Finite Group Databasebeta

← #13069827

Subgroups — #13069827

Order 1408.

326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×C11×#100C211yesmaximal, characteristic, complemented
3#10622834C211yesmaximal, characteristic, complemented
4C2×#66889C211yesmaximal, characteristic, complemented
5#10622746C211yesmaximal, characteristic, complemented
6#10622734C211yesmaximal, characteristic, complemented
7#10622193C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12#67006—22no—
13C2×C22⋊Dic11—22no—
14#66993—21no—
15#66991—21no—
16#66991—21no—
17#66989—21no—
18#66979C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4×Dic11C2211yescharacteristic
21C11×#100—22no—
22#66889—22no—
23#66885—21no—
24#66882—21no—
25#66881—21no—
26#66880—21no—
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×C11C2311yescharacteristic
35C2×C22⋊D11—22no—
36C2×C22⋊D11—22no—
37C2×C22⋊D11—21no—
38C22×Dic11—21no—
39C22×Dic11—21no—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22D411yescharacteristic
47C11×M16—21no—
48C11×M16—21no—
49C11×M16—21no—
50C11×M16D412yescomplemented
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C22⋊Dic11—22no—
54C22⋊Dic11—22no—
55C22⋊Dic11—21no—
56C22⋊Dic11—44no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11D411yescharacteristic
60C4⋊Dic11D411yescharacteristic
61C4×Dic11—21no—
62C4×Dic11—21no—
63C4×Dic11—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×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11#4111yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C22⋊D11—41no—
83C22⋊D11—41no—
84C22⋊D11—82no—
85C22⋊D11—82no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—42no—
93C2×Dic11—41no—
94D44—21no—
95D44—21no—
96C4×D11—41no—
97C4×D11—41no—
98Dic22—21no—
99Dic22—21no—
100C8×C11—22no—
101C8×C11—41no—
102#535—111no—
103#428—111no—
104C2×#104—111no—
105#417—111no—
106C2×#100D1111yescharacteristic, complemented
107#390—111no—
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#12111yescharacteristic
123C4×C11#12111yescharacteristic
124C4×C11#12311yescharacteristic
125C4×C11#12411yescharacteristic
126Dic11—42no—
127Dic11—41no—
128Dic11—41no—
129Dic11—41no—
130Dic11—81no—
131C2×#41—111no—
132C22×D4C2×D1111yescharacteristic
133C2×M16C2×D1111yescharacteristic
134C2×M16C2×D1111yescharacteristic
135#127—221no—
136#124—221no—
137#121—221no—
138#121—221no—
139#120—222no—
140#117—111no—
141C2×C4⋊C4—111no—
142C2×C22⋊C4—222no—
143C2×C42—111no—
144#107—221no—
145#106—221no—
146#104—222no—
147#103—221no—
148#102—221no—
149#100—22no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11—82no—
153C2×C11#39411yescharacteristic
154C2×C11#45311yescharacteristic
155C2×C11#45511yescharacteristic
156D11—81no—
157C24D4412yes—
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—221no—
174C22×C4—221no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177M16—21no—
178M16—21no—
179M16—21no—
180M16C22⋊D1112yescomplemented
181C2×C8—21no—
182C2×C8—21no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—221no—
190C22⋊C4—444no—
191C42—221no—
192C42—221no—
193C42—221no—
194C11#203711yescharacteristic, complemented, Sylow
195C23—22no—
196C23—22no—
197C23—22no—
198C23—42no—
199C23—42no—
200C23—221no—
201C23C2×D4411yescharacteristic
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—222no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4—441no—
221C2×C4—441no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4#433911yescharacteristic
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4#434111yescharacteristic
228C2×C4#434111yescharacteristic
229C2×C4C2×C22⋊D1111yescharacteristic
230C8—22no—
231C8—41no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—82no—
239C22—441no—
240C22—441no—
241C22—441no—
242C22#6693511yescharacteristic
243C22#6693911yescharacteristic
244C22#6698311yescharacteristic
245C4—442no—
246C4—441no—
247C4—441no—
248C4—441no—
249C4—881no—
250C4#6693611yescharacteristic
251C4#6693811yescharacteristic
252C4#6699111yescharacteristic
253C4#6699211yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—881no—
258C2#1062235911yescharacteristic
259C2#1062236011yescharacteristic
260C2#1062257411yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#100C2
socleC22×C11#120
prime radical#10623336C2
hypercenterC2×#100D11
hypocenterC11#2037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×C11×#100C2semidirect
3. #10622834C2semidirect
4. C2×#66889C2semidirect
5. #10622746C2semidirect
6. #10622734C2semidirect
7. #10622193C2semidirect
50. C11×M16D4semidirect
106. C2×#100D11semidirect
180. M16C22⋊D11semidirect
194. C11#2037semidirect

Maximal subgroups

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

subgroupindex
#106233362
C2×C11×#1002
#106228342
C2×#668892
#106227462
#106227342
#106221932
#203711