Finite Group Databasebeta

← #14684816

Subgroups — #14684816

Order 2816.

1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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
1C22×#66989C211yesmaximal, characteristic
2C2×#10622263C212yesmaximal, complemented
3#13066886C212yesmaximal, complemented
4#13066859C218yesmaximal, complemented
5#13066857C211yesmaximal, characteristic
6C11×#1438C211yesmaximal, characteristic
7C23×D4×C11C2211yescharacteristic
8C23×Dic22C2211yescharacteristic
9C22×C11×C22⋊C4C2214yes—
10C22×C22⋊Dic11C2214yes—
11C22×C22⋊Dic11C2214yes—
12C2×#66989—28no—
13C2×#66989C418yescomplemented
14C22×Dic11⋊C4C2214yes—
15C22×C4×Dic11C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2218yes—
20#10622263—28no—
21C25×C11C2312yes—
22C22×D4×C11—24no—
23C22×D4×C11—44no—
24C22×D4×C11C2×C414yes—
25C23×C4×C11C2314yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2314yes—
28C23×Dic11C2312yes—
29C23×Dic11C2312yes—
30C22×Dic22—24no—
31C22×Dic22—44no—
32C22×Dic22C2×C414yes—
33C2×C11×C22⋊C4—44no—
34C2×C11×C22⋊C4—48no—
35C2×C22⋊Dic11—28no—
36C2×C22⋊Dic11—28no—
37C2×C22⋊Dic11—44no—
38C2×C22⋊Dic11—48no—
39C2×C22⋊Dic11C2×C4116yes—
40#66989—232no—
41C2×Dic11⋊C4—28no—
42C2×Dic11⋊C4—48no—
43C2×C4×Dic11C2×C414yes—
44C2×C4×Dic11D418yes—
45C11×#95—24no—
46C11⋊#95—24no—
47C11⋊#95—28no—
48C11⋊#95—48no—
49#14662—111nomaximal, Sylow
50C24×C11—24no—
51C24×C11—28no—
52C24×C11—24no—
53C24×C11—24no—
54C24×C11—28no—
55C24×C11C22×C414yes—
56C24×C11C2411yescharacteristic
57C2×D4×C11—28no—
58C2×D4×C11—48no—
59C2×D4×C11—416no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—28no—
63C22×C4×C11—28no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C2×D414yes—
68C22×Dic11—24no—
69C22×Dic11—24no—
70C22×Dic11—24no—
71C22×Dic11—28no—
72C22×Dic11—28no—
73C22×Dic11—28no—
74C22×Dic11—24no—
75C22×Dic11—24no—
76C22×Dic11—24no—
77C22×Dic11C22×C414yes—
78C22×Dic11C22×C414yes—
79C22×Dic11C2×D414yes—
80C22×Dic11C2×D414yes—
81C2×Dic22—28no—
82C2×Dic22—48no—
83C2×Dic22—416no—
84C11×C22⋊C4—416no—
85C22⋊Dic11—232no—
86C22⋊Dic11—416no—
87Dic11⋊C4—416no—
88C4×Dic11C22⋊C4116yescomplemented
89C22×#124—111no—
90C2×#382—112no—
91#1446—112no—
92#1439—118no—
93#1438—111no—
94#1438D1111yescharacteristic
95C23×C11—24no—
96C23×C11—24no—
97C23×C11—24no—
98C23×C11—216no—
99C23×C11—48no—
100C23×C11—44no—
101C23×C11—44no—
102C23×C11—48no—
103C23×C11—44no—
104C23×C11—44no—
105C23×C11—48no—
106C23×C11—48no—
107C23×C11—44no—
108C23×C11—44no—
109C23×C11C23×C411yescharacteristic
110C23×C11C22×D412yes—
111C23×C11H(5,𝔽2)14yes—
112C23×C11H(5,𝔽2)14yes—
113C23×C112−1+414yes—
114D4×C11—416no—
115C2×C4×C11—24no—
116C2×C4×C11—28no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—48no—
121C2×C4×C11—48no—
122C2×C4×C11C2×C22⋊C414yes—
123C2×Dic11—28no—
124C2×Dic11—24no—
125C2×Dic11—24no—
126C2×Dic11—28no—
127C2×Dic11—24no—
128C2×Dic11—28no—
129C2×Dic11—48no—
130C2×Dic11—44no—
131C2×Dic11—44no—
132C2×Dic11—44no—
133C2×Dic11—48no—
134C2×Dic11—48no—
135C2×Dic11C2×C22⋊C418yes—
136Dic22—416no—
137C23×Q8—111no—
138C23×D4C2×D1111yescharacteristic
139C2×#124—118no—
140C2×#124—228no—
141C22×C4⋊C4—114no—
142C22×C22⋊C4—114no—
143C22×C22⋊C4—114no—
144C22×C22⋊C4C2×D1114yes—
145C22×C42—111no—
146#382—228no—
147C2×#95—112no—
148C2×#95—114no—
149C2×#95—118no—
150C2×#95C2×D1112yes—
151C22×C11—44no—
152C22×C11—48no—
