Finite Group Databasebeta

← #14738963

Subgroups — #14738963

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#13079561C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic
3C2×#10622459C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic
5#13068070C214yesmaximal, complemented
6#13067980C214yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067300C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66885—21no—
16C2×#66882—21no—
17#10622706C2212yescomplemented
18#10622705C2212yescomplemented
19#10622700C2212yes—
20#10622697C2212yes—
21#10622679—22no—
22#10622663—22no—
23#10622644—22no—
24#10622614—21no—
25#10622608—21no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622459—22no—
29#10622459C2214yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#333C2212yescomplemented
34C11×#332C2212yescomplemented
35#10622120C2214yescomplemented
36#10622117C2214yescomplemented
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×Dic22—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8C2311yescharacteristic
42C11×C4⋊Q8C2311yescharacteristic
43C11×#125—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11D411yescharacteristic
55C2×#4318—21no—
56C2×C8×D11—24no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44D412yes—
60C4×D44C2312yes—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922C2312yes—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C4⋊C8C2312yes—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70C22⋊(C11⋊C8)D412yes—
71#66885—24no—
72(C2×D11)⋊C8—24no—
73#66882—24no—
74#66874—24no—
75#66873—22no—
76#66873—22no—
77#66872—22no—
78#66871—22no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8C2312yes—
83#19387—111nomaximal, Sylow
84C23×D11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—41no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44Q1614yescomplemented
95C2×D44C2×D412yes—
96C2×C4×D11—22no—
97C2×C4×D11—22no—
98C2×C4×D11—82no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C2×Dic22—82no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117#4326—84no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11C2×D412yes—
126#4318—42no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8C2×D414yes—
129C8×D11—84no—
130#3209—111no—
131#3077—111no—
132C2×#474—111no—
133#2972—111no—
134#1683—114no—
135#1669—114no—
136#1571—111no—
137#1549—111no—
138#1542D1111yescharacteristic, complemented
139C23×C11#12111yescharacteristic
140C22×D11—22no—
141C22×D11—24no—
142C22×D11—81no—
143C22×D11—81no—
144Q8×C11—42no—
145Q8×C11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×Q1612yes—
154C2×C4×C11#13512yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—42no—
160C2×Dic11—81no—
161C2×Dic11—82no—
162D44—22no—
163D44—24no—
164D44C2×Q1614yes—
165C4×D11—44no—
166C4×D11—82no—
167Dic22—44no—
168Dic22—82no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—42no—
173#533C2×D1111yescharacteristic
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#423—111no—
192C2×C4⋊C8C2×D1111yescharacteristic
193#418—221no—
194C2×#102—221no—
195C2×C22⋊C8—222no—
196#335—114no—
197#333C2×D1112yescomplemented
198#332—114no—
199#332C2×D1112yescomplemented
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—81no—
212C4×C11—81no—
213C4×C11#46712yes—
214C4×C11C22×Q1611yescharacteristic
215C4×C11C2×#13511yescharacteristic
216C4×C11#57612yes—
217Dic11—42no—
218Dic11—82no—
219C22×Q8—221no—
220C22×D4—111no—
221C23×C4—221no—
222C2×Q16—224no—
223C2×M16—221no—
224C22×C8—21no—
225C22×C8—224no—
226C4⋊Q8—112no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4⋊Q8—221no—
230C4⋊Q8C22×D1111yescharacteristic
231C4⋊Q8C22×D1111yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—112no—
238C4×D4—112no—
239C4×D4—221no—
240C4×D4—221no—
241#117—21no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42C22×D1111yescharacteristic
247#107—222no—
248#107—224no—
249#106—222no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8C22×D1112yes—
255C4⋊C8C22×D1112yes—
256#103—224no—
257#102—222no—
258#102—222no—
259#102—224no—
260C22⋊C8—21no—
261C22⋊C8—112no—
262C22⋊C8—224no—
263C4×C8—21no—
264C4×C8—112no—
265C2×C11—22no—
266C2×C11#304111yescharacteristic
267C2×C11C2×#46711yescharacteristic
268C2×C11#306911yescharacteristic
269D11—44no—
270C24—221no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—222no—
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×C4#433911yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288Q16—884no—
289M16—442no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—114no—
294C2×C8—222no—
295C2×C8—884no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—112no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—41no—
309C22⋊C4—222no—
310C22⋊C4—222no—
311C42—41no—
312C42#433911yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C23×D1111yescharacteristic
316C11#1938711yescharacteristic, complemented, Sylow
317C23—222no—
318C23—224no—
319C23—881no—
320C23—881no—
321C23#6693711yescharacteristic
322Q8—42no—
323Q8—81no—
324Q8—444no—
325Q8—882no—
326D4—114no—
327D4—222no—
328D4—224no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—222no—
334C2×C4—444no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4—881no—
338C2×C4—882no—
339C2×C4#6693711yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6696912yes—
343C2×C4Q16×D1112yes—
344C2×C4C2×#433911yescharacteristic
345C2×C4C2×D4×D1111yescharacteristic
346C2×C4C2×D4×D1111yescharacteristic
347C8—42no—
348C8—42no—
349C8—224no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—224no—
354C22—442no—
355C22—442no—
356C22—884no—
357C22#1062242612yes—
358C22C2×#6693711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—442no—
365C4—882no—
366C4#1062242612yes—
367C4C2×#6696911yescharacteristic
368C4C2×Q16×D1111yescharacteristic
369C4#1062330012yes—
370C2—22no—
371C2—444no—
372C2#1307812211yescharacteristic
373C2C2×#1062242611yescharacteristic
374C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1542D11
hypocenterC11#19387
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
5. #13068070C2semidirect
6. #13067980C2semidirect
7. #13067390C2semidirect
8. #13067300C2semidirect
9. C11×#1542C2semidirect
17. #10622706C22semidirect
18. #10622705C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
35. #10622120C22semidirect
36. #10622117C22semidirect
94. C2×D44Q16semidirect
138. #1542D11semidirect
197. #333C2×D11semidirect
199. #332C2×D11semidirect
316. C11#19387semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130784092
C2×#106224592
#130776392
#130680702
#130679802
#130673902
#130673002
C11×#15422
#1938711