Finite Group Databasebeta

← #14683837

Subgroups — #14683837

Order 2816.

2498 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C216yesmaximal, complemented
2#13066878C212yesmaximal, complemented
3#13066861C213yesmaximal, complemented
4#13066838C213yesmaximal, complemented
5C2×C11×#392C211yesmaximal, characteristic
6C23×D4×C11C2213yes—
7C24×Dic11C2213yes—
8C22×C11×C22⋊C4C2213yes—
9C22×C22⋊Dic11C2216yes—
10C22×C22⋊Dic11C2213yes—
11C22×C4⋊Dic11C2211yescharacteristic
12C11×#392C418yescomplemented
13C2×C11×#95C2211yescharacteristic
14#10622833—224no—
15C2×C11⋊#95C2216yes—
16C2×C11⋊#95C2216yes—
17C2×C11⋊#95C2213yes—
18C25×C11C2313yes—
19C22×D4×C11—212no—
20C22×D4×C11—212no—
21C22×D4×C11—43no—
22C22×D4×C11—43no—
23C22×D4×C11C2×C4112yescomplemented
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×Dic11—26no—
27C23×Dic11—212no—
28C23×Dic11—46no—
29C23×Dic11—43no—
30C23×Dic11—43no—
31C23×Dic11C2312yes—
32C23×Dic11C2316yes—
33C2×C11×C22⋊C4—43no—
34C2×C11×C22⋊C4—43no—
35C2×C11×C22⋊C4C2×C4112yescomplemented
36C2×C22⋊Dic11—212no—
37C2×C22⋊Dic11—212no—
38C2×C22⋊Dic11—43no—
39C2×C22⋊Dic11—43no—
40C2×C22⋊Dic11—46no—
41C2×C22⋊Dic11D4112yescomplemented
42C2×C4⋊Dic11—43no—
43C11×#95C2×C414yescomplemented
44C11⋊#95—212no—
45C11⋊#95—212no—
46C11⋊#95—43no—
47#14572—111nomaximal, Sylow
48C24×C11—26no—
49C24×C11—26no—
50C24×C11—23no—
51C24×C11—23no—
52C24×C11—26no—
53C24×C11—23no—
54C24×C11—26no—
55C24×C11—23no—
56C24×C11C22×C416yes—
57C24×C11C2×D416yes—
58C24×C11#4116yes—
59C24×C11C2411yescharacteristic
60C2×D4×C11—248no—
61C2×D4×C11—412no—
62C2×D4×C11—412no—
63C2×D4×C11—424no—
64C2×D4×C11—412no—
65C22×C4×C11—26no—
66C22×C4×C11—26no—
67C22×C4×C11—23no—
68C22×C4×C11—23no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11C22×C416yes—
72C22×C4×C11C22×C412yes—
73C22×Dic11—26no—
74C22×Dic11—26no—
75C22×Dic11—26no—
76C22×Dic11—26no—
77C22×Dic11—26no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—26no—
81C22×Dic11—22no—
82C22×Dic11—424no—
83C22×Dic11—412no—
84C22×Dic11—412no—
85C22×Dic11—424no—
86C22×Dic11—412no—
87C22×Dic11C2×D4112yes—
88C11×C22⋊C4—412no—
89C22⋊Dic11—412no—
90C22⋊Dic11—424no—
91C4⋊Dic11—44no—
92C2×#392D1111yescharacteristic
93C2×#386—116no—
94#1443—112no—
95#1439—113no—
96C22⋊#95—113no—
97C23×C11—212no—
98C23×C11—26no—
99C23×C11—212no—
100C23×C11—26no—
101C23×C11—26no—
102C23×C11—26no—
103C23×C11—26no—
104C23×C11—26no—
105C23×C11—212no—
106C23×C11—212no—
107C23×C11—212no—
108C23×C11—212no—
109C23×C11—46no—
110C23×C11—46no—
111C23×C11—46no—
112C23×C11—46no—
113C23×C11—43no—
114C23×C11—46no—
115C23×C11—43no—
116C23×C11—43no—
117C23×C11—46no—
118C23×C11—43no—
119C23×C11C4×D4112yes—
120C23×C11C23×C411yescharacteristic
121C23×C11C22×D413yes—
122C23×C11C2×#4113yes—
123C23×C11H(5,𝔽2)13yes—
124C23×C11H(5,𝔽2)13yes—
125C23×C11H(5,𝔽2)11yescharacteristic
126C23×C112−1+411yescharacteristic
127D4×C11—448no—
128C2×C4×C11—212no—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—43no—
132C2×C4×C11—46no—
133C2×C4×C11—43no—
134C2×C4×C11—41no—
135C2×C4×C11—43no—
136C2×Dic11—212no—
137C2×Dic11—212no—
138C2×Dic11—212no—
139C2×Dic11—448no—
140C2×Dic11—46no—
141C2×Dic11—46no—
142C2×Dic11—46no—
143C2×Dic11—46no—
144C2×Dic11—46no—
145C2×Dic11—46no—
146C2×Dic11—42no—
147C23×D4C2×D1113yes—
148C24×C4—113no—
149C22×C4⋊C4—111no—
150C22×C22⋊C4—113no—
151C22×C22⋊C4—116no—
152C22×C22⋊C4C2×D1113yes—
153#392Dic1118yescomplemented
154#386—2224no—
155C2×#95—116no—
156C2×#95—116no—
157C2×#95—113no—
158C2×#95C2×D1111yescharacteristic
159C22×C11—212no—
160C22×C11—224no—
161C22×C11—412no—
162C22×C11—46no—
163C22×C11—46no—
164C22×C11—412no—
165C22×C11—46no—
166C22×C11—46no—
167C22×C11—46no—
168C22×C11—412no—
169C22×C11—46no—
170C22×C11C2×C4×D413yes—
171C22×C11#51813yes—
172C22×C11#52011yescharacteristic
173C22×C11#53413yes—
174C22×C11#53713yes—
175C22×C11#53813yes—
176C22×C11#53913yes—
