Finite Group Databasebeta

← #14656799

Subgroups — #14656799

Order 2816.

500 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 121 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#13073858C211yesmaximal, characteristic, complemented
2#13069542C212yesmaximal
3#13069421C211yesmaximal, characteristic
4#13066455C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8C11×#384C2211yescharacteristic
9C2×#66885—22no—
10C2×#66885—22no—
11#10622599—22no—
12#10622598—22no—
13#10622590—22no—
14C2×#66873—22no—
15C4×C4⋊Dic11C2212yes—
16C2×C4×C11⋊C8C2211yescharacteristic
17C22×D44—22no—
18C22×D44—21no—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C42×C11C2311yescharacteristic
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×C4×Dic11—22no—
27C22×C11⋊C8—21no—
28#66927—22no—
29#66927—21no—
30#66927Q812yes—
31C11×C4⋊C8—22no—
32C11×C4⋊C8—22no—
33C11⋊#95—22no—
34C11⋊#95—24no—
35C11⋊#95—22no—
36#66885—44no—
37#66885—44no—
38#66873—44no—
39C4×C11⋊C8—22no—
40#10351—111nomaximal, Sylow
41C23×D11—41no—
42C22×C4×C11—22no—
43C22×C4×C11C2×D411yescharacteristic
44C22×C4×C11C2×D412yes—
45C22×Dic11—22no—
46C22×Dic11—22no—
47C2×D44—24no—
48C2×D44—22no—
49C2×D44—42no—
50C2×D44—42no—
51C2×D44—41no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—42no—
55C2×D44—42no—
56C2×D44—42no—
57C2×C8×C11—42no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C42×C11C2×Q811yescharacteristic
64C42×C11#4112yes—
65C42×C11#4111yescharacteristic
66C4⋊Dic11—22no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—82no—
71C4×Dic11—42no—
72C4×Dic11—42no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—41no—
76#2571—111no—
77#1982—112no—
78#1957—111no—
79#1296D1111yescharacteristic, complemented
80#1279—112no—
81C23×C11#12011yescharacteristic
82C22×D11—42no—
83C22×D11—82no—
84C22×D11—82no—
85C22×D11—81no—
86C22×D11—81no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—44no—
90C2×C4×C11—42no—
91C2×C4×C11C22⋊Q812yes—
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11#12412yes—
95C2×C4×C11#13512yes—
96C2×C4×C11#13512yes—
97C2×C4×C11AGL(1,ℤ/8)12yes—
98C2×C4×C11AGL(1,ℤ/8)12yes—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105D44—44no—
106D44—44no—
107D44—44no—
108D44—82no—
109D44—82no—
110D44—82no—
111C8×C11—82no—
112C11⋊C8—42no—
113C2×#127—111no—
114C2×C4⋊C8C2×D1112yes—
115C2×#102—222no—
116C2×#102—222no—
117C2×#102—222no—
118C2×C4×C8—111no—
119#400—222no—
120#389—222no—
121#384C2×D1111yescharacteristic
122#382—222no—
123C4×C4⋊C4—112no—
124C22×C11#39311yescharacteristic
125C22×C11#44912yes—
126C22×C11#44912yes—
127C22×C11#45311yescharacteristic
128C22×C11#45411yescharacteristic
129C2×D11—84no—
130C2×D11—82no—
131C2×D11—161no—
132C2×D11—161no—
133C2×D11—162no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—82no—
137C4×C11#47812yes—
138C4×C11#47812yes—
139C4×C11#48812yes—
140C4×C11#49012yes—
141Dic11—82no—
142Dic11—82no—
143C22×D4—221no—
144C22×D4—222no—
145C22×C8—22no—
146C22×C8—221no—
147#127—112no—
148#127—222no—
149#127—221no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4D4412yes—
155C2×C42—222no—
156C2×C42C22×D1111yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—22no—
159#102—444no—
160#102—444no—
161#102—444no—
162C4×C8—222no—
163#95—222no—
164#95—224no—
165#95—222no—
166C2×C11#162011yescharacteristic
167C2×C11#162411yescharacteristic
168C2×C11#162812yes—
169C2×C11#202512yes—
170C2×C11#202711yescharacteristic
171D11—162no—
172C24—441no—
173C2×D4—224no—
174C2×D4—222no—
175C2×D4—442no—
176C2×D4—442no—
177C2×D4—441no—
178C2×D4—442no—
179C2×D4—442no—
180C2×D4—442no—
181C2×D4—442no—
182C2×D4—442no—
183C22×C4—22no—
184C22×C4—222no—
185C22×C4—222no—
186C22×C4C2×D4411yescharacteristic
187C22×C4D4×D1112yes—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—222no—
192C2×C8—441no—
193C2×C8—441no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—222no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—882no—
202C42—442no—
203C42—442no—
204C42#433912yes—
205C42#434111yescharacteristic
206C42Q8×D1111yescharacteristic
207C11#1035111yescharacteristic, complemented, Sylow
208C23—442no—
209C23—881no—
210C23—881no—
211C23—882no—
212C23—882no—
213C23#6693511yescharacteristic
214D4—444no—
215D4—444no—
216D4—444no—
217D4—882no—
218D4—882no—
219D4—882no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4#6692811yescharacteristic
231C2×C4#6693812yes—
232C2×C4#6694912yes—
233C2×C4#6695011yescharacteristic
234C2×C4#6696412yes—
235C2×C4#6696712yes—
236C2×C4#6696912yes—
237C2×C4#6697212yes—
238C8—82no—
239C8—442no—
240C22—884no—
241C22—882no—
242C22—1761no—
243C22—1761no—
244C22—1762no—
245C22#1062228611yescharacteristic
246C22#1062236011yescharacteristic
247C22#1062236611yescharacteristic
248C22#1062239412yes—
249C22#1062242412yes—
250C4—21no—
251C4—21no—
252C4—82no—
253C4—882no—
254C4—882no—
255C4#1062237712yes—
256C4#1062241312yes—
257C4#1062248412yes—
258C4#1062250412yes—
259C2—1762no—
260C2#1306767611yescharacteristic
261C2#1306770011yescharacteristic
262C2#1306772712yes—
263C2#1306976112yes—
264C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1296D11
hypocenterC11#10351
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. #13073858C2semidirect
4. #13066455C2semidirect
5. C11×#1296C2semidirect
79. #1296D11semidirect
207. C11#10351semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130695422
#130694212
#130664552
C11×#12962
#1035111