Finite Group Databasebeta

← #14781185

Subgroups — #14781185

Order 2816.

1402 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1402 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
1#13082018C211yesmaximal, characteristic, complemented
2#13071197C213yesmaximal
3#13069781C213yesmaximal, complemented
4#13069780C213yesmaximal, complemented
5#13069779C211yesmaximal, characteristic, complemented
6#13068347C213yesmaximal, complemented
7C11×#2029C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623154—26no—
11#10623153—26no—
12#10623014C2213yes—
13C2×#66930C2213yes—
14C2×#66930C2213yes—
15C11×#379C2213yes—
16#10622860C2213yes—
17#10622570—26no—
18#10622570—26no—
19#10622568C2213yes—
20#10622568C2213yes—
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
31C11×C22⋊Q8—26no—
32C2×C11×C22⋊C4—26no—
33C2×C11×C22⋊C4C2313yes—
34C2×C11×C22⋊C4C2313yes—
35C2×C22⋊Dic11—26no—
36C2×C22⋊Dic11C2313yes—
37C2×C22⋊Dic11C2313yes—
38Q8×Dic11—22no—
39#66997—26no—
40C2×(C2×D11)⋊C4—26no—
41C2×(C2×D11)⋊C4—26no—
42#66977—26no—
43C2×Dic11⋊C4—23no—
44C2×Dic11⋊C4D416yes—
45C2×C4×Dic11—23no—
46C2×C4×Dic11D416yes—
47#66942—212no—
48#66941—26no—
49#66940—26no—
50#66931—212no—
51#66930—26no—
52#66930—26no—
53#66930—212no—
54#23469—111nomaximal, Sylow
55C24×C11—23no—
56C24×C11—23no—
57C24×C11—82no—
58C24×C11C2×Q812yes—
59C24×C11C2411yescharacteristic
60C23×D11—23no—
61C23×D11—23no—
62C23×D11—82no—
63C23×D11C2×Q812yes—
64C2×Q8×C11—22no—
65C22×C4×C11—23no—
66C22×C4×C11C2×D416yes—
67C2×C22⋊D11—212no—
68C2×C22⋊D11—212no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—43no—
71C2×C22⋊D11—46no—
72C2×C22⋊D11—46no—
73C22×Dic11—23no—
74C22×Dic11C2×D416yes—
75C22×Dic11C2×D413yes—
76C22×Dic11C2×D413yes—
77C22×Dic11C2×Q812yes—
78C22×Dic11#4116yes—
79C2×Dic22—26no—
80C11×C4⋊C4—26no—
81C11×C22⋊C4—26no—
82C11×C22⋊C4—26no—
83C11×C22⋊C4—86no—
84C22⋊Dic11—26no—
85C22⋊Dic11—26no—
86C22⋊Dic11—86no—
87(C2×D11)⋊C4—86no—
88(C2×D11)⋊C4—86no—
89C4⋊Dic11—26no—
90Dic11⋊C4—212no—
91Dic11⋊C4—212no—
92Dic11⋊C4—46no—
93C4×Dic11—26no—
94C4×Dic11—26no—
95C4×Dic11—46no—
96#3458—111no—
97#2309—113no—
98#2029—113no—
99#2029—113no—
100#2029—111no—
101#2029D1111yescharacteristic, complemented
102#1740—113no—
103C23×C11—26no—
104C23×C11—42no—
105C23×C11—46no—
106C23×C11—46no—
107C23×C11—41no—
108C23×C11—43no—
109C23×C11—82no—
110C23×C11—86no—
111C23×C11C22×D413yes—
112C23×C11C22×Q811yescharacteristic
113C23×C11C2×#4113yes—
114C22×D11—26no—
115C22×D11—46no—
116C22×D11—46no—
117C22×D11—41no—
118C22×D11—43no—
119C22×D11—82no—
120C22×D11—86no—
121Q8×C11—82no—
122C2×C4×C11—26no—
123C2×C4×C11—46no—
124C2×C4×C11—46no—
125C2×C4×C11—43no—
126C22⋊D11—44no—
127C22⋊D11—412no—
128C2×Dic11—26no—
129C2×Dic11—46no—
130C2×Dic11—46no—
131C2×Dic11—43no—
132C2×Dic11#12011yescharacteristic
133C2×Dic11#12013yes—
134C2×Dic11C22⋊Q816yes—
135C2×Dic11C22⋊Q816yes—
136C2×Dic11#12416yes—
137C2×Dic11#12416yes—
138Dic22—86no—
139C23×D4—111no—
140#544—226no—
141#543—113no—
142#543C2×D1111yescharacteristic
143#533—226no—
144C2×#117—113no—
145C2×#117—113no—
146#390—226no—
147#390—226no—
148#379—113no—
149#379—113no—
150#379—113no—
151#379C2×D1113yes—
152#342—113no—
153#342—116no—
154#342C2×D1113yes—
155C22×C11—26no—
156C22×C11—41no—
157C22×C11—43no—
158C22×C11—46no—
159C22×C11—46no—
160C22×C11—42no—
