Finite Group Databasebeta

← #14729839

Subgroups — #14729839

Order 2816.

1716 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079066C211yesmaximal, characteristic, complemented
2#13078707C212yesmaximal, complemented
3#13067732C214yesmaximal, complemented
4#13067670C214yesmaximal, complemented
5#13067330C211yesmaximal, characteristic, complemented
6#13067059C212yesmaximal, complemented
7C2×D42×C11C211yesmaximal, characteristic, complemented
8C23×D4×C11—22no—
9D42×C11—22no—
10D42×C11—24no—
11D42×C11C2214yes—
12C2×C11×#127C2211yescharacteristic
13C2×C11×#121—22no—
14C2×C11×#120—22no—
15C2×C4×D4×C11C2212yes—
16C2×#66985—22no—
17#10623008C2211yescharacteristic, complemented
18#10622830—22no—
19#10622689C2212yescomplemented
20#10622687—22no—
21#10622686C2212yescomplemented
22#10622628C2214yescomplemented
23#10622627—24no—
24#10622621C2214yescomplemented
25#10622581—22no—
26#10622539C2212yescomplemented
27C4×#4318C2211yescharacteristic, complemented
28#10622182C2214yescomplemented
29D4⋊(C11⋊C8)C2218yescomplemented
30C25×C11—22no—
31C22×D4×C11—24no—
32C22×D4×C11—28no—
33C22×D4×C11—28no—
34C22×D4×C11—22no—
35C22×D4×C11—416no—
36C22×D4×C11D412yes—
37C22×D4×C11D412yes—
38C23×C4×C11—22no—
39C2×#4339—21no—
40C11×#127—22no—
41C11×#127D412yes—
42C11×#127C2312yes—
43C11×#121—28no—
44C11×#121—28no—
45C11×#120—28no—
46C11×#120—28no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C4×D4×C11D414yes—
50C4×D4×C11C2314yes—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11C2311yescharacteristic
55C2×#4324—24no—
56#66985—48no—
57C2×#4323—24no—
58C2×#4323—24no—
59#66983—22no—
60C2×#4318—21no—
61#66928—21no—
62#66927C2311yescharacteristic, complemented
63C4×D44—22no—
64#66922C2311yescharacteristic, complemented
65#66896—24no—
66C22⋊(C11⋊C8)—22no—
67#66873—24no—
68#66872—24no—
69C4⋊(C11⋊C8)C2314yescomplemented
70#66867—21no—
71#66867—22no—
72C4×C11⋊C8C2312yescomplemented
73#18524—111nomaximal, Sylow
74C24×C11—22no—
75C24×C11—28no—
76C24×C11—22no—
77C24×C11—416no—
78C24×C11—84no—
79C2×D4×C11—28no—
80C2×D4×C11—216no—
81C2×D4×C11—22no—
82C2×D4×C11—24no—
83C2×D4×C11—22no—
84C2×D4×C11—24no—
85C2×D4×C11—48no—
86C2×D4×C11—44no—
87C2×D4×C11—432no—
88C2×D4×C11—416no—
89C2×D4×C11—416no—
90C2×D4×C11—416no—
91C2×D4×C11C2×D414yes—
92C2×D4×C11C2×D414yes—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—48no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100#4339—44no—
101C2×D44—22no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×Dic22—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4C2×D414yes—
107C11×C22⋊C4—28no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C42×C11C2×D412yes—
111C42×C11C2×D411yescharacteristic
112C42×C11C2411yescharacteristic
113#4324—48no—
114#4323—48no—
115#4323—48no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—22no—
118#4318—24no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—24no—
121C2×D42D1111yescharacteristic, complemented
122#3151—111no—
123#3109—112no—
124#1629—114no—
125#1619—114no—
126#1555—111no—
127#1490—112no—
128C23×C11—28no—
129C23×C11—24no—
130C23×C11—24no—
131C23×C11—44no—
132C23×C11—48no—
133C23×C11—432no—
134C23×C11—44no—
135C23×C11—44no—
136C23×C11—88no—
137C23×C11—832no—
138C23×C11#12011yescharacteristic
139C22×D11—41no—
140D4×C11—28no—
141D4×C11—24no—
142D4×C11—44no—
143D4×C11—48no—
144D4×C11—432no—
145D4×C11—48no—
146D4×C11—82no—
147D4×C11AGL(1,ℤ/8)18yescomplemented
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—48no—
152C2×C4×C11—44no—
153C2×C4×C11—48no—
154C2×C4×C11#12012yes—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×D412yes—
158C22⋊D11—82no—
159C2×Dic11—41no—
160D44—42no—
161D44—44no—
162C4×D11—82no—
163Dic22—42no—
164C11⋊C8—24no—
165C11⋊C8—44no—
166C23×D4—22no—
167C2×AGL(1,ℤ/8)—222no—
168D42—22no—
169D42—24no—
170D42C2×D1114yes—
171#532—111no—
172C2×#127C2×D1111yescharacteristic
173C2×#121—22no—
174C2×#120—22no—
175C2×C4×D4C2×D1112yes—
176#496—222no—
177#493—112no—
178#492—112no—
179#481—222no—
180#476—114no—
181#459—114no—
182#447—222no—
183#442—224no—
184#432—112no—
185C4×M16—111no—
186#331—114no—
187D4⋊C8—118no—
