Finite Group Databasebeta

← #14667777

Subgroups — #14667777

Order 2816.

286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070903C211yesmaximal, characteristic, complemented
2#13070753C211yesmaximal, characteristic, complemented
3#13068139C211yesmaximal, characteristic, complemented
4#13066668C211yesmaximal, characteristic, complemented
5#13066583C211yesmaximal, characteristic, complemented
6#13066574C211yesmaximal, characteristic, complemented
7C11×#3355C211yesmaximal, characteristic
8C11×#553—21no—
9C11×#499C2211yescharacteristic
10C11×#482—21no—
11C11×#480—21no—
12C11×#478—21no—
13C11×#469—21no—
14C4×C11×D8C2211yescharacteristic
15C11×#436C2211yescharacteristic
16C11×#428—21no—
17#10622621—21no—
18#10622295C2211yescharacteristic
19#10622200—21no—
20#10622128—21no—
21#10622127—21no—
22#10622127—21no—
23#10622119—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×D8D411yescharacteristic
28C2×C11×M16—21no—
29C11×#126—41no—
30C11×#125—21no—
31C11×#123—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—41no—
35C4×D4×C11—21no—
36C4×D4×C11—41no—
37C4×D4×C11D411yescharacteristic
38C11×#117—21no—
39C2×C11×C4⋊C4—21no—
40#66922—21no—
41C11×#107—21no—
42C11×#107D411yescharacteristic
43C11×#107D411yescharacteristic
44C11×#107D411yescharacteristic
45C11×#106—21no—
46C11×#106—21no—
47C11×C4⋊C8D411yescharacteristic
48C11×#102—21no—
49C11×#102—21no—
50C11×#102—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11C2311yescharacteristic
53#66896—41no—
54#66882—21no—
55#66882—21no—
56C2×C11⋊C16—21no—
57C2×C11⋊C16—21no—
58#66872—41no—
59C4⋊(C11⋊C8)—21no—
60#12400—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11D811yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C2×Dic22—41no—
69C11×D8—21no—
70C11×D8—21no—
71C11×M16—41no—
72C11×M16—41no—
73C2×C8×C11—21no—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4D811yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—41no—
89C42×C11C2×D411yescharacteristic
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C2×C11⋊C8—41no—
93C11⋊C16—22no—
94C11⋊C16—41no—
95#3355D1111yescharacteristic
96#2255—111no—
97#2224—111no—
98#1695—111no—
99#1363—111no—
100#1333—111no—
101#1330—111no—
102C23×C11—21no—
103C23×C11—41no—
104D4×C11—41no—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—82no—
108D4×C11—161no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—161no—
116C2×C4×C11—161no—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11C2×D811yescharacteristic
119C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
120C2×Dic11—81no—
121Dic22—161no—
122C8×C11—21no—
123C8×C11—41no—
124C8×C11#13511yescharacteristic
125C8×C11#13711yescharacteristic
126C11⋊C8—81no—
127#553—21no—
128#500—111no—
129#499C2×D1111yescharacteristic
130#482—21no—
131#480—21no—
132#478—21no—
133#476—221no—
134#469—21no—
135C4×D8C2×D1111yescharacteristic
136#436C2×D1111yescharacteristic
137#428—21no—
138#367—221no—
139#366—221no—
140#366—221no—
141C4⋊C16—111no—
142#357—221no—
143#346—111no—
144#334—111no—
145#333—221no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11—81no—
152C22×C11#44711yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11—81no—
157C4×C11—81no—
158C4×C11—81no—
159C4×C11#45211yescharacteristic
160C4×C11#45611yescharacteristic
161Dic11—161no—
162C2×D8C22⋊D1111yescharacteristic
163C2×M16—21no—
164C4⋊Q8—221no—
165#126—41no—
166#125—21no—
167#123—41no—
168#121—21no—
169#121—21no—
170#121—41no—
171C4×D4—21no—
172C4×D4—41no—
173C4×D4C22⋊D1111yescharacteristic
174#117—21no—
175C2×C4⋊C4—21no—
176C2×C16—221no—
177C2×C16—221no—
178#107—21no—
179#107—221no—
180#107—221no—
181#107C22⋊D1111yescharacteristic
182#107C22⋊D1111yescharacteristic
183#107C22⋊D1111yescharacteristic
184#106—21no—
185#106—21no—
186#106—441no—
187C4⋊C8—221no—
188C4⋊C8C22⋊D1111yescharacteristic
189#102—21no—
190#102—21no—
191#102—21no—
192#102—441no—
193C22⋊C8—21no—
194C4×C8C22×D1111yescharacteristic
195C2×C11—81no—
196C2×C11—161no—
197C2×C11#164711yescharacteristic
198C2×C11#219111yescharacteristic
199C2×C11#219211yescharacteristic
200C2×Q8—441no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4#432311yescharacteristic
205C22×C4—21no—
206C22×C4—41no—
207C22×C4—41no—
208D8—21no—
209D8—21no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—441no—
214C2×C8C2×C22⋊D1111yescharacteristic
215C2×C8C2×C22⋊D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4#432311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C42—41no—
231C42C2×C22⋊D1111yescharacteristic
232C16—222no—
233C16—441no—
234C11#1240011yescharacteristic, complemented, Sylow
235C23—21no—
236C23—41no—
237Q8—1761no—
238D4—41no—
239D4—41no—
240D4—41no—
241D4—82no—
242D4—161no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—161no—
250C2×C4—161no—
251C2×C4—881no—
252C2×C4C2×#432311yescharacteristic
253C2×C4#6698511yescharacteristic
254C2×C4#6700611yescharacteristic
255C8—21no—
256C8—41no—
257C8—881no—
258C8#6700311yescharacteristic
259C8#6700411yescharacteristic
260C22—41no—
261C22—41no—
262C22—41no—
263C22—81no—
264C22—81no—
265C22—81no—
266C22#1062283011yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—81no—
271C4—81no—
272C4—81no—
273C4—1761no—
274C4#1062285211yescharacteristic
275C4#1062285911yescharacteristic
276C2—81no—
277C2—161no—
278C2#1306785111yescharacteristic
279C2#1307056711yescharacteristic
280C2#1307057311yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#3355C2
socleC22×C11#447
hypercenter#3355D11
hypocenterC11#12400
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #3355

Complements

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

NH ≅ G/Ntype
1. #13070903C2semidirect
2. #13070753C2semidirect
3. #13068139C2semidirect
4. #13066668C2semidirect
5. #13066583C2semidirect
6. #13066574C2semidirect
234. C11#12400semidirect

Maximal subgroups

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

subgroupindex
#130709032
#130707532
#130681392
#130666682
#130665832
#130665742
C11×#33552
#1240011