161C22×C11—86no—
162C22×C11—82no—
163C22×C11C2×#12011yescharacteristic
164C22×C11C2×C22⋊Q813yes—
165C22×C11C2×#12413yes—
166C2×D11—46no—
167C2×D11—46no—
168C2×D11—42no—
169C2×D11—86no—
170C2×D11—82no—
171C4×C11—46no—
172C4×C11—83no—
173Dic11—46no—
174Dic11—83no—
175Dic11#39312yes—
176Dic11#39316yes—
177C25—111no—
178C25C22×D1111yescharacteristic
179C22×D4—114no—
180C22×D4—223no—
181C22×D4—223no—
182C22×D4—226no—
183C23×C4—111no—
184C4⋊Q8—226no—
185C4⋊Q8—226no—
186#125—2212no—
187C22⋊Q8—26no—
188C22⋊Q8—2212no—
189C22⋊Q8—226no—
190C4×Q8—226no—
191C4×Q8—222no—
192#117—226no—
193#117—226no—
194#117—2212no—
195C2×C4⋊C4—116no—
196C2×C4⋊C4—223no—
197C2×C22⋊C4—26no—
198C2×C22⋊C4—113no—
199C2×C22⋊C4—113no—
200C2×C22⋊C4—226no—
201C2×C22⋊C4—226no—
202C2×C22⋊C4—226no—
203C2×C22⋊C4C22×D1113yes—
204C2×C22⋊C4C22×D1113yes—
205C2×C42—116no—
206C2×C42—223no—
207C2×C11—23no—
208C2×C11—23no—
209C2×C11—82no—
210C2×C11C2×#39311yescharacteristic
211C2×C11#302712yes—
212D11—82no—
213C24—23no—
214C24—23no—
215C24—82no—
216C24—112no—
217C24—223no—
218C24—223no—
219C24—882no—
220C24Q8×D1112yes—
221C24C23×D1111yescharacteristic
222C2×Q8—22no—
223C2×Q8—226no—
224C2×D4—2212no—
225C2×D4—2212no—
226C2×D4—441no—
227C2×D4—443no—
228C2×D4—446no—
229C2×D4—446no—
230C22×C4—23no—
231C22×C4—113no—
232C22×C4—113no—
233C22×C4—112no—
234C22×C4—116no—
235C22×C4—116no—
236C22×C4—223no—
237C22×C4D4×D1116yes—
238C4⋊C4—26no—
239C4⋊C4—2212no—
240C4⋊C4—2212no—
241C4⋊C4—226no—
242C4⋊C4—446no—
243C22⋊C4—26no—
244C22⋊C4—26no—
245C22⋊C4—86no—
246C22⋊C4—226no—
247C22⋊C4—226no—
248C22⋊C4—886no—
249C22⋊C4—886no—
250C22⋊C4—886no—
251C42—226no—
252C42—226no—
253C42—446no—
254C11#2346911yescharacteristic, complemented, Sylow
255C23—26no—
256C23—42no—
257C23—46no—
258C23—46no—
259C23—41no—
260C23—43no—
261C23—82no—
262C23—86no—
263C23—226no—
264C23—446no—
265C23—446no—
266C23—441no—
267C23—443no—
268C23—882no—
269C23—886no—
270C23C2×D4×D1113yes—
271C23C2×Q8×D1111yescharacteristic
272C23#41×D1113yes—
273Q8—82no—
274Q8—886no—
275D4—444no—
276D4—4412no—
277C2×C4—26no—
278C2×C4—46no—
279C2×C4—46no—
280C2×C4—43no—
281C2×C4—111no—
282C2×C4—113no—
283C2×C4—116no—
284C2×C4—116no—
285C2×C4—116no—
286C2×C4—116no—
287C2×C4—226no—
288C2×C4—446no—
289C2×C4—446no—
290C2×C4—443no—
291C22—26no—
292C22—41no—
293C22—43no—
294C22—46no—
295C22—46no—
296C22—42no—
297C22—86no—
298C22—82no—
299C22—446no—
300C22—446no—
301C22—442no—
302C22—886no—
303C22—882no—
304C22D11×#12011yescharacteristic
305C22D11×C22⋊Q813yes—
306C22D11×#12413yes—
307C4—46no—
308C4—83no—
309C4—112no—
310C4—116no—
311C4—446no—
312C4—883no—
313C2—23no—
314C2—23no—
315C2—82no—
316C2—882no—
317C2D11×#39311yescharacteristic
318C2#1307801612yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2029C2
socleC22×C11C2×#120
prime radicalC23×C22⋊D11C22
hypercenter#2029D11
hypocenterC11#23469
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. #13082018C2semidirect
3. #13069781C2semidirect
4. #13069780C2semidirect
5. #13069779C2semidirect
6. #13068347C2semidirect
7. C11×#2029C2semidirect
29. C22×C22⋊D11Q8semidirect
101. #2029D11semidirect
254. C11#23469semidirect

Maximal subgroups

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

subgroupindex
#130820182
#130711972
#130697812
#130697802
#130697792
#130683472
C11×#20292
#2346911