Finite Group Databasebeta

← D11×#1412 #14674116

Subgroups — D11×#1412 #14674116

Order 2816.

390 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 61 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
1D11×#490C211yesmaximal, characteristic
2D11×#353C212yesmaximal
3#13066787C211yesmaximal, characteristic, complemented
4#13066786C212yesmaximal, complemented
5C11×#1412C211yesmaximal, characteristic, complemented
6D11×#127C2211yescharacteristic
7D11×#125C411yescharacteristic, complemented
8C11×#490C2211yescharacteristic
9#10622684C2211yescharacteristic
10#10622680C411yescharacteristic, complemented
11D11×#102—22no—
12#10622377—22no—
13D11×#99—22no—
14#10622326C411yescharacteristic, complemented
15D11×#97C411yescharacteristic, 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×C8×D11—21no—
26C4⋊C4×D11—21no—
27C4⋊C4×D11—41no—
28#66943—21no—
29#66942—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—
40#66879—21no—
41#66873—22no—
42#66870—42no—
43#66867C2×C411yescharacteristic, complemented
44C2×#1412—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—41no—
57C2×C4×D11—82no—
58C2×C4×D11C22⋊C411yescharacteristic
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—82no—
66C4⋊Dic11—21no—
67C4⋊Dic11—41no—
68Dic11⋊C4—41no—
69Dic11⋊C4—41no—
70Dic11⋊C4—41no—
71C4×Dic11—21no—
72C4×Dic11C22⋊C411yescharacteristic
73C2×C11⋊C8—21no—
74C8×D11—41no—
75C8×D11—41no—
76C2×#490—111no—
77C2×#353—112no—
78#1412—111no—
79#1412—112no—
80#1412D1111yescharacteristic, direct product factor
81C23×C11—22no—
82C22×D11—22no—
83C22×D11—42no—
84C22×D11—42no—
85C22×D11—84no—
86C22×D11#9911yescharacteristic
87D4×C11—42no—
88D4×C11—82no—
89C2×C4×C11—21no—
90C2×C4×C11—41no—
91C2×C4×C11—82no—
92C2×C4×C11C2×C22⋊C411yescharacteristic
93C22⋊D11—82no—
94C22⋊D11—84no—
95C2×Dic11—21no—
96C2×Dic11—41no—
97C2×Dic11—82no—
98C2×Dic11#9911yescharacteristic
99D44—42no—
100D44—82no—
101C4×D11—21no—
102C4×D11—21no—
103C4×D11—42no—
104C4×D11—82no—
105C4×D11—164no—
106C8×C11—41no—
107C11⋊C8—41no—
108C2×#127—111no—
109C2×#125—111no—
110#490—111no—
111#490—111no—
112#490—111no—
113#490—222no—
114#490C2×D1111yescharacteristic
115C2×#102—222no—
116C2×#99—222no—
117C2×#97—111no—
118#353—112no—
119#353—222no—
120#353C2×D1112yes—
121C22×C11—42no—
122C22×C11—82no—
123C22×C11C2×#9911yescharacteristic
124C2×D11—22no—
125C2×D11—42no—
126C2×D11—84no—
127C2×D11—82no—
128C2×D11—162no—
129C2×D11#35411yescharacteristic
130C2×D11#35411yescharacteristic
131C4×C11—21no—
132C4×C11—41no—
133C4×C11—81no—
134C4×C11—162no—
135Dic11—21no—
136Dic11—41no—
137Dic11—81no—
138Dic11—162no—
139C22×D4—112no—
140C22×D4—441no—
141C22×C8—221no—
142#127—112no—
143#127—111no—
144#127—441no—
145#127C22×D1111yescharacteristic
146#125—111no—
147#125—221no—
148#125—441no—
149#125C4×D1111yescharacteristic, complemented
150C2×C4⋊C4—221no—
151C2×C4⋊C4—441no—
152C2×C22⋊C4—442no—
153C2×C42—111no—
154#102—22no—
155#102—222no—
156#102—222no—
157#102—222no—
158#99—22no—
159#99—222no—
160#99—442no—
161#97—111no—
162#97—221no—
163#97C4×D1111yescharacteristic, complemented
164C2×C11—21no—
165C2×C11—82no—
166C2×C11C2×#35411yescharacteristic
167D11—21no—
168D11—82no—
169D11#141212yesdirect product factor
170C24—222no—
171C2×D4—41no—
172C2×D4—112no—
173C2×D4—222no—
174C2×D4—441no—
175C2×D4—442no—
176C2×D4—442no—
177C2×D4—442no—
178C2×D4—884no—
179C2×D4D4×D1112yes—
180C22×C4—111no—
181C22×C4—221no—
182C22×C4—441no—
183C22×C4—882no—
184C2×C8—21no—
185C2×C8—221no—
186C2×C8—441no—
187C2×C8—441no—
188C4⋊C4—21no—
189C4⋊C4—41no—
190C4⋊C4—221no—
191C4⋊C4—441no—
192C4⋊C4—441no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C22⋊C4—42no—
196C22⋊C4—442no—
197C22⋊C4—882no—
198C42—111no—
199C42—221no—
200C42C2×C4×D1111yescharacteristic
201C11C2×#141211yescharacteristic, complemented, Sylow
202C23—22no—
203C23—111no—
204C23—222no—
205C23—442no—
206C23—442no—
207C23—884no—
208D4—42no—
209D4—82no—
210D4—442no—
211D4—882no—
212D4—882no—
213D4—884no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—82no—
217C2×C4—111no—
218C2×C4—221no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—442no—
222C2×C4—441no—
223C2×C4—882no—
224C2×C4—882no—
225C2×C4—1764no—
226C2×C4C22⋊C4×D1111yescharacteristic
227C8—41no—
228C8—441no—
229C22—42no—
230C22—82no—
231C22—111no—
232C22—111no—
233C22—222no—
234C22—442no—
235C22—882no—
236C22—884no—
237C22—1762no—
238C22D11×#9911yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—162no—
243C4—221no—
244C4—441no—
245C4—881no—
246C4—1762no—
247C2—21no—
248C2—82no—
249C2—112no—
250C2—221no—
251C2—882no—
252C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#1412C2
socleC2×C11C2×#354
prime radicalD11×#127C22
cosocleC11×#127C23
hypercenter#1412D11
hypocenterC11C2×#1412
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. D11×#125C4semidirect
10. #10622680C4semidirect
14. #10622326C4semidirect
15. D11×#97C4semidirect
22. C11×#125C2×C4semidirect
33. #66923C2×C4semidirect
36. C11×#97C2×C4semidirect
43. #66867C2×C4semidirect
80. #1412D11direct (N × H)
149. #125C4×D11semidirect
163. #97C4×D11semidirect
169. D11#1412direct (N × H)
201. C11C2×#1412semidirect

Maximal subgroups

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

subgroupindex
D11×#4902
D11×#3532
#130667872
#130667862
C11×#14122
C2×#141211