Finite Group Databasebeta

← #13081328

Subgroups — #13081328

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#10623261C211yesmaximal, characteristic, complemented
2#10623249C211yesmaximal, characteristic, complemented
3C11×#486C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622685C211yesmaximal, characteristic, complemented
6#10622399C212yesmaximal, complemented
7#10622398C212yesmaximal, complemented
8#10622379C212yesmaximal, complemented
9#10622377C212yesmaximal, complemented
10C4×D88C211yesmaximal, characteristic, complemented
11#10622292C211yesmaximal, characteristic, complemented
12C2×#4341—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#127C2211yescharacteristic
15#66999—22no—
16#66993C2212yes—
17#66992—22no—
18#66991—21no—
19D4×Dic11C2212yes—
20C2×#4323C2212yes—
21C2×D88C2211yescharacteristic
22#66950—21no—
23#66946C2212yes—
24C4⋊C4×D11—21no—
25#66943C2212yes—
26C4×D44C2211yescharacteristic
27C4×D44C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#102C2212yes—
30C11×#102C2212yes—
31C4×C8×C11C2211yescharacteristic
32#66896C2212yes—
33#66885C2211yescharacteristic
34#66885C2211yescharacteristic
35#66882C2211yescharacteristic
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66873C2212yes—
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—44no—
49C2×D44C2311yescharacteristic
50C2×D44C2311yescharacteristic
51C2×C4×D11—22no—
52C2×C4×D11—21no—
53C2×C4×D11—21no—
54C2×Dic22D411yescharacteristic
55C2×C8×C11C2311yescharacteristic
56C2×C8×C11C2311yescharacteristic
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C42×C11C2311yescharacteristic
60C22⋊Dic11—22no—
61#4323—24no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—21no—
64(C2×D11)⋊C4—21no—
65C4⋊Dic11—22no—
66C4⋊Dic11D411yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4D412yes—
71C4×Dic11C2312yes—
72C2×C11⋊C8C2312yes—
73D88—22no—
74#3366—111nomaximal, Sylow
75C23×C11—22no—
76C22×D11—21no—
77C22×D11—21no—
78Q8×C11—81no—
79D4×C11—22no—
80D4×C11—22no—
81D4×C11—42no—
82D4×C11—81no—
83C2×C4×C11—22no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2411yescharacteristic
87C22⋊D11—44no—
88C22⋊D11—82no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—44no—
92C2×Dic11C2×D412yes—
93C2×Dic11C2×D412yes—
94D44—21no—
95D44—21no—
96D44—21no—
97D44#4112yescomplemented
98C4×D11—42no—
99C4×D11—42no—
100C4×D11—82no—
101Dic22—22no—
102C8×C11—21no—
103C8×C11—21no—
104C11⋊C8—22no—
105#554—111no—
106#550—111no—
107#490—112no—
108#486D1111yescharacteristic, complemented
109#478—112no—
110#476—111no—
111#459—111no—
112#459—112no—
113#446—111no—
114#442—112no—
115C4×D8—111no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11C22×D411yescharacteristic
120C2×D11—22no—
121C2×D11—41no—
122C2×D11—41no—
123C2×D11—41no—
124C2×D11—41no—
125C2×D11—41no—
126C4×C11—21no—
127C4×C11—42no—
128C4×C11AGL(1,ℤ/8)12yes—
129C4×C11C2×#4111yescharacteristic
130C4×C112−1+411yescharacteristic
131Dic11—22no—
132Dic11—22no—
133Dic11—41no—
134Dic11—41no—
135C2×#41—221no—
136C2×D8—112no—
137C2×D8—111no—
138C4⋊Q8C2×D1111yescharacteristic
139#127—112no—
140#127C2×D1111yescharacteristic
141#125—112no—
142C22⋊Q8—221no—
143C22⋊Q8—222no—
144#121—221no—
145#121—222no—
146C4×Q8—111no—
147C4×D4—112no—
148C4×D4—112no—
149C4×D4—111no—
150C4×D4—111no—
151C2×C4⋊C4—221no—
152#107—111no—
153#106—112no—
154C4⋊C8—112no—
155C4⋊C8—111no—
156#102—112no—
157#102—111no—
158#102—111no—
159#102—112no—
160#102C2×D1112yes—
161#102C2×D1112yes—
162#97—112no—
163C4×C8C2×D1111yescharacteristic
164C2×C11—82no—
165C2×C11#54811yescharacteristic
166C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C11#57611yescharacteristic
168D11—42no—
169D11—81no—
170#41—444no—
171C2×Q8—21no—
172C2×Q8—111no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—111no—
176C2×D4—111no—
177C2×D4—222no—
178C2×D4—222no—
179C2×D4C22×D1112yes—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4—221no—
183C22×C4—221no—
184D8—222no—
185D8—224no—
186C2×C8—112no—
187C2×C8C22×D1111yescharacteristic
188C2×C8C22×D1111yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—111no—
191C4⋊C4—112no—
192C4⋊C4—111no—
193C4⋊C4—111no—
194C4⋊C4—222no—
195C4⋊C4—222no—
196C4⋊C4C22×D1112yes—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C22⋊C4—221no—
200C22⋊C4—221no—
201C42—112no—
202C42C22×D1111yescharacteristic
203C11#336611yescharacteristic, complemented, Sylow
204C23—22no—
205C23—221no—
206C23—221no—
207Q8—81no—
208Q8—222no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—112no—
214D4—221no—
215D4—221no—
216D4—221no—
217D4—444no—
218D4—882no—
219C2×C4—22no—
220C2×C4—112no—
221C2×C4—112no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—444no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—882no—
228C2×C4D4×D1111yescharacteristic
229C2×C4D4×D1111yescharacteristic
230C2×C4C23×D1111yescharacteristic
231C8—21no—
232C8—21no—
233C8—222no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—222no—
238C22—441no—
239C22—441no—
240C22—441no—
241C22—441no—
242C22—441no—
243C22C2×D4×D1111yescharacteristic
244C4—21no—
245C4—42no—
246C4—222no—
247C4—222no—
248C4—441no—
249C4—441no—
250C4#6696712yes—
251C4#41×D1111yescharacteristic
252C4#6704311yescharacteristic
253C2—82no—
254C2—442no—
255C2—881no—
256C2#1062320811yescharacteristic
257C2#1062328811yescharacteristic
258C2C2×#6696711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
hypercenter#486D11
hypocenterC11#3366
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. #10623261C2semidirect
2. #10623249C2semidirect
3. C11×#486C2semidirect
4. #10622697C2semidirect
5. #10622685C2semidirect
6. #10622399C2semidirect
7. #10622398C2semidirect
8. #10622379C2semidirect
9. #10622377C2semidirect
10. C4×D88C2semidirect
11. #10622292C2semidirect
97. D44#41semidirect
108. #486D11semidirect
203. C11#3366semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106232492
C11×#4862
#106226972
#106226852
#106223992
#106223982
#106223792
#106223772
C4×D882
#106222922
#336611