Finite Group Databasebeta

← #14680302

Subgroups — #14680302

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C212yesmaximal, complemented
2C2×#10622834C212yesmaximal
3C2×#10622548C211yesmaximal, characteristic, complemented
4C2×#10622545C211yesmaximal, characteristic, complemented
5#13066861C218yesmaximal, complemented
6C22×C11×#124C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C23×D4×C11C2211yescharacteristic
9C2×C11×#124—24no—
10C2×C11×#124—24no—
11C2×C11×#124C418yescomplemented
12C22×C11×C22⋊C4C2214yes—
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2218yes—
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2214yes—
17C22×C4×Dic11C2212yes—
18#10622843—28no—
19#10622834—28no—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2218yes—
22#10622548—24no—
23#10622545—24no—
24C25×C11C2312yes—
25C22×Q8×C11—24no—
26C22×Q8×C11—22no—
27C22×Q8×C11—22no—
28C22×Q8×C11—24no—
29C22×Q8×C11C2×C414yes—
30C22×D4×C11—24no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11C2×C414yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2314yes—
39C23×Dic11C2314yes—
40C11×#124—232no—
41C2×C11×C22⋊C4—28no—
42C2×C11×C22⋊C4—28no—
43C2×C11×C22⋊C4C2×C4116yes—
44C2×C42×C11C2×C414yes—
45C2×C42×C11D414yes—
46C2×C42×C11D414yes—
47C2×C22⋊Dic11—216no—
48C2×C22⋊Dic11—416no—
49C2×C4⋊Dic11—28no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—48no—
54C2×C4×Dic11—24no—
55C2×C4×Dic11—24no—
56C2×C4×Dic11D418yes—
57C11⋊#95—28no—
58C11⋊#95—216no—
59#14273—111nomaximal, Sylow
60C24×C11—24no—
61C24×C11—22no—
62C24×C11—22no—
63C24×C11—24no—
64C24×C11—28no—
65C24×C11—28no—
66C24×C11C22×C414yes—
67C24×C11C2411yescharacteristic
68C2×Q8×C11—28no—
69C2×Q8×C11—216no—
70C2×Q8×C11—48no—
71C2×Q8×C11—44no—
72C2×Q8×C11—44no—
73C2×D4×C11—28no—
74C2×D4×C11—216no—
75C2×D4×C11—48no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—24no—
84C22×C4×C11C22×C414yes—
85C22×C4×C11C22×C414yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C2×D414yes—
88C22×C4×C11C2×D414yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11#4114yes—
93C22×Dic11—24no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—28no—
99C22×Dic11—216no—
100C22×Dic11—28no—
101C22×Dic11C2×D418yes—
102C11×C22⋊C4—232no—
103C42×C11C22⋊C4116yescomplemented
104C22⋊Dic11—432no—
105C4⋊Dic11—416no—
106C4⋊Dic11—48no—
107C4×Dic11—216no—
108C22×#124D1111yescharacteristic
109C2×#391—112no—
110C2×#390—112no—
111C2×#384—111no—
112C2×#376—111no—
113#1439—118no—
114C23×C11—24no—
115C23×C11—28no—
116C23×C11—216no—
117C23×C11—44no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—48no—
121C23×C11—44no—
122C23×C11—44no—
123C23×C11—48no—
124C23×C11—48no—
125C23×C11—416no—
126C23×C11C23×C411yescharacteristic
127C23×C11C22×D412yes—
128C23×C11C22×D411yescharacteristic
129C23×C11C22×D411yescharacteristic
130C23×C11C2×#4112yes—
131C23×C11H(5,𝔽2)14yes—
132C23×C112−1+414yes—
133Q8×C11—416no—
134D4×C11—416no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—28no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—44no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C2×C22⋊C418yes—
145C2×C4×C11C2×C22⋊C414yes—
146C2×C4×C11C4×D418yes—
147C2×C4×C11#12118yes—
148C2×C4×C11#12414yes—
149C2×C4×C11#12714yes—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—28no—
153C2×Dic11—48no—
154C2×Dic11—48no—
155C2×Dic11—44no—
156C2×Dic11—48no—
157C2×Dic11—48no—
158C2×Dic11—48no—
159C23×Q8C2×D1111yescharacteristic
160C23×D4C2×D1111yescharacteristic
161C2×#124—24no—
162C2×#124—24no—
163C2×#124Dic1118yescomplemented
164C22×C4⋊C4—112no—
165C22×C4⋊C4—114no—
166C22×C22⋊C4—118no—
167C22×C22⋊C4C2×D1114yes—
168C22×C42—112no—
169C22×C42C2×D1111yescharacteristic
170#391—228no—
171#390—228no—
172#384—224no—
173#376—224no—
174C2×#95—114no—
175C2×#95—118no—
176C22×C11—48no—
177C22×C11—416no—
178C22×C11—44no—
179C22×C11—88no—
180C22×C11—84no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11C22×C22⋊C411yescharacteristic
184C22×C11C2×C4×D412yes—
185C22×C11#52014yes—
186C22×C11C2×#12112yes—
187C22×C11C2×#12411yescharacteristic
