Finite Group Databasebeta

← #14781156

Subgroups — #14781156

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622614C212yesmaximal
2#13071196C211yesmaximal, characteristic
3#13069769C218yesmaximal, complemented
4#13068355C211yesmaximal, characteristic, complemented
5#13068325C212yesmaximal, complemented
6C11×#3458C211yesmaximal, characteristic, complemented
7C23×D44C2211yescharacteristic
8C11×#544—24no—
9C11×#544C2214yescomplemented
10C11×#543—22no—
11C11×#533—24no—
12C11×#533—22no—
13C2×C11×#117C2212yes—
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2212yes—
17#10622614—24no—
18#10622614C2218yes—
19#10622601C2214yes—
20C2×#66873—24no—
21#10622568—22no—
22#10622552—22no—
23#10622170C2218yescomplemented
24#10622168C2214yescomplemented
25C24×D11—21no—
26C23×C4×C11C2311yescharacteristic
27C22×D44—22no—
28C22×D44—22no—
29C22×D44—24no—
30C22×D44—21no—
31C22×D44—22no—
32C22×D44Q814yescomplemented
33C22×D44C2312yes—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—28no—
36C11×#125—24no—
37C11×#125—28no—
38C11×C22⋊Q8—216no—
39C11×C22⋊Q8—28no—
40C4×Q8×C11—28no—
41C11×#117—22no—
42C11×#117—22no—
43C11×#117—22no—
44C11×#117—22no—
45C11×#117D414yes—
46C11×#117C2314yes—
47C2×C11×C4⋊C4D414yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4D412yes—
51C2×C42×C11—22no—
52C2×C42×C11D412yes—
53C2×C22⋊Dic11—21no—
54C2×(C2×D11)⋊C4—28no—
55#66979—24no—
56C2×C4⋊Dic11—21no—
57C2×C4×Dic11C2312yes—
58C2×#4318—22no—
59C2×#4318—24no—
60C2×#4318—24no—
61C2×#4318C2314yes—
62C22×C11⋊C8—22no—
63#66873—216no—
64#23463—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—22no—
67C23×D11—24no—
68C23×D11—42no—
69C23×D11—42no—
70C23×D11—84no—
71C2×Q8×C11—28no—
72C22×C4×C11—24no—
73C22×C4×C11C2×D414yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×Q812yes—
78C22×C4×C11#4114yes—
79C22×C4×C11#4112yes—
80C22×C4×C11C2411yescharacteristic
81C22×Dic11—22no—
82C2×D44—24no—
83C2×D44—28no—
84C2×D44—28no—
85C2×D44—24no—
86C2×D44—22no—
87C2×D44—24no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—44no—
91C2×D44—44no—
92C2×D44—42no—
93C2×D44C2×Q814yes—
94C11×C4⋊C4—216no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4C2×D418yes—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—24no—
102C42×C11—24no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—24no—
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—88no—
108C4⋊Dic11—42no—
109C4×Dic11—24no—
110#4318—24no—
111#4318—24no—
112#4318—44no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—44no—
115#3458D1111yescharacteristic, complemented
116C2×#418—112no—
117#2309—111no—
118#2027—118no—
119#1742—111no—
120#1733—112no—
121C23×C11—42no—
122C23×C11#12012yes—
123C23×C11C22⋊Q812yes—
124C23×C11#12412yes—
125C23×C11C22×D411yescharacteristic
126C22×D11—24no—
127C22×D11—48no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—48no—
131C22×D11—88no—
132C22×D11—88no—
133C22×D11—88no—
134Q8×C11—88no—
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11—44no—
138C2×C4×C11—84no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22⋊Q814yes—
142C2×C4×C11C22⋊Q814yes—
143C2×C4×C11C22⋊Q812yes—
144C2×C4×C11#12414yes—
145C2×C4×C11#12414yes—
146C2×C4×C11#12412yes—
147C2×C4×C11C22×D412yes—
148C2×C4×C11C22×Q811yescharacteristic
149C2×C4×C11C2×#4112yes—
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—44no—
152C2×Dic11—42no—
153D44—28no—
154D44—44no—
155D44—44no—
156D44—44no—
157C11⋊C8—44no—
158C23×D4—111no—
159C22×M16—112no—
160#544—24no—
161#544C2×D1114yescomplemented
162#543—22no—
163#533—24no—
164#533—22no—
165C2×#117—111no—
166C2×#117C2×D1112yes—
167C2×#117C2×D1111yescharacteristic
168#418—118no—
169#418—224no—
170C2×#102—224no—
171#390—114no—
172#390—222no—
173#379—222no—
174#343—114no—
175#339—118no—
176C22×C11—22no—
177C22×C11—24no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11#39314yes—
181C22×C11C2×#12011yescharacteristic
182C22×C11C2×C22⋊Q811yescharacteristic
