Finite Group Databasebeta

← #13081344

Subgroups — #13081344

Order 1408.

382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623252C211yesmaximal, characteristic, complemented
2#10623084C211yesmaximal, characteristic
3C11×#474C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5C4×#4324C211yesmaximal, characteristic, complemented
6#10622504C212yesmaximal, complemented
7#10622502C212yesmaximal, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622377C212yesmaximal, complemented
11#10622375C212yesmaximal, complemented
12C2×#4339—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C4×D4×C11C2211yescharacteristic
15Q8×Dic11—21no—
16#66997—21no—
17#66993C2212yes—
18C2×#4324C2211yescharacteristic
19#66983—21no—
20C2×#4314C2212yes—
21#66946C2212yes—
22#66943C2212yes—
23#66942—22no—
24#66940C2212yes—
25#66937—22no—
26#66927C2211yescharacteristic
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#107C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#102C2212yes—
32#66896C2211yescharacteristic
33#66885C2212yes—
34#66879C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2211yescharacteristic
37#66873C2212yes—
38#66873C2212yes—
39#66872C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46#4339—44no—
47C2×D44—21no—
48C2×D44—21no—
49C2×D44C2312yes—
50C2×C4×D11—22no—
51C2×Dic22D411yescharacteristic
52C2×Dic22C2311yescharacteristic
53C2×C8×C11C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4C2311yescharacteristic
56C11×C4⋊C4C2312yes—
57C11×C22⋊C4—21no—
58C42×C11C2311yescharacteristic
59#4324—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11D411yescharacteristic
63C4⋊Dic11C2311yescharacteristic
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—21no—
67Dic11⋊C4D412yes—
68C4×Dic11—22no—
69C4×Dic11—21no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#4314—24no—
74#3368—111nomaximal, Sylow
75C23×C11—21no—
76C22×D11—22no—
77Q8×C11—42no—
78D4×C11—21no—
79D4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—42no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—44no—
87C22⋊D11—82no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92D44—22no—
93D44—22no—
94D44—42no—
95D44—81no—
96C4×D11—44no—
97Dic22—22no—
98Dic22—21no—
99Dic22#4112yescomplemented
100C8×C11—22no—
101C11⋊C8—21no—
102C11⋊C8—21no—
103#557—111no—
104#550—111no—
105#490—112no—
106#486—111no—
107#478—112no—
108#474D1111yescharacteristic, complemented
109#460—111no—
110#460—112no—
111#446—111no—
112#440—112no—
113C4×SD16—111no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11—41no—
117C22×C11C22×D411yescharacteristic
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—42no—
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—42no—
124C4×C11AGL(1,ℤ/8)12yes—
125C4×C11C2×#4111yescharacteristic
126C4×C112−1+411yescharacteristic
127Dic11—22no—
128Dic11—22no—
129Dic11—22no—
130Dic11—41no—
131C2×#41—221no—
132C2×SD16—111no—
133C2×SD16—112no—
134C4⋊Q8—221no—
135C4⋊Q8C2×D1111yescharacteristic
136#127—112no—
137#127—111no—
138#125—112no—
139#125—222no—
140#121—222no—
141#121—221no—
142C4×Q8—111no—
143C4×Q8—112no—
144C4×Q8—111no—
145C4×Q8—221no—
146C4×D4—112no—
147C4×D4C2×D1111yescharacteristic
148#107C2×D1112yes—
149#106—111no—
150C4⋊C8—112no—
151C4⋊C8C2×D1111yescharacteristic
152#103—111no—
153#102—111no—
154#102—112no—
155#102—112no—
156#102—112no—
157#102C2×D1112yes—
158#97—112no—
159C4×C8—111no—
160C2×C11—81no—
161C2×C11#54811yescharacteristic
162C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C11#57711yescharacteristic
164D11—82no—
165#41—444no—
166C2×Q8—21no—
167C2×Q8—111no—
168C2×Q8—111no—
169C2×D4—112no—
170C2×D4—222no—
171C2×D4—222no—
172C2×D4—221no—
173C2×D4—221no—
174C2×D4C22×D1111yescharacteristic
175C22×C4—21no—
176C22×C4—222no—
177SD16—224no—
178SD16—222no—
179C2×C8—111no—
180C2×C8—111no—
181C2×C8C22×D1112yes—
182C4⋊C4—21no—
183C4⋊C4—111no—
184C4⋊C4—112no—
185C4⋊C4—111no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4C22×D1112yes—
191C4⋊C4C22×D1111yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—222no—
194C42—112no—
195C42—222no—
196C42—221no—
197C42C22×D1111yescharacteristic
198C11#336811yescharacteristic, complemented, Sylow
199C23—21no—
200C23—222no—
201Q8—42no—
202Q8—112no—
203Q8—222no—
204Q8—221no—
205D4—21no—
206D4—21no—
207D4—222no—
208D4—222no—
209D4—444no—
210D4—442no—
211D4—881no—
212D4—882no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—112no—
217C2×C4—112no—
218C2×C4—221no—
219C2×C4—221no—
220C2×C4—444no—
221C2×C4D4×D1111yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4C23×D1111yescharacteristic
224C8—22no—
225C8—221no—
226C8—221no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—442no—
231C22—442no—
232C22—442no—
233C22C2×D4×D1111yescharacteristic
234C4—21no—
235C4—41no—
236C4—42no—
237C4—222no—
238C4—222no—
239C4—222no—
240C4—441no—
241C4#6696412yes—
242C4#6704011yescharacteristic
243C4#41×D1111yescharacteristic
244C2—81no—
245C2—882no—
246C2#1062316411yescharacteristic
247C2C2×#6696411yescharacteristic
248C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
prime radical#10623084C2
hypercenter#474D11
hypocenterC11#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623252C2semidirect
3. C11×#474C2semidirect
4. #10622701C2semidirect
5. C4×#4324C2semidirect
6. #10622504C2semidirect
7. #10622502C2semidirect
8. #10622461C2semidirect
9. #10622444C2semidirect
10. #10622377C2semidirect
11. #10622375C2semidirect
99. Dic22#41semidirect
108. #474D11semidirect
198. C11#3368semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106230842
C11×#4742
#106227012
C4×#43242
#106225042
#106225022
#106224612
#106224442
#106223772
#106223752
#336811