Finite Group Databasebeta

← #14913554

Subgroups — #14913554

Order 2816.

2834 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071728C214yesmaximal, complemented
2#13071706C212yesmaximal, complemented
3#13071681C212yesmaximal, complemented
4#13071658C218yesmaximal, complemented
5#13071107C214yesmaximal, complemented
6#13071081C214yesmaximal, complemented
7C4×D4×Dic11C214yesmaximal, complemented
8C4×#66979C212yesmaximal, complemented
9C2×C11×#532C211yesmaximal, characteristic
10C22×C11×#41C2212yes—
11C11×#532C4116yescomplemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#121C2214yes—
16C2×C4×D4×C11C2214yes—
17C22×C42×C11C2211yescharacteristic
18C2×D4×Dic11C2218yes—
19C2×#66979C2214yes—
20C2×#66979C2214yes—
21C22×C4×Dic11C2214yes—
22#10622843C2218yes—
23#10622834C2218yes—
24#10622834C2218yes—
25#10622833C2218yes—
26#10622833C2218yes—
27C4×C22⋊Dic11C2214yes—
28C4×C22⋊Dic11C2218yes—
29C4×C22⋊Dic11C2214yes—
30#10622598C2218yes—
31C4⋊C4×Dic11C2218yes—
32#10622564C22116yes—
33C22⋊C4×Dic11C22116yes—
34C4×C4⋊Dic11C2214yes—
35C4×C4⋊Dic11C2212yes—
36C4×C4⋊Dic11C2212yes—
37#10622545C2214yes—
38C42×Dic11C2214yes—
39C2×C11×#41—44no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C4116yescomplemented
42C22×Q8×C11C2312yes—
43C22×D4×C11C2314yes—
44C22×D4×C11C2312yes—
45C22×D4×C11C2314yes—
46C23×C4×C11C2314yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2318yes—
50C11×C4⋊Q8C2×C418yescomplemented
51C11×#127C2×C418yes—
52C11×#124C2×C4116yescomplemented
53C11×#121C2×C4132yescomplemented
54C4×D4×C11C2×C4132yescomplemented
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C22⋊C4C2318yes—
57C2×C42×C11C2×C418yescomplemented
58C2×C42×C11C2312yes—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11C2318yes—
62C2×C22⋊Dic11C23116yes—
63C2×C22⋊Dic11C2318yes—
64D4×Dic11—232no—
65#66979—216no—
66#66979—48no—
67C2×C4⋊Dic11C2314yes—
68C2×C4⋊Dic11C2318yes—
69C2×C4⋊Dic11C2314yes—
70C2×C4×Dic11—48no—
71C2×C4×Dic11C2318yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2318yes—
75C2×C4×Dic11C2318yes—
76C11⋊#95C2314yes—
77C11⋊#95C2314yes—
78C11⋊#95C2318yes—
79C11⋊#95C23116yes—
80#34155—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C24×C11C2414yes—
83C11×#41—432no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11C22×C418yes—
87C2×D4×C11—216no—
88C2×D4×C11—44no—
89C2×D4×C11—44no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11C22×C4116yes—
93C2×D4×C11C22×C4116yes—
94C2×D4×C11C22×C418yes—
95C22×C4×C11—28no—
96C22×C4×C11—28no—
97C22×C4×C11—28no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C22×C418yes—
101C22×C4×C11C22×C414yes—
102C22×C4×C11C22×C4116yes—
103C22×C4×C11C2411yescharacteristic
104C22×C4×C11C2412yes—
105C22×C4×C11C2414yes—
106C22×C4×C11C2412yes—
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—232no—
109C22×Dic11—48no—
110C22×Dic11C2418yes—
111C22×Dic11C2418yes—
112C11×C4⋊C4C22×C4116yes—
113C11×C22⋊C4C22×C4132yes—
114C42×C11C22×C418yes—
115C42×C11C22×C414yes—
116C42×C11C22×C414yes—
117C22⋊Dic11—216no—
118C22⋊Dic11—232no—
119C22⋊Dic11—48no—
120C4⋊Dic11—28no—
121C4⋊Dic11—48no—