188C22×C11C2×#12711yescharacteristic
189C22×C11#53512yes—
190C22×C11#53514yes—
191C22×C11#53612yes—
192C22×C11#53614yes—
193C22×C11#53714yes—
194C22×C11#54218yes—
195C4×C11—28no—
196C4×C11—44no—
197C4×C11#39018yes—
198Dic11—48no—
199Dic11—84no—
200C25C22×D1112yes—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8C2×Dic1114yes—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4C2×Dic1114yes—
211C23×C4—114no—
212C23×C4—114no—
213C23×C4C22×D1112yes—
214C23×C4C22×D1112yes—
215C23×C4C22×D1111yescharacteristic
216#124—232no—
217C2×C4⋊C4—224no—
218C2×C4⋊C4—224no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—224no—
221C2×C4⋊C4—448no—
222C2×C22⋊C4—28no—
223C2×C22⋊C4—28no—
224C2×C22⋊C4—2216no—
225C2×C22⋊C4—4416no—
226C2×C22⋊C4C2×Dic11116yes—
227C2×C42—118no—
228C2×C42—224no—
229C2×C42—224no—
230C2×C42C2×Dic1114yes—
231C2×C42C22⋊D1114yes—
232C2×C42C22⋊D1114yes—
233#95—2216no—
234#95—228no—
235C2×C11—84no—
236C2×C11C2×#39011yescharacteristic
237C2×C11#231112yes—
238C2×C11#232614yes—
239C2×C11#262014yes—
240C2×C11#264012yes—
241C2×C11#265711yescharacteristic
242C2×C11#265811yescharacteristic
243C24—24no—
244C24—24no—
245C24—28no—
246C24—28no—
247C24—22no—
248C24—22no—
249C24C22×Dic1114yes—
250C24C23×D1111yescharacteristic
251C2×Q8—216no—
252C2×Q8—28no—
253C2×Q8—44no—
254C2×Q8—48no—
255C2×Q8—44no—
256C2×D4—216no—
257C2×D4—28no—
258C2×D4—44no—
259C2×D4—48no—
260C2×D4—44no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—118no—
268C22×C4—224no—
269C22×C4—228no—
270C22×C4—228no—
271C22×C4—224no—
272C22×C4—224no—
273C22×C4—224no—
274C22×C4—2216no—
275C22×C4—224no—
276C22×C4D4×D1114yes—
277C22×C4#434114yes—
278C22×C4C22×Dic1114yes—
279C22×C4C22×Dic1114yes—
280C22×C4C22×Dic1112yes—
281C22×C4C2×C22⋊D1114yes—
282C22×C4C2×C22⋊D1114yes—
283C22×C4C2×C22⋊D1112yes—
284C22×C4C2×C22⋊D1112yes—
285C4⋊C4—4416no—
286C4⋊C4—448no—
287C22⋊C4—232no—
288C22⋊C4—4432no—
289C42—2216no—
290C42C22⋊Dic11116yescomplemented
291C11#1427311yescharacteristic, complemented, Sylow
292C23—28no—
293C23—216no—
294C23—24no—
295C23—42no—
296C23—44no—
297C23—42no—
298C23—44no—
299C23—44no—
300C23—48no—
301C23—48no—
302C23—48no—
303C23—416no—
304C23C2×D4×D1112yes—
305C23C2×#434112yes—
306C23#6704214yes—
307C23#6704314yes—
308C23C23×Dic1111yescharacteristic
309C23C22×C22⋊D1111yescharacteristic
310C23C22×C22⋊D1111yescharacteristic
311Q8—416no—
312D4—416no—
313C2×C4—24no—
314C2×C4—28no—
315C2×C4—24no—
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—24no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—228no—
323C2×C4—228no—
324C2×C4—228no—
325C2×C4—448no—
326C2×C4—448no—
327C2×C4—444no—
328C2×C4—448no—
329C2×C4—448no—
330C2×C4—448no—
331C2×C4D4×Dic1118yes—
332C2×C4#6698914yes—
333C2×C4#6699118yes—
334C2×C4#6699314yes—
335C2×C4C2×C22⋊Dic1118yes—
336C2×C4C2×C22⋊Dic1114yes—
337C22—48no—
338C22—44no—
339C22—416no—
340C22—82no—
341C22—82no—
342C22—84no—
343C22—88no—
344C22#1062320514yes—
345C22#1062320614yes—
346C22#1062321318yes—
347C22C2×D4×Dic1112yes—
348C22C2×#6698911yescharacteristic
349C22C2×#6699112yes—
350C22C2×#6699311yescharacteristic
351C22#1062335612yes—
352C22#1062335814yes—
353C22#1062336112yes—
354C22#1062336414yes—
355C22C22×C22⋊Dic1111yescharacteristic
356C4—28no—
357C4—44no—
358C4—448no—
359C4—884no—
360C4#1062283418yes—
361C2—84no—
362C2C2×#1062283411yescharacteristic
363C2#1307120812yes—
364C2#1307132914yes—
365C2#1307437414yes—
366C2#1307455612yes—
367C2#1307472411yescharacteristic
368C2#1307472711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#124C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#124D11
hypocenterC11#14273
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10622843C2semidirect
3. C2×#10622548C2semidirect
4. C2×#10622545C2semidirect
5. #13066861C2semidirect
11. C2×C11×#124C4semidirect
103. C42×C11C22⋊C4semidirect
163. C2×#124Dic11semidirect
290. C42C22⋊Dic11semidirect
291. C11#14273semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
C2×#106228342
C2×#106225482
C2×#106225452
#130668612
C22×C11×#1242
#1427311