Finite Group Databasebeta

← #13079807

Subgroups — #13079807

Order 1408.

368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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#10623256C211yesmaximal, characteristic
2D11×#125C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622680C211yesmaximal, characteristic, complemented
6#10622504C212yesmaximal, complemented
7#10622495C212yesmaximal, complemented
8#10622484C212yesmaximal, complemented
9#10622476C212yesmaximal, complemented
10#10622326C211yesmaximal, characteristic, complemented
11#10622318C211yesmaximal, characteristic, complemented
12C2×#4343—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#125C2211yescharacteristic
15#67000—21no—
16#66948—21no—
17#66948C2212yes—
18#66946—21no—
19#66946C2212yes—
20C4⋊C4×D11—21no—
21C4⋊C4×D11—21no—
22C4⋊C4×D11C2211yescharacteristic
23C4⋊C4×D11C2211yescharacteristic
24#66943C2211yescharacteristic
25#66943C2211yescharacteristic
26#66942—21no—
27#66942—21no—
28#66927C2211yescharacteristic
29C42×D11C2211yescharacteristic
30#66923C2211yescharacteristic
31C11×#107C2212yes—
32C11×#106C2212yes—
33C11×#97C2211yescharacteristic
34#66885C2212yes—
35#66885C2212yes—
36(C2×D11)⋊C8C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2212yes—
39#66873C2212yes—
40#66872C2212yes—
41#66871C2212yes—
42#66867C2211yescharacteristic
43C2×Q8×C11—21no—
44#4343—44no—
45C2×D44—22no—
46C2×D44—21no—
47C2×D44—21no—
48C2×D44C2312yes—
49C2×C4×D11—22no—
50C2×C4×D11—21no—
51C2×C4×D11—21no—
52C2×C4×D11D411yescharacteristic
53C2×C4×D11D411yescharacteristic
54C2×C4×D11C2311yescharacteristic
55C2×C8×C11C2312yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4C2312yes—
60C11×C4⋊C4C2311yescharacteristic
61C11×C4⋊C4C2311yescharacteristic
62C42×C11C2311yescharacteristic
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75C4×Dic11D411yescharacteristic
76C4×Dic11D411yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3234—111nomaximal, Sylow
80C22×D11—22no—
81C22×D11C2×D411yescharacteristic
82Q8×C11—42no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11C2×D411yescharacteristic
92C2×Dic11C2×D411yescharacteristic
93C2×Dic11C2×D411yescharacteristic
94D44—24no—
95D44—42no—
96D44—42no—
97D44—44no—
98C4×D11—22no—
99C4×D11—22no—
100C4×D11—41no—
101C4×D11—44no—
102C4×D11—42no—
103C4×D11—42no—
104C8×C11—22no—
105C11⋊C8—22no—
106#532—111no—
107C2×#125—111no—
108#501—111no—
109#501D1111yescharacteristic, complemented
110#490—111no—
111#490—111no—
112#481—112no—
113#480—112no—
114#478—112no—
115#478—112no—
116#432—111no—
117C22×C11C22×D411yescharacteristic
118C2×D11—21no—
119C2×D11—21no—
120C2×D11—42no—
121C2×D11—42no—
122C2×D11—42no—
123C2×D11AGL(1,ℤ/8)12yes—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—42no—
127C4×C11—41no—
128C4×C11—41no—
129C4×C112−1+412yes—
130Dic11—21no—
131Dic11—21no—
132Dic11—21no—
133Dic11—41no—
134Dic11—41no—
135C2×#41—221no—
136C4⋊Q8C2×D1111yescharacteristic
137#127—111no—
138#125—111no—
139#125—111no—
140#125—111no—
141#125—221no—
142#125—221no—
143#125C2×D1111yescharacteristic
144#124—221no—
145#121—112no—
146#121—221no—
147C4×D4—112no—
148C4×D4—221no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—221no—
153C2×C42—111no—
154#107—112no—
155#107C2×D1112yes—
156#106—112no—
157#106C2×D1112yes—
158C4⋊C8—112no—
159#102—112no—
160#102—112no—
161#102—112no—
162#102—112no—
163C22⋊C8—112no—
164#97—111no—
165#97C2×D1111yescharacteristic
166C2×C11#53611yescharacteristic
167C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C11#57511yescharacteristic
169D11—22no—
170D11—82no—
171#41—444no—
172C2×Q8—21no—
173C2×D4—112no—
174C2×D4—222no—
175C2×D4—221no—
176C2×D4—221no—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—222no—
181C22×C4—221no—
182C22×C4—221no—
183C2×C8—112no—
184C2×C8C22×D1112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—111no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4C22×D1111yescharacteristic
199C4⋊C4C22×D1111yescharacteristic
200C4⋊C4C22×D1112yes—
201C22⋊C4—222no—
202C22⋊C4—222no—
203C42—111no—
204C42—111no—
205C42—111no—
206C42C22×D1111yescharacteristic
207C11#323411yescharacteristic, complemented, Sylow
208C23—111no—
209C23—222no—
210Q8—42no—
211D4—224no—
212D4—442no—
213D4—442no—
214D4—444no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—111no—
219C2×C4—111no—
220C2×C4—111no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—441no—
226C2×C4—444no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4D4×D1111yescharacteristic
230C2×C4D4×D1111yescharacteristic
231C2×C4C23×D1111yescharacteristic
232C8—22no—
233C8—222no—
234C22—112no—
235C22—221no—
236C22—221no—
237C22—442no—
238C22—442no—
239C22—442no—
240C22C2×D4×D1111yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—221no—
247C4—221no—
248C4—221no—
249C4—441no—
250C4—441no—
251C4#6704012yes—
252C2—222no—
253C2—882no—
254C2#1062325511yescharacteristic
255C2D11×AGL(1,ℤ/8)11yescharacteristic
256C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radical#10623256C2
hypercenter#501D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. D11×#125C2semidirect
3. C11×#501C2semidirect
4. #10622693C2semidirect
5. #10622680C2semidirect
6. #10622504C2semidirect
7. #10622495C2semidirect
8. #10622484C2semidirect
9. #10622476C2semidirect
10. #10622326C2semidirect
11. #10622318C2semidirect
109. #501D11semidirect
207. C11#3234semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106232562
D11×#1252
C11×#5012
#106226932
#106226802
#106225042
#106224952
#106224842
#106224762
#106223262
#106223182
#323411