Finite Group Databasebeta

← #14667995

Subgroups — #14667995

Order 2816.

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

normal subgroups only

This group has 262 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#13070865C211yesmaximal, characteristic, complemented
2#13070447C211yesmaximal, characteristic, complemented
3#13067972C211yesmaximal, characteristic, complemented
4#13067968C211yesmaximal, characteristic, complemented
5#13066689C211yesmaximal, characteristic, complemented
6#13066663C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic, complemented
8C11×#493C2211yescharacteristic
9C2×#66890—21no—
10C2×#66890—21no—
11#10622685—21no—
12C2×#66862—21no—
13#10622456—21no—
14#10622308C2211yescharacteristic
15C8×D44C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C11×#335C2211yescharacteristic
18#10622182—21no—
19(C2×D11)⋊C16—21no—
20#10622123—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4323—41no—
27C2×D88—21no—
28C2×D88—21no—
29C2×D88—41no—
30C2×C8×D11—21no—
31#66927—21no—
32C4×D44D411yescharacteristic
33C2×C11×C16—21no—
34C11×C4⋊C8—21no—
35C4×C8×C11C2311yescharacteristic
36#66896—41no—
37#66890—42no—
38#66890—42no—
39#66885—41no—
40(C2×D11)⋊C8—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45#66862—42no—
46#12433—111nomaximal, Sylow
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D44—41no—
51C2×D44—41no—
52C2×D44—41no—
53C2×D44D811yescharacteristic
54C2×C4×D11—21no—
55C11×D8—41no—
56C11×D8—41no—
57C11×D8—81no—
58C2×C8×C11—41no—
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11#4111yescharacteristic
61C42×C11C2×D411yescharacteristic
62#4323—82no—
63(C2×D11)⋊C4—21no—
64C4⋊Dic11D811yescharacteristic
65C2×C11⋊C8—21no—
66C2×C11⋊C8—41no—
67D88—41no—
68D88—41no—
69D88—81no—
70D88—82no—
71C8×D11—41no—
72C8×D11—41no—
73C11×C16—41no—
74C11⋊C16—21no—
75C11⋊C16D812yescomplemented
76#2246—111no—
77#2169—111no—
78#1667—111no—
79#1667—111no—
80#1372—111no—
81#1361—111no—
82#1361D1111yescharacteristic, complemented
83C23×C11—81no—
84C22×D11—21no—
85C22×D11—81no—
86D4×C11—81no—
87D4×C11—81no—
88D4×C11—81no—
89D4×C11—81no—
90D4×C11—161no—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11C2×D811yescharacteristic
93C2×C4×C11#13511yescharacteristic
94C2×Dic11—21no—
95D44—21no—
96D44—21no—
97D44—81no—
98D44—81no—
99D44—81no—
100D44—81no—
101D44—161no—
102C4×D11—41no—
103C4×D11—41no—
104C8×C11—21no—
105C8×C11—81no—
106C8×C11C2×D811yescharacteristic
107C8×C11AGL(1,ℤ/8)11yescharacteristic
108C11⋊C8—41no—
109C11⋊C8—81no—
110C2×D16—221no—
111C2×D16—221no—
112C2×M32—221no—
113#493—111no—
114#493C2×D1111yescharacteristic
115#459—221no—
116#459—221no—
117C8×D4—111no—
118C4⋊C16C2×D1111yescharacteristic
119C22⋊C16—221no—
120C4×C16—111no—
121#335—111no—
122#335C2×D1111yescharacteristic
123#331—221no—
124#331—221no—
125C22×C11—161no—
126C22×C11—161no—
127C22×C11—161no—
128C22×C11#46611yescharacteristic
129C2×D11—41no—
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—161no—
133C2×D11—161no—
134C2×D11—161no—
135C4×C11—21no—
136C4×C11#45911yescharacteristic
137C4×C11#47211yescharacteristic
138C4×C11#50911yescharacteristic
139C4×C11#50911yescharacteristic
140Dic11—41no—
141C2×D8—21no—
142C2×D8—21no—
143C2×D8—221no—
144C2×D8—221no—
145C2×D8—441no—
146C2×D8—441no—
147C22×C8—221no—
148#127—21no—
149#127—221no—
150C4×D4—111no—
151D16—442no—
152D16—442no—
153M32—442no—
154C2×C16—21no—
155C2×C16—111no—
156C2×C16—111no—
157C4⋊C8—21no—
158C4⋊C8—111no—
159C4⋊C8—221no—
160#102—441no—
161#102—441no—
162C22⋊C8—221no—
163C4×C8C22×D1111yescharacteristic
164C2×C11—321no—
165C2×C11#166711yescharacteristic
166C2×C11#221811yescharacteristic
167C2×C11#222111yescharacteristic
168D11—81no—
169D11—321no—
170C2×D4—41no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—111no—
174C2×D4—441no—
175C2×D4—441no—
176C2×D4—441no—
177C22×C4—221no—
178D8—41no—
179D8—41no—
180D8—81no—
181D8—441no—
182D8—441no—
183D8—881no—
184D8—882no—
185D8—882no—
186C2×C8—41no—
187C2×C8—221no—
188C2×C8—441no—
189C2×C8—441no—
190C2×C8—441no—
191C2×C8#433911yescharacteristic
192C2×C8D4×D1111yescharacteristic
193C4⋊C4—111no—
194C22⋊C4—221no—
195C42D4×D1111yescharacteristic
196C16—41no—
197C16—112no—
198C16—221no—
199C11#1243311yescharacteristic, complemented, Sylow
200C23—81no—
201C23—221no—
202C23—881no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—81no—
207D4—161no—
208D4—221no—
209D4—221no—
210D4—881no—
211D4—881no—
212D4—881no—
213D4—881no—
214D4—1761no—
215C2×C4—221no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4#6693711yescharacteristic
219C2×C4D8×D1111yescharacteristic
220C2×C4#6696911yescharacteristic
221C8—21no—
222C8—81no—
223C8—441no—
224C8—881no—
225C8D8×D1111yescharacteristic
226C8#6696711yescharacteristic
227C22—161no—
228C22—161no—
229C22—161no—
230C22—441no—
231C22—441no—
232C22—441no—
233C22—1761no—
234C22—1761no—
235C22—1761no—
236C22#1062238811yescharacteristic
237C4—21no—
238C4—441no—
239C4#1062236211yescharacteristic
240C4#1062239911yescharacteristic
241C4#1062252411yescharacteristic
242C4#1062252711yescharacteristic
243C2—321no—
244C2—881no—
245C2—3521no—
246C2#1306797011yescharacteristic
247C2#1307071811yescharacteristic
248C2#1307073511yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#466
hypercenter#1361D11
hypocenterC11#12433
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. #13070865C2semidirect
2. #13070447C2semidirect
3. #13067972C2semidirect
4. #13067968C2semidirect
5. #13066689C2semidirect
6. #13066663C2semidirect
7. C11×#1361C2semidirect
75. C11⋊C16D8semidirect
82. #1361D11semidirect
199. C11#12433semidirect

Maximal subgroups

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

subgroupindex
#130708652
#130704472
#130679722
#130679682
#130666892
#130666632
C11×#13612
#1243311