Finite Group Databasebeta

← #14667800

Subgroups — #14667800

Order 2816.

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

normal subgroups only

This group has 280 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#13081190C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070769C211yesmaximal, characteristic, complemented
4#13068129C211yesmaximal, characteristic
5#13066667C211yesmaximal, characteristic, complemented
6#13066587C211yesmaximal, characteristic, complemented
7C11×#1330C211yesmaximal, characteristic
8#10623072—21no—
9C11×#436C2211yescharacteristic
10#10622750—21no—
11#10622734—21no—
12#10622632—21no—
13#10622442—21no—
14#10622336—21no—
15#10622335—21no—
16C4×Dic44C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#346C2211yescharacteristic
21#10622143—21no—
22#10622142—21no—
23#10622142—21no—
24#10622141—21no—
25#10622124—21no—
26#10622095C2211yescharacteristic
27C2×C11×M16—21no—
28C4×D4×C11D411yescharacteristic
29#66988—41no—
30C2×#4324—41no—
31#66979—21no—
32C2×C4⋊Dic11—21no—
33#66977—21no—
34#66977—21no—
35C2×Dic44D411yescharacteristic
36#66942—41no—
37#66932—41no—
38#66930—41no—
39#66923—21no—
40#66922—21no—
41C4×Dic22—21no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C11×C4⋊C8D411yescharacteristic
45C11×C22⋊C8—21no—
46C4×C8×C11C2311yescharacteristic
47#66882—21no—
48#66882—21no—
49#66882—21no—
50#66882D411yescharacteristic
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66881—21no—
54#66881—21no—
55#66880—21no—
56#66880—21no—
57#66880—21no—
58#66874—41no—
59C4⋊(C11⋊C8)—21no—
60#12403—111nomaximal, Sylow
61C2×D4×C11D811yescharacteristic
62C22×C4×C11—21no—
63C22×Dic11—41no—
64C2×Dic22—21no—
65C2×Dic22—41no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—21no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4D811yescharacteristic
72C11×C22⋊C4—21no—
73C42×C11C2×D411yescharacteristic
74C22⋊Dic11—41no—
75C22⋊Dic11—41no—
76C22⋊Dic11—41no—
77#4324—82no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91C2×C11⋊C8—41no—
92Dic44—21no—
93Dic44—21no—
94C11×C16—22no—
95C11×C16—41no—
96#3352—111no—
97#2255—111no—
98#2227—111no—
99#1693—111no—
100#1363—111no—
101#1334—111no—
102#1330D1111yescharacteristic
103C23×C11—21no—
104D4×C11—41no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—82no—
116C2×Dic11—81no—
117Dic22—41no—
118Dic22—41no—
119Dic22—81no—
120Dic22—81no—
121C8×C11—21no—
122C8×C11—41no—
123C8×C11#13511yescharacteristic
124C8×C11#13711yescharacteristic
125C11⋊C8—81no—
126#552—221no—
127#500—111no—
128#499—111no—
129#485—221no—
130#484—221no—
131#479—221no—
132#470—221no—
133#461—221no—
134C4×Q16—111no—
135#436C2×D1111yescharacteristic
136#428—221no—
137#367—221no—
138#366—221no—
139#366—221no—
140C4⋊C16C2×D1111yescharacteristic
141#358—221no—
142#346C2×D1111yescharacteristic
143#334—111no—
144#332—221no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11#44711yescharacteristic
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—41no—
152C4×C11#45211yescharacteristic
153C4×C11#45611yescharacteristic
154Dic11—81no—
155Dic11—81no—
156Dic11—81no—
157Dic11—81no—
158Dic11—161no—
159C2×Q16—111no—
160C2×SD16—441no—
161C2×M16—21no—
162C4⋊Q8—221no—
163#126—441no—
164#125—221no—
165#125—441no—
166#123—441no—
167C22⋊Q8—221no—
168C22⋊Q8—221no—
169C4×Q8—221no—
170C4×D4D4411yescharacteristic
171#117—221no—
172#117—441no—
173C2×C4⋊C4—221no—
174C2×C16—21no—
175C2×C16—21no—
176#107—111no—
177#107—111no—
178#107—111no—
179#107—221no—
180#107—221no—
181#107—221no—
182#106—221no—
183#106—221no—
184C4⋊C8—221no—
185C4⋊C8D4411yescharacteristic
186#103—221no—
187#103—221no—
188#103—221no—
189#103—441no—
190C22⋊C8—21no—
191C4×C8C22×D1111yescharacteristic
192C2×C11—81no—
193C2×C11#164711yescharacteristic
194C2×C11#219011yescharacteristic
195C2×C11#219511yescharacteristic
196C2×Q8—221no—
197C2×Q8—441no—
198C2×D4D8811yescharacteristic
199C22×C4—21no—
200C22×C4—441no—
201Q16—221no—
202Q16—221no—
203SD16—882no—
204M16—41no—
205M16—41no—
206C2×C8—21no—
207C2×C8—441no—
208C2×C8D4×D1111yescharacteristic
209C2×C8D4×D1111yescharacteristic
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—221no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4D8811yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—441no—
224C22⋊C4—441no—
225C22⋊C4—441no—
226C42—441no—
227C42—441no—
228C42C2×D4411yescharacteristic
229C16—22no—
230C16—41no—
231C11#1240311yescharacteristic, complemented, Sylow
232C23—21no—
233Q8—441no—
234Q8—441no—
235Q8—881no—
236Q8—881no—
237D4—41no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—441no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—441no—
245C2×C4—882no—
246C2×C4—881no—
247C2×C4#6693511yescharacteristic
248C2×C4C2×D8811yescharacteristic
249C2×C4#6696111yescharacteristic
250C8—21no—
251C8—41no—
252C8—881no—
253C8#6696511yescharacteristic
254C8#6696811yescharacteristic
255C22—41no—
256C22—41no—
257C22—41no—
258C22#1062234511yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—881no—
263C4—881no—
264C4—881no—
265C4—881no—
266C4—1761no—
267C4#1062239611yescharacteristic
268C4#1062243911yescharacteristic
269C2—81no—
270C2#1306785311yescharacteristic
271C2#1307056411yescharacteristic
272C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1330C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenter#1330D11
hypocenterC11#12403
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. #13070769C2semidirect
5. #13066667C2semidirect
6. #13066587C2semidirect
231. C11#12403semidirect

Maximal subgroups

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

subgroupindex
#130811902
#130709022
#130707692
#130681292
#130666672
#130665872
C11×#13302
#1240311