Finite Group Databasebeta

← #14912020

Subgroups — #14912020

Order 2816.

3402 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C212yesmaximal
2C22×#66940C211yesmaximal, characteristic
3#13070980C218yesmaximal, complemented
4#13070973C211yesmaximal, characteristic
5#13070971C214yesmaximal
6C4×#66940C218yesmaximal, complemented
7#117×Dic11C212yesmaximal
8C4×#66930C214yesmaximal
9C11×#2274C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C2×C11×#117C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17#10623047C4132yescomplemented
18C2×#66940C4116yescomplemented
19C2×#66940C2214yes—
20C2×#66940C2214yes—
21C2×#66940C2218yes—
22C2×#66930C2218yes—
23C2×C4×Dic22C2218yes—
24C4×C11×C4⋊C4C2218yes—
25C4×C11×C22⋊C4C2214yes—
26C4×C22⋊Dic11C2214yes—
27C4⋊C4×Dic11C2214yes—
28C4⋊C4×Dic11C2214yes—
29C4⋊C4×Dic11C2218yes—
30C22⋊C4×Dic11C2214yes—
31C22⋊C4×Dic11C2214yes—
32#10622545C2214yes—
33C4×Dic11⋊C4C2218yes—
34C4×Dic11⋊C4C22116yes—
35C42×Dic11C2218yes—
36C42×Dic11C2214yes—
37#10622262C2218yes—
38#10622262C22116yes—
39#10622261C2218yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2312yes—
45C22×Dic22C2×C418yes—
46C22×Dic22C2×C4116yes—
47C22×Dic22C2314yes—
48C11×#117C2×C4116yes—
49C2×C11×C4⋊C4C2×C418yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C22⋊C4C2314yes—
53C2×C42×C11C2318yes—
54C2×C42×C11C2314yes—
55C2×C22⋊Dic11C2314yes—
56#66979C2×C4116yes—
57C2×C4⋊Dic11C2314yes—
58C2×Dic11⋊C4C2×C4116yes—
59C2×Dic11⋊C4C23116yes—
60C2×Dic11⋊C4C2318yes—
61C2×C4×Dic11C2×C418yes—
62C2×C4×Dic11C2×C4116yes—
63C2×C4×Dic11C2318yes—
64C2×C4×Dic11C2318yes—
65C2×C4×Dic11C2318yes—
66C2×C4×Dic11C23116yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C2314yes—
69C2×C4×Dic11C2312yes—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2312yes—
72#66940C2×C4132yes—
73#66940C2×C4132yes—
74#66940C2×C4164yescomplemented
75#66930C2×C4164yes—
76C4×Dic22C2×C4164yescomplemented
77C11×#95C2318yes—
78C11⋊#95C2318yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C4×#519—111nomaximal, Sylow
82C24×C11C2411yescharacteristic
83C22×C4×C11—44no—
84C22×C4×C11C22×C418yes—
85C22×C4×C11C22×C414yes—
86C22×C4×C11C22×C418yes—
87C22×C4×C11C2418yes—
88C22×C4×C11C2414yes—
89C22×C4×C11C2412yes—
90C22×Dic11—24no—
91C22×Dic11—42no—
92C22×Dic11C22×C414yes—
93C22×Dic11C22×C414yes—
94C22×Dic11C22×C4116yes—
95C22×Dic11C22×C418yes—
96C22×Dic11C2411yescharacteristic
97C22×Dic11C2418yes—
98C22×Dic11C2412yes—
99C22×Dic11C2414yes—
100C22×Dic11C2411yescharacteristic
101C2×Dic22C42164yescomplemented
102C2×Dic22C22×C4116yes—
103C2×Dic22C22×C4116yes—
104C2×Dic22C22×C4116yes—
105C11×C4⋊C4C22×C4116yes—
106C11×C4⋊C4C22×C4116yes—
107C11×C22⋊C4C22×C4116yes—
108C42×C11—48no—
109C42×C11C22×C4116yes—
