Finite Group Databasebeta

← #13069653

Subgroups — #13069653

Order 1408.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#66997C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic
3#10623057C211yesmaximal, characteristic
4C11×#419C211yesmaximal, characteristic, complemented
5C2×#66889C211yesmaximal, characteristic
6C2×#66888C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C11×#117C2211yescharacteristic
13#66997—22no—
14#66997—22no—
15C2×#4326—21no—
16#66995—22no—
17#66995—22no—
18C2×#4325—21no—
19C2×Dic11⋊C4—22no—
20C2×C4×Dic11C2211yescharacteristic
21C2×#4318C2211yescharacteristic
22#66950—22no—
23#66939—22no—
24#66928—21no—
25#66922—21no—
26C11×#103—22no—
27#66889—22no—
28#66888—22no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11D412yes—
35C22×C4×C11—21no—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—21no—
38C22×Dic11—21no—
39C22×Dic11D412yes—
40#4339—21no—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22—21no—
52C2×Dic22D411yescharacteristic
53C11×M16—21no—
54C11×M16—21no—
55C2×C8×C11—21no—
56C11×C4⋊C4D412yes—
57C11×C22⋊C4—21no—
58C42×C11—21no—
59#4326—24no—
60#4325—24no—
61(C2×D11)⋊C4—24no—
62C4⋊Dic11—24no—
63Dic11⋊C4—28no—
64C4×Dic11—21no—
65C4×Dic11D412yes—
66#4318—21no—
67#4318D412yes—
68C2×C11⋊C8—21no—
69#2005—111nomaximal, Sylow
70C23×C11C2×D411yescharacteristic
71C22×D11—21no—
72Q8×C11—22no—
73Q8×C11—22no—
74Q8×C11—41no—
75Q8×C11—41no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C22⋊D11—41no—
87C22⋊D11—41no—
88C2×Dic11—24no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94D44—21no—
95D44—21no—
96C4×D11—41no—
97C4×D11—41no—
98Dic22—21no—
99Dic22—21no—
100Dic22—41no—
101Dic22—41no—
102Dic22—41no—
103Dic22—41no—
104C8×C11—41no—
105C11⋊C8—22no—
106C2×#137—111no—
107#536—111no—
108C2×C4⋊Q8—111no—
109C2×#104—111no—
110#419D1111yescharacteristic, complemented
111C2×#101—111no—
112#339—111no—
113C22×C11—22no—
114C22×C11#12011yescharacteristic
115C22×C11#12011yescharacteristic
116C22×C11#12111yescharacteristic
117C2×D11—41no—
118C2×D11—42no—
119C4×C11—42no—
120C4×C11—42no—
121C4×C11#12011yescharacteristic
122C4×C11#12111yescharacteristic
123C4×C11#12111yescharacteristic
124C4×C11#12711yescharacteristic
125Dic11—24no—
126Dic11—41no—
127Dic11—42no—
128C2×#41—111no—
129C22×Q8—111no—
130C22×Q8C2×D1111yescharacteristic
131#137—222no—
132#137—222no—
133C2×Q16—221no—
134C2×SD16—221no—
135C2×M16—111no—
136C2×M16C2×D1111yescharacteristic
137C4⋊Q8—221no—
138C4⋊Q8—222no—
139C4⋊Q8—222no—
140#124—221no—
141#123—222no—
142C22⋊Q8—222no—
143#117C2×D1111yescharacteristic
144C2×C4⋊C4—222no—
145C2×C42—111no—
146#104—222no—
147#103—22no—
148#101—222no—
149C2×C11—21no—
150C2×C11—21no—
151C2×C11#39211yescharacteristic
152C2×C11#45612yes—
153D11—81no—
154#41—221no—
155#41—221no—
156#41—221no—
157#41—221no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—111no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×Q8—221no—
169C2×Q8—221no—
170C2×Q8D4412yes—
171C2×D4—111no—
172C2×D4—221no—
173C22×C4—21no—
174C22×C4—112no—
175C22×C4—221no—
176C22×C4—221no—
177C22×C4C22×D1111yescharacteristic
178Q16—224no—
179SD16—224no—
180M16—21no—
181M16—21no—
182M16—112no—
183M16—221no—
184C2×C8—21no—
185C2×C8—221no—
186C4⋊C4—228no—
187C4⋊C4—224no—
188C4⋊C4C22⋊D1112yes—
189C22⋊C4—21no—
190C22⋊C4—224no—
191C42—21no—
192C42—112no—
193C42—221no—
194C11#200511yescharacteristic, complemented, Sylow
195C23—221no—
196C23D4×D1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—221no—
202Q8—221no—
203Q8—441no—
204Q8—441no—
205Q8—441no—
206Q8—441no—
207D4—221no—
208D4—221no—
209D4—441no—
210D4—441no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—224no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—221no—
221C2×C4—441no—
222C2×C4—441no—
223C2×C4C2×D4411yescharacteristic
224C2×C4#433911yescharacteristic
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4D4×D1111yescharacteristic
228C2×C4C2×C22⋊D1111yescharacteristic
229C8—41no—
230C8—222no—
231C22—22no—
232C22—442no—
233C22—441no—
234C22#6693511yescharacteristic
235C22#6693711yescharacteristic
236C22#6699011yescharacteristic
237C4—42no—
238C4—42no—
239C4—224no—
240C4—442no—
241C4—441no—
242C4#6693511yescharacteristic
243C4#6693711yescharacteristic
244C4#6698311yescharacteristic
245C4#6699311yescharacteristic
246C2—21no—
247C2—21no—
248C2—881no—
249C2#1062257311yescharacteristic
250C2#1062281812yes—
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#419C2
socleC22×C11#120
prime radicalC2×#4339C22
hypercenter#419D11
hypocenterC11#2005
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#66997C2semidirect
4. C11×#419C2semidirect
6. C2×#66888C2semidirect
7. #10622170C2semidirect
110. #419D11semidirect
194. C11#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669952
#106230572
C11×#4192
C2×#668892
C2×#668882
#106221702
#200511