Finite Group Databasebeta

← #14685116

Subgroups — #14685116

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C2×#10622542C212yesmaximal, complemented
3C2×#10622552C212yesmaximal
4C2×#10622549C211yesmaximal, characteristic, complemented
5#13066854C218yesmaximal, complemented
6C2×C43×C11C211yesmaximal, characteristic, complemented
7C23×D44C2211yescharacteristic
8C23×Dic22C2211yescharacteristic
9C22×C42×C11C2214yes—
10C22×C42×C11C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4C2218yes—
13C22×(C2×D11)⋊C4C2214yes—
14C22×C4⋊Dic11C2212yes—
15C2×#66928—24no—
16C2×#66928—24no—
17C2×#66928C418yescomplemented
18C43×C11—24no—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2218yes—
21#10622552—28no—
22#10622549—24no—
23#10622542—28no—
24C24×D11C2312yes—
25C23×C4×C11C2312yes—
26C23×C4×C11C2314yes—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11C2314yes—
29C23×Dic11C2312yes—
30C22×D44—22no—
31C22×D44—22no—
32C22×D44—24no—
33C22×D44—24no—
34C22×D44C2×C414yes—
35C22×Dic22—22no—
36C22×Dic22—22no—
37C22×Dic22—24no—
38C22×Dic22—24no—
39C22×Dic22C2×C414yes—
40C2×C42×C11—28no—
41C2×C42×C11—24no—
42C2×C42×C11—216no—
43C2×C42×C11—24no—
44C2×C42×C11C2×C414yes—
45C2×C42×C11D418yes—
46C2×C42×C11D414yes—
47C2×C42×C11D414yes—
48C2×(C2×D11)⋊C4—28no—
49C2×(C2×D11)⋊C4—28no—
50C2×(C2×D11)⋊C4—216no—
51C2×(C2×D11)⋊C4—232no—
52C2×(C2×D11)⋊C4C2×C4116yes—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—24no—
55C2×C4⋊Dic11—24no—
56#66928—232no—
57C11⋊#95—216no—
58C11⋊#95—28no—
59#14708—111nomaximal, Sylow
60C24×C11C2411yescharacteristic
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—24no—
64C23×D11—216no—
65C23×D11—24no—
66C23×D11C22×C414yes—
67C22×C4×C11—24no—
68C22×C4×C11—28no—
69C22×C4×C11—24no—
70C22×C4×C11—28no—
71C22×C4×C11C22×C414yes—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C2×D414yes—
74C22×C4×C11C2×D414yes—
75C22×C4×C11C2×D418yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D414yes—
79C22×C4×C11#41116yes—
80C22×C4×C11#4114yes—
81C22×Dic11—24no—
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11—24no—
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—216no—
89C22×Dic11C22×C414yes—
90C2×D44—28no—
91C2×D44—216no—
92C2×D44—48no—
93C2×D44—44no—
94C2×D44—44no—
95C2×Dic22—28no—
96C2×Dic22—216no—
97C2×Dic22—48no—
98C2×Dic22—44no—
99C2×Dic22—44no—
100C42×C11—232no—
101C42×C11—216no—
102C42×C11C22⋊C4116yescomplemented
103(C2×D11)⋊C4—232no—
104(C2×D11)⋊C4—432no—
105C4⋊Dic11—48no—
106C22×#124—111no—
107C2×#391—112no—
108C2×#390—112no—
109C2×#382—111no—
110C2×C43D1111yescharacteristic, complemented
111#1437—118no—
112C23×C11C23×C411yescharacteristic
113C23×C11C22×D411yescharacteristic
114C23×C11C22×D412yes—
115C23×C11C22×D411yescharacteristic
116C23×C11C2×#4112yes—
117C23×C11C2×#4118yes—
118C22×D11—24no—
119C22×D11—28no—
120C22×D11—216no—
121C22×D11—44no—
122C22×D11—48no—
123C22×D11—48no—
124C22×D11—42no—
125C22×D11—416no—
126C22×D11—42no—
127C22×D11—48no—
128C22×D11—48no—
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—216no—
133C2×C4×C11—216no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11C2×C22⋊C418yes—
137C2×C4×C11C2×C22⋊C414yes—
138C2×C4×C11C4×D418yes—
139C2×C4×C11#12118yes—
140C2×C4×C11#12414yes—
141C2×C4×C11#124116yescomplemented
142C2×C4×C11#12714yes—
143C2×Dic11—24no—
144C2×Dic11—28no—
145C2×Dic11—44no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—48no—
149C2×Dic11—44no—
150C2×Dic11—48no—
151C2×Dic11—48no—
152D44—416no—
153Dic22—416no—
154C23×Q8—111no—
155C23×D4—111no—
156C2×#124—118no—
157C2×#124—224no—
158C2×#124—224no—
159C22×C4⋊C4—112no—
160C22×C22⋊C4—114no—
161C22×C22⋊C4—118no—
162C22×C42C2×D1114yes—
163C22×C42C2×D1112yes—
164C22×C42C2×D1111yescharacteristic
165#391—228no—
166#390—228no—
167#382—224no—
168C2×#95—114no—
169C2×#95—118no—
170C43—24no—
171C22×C11C22×C22⋊C411yescharacteristic
172C22×C11C2×C4×D412yes—
173C22×C11C4×#4114yes—
174C22×C11C2×#12112yes—
175C22×C11#52514yes—
176C22×C11C2×#12414yes—
