Finite Group Databasebeta

← #14684776

Subgroups — #14684776

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622842C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic
3#13066882C213yesmaximal
4#13066877C213yesmaximal
5#13066876C213yesmaximal
6#13066847C213yesmaximal
7C11×#1446C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×Dic11⋊C4C2213yes—
10C22×C4×Dic11C2211yescharacteristic
11C2×C11×#95C2213yes—
12C2×C11×#95C2213yes—
13#10622842C418yescomplemented
14C2×C11⋊#95C2213yes—
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C22×Q8×C11—43no—
23C22×Q8×C11—43no—
24C22×Q8×C11C2×C414yes—
25C23×C4×C11C2313yes—
26C23×C4×C11C2313yes—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11C2313yes—
29C23×Dic11C2311yescharacteristic
30C23×Dic11C2313yes—
31C23×Dic11C2311yescharacteristic
32C2×Dic11⋊C4—43no—
33C2×Dic11⋊C4—43no—
34C2×Dic11⋊C4C2×C4112yes—
35C2×C4×Dic11—43no—
36C11×#95—43no—
37C11×#95—43no—
38C11⋊#95—26no—
39C11⋊#95—26no—
40C11⋊#95—43no—
41C11⋊#95—43no—
42C11⋊#95—43no—
43C11⋊#95—43no—
44C11⋊#95—43no—
45C11⋊#95C2×C4112yes—
46#14655—111nomaximal, Sylow
47C24×C11C2411yescharacteristic
48C2×Q8×C11—412no—
49C2×Q8×C11—412no—
50C2×Q8×C11—44no—
51C22×C4×C11—23no—
52C22×C4×C11—23no—
53C22×C4×C11—23no—
54C22×C4×C11—23no—
55C22×C4×C11—23no—
56C22×C4×C11—23no—
57C22×C4×C11—23no—
58C22×C4×C11—23no—
59C22×C4×C11—23no—
60C22×C4×C11—23no—
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11C22×C416yes—
67C22×C4×C11#4112yes—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11—23no—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11—23no—
84C22×Dic11—23no—
85C22×Dic11C22×C416yes—
86C22×Dic11C22×C412yes—
87C22×Dic11#4112yes—
88Dic11⋊C4—412no—
89C4×Dic11—44no—
90C2×#395—111no—
91#1446—111no—
92#1446D1111yescharacteristic
93#1445—113no—
94#1443—113no—
95#1443—113no—
96#1436—113no—
97C23×C11C23×C411yescharacteristic
98C23×C11C2×#4111yescharacteristic
99C23×C11C2×#4111yescharacteristic
100C23×C11H(5,𝔽2)13yes—
101C23×C11H(5,𝔽2)13yes—
102C23×C112−1+413yes—
103C23×C112−1+413yes—
104Q8×C11—416no—
105C2×C4×C11—26no—
106C2×C4×C11—26no—
107C2×C4×C11—26no—
108C2×C4×C11—26no—
109C2×C4×C11—43no—
110C2×C4×C11—43no—
111C2×C4×C11—43no—
112C2×C4×C11—41no—
113C2×C4×C11—43no—
114C2×C4×C11—43no—
115C2×C4×C11—43no—
116C2×C4×C11—43no—
117C2×C4×C11—43no—
118C2×C4×C11—43no—
119C2×C4×C11—43no—
120C2×C4×C11—43no—
121C2×C4×C11—43no—
122C2×Dic11—26no—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—26no—
126C2×Dic11—26no—
127C2×Dic11—43no—
128C2×Dic11—43no—
129C2×Dic11—43no—
130C2×Dic11—43no—
131C2×Dic11—43no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—43no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—43no—
138C2×Dic11—43no—
139C2×Dic11—43no—
140C2×Dic11—43no—
141C2×Dic11—43no—
142C23×Q8C2×D1111yescharacteristic
143C22×C4⋊C4—113no—
144C22×C42—111no—
145#395—118no—
146C2×#95—113no—
147C2×#95—113no—
148C2×#95—113no—
149C2×#95—113no—
150C2×#95—113no—
151C2×#95—113no—
152C2×#95—113no—
153C2×#95—113no—
154C2×#95C2×D1113yes—
155C2×#95C2×D1113yes—
156C22×C11C4×#4111yescharacteristic
157C22×C11#51813yes—
158C22×C11#51913yes—
159C22×C11#53913yes—
160C22×C11#53913yes—
161C22×C11#54213yes—
162C22×C11#54213yes—
163C22×C11#56013yes—
164C22×C11H(3,𝔽4)11yescharacteristic
165C22×C11#56313yes—
