Finite Group Databasebeta

← #14781182

Subgroups — #14781182

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#13071193C213yesmaximal
3#13069783C213yesmaximal, complemented
4#13069781C213yesmaximal, complemented
5#13069779C211yesmaximal, characteristic, complemented
6D11×#342C213yesmaximal, complemented
7C11×#2030C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623165—26no—
11D11×C22⋊Q8—26no—
12C2×C22⋊C4×D11C2213yes—
13C2×C22⋊C4×D11C2213yes—
14#10623014C2213yes—
15C11×#381C2213yes—
16#10622824C2213yes—
17#10622568C2213yes—
18#10622568C2213yes—
19#10622278—26no—
20#10622278—26no—
21C11×#342C2213yes—
22#10622165C2216yes—
23#10622164C2213yes—
24C24×D11C2311yescharacteristic
25C24×D11C2311yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C2×Q8×D11—22no—
28C22×D44—23no—
29C22×D44—23no—
30C22×D44—26no—
31C22×D44Q814yescomplemented
32C22×C4×D11—23no—
33C22×C4×D11D416yes—
34C11×C22⋊Q8—26no—
35C2×C11×C22⋊C4C2313yes—
36C2×C11×C22⋊C4C2313yes—
37C2×C22⋊Dic11C2313yes—
38C2×C22⋊Dic11C2313yes—
39#66999—26no—
40C2×(C2×D11)⋊C4—23no—
41C2×(C2×D11)⋊C4—26no—
42C2×(C2×D11)⋊C4—26no—
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×C11C2411yescharacteristic
56C23×D11—23no—
57C23×D11—23no—
58C23×D11—82no—
59C23×D11—82no—
60C23×D11C2×D413yes—
61C23×D11C2×D413yes—
62C23×D11C2×Q812yes—
63C23×D11C2×Q812yescomplemented
64C23×D11#4116yes—
65C2×Q8×C11—22no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—23no—
69C22×C4×C11C2×D416yes—
70C22×C4×C11C2×Q812yescomplemented
71C22×Dic11—23no—
72C22×Dic11C2×D416yes—
73Q8×D11—84no—
74C2×D44—212no—
75C2×D44—212no—
76C2×D44—43no—
77C2×D44—41no—
78C2×D44—46no—
79C2×D44—46no—
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—
89C22⋊Dic11—26no—
90C22⋊Dic11—26no—
91(C2×D11)⋊C4—212no—
92(C2×D11)⋊C4—46no—
93(C2×D11)⋊C4—86no—
94(C2×D11)⋊C4—86no—
95C4⋊Dic11—26no—
96Dic11⋊C4—212no—
97C2×#543—111no—
98#2308—113no—
99#2030—113no—
100#2030D1111yescharacteristic, complemented
101#2029—113no—
102#2029—111no—
103C2×#342—113no—
104C23×C11—42no—
105C23×C11C22×D413yes—
106C23×C11C22×Q811yescharacteristic
107C23×C11C2×#4113yes—
108C22×D11—26no—
109C22×D11—46no—
110C22×D11—46no—
111C22×D11—46no—
112C22×D11—46no—
113C22×D11—41no—
114C22×D11—43no—
115C22×D11—82no—
116C22×D11—82no—
117C22×D11—86no—
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—26no—
128C2×C4×C11—41no—
129C2×C4×C11—43no—
130C2×C4×C11—46no—
131C2×C4×C11—46no—
132C2×C4×C11—43no—
133C2×Dic11—26no—
134C2×Dic11—46no—
135C2×Dic11—46no—
136C2×Dic11—43no—
137D44—412no—
138D44—44no—
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#381C2×D1113yes—
154#379—113no—
155#379—113no—
156#342—113no—
157#342—116no—
158#342C2×D1113yes—
159C22×C11—26no—
160C22×C11—41no—
161C22×C11—43no—
162C22×C11C2×#12011yescharacteristic
163C22×C11C2×C22⋊Q813yes—
164C22×C11C2×#12413yes—
165C2×D11—22no—
166C2×D11—26no—
167C2×D11—46no—
168C2×D11—46no—
169C2×D11—46no—
170C2×D11—46no—
171C2×D11—46no—
172C2×D11—46no—
173C2×D11—42no—
174C2×D11—86no—
175C2×D11—82no—
176C2×D11#39316yes—
