Finite Group Databasebeta

← #14667992

Subgroups — #14667992

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#13070873C211yesmaximal, characteristic, complemented
2#13070435C211yesmaximal, characteristic, complemented
3#13067978C211yesmaximal, characteristic, complemented
4#13067972C211yesmaximal, characteristic
5#13066689C211yesmaximal, characteristic, complemented
6#13066663C211yesmaximal, characteristic, complemented
7C11×#1362C211yesmaximal, characteristic, complemented
8C11×#494C2211yescharacteristic
9C2×#66892—21no—
10C2×#66892—21no—
11#10622700—21no—
12C2×C16×D11—21no—
13#10622456—21no—
14#10622308C2211yescharacteristic
15C8×D44C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C11×#335C2211yescharacteristic
18#10622185—21no—
19(C2×D11)⋊C16—21no—
20#10622123—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×D88—21no—
27C2×D88—21no—
28C2×D88—41no—
29C2×C8×D11—21no—
30#66927—21no—
31C4×D44D411yescharacteristic
32C2×C11×C16—21no—
33C11×C4⋊C8—21no—
34C4×C8×C11C2311yescharacteristic
35#66892—42no—
36#66892—42no—
37#66885—41no—
38(C2×D11)⋊C8—21no—
39C2×C11⋊C16D411yescharacteristic
40C2×C11⋊C16D411yescharacteristic
41#66873—41no—
42#66871—41no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45C16×D11—42no—
46#12432—111nomaximal, Sylow
47C2×Q8×C11—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44—41no—
51C2×D44D811yescharacteristic
52C2×C4×D11—21no—
53C11×Q16—41no—
54C11×Q16—41no—
55C11×Q16—81no—
56C2×C8×C11—41no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C42×C11C2×D411yescharacteristic
62(C2×D11)⋊C4—21no—
63C4⋊Dic11D811yescharacteristic
64C2×C11⋊C8—21no—
65C2×C11⋊C8—41no—
66D88—41no—
67D88—41no—
68D88—81no—
69D88—82no—
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#1362D1111yescharacteristic, complemented
81#1361—111no—
82C22×D11—21no—
83C22×D11—81no—
84Q8×C11—81no—
85Q8×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11#12111yescharacteristic
88C2×C4×C11C2×D811yescharacteristic
89C2×C4×C11#13511yescharacteristic
90C2×Dic11—21no—
91D44—21no—
92D44—81no—
93D44—81no—
94D44—81no—
95D44—81no—
96D44—161no—
97D44SD3212yescomplemented
98C4×D11—41no—
99C4×D11—41no—
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#494C2×D1111yescharacteristic
110#493—111no—
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#46611yescharacteristic
122C2×D11—22no—
123C2×D11—41no—
124C2×D11—41no—
125C2×D11—161no—
126C2×D11—161no—
127C2×D11—161no—
128C4×C11—21no—
129C4×C11—161no—
130C4×C11#45911yescharacteristic
131C4×C11#47211yescharacteristic
132C4×C11C2×SD3211yescharacteristic
133C4×C11#50811yescharacteristic
134Dic11—41no—
135C2×Q16—21no—
136C2×Q16—21no—
137C2×D8—221no—
138C2×D8—221no—
139C2×D8—441no—
140C22×C8—221no—
141C4⋊Q8—21no—
142#127—221no—
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#166711yescharacteristic
159C2×C11#221711yescharacteristic
160C2×C11#222311yescharacteristic
161D11—42no—
162D11—321no—
163C2×Q8—41no—
164C2×D4—111no—
165C2×D4—441no—
166C2×D4—441no—
167C2×D4—441no—
168C22×C4—221no—
169Q16—41no—
170Q16—41no—
171Q16—81no—
172D8—441no—
173D8—441no—
174D8—881no—
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—41no—
184C4⋊C4—41no—
185C4⋊C4—111no—
186C22⋊C4—221no—
187C42D4×D1111yescharacteristic
188C16—41no—
189C16—112no—
190C16—221no—
191C11#1243211yescharacteristic, complemented, Sylow
192C23—221no—
193C23—881no—
194Q8—81no—
195Q8—81no—
196D4—112no—
197D4—221no—
198D4—881no—
199D4—881no—
200D4—881no—
201D4—881no—
202D4—1761no—
203C2×C4—81no—
204C2×C4—221no—
205C2×C4—441no—
206C2×C4—441no—
207C2×C4#6693711yescharacteristic
208C2×C4D8×D1111yescharacteristic
209C2×C4#6696911yescharacteristic
210C8—21no—
211C8—81no—
212C8—441no—
213C8—881no—
214C8D8×D1111yescharacteristic
215C8#6696711yescharacteristic
216C22—222no—
217C22—441no—
218C22—441no—
219C22—1761no—
220C22—1761no—
221C22—1761no—
222C22#1062238811yescharacteristic
223C4—21no—
224C4—161no—
225C4—441no—
226C4#1062236211yescharacteristic
227C4#1062239911yescharacteristic
228C4D11×SD3211yescharacteristic
229C4#1062253211yescharacteristic
230C2—442no—
231C2—3521no—
232C2#1306797011yescharacteristic
233C2#1307071511yescharacteristic
234C2#1307074911yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socleC22×C11#466
prime radical#13067972C2
hypercenter#1362D11
hypocenterC11#12432
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13070873C2semidirect
2. #13070435C2semidirect
3. #13067978C2semidirect
5. #13066689C2semidirect
6. #13066663C2semidirect
7. C11×#1362C2semidirect
74. C11⋊C16D8semidirect
80. #1362D11semidirect
97. D44SD32semidirect
191. C11#12432semidirect

Maximal subgroups

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

subgroupindex
#130708732
#130704352
#130679782
#130679722
#130666892
#130666632
C11×#13622
#1243211