177C22×C11D4213yes—
178C22×C11#54616yes—
179C22×C11#55113yes—
180C22×C11#56013yes—
181C22×C11#56011yescharacteristic
182C4×C11—46no—
183C4×C11—42no—
184Dic11—412no—
185Dic11—82no—
186C25C22×D1113yes—
187C22×D4—212no—
188C22×D4—212no—
189C22×D4—43no—
190C22×D4—43no—
191C22×D4C2×Dic11112yescomplemented
192C23×C4—116no—
193C23×C4—112no—
194C23×C4—2212no—
195C23×C4—226no—
196C23×C4—446no—
197C23×C4—443no—
198C23×C4—443no—
199C23×C4C22×D1111yescharacteristic
200C23×C4C22×D1113yes—
201C2×C4⋊C4—443no—
202C2×C22⋊C4—43no—
203C2×C22⋊C4—43no—
204C2×C22⋊C4—1112no—
205C2×C22⋊C4—2212no—
206C2×C22⋊C4—2212no—
207C2×C22⋊C4—443no—
208C2×C22⋊C4—443no—
209C2×C22⋊C4—446no—
210C2×C22⋊C4C2×Dic11112yescomplemented
211#95—2212no—
212#95—2212no—
213#95—443no—
214#95C2×Dic1114yescomplemented
215C2×C11—412no—
216C2×C11#232513yes—
217C2×C11#235813yes—
218C2×C11#238011yescharacteristic
219C2×C11#266813yes—
220C2×C11#267511yescharacteristic
221C2×C11#269313yes—
222C2×C11#276011yescharacteristic
223C24—26no—
224C24—26no—
225C24—23no—
226C24—23no—
227C24—26no—
228C24—26no—
229C24—23no—
230C24—23no—
231C24D4×D1116yes—
232C24#434116yes—
233C24C22×Dic1116yes—
234C24C23×D1111yescharacteristic
235C2×D4—248no—
236C2×D4—412no—
237C2×D4—412no—
238C2×D4—412no—
239C2×D4—424no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—1112no—
247C22×C4—226no—
248C22×C4—226no—
249C22×C4—226no—
250C22×C4—226no—
251C22×C4—226no—
252C22×C4—226no—
253C22×C4—226no—
254C22×C4—226no—
255C22×C4—222no—
256C22×C4—4412no—
257C22×C4—4424no—
258C22×C4—4424no—
259C22×C4—4412no—
260C22×C4—4412no—
261C22×C4C22×Dic1116yes—
262C22×C4C22×Dic1112yes—
263C4⋊C4—444no—
264C22⋊C4—412no—
265C22⋊C4—4412no—
266C22⋊C4—4424no—
267C11#1457211yescharacteristic, complemented, Sylow
268C23—212no—
269C23—26no—
270C23—212no—
271C23—26no—
272C23—212no—
273C23—212no—
274C23—212no—
275C23—212no—
276C23—26no—
277C23—26no—
278C23—26no—
279C23—26no—
280C23—43no—
281C23—43no—
282C23—46no—
283C23—43no—
284C23—43no—
285C23—46no—
286C23—46no—
287C23—46no—
288C23—46no—
289C23—46no—
290C23D4×Dic11112yes—
291C23C2×D4×D1113yes—
292C23C2×#434113yes—
293C23#6703713yes—
294C23#6703713yes—
295C23#6704211yescharacteristic
296C23#6704311yescharacteristic
297C23C23×Dic1111yescharacteristic
298D4—448no—
299C2×C4—212no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—41no—
303C2×C4—43no—
304C2×C4—43no—
305C2×C4—43no—
306C2×C4—46no—
307C2×C4—2212no—
308C2×C4—2212no—
309C2×C4—2212no—
310C2×C4—4448no—
311C2×C4—446no—
312C2×C4—446no—
313C2×C4—446no—
314C2×C4—446no—
315C2×C4—442no—
316C2×C4—446no—
317C2×C4—446no—
318C22—212no—
319C22—224no—
320C22—46no—
321C22—46no—
322C22—412no—
323C22—46no—
324C22—412no—
325C22—46no—
326C22—412no—
327C22—46no—
328C22—46no—
329C22#1062311813yes—
330C22#1062312113yes—
331C22#1062312216yes—
332C22#1062312813yes—
333C22#1062313313yes—
334C22#1062313613yes—
335C22#1062314813yes—
336C22#1062325111yescharacteristic
337C22#1062325113yes—
338C22C2×D4×Dic1113yes—
339C22#1062332913yes—
340C22#1062335811yescharacteristic
341C4—42no—
342C4—46no—
343C4—4412no—
344C4—882no—
345C2—412no—
346C2#1307132113yes—
347C2#1307160013yes—
348C2#1307179311yescharacteristic
349C2#1307481813yes—
350C2#1307490511yescharacteristic
351C2#1307512413yes—
352C2#1307599511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14572
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10622833C2semidirect
2. #13066878C2semidirect
3. #13066861C2semidirect
4. #13066838C2semidirect
12. C11×#392C4semidirect
23. C22×D4×C11C2×C4semidirect
35. C2×C11×C22⋊C4C2×C4semidirect
41. C2×C22⋊Dic11D4semidirect
43. C11×#95C2×C4semidirect
153. #392Dic11semidirect
191. C22×D4C2×Dic11semidirect
210. C2×C22⋊C4C2×Dic11semidirect
214. #95C2×Dic11semidirect
267. C11#14572semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
#130668782
#130668612
#130668382
C2×C11×#3922
#1457211