Finite Group Databasebeta

← #13078482

Subgroups — #13078482

Order 1408.

376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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#10623358C211yesmaximal, characteristic
2#10623031C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic
4#10622846C211yesmaximal, characteristic
5#10622734C211yesmaximal, characteristic, complemented
6#10622732C211yesmaximal, characteristic, complemented
7C2×#66872C211yesmaximal, characteristic, complemented
8#10622409C212yesmaximal, complemented
9#10622404C212yesmaximal, complemented
10#10622379C212yesmaximal, complemented
11#10622374C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15Q8×Dic11C2212yes—
16D4×Dic11—22no—
17D4×Dic11C2212yes—
18#66979—21no—
19#66979C2211yescharacteristic
20#66979C2211yescharacteristic
21C2×C4⋊Dic11—21no—
22C2×C4⋊Dic11C2211yescharacteristic
23#66977—22no—
24C22×C11⋊C8C2211yescharacteristic
25#66943—21no—
26#66943C2212yes—
27#66941—21no—
28#66941C2212yes—
29C11×#103C2212yes—
30C11×#102C2212yes—
31#66899C2211yescharacteristic
32#66899C2211yescharacteristic
33#66896C2211yescharacteristic
34#66896C2211yescharacteristic
35#66882C2212yes—
36#66881C2212yes—
37Dic11⋊C8C2212yes—
38Dic11⋊C8C2212yes—
39#66872C2212yes—
40#66872C2212yes—
41C11×#41—22no—
42C11×#41Q814yescomplemented
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2311yescharacteristic
49C22×Dic11—22no—
50C22×Dic11—21no—
51C2×Dic22—22no—
52C11×M16—22no—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—21no—
55C11×C4⋊C4C2312yes—
56C22⋊Dic11—22no—
57C22⋊Dic11—21no—
58C22⋊Dic11D412yes—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11D411yescharacteristic
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11C2312yes—
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C4×Dic11—21no—
71C4×Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#3084—111nomaximal, Sylow
76C23×C11—21no—
77C23×C11C2×D411yescharacteristic
78Q8×C11—21no—
79Q8×C11C2×Q812yes—
80D4×C11—24no—
81D4×C11—21no—
82D4×C11C2×Q812yes—
83C2×C4×C11—21no—
84C2×C4×C11—24no—
85C2×C4×C11—22no—
86C2×C4×C11—81no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×Q812yes—
89C2×C4×C11#4112yes—
90C2×C4×C11C2411yescharacteristic
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—82no—
95C2×Dic11—81no—
96C2×Dic11C2×D412yes—
97C2×Dic11C2×D412yes—
98Dic22—82no—
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#428—111no—
109C2×#106—111no—
110#424—111no—
111#417D1111yescharacteristic
112#416—111no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11C22⋊Q812yes—
119C22×C11C22×D411yescharacteristic
120C4×C11—22no—
121C4×C11—42no—
122C4×C11C22⋊Q812yes—
123C4×C11C22×Q811yescharacteristic
124C4×C11C2×#4111yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—41no—
128Dic11—41no—
129Dic11—42no—
130C2×#41C2×D1111yescharacteristic
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—111no—
143#117—221no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4C2×D1111yescharacteristic
147#107—112no—
148#106—112no—
149#106—112no—
150#106—112no—
151C4⋊C8—112no—
152C4⋊C8—112no—
153#103—111no—
154#103—111no—
155#103C2×D1112yes—
156#102—111no—
157#102—111no—
158#102C2×D1112yes—
159C2×C11—22no—
160C2×C11—42no—
161C2×C11C2×C22⋊Q811yescharacteristic
162C2×C11#57711yescharacteristic
163C2×C11#57711yescharacteristic
164#41—22no—
165#41Dic2214yescomplemented
166C2×Q8—222no—
167C2×Q8C22×D1111yescharacteristic
168C2×D4—21no—
169C2×D4C22×D1111yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—222no—
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—111no—
184C4⋊C4—111no—
185C4⋊C4—112no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—221no—
191C4⋊C4C22×D1112yes—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—221no—
195C42—112no—
196C42—222no—
197C42—221no—
198C11#308411yescharacteristic, complemented, Sylow
199C23—21no—
200C23D4×D1111yescharacteristic
201Q8—21no—
202Q8—882no—
203Q8C2×Dic2212yes—
204D4—24no—
205D4—21no—
206D4C2×Dic2212yes—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—112no—
212C2×C4—112no—
213C2×C4—221no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—882no—
217C2×C4—881no—
218C2×C4C2×Dic2212yes—
219C2×C4D4×D1111yescharacteristic
220C2×C4#434112yes—
221C2×C4C23×D1111yescharacteristic
222C8—22no—
223C8—221no—
224C8—221no—
225C22—21no—
226C22—21no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22#6693112yes—
231C22C2×D4×D1111yescharacteristic
232C4—22no—
233C4—42no—
234C4—222no—
235C4—222no—
236C4—441no—
237C4—442no—
238C4—441no—
239C4#6693112yes—
240C4C22×Dic2211yescharacteristic
241C4C2×#434111yescharacteristic
242C2—22no—
243C2—42no—
244C2C2×#6693111yescharacteristic
245C2#1062330611yescharacteristic
246C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#417D11
hypocenterC11#3084
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #10623031C2semidirect
5. #10622734C2semidirect
6. #10622732C2semidirect
7. C2×#66872C2semidirect
8. #10622409C2semidirect
9. #10622404C2semidirect
10. #10622379C2semidirect
11. #10622374C2semidirect
42. C11×#41Q8semidirect
165. #41Dic22semidirect
198. C11#3084semidirect

Maximal subgroups

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

subgroupindex
#106233582
#106230312
C11×#4172
#106228462
#106227342
#106227322
C2×#668722
#106224092
#106224042
#106223792
#106223742
#308411