Finite Group Databasebeta

← #14674122

Subgroups — #14674122

Order 2816.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#13078989C211yesmaximal, characteristic
2D11×#353C212yesmaximal
3#13066787C211yesmaximal, characteristic, complemented
4#13066786C212yesmaximal, complemented
5C11×#1412C211yesmaximal, characteristic, complemented
6D11×#127C2211yescharacteristic
7#10623219C411yescharacteristic, complemented
8C11×#490C2211yescharacteristic
9#10622684C2211yescharacteristic
10#10622680C411yescharacteristic, complemented
11#10622383—22no—
12#10622373—22no—
13D11×#99—22no—
14#10622326C411yescharacteristic, complemented
15#10622320C411yescharacteristic, complemented
16C11×#353C2212yes—
17#10622183C2212yes—
18#10622112—22no—
19C2×D4×D11—41no—
20C2×D4×D11D412yes—
21C11×#127C2311yescharacteristic
22C11×#125C2×C411yescharacteristic, complemented
23#66993—41no—
24#66993D412yes—
25C2×#4313—21no—
26#66949—41no—
27#66945—21no—
28#66941—21no—
29#66940—41no—
30C22⋊C4×D11—42no—
31#66927C2×C411yescharacteristic
32C42×D11C2×C411yescharacteristic
33#66923C2×C411yescharacteristic, complemented
34C11×#102—22no—
35C11×#99—22no—
36C11×#97C2×C411yescharacteristic, complemented
37#66898—22no—
38#66896—22no—
39#66885—22no—
40C8×Dic11—21no—
41#66873—22no—
42#66870—42no—
43#66867C2×C411yescharacteristic, complemented
44#13595—111nomaximal, Sylow
45C23×D11—22no—
46C2×D4×C11—41no—
47C2×D4×C11C2×D412yes—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—42no—
50D4×D11—42no—
51D4×D11—42no—
52D4×D11—84no—
53C2×D44—41no—
54C2×D44C22⋊C412yes—
55C2×C4×D11—21no—
56C2×C4×D11—82no—
57C2×C4×D11C22⋊C411yescharacteristic
58C2×Dic22—41no—
59C2×C8×C11—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—41no—
62C11×C22⋊C4—42no—
63C42×C11C22×C411yescharacteristic
64C22⋊Dic11—42no—
65(C2×D11)⋊C4—41no—
66(C2×D11)⋊C4—82no—
67C4⋊Dic11—21no—
68Dic11⋊C4—41no—
69Dic11⋊C4—41no—
70C4×Dic11—21no—
71C4×Dic11—41no—
72C4×Dic11C22⋊C411yescharacteristic
73C2×C11⋊C8—21no—
74#4313—42no—
75#3138—111no—
76C2×#353—112no—
77#1412—111no—
78#1412—112no—
79#1412D1111yescharacteristic, complemented
80C23×C11—22no—
81C22×D11—22no—
82C22×D11—42no—
83C22×D11—42no—
84C22×D11—84no—
85C22×D11#9911yescharacteristic
86D4×C11—42no—
87D4×C11—82no—
88C2×C4×C11—21no—
89C2×C4×C11—41no—
90C2×C4×C11—82no—
91C2×C4×C11C2×C22⋊C411yescharacteristic
92C22⋊D11—82no—
93C22⋊D11—84no—
94C2×Dic11—21no—
95C2×Dic11—41no—
96C2×Dic11—82no—
97C2×Dic11#9911yescharacteristic
98D44—42no—
99D44—82no—
100C4×D11—22no—
101C4×D11—42no—
102C4×D11—164no—
103Dic22—82no—
104C8×C11—41no—
105C11⋊C8—41no—
106#533—111no—
107C2×#127—111no—
108#490—111no—
109#490—111no—
110#490—111no—
111#490C2×D1111yescharacteristic
112#486—222no—
113#418—222no—
114C2×#99—222no—
115C4×M16—111no—
116#353—112no—
117#353—222no—
118#353C2×D1112yes—
119C22×C11—42no—
120C22×C11—82no—
121C22×C11C2×#9911yescharacteristic
