Finite Group Databasebeta

← #14781189

Subgroups — #14781189

Order 2816.

1178 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1178 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
2#13071201C213yesmaximal
3#13069784C213yesmaximal
4#13069783C213yesmaximal
5#13069782C211yesmaximal, characteristic
6#13068347C213yesmaximal
7C11×#2030C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C11×#543C2211yescharacteristic
10#10623154—26no—
11#10623153—26no—
12#10623014C2213yes—
13C2×#66930C2213yes—
14C2×#66930C2213yes—
15C11×#381C2213yes—
16#10622824C2213yes—
17#10622556C2213yes—
18#10622556C2213yes—
19#10622259—26no—
20#10622259—26no—
21C11×#342C2213yes—
22#10622165C2216yes—
23#10622164C2213yes—
24C23×C4×C11C2311yescharacteristic
25C23×Dic11C2311yescharacteristic
26C23×Dic11C2311yescharacteristic
27C22×Dic22—23no—
28C22×Dic22—23no—
29C22×Dic22—26no—
30C22×Dic22Q814yescomplemented
31C11×C22⋊Q8—26no—
32C2×C11×C22⋊C4C2313yes—
33C2×C11×C22⋊C4C2313yes—
34C2×C22⋊Dic11C2313yes—
35C2×C22⋊Dic11C2313yes—
36Q8×Dic11—22no—
37#66997—26no—
38#66977—26no—
39C2×Dic11⋊C4—23no—
40C2×Dic11⋊C4D416yes—
41C2×C4×Dic11—23no—
42C2×C4×Dic11D416yes—
43#66942—212no—
44#66941—26no—
45#66940—26no—
46#66931—212no—
47#66930—26no—
48#66930—26no—
49#66930—212no—
50C11×#95—26no—
51C11⋊#95—26no—
52C11⋊#95—26no—
53C11⋊#95—26no—
54#23470—111nomaximal, Sylow
55C24×C11C2411yescharacteristic
56C2×Q8×C11—22no—
57C22×C4×C11—23no—
58C22×C4×C11—23no—
59C22×C4×C11—23no—
60C22×C4×C11C2×D416yes—
61C22×C4×C11C2×Q812yes—
62C22×Dic11—23no—
63C22×Dic11—23no—
64C22×Dic11—23no—
65C22×Dic11C2×D416yes—
66C22×Dic11C2×D413yes—
67C22×Dic11C2×D413yes—
68C22×Dic11C2×Q812yes—
69C22×Dic11C2×Q812yes—
70C22×Dic11#4116yes—
71C2×Dic22—212no—
72C2×Dic22—212no—
73C2×Dic22—26no—
74C2×Dic22—41no—
75C2×Dic22—43no—
76C2×Dic22—46no—
77C2×Dic22—46no—
78C11×C4⋊C4—26no—
79C11×C22⋊C4—26no—
80C11×C22⋊C4—26no—
81C22⋊Dic11—26no—
82C22⋊Dic11—26no—
83C4⋊Dic11—26no—
84Dic11⋊C4—212no—
85Dic11⋊C4—212no—
86Dic11⋊C4—46no—
87C4×Dic11—26no—
88C4×Dic11—26no—
89C4×Dic11—46no—
90#3458—111no—
91#2310—113no—
92#2030—113no—
93#2030—113no—
94#2030—111no—
95#2030D1111yescharacteristic
96#1740—113no—
97C23×C11—42no—
98C23×C11C22×D413yes—
99C23×C11C22×Q811yescharacteristic
100C23×C11C2×#4113yes—
101Q8×C11—82no—
102C2×C4×C11—26no—
103C2×C4×C11—26no—
104C2×C4×C11—41no—
105C2×C4×C11—43no—
106C2×C4×C11—46no—
107C2×C4×C11—46no—
108C2×C4×C11—43no—
109C2×Dic11—26no—
110C2×Dic11—26no—
111C2×Dic11—41no—
112C2×Dic11—43no—
113C2×Dic11—46no—
114C2×Dic11—46no—
115C2×Dic11—43no—
116C2×Dic11#12011yescharacteristic
117C2×Dic11#12013yes—
118C2×Dic11C22⋊Q816yes—
119C2×Dic11C22⋊Q816yes—
120C2×Dic11#12416yes—
121C2×Dic11#12416yes—
122Dic22—44no—
123Dic22—412no—
124Dic22—86no—
125C23×Q8—111no—
126#544—226no—
127#543—113no—
128#543C2×D1111yescharacteristic
129#533—226no—
130C2×#117—113no—
131C2×#117—113no—
132#391—226no—
133#391—226no—
