Finite Group Databasebeta

← #14684793

Subgroups — #14684793

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C212yesmaximal, complemented
2#13066869C214yesmaximal, complemented
3#13066865C212yesmaximal, complemented
4#13066861C214yesmaximal, complemented
5#13066857C212yesmaximal
6C22×C11×#123C211yesmaximal, characteristic
7C23×D4×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C2×C11×#123—28no—
10C2×C11×#123C418yescomplemented
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2214yes—
15C22×C22⋊Dic11C2214yes—
16C22×C4⋊Dic11C2214yes—
17#10622825—28no—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2218yes—
21C25×C11C2311yescharacteristic
22C25×C11C2311yescharacteristic
23C22×D4×C11—24no—
24C22×D4×C11—44no—
25C22×D4×C11C2×C414yes—
26C23×C4×C11—44no—
27C23×C4×C11C2×C414yes—
28C23×C4×C11D418yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2312yes—
32C23×Dic11C2318yes—
33C11×#123—232no—
34C2×C11×C4⋊C4—24no—
35C2×C11×C4⋊C4—24no—
36C2×C11×C4⋊C4C2×C418yes—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4—24no—
39C2×C11×C22⋊C4—24no—
40C2×C11×C22⋊C4C2×C414yes—
41C2×C11×C22⋊C4C2×C418yes—
42C2×C22⋊Dic11—28no—
43C2×C22⋊Dic11—48no—
44C2×C22⋊Dic11—48no—
45C2×C22⋊Dic11—44no—
46C2×C4⋊Dic11—28no—
47C2×C4⋊Dic11—48no—
48C11⋊#95—28no—
49C11⋊#95—44no—
50C11⋊#95—48no—
51#14658—111nomaximal, Sylow
52C24×C11—24no—
53C24×C11—24no—
54C24×C11—24no—
55C24×C11—22no—
56C24×C11—24no—
57C24×C11—24no—
58C24×C11—24no—
59C24×C11C22×C412yes—
60C24×C11C22×C412yes—
61C24×C11C2×D414yes—
62C24×C11C2411yescharacteristic
63C2×D4×C11—28no—
64C2×D4×C11—48no—
65C2×D4×C11—416no—
66C22×C4×C11—28no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—48no—
74C22×C4×C11—416no—
75C22×C4×C11C22⋊C4116yescomplemented
76C22×C4×C11C22×C414yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×D414yes—
81C22×Dic11—28no—
82C22×Dic11—28no—
83C22×Dic11—28no—
84C22×Dic11—28no—
85C22×Dic11—28no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C11×C4⋊C4—216no—
89C11×C22⋊C4—28no—
90C11×C22⋊C4—216no—
91C22⋊Dic11—416no—
92C22⋊Dic11—416no—
93C4⋊Dic11—416no—
94C22×#123D1111yescharacteristic
95C2×#380—112no—
96#1441—114no—
97#1440—112no—
98#1439—114no—
99#1438—112no—
100C23×C11—24no—
101C23×C11—28no—
102C23×C11—28no—
103C23×C11—24no—
104C23×C11—24no—
105C23×C11—28no—
106C23×C11—22no—
107C23×C11—24no—
108C23×C11—28no—
109C23×C11—44no—
110C23×C11—48no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—44no—
116C23×C11—44no—
117C23×C11—48no—
118C23×C11—44no—
119C23×C11C2×C22⋊C414yes—
120C23×C11C23×C411yescharacteristic
121C23×C11C22×D412yes—
122C23×C11H(5,𝔽2)14yes—
123C23×C11H(5,𝔽2)14yes—
124C23×C112−1+414yes—
125D4×C11—416no—
126C2×C4×C11—28no—
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—28no—
133C2×C4×C11—416no—
134C2×C4×C11—44no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—44no—
138C2×C4×C11C2×C22⋊C418yes—
139C2×Dic11—48no—
140C2×Dic11—48no—
141C2×Dic11—48no—
142C2×Dic11—48no—
143C2×Dic11—48no—
144C2×Dic11—48no—
145C2×Dic11—48no—
146C23×D4C2×D1111yescharacteristic
147C24×C4C2×D1111yescharacteristic
148C2×#123—28no—
149C2×#123Dic1118yescomplemented
150C22×C4⋊C4—114no—
151C22×C4⋊C4C2×D1112yes—
152C22×C22⋊C4—114no—
153C22×C22⋊C4—114no—
154C22×C22⋊C4C2×D1112yes—
155C22×C22⋊C4C2×D1111yescharacteristic
156#380—228no—
157C2×#95—114no—
158C2×#95—114no—
159C2×#95—118no—
160C22×C11—24no—
161C22×C11—28no—
162C22×C11—48no—
163C22×C11—48no—
164C22×C11—48no—
165C22×C11—42no—
166C22×C11—44no—
167C22×C11—48no—
168C22×C11—84no—
169C22×C11—84no—
170C22×C11C22×C22⋊C411yescharacteristic
