Finite Group Databasebeta

← #14667780

Subgroups — #14667780

Order 2816.

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

normal subgroups only

This group has 286 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#13070753C211yesmaximal, characteristic, complemented
4#13068140C211yesmaximal, 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#10622455—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#10622127—21no—
25#10622119—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×#4313—21no—
34#66945—21no—
35C4⋊C4×D11—21no—
36#66937—41no—
37#66932—41no—
38C4×D44D411yescharacteristic
39#66923—21no—
40#66922—21no—
41C2×C11×C16—21no—
42C11×#107D411yescharacteristic
43C11×C4⋊C8—21no—
44C11×#102—21no—
45C4×C8×C11C2311yescharacteristic
46#66896—21no—
47#66896—21no—
48#66885—41no—
49(C2×D11)⋊C8—21no—
50#66882—21no—
51#66882—21no—
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66881—41no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)D411yescharacteristic
60#12400—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#4313—41no—
92#4313—41no—
93C11×C16—22no—
94C11⋊C16—41no—
95#3355—111no—
96#2255—111no—
97#2224—111no—
98#1695—111no—
99#1363—111no—
100#1333D1111yescharacteristic, complemented
101#1330—111no—
102C23×C11—41no—
103C22×D11—21no—
104D4×C11—41no—
105D4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—161no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C22⋊D11—82no—
112C22⋊D11—161no—
113C2×Dic11—21no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—81no—
117D44—41no—
118C4×D11—41no—
119C4×D11—41no—
120C4×D11—161no—
121Dic22—161no—
122C8×C11—21no—
123C8×C11—81no—
124C8×C11#13511yescharacteristic
125C8×C11#13711yescharacteristic
126C11⋊C8—41no—
127#553—221no—
128#500—111no—
129#499—111no—
130#482—221no—
131#480—221no—
132#478—221no—
133#476—221no—
134#469—221no—
135C4×D8C2×D1111yescharacteristic
136#436—111no—
137#428—221no—
138#367—221no—
139#366—221no—
140#366—221no—
141C4⋊C16—111no—
142#357—221no—
143#346C2×D1111yescharacteristic
144#334C2×D1111yescharacteristic
145#333—221no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11—81no—
149C22×C11#44711yescharacteristic
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—81no—
156C4×C11#45211yescharacteristic
157C4×C11#45611yescharacteristic
158Dic11—41no—
159Dic11—81no—
160Dic11—81no—
161Dic11—161no—
162C2×D8D4411yescharacteristic
163C2×M16—221no—
164C4⋊Q8—221no—
165#126—441no—
166#125—221no—
167#123—441no—
168#121—221no—
169#121—221no—
170#121—441no—
171C4×D4—21no—
172C4×D4—111no—
173C4×D4—441no—
174#117—221no—
175C2×C4⋊C4—221no—
176C2×C16—21no—
177C2×C16—221no—
178#107—111no—
179#107—111no—
180#107—221no—
181#107—221no—
182#107—221no—
183#107D4411yescharacteristic
184#106—221no—
185#106—221no—
186#106—441no—
187C4⋊C8—21no—
188C4⋊C8—111no—
189#102—21no—
190#102—221no—
191#102—221no—
192#102—441no—
193C22⋊C8—221no—
194C4×C8C22×D1111yescharacteristic
195C2×C11—161no—
196C2×C11#164711yescharacteristic
197C2×C11#219111yescharacteristic
198C2×C11#219211yescharacteristic
199D11—81no—
200C2×Q8—441no—
201C2×D4—21no—
202C2×D4—111no—
203C2×D4—441no—
204C2×D4—441no—
205C22×C4—41no—
206C22×C4—221no—
207C22×C4—441no—
208D8—21no—
209D8—21no—
210M16—441no—
211M16—441no—
212C2×C8—41no—
213C2×C8—221no—
214C2×C8C2×D4411yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—111no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C22⋊C4—41no—
226C22⋊C4—221no—
227C22⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—441no—
230C42—441no—
231C42D4×D1111yescharacteristic
232C16—22no—
233C16—441no—
234C11#1240011yescharacteristic, complemented, Sylow
235C23—41no—
236C23—221no—
237Q8—1761no—
238D4—41no—
239D4—41no—
240D4—441no—
241D4—882no—
242D4—1761no—
243C2×C4—41no—
244C2×C4—161no—
245C2×C4—221no—
246C2×C4—441no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—441no—
250C2×C4—881no—
251C2×C4—1761no—
252C2×C4#6693511yescharacteristic
253C2×C4D8×D1111yescharacteristic
254C2×C4#6696711yescharacteristic
255C8—21no—
256C8—81no—
257C8—441no—
258C8#6695711yescharacteristic
259C8#6696211yescharacteristic
260C22—81no—
261C22—81no—
262C22—81no—
263C22—441no—
264C22—441no—
265C22—441no—
266C22#1062238611yescharacteristic
267C4—21no—
268C4—21no—
269C4—81no—
270C4—441no—
271C4—881no—
272C4—881no—
273C4—1761no—
274C4#1062234611yescharacteristic
275C4#1062243911yescharacteristic
276C2—161no—
277C2—881no—
278C2#1306785411yescharacteristic
279C2#1307056811yescharacteristic
280C2#1307057611yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1333C2
socleC22×C11#447
prime radical#13081223C2
hypercenter#1333D11
hypocenterC11#12400
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. #13070753C2semidirect
4. #13068140C2semidirect
5. #13066669C2semidirect
6. #13066575C2semidirect
7. C11×#1333C2semidirect
100. #1333D11semidirect
234. C11#12400semidirect

Maximal subgroups

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

subgroupindex
#130812232
#130709022
#130707532
#130681402
#130666692
#130665752
C11×#13332
#1240011