Finite Group Databasebeta

← #20243397

Subgroups — #20243397

Order 6016.

356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13093986C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4C2×#13093944C211yesmaximal, characteristic
5#15688988C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C4×D47—21no—
10C22×C47⋊C8C2211yescharacteristic
11#13093986—22no—
12#13093986C414yescomplemented
13C2×C4⋊Dic47C2211yescharacteristic
14C2×(C2×D47)⋊C4—21no—
15C2×C4×Dic47C2211yescharacteristic
16Dic47⋊C8—22no—
17#13093946—22no—
18#13093944—22no—
19C47⋊#95—21no—
20C47⋊#95—21no—
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C23×D47—21no—
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47D411yescharacteristic
30C22×Dic47D411yescharacteristic
31C2×D188—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188C2×C412yes—
35C2×D188D412yes—
36C2×D188Q812yes—
37C2×C4×D47—24no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47C2×C412yes—
47(C2×D47)⋊C4—24no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4×Dic47C2×C412yes—
51C4×Dic47D412yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C22×D47—22no—
57C22×D47—22no—
58C22×D47—22no—
59C22×D47—41no—
60C22×D47—41no—
61C22×D47—41no—
62C22×D47—41no—
63C2×C4×C47—22no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×Q811yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47C22⋊C412yes—
83C2×Dic47C22⋊C412yes—
84D188—22no—
85D188—22no—
86D188—22no—
87D188C4⋊C414yes—
88C4×D47—48no—
89C8×C47—41no—
90C47⋊C8—41no—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47#12111yescharacteristic
93C22×C47C22⋊Q811yescharacteristic
94C22×C47#13511yescharacteristic
95C22×C47#13511yescharacteristic
96C22×C47AGL(1,ℤ/8)11yescharacteristic
97C22×C47AGL(1,ℤ/8)11yescharacteristic
98C2×D47—24no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—42no—
105C4×C47—42no—
106C4×C47—81no—
107C4×C47C2×C4⋊C411yescharacteristic
108C4×C47#11711yescharacteristic
109C4×C47#12111yescharacteristic
110C4×C47C22⋊Q811yescharacteristic
111Dic47—22no—
112Dic47—22no—
113Dic47—81no—
114#1804—471nomaximal, Sylow
115C2×C47#38011yescharacteristic
116C2×C47#41611yescharacteristic
117C2×C47#41811yescharacteristic
118C2×C47#46311yescharacteristic
119C2×C47#46311yescharacteristic
120C2×C47#47811yescharacteristic
121C2×C47#47811yescharacteristic
122D47—44no—
123C2×C4×D4—471no—
124C2×C4⋊C8—471no—
125C2×#102—471no—
126C2×#102—471no—
127#382—471no—
128#340—471no—
129#340D4711yescharacteristic, complemented
130C47#180411yescharacteristic, complemented, Sylow
131C22×D4—471no—
132C23×C4—941no—
133C22×C8—471no—
134C22×C8C2×D4711yescharacteristic
135C4×D4—474no—
136C4×D4—942no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C4⋊C4C2×D4711yescharacteristic
140C2×C22⋊C4—941no—
141C2×C42—471no—
142C4⋊C8—942no—
143#102—942no—
144#102—942no—
145#95—941no—
146#95—941no—
147C24—941no—
148C2×D4—472no—
149C2×D4—472no—
150C2×D4—472no—
151C2×D4—941no—
152C2×D4—941no—
153C2×D4—941no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—944no—
159C22×C4—941no—
160C22×C4—1882no—
161C22×C4—1882no—
162C22×C4C22×D4711yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—941no—
167C2×C8—941no—
168C2×C8—941no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4C4×D4712yes—
175C22⋊C4—944no—
176C42—472no—
177C42—472no—
178C23—942no—
179C23—942no—
180C23—942no—
181C23—1881no—
182C23—1881no—
183C23—1881no—
184C23—1881no—
185C23D4×D4711yescharacteristic
186D4—474no—
187D4—942no—
188D4—942no—
189D4—942no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—472no—
197C2×C4—472no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—1888no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4C2×C4×D4711yescharacteristic
207C2×C4#1062535011yescharacteristic
208C2×C4#1062535011yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4Q8×D4711yescharacteristic
212C8—41no—
213C8—1881no—
214C22—944no—
215C22—1882no—
216C22—1882no—
217C22—1882no—
218C22—1882no—
219C22—1882no—
220C22—1882no—
221C22C22⋊C4×D4711yescharacteristic
222C22#1309399711yescharacteristic
223C22#1309400211yescharacteristic
224C22#1309404511yescharacteristic
225C22#1309404711yescharacteristic
226C22#1309404811yescharacteristic
227C22#1309405111yescharacteristic
228C4—42no—
229C4—81no—
230C4—942no—
231C4—942no—
232C4—3761no—
233C4C4⋊C4×D4711yescharacteristic
234C4#1309398111yescharacteristic
235C4#1309399711yescharacteristic
236C4#1309400211yescharacteristic
237C2—1884no—
238C2#1568898211yescharacteristic
239C2#1568911811yescharacteristic
240C2#1568912611yescharacteristic
241C2#1568933711yescharacteristic
242C2#1568934111yescharacteristic
243C2#1568942211yescharacteristic
244C2#1568942611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1804
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C8C2semidirect
5. #15688988C2semidirect
6. #15688885C2semidirect
7. C47×#340C2semidirect
12. #13093986C4semidirect
129. #340D47semidirect
130. C47#1804semidirect