122C4⋊Dic11#41116yescomplemented
123C4×Dic11—216no—
124C4×Dic11—216no—
125C4×Dic11—28no—
126C4×Dic11—28no—
127C4×Dic11—48no—
128C2×#532D1111yescharacteristic
129#2372—114no—
130#2369—112no—
131#2366—112no—
132#2363—118no—
133#2297—114no—
134#2293—114no—
135C42×D4—114no—
136C4×#117—112no—
137C23×C11—24no—
138C23×C11—216no—
139C23×C11—24no—
140C23×C11—24no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11C23×C418yes—
144C23×C11C23×C412yes—
145C23×C11C2511yescharacteristic
146Q8×C11—48no—
147D4×C11—232no—
148D4×C11—48no—
149D4×C11—416no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—216no—
156C2×C4×C11—232no—
157C2×C4×C11—28no—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C412yes—
160C2×C4×C11C23×C418yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C412yes—
163C2×C4×C11C2×#4118yes—
164C2×C4×C11H(5,𝔽2)12yes—
165C2×C4×C11H(5,𝔽2)12yes—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—28no—
169C2×Dic11—28no—
170C2×Dic11—28no—
171C2×Dic11—432no—
172C2×Dic11C2×#41116yes—
173C22×#41C2×D1112yes—
174#532Dic11116yescomplemented
175C2×C4⋊Q8C2×D1111yescharacteristic
176C2×#127C2×D1111yescharacteristic
177C2×#124C2×D1112yes—
178C2×#121C2×D1114yes—
179C2×C4×D4—118no—
180C2×C4×D4C2×D1114yes—
181C2×#117—114no—
182C2×#117—114no—
183C22×C42—114no—
184C22×C42C2×D1111yescharacteristic
185#391—118no—
186#390—118no—
187#390—118no—
188#389—118no—
189#388—1116no—
190#386—118no—
191#386—118no—
192C4×C4⋊C4—118no—
193C4×C4⋊C4—114no—
194C4×C4⋊C4—112no—
195C4×C4⋊C4—112no—
196C4×C22⋊C4—114no—
197C4×C22⋊C4—114no—
198C4×C22⋊C4—118no—
199C4×C22⋊C4—1116no—
200#376—114no—
201C43—114no—
202C22×C11—24no—
203C22×C11—216no—
204C22×C11—22no—
205C22×C11—28no—
206C22×C11—42no—
207C22×C11—48no—
208C22×C11—42no—
209C22×C11—48no—
210C22×C11C24×C411yescharacteristic
211C22×C11C22×#4114yes—
212C22×C11C2×H(5,𝔽2)11yescharacteristic
213C22×C11C2×H(5,𝔽2)11yescharacteristic
214C4×C11—24no—
215C4×C11—22no—
216C4×C11—28no—
217C4×C11C4×#4118yes—
218C4×C11#51814yes—
219Dic11—216no—
220Dic11—48no—
221C2×#41—44no—
222C2×#41—44no—
223C2×#41C2×Dic11116yescomplemented
224C22×Q8C22×D1112yes—
225C22×D4C22×D1114yes—
226C22×D4C22×D1114yes—
227C22×D4C22×D1112yes—
228C23×C4—118no—
229C23×C4C22×D1112yes—
230C23×C4C22×D1114yes—
231C23×C4C22×D1111yescharacteristic
232C4⋊Q8C2×Dic1118yescomplemented
233#127C2×Dic1118yes—
234#124C2×Dic11116yescomplemented
235#121C2×Dic11132yescomplemented
236C4×D4—2232no—
237C4×D4C2×Dic11132yescomplemented
238#117—2216no—
239#117—448no—
240C2×C4⋊C4—114no—
241C2×C4⋊C4—114no—
242C2×C4⋊C4—118no—
243C2×C4⋊C4C22×D1114yes—
244C2×C22⋊C4—118no—
245C2×C22⋊C4—1116no—
246C2×C22⋊C4—118no—
247C2×C22⋊C4C22×D1118yes—
248C2×C42—118no—
249C2×C42—118no—
250C2×C42—114no—
251C2×C42—114no—
252C2×C42—118no—
253C2×C42—448no—
254C2×C42C2×Dic1118yescomplemented
255C2×C42C22×D1111yescharacteristic
256C2×C42C22×D1111yescharacteristic
257C2×C42C22×D1112yes—
258#95—114no—
259#95—118no—
260#95—114no—
261#95—1116no—
262C2×C11—42no—
263C2×C11—48no—
264C2×C11C2×C4×#4112yes—
265C2×C11C2×#51811yescharacteristic
266C2×C11#348112yes—
267C2×C11#348312yes—