134#381—113no—
135#381—113no—
136#381—113no—
137#381C2×D1113yes—
138#342—113no—
139#342—116no—
140#342C2×D1113yes—
141C22×C11—26no—
142C22×C11—41no—
143C22×C11—43no—
144C22×C11C2×#12011yescharacteristic
145C22×C11C2×C22⋊Q813yes—
146C22×C11C2×#12413yes—
147C4×C11—42no—
148C4×C11—46no—
149C4×C11—83no—
150Dic11—42no—
151Dic11—46no—
152Dic11—83no—
153Dic11#39312yes—
154Dic11#39316yes—
155C22×Q8—114no—
156C22×Q8—223no—
157C22×Q8—223no—
158C22×Q8—226no—
159C23×C4—111no—
160C23×C4—111no—
161C23×C4C22×D1111yescharacteristic
162C4⋊Q8—226no—
163C4⋊Q8—226no—
164#125—2212no—
165C22⋊Q8—26no—
166C22⋊Q8—2212no—
167C22⋊Q8—226no—
168C4×Q8—226no—
169C4×Q8—222no—
170#117—226no—
171#117—226no—
172#117—2212no—
173C2×C4⋊C4—116no—
174C2×C4⋊C4—223no—
175C2×C22⋊C4—113no—
176C2×C22⋊C4—113no—
177C2×C22⋊C4C22×D1113yes—
178C2×C22⋊C4C22×D1113yes—
179C2×C42—116no—
180C2×C42—223no—
181#95—26no—
182#95—226no—
183#95—226no—
184#95—226no—
185C2×C11—23no—
186C2×C11—23no—
187C2×C11C2×#39311yescharacteristic
188C2×C11#302812yes—
189C24C23×D1111yescharacteristic
190C2×Q8—22no—
191C2×Q8—2212no—
192C2×Q8—2212no—
193C2×Q8—226no—
194C2×Q8—441no—
195C2×Q8—443no—
196C2×Q8—446no—
197C2×Q8—446no—
198C22×C4—23no—
199C22×C4—23no—
200C22×C4—23no—
201C22×C4—113no—
202C22×C4—113no—
203C22×C4—112no—
204C22×C4—116no—
205C22×C4—112no—
206C22×C4—116no—
207C22×C4—223no—
208C22×C4—223no—
209C22×C4—223no—
210C22×C4D4×D1116yes—
211C22×C4Q8×D1112yes—
212C4⋊C4—26no—
213C4⋊C4—2212no—
214C4⋊C4—2212no—
215C4⋊C4—226no—
216C4⋊C4—446no—
217C22⋊C4—26no—
218C22⋊C4—26no—
219C22⋊C4—226no—
220C22⋊C4—226no—
221C42—226no—
222C42—226no—
223C42—446no—
224C11#2347011yescharacteristic, complemented, Sylow
225C23—42no—
226C23C2×D4×D1113yes—
227C23C2×Q8×D1111yescharacteristic
228C23#41×D1113yes—
229Q8—82no—
230Q8—444no—
231Q8—4412no—
232Q8—886no—
233C2×C4—26no—
234C2×C4—26no—
235C2×C4—41no—
236C2×C4—43no—
237C2×C4—46no—
238C2×C4—46no—
239C2×C4—43no—
240C2×C4—111no—
241C2×C4—113no—
242C2×C4—116no—
243C2×C4—116no—
244C2×C4—116no—
245C2×C4—116no—
246C2×C4—226no—
247C2×C4—226no—
248C2×C4—441no—
249C2×C4—443no—
250C2×C4—446no—
251C2×C4—446no—
252C2×C4—443no—
253C22—26no—
254C22—41no—
255C22—43no—
256C22D11×#12011yescharacteristic
257C22D11×C22⋊Q813yes—
258C22D11×#12413yes—
259C4—46no—
260C4—42no—
261C4—83no—
262C4—112no—
263C4—116no—
264C4—446no—
265C4—442no—
266C4—883no—
267C2—23no—
268C2—23no—
269C2D11×#39311yescharacteristic
270C2#1307802012yes—
subgroupG/H
centerC22D11×#120
commutator, prime radical, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2030C2
socleC22×C11C2×#120
hypercenter#2030D11
hypocenterC11#23470
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
30. C22×Dic22Q8semidirect
224. C11#23470semidirect

Maximal subgroups

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

subgroupindex
#130820182
#130712012
#130697842
#130697832
#130697822
#130683472
C11×#20302
#2347011