Finite Group Databasebeta

← D11×#2029 #14781167

Subgroups — D11×#2029 #14781167

Order 2816.

2818 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 217 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×#543C211yesmaximal, characteristic, complemented
2D11×#379C213yesmaximal
3#13069781C213yesmaximal, complemented
4#13069780C213yesmaximal, complemented
5#13069779C211yesmaximal, characteristic, complemented
6D11×#342C213yesmaximal, complemented
7C11×#2029C211yesmaximal, characteristic, complemented
8C25×D11C2211yescharacteristic
9C11×#543C2211yescharacteristic, complemented
10#10623165—26no—
11D11×C22⋊Q8—26no—
12C2×C22⋊C4×D11—26no—
13C2×C22⋊C4×D11C2213yes—
14C2×C22⋊C4×D11C2213yes—
15#10623014C2213yescomplemented
16C11×#379C2213yes—
17#10622860C2213yes—
18#10622568—26no—
19#10622568C2213yes—
20#10622568C2213yes—
21C11×#342C2213yescomplemented
22#10622165C2216yescomplemented
23#10622164C2213yescomplemented
24C25×C11C2311yescharacteristic
25C24×D11—23no—
26C24×D11—23no—
27C24×D11—26no—
28C24×D11—48no—
29C24×D11Q814yescomplemented
30C24×D11C2311yescharacteristic
31C24×D11C2311yescharacteristic
32C2×Q8×D11—22no—
33C22×C4×D11—23no—
34C22×C4×D11D416yes—
35C11×C22⋊Q8—26no—
36C2×C11×C22⋊C4—26no—
37C2×C11×C22⋊C4C2313yes—
38C2×C11×C22⋊C4C2313yes—
39C2×C22⋊Dic11—26no—
40C2×C22⋊Dic11C2313yes—
41C2×C22⋊Dic11C2313yes—
42#66999—26no—
43C2×(C2×D11)⋊C4—23no—
44C2×(C2×D11)⋊C4—26no—
45C2×(C2×D11)⋊C4—26no—
46C2×(C2×D11)⋊C4D416yes—
47#66977—26no—
48#66950—26no—
49#66949—212no—
50C4⋊C4×D11—26no—
51C22⋊C4×D11—26no—
52C22⋊C4×D11—26no—
53C22⋊C4×D11—212no—
54C22⋊C4×D11—424no—
55#66931—212no—
56C2×#2029—111nomaximal, Sylow
57C24×C11—23no—
58C24×C11—23no—
59C24×C11—44no—
60C24×C11C2×Q812yescomplemented
61C24×C11C2411yescharacteristic
62C23×D11—224no—
63C23×D11—23no—
64C23×D11—212no—
65C23×D11—23no—
66C23×D11—212no—
67C23×D11—416no—
68C23×D11—44no—
69C23×D11—44no—
70C23×D11—412no—
71C23×D11—412no—
72C23×D11—448no—
73C23×D11—412no—
74C23×D11—43no—
75C23×D11—41no—
76C23×D11—46no—
77C23×D11—46no—
78C23×D11C2×D413yes—
79C23×D11C2×D413yes—
80C23×D11C2×Q812yes—
81C23×D11C2×Q812yescomplemented
82C23×D11#4116yes—
83C2×Q8×C11—22no—
84C22×C4×C11—23no—
85C22×C4×C11C2×D416yes—
86C22×Dic11—23no—
87C22×Dic11C2×D416yes—
88Q8×D11—84no—
89C2×C4×D11—26no—
90C2×C4×D11—26no—
91C2×C4×D11—412no—
92C2×C4×D11—412no—
93C2×C4×D11—46no—
94C2×Dic22—26no—
95C11×C4⋊C4—26no—
96C11×C22⋊C4—26no—
97C11×C22⋊C4—26no—
98C11×C22⋊C4—412no—
99C22⋊Dic11—26no—
100C22⋊Dic11—26no—
101C22⋊Dic11—412no—
102(C2×D11)⋊C4—212no—
103(C2×D11)⋊C4—412no—
104(C2×D11)⋊C4—412no—
105(C2×D11)⋊C4—46no—
106C4⋊Dic11—26no—
107Dic11⋊C4—212no—
108C2×#543—111no—
109C2×#379—113no—
110#2029—113no—
111#2029—113no—
112#2029—111no—
113#2029D1111yescharacteristic, direct product factor
114C2×#342—113no—
115C23×C11—212no—
116C23×C11—26no—
117C23×C11—44no—
118C23×C11—42no—
119C23×C11—46no—
120C23×C11—412no—
