Finite Group Databasebeta

← #14655066

Subgroups — #14655066

Order 2816.

552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#10622326C212yesmaximal
2#13076684C211yesmaximal, characteristic, complemented
3#13069439C211yesmaximal, characteristic
4C2×#10622103C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C2×#66923C2212yes—
8C2×C11×#97C2212yes—
9C11×#382C2211yescharacteristic
10C2×#66885—22no—
11C2×#66885—22no—
12#10622596—22no—
13C2×#66873—22no—
14C2×#66867C2211yescharacteristic
15#10622326—24no—
16#10622326—24no—
17#10622274—22no—
18#10622272—22no—
19#10622103—24no—
20C22×D44—22no—
21C22×D44—21no—
22C22×C8×C11—22no—
23C2×C11×C4⋊C4D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11D412yes—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—21no—
31#66927—22no—
32#66927—21no—
33#66927D412yes—
34#66923—22no—
35#66923—22no—
36#66923—22no—
37#66923—22no—
38C11×#97—22no—
39C11×#97D414yes—
40C11×#95—22no—
41C11⋊#95—22no—
42C11⋊#95—24no—
43#66885—28no—
44#66885—28no—
45#66873—44no—
46#66867—22no—
47#10080—111nomaximal, Sylow
48C23×D11—41no—
49C22×C4×C11—22no—
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×D411yescharacteristic
52C22×Dic11—22no—
53C22×Dic11—22no—
54C2×D44—24no—
55C2×D44—22no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—48no—
59C2×D44—42no—
60C2×D44—41no—
61C2×C8×C11—24no—
62C2×C8×C11—44no—
63C11×C4⋊C4—42no—
64C42×C11C2×D411yescharacteristic
65C42×C11C2×D412yes—
66C42×C11#4111yescharacteristic
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—82no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—41no—
79C2×#490—112no—
80#2822—111no—
81#1961—111no—
82C2×#330—112no—
83#1295D1111yescharacteristic, complemented
84C23×C11#12011yescharacteristic
85C22×D11—42no—
86C22×D11—81no—
87C22×D11—81no—
88C22×D11—84no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—24no—
92C2×C4×C11—42no—
93C2×C4×C11—44no—
94C2×C4×C11#12012yes—
95C2×C4×C11#12111yescharacteristic
96C2×C4×C11#12112yes—
97C2×C4×C11#12711yescharacteristic
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—44no—
103D44—48no—
104D44—44no—
105D44—84no—
106D44—82no—
107C8×C11—44no—
108C11⋊C8—42no—
109C2×#127—111no—
110C2×#125—112no—
111#490—224no—
112#490—224no—
113C2×#102—222no—
114C2×#102—222no—
115C2×#102—222no—
116C2×#97—111no—
117C2×#97C2×D1112yes—
118#400—222no—
119#398—222no—
120#398—222no—
121#382C2×D1111yescharacteristic
122#330—224no—
123C22×C11#39211yescharacteristic
124C22×C11#45311yescharacteristic
125C22×C11#45411yescharacteristic
126C22×C11#45414yes—
127C2×D11—84no—
128C2×D11—82no—
129C2×D11—162no—
130C2×D11—162no—
131C4×C11—22no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—82no—
136Dic11—82no—
137Dic11—82no—
138C22×D4—221no—
139C22×D4—222no—
140C22×C8—22no—
141C22×C8—221no—
142#127—112no—
143#127—222no—
144#127—221no—
145#125—222no—
146#125—222no—
147#125—222no—
148#125—222no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—222no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4D4412yes—
155C2×C42C22×D1111yescharacteristic
156#102—228no—
157#102—228no—
158#102—444no—
159#97—22no—
160#97—222no—
161#97D4414yes—
162#95—22no—
163#95—224no—
164#95—222no—
165C2×C11#165712yes—
166C2×C11#165812yes—
167C2×C11#200312yes—
168C2×C11#200611yescharacteristic
169D11—162no—
170C24—441no—
171C2×D4—224no—
172C2×D4—222no—
173C2×D4—442no—
174C2×D4—442no—
175C2×D4—448no—
176C2×D4—441no—
177C2×D4—442no—
178C22×C4—22no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4C2×D4411yescharacteristic
182C22×C4D4×D1112yes—
183C2×C8—24no—
184C2×C8—44no—
185C2×C8—222no—
186C2×C8—441no—
187C2×C8—441no—
188C4⋊C4—42no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C4⋊C4—882no—
198C42C2×D4412yes—
199C42D4×D1111yescharacteristic
200C42#434311yescharacteristic
201C11#1008011yescharacteristic, complemented, Sylow
202C23—442no—
203C23—881no—
204C23—881no—
205C23—884no—
206C23#6693511yescharacteristic
207D4—448no—
208D4—444no—
209D4—884no—
210D4—882no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—444no—
221C2×C4#6692711yescharacteristic
222C2×C4#6693512yes—
223C2×C4#6694812yes—
224C2×C4#6694811yescharacteristic
225C8—44no—
226C8—442no—
227C22—884no—
228C22—882no—
229C22—1762no—
230C22—1762no—
231C22#1062228411yescharacteristic
232C22#1062236011yescharacteristic
233C22#1062236611yescharacteristic
234C22#1062244014yes—
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—882no—
241C4—882no—
242C2—1762no—
243C2#1306791512yes—
244C2#1306791912yes—
245C2#1306964112yes—
246C2#1306966011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1295D11
hypocenterC11#10080
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #13076684C2semidirect
4. C2×#10622103C2semidirect
5. C11×#1295C2semidirect
83. #1295D11semidirect
201. C11#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#106223262
#130766842
#130694392
C2×#106221032
C11×#12952
#1008011