Finite Group Databasebeta

← #14667791

Subgroups — #14667791

Order 2816.

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

normal subgroups only

This group has 292 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#13070763C211yesmaximal, characteristic, complemented
3#13068129C211yesmaximal, 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#10622632—21no—
18#10622295C2211yescharacteristic
19#10622200—21no—
20#10622128—21no—
21#10622128—21no—
22#10622127—21no—
23#10622124—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—
40C2×#4324—41no—
41#66922—21no—
42C11×#107—21no—
43C11×#107D411yescharacteristic
44C11×#107D411yescharacteristic
45C11×#107D411yescharacteristic
46C11×#106—21no—
47C11×#106—21no—
48C11×C4⋊C8D411yescharacteristic
49C11×#102—21no—
50C11×#102—21no—
51C11×#102—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11C2311yescharacteristic
54#66882—21no—
55#66882—21no—
56C2×C11⋊C16—21no—
57C2×C11⋊C16—21no—
58#66874—41no—
59C4⋊(C11⋊C8)—21no—
60#12402—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
90#4324—82no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C2×C11⋊C8—41no—
94C11⋊C16—22no—
95C11⋊C16—41no—
96#3355D1111yescharacteristic
97#2255—111no—
98#2226—111no—
99#1693—111no—
100#1363—111no—
101#1333—111no—
102#1330—111no—
103C23×C11—21no—
104C23×C11—41no—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—41no—
108D4×C11—82no—
109D4×C11—161no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—161no—
117C2×C4×C11—161no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×Dic11—81no—
122Dic22—81no—
123Dic22—81no—
124C8×C11—21no—
125C8×C11—41no—
126C8×C11#13511yescharacteristic
127C8×C11#13711yescharacteristic
128C11⋊C8—81no—
129#553—21no—
130#500—111no—
131#499C2×D1111yescharacteristic
132#482—21no—
133#480—21no—
134#478—21no—
135#469—21no—
136#461—221no—
137C4×D8C2×D1111yescharacteristic
138#436C2×D1111yescharacteristic
139#428—21no—
140#367—221no—
141#367—221no—
142#366—221no—
143C4⋊C16—111no—
144#357—221no—
145#346—111no—
146#334—111no—
147#332—221no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—81no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11#44711yescharacteristic
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—81no—
159C4×C11—81no—
160C4×C11—81no—
161C4×C11#45211yescharacteristic
162C4×C11#45611yescharacteristic
163Dic11—161no—
164C2×SD16—441no—
165C2×D8C22⋊D1111yescharacteristic
166C2×M16—21no—
167C4⋊Q8—221no—
168#126—41no—
169#125—21no—
170#123—41no—
171#121—21no—
172#121—21no—
173#121—41no—
174C4×D4—21no—
175C4×D4—41no—
176C4×D4C22⋊D1111yescharacteristic
177#117—21no—
178C2×C4⋊C4—21no—
179C2×C16—221no—
180C2×C16—221no—
181#107—21no—
182#107—221no—
183#107—221no—
184#107C22⋊D1111yescharacteristic
185#107C22⋊D1111yescharacteristic
186#107C22⋊D1111yescharacteristic
187#106—21no—
188#106—21no—
189C4⋊C8—221no—
190C4⋊C8C22⋊D1111yescharacteristic
191#103—441no—
192#102—21no—
193#102—21no—
194#102—21no—
195C22⋊C8—21no—
196C4×C8C22×D1111yescharacteristic
197C2×C11—81no—
198C2×C11—161no—
199C2×C11#164711yescharacteristic
200C2×C11#219011yescharacteristic
201C2×C11#219411yescharacteristic
202C2×Q8—441no—
203C2×D4—21no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4#432311yescharacteristic
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210SD16—882no—
211D8—21no—
212D8—21no—
213M16—41no—
214M16—41no—
215C2×C8—21no—
216C2×C8—441no—
217C2×C8C2×C22⋊D1111yescharacteristic
218C2×C8C2×C22⋊D1111yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4#432311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C42—41no—
234C42C2×C22⋊D1111yescharacteristic
235C16—222no—
236C16—441no—
237C11#1240211yescharacteristic, complemented, Sylow
238C23—21no—
239C23—41no—
240Q8—881no—
241Q8—881no—
242D4—41no—
243D4—41no—
244D4—41no—
245D4—82no—
246D4—161no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—161no—
254C2×C4—161no—
255C2×C4—881no—
256C2×C4C2×#432311yescharacteristic
257C2×C4#6698511yescharacteristic
258C2×C4#6700611yescharacteristic
259C8—21no—
260C8—41no—
261C8—881no—
262C8#6700311yescharacteristic
263C8#6700411yescharacteristic
264C22—41no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1062283011yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—81no—
275C4—81no—
276C4—81no—
277C4—1761no—
278C4#1062285211yescharacteristic
279C4#1062285911yescharacteristic
280C2—81no—
281C2—161no—
282C2#1306785111yescharacteristic
283C2#1307056211yescharacteristic
284C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#3355C2
socleC22×C11#447
hypercenter#3355D11
hypocenterC11#12402
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. #13070763C2semidirect
3. #13068129C2semidirect
4. #13066668C2semidirect
5. #13066583C2semidirect
6. #13066574C2semidirect
237. C11#12402semidirect

Maximal subgroups

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

subgroupindex
#130709032
#130707632
#130681292
#130666682
#130665832
#130665742
C11×#33552
#1240211