177C2×D11#39312yes—
178C4×C11—42no—
179C4×C11—46no—
180C4×C11—83no—
181Dic11—46no—
182Dic11—83no—
183C25—111no—
184C25—111no—
185C22×Q8—222no—
186C22×D4—114no—
187C22×D4—223no—
188C22×D4—223no—
189C22×D4—226no—
190C23×C4—116no—
191C23×C4—223no—
192C23×C4C22×D1111yescharacteristic
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—113no—
201C2×C22⋊C4—116no—
202C2×C22⋊C4—113no—
203C2×C22⋊C4—226no—
204C2×C22⋊C4—226no—
205C2×C22⋊C4—2212no—
206C2×C22⋊C4—223no—
207C2×C22⋊C4—226no—
208C2×C22⋊C4—226no—
209C2×C22⋊C4C22×D1113yes—
210C2×C22⋊C4C22×D1113yes—
211#95—26no—
212#95—226no—
213C2×C11—23no—
214C2×C11—23no—
215C2×C11C2×#39311yescharacteristic
216C2×C11#302612yes—
217D11—22no—
218D11—26no—
219D11—82no—
220C24—113no—
221C24—113no—
222C24—112no—
223C24—116no—
224C24—112no—
225C24—223no—
226C24—223no—
227C24—882no—
228C24—882no—
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—23no—
241C22×C4—23no—
242C22×C4—116no—
243C22×C4—226no—
244C22×C4—226no—
245C22×C4—223no—
246C22×C4—446no—
247C22×C4—886no—
248C22×C4—886no—
249C22×C4D4×D1116yes—
250C22×C4Q8×D1112yescomplemented
251C4⋊C4—26no—
252C4⋊C4—2212no—
253C4⋊C4—226no—
254C22⋊C4—26no—
255C22⋊C4—26no—
256C22⋊C4—2212no—
257C22⋊C4—226no—
258C22⋊C4—226no—
259C22⋊C4—446no—
260C22⋊C4—886no—
261C22⋊C4—886no—
262C11#2346811yescharacteristic, complemented, Sylow
263C23—42no—
264C23—113no—
265C23—111no—
266C23—116no—
267C23—116no—
268C23—116no—
269C23—116no—
270C23—226no—
271C23—446no—
272C23—446no—
273C23—446no—
274C23—446no—
275C23—441no—
276C23—443no—
277C23—882no—
278C23—882no—
279C23—886no—
280C23—886no—
281C23C2×D4×D1113yes—
282C23C2×Q8×D1111yescharacteristic
283C23#41×D1113yes—
284Q8—82no—
285Q8—886no—
286D4—4412no—
287D4—444no—
288C2×C4—26no—
289C2×C4—26no—
290C2×C4—41no—
291C2×C4—43no—
292C2×C4—46no—
293C2×C4—46no—
294C2×C4—43no—
295C2×C4—226no—
296C2×C4—4412no—
297C2×C4—446no—
298C2×C4—446no—
299C2×C4—443no—
300C2×C4—886no—
301C2×C4—8812no—
302C22—26no—
303C22—41no—
304C22—43no—
305C22—116no—
306C22—112no—
307C22—222no—
308C22—226no—
309C22—446no—
310C22—446no—
311C22—446no—
312C22—446no—
313C22—446no—
314C22—446no—
315C22—442no—
316C22—886no—
317C22—882no—
318C22D11×#12011yescharacteristic
319C22D11×C22⋊Q813yes—
320C22D11×#12413yes—
321C4—42no—
322C4—46no—
323C4—83no—
324C4—446no—
325C4—883no—
326C2—23no—
327C2—23no—
328C2—222no—
329C2—226no—
330C2—882no—
331C2D11×#39311yescharacteristic
332C2#1307801412yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2030C2
socleC22×C11C2×#120
prime radicalC23×D44C22
hypercenter#2030D11
hypocenterC11#23468
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
1. D11×#543C2semidirect
3. #13069783C2semidirect
4. #13069781C2semidirect
5. #13069779C2semidirect
6. D11×#342C2semidirect
7. C11×#2030C2semidirect
31. C22×D44Q8semidirect
63. C23×D11C2×Q8semidirect
70. C22×C4×C11C2×Q8semidirect
100. #2030D11semidirect
250. C22×C4Q8×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
#130711932
#130697832
#130697812
#130697792
D11×#3422
C11×#20302
#2346811