Finite Group Databasebeta

← #13078477

Subgroups — #13078477

Order 1408.

376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623050C211yesmaximal, characteristic, complemented
2#10623035C211yesmaximal, characteristic
3C11×#428C211yesmaximal, characteristic, complemented
4#10622746C211yesmaximal, characteristic
5#10622732C211yesmaximal, characteristic, complemented
6#10622615C211yesmaximal, characteristic
7C2×#66872C211yesmaximal, characteristic, complemented
8#10622504C212yesmaximal, complemented
9#10622490C212yesmaximal, complemented
10#10622483C212yesmaximal, complemented
11#10622467C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C11×#117C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C4×C22⋊D11—22no—
17#66979C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66946C2212yes—
21#66945—21no—
22C4⋊C4×D11—21no—
23#66943C2212yes—
24#66941C2212yes—
25#66940C2212yes—
26#66931—22no—
27#66923—21no—
28#66922—21no—
29C11×#107C2212yes—
30C11×#106C2212yes—
31#66885C2212yes—
32#66880C2212yes—
33Dic11⋊C8C2212yes—
34Dic11⋊C8C2212yes—
35#66874C2211yescharacteristic
36#66874C2211yescharacteristic
37#66873C2211yescharacteristic
38#66873C2211yescharacteristic
39#66872C2212yes—
40#66872C2212yes—
41C22×C4×C11—21no—
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—21no—
44C22×Dic11—21no—
45#4339—22no—
46#4339Q814yescomplemented
47C2×D44C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—21no—
50C2×Dic22—22no—
51C2×Dic22C2311yescharacteristic
52C11×M16—22no—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4C2312yes—
56C11×C4⋊C4C2311yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C42×C11—21no—
60C22⋊Dic11D412yes—
61(C2×D11)⋊C4—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2312yes—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C4×Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#3084—111nomaximal, Sylow
76C23×C11C2×D411yescharacteristic
77C22×D11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—81no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×Q812yes—
84C2×C4×C11#4112yes—
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—24no—
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11—81no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92D44—21no—
93D44C2×Q812yes—
94C4×D11—24no—
95C4×D11—82no—
96Dic22—21no—
97Dic22—82no—
98Dic22C2×Q812yes—
99C8×C11—22no—
100C11⋊C8—21no—
101C11⋊C8—21no—
102#544—111no—
103#520—111no—
104#479—112no—
105#478—112no—
106#476—112no—
107#475—112no—
108#428D1111yescharacteristic, complemented
109C2×#106—111no—
110#424—111no—
111#417—111no—
112#416—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11C22⋊Q812yes—
116C22×C11C22×D411yescharacteristic
117C2×D11—22no—
118C2×D11—41no—
119C2×D11—41no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11C22⋊Q812yes—
124C4×C11C22×Q811yescharacteristic
125C4×C11C2×#4111yescharacteristic
126Dic11—22no—
127Dic11—22no—
128Dic11—22no—
129Dic11—42no—
130C2×#41—111no—
131C2×M16C2×D1111yescharacteristic
132C22×C8—111no—
133C4⋊Q8—112no—
134C4⋊Q8—221no—
135#125—112no—
136#125—221no—
137C22⋊Q8—222no—
138C4×Q8—112no—
139C4×D4—112no—
140C4×D4—222no—
141#117—111no—
142#117—221no—
143#117C2×D1111yescharacteristic
144C2×C4⋊C4—111no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4C2×D1111yescharacteristic
147#107C2×D1112yes—
148#106—112no—
149#106—112no—
150#106C2×D1112yes—
151C4⋊C8—112no—
152C4⋊C8—112no—
153#103—112no—
154#103—111no—
155#103—111no—
156#102—112no—
157#102—111no—
158#102—111no—
159C2×C11—22no—
160C2×C11C2×C22⋊Q811yescharacteristic
161C2×C11#57711yescharacteristic
162C2×C11#57711yescharacteristic
163D11—42no—
164#41—114no—
165#41—222no—
166C2×Q8—111no—
167C2×Q8—222no—
168C2×D4—111no—
169C2×D4—221no—
170C22×C4—21no—
171C22×C4—222no—
172C22×C4—221no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175M16—22no—
176C2×C8—111no—
177C2×C8—111no—
178C2×C8—222no—
179C2×C8C22×D1112yes—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—111no—
183C4⋊C4—112no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—221no—
189C4⋊C4C22×D1111yescharacteristic
190C4⋊C4C22×D1111yescharacteristic
191C4⋊C4C22×D1112yes—
192C22⋊C4—21no—
193C22⋊C4—112no—
194C22⋊C4—222no—
195C42—21no—
196C42—112no—
197C42—222no—
198C11#308411yescharacteristic, complemented, Sylow
199C23—221no—
200C23D4×D1111yescharacteristic
201Q8—112no—
202Q8—221no—
203Q8—882no—
204D4—112no—
205D4—224no—
206D4—221no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—112no—
212C2×C4—112no—
213C2×C4—221no—
214C2×C4—224no—
215C2×C4—222no—
216C2×C4—882no—
217C2×C4—881no—
218C2×C4#433912yes—
219C2×C4D4×D1111yescharacteristic
220C2×C4Q8×D1112yes—
221C2×C4C23×D1111yescharacteristic
222C8—22no—
223C8—221no—
224C8—221no—
225C22—21no—
226C22—21no—
227C22—222no—
228C22—441no—
229C22—441no—
230C22#6694912yes—
231C22C2×D4×D1111yescharacteristic
232C4—42no—
233C4—41no—
234C4—41no—
235C4—222no—
236C4—222no—
237C4—222no—
238C4—442no—
239C4#6694912yes—
240C4C2×#433911yescharacteristic
241C4C2×Q8×D1111yescharacteristic
242C2—22no—
243C2—442no—
244C2C2×#6694911yescharacteristic
245C2#1062330611yescharacteristic
246C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#428D11
hypocenterC11#3084
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10623050C2semidirect
3. C11×#428C2semidirect
5. #10622732C2semidirect
7. C2×#66872C2semidirect
8. #10622504C2semidirect
9. #10622490C2semidirect
10. #10622483C2semidirect
11. #10622467C2semidirect
46. #4339Q8semidirect
108. #428D11semidirect
198. C11#3084semidirect

Maximal subgroups

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

subgroupindex
#106230502
#106230352
C11×#4282
#106227462
#106227322
#106226152
C2×#668722
#106225042
#106224902
#106224832
#106224672
#308411