188C22×C11—22no—
189C22×C11—28no—
190C22×C11—416no—
191C22×C11—44no—
192C22×C11—44no—
193C22×C11—48no—
194C22×C11—44no—
195C22×C11—88no—
196C22×C11—832no—
197C22×C11#45312yes—
198C22×C11C2×#12011yescharacteristic
199C2×D11—82no—
200C2×D11—81no—
201C4×C11—22no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—44no—
205C4×C11C2×AGL(1,ℤ/8)14yes—
206Dic11—81no—
207C25—22no—
208C2×#41—221no—
209C22×D4—24no—
210C22×D4—28no—
211C22×D4—28no—
212C22×D4—22no—
213C22×D4—416no—
214C22×D4C22⋊D1112yes—
215C22×D4C22⋊D1112yes—
216C23×C4—22no—
217AGL(1,ℤ/8)—448no—
218C2×SD16—224no—
219C2×D8—224no—
220C2×D8—224no—
221C2×M16—221no—
222C4⋊Q8—111no—
223#127—22no—
224#127—111no—
225#127C22⋊D1112yes—
226#127C22×D1112yes—
227#124—221no—
228#121—28no—
229#121—28no—
230#121—222no—
231#120—28no—
232#120—28no—
233C4×D4—22no—
234C4×D4—22no—
235C4×D4—222no—
236C4×D4C22⋊D1114yes—
237C4×D4C22×D1114yes—
238C2×C4⋊C4C22⋊D1112yes—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42C22×D1111yescharacteristic
242#106—224no—
243C4⋊C8—114no—
244#102—224no—
245#102—224no—
246C22⋊C8—222no—
247#97—221no—
248#97—222no—
249C4×C8—112no—
250C2×C11—22no—
251C2×C11—48no—
252C2×C11—84no—
253C2×C11#300312yes—
254C2×C11C2×#45311yescharacteristic
255D11—161no—
256C24—22no—
257C24—28no—
258C24—22no—
259C24—416no—
260C24—84no—
261#41—444no—
262C2×Q8—221no—
263C2×D4—28no—
264C2×D4—216no—
265C2×D4—22no—
266C2×D4—24no—
267C2×D4—22no—
268C2×D4—24no—
269C2×D4—48no—
270C2×D4—44no—
271C2×D4—432no—
272C2×D4—416no—
273C2×D4—416no—
274C2×D4—416no—
275C2×D4—222no—
276C2×D4—221no—
277C2×D4—441no—
278C2×D4C2×C22⋊D1114yes—
279C2×D4C2×C22⋊D1114yes—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—48no—
284C22×C4—441no—
285C22×C4C2×C22⋊D1112yes—
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—448no—
288D8—448no—
289D8—448no—
290M16—224no—
291C2×C8—222no—
292C2×C8—224no—
293C4⋊C4—22no—
294C4⋊C4—222no—
295C4⋊C4C2×C22⋊D1114yes—
296C22⋊C4—28no—
297C22⋊C4—24no—
298C22⋊C4—24no—
299C22⋊C4—442no—
300C42C2×C22⋊D1111yescharacteristic
301C42C2×C22⋊D1112yes—
302C42C23×D1111yescharacteristic
303C11#1852411yescharacteristic, complemented, Sylow
304C23—28no—
305C23—24no—
306C23—24no—
307C23—44no—
308C23—48no—
309C23—432no—
310C23—44no—
311C23—44no—
312C23—88no—
313C23—832no—
314C23—441no—
315C23#6700611yescharacteristic
316Q8—442no—
317D4—28no—
318D4—24no—
319D4—44no—
320D4—48no—
321D4—432no—
322D4—48no—
323D4—82no—
324D4—442no—
325D4—444no—
326D4—882no—
327D4#6698518yescomplemented
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—48no—
332C2×C4—44no—
333C2×C4—48no—
334C2×C4—441no—
335C2×C4—882no—
336C2×C4#6700611yescharacteristic
337C2×C4#6700612yes—
338C2×C4C22×C22⋊D1111yescharacteristic
339C2×C4C22×C22⋊D1112yes—
340C8—224no—
341C8—444no—
342C22—22no—
343C22—28no—
344C22—416no—
345C22—44no—
346C22—44no—
347C22—48no—
348C22—44no—
349C22—88no—
350C22—832no—
351C22—882no—
352C22—881no—
353C22#1062285412yes—
354C22C2×#6700611yescharacteristic
355C4—22no—
356C4—21no—
357C4—21no—
358C4—44no—
359C4—881no—
360C4C2×#6698514yes—
361C2—22no—
362C2—48no—
363C2—84no—
364C2—1761no—
365C2#1307784312yes—
366C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D42×C11C2
socleC22×C11C2×#120
hypercenterC2×D42D11
hypocenterC11#18524
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #13079066C2semidirect
2. #13078707C2semidirect
3. #13067732C2semidirect
4. #13067670C2semidirect
5. #13067330C2semidirect
6. #13067059C2semidirect
7. C2×D42×C11C2semidirect
17. #10623008C22semidirect
19. #10622689C22semidirect
21. #10622686C22semidirect
22. #10622628C22semidirect
24. #10622621C22semidirect
26. #10622539C22semidirect
27. C4×#4318C22semidirect
28. #10622182C22semidirect
29. D4⋊(C11⋊C8)C22semidirect
62. #66927C23semidirect
64. #66922C23semidirect
69. C4⋊(C11⋊C8)C23semidirect
72. C4×C11⋊C8C23semidirect
121. C2×D42D11semidirect
147. D4×C11AGL(1,ℤ/8)semidirect
303. C11#18524semidirect
327. D4#66985semidirect

Maximal subgroups

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

subgroupindex
#130790662
#130787072
#130677322
#130676702
#130673302
#130670592
C2×D42×C112
#1852411