121C23×C11—41no—
122C23×C11—43no—
123C23×C11C22×D413yes—
124C23×C11C22×Q811yescharacteristic
125C23×C11C2×#4113yes—
126C22×D11—212no—
127C22×D11—212no—
128C22×D11—248no—
129C22×D11—26no—
130C22×D11—44no—
131C22×D11—44no—
132C22×D11—412no—
133C22×D11—46no—
134C22×D11—424no—
135C22×D11—424no—
136C22×D11—448no—
137C22×D11—424no—
138C22×D11—412no—
139C22×D11—424no—
140C22×D11—46no—
141C22×D11—448no—
142C22×D11—41no—
143C22×D11—43no—
144C22×D11—412no—
145C22×D11—44no—
146C22×D11—48no—
147C22×D11#12013yes—
148C22×D11#12011yescharacteristic
149C22×D11C22⋊Q816yes—
150C22×D11C22⋊Q816yes—
151C22×D11#12416yes—
152C22×D11#12416yes—
153Q8×C11—82no—
154C2×C4×C11—26no—
155C2×C4×C11—46no—
156C2×C4×C11—46no—
157C2×C4×C11—43no—
158C2×Dic11—26no—
159C2×Dic11—46no—
160C2×Dic11—46no—
161C2×Dic11—43no—
162C4×D11—412no—
163C4×D11—86no—
164C4×D11—812no—
165Dic22—86no—
166C26—111no—
167#543—113no—
168#543—226no—
169#543C2×D1111yescharacteristic, complemented
170C2×C22⋊Q8—226no—
171C22×C22⋊C4—113no—
172C22×C22⋊C4—113no—
173C22×C22⋊C4—226no—
174#379—113no—
175#379—113no—
176#379—113no—
177#379—226no—
178#379C2×D1113yes—
179#342—113no—
180#342—116no—
181#342C2×D1113yescomplemented
182C22×C11—26no—
183C22×C11—212no—
184C22×C11—41no—
185C22×C11—43no—
186C22×C11—412no—
187C22×C11—46no—
188C22×C11—42no—
189C22×C11—44no—
190C22×C11C2×#12011yescharacteristic
191C22×C11C2×C22⋊Q813yes—
192C22×C11C2×#12413yes—
193C2×D11—26no—
194C2×D11—212no—
195C2×D11—212no—
196C2×D11—212no—
197C2×D11—46no—
198C2×D11—46no—
199C2×D11—448no—
200C2×D11—412no—
201C2×D11—46no—
202C2×D11—42no—
203C2×D11—44no—
204C2×D11—416no—
205C2×D11#39316yes—
206C2×D11#39312yes—
207C2×D11B(4,𝔽2)14yes—
208C4×C11—46no—
209C4×C11—83no—
210Dic11—46no—
211Dic11—83no—
212C25—111no—
213C25—114no—
214C25—111no—
215C25—223no—
216C25—223no—
217C25—226no—
218C25—448no—
219C25C22×D1111yescharacteristic
220C22×Q8—222no—
221C23×C4—116no—
222C23×C4—223no—
223C22⋊Q8—26no—
224C22⋊Q8—2212no—
225C22⋊Q8—2212no—
226C22⋊Q8—226no—
227C22⋊Q8—226no—
228C22⋊Q8—226no—
229C2×C4⋊C4—226no—
230C2×C22⋊C4—26no—
231C2×C22⋊C4—113no—
232C2×C22⋊C4—116no—
233C2×C22⋊C4—113no—
234C2×C22⋊C4—226no—
235C2×C22⋊C4—226no—
236C2×C22⋊C4—2212no—
237C2×C22⋊C4—226no—
238C2×C22⋊C4—223no—
239C2×C22⋊C4—226no—
240C2×C22⋊C4—226no—
241C2×C22⋊C4—4424no—
242C2×C22⋊C4C22×D1113yes—
243C2×C22⋊C4C22×D1113yes—
244C2×C11—23no—
245C2×C11—23no—
246C2×C11—44no—
247C2×C11C2×#39311yescharacteristic
248C2×C11C2×B(4,𝔽2)12yes—
249D11—26no—
250D11—44no—
251D11#202914yesdirect product factor
252C24—23no—
253C24—23no—
254C24—44no—
255C24—113no—
256C24—113no—
257C24—112no—
258C24—116no—
259C24—112no—
260C24—2212no—
261C24—2212no—
262C24—2224no—
263C24—223no—
264C24—223no—
265C24—4412no—
266C24—441no—
267C24—443no—
268C24—446no—
269C24—446no—
270C24—4416no—
271C24—444no—
272C24—444no—
273C24—4412no—
274C24—4412no—
275C24—4448no—
276C24Q8×D1112yescomplemented
