Finite Group Databasebeta

← #14667160

Subgroups — #14667160

Order 2816.

280 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070833C211yesmaximal, characteristic, complemented
2#13070828C211yesmaximal, characteristic
3#13070191C211yesmaximal, characteristic, complemented
4#13066604C211yesmaximal, characteristic, complemented
5#13066601C211yesmaximal, characteristic
6#13066567C211yesmaximal, characteristic, complemented
7C11×#3256C211yesmaximal, characteristic
8C11×#529—21no—
9C11×#479—21no—
10C11×#478—21no—
11C11×#470C2211yescharacteristic
12C11×#469C2211yescharacteristic
13C11×#468—21no—
14C11×#464—21no—
15C11×#463—21no—
16C11×#423C2211yescharacteristic
17#10622738C2211yescharacteristic
18#10622203—21no—
19#10622201—21no—
20#10622197—21no—
21#10622195C2211yescharacteristic
22#10622191C2211yescharacteristic
23#10622191C2211yescharacteristic
24#10622161—21no—
25#10622125—21no—
26#10622125—21no—
27C2×C11×Q16D411yescharacteristic
28C2×C11×SD16—21no—
29C2×C11×D8D411yescharacteristic
30C2×C11×M16D411yescharacteristic
31C2×C11×M16C2311yescharacteristic
32C11×#126—41no—
33C11×#125—21no—
34C11×#124—21no—
35C11×#123—41no—
36C11×C22⋊Q8—21no—
37C11×#121—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—41no—
41C11×#117—41no—
42C2×C42×C11D411yescharacteristic
43#66979—21no—
44C2×#4318—21no—
45C11×#107—21no—
46C11×#106D411yescharacteristic
47C11×#106D411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×#103—21no—
51C11×#103—21no—
52C11×#102—21no—
53C11×#102—21no—
54#66883—21no—
55#66883—21no—
56#66876—21no—
57#66876—21no—
58#12309—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C11×Q16—41no—
66C11×SD16—81no—
67C11×D8—41no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—21no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—21no—
85C42×C11—41no—
86C42×C11SD1611yescharacteristic
87C42×C11SD1611yescharacteristic
88C22⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4×Dic11—41no—
91#4318—41no—
92#4318—41no—
93C2×C11⋊C8—41no—
94C11⋊C16—41no—
95C11⋊C16—41no—
96#3256D1111yescharacteristic
97#2239—111no—
98#2238—111no—
99#2102—111no—
100#1340—111no—
101#1339—111no—
102#1327—111no—
103C23×C11—41no—
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105Q8×C11—41no—
106Q8×C11—41no—
107D4×C11—41no—
108D4×C11—41no—
109D4×C11—82no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11—82no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×Dic11—81no—
122C8×C11—21no—
123C8×C11—21no—
124C8×C11—41no—
125C11⋊C8—81no—
126#529—21no—
127#479—21no—
128#478—21no—
129#470C2×D1111yescharacteristic
130#469C2×D1111yescharacteristic
131#468—21no—
132#464—21no—
133#463—21no—
134#430—111no—
135#423C2×D1111yescharacteristic
136#365—221no—
137#365—221no—
138#362—221no—
139#361—221no—
140#349—111no—
141#349—111no—
142#344—221no—
143#339—221no—
144H(3,ℤ/4)—111no—
145C22×C11—21no—
146C22×C11—41no—
147C22×C11—81no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11#45011yescharacteristic
151C4×C11—21no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—81no—
155C4×C11—81no—
156C4×C11—81no—
157C4×C11#45411yescharacteristic
158C4×C11#45811yescharacteristic
159Dic11—161no—
160C2×Q16C22⋊D1111yescharacteristic
161C2×SD16—21no—
162C2×D8C22⋊D1111yescharacteristic
163C2×M16—221no—
164C2×M16C22⋊D1111yescharacteristic
165C2×M16C22×D1111yescharacteristic
166#126—41no—
167#125—21no—
168#124—21no—
169#123—41no—
170C22⋊Q8—21no—
171#121—21no—
172C4×Q8—21no—
173C4×D4—21no—
174C4×D4—41no—
175#117—41no—
176#117—221no—
177C2×C42C22⋊D1111yescharacteristic
178M32—221no—
179M32—221no—
180#108—221no—
181#108—221no—
182#107—21no—
183#106C22⋊D1111yescharacteristic
184#106C22⋊D1111yescharacteristic
185C4⋊C8—21no—
186C4⋊C8—21no—
187#103—21no—
188#103—21no—
189#102—21no—
190#102—21no—
191C2×C11—21no—
192C2×C11—41no—
193C2×C11—161no—
194C2×C11#161611yescharacteristic
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—21no—
199C22×C4—41no—
200C22×C4C2×C22⋊D1111yescharacteristic
201Q16—41no—
202SD16—81no—
203D8—41no—
204M16—41no—
205M16—41no—
206M16—441no—
207M16—441no—
208C2×C8—21no—
209C2×C8—441no—
210C2×C8C2×C22⋊D1111yescharacteristic
211C2×C8C2×C22⋊D1111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—441no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—441no—
225C42—21no—
226C42—41no—
227C42—441no—
228C42#432411yescharacteristic
229C42#432411yescharacteristic
230C16—441no—
231C16—441no—
232C11#1230911yescharacteristic, complemented, Sylow
233C23—41no—
234C23#6698511yescharacteristic
235Q8—41no—
236Q8—41no—
237D4—41no—
238D4—41no—
239D4—82no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—881no—
250C2×C4C2×#432411yescharacteristic
251C2×C4#6700611yescharacteristic
252C8—21no—
253C8—21no—
254C8—41no—
255C8—881no—
256C22—21no—
257C22—41no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22#1062283111yescharacteristic
262C4—21no—
263C4—41no—
264C4—41no—
265C4—81no—
266C4—81no—
267C4—81no—
268C4—1761no—
269C4#1062285611yescharacteristic
270C4#1062285811yescharacteristic
271C2—21no—
272C2—41no—
273C2—161no—
274C2#1306765311yescharacteristic
subgroupG/H
centerC2#13067653
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3256C2
socleC2×C11#1616
prime radicalC11×#469C22
hypercenter#3256D11
hypocenterC11#12309
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3256

Complements

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

NH ≅ G/Ntype
1. #13070833C2semidirect
3. #13070191C2semidirect
4. #13066604C2semidirect
6. #13066567C2semidirect
232. C11#12309semidirect

Maximal subgroups

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

subgroupindex
#130708332
#130708282
#130701912
#130666042
#130666012
#130665672
C11×#32562
#1230911