Finite Group Databasebeta

← #14667793

Subgroups — #14667793

Order 2816.

292 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081221C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070764C211yesmaximal, characteristic, complemented
4#13068129C211yesmaximal, characteristic, complemented
5#13066667C211yesmaximal, characteristic, complemented
6#13066584C211yesmaximal, characteristic, complemented
7C11×#1330C211yesmaximal, characteristic, complemented
8#10623096—21no—
9C11×#436C2211yescharacteristic
10#10622748—21no—
11#10622734—21no—
12#10622632—21no—
13#10622460—21no—
14#10622350—21no—
15#10622349—21no—
16C4×D88C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#346C2211yescharacteristic
21#10622147—21no—
22#10622143—21no—
23#10622143—21no—
24#10622142—21no—
25#10622124—21no—
26#10622095C2211yescharacteristic
27C2×C11×M16—21no—
28C4×D4×C11D411yescharacteristic
29#66992—41no—
30C2×#4324—41no—
31#66983—21no—
32#66983—21no—
33#66979—21no—
34C2×C4⋊Dic11—21no—
35C2×D88D411yescharacteristic
36#66951—41no—
37#66936—41no—
38(C22⋊D11)⋊C4—41no—
39C4×D44—21no—
40#66923—21no—
41#66922—21no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C11×C4⋊C8D411yescharacteristic
45C11×C22⋊C8—21no—
46C4×C8×C11C2311yescharacteristic
47#66885—21no—
48#66885—21no—
49#66885—21no—
50#66882—21no—
51#66882—21no—
52#66882—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66882D411yescharacteristic
56#66881—21no—
57#66881—21no—
58#66874—41no—
59C4⋊(C11⋊C8)—21no—
60#12402—111nomaximal, Sylow
61C2×D4×C11D811yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11—41no—
65C22×Dic11—41no—
66C2×D44—21no—
67C2×C4×D11—41no—
68C2×Dic22—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4D811yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11C2×D411yescharacteristic
77C22⋊Dic11—41no—
78#4324—82no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—41no—
91C2×C11⋊C8—41no—
92D88—21no—
93D88—21no—
94C11×C16—22no—
95C11×C16—41no—
96#3355—111no—
97#2255—111no—
98#2226—111no—
99#1693—111no—
100#1363—111no—
101#1333—111no—
102#1330D1111yescharacteristic, complemented
103C23×C11—21no—
104C22×D11—41no—
105D4×C11—41no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C22⋊D11—82no—
113C22⋊D11—161no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—81no—
118C2×Dic11—161no—
119D44—41no—
120D44—41no—
121C4×D11—161no—
122Dic22—81no—
123Dic22—81no—
124C8×C11—21no—
125C8×C11—41no—
126C8×C11#13511yescharacteristic
127C8×C11#13711yescharacteristic
128C11⋊C8—81no—
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×D8—111no—
138#436C2×D1111yescharacteristic
139#428—221no—
140#367—221no—
141#367—221no—
142#366—221no—
143C4⋊C16C2×D1111yescharacteristic
144#357—221no—
145#346C2×D1111yescharacteristic
146#334—111no—
147#332—221no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11#44711yescharacteristic
152C2×D11—81no—
153C2×D11—81no—
154C2×D11—81no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11#45211yescharacteristic
159C4×C11#45611yescharacteristic
160Dic11—81no—
161Dic11—81no—
162Dic11—81no—
163Dic11—161no—
164C2×SD16—441no—
165C2×D8—111no—
166C2×M16—21no—
167C4⋊Q8—221no—
168#126—441no—
169#125—221no—
170#123—441no—
171#121—221no—
172#121—221no—
173#121—441no—
174C4×D4—221no—
175C4×D4—441no—
176C4×D4D4411yescharacteristic
177#117—221no—
178C2×C4⋊C4—221no—
179C2×C16—21no—
180C2×C16—21no—
181#107—111no—
182#107—111no—
183#107—111no—
184#107—221no—
185#107—221no—
186#107—221no—
187#106—221no—
188#106—221no—
189C4⋊C8—221no—
190C4⋊C8D4411yescharacteristic
191#103—441no—
192#102—221no—
193#102—221no—
194#102—221no—
195C22⋊C8—21no—
196C4×C8C22×D1111yescharacteristic
197C2×C11—81no—
198C2×C11#164711yescharacteristic
199C2×C11#219011yescharacteristic
200C2×C11#219411yescharacteristic
201D11—161no—
202C2×Q8—441no—
203C2×D4—221no—
204C2×D4—441no—
205C2×D4—441no—
206C2×D4D8811yescharacteristic
207C22×C4—21no—
208C22×C4—441no—
209C22×C4—441no—
210SD16—882no—
211D8—221no—
212D8—221no—
213M16—41no—
214M16—41no—
215C2×C8—21no—
216C2×C8—441no—
217C2×C8D4×D1111yescharacteristic
218C2×C8D4×D1111yescharacteristic
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4—221no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4D8811yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—441no—
230C22⋊C4—441no—
231C22⋊C4—441no—
232C22⋊C4—441no—
233C42—441no—
234C42C2×D4411yescharacteristic
235C16—22no—
236C16—41no—
237C11#1240211yescharacteristic, complemented, Sylow
238C23—21no—
239C23—441no—
240Q8—881no—
241Q8—881no—
242D4—41no—
243D4—441no—
244D4—441no—
245D4—882no—
246D4—1761no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4—881no—
254C2×C4—1761no—
255C2×C4—1761no—
256C2×C4#6693511yescharacteristic
257C2×C4C2×D8811yescharacteristic
258C2×C4#6696111yescharacteristic
259C8—21no—
260C8—41no—
261C8—881no—
262C8#6696511yescharacteristic
263C8#6696811yescharacteristic
264C22—41no—
265C22—41no—
266C22—41no—
267C22—881no—
268C22—881no—
269C22—881no—
270C22#1062234511yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—881no—
275C4—881no—
276C4—881no—
277C4—1761no—
278C4#1062239611yescharacteristic
279C4#1062243911yescharacteristic
280C2—81no—
281C2—1761no—
282C2#1306785311yescharacteristic
283C2#1307056411yescharacteristic
284C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1330C2
socleC22×C11#447
prime radical#13081221C2
hypercenter#1330D11
hypocenterC11#12402
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #13070902C2semidirect
3. #13070764C2semidirect
4. #13068129C2semidirect
5. #13066667C2semidirect
6. #13066584C2semidirect
7. C11×#1330C2semidirect
102. #1330D11semidirect
237. C11#12402semidirect

Maximal subgroups

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

subgroupindex
#130812212
#130709022
#130707642
#130681292
#130666672
#130665842
C11×#13302
#1240211