268C24C23×D1111yescharacteristic
269C24C23×D1114yes—
270#41—432no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8C22×Dic1118yes—
274C2×D4—216no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4C22×Dic11116yes—
280C2×D4C22×Dic11116yes—
281C2×D4C22×Dic1118yes—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—28no—
287C22×C4—118no—
288C22×C4—118no—
289C22×C4—2232no—
290C22×C4—448no—
291C22×C4C22×Dic1118yes—
292C22×C4C22×Dic1114yes—
293C22×C4C22×Dic11116yes—
294C22×C4C23×D1111yescharacteristic
295C22×C4C23×D1112yes—
296C22×C4C23×D1114yes—
297C22×C4C23×D1112yes—
298C22×C4C23×D1111yescharacteristic
299C4⋊C4—1116no—
300C4⋊C4—228no—
301C4⋊C4—448no—
302C4⋊C4C22×Dic11116yes—
303C22⋊C4—2216no—
304C22⋊C4—2232no—
305C22⋊C4—448no—
306C22⋊C4C22×Dic11132yes—
307C42—2216no—
308C42—228no—
309C42—228no—
310C42—2216no—
311C42—448no—
312C42C22×Dic1118yes—
313C42C22×Dic1114yes—
314C42C22×Dic1114yes—
315C11#3415511yescharacteristic, complemented, Sylow
316C23—24no—
317C23—24no—
318C23—21no—
319C23—21no—
320C23—24no—
321C23—216no—
322C23C23×Dic1118yes—
323C23C23×Dic1112yes—
324C23C24×D1111yescharacteristic
325Q8—48no—
326D4—232no—
327D4—48no—
328D4—416no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—24no—
334C2×C4—232no—
335C2×C4—28no—
336C2×C4—216no—
337C2×C4—1116no—
338C2×C4—228no—
339C2×C4—228no—
340C2×C4—228no—
341C2×C4—228no—
342C2×C4—228no—
343C2×C4—4432no—
344C2×C4#6703712yes—
345C2×C4#6703712yes—
346C2×C4#41×D1118yes—
347C2×C4C23×Dic1114yes—
348C2×C4C23×Dic1112yes—
349C2×C4C23×Dic1118yes—
350C2×C4C23×Dic1112yes—
351C2×C4C23×Dic1114yes—
352C22—24no—
353C22—216no—
354C22—22no—
355C22—28no—
356C22—48no—
357C22—42no—
358C22—48no—
359C22—42no—
360C22C2×#6703711yescharacteristic
361C22C2×#6703711yescharacteristic
362C22C2×#41×D1114yes—
363C22C24×Dic1111yescharacteristic
364C4—24no—
365C4—22no—
366C4—28no—
367C4—2216no—
368C4—448no—
369C4#1062332914yes—
370C4#41×Dic1118yes—
371C2—42no—
372C2—48no—
373C2C2×#41×Dic1112yes—
374C2C2×#1062332911yescharacteristic
375C2#1308222412yes—
376C2#1308224012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#532C2
socle, cosocleC23×C11C25
hypercenterC2×#532D11
hypocenterC11#34155
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13071728C2semidirect
2. #13071706C2semidirect
3. #13071681C2semidirect
4. #13071658C2semidirect
5. #13071107C2semidirect
6. #13071081C2semidirect
7. C4×D4×Dic11C2semidirect
8. C4×#66979C2semidirect
11. C11×#532C4semidirect
41. C2×C11×#41C2×C4semidirect
50. C11×C4⋊Q8C2×C4semidirect
52. C11×#124C2×C4semidirect
53. C11×#121C2×C4semidirect
54. C4×D4×C11C2×C4semidirect
57. C2×C42×C11C2×C4semidirect
122. C4⋊Dic11#41semidirect
174. #532Dic11semidirect
223. C2×#41C2×Dic11semidirect
232. C4⋊Q8C2×Dic11semidirect
234. #124C2×Dic11semidirect
235. #121C2×Dic11semidirect
237. C4×D4C2×Dic11semidirect
254. C2×C42C2×Dic11semidirect
315. C11#34155semidirect

Maximal subgroups

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

subgroupindex
#130717282
#130717062
#130716812
#130716582
#130711072
#130710812
C4×D4×Dic112
C4×#669792
C2×C11×#5322
#3415511