Finite Group Databasebeta

← #14667990

Subgroups — #14667990

Order 2816.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#13070872C211yesmaximal, characteristic, complemented
2C16×D44C211yesmaximal, characteristic, complemented
3#13067982C211yesmaximal, characteristic, complemented
4#13067972C211yesmaximal, characteristic
5#13066664C211yesmaximal, characteristic, complemented
6#13066661C211yesmaximal, characteristic, complemented
7C11×#1372C211yesmaximal, characteristic, complemented
8C2×#66864—21no—
9C2×#66864—21no—
10C2×C16×D11—21no—
11#10622459—21no—
12#10622456—21no—
13#10622312C2211yescharacteristic
14#10622308C2211yescharacteristic
15C8×D44C2211yescharacteristic
16C4×C11×C16C2211yescharacteristic
17C11×#335C2211yescharacteristic
18C11×#335C2211yescharacteristic
19(C2×D11)⋊C16—21no—
20#10622124—21no—
21#10622123—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C2×Dic44—21no—
24C2×Dic44—21no—
25C2×D88—21no—
26C2×D88—21no—
27C2×D88—41no—
28C2×C8×D11—21no—
29#66927—21no—
30C4×D44D411yescharacteristic
31#66922—21no—
32C2×C11×C16D411yescharacteristic
33C2×C11×C16D411yescharacteristic
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C4×C8×C11C2311yescharacteristic
37#66885—41no—
38#66885—41no—
39(C2×D11)⋊C8—21no—
40#66882—41no—
41C2×C11⋊C16—21no—
42C4⋊(C11⋊C8)D411yescharacteristic
43#66864—42no—
44#66864—42no—
45C16×D11—42no—
46#12432—111nomaximal, Sylow
47C2×D44—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44D811yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22—41no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C42×C11C2×D411yescharacteristic
58(C2×D11)⋊C4—21no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61C4⋊Dic11D811yescharacteristic
62C2×C11⋊C8—21no—
63Dic44—41no—
64Dic44—41no—
65Dic44—81no—
66D88—41no—
67D88—41no—
68D88—81no—
69D88—82no—
70C8×D11—41no—
71C8×D11—41no—
72C11×C16—21no—
73C11×C16D812yescomplemented
74C11⋊C16—41no—
75#2248—111no—
76D4×C16—111no—
77#1669—111no—
78#1667—111no—
79#1372D1111yescharacteristic, complemented
80#1362—111no—
81#1361—111no—
82C22×D11—21no—
83C22×D11—81no—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11#13511yescharacteristic
87C2×Dic11—21no—
88C2×Dic11—81no—
89D44—21no—
90D44—81no—
91D44—81no—
92D44—81no—
93D44—81no—
94D44—161no—
95D44SD3212yescomplemented
96C4×D11—41no—
97C4×D11—41no—
98Dic22—81no—
99Dic22—81no—
100C8×C11—21no—
101C8×C11—81no—
102C8×C11—81no—
103C8×C11C2×D811yescharacteristic
104C8×C11AGL(1,ℤ/8)11yescharacteristic
105C11⋊C8—41no—
106C2×SD32—221no—
107C2×SD32—221no—
108C22×C16—221no—
109#494—111no—
110#493—111no—
111#474—221no—
112#459—221no—
113C8×D4—111no—
114C4⋊C16—111no—
115C22⋊C16—221no—
116C4×C16C2×D1111yescharacteristic
117#335C2×D1111yescharacteristic
118#335C2×D1111yescharacteristic
119#332—221no—
120#331—221no—
121C22×C11#46611yescharacteristic
122C2×D11—22no—
123C2×D11—41no—
124C2×D11—41no—
125C2×D11—161no—
126C2×D11—161no—
127C2×D11—161no—
128C4×C11—21no—
129C4×C11#45911yescharacteristic
130C4×C11#47211yescharacteristic
131C4×C11C2×SD3211yescharacteristic
132C4×C11#50811yescharacteristic
133Dic11—41no—
134Dic11—161no—
135C2×Q16—221no—
136C2×Q16—221no—
137C2×D8—221no—
138C2×D8—221no—
139C2×D8—441no—
140C22×C8—221no—
141C4⋊Q8—221no—
142#127—221no—
143C4×D4—111no—
144SD32—442no—
145SD32—442no—
146C2×C16—221no—
147C2×C16—442no—
148C2×C16D4411yescharacteristic
149C2×C16D4411yescharacteristic
150#107—441no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—111no—
154#102—441no—
155#102—441no—
156C22⋊C8—221no—
157C4×C8C22×D1111yescharacteristic
158C2×C11#166711yescharacteristic
159C2×C11#221711yescharacteristic
160C2×C11#222311yescharacteristic
161D11—42no—
162D11—321no—
163C2×Q8—441no—
164C2×D4—111no—
165C2×D4—441no—
166C2×D4—441no—
167C2×D4—441no—
168C22×C4—221no—
169Q16—441no—
170Q16—441no—
171Q16—881no—
172D8—441no—
173D8—441no—
174D8—881no—
175D8—882no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—221no—
179C2×C8—441no—
180C2×C8—441no—
181C2×C8C2×D4411yescharacteristic
182C2×C8#434311yescharacteristic
183C4⋊C4—111no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C22⋊C4—221no—
187C42D4×D1111yescharacteristic
188C16—21no—
189C16—441no—
190C16D8812yescomplemented
191C11#1243211yescharacteristic, complemented, Sylow
192C23—221no—
193C23—881no—
194Q8—881no—
195Q8—881no—
196D4—112no—
197D4—221no—
198D4—881no—
199D4—881no—
200D4—881no—
201D4—881no—
202D4—1761no—
203C2×C4—221no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—881no—
207C2×C4#6694811yescharacteristic
208C2×C4D8×D1111yescharacteristic
209C2×C4#6697211yescharacteristic
210C8—21no—
211C8—81no—
212C8—81no—
213C8—441no—
214C8C2×D8811yescharacteristic
215C8#6696111yescharacteristic
216C22—222no—
217C22—441no—
218C22—441no—
219C22—1761no—
220C22—1761no—
221C22—1761no—
222C22#1062249611yescharacteristic
223C4—21no—
224C4—441no—
225C4—1761no—
226C4#1062245611yescharacteristic
227C4#1062251011yescharacteristic
228C4D11×SD3211yescharacteristic
229C4#1062252911yescharacteristic
230C2—442no—
231C2—3521no—
232C2#1306797211yescharacteristic
233C2#1307071311yescharacteristic
234C2#1307074711yescharacteristic
subgroupG/H
centerC22#10622496
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1372C2
socleC22×C11#466
prime radical#13067972C2
hypercenter#1372D11
hypocenterC11#12432
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
1. #13070872C2semidirect
2. C16×D44C2semidirect
3. #13067982C2semidirect
5. #13066664C2semidirect
6. #13066661C2semidirect
7. C11×#1372C2semidirect
73. C11×C16D8semidirect
79. #1372D11semidirect
95. D44SD32semidirect
190. C16D88semidirect
191. C11#12432semidirect

Maximal subgroups

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

subgroupindex
#130708722
C16×D442
#130679822
#130679722
#130666642
#130666612
C11×#13722
#1243211