110C22⋊Dic11C22×C4116yes—
111C4⋊Dic11C22×C4116yes—
112Dic11⋊C4C22×C4164yes—
113Dic11⋊C4C22×C4132yes—
114C4×Dic11—216no—
115C4×Dic11—48no—
116C4×Dic11—48no—
117C4×Dic11C22×C4164yes—
118C4×Dic11C22×C4116yes—
119C4×Dic11C22×C4116yes—
120C4×Dic11C22×C418yes—
121C4×Dic11C22×C418yes—
122C4×Dic11C22×C4116yes—
123C2×#519—112no—
124C22×C4×Q8—111no—
125#2276—118no—
126#2274—114no—
127#2274—111no—
128#2274D1111yescharacteristic
129C42×Q8—118no—
130C4×#117—114no—
131C4×#117—112no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11C23×C414yes—
135C23×C11C23×C412yes—
136C23×C11C2511yescharacteristic
137C2×C4×C11—28no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11—48no—
141C2×C4×C11C2×C42116yes—
142C2×C4×C11C23×C4116yes—
143C2×C4×C11C23×C418yes—
144C2×C4×C11C23×C414yes—
145C2×C4×C11C23×C414yes—
146C2×C4×C11C23×C414yes—
147C2×Dic11—28no—
148C2×Dic11—22no—
149C2×Dic11—28no—
150C2×Dic11—24no—
151C2×Dic11—28no—
152C2×Dic11—44no—
153C2×Dic11C2×C42132yes—
154C2×Dic11C23×C412yes—
155C2×Dic11C23×C4116yes—
156C2×Dic11C23×C414yes—
157C2×Dic11C23×C412yes—
158C2×Dic11C23×C418yes—
159C2×Dic11C23×C4116yes—
160C2×Dic112−1+414yes—
161Dic22C2×C42164yes—
162C23×Q8—111no—
163#519—1132no—
164C2×C4×Q8—114no—
165C2×C4×Q8—114no—
166C2×C4×Q8—118no—
167C2×C4×Q8—1116no—
168C2×C4×Q8—118no—
169C2×#117—112no—
170C2×#117—118no—
171C2×#117C2×D1112yes—
172C22×C4⋊C4—112no—
173C22×C4⋊C4C2×D1111yescharacteristic
174C22×C42—112no—
175C22×C42—111no—
176C4×C4⋊C4—114no—
177C4×C4⋊C4—114no—
178C4×C4⋊C4—118no—
179C4×C4⋊C4—118no—
180C4×C4⋊C4—1116no—
181C4×C4⋊C4—118no—
182C4×C4⋊C4—1116no—
183C4×C4⋊C4C2×D1118yes—
184C4×C22⋊C4—114no—
185C4×C22⋊C4—114no—
186C4×C22⋊C4—114no—
187C4×C22⋊C4C2×D1114yes—
188#376—114no—
189#376—118no—
190C43—118no—
191C43—114no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—28no—
195C22×C11C22×C4214yes—
196C22×C11C24×C411yescharacteristic
197C22×C11C24×C412yes—
198C22×C11C2×2−1+412yes—
199C22×C11#58512yes—
200C4×C11—28no—
201C4×C11—216no—
202C4×C11C22×C4218yes—
203Dic11—22no—
204Dic11—24no—
205Dic11—216no—
206Dic11C22×C42116yes—
207Dic11#51914yescomplemented
208C22×Q8—118no—
209C22×Q8—1116no—
210C22×Q8—114no—
211C23×C4—112no—
212C23×C4—111no—
213C23×C4—111no—
214C23×C4C22×D1112yes—
215C23×C4C22×D1111yescharacteristic
216C4×Q8—1132no—
217C4×Q8—1132no—
218C4×Q8—1164no—
219C4×Q8—1164no—
220#117—1116no—
221#117—1164no—
222#117C4×D11116yes—
223C2×C4⋊C4—1116no—
224C2×C4⋊C4—118no—
225C2×C4⋊C4—1116no—
226C2×C4⋊C4—114no—
227C2×C4⋊C4C4×D1118yes—
228C2×C4⋊C4C22×D1114yes—
229C2×C4⋊C4C22×D1114yes—
230C2×C22⋊C4—114no—
231C2×C22⋊C4C22×D1114yes—
232C2×C42—1116no—
233C2×C42—118no—
234C2×C42—1116no—
235C2×C42—114no—
236C2×C42—114no—
237C2×C42—112no—
238C2×C42—114no—