177C22×C11C2×#12411yescharacteristic
178C22×C11#52918yes—
179C22×C11C2×#12711yescharacteristic
180C22×C11#53214yes—
181C22×C11#53214yes—
182C2×D11—44no—
183C2×D11—48no—
184C2×D11—416no—
185C2×D11—88no—
186C2×D11—84no—
187C2×D11—84no—
188C4×C11—216no—
189C4×C11—28no—
190C4×C11#39018yes—
191Dic11—44no—
192Dic11—84no—
193C25—112no—
194C22×Q8—114no—
195C22×Q8—222no—
196C22×Q8—224no—
197C22×Q8—224no—
198C22×Q8—222no—
199C22×D4—114no—
200C22×D4—222no—
201C22×D4—224no—
202C22×D4—224no—
203C22×D4—222no—
204C23×C4—112no—
205C23×C4—114no—
206C23×C4C22×D1112yes—
207C23×C4C22×D1114yes—
208C23×C4C22×D1111yescharacteristic
209#124—2232no—
210C2×C4⋊C4—224no—
211C2×C4⋊C4—224no—
212C2×C4⋊C4—224no—
213C2×C22⋊C4—1116no—
214C2×C22⋊C4—228no—
215C2×C22⋊C4—228no—
216C2×C22⋊C4—2216no—
217C2×C22⋊C4—2232no—
218C2×C42—216no—
219C2×C42—24no—
220C2×C42—28no—
221C2×C42—24no—
222C2×C42C4×D1114yes—
223C2×C42D4418yes—
224C2×C42D4414yes—
225C2×C42C22⋊D1114yes—
226#95—228no—
227#95—2216no—
228C2×C11C2×#39011yescharacteristic
229C2×C11#229712yes—
230C2×C11C4×#12414yes—
231C2×C11#285014yes—
232C2×C11#285812yes—
233C2×C11#286112yes—
234D11—84no—
235C24—114no—
236C24—224no—
237C24—222no—
238C24—2216no—
239C24—224no—
240C24—222no—
241C24C23×D1111yescharacteristic
242C2×Q8—2216no—
243C2×Q8—228no—
244C2×Q8—444no—
245C2×Q8—444no—
246C2×Q8—448no—
247C2×D4—2216no—
248C2×D4—228no—
249C2×D4—444no—
250C2×D4—444no—
251C2×D4—448no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—114no—
257C22×C4—224no—
258C22×C4—222no—
259C22×C4—224no—
260C22×C4—222no—
261C22×C4—224no—
262C22×C4—224no—
263C22×C4—224no—
264C22×C4—2216no—
265C22×C4C2×C4×D1114yes—
266C22×C4C2×C4×D1112yes—
267C22×C4C2×D4418yes—
268C22×C4C2×D4414yes—
269C22×C4C2×D4414yes—
270C22×C4C2×D4412yes—
271C22×C4#4339116yes—
272C22×C4#433914yes—
273C22×C4C2×C22⋊D1114yes—
274C22×C4C2×C22⋊D1112yes—
275C4⋊C4—448no—
276C22⋊C4—2232no—
277C22⋊C4—4432no—
278C42—232no—
279C42—216no—
280C42(C2×D11)⋊C4116yescomplemented
281C11#1470811yescharacteristic, complemented, Sylow
282C23—228no—
283C23—2216no—
284C23—224no—
285C23—442no—
286C23—448no—
287C23—442no—
288C23—448no—
289C23—448no—
290C23—4416no—
291C23—444no—
292C23—448no—
293C23C22×C4×D1111yescharacteristic
294C23C22×D4412yes—
295C23C22×D4411yescharacteristic
296C23C2×#433912yes—
297C23C2×#433918yes—
298C23C22×C22⋊D1111yescharacteristic
299Q8—4416no—
300D4—4416no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—216no—
305C2×C4—28no—
306C2×C4—216no—
307C2×C4—28no—
308C2×C4—228no—
309C2×C4—224no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4—444no—
313C2×C4—444no—
314C2×C4—448no—
315C2×C4—448no—
316C2×C4—448no—
317C2×C4C4×D4418yes—
318C2×C4#6692714yes—
319C2×C4#6692814yes—
320C2×C4#66928116yescomplemented
321C2×C4C2×(C2×D11)⋊C418yes—
322C2×C4C2×(C2×D11)⋊C414yes—
323C2×C4#6698318yes—
324C22—448no—
325C22—4416no—
326C22—444no—
327C22—888no—
328C22—884no—
329C22—884no—
330C22C2×C4×D4412yes—
331C22C4×#433914yes—
332C22C2×#6692711yescharacteristic
333C22C2×#6692814yes—
334C22C2×#6692811yescharacteristic
335C22#1062300814yes—
336C22#1062300814yes—
337C22#1062301018yes—
338C22C22×(C2×D11)⋊C411yescharacteristic
339C22C2×#6698312yes—
340C22#1062332214yes—
341C4—28no—
342C4—216no—
343C4—444no—
344C4—884no—
345C4#1062255218yes—
346C2—884no—
347C2C2×#1062255211yescharacteristic
348C2#1307110612yes—
349C2C4×#6692814yes—
350C2#1307691714yes—
351C2#1307697312yes—
352C2#1307698812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C43×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C43D11
hypocenterC11#14708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
4. C2×#10622549C2semidirect
5. #13066854C2semidirect
6. C2×C43×C11C2semidirect
17. C2×#66928C4semidirect
102. C42×C11C22⋊C4semidirect
110. C2×C43D11semidirect
141. C2×C4×C11#124semidirect
280. C42(C2×D11)⋊C4semidirect
281. C11#14708semidirect
320. C2×C4#66928semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C2×#106225422
C2×#106225522
C2×#106225492
#130668542
C2×C43×C112
#1470811