Finite Group Databasebeta

← #14781180

Subgroups — #14781180

Order 2816.

1506 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 209 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
2#13071192C213yesmaximal
3#13069784C213yesmaximal, complemented
4#13069782C211yesmaximal, characteristic, complemented
5#13069780C213yesmaximal, complemented
6D11×#342C213yesmaximal, complemented
7C11×#2029C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623165—26no—
11D11×C22⋊Q8—26no—
12C2×C22⋊C4×D11C2213yes—
13C2×C22⋊C4×D11C2213yes—
14#10623014C2213yes—
15C11×#379C2213yes—
16#10622860C2213yes—
17#10622569—26no—
18#10622569—26no—
19#10622556C2213yes—
20#10622556C2213yes—
21C11×#342C2213yes—
22#10622165C2216yes—
23#10622164C2213yes—
24C25×C11C2311yescharacteristic
25C24×D11C2311yescharacteristic
26C22×C22⋊D11—23no—
27C22×C22⋊D11—23no—
28C22×C22⋊D11—26no—
29C22×C22⋊D11Q814yescomplemented
30C23×Dic11C2311yescharacteristic
31C2×Q8×D11—22no—
32C22×C4×D11—23no—
33C22×C4×D11D416yes—
34C11×C22⋊Q8—26no—
35C2×C11×C22⋊C4—26no—
36C2×C11×C22⋊C4C2313yes—
37C2×C11×C22⋊C4C2313yes—
38C2×C22⋊Dic11—26no—
39C2×C22⋊Dic11C2313yes—
40C2×C22⋊Dic11C2313yes—
41#66999—26no—
42C2×(C2×D11)⋊C4—23no—
43C2×(C2×D11)⋊C4D416yes—
44#66977—26no—
45#66950—26no—
46#66949—212no—
47C4⋊C4×D11—26no—
48C22⋊C4×D11—26no—
49C22⋊C4×D11—26no—
50C22⋊C4×D11—212no—
51#66931—212no—
52C11⋊#95—26no—
53C11⋊#95—26no—
54#23468—111nomaximal, Sylow
55C24×C11—23no—
56C24×C11—23no—
57C24×C11—82no—
58C24×C11C2×Q812yescomplemented
59C24×C11C2411yescharacteristic
60C23×D11—82no—
61C23×D11C2×D413yes—
62C23×D11C2×D413yes—
63C23×D11C2×Q812yes—
64C23×D11#4116yes—
65C2×Q8×C11—22no—
66C22×C4×C11—23no—
67C22×C4×C11C2×D416yes—
68C2×C22⋊D11—212no—
69C2×C22⋊D11—212no—
70C2×C22⋊D11—43no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—46no—
73C2×C22⋊D11—46no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11C2×D416yes—
78C22×Dic11C2×Q812yescomplemented
79Q8×D11—84no—
80C2×C4×D11—26no—
81C2×C4×D11—26no—
82C2×C4×D11—46no—
83C2×C4×D11—86no—
84C2×C4×D11—86no—
85C2×Dic22—26no—
86C11×C4⋊C4—26no—
87C11×C22⋊C4—26no—
88C11×C22⋊C4—26no—
89C11×C22⋊C4—86no—
90C22⋊Dic11—26no—
91C22⋊Dic11—26no—
92C22⋊Dic11—86no—
93(C2×D11)⋊C4—212no—
94(C2×D11)⋊C4—46no—
95C4⋊Dic11—26no—
96Dic11⋊C4—212no—
97C2×#543—111no—
98#2308—113no—
99#2030—113no—
100#2030—111no—
101#2029—113no—
102#2029D1111yescharacteristic, complemented
103C2×#342—113no—
104C23×C11—26no—
105C23×C11—42no—
106C23×C11—46no—
107C23×C11—46no—
108C23×C11—41no—
109C23×C11—43no—
110C23×C11—82no—
111C23×C11—86no—
112C23×C11C22×D413yes—
113C23×C11C22×Q811yescharacteristic
114C23×C11C2×#4113yes—
115C22×D11—46no—
116C22×D11—46no—
117C22×D11—82no—
118C22×D11—86no—
119C22×D11#12013yes—
120C22×D11#12011yescharacteristic
121C22×D11C22⋊Q816yes—
122C22×D11C22⋊Q816yes—
123C22×D11#12416yes—
124C22×D11#12416yes—
125Q8×C11—82no—
126C2×C4×C11—26no—
127C2×C4×C11—46no—
128C2×C4×C11—46no—
129C2×C4×C11—43no—
130C22⋊D11—412no—
131C22⋊D11—44no—
132C2×Dic11—26no—
133C2×Dic11—26no—
134C2×Dic11—41no—
135C2×Dic11—43no—
136C2×Dic11—46no—
137C2×Dic11—46no—
138C2×Dic11—43no—
139C4×D11—412no—
140C4×D11—86no—
141C4×D11—812no—
142Dic22—86no—
143C23×D4—111no—
144#543—113no—
145#543—226no—
146#543C2×D1111yescharacteristic
147C2×C22⋊Q8—226no—
148C22×C22⋊C4—113no—
149C22×C22⋊C4—113no—
150#386—226no—
151#386—226no—
152#381—113no—
153#381—113no—
154#379—113no—
155#379C2×D1113yes—
156#342—113no—
157#342—116no—
158#342C2×D1113yes—
159C22×C11—26no—
160C22×C11—41no—
161C22×C11—43no—
162C22×C11—46no—
163C22×C11—46no—
164C22×C11—42no—