277C24C23×D1111yescharacteristic
278C2×Q8—22no—
279C2×Q8—226no—
280C2×Q8—884no—
281C22×C4—23no—
282C22×C4—116no—
283C22×C4—226no—
284C22×C4—226no—
285C22×C4—223no—
286C22×C4—4412no—
287C22×C4—446no—
288C22×C4—4412no—
289C22×C4D4×D1116yes—
290C4⋊C4—26no—
291C4⋊C4—2212no—
292C4⋊C4—226no—
293C22⋊C4—26no—
294C22⋊C4—26no—
295C22⋊C4—412no—
296C22⋊C4—2212no—
297C22⋊C4—226no—
298C22⋊C4—226no—
299C22⋊C4—446no—
300C22⋊C4—4412no—
301C22⋊C4—4412no—
302C22⋊C4—4412no—
303C11C2×#202911yescharacteristic, complemented, Sylow
304C23—212no—
305C23—26no—
306C23—44no—
307C23—42no—
308C23—46no—
309C23—412no—
310C23—41no—
311C23—43no—
312C23—111no—
313C23—113no—
314C23—116no—
315C23—116no—
316C23—116no—
317C23—116no—
318C23—2212no—
319C23—2212no—
320C23—2248no—
321C23—226no—
322C23—446no—
323C23—446no—
324C23—4424no—
325C23—444no—
326C23—4412no—
327C23—448no—
328C23—444no—
329C23—444no—
330C23—4412no—
331C23—4412no—
332C23—4448no—
333C23—4424no—
334C23—4424no—
335C23—4424no—
336C23—4448no—
337C23—441no—
338C23—443no—
339C23C2×D4×D1113yes—
340C23C2×Q8×D1111yescharacteristic
341C23#41×D1113yes—
342Q8—82no—
343Q8—886no—
344C2×C4—26no—
345C2×C4—46no—
346C2×C4—46no—
347C2×C4—43no—
348C2×C4—226no—
349C2×C4—4412no—
350C2×C4—446no—
351C2×C4—446no—
352C2×C4—443no—
353C2×C4—886no—
354C2×C4—8812no—
355C22—26no—
356C22—212no—
357C22—41no—
358C22—43no—
359C22—412no—
360C22—46no—
361C22—42no—
362C22—44no—
363C22—112no—
364C22—114no—
365C22—116no—
366C22—2212no—
367C22—2212no—
368C22—2212no—
369C22—226no—
370C22—446no—
371C22—446no—
372C22—4412no—
373C22—446no—
374C22—4416no—
375C22—4448no—
376C22—442no—
377C22—444no—
378C22D11×#12011yescharacteristic
379C22D11×C22⋊Q813yes—
380C22D11×#12413yes—
381C4—46no—
382C4—83no—
383C4—446no—
384C4—883no—
385C2—23no—
386C2—23no—
387C2—44no—
388C2—114no—
389C2—226no—
390C2—444no—
391C2D11×#39311yescharacteristic
392C2D11×B(4,𝔽2)12yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2029C2
socleC22×C11C2×#120
prime radicalC25×D11C22
hypercenter#2029D11
hypocenterC11C2×#2029
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #2029

Complements

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

NH ≅ G/Ntype
1. D11×#543C2semidirect
3. #13069781C2semidirect
4. #13069780C2semidirect
5. #13069779C2semidirect
6. D11×#342C2semidirect
7. C11×#2029C2semidirect
9. C11×#543C22semidirect
15. #10623014C22semidirect
21. C11×#342C22semidirect
22. #10622165C22semidirect
23. #10622164C22semidirect
29. C24×D11Q8semidirect
60. C24×C11C2×Q8semidirect
81. C23×D11C2×Q8semidirect
113. #2029D11direct (N × H)
169. #543C2×D11semidirect
181. #342C2×D11semidirect
251. D11#2029direct (N × H)
276. C24Q8×D11semidirect
303. C11C2×#2029semidirect

Maximal subgroups

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

subgroupindex
D11×#5432
D11×#3792
#130697812
#130697802
#130697792
D11×#3422
C11×#20292
C2×#202911