Finite Group Databasebeta

← #14667794

Subgroups — #14667794

Order 2816.

292 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 61 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#13081223C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070763C211yesmaximal, characteristic, complemented
4#13068130C211yesmaximal, characteristic, complemented
5#13066669C211yesmaximal, characteristic, complemented
6#13066575C211yesmaximal, characteristic, complemented
7C11×#1333C211yesmaximal, characteristic, complemented
8#10623089—21no—
9C4×C11×D8C2211yescharacteristic
10#10622772—21no—
11#10622622—21no—
12#10622494—21no—
13#10622454—21no—
14#10622397—21no—
15#10622387—21no—
16#10622301C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×#346C2211yescharacteristic
20C11×#334C2211yescharacteristic
21#10622200—21no—
22#10622143—21no—
23#10622142—21no—
24#10622128—21no—
25#10622120—21no—
26C4⋊(C11⋊C16)C2211yescharacteristic
27C2×C11×D8D411yescharacteristic
28C4×D4×C11—21no—
29#66991—21no—
30#66991—21no—
31#66982—41no—
32C4×C22⋊D11—41no—
33C2×#4314—41no—
34C2×#4313—21no—
35#66945—21no—
36C4⋊C4×D11—21no—
37#66937—41no—
38#66932—41no—
39C4×D44D411yescharacteristic
40#66923—21no—
41#66922—21no—
42C2×C11×C16—21no—
43C11×#107D411yescharacteristic
44C11×C4⋊C8—21no—
45C11×#102—21no—
46C4×C8×C11C2311yescharacteristic
47#66896—21no—
48#66896—21no—
49(C2×D11)⋊C8—21no—
50#66882—21no—
51#66882—21no—
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66880—41no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)D411yescharacteristic
60#12402—111nomaximal, Sylow
61C2×D4×C11—21no—
62C22×C4×C11—41no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11—41no—
65C2×D44D811yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—41no—
68C2×Dic22—41no—
69C11×D8—21no—
70C11×D8—21no—
71C2×C8×C11—41no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C22⋊C4—41no—
76C42×C11C2×D411yescharacteristic
77C22⋊Dic11—41no—
78C22⋊Dic11—41no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—41no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11D811yescharacteristic
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C2×C11⋊C8—21no—
91#4314—82no—
92#4313—41no—
93#4313—41no—
94C11×C16—22no—
95C11⋊C16—41no—
96#3355—111no—
97#2255—111no—
98#2226—111no—
99#1693—111no—
100#1363—111no—
101#1333D1111yescharacteristic, complemented
102#1330—111no—
103C23×C11—41no—
104C22×D11—21no—
105D4×C11—41no—
106D4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—161no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C22⋊D11—82no—
113C22⋊D11—161no—
114C2×Dic11—21no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—81no—
118D44—41no—
119C4×D11—41no—
120C4×D11—41no—
121C4×D11—161no—
122Dic22—81no—
123Dic22—81no—
124C8×C11—21no—
125C8×C11—81no—
126C8×C11#13511yescharacteristic
127C8×C11#13711yescharacteristic
128C11⋊C8—41no—
129#553—221no—
130#500—111no—
131#499—111no—
132#482—221no—
133#480—221no—
134#478—221no—
135#469—221no—
136#461—221no—
137C4×D8C2×D1111yescharacteristic
138#436—111no—
139#428—221no—
140#367—221no—
141#367—221no—
142#366—221no—
143C4⋊C16—111no—
144#357—221no—
145#346C2×D1111yescharacteristic
146#334C2×D1111yescharacteristic
147#332—221no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11#44711yescharacteristic
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—81no—
158C4×C11#45211yescharacteristic
159C4×C11#45611yescharacteristic
160Dic11—41no—
161Dic11—81no—
162Dic11—81no—
163Dic11—161no—
164C2×SD16—441no—
165C2×D8D4411yescharacteristic
166C2×M16—221no—
167C4⋊Q8—221no—
168#126—441no—
169#125—221no—
170#123—441no—
171#121—221no—
172#121—221no—
173#121—441no—
174C4×D4—21no—
175C4×D4—111no—
176C4×D4—441no—
177#117—221no—
178C2×C4⋊C4—221no—
179C2×C16—21no—
180C2×C16—221no—
181#107—111no—
182#107—111no—
183#107—221no—
184#107—221no—
185#107—221no—
186#107D4411yescharacteristic
187#106—221no—
188#106—221no—
189C4⋊C8—21no—
190C4⋊C8—111no—
191#103—441no—
192#102—21no—
193#102—221no—
194#102—221no—
195C22⋊C8—221no—
196C4×C8C22×D1111yescharacteristic
197C2×C11—161no—
198C2×C11#164711yescharacteristic
199C2×C11#219011yescharacteristic
200C2×C11#219411yescharacteristic
201D11—81no—
202C2×Q8—441no—
203C2×D4—21no—
204C2×D4—111no—
205C2×D4—441no—
206C2×D4—441no—
207C22×C4—41no—
208C22×C4—221no—
209C22×C4—441no—
210SD16—882no—
211D8—21no—
212D8—21no—
213M16—441no—
214M16—441no—
215C2×C8—41no—
216C2×C8—221no—
217C2×C8C2×D4411yescharacteristic
218C2×C8D4×D1111yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—111no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C22⋊C4—41no—
229C22⋊C4—221no—
230C22⋊C4—441no—
231C22⋊C4—441no—
232C22⋊C4—441no—
233C42—441no—
234C42D4×D1111yescharacteristic
235C16—22no—
236C16—441no—
237C11#1240211yescharacteristic, complemented, Sylow
238C23—41no—
239C23—221no—
240Q8—881no—
241Q8—881no—
242D4—41no—
243D4—41no—
244D4—441no—
245D4—882no—
246D4—1761no—
247C2×C4—41no—
248C2×C4—161no—
249C2×C4—221no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—441no—
254C2×C4—881no—
255C2×C4—1761no—
256C2×C4#6693511yescharacteristic
257C2×C4D8×D1111yescharacteristic
258C2×C4#6696711yescharacteristic
259C8—21no—
260C8—81no—
261C8—441no—
262C8#6695711yescharacteristic
263C8#6696211yescharacteristic
264C22—81no—
265C22—81no—
266C22—81no—
267C22—441no—
268C22—441no—
269C22—441no—
270C22#1062238611yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—441no—
275C4—881no—
276C4—881no—
277C4—1761no—
278C4#1062234611yescharacteristic
279C4#1062243911yescharacteristic
280C2—161no—
281C2—881no—
282C2#1306785411yescharacteristic
283C2#1307056311yescharacteristic
284C2#1307059011yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1333C2
socleC22×C11#447
prime radical#13081223C2
hypercenter#1333D11
hypocenterC11#12402
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
2. #13070902C2semidirect
3. #13070763C2semidirect
4. #13068130C2semidirect
5. #13066669C2semidirect
6. #13066575C2semidirect
7. C11×#1333C2semidirect
101. #1333D11semidirect
237. C11#12402semidirect

Maximal subgroups

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

subgroupindex
#130812232
#130709022
#130707632
#130681302
#130666692
#130665752
C11×#13332
#1240211