171C22×C11#51812yes—
172C22×C11#52014yes—
173C22×C11#53414yes—
174C22×C11#53512yes—
175C22×C11#53612yes—
176C22×C11#53714yes—
177C22×C11#56014yes—
178C22×C11#56218yes—
179C22×C11#56314yes—
180C4×C11—28no—
181C4×C11—42no—
182C4×C11—44no—
183Dic11—88no—
184C25C22×D1111yescharacteristic
185C25C22×D1111yescharacteristic
186C22×D4—24no—
187C22×D4—44no—
188C22×D4C2×Dic1114yes—
189C23×C4—44no—
190C23×C4—118no—
191C23×C4C2×Dic1114yes—
192C23×C4C22⋊D1118yes—
193C23×C4C22×D1112yes—
194C23×C4C22×D1111yescharacteristic
195C23×C4C22×D1112yes—
196#123—232no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—228no—
200C2×C4⋊C4—448no—
201C2×C4⋊C4C2×Dic1118yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—228no—
206C2×C22⋊C4—448no—
207C2×C22⋊C4—444no—
208C2×C22⋊C4—448no—
209C2×C22⋊C4C2×Dic1114yes—
210C2×C22⋊C4C2×Dic1118yes—
211#95—228no—
212#95—444no—
213#95—448no—
214C2×C11—44no—
215C2×C11—82no—
216C2×C11#230811yescharacteristic
217C2×C11#231112yes—
218C2×C11#237614yes—
219C2×C11#281314yes—
220C2×C11#281414yes—
221C24—24no—
222C24—24no—
223C24—24no—
224C24—24no—
225C24—24no—
226C24—24no—
227C24—22no—
228C24C22×Dic1112yes—
229C24C22×Dic1112yes—
230C24C2×C22⋊D1114yes—
231C24C23×D1111yescharacteristic
232C2×D4—28no—
233C2×D4—48no—
234C2×D4—416no—
235C22×C4—28no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—48no—
243C22×C4—416no—
244C22×C4—228no—
245C22×C4—228no—
246C22×C4—228no—
247C22×C4—228no—
248C22×C4—228no—
249C22×C4—228no—
250C22×C4—228no—
251C22×C4C22⋊Dic11116yescomplemented
252C22×C4C22×Dic1114yes—
253C22×C4C22×Dic1112yes—
254C22×C4C22×Dic1114yes—
255C22×C4C2×C22⋊D1114yes—
256C22×C4C2×C22⋊D1114yes—
257C4⋊C4—216no—
258C4⋊C4—4416no—
259C22⋊C4—28no—
260C22⋊C4—216no—
261C22⋊C4—4416no—
262C22⋊C4—4416no—
263C11#1465811yescharacteristic, complemented, Sylow
264C23—24no—
265C23—28no—
266C23—24no—
267C23—28no—
268C23—24no—
269C23—28no—
270C23—24no—
271C23—28no—
272C23—22no—
273C23—44no—
274C23—44no—
275C23—48no—
276C23—44no—
277C23—42no—
278C23—42no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23—48no—
283C23C2×C22⋊Dic1114yes—
284C23#6703714yes—
285C23#6704214yes—
286C23#6704314yes—
287C23C23×Dic1111yescharacteristic
288C23C22×C22⋊D1112yes—
289D4—416no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—24no—
294C2×C4—28no—
295C2×C4—24no—
296C2×C4—22no—
297C2×C4—416no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—448no—
303C2×C4—448no—
304C2×C4—448no—
305C2×C4—448no—
306C2×C4—448no—
307C2×C4—448no—
308C2×C4—448no—
309C2×C4C2×C22⋊Dic1118yes—
310C22—24no—
311C22—28no—
312C22—48no—
313C22—48no—
314C22—48no—
315C22—42no—
316C22—44no—
317C22—48no—
318C22—84no—
319C22—84no—
320C22#1062318214yes—
321C22#1062319714yes—
322C22#1062319818yes—
323C22#1062332912yes—
324C22#1062333514yes—
325C22#1062335612yes—
326C22#1062335814yes—
327C22#1062336112yes—
328C22#1062336414yes—
329C22C22×C22⋊Dic1111yescharacteristic
330C4—28no—
331C4—42no—
332C4—44no—
333C4—888no—
334C2—44no—
335C2—82no—
336C2#1307119411yescharacteristic
337C2#1307120812yes—
338C2#1307176414yes—
339C2#1307661814yes—
340C2#1307662914yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#14658
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10622825C2semidirect
2. #13066869C2semidirect
3. #13066865C2semidirect
4. #13066861C2semidirect
10. C2×C11×#123C4semidirect
75. C22×C4×C11C22⋊C4semidirect
149. C2×#123Dic11semidirect
251. C22×C4C22⋊Dic11semidirect
263. C11#14658semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130668692
#130668652
#130668612
#130668572
C22×C11×#1232
#1465811