122C2×D11—41no—
123C2×D11—42no—
124C2×D11—84no—
125C2×D11—82no—
126C2×D11—162no—
127C2×D11#35412yes—
128C4×C11—21no—
129C4×C11—41no—
130C4×C11—81no—
131C4×C11—162no—
132Dic11—22no—
133Dic11—21no—
134Dic11—81no—
135Dic11—162no—
136C22×D4—112no—
137C22×D4—441no—
138C2×M16—221no—
139C4⋊Q8—221no—
140#127—112no—
141#127—111no—
142#127—441no—
143#127C22×D1111yescharacteristic
144#125—111no—
145#125C4×D1111yescharacteristic, complemented
146C22⋊Q8—441no—
147C4×Q8—441no—
148#117—221no—
149C2×C22⋊C4—442no—
150C2×C42—111no—
151#102—22no—
152#102—222no—
153#102—222no—
154#102—222no—
155#99—22no—
156#99—222no—
157#99—442no—
158#97—111no—
159#97C4×D1111yescharacteristic, complemented
160C4×C8—221no—
161C2×C11—21no—
162C2×C11—82no—
163C2×C11C2×#35411yescharacteristic
164D11—22no—
165D11—82no—
166C24—222no—
167C2×Q8—441no—
168C2×D4—41no—
169C2×D4—112no—
170C2×D4—222no—
171C2×D4—441no—
172C2×D4—442no—
173C2×D4—442no—
174C2×D4—442no—
175C2×D4—884no—
176C2×D4D4×D1112yes—
177C22×C4—111no—
178C22×C4—221no—
179C22×C4—882no—
180M16—442no—
181C2×C8—21no—
182C2×C8—221no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—221no—
186C4⋊C4—441no—
187C4⋊C4—441no—
188C22⋊C4—42no—
189C22⋊C4—441no—
190C22⋊C4—442no—
191C22⋊C4—882no—
192C42—111no—
193C42—221no—
194C42—441no—
195C42C2×C4×D1111yescharacteristic
196C11#1359511yescharacteristic, complemented, Sylow
197C23—22no—
198C23—111no—
199C23—222no—
200C23—442no—
201C23—442no—
202C23—884no—
203Q8—882no—
204D4—42no—
205D4—82no—
206D4—442no—
207D4—882no—
208D4—882no—
209D4—884no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—82no—
213C2×C4—111no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—442no—
217C2×C4—441no—
218C2×C4—882no—
219C2×C4—1764no—
220C2×C4C22⋊C4×D1111yescharacteristic
221C8—41no—
222C8—441no—
223C22—42no—
224C22—82no—
225C22—112no—
226C22—441no—
227C22—442no—
228C22—882no—
229C22—884no—
230C22—1762no—
231C22D11×#9911yescharacteristic
232C4—21no—
233C4—41no—
234C4—81no—
235C4—162no—
236C4—222no—
237C4—221no—
238C4—881no—
239C4—1762no—
240C2—21no—
241C2—82no—
242C2—222no—
243C2—882no—
244C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#1412C2
socleC2×C11C2×#354
prime radicalD11×#127C22
cosocleC11×#127C23
hypercenter#1412D11
hypocenterC11#13595
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #13066787C2semidirect
4. #13066786C2semidirect
5. C11×#1412C2semidirect
7. #10623219C4semidirect
10. #10622680C4semidirect
14. #10622326C4semidirect
15. #10622320C4semidirect
22. C11×#125C2×C4semidirect
33. #66923C2×C4semidirect
36. C11×#97C2×C4semidirect
43. #66867C2×C4semidirect
79. #1412D11semidirect
145. #125C4×D11semidirect
159. #97C4×D11semidirect
196. C11#13595semidirect

Maximal subgroups

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

subgroupindex
#130789892
D11×#3532
#130667872
#130667862
C11×#14122
#1359511