Finite Group Databasebeta

← #14667988

Subgroups — #14667988

Order 2816.

252 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 65 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#13070871C211yesmaximal, characteristic, complemented
2#13070435C211yesmaximal, characteristic, complemented
3#13067982C211yesmaximal, characteristic, complemented
4#13067968C211yesmaximal, characteristic
5#13066689C211yesmaximal, characteristic, complemented
6#13066666C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic, complemented
8C11×#493C2211yescharacteristic
9C2×#66891—21no—
10C2×#66891—21no—
11#10622685—21no—
12C2×C16×D11—21no—
13#10622459—21no—
14#10622312C2211yescharacteristic
15C8×D44C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C11×#335C2211yescharacteristic
18#10622182—21no—
19(C2×D11)⋊C16—21no—
20#10622124—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4323—41no—
27C2×Dic44—21no—
28C2×Dic44—21no—
29C2×C8×D11—21no—
30C4×D44D411yescharacteristic
31#66922—21no—
32C2×C11×C16—21no—
33C11×C4⋊C8—21no—
34C4×C8×C11C2311yescharacteristic
35#66896—41no—
36#66891—42no—
37#66891—42no—
38#66885—41no—
39(C2×D11)⋊C8—21no—
40#66882—41no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45C16×D11—42no—
46#12432—111nomaximal, Sylow
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D44D811yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22—41no—
53C11×D8—41no—
54C11×D8—41no—
55C11×D8—81no—
56C2×C8×C11—41no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C42×C11C2×D411yescharacteristic
60#4323—82no—
61(C2×D11)⋊C4—21no—
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64C4⋊Dic11D811yescharacteristic
65C2×C11⋊C8—21no—
66C2×C11⋊C8—41no—
67Dic44—41no—
68Dic44—41no—
69Dic44—81no—
70C8×D11—41no—
71C8×D11—41no—
72C11×C16—41no—
73C11⋊C16—21no—
74C11⋊C16D812yescomplemented
75#2248—111no—
76D4×C16—111no—
77#1669—111no—
78#1667—111no—
79#1372—111no—
80#1362—111no—
81#1361D1111yescharacteristic, complemented
82C23×C11—81no—
83C22×D11—21no—
84D4×C11—81no—
85D4×C11—81no—
86D4×C11—81no—
87D4×C11—81no—
88D4×C11—161no—
89C2×C4×C11#12111yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11#13511yescharacteristic
92C2×Dic11—21no—
93C2×Dic11—81no—
94D44—21no—
95D44SD3212yescomplemented
96C4×D11—41no—
97C4×D11—41no—
98Dic22—81no—
99Dic22—81no—
100C8×C11—21no—
101C8×C11—81no—
102C8×C11C2×D811yescharacteristic
103C8×C11AGL(1,ℤ/8)11yescharacteristic
104C11⋊C8—41no—
105C11⋊C8—81no—
106C2×SD32—221no—
107C2×SD32—221no—
108C22×C16—221no—
109#494—111no—
110#493C2×D1111yescharacteristic
111#474—221no—
112#459—221no—
113C8×D4—111no—
114C4⋊C16C2×D1111yescharacteristic
115C22⋊C16—221no—
116C4×C16—111no—
117#335—111no—
118#335C2×D1111yescharacteristic
119#332—221no—
120#331—221no—
121C22×C11—161no—
122C22×C11—161no—
123C22×C11—161no—
124C22×C11#46611yescharacteristic
125C2×D11—22no—
126C2×D11—41no—
127C2×D11—41no—
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—21no—
138C2×D8—21no—
139C2×D8—441no—
140C22×C8—221no—
141C4⋊Q8—221no—
142#127—21no—
143C4×D4—111no—
144SD32—442no—
145SD32—442no—
146C2×C16—21no—
147C2×C16—111no—
148C2×C16—111no—
149C2×C16—442no—
150#107—441no—
151C4⋊C8—21no—
152C4⋊C8—111no—
153C4⋊C8—221no—
154#102—441no—
155#102—441no—
156C22⋊C8—221no—
157C4×C8C22×D1111yescharacteristic
158C2×C11—321no—
159C2×C11#166711yescharacteristic
160C2×C11#221711yescharacteristic
161C2×C11#222311yescharacteristic
162D11—42no—
163C2×Q8—441no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—111no—
168C22×C4—221no—
169Q16—441no—
170Q16—441no—
171Q16—881no—
172D8—41no—
173D8—41no—
174D8—81no—
175D8—882no—
176C2×C8—41no—
177C2×C8—221no—
178C2×C8—441no—
179C2×C8—441no—
180C2×C8—441no—
181C2×C8#433911yescharacteristic
182C2×C8D4×D1111yescharacteristic
183C4⋊C4—111no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C22⋊C4—221no—
187C42D4×D1111yescharacteristic
188C16—41no—
189C16—112no—
190C16—221no—
191C11#1243211yescharacteristic, complemented, Sylow
192C23—81no—
193C23—221no—
194Q8—881no—
195Q8—881no—
196D4—81no—
197D4—81no—
198D4—81no—
199D4—81no—
200D4—112no—
201D4—161no—
202D4—221no—
203C2×C4—221no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—881no—
207C2×C4#6693711yescharacteristic
208C2×C4D8×D1111yescharacteristic
209C2×C4#6696911yescharacteristic
210C8—21no—
211C8—81no—
212C8—441no—
213C8—881no—
214C8D8×D1111yescharacteristic
215C8#6696711yescharacteristic
216C22—161no—
217C22—161no—
218C22—161no—
219C22—222no—
220C22—441no—
221C22—441no—
222C22#1062238811yescharacteristic
223C4—21no—
224C4—441no—
225C4—1761no—
226C4#1062236211yescharacteristic
227C4#1062239911yescharacteristic
228C4#1062252511yescharacteristic
229C4D11×SD3211yescharacteristic
230C2—321no—
231C2—442no—
232C2#1306797011yescharacteristic
233C2#1307071111yescharacteristic
234C2#1307074511yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#466
prime radical#13067968C2
hypercenter#1361D11
hypocenterC11#12432
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #13070871C2semidirect
2. #13070435C2semidirect
3. #13067982C2semidirect
5. #13066689C2semidirect
6. #13066666C2semidirect
7. C11×#1361C2semidirect
74. C11⋊C16D8semidirect
81. #1361D11semidirect
95. D44SD32semidirect
191. C11#12432semidirect

Maximal subgroups

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

subgroupindex
#130708712
#130704352
#130679822
#130679682
#130666892
#130666662
C11×#13612
#1243211