153C22×C11—48no—
154C22×C11—48no—
155C22×C11—88no—
156C22×C11—88no—
157C22×C11C22×C22⋊C411yescharacteristic
158C22×C11#51812yes—
159C22×C11#52014yes—
160C22×C11#53512yes—
161C22×C11#53514yes—
162C22×C11#53612yes—
163C22×C11#53714yes—
164C22×C11H(3,𝔽4)14yes—
165C22×C11#56218yes—
166C22×C11#56314yes—
167C4×C11—24no—
168C4×C11—84no—
169Dic11—28no—
170Dic11—44no—
171Dic11—84no—
172C25C22×D1112yes—
173C22×Q8—114no—
174C22×Q8—224no—
175C22×Q8—444no—
176C22×D4—24no—
177C22×D4—44no—
178C22×D4C4×D1114yes—
179C23×C4—112no—
180C23×C4—112no—
181C23×C4—114no—
182C23×C4C22×D1114yes—
183C23×C4C22×D1111yescharacteristic
184#124—2232no—
185C2×C4⋊C4—228no—
186C2×C4⋊C4—448no—
187C2×C22⋊C4—44no—
188C2×C22⋊C4—48no—
189C2×C22⋊C4—1116no—
190C2×C22⋊C4—228no—
191C2×C22⋊C4—228no—
192C2×C22⋊C4—444no—
193C2×C22⋊C4—448no—
194C2×C42—114no—
195C2×C42—118no—
196#95—24no—
197#95—228no—
198#95—224no—
199#95—448no—
200C2×C11—84no—
201C2×C11#230911yescharacteristic
202C2×C11#231112yes—
203C2×C11#237914yes—
204C2×C11#281914yes—
205C2×C11#282014yes—
206C24—24no—
207C24—28no—
208C24—24no—
209C24—24no—
210C24—28no—
211C24C2×C4×D1114yes—
212C24C23×D1111yescharacteristic
213C2×Q8—228no—
214C2×Q8—448no—
215C2×Q8—4416no—
216C2×D4—28no—
217C2×D4—48no—
218C2×D4—416no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—24no—
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—114no—
226C22×C4—114no—
227C22×C4—114no—
228C22×C4—114no—
229C22×C4—224no—
230C22×C4—224no—
231C22×C4—224no—
232C22×C4—228no—
233C22×C4—224no—
234C22×C4—228no—
235C22×C4—224no—
236C22×C4—228no—
237C22×C4—224no—
238C22×C4C2×C4×D1112yes—
239C22×C4D4×D1114yes—
240C4⋊C4—4416no—
241C22⋊C4—416no—
242C22⋊C4—2232no—
243C22⋊C4—4416no—
244C42—1116no—
245C11#1466211yescharacteristic, complemented, Sylow
246C23—24no—
247C23—24no—
248C23—24no—
249C23—216no—
250C23—44no—
251C23—48no—
252C23—44no—
253C23—44no—
254C23—48no—
255C23—48no—
256C23—48no—
257C23—44no—
258C23—44no—
259C23—44no—
260C23C22×C4×D1111yescharacteristic
261C23C2×D4×D1112yes—
262C23#6703714yes—
263C23#6703714yes—
264C23#6704314yes—
265Q8—4416no—
266D4—416no—
267C2×C4—24no—
268C2×C4—28no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—48no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—118no—
275C2×C4—224no—
276C2×C4—228no—
277C2×C4—228no—
278C2×C4—224no—
279C2×C4—224no—
280C2×C4—228no—
281C2×C4—448no—
282C2×C4—444no—
283C2×C4—444no—
284C2×C4—448no—
285C2×C4—444no—
286C2×C4—448no—
287C2×C4C22⋊C4×D1114yes—
288C22—44no—
289C22—48no—
290C22—48no—
291C22—48no—
292C22—88no—
293C22—88no—
294C22C2×C22⋊C4×D1111yescharacteristic
295C22#1062301712yes—
296C22#1062307714yes—
297C22#1062312314yes—
298C22#1062312514yes—
299C22#1062313914yes—
300C22#1062315218yes—
301C22#1062318214yes—
302C22#1062320612yes—
303C22#1062324612yes—
304C4—24no—
305C4—84no—
306C4—228no—
307C4—444no—
308C4—884no—
309C2—84no—
310C2#1307119711yescharacteristic
311C2#1307120612yes—
312C2#1307178614yes—
313C2#1307666314yes—
314C2#1307666914yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. #13066886C2semidirect
4. #13066859C2semidirect
13. C2×#66989C4semidirect
88. C4×Dic11C22⋊C4semidirect
245. C11#14662semidirect

Maximal subgroups

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

subgroupindex
C22×#669892
C2×#106222632
#130668862
#130668592
#130668572
C11×#14382
#1466211