183C22×C11C2×#12411yescharacteristic
184C2×D11—48no—
185C2×D11—44no—
186C2×D11—84no—
187C2×D11—816no—
188C2×D11—84no—
189C4×C11—44no—
190C4×C11—48no—
191C4×C11#39312yes—
192C4×C11#39312yes—
193C4×C11C2×C22⋊Q812yes—
194C4×C11C2×#12412yes—
195Dic11—82no—
196C25—221no—
197C22×D4—114no—
198C22×D4—112no—
199C22×D4—224no—
200C22×D4—222no—
201C22×D4—222no—
202C22×D4—222no—
203C22×D4—221no—
204C23×C4C22×D1111yescharacteristic
205C2×M16—114no—
206C2×M16—222no—
207C2×M16—224no—
208C2×M16—224no—
209C22×C8—222no—
210C4⋊Q8—24no—
211C4⋊Q8—28no—
212#125—24no—
213#125—28no—
214C22⋊Q8—216no—
215C22⋊Q8—28no—
216C4×Q8—28no—
217#117—22no—
218#117—22no—
219#117—22no—
220#117—22no—
221#117—224no—
222#117C22⋊D1114yes—
223#117C22×D1114yes—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22⋊D1114yes—
226C2×C4⋊C4C22×D1112yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—228no—
230C2×C22⋊C4C22⋊D1112yes—
231C2×C42—22no—
232C2×C42—112no—
233C2×C42C22⋊D1112yes—
234#102—2216no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—24no—
238C2×C11C2×#39311yescharacteristic
239C2×C11#302112yes—
240D11—84no—
241C24—222no—
242C24—224no—
243C24—442no—
244C24—442no—
245C24—884no—
246C24C2×C22⋊D1111yescharacteristic
247C2×Q8—28no—
248C2×D4—114no—
249C2×D4—228no—
250C2×D4—228no—
251C2×D4—224no—
252C2×D4—224no—
253C2×D4—222no—
254C2×D4—224no—
255C2×D4—444no—
256C2×D4—444no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—441no—
260C22×C4—24no—
261C22×C4—222no—
262C22×C4Q8×D1112yes—
263C22×C4#434314yes—
264C22×C4#434312yes—
265C22×C4C2×C22⋊D1114yes—
266C22×C4C2×C22⋊D1111yescharacteristic
267C22×C4C2×C22⋊D1112yes—
268C22×C4C2×C22⋊D1112yes—
269C22×C4C23×D1111yescharacteristic
270M16—224no—
271M16—224no—
272M16—444no—
273C2×C8—224no—
274C2×C8—444no—
275C4⋊C4—216no—
276C4⋊C4—28no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—442no—
280C4⋊C4C2×C22⋊D1118yes—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—442no—
285C22⋊C4—888no—
286C42—24no—
287C42—22no—
288C42—22no—
289C42—24no—
290C42—224no—
291C11#2346311yescharacteristic, complemented, Sylow
292C23—42no—
293C23—224no—
294C23—448no—
295C23—442no—
296C23—448no—
297C23—442no—
298C23—888no—
299C23—888no—
300C23—888no—
301C23#6699912yes—
302C23#6700012yes—
303C23#6700612yes—
304C23C22×C22⋊D1111yescharacteristic
305Q8—88no—
306D4—228no—
307D4—444no—
308D4—444no—
309D4—444no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—44no—
313C2×C4—84no—
314C2×C4—444no—
315C2×C4—442no—
316C2×C4#6699914yes—
317C2×C4#6699914yes—
318C2×C4#6699912yes—
319C2×C4#6700014yes—
320C2×C4#6700014yes—
321C2×C4#6700012yes—
322C2×C4#6700611yescharacteristic
323C2×C4#6700611yescharacteristic
324C2×C4C2×Q8×D1111yescharacteristic
325C2×C4C2×#434312yes—
326C2×C4C2×#434311yescharacteristic
327C2×C4C22×C22⋊D1112yes—
328C8—444no—
329C22—22no—
330C22—24no—
331C22—42no—
332C22—42no—
333C22—448no—
334C22—444no—
335C22—884no—
336C22—8816no—
337C22—884no—
338C22#1062284414yes—
339C22C2×#6699911yescharacteristic
340C22C2×#6700011yescharacteristic
341C22C2×#6700611yescharacteristic
342C4—44no—
343C4—48no—
344C4—882no—
345C4#1062284412yes—
346C4#1062284412yes—
347C4C2×#6699912yes—
348C4C2×#6700012yes—
349C2—21no—
350C2—21no—
351C2—24no—
352C2—884no—
353C2C2×#1062284411yescharacteristic
354C2#1307798812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC23×D44C22
hypercenter#3458D11
hypocenterC11#23463
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
3. #13069769C2semidirect
4. #13068355C2semidirect
5. #13068325C2semidirect
6. C11×#3458C2semidirect
9. C11×#544C22semidirect
23. #10622170C22semidirect
24. #10622168C22semidirect
32. C22×D44Q8semidirect
115. #3458D11semidirect
161. #544C2×D11semidirect
291. C11#23463semidirect

Maximal subgroups

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

subgroupindex
C2×#106226142
#130711962
#130697692
#130683552
#130683252
C11×#34582
#2346311