Finite Group Databasebeta

← #13069826

Subgroups — #13069826

Order 1408.

326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623336C211yesmaximal, characteristic
2C11×#390C211yesmaximal, characteristic, complemented
3C2×#66897C211yesmaximal, characteristic, complemented
4#10622579C211yesmaximal, characteristic, complemented
5#10622577C211yesmaximal, characteristic, complemented
6C2×#66869C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4—22no—
12C2×C42×C11C2211yescharacteristic
13#67006—22no—
14#66993—21no—
15#66991—21no—
16#66991—21no—
17#66989—21no—
18#66979C2211yescharacteristic
19C2×#4318C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21#66897—22no—
22#66874—21no—
23#66873—21no—
24#66872—21no—
25#66871—21no—
26#66869—22no—
27C24×C11D412yes—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×C22⋊D11—22no—
39C2×C22⋊D11—21no—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22D411yescharacteristic
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C22⋊C4—44no—
50C42×C11—21no—
51C42×C11—21no—
52C22⋊Dic11—22no—
53C22⋊Dic11—22no—
54C22⋊Dic11—21no—
55C4⋊Dic11D411yescharacteristic
56C4⋊Dic11D411yescharacteristic
57C4×Dic11—21no—
58#4318—21no—
59#4318—21no—
60#4318—21no—
61#4318D412yescomplemented
62C2×C11⋊C8—21no—
63C2×C11⋊C8—21no—
64#2037—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—42no—
69C23×C11—42no—
70C23×C11C2×D411yescharacteristic
71C22×D11—21no—
72D4×C11—41no—
73D4×C11—41no—
74D4×C11—41no—
75D4×C11—41no—
76C2×C4×C11—22no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—42no—
80C2×C4×C11—41no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11#4111yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C2×C4×C11#4111yescharacteristic
87C22⋊D11—41no—
88C22⋊D11—41no—
89C22⋊D11—82no—
90C22⋊D11—82no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94D44—21no—
95D44—21no—
96C4×D11—41no—
97C4×D11—41no—
98Dic22—21no—
99Dic22—21no—
100C11⋊C8—22no—
101C11⋊C8—41no—
102#535—111no—
103#428—111no—
104C2×#104—111no—
105#417—111no—
106C2×#100—111no—
107#390D1111yescharacteristic, complemented
108#339—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—44no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—82no—
116C22×C11#12011yescharacteristic
117C22×C11#12111yescharacteristic
118C22×C11#12311yescharacteristic
119C2×D11—41no—
120C2×D11—41no—
121C2×D11—41no—
122C4×C11—42no—
123C4×C11—81no—
124C4×C11#12111yescharacteristic
125C4×C11#12111yescharacteristic
126C4×C11#12311yescharacteristic
127C4×C11#12411yescharacteristic
128Dic11—41no—
129Dic11—41no—
130Dic11—41no—
131C2×#41—111no—
132C22×D4C2×D1111yescharacteristic
133C2×M16—111no—
134C2×M16—111no—
135#127—221no—
136#124—221no—
137#121—221no—
138#121—221no—
139#120—222no—
140#117—111no—
141C2×C4⋊C4C2×D1111yescharacteristic
142C2×C22⋊C4—22no—
143C2×C42C2×D1111yescharacteristic
144#107—221no—
145#106—221no—
146#104—222no—
147#103—221no—
148#102—221no—
149#100—222no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11—82no—
153C2×C11#39411yescharacteristic
154C2×C11#45311yescharacteristic
155C2×C11#45511yescharacteristic
156D11—81no—
157C24C22⋊D1112yes—
158#41—221no—
159#41—221no—
160#41—221no—
161#41—221no—
162C2×Q8—111no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—111no—
170C2×D4—221no—
171C2×D4—222no—
172C2×D4—222no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177M16—112no—
178M16—221no—
179M16—221no—
180M16—221no—
181C2×C8—221no—
182C2×C8—221no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—111no—
186C4⋊C4—111no—
187C22⋊C4—44no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4—221no—
191C42—21no—
192C42—21no—
193C42—221no—
194C11#203711yescharacteristic, complemented, Sylow
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—221no—
201C23C2×C22⋊D1111yescharacteristic
202Q8—221no—
203Q8—221no—
204D4—41no—
205D4—41no—
206D4—41no—
207D4—41no—
208D4—221no—
209D4—221no—
210D4—441no—
211D4—441no—
212D4—882no—
213D4—882no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—441no—
223C2×C4—441no—
224C2×C4#433911yescharacteristic
225C2×C4#433911yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4D4×D1111yescharacteristic
228C2×C4D4×D1111yescharacteristic
229C2×C4#434111yescharacteristic
230C8—222no—
231C8—441no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—441no—
240C22—441no—
241C22—441no—
242C22#6698211yescharacteristic
243C22#6699011yescharacteristic
244C22#6699211yescharacteristic
245C4—42no—
246C4—81no—
247C4—441no—
248C4—441no—
249C4—441no—
250C4#6693611yescharacteristic
251C4#6693711yescharacteristic
252C4#6693711yescharacteristic
253C4#6693811yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—881no—
258C2#1062257211yescharacteristic
259C2#1062267411yescharacteristic
260C2#1062269011yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC22×C11#120
prime radical#10623336C2
hypercenter#390D11
hypocenterC11#2037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C11×#390C2semidirect
3. C2×#66897C2semidirect
4. #10622579C2semidirect
5. #10622577C2semidirect
6. C2×#66869C2semidirect
7. #10622161C2semidirect
61. #4318D4semidirect
107. #390D11semidirect
194. C11#2037semidirect

Maximal subgroups

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

subgroupindex
#106233362
C11×#3902
C2×#668972
#106225792
#106225772
C2×#668692
#106221612
#203711