Finite Group Databasebeta

← #14729855

Subgroups — #14729855

Order 2816.

1068 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 179 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
2#13078738C212yesmaximal, complemented
3#13067737C214yesmaximal, complemented
4#13067675C214yesmaximal, complemented
5#13067330C211yesmaximal, characteristic, complemented
6#13067063C212yesmaximal, complemented
7C2×C11×#559C211yesmaximal, characteristic, complemented
8C11×#559—22no—
9C11×#559—24no—
10C11×#559C2214yes—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#124—22no—
13C2×C11×#123—22no—
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11—22no—
16C2×#66985—22no—
17#10623008C2211yescharacteristic
18#10622840—22no—
19#10622689C2212yes—
20#10622687—22no—
21#10622686C2212yes—
22#10622640C2214yescomplemented
23#10622639—24no—
24#10622634C2214yescomplemented
25#10622580—22no—
26#10622539C2212yes—
27C4×#4318C2211yescharacteristic
28#10622182C2214yes—
29Q8⋊(C11⋊C8)C2218yescomplemented
30C22×Q8×C11D412yes—
31C22×D4×C11—22no—
32C22×D4×C11D412yes—
33C23×C4×C11—22no—
34C2×#4339—21no—
35C11×#127—22no—
36C11×#127D412yes—
37C11×#127C2312yes—
38C11×#124—28no—
39C11×#124—28no—
40C11×#123—28no—
41C11×#123—28no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11D414yes—
45C4×Q8×C11C2314yes—
46C4×D4×C11—28no—
47C4×D4×C11—28no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4D412yes—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—22no—
52C2×C42×C11—22no—
53C2×C42×C11C2311yescharacteristic
54C2×#4325—24no—
55C2×#4324—24no—
56#66985—48no—
57C2×#4323—24no—
58#66983—22no—
59C2×#4318—21no—
60#66928—21no—
61#66927C2311yescharacteristic
62C4×D44—22no—
63#66922C2311yescharacteristic
64#66899—24no—
65C22⋊(C11⋊C8)—22no—
66#66873—24no—
67#66871—24no—
68C4⋊(C11⋊C8)C2314yes—
69#66867—21no—
70#66867—22no—
71C4×C11⋊C8C2312yes—
72#18526—111nomaximal, Sylow
73C24×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×Q8×C11C2×D414yes—
77C2×D4×C11—24no—
78C2×D4×C11—22no—
79C2×D4×C11—24no—
80C2×D4×C11—48no—
81C2×D4×C11—44no—
82C2×D4×C11C2×D414yes—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—28no—
86C22×C4×C11—84no—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—41no—
90#4339—44no—
91C2×D44—22no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4C2×D414yes—
99C11×C22⋊C4—216no—
100C11×C22⋊C4—28no—
101C42×C11—24no—
102C42×C11—24no—
103C42×C11C2×D412yes—
104C42×C11C2×D411yescharacteristic
105C42×C11C2411yescharacteristic
106#4325—48no—
107#4324—48no—
108#4323—48no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111#4318—24no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—24no—
114C2×#559D1111yescharacteristic, complemented
115#3151—111no—
116#3112—112no—
117#1630—114no—
118#1620—114no—
119#1555—111no—
120#1491—112no—
121C23×C11—24no—
122C23×C11—48no—
123C23×C11—44no—
124C23×C11#12011yescharacteristic
125C22×D11—41no—
126Q8×C11—24no—
127Q8×C11—24no—
128Q8×C11—44no—
129D4×C11—44no—
130D4×C11—48no—
131D4×C11—48no—
132D4×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—88no—
140C2×C4×C11#12012yes—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D412yes—
144C22⋊D11—82no—
145C2×Dic11—41no—
146D44—42no—
147D44—44no—
148C4×D11—82no—
149Dic22—42no—
150C11⋊C8—24no—
151C11⋊C8—44no—
152C2×AGL(1,ℤ/8)—222no—
153#559—22no—
154#559—24no—
155#559C2×D1114yes—
156#532—111no—
157C2×#127C2×D1111yescharacteristic
158C2×#124—22no—
159C2×#123—22no—
160C2×C4×Q8C2×D1112yes—
161C2×C4×D4—22no—
162#496—222no—
163#493—112no—
164#492—112no—
165#480—222no—