165C22×C11—86no—
166C22×C11—82no—
167C22×C11C2×#12011yescharacteristic
168C22×C11C2×C22⋊Q813yes—
169C22×C11C2×#12413yes—
170C2×D11—22no—
171C2×D11—26no—
172C2×D11—46no—
173C2×D11—46no—
174C2×D11—46no—
175C2×D11—46no—
176C2×D11#39316yes—
177C2×D11#39312yes—
178C4×C11—46no—
179C4×C11—83no—
180Dic11—42no—
181Dic11—46no—
182Dic11—83no—
183C25—111no—
184C25C22×D1111yescharacteristic
185C22×Q8—222no—
186C22×D4—114no—
187C22×D4—223no—
188C22×D4—223no—
189C22×D4—226no—
190C23×C4—111no—
191C23×C4—116no—
192C23×C4—223no—
193C22⋊Q8—26no—
194C22⋊Q8—2212no—
195C22⋊Q8—2212no—
196C22⋊Q8—226no—
197C22⋊Q8—226no—
198C22⋊Q8—226no—
199C2×C4⋊C4—226no—
200C2×C22⋊C4—26no—
201C2×C22⋊C4—113no—
202C2×C22⋊C4—116no—
203C2×C22⋊C4—113no—
204C2×C22⋊C4—226no—
205C2×C22⋊C4—226no—
206C2×C22⋊C4—2212no—
207C2×C22⋊C4—223no—
208C2×C22⋊C4—226no—
209C2×C22⋊C4C22×D1113yes—
210C2×C22⋊C4C22×D1113yes—
211#95—226no—
212#95—226no—
213C2×C11—23no—
214C2×C11—23no—
215C2×C11—82no—
216C2×C11C2×#39311yescharacteristic
217C2×C11#302612yes—
218D11—22no—
219D11—26no—
220C24—23no—
221C24—23no—
222C24—82no—
223C24—113no—
224C24—113no—
225C24—112no—
226C24—116no—
227C24—882no—
228C24Q8×D1112yescomplemented
229C24C23×D1111yescharacteristic
230C2×Q8—22no—
231C2×Q8—226no—
232C2×Q8—884no—
233C2×D4—2212no—
234C2×D4—2212no—
235C2×D4—443no—
236C2×D4—441no—
237C2×D4—446no—
238C2×D4—446no—
239C22×C4—23no—
240C22×C4—112no—
241C22×C4—116no—
242C22×C4—226no—
243C22×C4—226no—
244C22×C4—223no—
245C22×C4—223no—
246C22×C4—223no—
247C22×C4—446no—
248C22×C4—886no—
249C22×C4—886no—
250C22×C4D4×D1116yes—
251C4⋊C4—26no—
252C4⋊C4—2212no—
253C4⋊C4—226no—
254C22⋊C4—26no—
255C22⋊C4—26no—
256C22⋊C4—86no—
257C22⋊C4—2212no—
258C22⋊C4—226no—
259C22⋊C4—226no—
260C22⋊C4—446no—
261C22⋊C4—886no—
262C11#2346811yescharacteristic, complemented, Sylow
263C23—26no—
264C23—42no—
265C23—46no—
266C23—46no—
267C23—41no—
268C23—43no—
269C23—82no—
270C23—86no—
271C23—113no—
272C23—111no—
273C23—116no—
274C23—116no—
275C23—116no—
276C23—116no—
277C23—446no—
278C23—446no—
279C23—882no—
280C23—886no—
281C23C2×D4×D1113yes—
282C23C2×Q8×D1111yescharacteristic
283C23#41×D1113yes—
284Q8—82no—
285Q8—886no—
286D4—4412no—
287D4—444no—
288C2×C4—26no—
289C2×C4—46no—
290C2×C4—46no—
291C2×C4—43no—
292C2×C4—226no—
293C2×C4—226no—
294C2×C4—4412no—
295C2×C4—441no—
296C2×C4—443no—
297C2×C4—446no—
298C2×C4—446no—
299C2×C4—443no—
300C2×C4—886no—
301C2×C4—8812no—
302C22—26no—
303C22—41no—
304C22—43no—
305C22—46no—
306C22—46no—
307C22—42no—
308C22—86no—
309C22—82no—
310C22—116no—
311C22—112no—
312C22—222no—
313C22—226no—
314C22—446no—
315C22—446no—
316C22—446no—
317C22—446no—
318C22D11×#12011yescharacteristic
319C22D11×C22⋊Q813yes—
320C22D11×#12413yes—
321C4—46no—
322C4—83no—
323C4—442no—
324C4—446no—
325C4—883no—
326C2—23no—
327C2—23no—
328C2—82no—
329C2—222no—
330C2—226no—
331C2D11×#39311yescharacteristic
332C2#1307801112yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2029C2
socleC22×C11C2×#120
prime radicalC23×C22⋊D11C22
hypercenter#2029D11
hypocenterC11#23468
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. #13069784C2semidirect
4. #13069782C2semidirect
5. #13069780C2semidirect
6. D11×#342C2semidirect
7. C11×#2029C2semidirect
29. C22×C22⋊D11Q8semidirect
58. C24×C11C2×Q8semidirect
78. C22×Dic11C2×Q8semidirect
102. #2029D11semidirect
228. C24Q8×D11semidirect
262. C11#23468semidirect

Maximal subgroups

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

subgroupindex
D11×#5432
#130711922
#130697842
#130697822
#130697802
D11×#3422
C11×#20292
#2346811