239C2×C42—112no—
240C2×C42—118no—
241C2×C42—118no—
242C2×C42—118no—
243C2×C42C22×D1118yes—
244C2×C42C22×D1114yes—
245#95—118no—
246#95—118no—
247#95—118no—
248#95C22×D1118yes—
249C2×C11—24no—
250C2×C11C23×C4211yescharacteristic
251C2×C11C2×#51911yescharacteristic
252C2×C11#342811yescharacteristic
253C2×C11C4×2−1+414yes—
254C24C23×D1111yescharacteristic
255C2×Q8—1164no—
256C2×Q8—1116no—
257C2×Q8—1116no—
258C2×Q8—1116no—
259C22×C4—44no—
260C22×C4—118no—
261C22×C4—1116no—
262C22×C4—111no—
263C22×C4—114no—
264C22×C4—114no—
265C22×C4—111no—
266C22×C4—118no—
267C22×C4—112no—
268C22×C4—114no—
269C22×C4—224no—
270C22×C4—442no—
271C22×C4C2×C4×D1118yes—
272C22×C4C2×C4×D1114yes—
273C22×C4C2×C4×D1118yes—
274C22×C4C23×D1118yes—
275C22×C4C23×D1114yes—
276C22×C4C23×D1112yes—
277C4⋊C4—1132no—
278C4⋊C4—1164no—
279C4⋊C4—1116no—
280C4⋊C4C2×C4×D11116yes—
281C4⋊C4C2×C4×D11116yes—
282C22⋊C4—1116no—
283C22⋊C4C2×C4×D11116yes—
284C42—48no—
285C42—1116no—
286C42—118no—
287C42—1116no—
288C42—118no—
289C42—1164no—
290C42—1116no—
291C42—2216no—
292C42—448no—
293C42—448no—
294C42C2×C4×D11116yes—
295C11C4×#51911yescharacteristic, complemented, Sylow
296C23—22no—
297C23—22no—
298C23C22×C4×D1114yes—
299C23C22×C4×D1112yes—
300C23C24×D1111yescharacteristic
301Q8—1164no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—48no—
306C2×C4—1132no—
307C2×C4—112no—
308C2×C4—118no—
309C2×C4—1116no—
310C2×C4—114no—
311C2×C4—112no—
312C2×C4—1116no—
313C2×C4—114no—
314C2×C4—228no—
315C2×C4—228no—
316C2×C4—224no—
317C2×C4—228no—
318C2×C4—222no—
319C2×C4—444no—
320C2×C4C42×D11116yes—
321C2×C4C22×C4×D11116yes—
322C2×C4C22×C4×D1118yes—
323C2×C4C22×C4×D1114yes—
324C2×C4C22×C4×D1114yes—
325C2×C4C22×C4×D1114yes—
326C22—22no—
327C22—22no—
328C22—28no—
329C22C2×C42×D1114yes—
330C22C23×C4×D1111yescharacteristic
331C22C23×C4×D1112yes—
332C22#1062345512yes—
333C22D11×2−1+412yes—
334C4—28no—
335C4—216no—
336C4—1116no—
337C4—114no—
338C4—222no—
339C4—224no—
340C4—2216no—
341C4C2×C42×D1118yes—
342C2—24no—
343C2C22×C42×D1111yescharacteristic
344C2D11×#51911yescharacteristic
345C2#1308181411yescharacteristic
346C2#1308182714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC2×C11C23×C42
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2274D11
hypocenterC11C4×#519
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13070980C2semidirect
6. C4×#66940C2semidirect
17. #10623047C4semidirect
18. C2×#66940C4semidirect
74. #66940C2×C4semidirect
76. C4×Dic22C2×C4semidirect
101. C2×Dic22C42semidirect
207. Dic11#519semidirect
295. C11C4×#519semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
C22×#669402
#130709802
#130709732
#130709712
C4×#669402
#117×Dic112
C4×#669302
C11×#22742
C4×#51911