Finite Group Databasebeta

← #13080554

Subgroups — #13080554

Order 1408.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623263C211yesmaximal, characteristic, complemented
2#10623249C211yesmaximal, characteristic
3C11×#486C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622688C211yesmaximal, characteristic, complemented
6#10622397C212yesmaximal, complemented
7#10622396C212yesmaximal, complemented
8#10622391C212yesmaximal, complemented
9#10622385C212yesmaximal, complemented
10C4×Dic44C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic, complemented
12C2×#4341C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#127C2211yescharacteristic
15#67000—21no—
16Q8×Dic11—21no—
17#66993—21no—
18#66992—22no—
19#66991C2212yes—
20D4×Dic11—21no—
21C2×#4324C2212yes—
22C2×Dic44C2211yescharacteristic
23C2×C8×D11C2212yes—
24#66951—22no—
25#66950C2212yes—
26#66945C2212yes—
27C4×D44C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30C11×#102C2212yes—
31C11×#102C2212yes—
32C4×C8×C11C2211yescharacteristic
33#66896C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66882C2211yescharacteristic
36#66880C2211yescharacteristic
37#66880C2211yescharacteristic
38#66874C2212yes—
39#66872C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11C2312yes—
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C22×Dic11—22no—
48#4341—24no—
49#4341—42no—
50C2×D44D411yescharacteristic
51C2×C4×D11C2312yes—
52C2×Dic22C2311yescharacteristic
53C2×Dic22C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C2×C8×C11C2311yescharacteristic
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2312yes—
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60#4324—42no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4D412yes—
64C4⋊Dic11—22no—
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—21no—
69Dic11⋊C4—21no—
70C4×Dic11—22no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73C2×C11⋊C8C2312yes—
74Dic44—22no—
75C8×D11—42no—
76#3304—111nomaximal, Sylow
77C23×C11—22no—
78C22×D11C2×D412yes—
79Q8×C11—42no—
80D4×C11—22no—
81D4×C11—22no—
82D4×C11—42no—
83D4×C11—81no—
84C2×C4×C11—22no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C22⋊D11—44no—
89C22⋊D11—82no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—44no—
95C2×Dic11C2×D412yes—
96D44—22no—
97C4×D11—22no—
98C4×D11—22no—
99Dic22—21no—
100Dic22—21no—
101Dic22—21no—
102Dic22#4112yes—
103C8×C11—21no—
104C8×C11—21no—
105C11⋊C8—22no—
106#556—111no—
107#550—111no—
108#486D1111yescharacteristic, complemented
109#482—112no—
110#475—111no—
111#465—112no—
112#460—111no—
113#452—112no—
114C4×Q16—111no—
115C8×D4—111no—
116#416—112no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—42no—
120C22×C11C22×D411yescharacteristic
121C2×D11—22no—
122C2×D11—22no—
123C2×D11—22no—
124C4×C11—21no—
125C4×C11—42no—
126C4×C11#13512yes—
127C4×C11C2×#4111yescharacteristic
128C4×C11H(5,𝔽2)11yescharacteristic
129Dic11—22no—
130Dic11—22no—
131Dic11—41no—
132Dic11—41no—
133Dic11—41no—
134C2×#41—112no—
135C2×Q16—111no—
136C2×SD16—112no—
137C22×C8—112no—
138C4⋊Q8C2×D1111yescharacteristic
139#127—221no—
140#127C2×D1111yescharacteristic
141#126—222no—
142#124—221no—
143C22⋊Q8—112no—
144#121—112no—
145#121—222no—
146C4×Q8—111no—
147C4×Q8—111no—
148C4×Q8—221no—
149C4×D4—111no—
150C4×D4—221no—
151#117—112no—
152#107—111no—
153#106—112no—
154C4⋊C8—111no—
155#103—111no—
156#103—111no—
157#103—112no—
158#102—112no—
159#102C2×D1112yes—
160#102C2×D1112yes—
161C22⋊C8—112no—
162C4×C8C2×D1111yescharacteristic
163C2×C11—82no—
164C2×C11#54611yescharacteristic
165C2×C11C2×#13511yescharacteristic
166C2×C11#57711yescharacteristic
167D11—42no—
168#41—224no—
169#41—442no—
170C2×Q8—21no—
171C2×Q8—111no—
172C2×Q8—111no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—111no—
176C2×D4—222no—
177C2×D4—222no—
178C2×D4C22×D1112yes—
179C22×C4—112no—
180C22×C4—222no—
181Q16—222no—
182SD16—442no—
183C2×C8—112no—
184C2×C8—442no—
185C2×C8C22×D1111yescharacteristic
186C2×C8C22×D1111yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—111no—
190C4⋊C4—111no—
191C4⋊C4—222no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4C22×D1112yes—
195C22⋊C4—112no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C42—222no—
200C42—221no—
201C42—221no—
202C42C22×D1111yescharacteristic
203C11#330411yescharacteristic, complemented, Sylow
204C23—22no—
205C23—112no—
206Q8—42no—
207Q8—112no—
208Q8—221no—
209Q8—221no—
210Q8—221no—
211D4—22no—
212D4—22no—
213D4—42no—
214D4—81no—
215D4—222no—
216D4—444no—
217D4—882no—
218C2×C4—22no—
219C2×C4—112no—
220C2×C4—221no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—444no—
227C2×C4D4×D1111yescharacteristic
228C2×C4D4×D1111yescharacteristic
229C2×C4C23×D1111yescharacteristic
230C8—21no—
231C8—21no—
232C8—222no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—222no—
237C22—222no—
238C22—222no—
239C22C2×D4×D1111yescharacteristic
240C4—21no—
241C4—42no—
242C4—222no—
243C4—222no—
244C4—441no—
245C4—441no—
246C4—441no—
247C4#6696512yes—
248C4#41×D1111yescharacteristic
249C4#6704211yescharacteristic
250C2—82no—
251C2—442no—
252C2#1062320711yescharacteristic
253C2C2×#6696511yescharacteristic
254C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
prime radical#10623249C2
hypercenter#486D11
hypocenterC11#3304
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623263C2semidirect
3. C11×#486C2semidirect
4. #10622707C2semidirect
5. #10622688C2semidirect
6. #10622397C2semidirect
7. #10622396C2semidirect
8. #10622391C2semidirect
9. #10622385C2semidirect
10. C4×Dic44C2semidirect
11. C8×D44C2semidirect
108. #486D11semidirect
203. C11#3304semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106232492
C11×#4862
#106227072
#106226882
#106223972
#106223962
#106223912
#106223852
C4×Dic442
C8×D442
#330411