166C22×C11#56313yes—
167C22×C11#56313yes—
168C22×C11#56313yes—
169C4×C11—42no—
170C4×C11—46no—
171C4×C11—83no—
172Dic11—42no—
173Dic11—46no—
174Dic11—42no—
175Dic11—83no—
176C22×Q8—43no—
177C22×Q8—43no—
178C22×Q8C4×D1114yes—
179C23×C4—111no—
180C23×C4—113no—
181C23×C4—111no—
182C23×C4—113no—
183C23×C4C22×D1113yes—
184C23×C4C22×D1113yes—
185C23×C4C22×D1111yescharacteristic
186C2×C4⋊C4—1112no—
187C2×C4⋊C4—443no—
188C2×C4⋊C4—443no—
189C2×C42—443no—
190#95—43no—
191#95—43no—
192#95—1112no—
193#95—226no—
194#95—226no—
195#95—443no—
196#95—443no—
197#95—443no—
198#95—443no—
199#95—443no—
200C2×C11#233213yes—
201C2×C11#237511yescharacteristic
202C2×C11#238113yes—
203C2×C11#283511yescharacteristic
204C2×C11#283511yescharacteristic
205C2×C11#283813yes—
206C2×C11#283813yes—
207C24C23×D1111yescharacteristic
208C2×Q8—412no—
209C2×Q8—44no—
210C2×Q8—412no—
211C22×C4—23no—
212C22×C4—23no—
213C22×C4—23no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—23no—
221C22×C4—23no—
222C22×C4—23no—
223C22×C4—23no—
224C22×C4—23no—
225C22×C4—23no—
226C22×C4—116no—
227C22×C4—112no—
228C22×C4—112no—
229C22×C4—223no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—223no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—223no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—223no—
239C22×C4—223no—
240C22×C4—223no—
241C22×C4—223no—
242C22×C4—223no—
243C22×C4—223no—
244C22×C4—223no—
245C22×C4—223no—
246C22×C4C2×C4×D1116yes—
247C22×C4#434312yes—
248C4⋊C4—4412no—
249C42—444no—
250C11#1465511yescharacteristic, complemented, Sylow
251C23C22×C4×D1111yescharacteristic
252C23#6703713yes—
253C23#6703713yes—
254C23C2×#434311yescharacteristic
255C23#6704013yes—
256C23#41×D1111yescharacteristic
257C23#6704313yes—
258Q8—416no—
259C2×C4—26no—
260C2×C4—26no—
261C2×C4—26no—
262C2×C4—26no—
263C2×C4—41no—
264C2×C4—43no—
265C2×C4—43no—
266C2×C4—43no—
267C2×C4—43no—
268C2×C4—43no—
269C2×C4—43no—
270C2×C4—43no—
271C2×C4—43no—
272C2×C4—43no—
273C2×C4—43no—
274C2×C4—43no—
275C2×C4—43no—
276C2×C4—226no—
277C2×C4—226no—
278C2×C4—226no—
279C2×C4—226no—
280C2×C4—226no—
281C2×C4—443no—
282C2×C4—443no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—443no—
286C2×C4—443no—
287C2×C4—443no—
288C2×C4—443no—
289C2×C4—443no—
290C2×C4—443no—
291C2×C4—443no—
292C2×C4—443no—
293C2×C4—443no—
294C2×C4—443no—
295C2×C4—443no—
296C22#1062301713yes—
297C22#1062310313yes—
298C22C4×#434311yescharacteristic
299C22#1062312511yescharacteristic
300C22#1062312613yes—
301C22#1062316913yes—
302C22#1062317613yes—
303C22#1062317713yes—
304C22#1062317713yes—
305C22#1062320013yes—
306C22#1062320313yes—
307C22#1062326413yes—
308C22#1062326613yes—
309C4—42no—
310C4—46no—
311C4—83no—
312C4—446no—
313C4—442no—
314C4—442no—
315C4—883no—
316C2#1307137113yes—
317C2#1307175511yescharacteristic
318C2#1307179513yes—
319C2#1307680511yescharacteristic
320C2#1307680711yescharacteristic
321C2#1307685013yes—
322C2#1307685113yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1446D11
hypocenterC11#14655
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
13. #10622842C4semidirect
250. C11#14655semidirect

Maximal subgroups

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

subgroupindex
C2×#106228422
#130668872
#130668822
#130668772
#130668762
#130668472
C11×#14462
#1465511