Finite Group Databasebeta

← #14781175

Subgroups — #14781175

Order 2816.

1378 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1378 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#13070994C213yesmaximal
3#13069784C213yesmaximal, complemented
4#13069782C211yesmaximal, characteristic, complemented
5#13069780C213yesmaximal
6#13068347C213yesmaximal, complemented
7C11×#2029C211yesmaximal, characteristic
8C24×Dic11C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623154—26no—
11#10623153—26no—
12#10623014C2213yes—
13C2×#66930C2213yes—
14C2×#66930C2213yes—
15C11×#379C2213yes—
16#10622860C2213yes—
17#10622556C2213yes—
18#10622556C2213yes—
19#10622555—26no—
20C22⋊C4×Dic11—26no—
21C11×#342C2213yes—
22#10622165C2216yes—
23#10622164C2213yes—
24C25×C11C2311yescharacteristic
25C23×Dic11—23no—
26C23×Dic11—23no—
27C23×Dic11—26no—
28C23×Dic11Q814yescomplemented
29C23×Dic11C2311yescharacteristic
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—
40#66977—26no—
41C2×Dic11⋊C4—23no—
42C2×Dic11⋊C4D416yes—
43C2×C4×Dic11—23no—
44C2×C4×Dic11D416yes—
45#66942—212no—
46#66941—26no—
47#66940—26no—
48#66931—212no—
49#66930—26no—
50#66930—26no—
51#66930—212no—
52C11⋊#95—26no—
53C11⋊#95—26no—
54#23467—111nomaximal, Sylow
55C24×C11—23no—
56C24×C11—23no—
57C24×C11—44no—
58C24×C11C2×Q812yes—
59C24×C11C2411yescharacteristic
60C2×Q8×C11—22no—
61C22×C4×C11—23no—
62C22×C4×C11C2×D416yes—
63C22×Dic11—212no—
64C22×Dic11—212no—
65C22×Dic11—23no—
66C22×Dic11—23no—
67C22×Dic11—23no—
68C22×Dic11—41no—
69C22×Dic11—43no—
70C22×Dic11—46no—
71C22×Dic11—46no—
72C22×Dic11C2×D416yes—
73C22×Dic11C2×D413yes—
74C22×Dic11C2×D413yes—
75C22×Dic11C2×Q812yes—
76C22×Dic11C2×Q812yes—
77C22×Dic11#4116yes—
78C2×Dic22—26no—
79C11×C4⋊C4—26no—
80C11×C22⋊C4—26no—
81C11×C22⋊C4—26no—
82C11×C22⋊C4—412no—
83C22⋊Dic11—26no—
84C22⋊Dic11—26no—
85C22⋊Dic11—412no—
86C4⋊Dic11—26no—
87Dic11⋊C4—212no—
88Dic11⋊C4—212no—
89Dic11⋊C4—46no—
90C4×Dic11—26no—
91C4×Dic11—26no—
92C4×Dic11—46no—
93#3458—111no—
94#2280—113no—
95#2030—113no—
96#2030—111no—
97#2029—113no—
98#2029D1111yescharacteristic
99#1740—113no—
100C23×C11—212no—
101C23×C11—26no—
102C23×C11—44no—
103C23×C11—42no—
104C23×C11—46no—
105C23×C11—412no—
106C23×C11—41no—
107C23×C11—43no—
108C23×C11C22×D413yes—
109C23×C11C22×Q811yescharacteristic
110C23×C11C2×#4113yes—
111Q8×C11—82no—
112C2×C4×C11—26no—
113C2×C4×C11—46no—
114C2×C4×C11—46no—
115C2×C4×C11—43no—
116C2×Dic11—26no—
117C2×Dic11—26no—
118C2×Dic11—41no—
119C2×Dic11—43no—
120C2×Dic11—44no—
121C2×Dic11—412no—
122C2×Dic11—46no—
123C2×Dic11—46no—
124C2×Dic11—43no—
125C2×Dic11#12011yescharacteristic
126C2×Dic11#12013yes—
127C2×Dic11C22⋊Q816yes—
128C2×Dic11C22⋊Q816yes—
129C2×Dic11#12416yes—
130C2×Dic11#12416yes—
131Dic22—86no—
132C24×C4—111no—
133#544—226no—
134#543—113no—
135#543C2×D1111yescharacteristic
136#533—226no—
137C2×#117—113no—
138C2×#117—113no—
139#381—113no—
140#381—113no—
141#380—226no—
142#379—113no—
143#379C2×D1113yes—
144C4×C22⋊C4—226no—
145#342—113no—
146#342—116no—
147#342C2×D1113yes—
148C22×C11—26no—
