Finite Group Databasebeta

← #14738961

Subgroups — #14738961

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079566C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622459C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic
5#13068068C214yesmaximal, complemented
6#13067982C214yesmaximal, complemented
7#13067302C211yesmaximal, characteristic, complemented
8#13067274C211yesmaximal, characteristic, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C2×C4×D44C2211yescharacteristic
11#10623001C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622744—21no—
17#10622734—21no—
18C2×#66885—21no—
19C2×#66882—21no—
20#10622538C2211yescharacteristic
21#10622462—22no—
22#10622460—22no—
23#10622459—22no—
24#10622459C2214yes—
25#10622459C2212yes—
26#10622455C2212yes—
27#10622447—22no—
28#10622352—22no—
29D11×C22⋊C8—22no—
30#10622312C2212yescomplemented
31C8×D44C2214yes—
32#10622294C2212yescomplemented
33C11×#335C2214yescomplemented
34#10622124C2212yescomplemented
35#10622124C2214yescomplemented
36#10622119C2212yescomplemented
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×Dic22—21no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—21no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48#66977—21no—
49#66977—21no—
50C2×Dic44—24no—
51C2×C8×D11—24no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44D412yes—
55C4×D44C2312yes—
56#66923—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922C2312yes—
61#66922C2311yescharacteristic
62#66922C2311yescharacteristic
63C4×Dic22—21no—
64C4×Dic22—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8D412yes—
71C4×C8×C11C2312yes—
72C22⋊(C11⋊C8)—21no—
73#66885—24no—
74#66885—22no—
75#66885—22no—
76(C2×D11)⋊C8—24no—
77#66882—22no—
78#66882—24no—
79#66881—22no—
80#66880—24no—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83#19387—111nomaximal, Sylow
84C23×D11—21no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—41no—
90C2×D44—21no—
91C2×D44—22no—
92C2×D44Q1614yescomplemented
93C2×D44C2×D412yes—
94C2×C4×D11—22no—
95C2×C4×D11—22no—
96C2×C4×D11—82no—
97C2×Dic22—22no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—41no—
101C2×Dic22—82no—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—42no—
106C2×C8×C11C2×D414yes—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11C2411yescharacteristic
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11C2×D412yes—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127C2×C11⋊C8—22no—
128Dic44—84no—
129C8×D11—84no—
130#3209—111no—
131#3077—111no—
132C2×#474—111no—
133#2972—111no—
134#1683—114no—
135#1669—114no—
136#1571D1111yescharacteristic, complemented
137#1549—111no—
138#1542—111no—
139C23×C11#12111yescharacteristic
140C22×D11—22no—
141C22×D11—24no—
142C22×D11—81no—
143C22×D11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11C2×Q1612yes—
150C2×C4×C11#13512yes—
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C2×#4111yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—81no—
159C2×Dic11—82no—
160D44—22no—
161D44—24no—
162D44C2×Q1614yes—
163C4×D11—44no—
164C4×D11—82no—
165Dic22—42no—
166Dic22—44no—
167Dic22—82no—
168Dic22—81no—
169C8×C11—24no—
170C8×C11—42no—
171C8×C11—42no—
172C11⋊C8—42no—
173#533—111no—
174C2×C4⋊Q8—111no—
175C2×C4×D4—111no—
176#494—112no—
177#487—112no—
178#478—222no—
179#476—112no—
180#474—112no—
181#474—114no—
182#474—222no—
183#462—222no—
184#451—222no—
185C8×D4—114no—
186C8×D4—222no—
187#431—111no—
188#431C2×D1111yescharacteristic
189#428—221no—
190C2×#107—221no—
191#423C2×D1111yescharacteristic
192C2×C4⋊C8C2×D1111yescharacteristic
193#418—221no—
194C2×#102—221no—
195C2×C22⋊C8—222no—
196#335C2×D1114yescomplemented
197#333—112no—
198#332—112no—
199#332—114no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11#46712yes—
