Finite Group Databasebeta

← #13069645

Subgroups — #13069645

Order 1408.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3#10623336C211yesmaximal, characteristic
4#10622838C211yesmaximal, characteristic, complemented
5C2×#66897C211yesmaximal, characteristic, complemented
6C2×#66869C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C2×#4339C2211yescharacteristic
11C11×#124—22no—
12C11×#124—22no—
13C2×C11×C22⋊C4—22no—
14C2×C42×C11C2211yescharacteristic
15#67006—22no—
16C2×#4326—21no—
17#66995—22no—
18#66995—22no—
19C2×#4325—21no—
20#66993—21no—
21#66991—22no—
22#66989—21no—
23#66979C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×#4318C2211yescharacteristic
26#66899—22no—
27#66897—22no—
28#66869—22no—
29C24×C11D412yes—
30C2×Q8×C11—21no—
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11D412yescomplemented
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—21no—
41C2×D4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—21no—
47#4339—21no—
48#4339—21no—
49#4339—21no—
50#4339—21no—
51C2×D44D411yescharacteristic
52C2×C4×D11—21no—
53C2×Dic22D411yescharacteristic
54C11×C22⋊C4—28no—
55C42×C11—21no—
56C42×C11D412yescomplemented
57C22⋊Dic11—24no—
58C22⋊Dic11—21no—
59#4326—24no—
60#4325—24no—
61C4⋊Dic11D412yes—
62C4×Dic11—21no—
63#4318—21no—
64#4318—21no—
65#4318—21no—
66#4318D412yescomplemented
67C2×C11⋊C8—21no—
68C2×C11⋊C8—21no—
69#2004—111nomaximal, Sylow
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—44no—
74C23×C11C2×D411yescharacteristic
75C22×D11—21no—
76Q8×C11—22no—
77Q8×C11—22no—
78Q8×C11—41no—
79Q8×C11—41no—
80D4×C11—41no—
81D4×C11—41no—
82D4×C11—41no—
83D4×C11—41no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—42no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C22⋊D11—41no—
96C22⋊D11—41no—
97C22⋊D11—84no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100D44—21no—
101D44—21no—
102C4×D11—41no—
103C4×D11—41no—
104Dic22—21no—
105Dic22—21no—
106C11⋊C8—22no—
107C11⋊C8—41no—
108C2×#137—111no—
109#535—111no—
110C2×#124D1111yescharacteristic, complemented
111C2×#104—111no—
112#419—111no—
113C2×#100—111no—
114#339—111no—
115C22×C11—22no—
116C22×C11—44no—
117C22×C11—42no—
118C22×C11—44no—
119C22×C11—82no—
120C22×C11#12011yescharacteristic
121C22×C11#12011yescharacteristic
122C22×C11#12111yescharacteristic
123C2×D11—41no—
124C2×D11—42no—
125C4×C11—42no—
126C4×C11—42no—
127C4×C11#12011yescharacteristic
128C4×C11#12111yescharacteristic
129C4×C11#12111yescharacteristic
130C4×C11#12711yescharacteristic
131Dic11—41no—
132Dic11—42no—
133C2×#41—111no—
134C22×Q8C2×D1111yescharacteristic
135C22×D4C2×D1111yescharacteristic
136#137—222no—
137#137—222no—
138C2×Q16—221no—
139C2×SD16—221no—
140C2×M16—111no—
141C2×M16—111no—
142#127—221no—
143#124—22no—
144#124—22no—
145#124—221no—
146#121—222no—
147#120—222no—
148#117—111no—
149C2×C22⋊C4—22no—
150C2×C42C2×D1111yescharacteristic
151#104—222no—
152#103—222no—
153#100—222no—
154C2×C11—21no—
155C2×C11—21no—
156C2×C11—82no—
157C2×C11#39211yescharacteristic
158C2×C11#45512yes—
159D11—81no—
160C24C22⋊D1112yes—
161#41—221no—
162#41—221no—
163#41—221no—
164#41—221no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—111no—
171C2×Q8C22⋊D1112yescomplemented
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—111no—
179C2×D4—221no—
180C2×D4—224no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—221no—
184C22×C4C22×D1111yescharacteristic
185Q16—224no—
186SD16—224no—
187M16—112no—
188M16—221no—
189M16—221no—
190M16—221no—
191C2×C8—221no—
192C2×C8—221no—
193C4⋊C4—112no—
194C22⋊C4—28no—
195C22⋊C4—224no—
196C22⋊C4—221no—
197C42—21no—
198C42—221no—
199C42C22⋊D1112yescomplemented
200C11#200411yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—221no—
206C23C2×C22⋊D1111yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—221no—
212Q8—221no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—221no—
218D4—221no—
219D4—441no—
220D4—441no—
221D4—884no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—222no—
228C2×C4—221no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4D4×D1111yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4#434111yescharacteristic
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C8—222no—
238C8—441no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—441no—
245C22—442no—
246C22#6699011yescharacteristic
247C22#6699211yescharacteristic
248C22#6700611yescharacteristic
249C4—42no—
250C4—42no—
251C4—441no—
252C4—442no—
253C4#6699011yescharacteristic
254C4#6699111yescharacteristic
255C4#6699211yescharacteristic
256C4#6699311yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—881no—
261C2#1062267412yes—
262C2#1062283611yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#124C2
socleC22×C11#120
prime radical#10623336C2
hypercenterC2×#124D11
hypocenterC11#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×#66995C2semidirect
4. #10622838C2semidirect
5. C2×#66897C2semidirect
6. C2×#66869C2semidirect
7. #10622161C2semidirect
35. C2×Q8×C11D4semidirect
56. C42×C11D4semidirect
66. #4318D4semidirect
110. C2×#124D11semidirect
171. C2×Q8C22⋊D11semidirect
199. C42C22⋊D11semidirect
200. C11#2004semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669952
#106233362
#106228382
C2×#668972
C2×#668692
#106221612
#200411