149C22×C11—212no—
150C22×C11—41no—
151C22×C11—43no—
152C22×C11—412no—
153C22×C11—46no—
154C22×C11—42no—
155C22×C11—44no—
156C22×C11C2×#12011yescharacteristic
157C22×C11C2×C22⋊Q813yes—
158C22×C11C2×#12413yes—
159C4×C11—46no—
160C4×C11—83no—
161Dic11—42no—
162Dic11—46no—
163Dic11—83no—
164Dic11#39312yes—
165Dic11#39316yes—
166C25C22×D1111yescharacteristic
167C23×C4—111no—
168C23×C4—114no—
169C23×C4—111no—
170C23×C4—223no—
171C23×C4—223no—
172C23×C4—226no—
173C4⋊Q8—226no—
174C4⋊Q8—226no—
175#125—2212no—
176C22⋊Q8—26no—
177C22⋊Q8—2212no—
178C22⋊Q8—226no—
179C4×Q8—226no—
180C4×Q8—222no—
181#117—226no—
182#117—226no—
183#117—2212no—
184C2×C4⋊C4—116no—
185C2×C4⋊C4—223no—
186C2×C22⋊C4—26no—
187C2×C22⋊C4—113no—
188C2×C22⋊C4—113no—
189C2×C22⋊C4—226no—
190C2×C22⋊C4C22×D1113yes—
191C2×C22⋊C4C22×D1113yes—
192C2×C42—116no—
193C2×C42—223no—
194#95—226no—
195#95—226no—
196C2×C11—23no—
197C2×C11—23no—
198C2×C11—44no—
199C2×C11C2×#39311yescharacteristic
200C2×C11#302512yes—
201C24—23no—
202C24—23no—
203C24—44no—
204C24Q8×D1112yes—
205C24C23×D1111yescharacteristic
206C2×Q8—22no—
207C2×Q8—226no—
208C22×C4—23no—
209C22×C4—113no—
210C22×C4—113no—
211C22×C4—112no—
212C22×C4—116no—
213C22×C4—112no—
214C22×C4—116no—
215C22×C4—2212no—
216C22×C4—2212no—
217C22×C4—223no—
218C22×C4—223no—
219C22×C4—223no—
220C22×C4—441no—
221C22×C4—443no—
222C22×C4—446no—
223C22×C4—446no—
224C22×C4D4×D1116yes—
225C4⋊C4—26no—
226C4⋊C4—2212no—
227C4⋊C4—2212no—
228C4⋊C4—226no—
229C4⋊C4—446no—
230C22⋊C4—26no—
231C22⋊C4—26no—
232C22⋊C4—412no—
233C22⋊C4—226no—
234C22⋊C4—226no—
235C22⋊C4—4412no—
236C42—226no—
237C42—226no—
238C42—446no—
239C11#2346711yescharacteristic, complemented, Sylow
240C23—212no—
241C23—26no—
242C23—44no—
243C23—42no—
244C23—46no—
245C23—412no—
246C23—41no—
247C23—43no—
248C23C2×D4×D1113yes—
249C23C2×Q8×D1111yescharacteristic
250C23#41×D1113yes—
251Q8—82no—
252Q8—886no—
253C2×C4—26no—
254C2×C4—46no—
255C2×C4—46no—
256C2×C4—43no—
257C2×C4—111no—
258C2×C4—113no—
259C2×C4—116no—
260C2×C4—116no—
261C2×C4—116no—
262C2×C4—116no—
263C2×C4—226no—
264C2×C4—226no—
265C2×C4—444no—
266C2×C4—4412no—
267C2×C4—441no—
268C2×C4—443no—
269C2×C4—446no—
270C2×C4—446no—
271C2×C4—443no—
272C22—26no—
273C22—212no—
274C22—41no—
275C22—43no—
276C22—412no—
277C22—46no—
278C22—42no—
279C22—44no—
280C22D11×#12011yescharacteristic
281C22D11×C22⋊Q813yes—
282C22D11×#12413yes—
283C4—46no—
284C4—83no—
285C4—112no—
286C4—116no—
287C4—442no—
288C4—446no—
289C4—883no—
290C2—23no—
291C2—23no—
292C2—44no—
293C2D11×#39311yescharacteristic
294C2#1307800612yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2029C2
socleC22×C11C2×#120
prime radicalC25×C11C23
hypercenter#2029D11
hypocenterC11#23467
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. #13069784C2semidirect
4. #13069782C2semidirect
6. #13068347C2semidirect
28. C23×Dic11Q8semidirect
239. C11#23467semidirect

Maximal subgroups

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

subgroupindex
#130820182
#130709942
#130697842
#130697822
#130697802
#130683472
C11×#20292
#2346711