166#477—114no—
167#460—114no—
168#448—222no—
169#440—224no—
170#432—112no—
171C4×M16—111no—
172#331—114no—
173Q8⋊C8—118no—
174C22×C11—22no—
175C22×C11—48no—
176C22×C11—44no—
177C22×C11—88no—
178C22×C11#45312yes—
179C22×C11C2×#12011yescharacteristic
180C2×D11—82no—
181C2×D11—81no—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—44no—
186C4×C11—44no—
187C4×C11#57514yes—
188Dic11—81no—
189C2×#41—221no—
190C22×Q8C22⋊D1112yes—
191C22×D4—22no—
192C22×D4C22⋊D1112yes—
193C23×C4—22no—
194AGL(1,ℤ/8)—448no—
195C2×SD16—224no—
196C2×SD16—224no—
197C2×D8—224no—
198C2×M16—221no—
199C4⋊Q8—111no—
200#127—22no—
201#127—111no—
202#127C22⋊D1112yes—
203#127C22×D1112yes—
204#124—28no—
205#124—28no—
206#124—221no—
207#123—28no—
208#123—28no—
209#121—222no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8C22⋊D1114yes—
213C4×Q8C22×D1114yes—
214C4×D4—28no—
215C4×D4—28no—
216C4×D4—222no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4C22⋊D1112yes—
219C2×C22⋊C4—24no—
220C2×C22⋊C4—22no—
221C2×C42—22no—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224C4⋊C8—114no—
225#103—224no—
226#102—224no—
227C22⋊C8—222no—
228#97—221no—
229#97—222no—
230C4×C8—112no—
231C2×C11—22no—
232C2×C11—84no—
233C2×C11#300512yes—
234C2×C11C2×#45311yescharacteristic
235D11—161no—
236C24—22no—
237#41—444no—
238C2×Q8—22no—
239C2×Q8—44no—
240C2×Q8—221no—
241C2×Q8C2×C22⋊D1114yes—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—24no—
245C2×D4—48no—
246C2×D4—44no—
247C2×D4—222no—
248C2×D4—221no—
249C2×D4—441no—
250C2×D4C2×C22⋊D1114yes—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—28no—
254C22×C4—84no—
255C22×C4—441no—
256C22×C4C2×C22⋊D1112yes—
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—448no—
259SD16—448no—
260D8—448no—
261M16—224no—
262C2×C8—222no—
263C2×C8—224no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4—222no—
268C4⋊C4C2×C22⋊D1114yes—
269C22⋊C4—216no—
270C22⋊C4—28no—
271C22⋊C4—442no—
272C42—24no—
273C42—24no—
274C42C2×C22⋊D1112yes—
275C42C2×C22⋊D1111yescharacteristic
276C42C23×D1111yescharacteristic
277C11#1852611yescharacteristic, complemented, Sylow
278C23—24no—
279C23—48no—
280C23—44no—
281C23—441no—
282C23#6700611yescharacteristic
283Q8—24no—
284Q8—24no—
285Q8—44no—
286Q8—442no—
287D4—44no—
288D4—48no—
289D4—48no—
290D4—82no—
291D4—442no—
292D4—444no—
293D4—882no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—88no—
301C2×C4—441no—
302C2×C4—882no—
303C2×C4#6700612yes—
304C2×C4#6700611yescharacteristic
305C2×C4C22×C22⋊D1111yescharacteristic
306C2×C4C22×C22⋊D1112yes—
307C8—224no—
308C8—444no—
309C22—22no—
310C22—48no—
311C22—44no—
312C22—88no—
313C22—882no—
314C22—881no—
315C22#1062285412yes—
316C22C2×#6700611yescharacteristic
317C4—22no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—44no—
322C4—881no—
323C4#1062335314yes—
324C2—22no—
325C2—84no—
326C2—1761no—
327C2#1307785812yes—
328C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#559C2
socleC22×C11C2×#120
prime radical#13079066C2
hypercenterC2×#559D11
hypocenterC11#18526
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #13078738C2semidirect
3. #13067737C2semidirect
4. #13067675C2semidirect
5. #13067330C2semidirect
6. #13067063C2semidirect
7. C2×C11×#559C2semidirect
22. #10622640C22semidirect
24. #10622634C22semidirect
29. Q8⋊(C11⋊C8)C22semidirect
114. C2×#559D11semidirect
277. C11#18526semidirect

Maximal subgroups

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

subgroupindex
#130790662
#130787382
#130677372
#130676752
#130673302
#130670632
C2×C11×#5592
#1852611