Finite Group Databasebeta

← #13079688

Subgroups — #13079688

Order 1408.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#535C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3#10622852C212yesmaximal, complemented
4#10622831C212yesmaximal, complemented
5#10622689C211yesmaximal, characteristic, complemented
6#10622688C212yesmaximal, complemented
7#10622684C211yesmaximal, characteristic, complemented
8#10622673C211yesmaximal, characteristic, complemented
9#10622669C211yesmaximal, characteristic, complemented
10#10622667C212yesmaximal, complemented
11#10622613C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C11×#127C2211yescharacteristic
15C11×#127C2211yescharacteristic
16C11×#124C2211yescharacteristic
17C11×#124C2211yescharacteristic
18C11×#121—22no—
19C11×#120—22no—
20C11×#117C2211yescharacteristic
21C2×#4326C2212yescomplemented
22C2×#4324C2212yes—
23C2×#4324C2212yes—
24C2×#4324C2212yescomplemented
25#66977C2212yes—
26#66942—22no—
27#66932—22no—
28#66923C2211yescharacteristic, complemented
29#66922C2211yescharacteristic, complemented
30C4×Dic22C2212yescomplemented
31#66899C2212yescomplemented
32#66896C2212yes—
33#66896C2212yes—
34#66896C2212yescomplemented
35C22⋊(C11⋊C8)C2212yes—
36C4⋊(C11⋊C8)C2212yescomplemented
37#66867C2211yescharacteristic, complemented
38C4×C11⋊C8C2211yescharacteristic, complemented
39C24×C11—21no—
40C11×#41—42no—
41C2×Q8×C11C2311yescharacteristic
42C2×D4×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—42no—
47C2×D4×C11C2311yescharacteristic
48C2×D4×C11C2311yescharacteristic
49C2×D4×C11C2311yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11C2311yescharacteristic
52C2×Dic22C2312yes—
53C11×C4⋊C4D412yes—
54C11×C22⋊C4—22no—
55C11×C22⋊C4—22no—
56C11×C22⋊C4D412yes—
57C42×C11C2311yescharacteristic
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60#4326—42no—
61#4324—42no—
62#4324—42no—
63#4324—42no—
64C4⋊Dic11—22no—
65C4⋊Dic11C2312yes—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C2×C11⋊C8C2312yes—
71C2×C11⋊C8C2312yes—
72#3222—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—42no—
77C23×C11—82no—
78C23×C11C2×D411yescharacteristic
79Q8×C11—22no—
80D4×C11—22no—
81D4×C11—22no—
82D4×C11—22no—
83D4×C11—42no—
84D4×C11—42no—
85D4×C11—82no—
86D4×C11—82no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D412yes—
93C2×C4×C11C2411yescharacteristic
94C2×Dic11—22no—
95C2×Dic11—22no—
96Dic22—22no—
97Dic22—22no—
98C11⋊C8—22no—
99C11⋊C8—22no—
100#541—111no—
101#535D1111yescharacteristic
102#497—111no—
103#492—111no—
104#490—111no—
105#488—111no—
106#464—112no—
107#460—112no—
108#452—112no—
109#450—112no—
110#433—111no—
111C22×C11—21no—
112C22×C11—22no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—84no—
120C22×C11C22×D411yescharacteristic
121C4×C11—21no—
122C4×C11—22no—
123C4×C11—22no—
124C4×C11—41no—
125C4×C11H(5,𝔽2)12yes—
126Dic11—42no—
127Dic11—42no—
128C2×#41C2×D1111yescharacteristic
129C22×D4C2×D1111yescharacteristic
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16—112no—
134C4⋊Q8—111no—
135#127C2×D1111yescharacteristic
136#127C2×D1111yescharacteristic
137#126—222no—
138#125—111no—
139#125—222no—
140#124C2×D1111yescharacteristic
141#124C2×D1111yescharacteristic
142C22⋊Q8—112no—
143#121—22no—
144#120—22no—
145C4×Q8—112no—
146#117C2×D1111yescharacteristic
147C4⋊C8—112no—
148#103—112no—
149#102—112no—
150#102—112no—
151#102—112no—
152C22⋊C8—112no—
153#97—111no—
154C4×C8—111no—
155C2×C11—41no—
156C2×C11—81no—
157C2×C11—81no—
158C2×C11—81no—
159C2×C11#53511yescharacteristic
160C2×C11#57712yes—
161C24—21no—
162#41—42no—
163C2×Q8—112no—
164C2×Q8C22×D1111yescharacteristic
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—42no—
170C2×D4C22×D1111yescharacteristic
171C2×D4C22×D1111yescharacteristic
172C2×D4C22×D1111yescharacteristic
173C22×C4—21no—
174C22×C4C22×D1111yescharacteristic
175Q16—442no—
176SD16—442no—
177SD16—442no—
178SD16—442no—
179C2×C8—112no—
180C2×C8—112no—
181C4⋊C4—112no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4C22⋊D1112yes—
187C22⋊C4—22no—
188C22⋊C4—22no—
189C22⋊C4—222no—
190C22⋊C4C22⋊D1112yes—
191C42—222no—
192C42C22×D1111yescharacteristic
193C42C22×D1111yescharacteristic
194C11#322211yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—82no—
200C23C2×C22⋊D1111yescharacteristic
201Q8—22no—
202Q8—222no—
203Q8—222no—
204D4—22no—
205D4—22no—
206D4—22no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4C2×C22⋊D1112yes—
217C2×C4C2×C22⋊D1112yes—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—222no—
221C8—222no—
222C22—21no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—84no—
231C22C22×C22⋊D1111yescharacteristic
232C4—21no—
233C4—22no—
234C4—22no—
235C4—41no—
236C4—442no—
237C4—442no—
238C4#6703712yes—
239C2—41no—
240C2—81no—
241C2—81no—
242C2—81no—
243C2#1062333611yescharacteristic
244C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
3. #10622852C2semidirect
4. #10622831C2semidirect
5. #10622689C2semidirect
6. #10622688C2semidirect
7. #10622684C2semidirect
8. #10622673C2semidirect
9. #10622669C2semidirect
10. #10622667C2semidirect
11. #10622613C2semidirect
21. C2×#4326C22semidirect
24. C2×#4324C22semidirect
28. #66923C22semidirect
29. #66922C22semidirect
30. C4×Dic22C22semidirect
31. #66899C22semidirect
34. #66896C22semidirect
36. C4⋊(C11⋊C8)C22semidirect
37. #66867C22semidirect
38. C4×C11⋊C8C22semidirect
194. C11#3222semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106230492
#106228522
#106228312
#106226892
#106226882
#106226842
#106226732
#106226692
#106226672
#106226132
#322211