203C22×C11C2×#12111yescharacteristic
204C2×D11—24no—
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—84no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11#46712yes—
212C4×C11C22×Q1611yescharacteristic
213C4×C11C2×#13511yescharacteristic
214C4×C11#57612yes—
215Dic11—42no—
216Dic11—82no—
217Dic11—81no—
218Dic11—81no—
219C22×Q8—221no—
220C22×D4—111no—
221C23×C4—221no—
222C2×Q16—224no—
223C2×M16—21no—
224C22×C8—21no—
225C22×C8—224no—
226C4⋊Q8—112no—
227C4⋊Q8—111no—
228C4⋊Q8—111no—
229C4⋊Q8—221no—
230C4⋊Q8—221no—
231C4⋊Q8—221no—
232#125—221no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235C4×Q8—221no—
236C4×Q8—221no—
237C4×D4—112no—
238C4×D4—112no—
239C4×D4—221no—
240C4×D4—221no—
241#117—221no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42C22×D1111yescharacteristic
247#107—224no—
248#107—222no—
249#106—222no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8D4412yes—
254C4⋊C8C22×D1112yes—
255C4⋊C8C22×D1112yes—
256#103—224no—
257#102—224no—
258#102—222no—
259#102—222no—
260C22⋊C8—221no—
261C22⋊C8—224no—
262C22⋊C8D4412yes—
263C4×C8—221no—
264C4×C8C22×D1112yes—
265C2×C11—22no—
266C2×C11#304111yescharacteristic
267C2×C11C2×#46711yescharacteristic
268C2×C11#306911yescharacteristic
269D11—44no—
270C24—221no—
271C2×Q8—222no—
272C2×Q8—221no—
273C2×Q8—221no—
274C2×Q8—441no—
275C2×Q8—882no—
276C2×D4—114no—
277C2×D4—112no—
278C2×D4—221no—
279C2×D4—222no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—441no—
284C22×C4—882no—
285C22×C4C2×D4411yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4#434311yescharacteristic
288Q16—884no—
289M16—42no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—222no—
294C2×C8—884no—
295C2×C8C2×D4414yes—
296C4⋊C4—112no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—222no—
309C22⋊C4—222no—
310C22⋊C4—441no—
311C42—441no—
312C42C2×D4411yescharacteristic
313C42D4×D1111yescharacteristic
314C42#434311yescharacteristic
315C42C23×D1111yescharacteristic
316C11#1938711yescharacteristic, complemented, Sylow
317C23—222no—
318C23—224no—
319C23—881no—
320C23—881no—
321C23#6694811yescharacteristic
322Q8—442no—
323Q8—444no—
324Q8—881no—
325Q8—882no—
326D4—114no—
327D4—224no—
328D4—222no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—222no—
332C2×C4—444no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4—881no—
338C2×C4—882no—
339C2×C4#6694811yescharacteristic
340C2×C4#6694811yescharacteristic
341C2×C4#6694811yescharacteristic
342C2×C4#6696512yes—
343C2×C4Q16×D1112yes—
344C2×C4C22×D4411yescharacteristic
345C2×C4C2×D4×D1111yescharacteristic
346C2×C4C2×#434311yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—224no—
354C22—442no—
355C22—442no—
356C22—884no—
357C22#1062250012yes—
358C22C2×#6694811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—442no—
363C4—881no—
364C4—882no—
365C4—881no—
366C4#1062250012yes—
367C4#1062328312yes—
368C4C2×#6696511yescharacteristic
369C4C2×Q16×D1111yescharacteristic
370C2—22no—
371C2—444no—
372C2#1307812011yescharacteristic
373C2C2×#1062250011yescharacteristic
374C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1571D11
hypocenterC11#19387
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
1. #13079566C2semidirect
5. #13068068C2semidirect
6. #13067982C2semidirect
7. #13067302C2semidirect
8. #13067274C2semidirect
9. C11×#1571C2semidirect
30. #10622312C22semidirect
32. #10622294C22semidirect
33. C11×#335C22semidirect
34. #10622124C22semidirect
35. #10622124C22semidirect
36. #10622119C22semidirect
92. C2×D44Q16semidirect
136. #1571D11semidirect
196. #335C2×D11semidirect
316. C11#19387semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784152
C2×#106224592
#130776392
#130680682
#130679822
#130673022
#130672742
C11×#15712
#1938711