#12311yescharacteristic
96C22×C47#12311yescharacteristic
97C22×C47#12311yescharacteristic
98C2×D47—22no—
99C2×D47—42no—
100C2×D47—81no—
101C2×D47—81no—
102C4×C47—42no—
103C4×C47—81no—
104C4×C47—81no—
105Dic47—22no—
106Dic47—42no—
107Dic47—81no—
108Dic47—81no—
109#1828—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—21no—
117C2×C47#38111yescharacteristic
118D47—42no—
119#518—471no—
120C2×#99—471no—
121C2×#99—471no—
122#342—471no—
123#342—471no—
124#342—471no—
125#342D4711yescharacteristic, complemented
126C47#182811yescharacteristic, complemented, Sylow
127C22×D4—471no—
128C4×D4—942no—
129C4×D4—942no—
130#117—472no—
131C2×C22⋊C4—471no—
132C2×C22⋊C4—472no—
133C2×C22⋊C4—471no—
134C2×C22⋊C4—471no—
135C2×C22⋊C4C2×D4711yescharacteristic
136C2×C22⋊C4C2×D4711yescharacteristic
137C2×C22⋊C4C2×D4711yescharacteristic
138#99—942no—
139#99—942no—
140C24—471no—
141C24C22×D4711yescharacteristic
142C2×D4—472no—
143C2×D4—472no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—471no—
152C22×C4—942no—
153C22×C4—941no—
154C22×C4—941no—
155C22×C4—941no—
156C4⋊C4—942no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—472no—
163C22⋊C4—942no—
164C22⋊C4—941no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C22⋊C4—941no—
169C22⋊C4C4×D4712yes—
170C42—942no—
171C23—81no—
172C23—472no—
173C23—941no—
174C23—941no—
175C23—3761no—
176C23C2×C4×D4711yescharacteristic
177C23#1062535011yescharacteristic
178C23#1062535011yescharacteristic
179C23D4×D4711yescharacteristic
180C23D4×D4711yescharacteristic
181C23#1062535211yescharacteristic
182C23#1062535411yescharacteristic
183D4—942no—
184D4—942no—
185D4—942no—
186D4—942no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—472no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—942no—
197C2×C4—3762no—
198C2×C4—3761no—
199C2×C4—3761no—
200C2×C4—3761no—
201C2×C4—1881no—
202C2×C4—1881no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—942no—
211C22—3761no—
212C22—3761no—
213C22—1882no—
214C22C22⋊C4×D4711yescharacteristic
215C22#1309398111yescharacteristic
216C22#1309398211yescharacteristic
217C22#1309400611yescharacteristic
218C22#1309400611yescharacteristic
219C22#1309400911yescharacteristic
220C22#1309400911yescharacteristic
221C4—42no—
222C4—81no—
223C4—81no—
224C4—942no—
225C4—3761no—
226C4—3761no—
227C4—1882no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—1882no—
236C2#1568898511yescharacteristic
subgroupG/H
centerC2#15688985
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#342C2
socleC2×C47#381
hypercenter#342D47
hypocenterC47#1828
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #15688890C2semidirect
5. #15688889C2semidirect
6. #15688889C2semidirect
7. C47×#342C2semidirect
11. #13093980C4semidirect
15. C22⋊C4×D47C4semidirect
125. #342D47semidirect
126. C47#1828semidirect