Finite Group Databasebeta

← #14656782

Subgroups — #14656782

Order 2816.

588 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 129 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#13073645C211yesmaximal, characteristic, complemented
2#13069542C212yesmaximal
3#13069421C211yesmaximal, characteristic
4#13066455C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C2×#66941—22no—
7C2×#66927C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C11×#384C2211yescharacteristic
10C2×#66885—22no—
11C2×#66885—22no—
12#10622592—22no—
13#10622586—22no—
14C2×#66873—22no—
15C4×C4⋊Dic11C2212yes—
16C2×C4×C11⋊C8C2211yescharacteristic
17C22×D44—22no—
18C22×D44—21no—
19C22×Dic22—22no—
20C22×C8×C11—22no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×Dic11⋊C4—24no—
27C2×C4×Dic11—22no—
28C22×C11⋊C8—21no—
29#66941—44no—
30#66941—44no—
31#66927—22no—
32#66927—21no—
33#66927Q812yescomplemented
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38#66885—44no—
39#66885—44no—
40#66873—44no—
41C4×C11⋊C8—22no—
42#10348—111nomaximal, Sylow
43C23×D11—41no—
44C22×C4×C11—22no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D412yes—
47C22×Dic11—22no—
48C22×Dic11—22no—
49C2×D44—24no—
50C2×D44—22no—
51C2×D44—42no—
52C2×D44—42no—
53C2×D44—41no—
54C2×D44—42no—
55C2×D44—42no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—42no—
59C2×Dic22—48no—
60C2×Dic22—82no—
61C2×C8×C11—42no—
62C2×C8×C11—42no—
63C2×C8×C11—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C42×C11C2×Q811yescharacteristic
68C42×C11#4112yes—
69C42×C11#4111yescharacteristic
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11D814yes—
73C4⋊Dic11SD1614yes—
74Dic11⋊C4—48no—
75C4×Dic11—42no—
76C4×Dic11—42no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80#2551—111no—
81#1982—112no—
82#1957—111no—
83#1296D1111yescharacteristic, complemented
84#1279—112no—
85C23×C11#12011yescharacteristic
86C22×D11—42no—
87C22×D11—82no—
88C22×D11—82no—
89C22×D11—81no—
90C22×D11—81no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—44no—
94C2×C4×C11—42no—
95C2×C4×C11C22⋊Q812yes—
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11#12411yescharacteristic
98C2×C4×C11#12412yes—
99C2×C4×C11C2×D812yes—
100C2×C4×C11C2×SD1612yes—
101C2×C4×C11AGL(1,ℤ/8)12yes—
102C2×C4×C11#13712yes—
103C2×Dic11—24no—
104C2×Dic11—24no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109D44—44no—
110D44—44no—
111D44—44no—
112D44—82no—
113D44—82no—
114D44—82no—
115Dic22—88no—
116C8×C11—82no—
117C11⋊C8—42no—
118C2×C4⋊Q8—222no—
119C2×#127—111no—
120C2×C4⋊C8C2×D1112yes—
121C2×#102—222no—
122C2×#102—222no—
123C2×#102—222no—
124C2×C4×C8—111no—
125#395—222no—
126#389—222no—
127#384C2×D1111yescharacteristic
128C4×C4⋊C4—112no—
129C22×C11#39311yescharacteristic
130C22×C11#44712yes—
131C22×C11#44812yes—
132C22×C11#45311yescharacteristic
133C22×C11#45411yescharacteristic
134C2×D11—84no—
135C2×D11—82no—
136C2×D11—161no—
137C2×D11—161no—
138C2×D11—162no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—82no—
142C4×C11#47412yes—
143C4×C11#47612yes—
144C4×C11#48612yes—
145C4×C11#48912yes—
146Dic11—44no—
147Dic11—44no—
148C22×Q8—222no—
149C22×D4—221no—
150C22×D4—222no—
151C22×C8—22no—
152C22×C8—221no—
153C4⋊Q8—444no—
154C4⋊Q8—444no—
155#127—112no—
156#127—222no—
157#127—221no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—224no—
162C2×C4⋊C4D4412yes—
163C2×C42—222no—
164C2×C42C22×D1111yescharacteristic
165C4⋊C8—22no—
166C4⋊C8—22no—
167#102—444no—
168#102—444no—
169#102—444no—
170C4×C8—222no—
171#95—222no—
172#95—222no—
173C2×C11#161911yescharacteristic
174C2×C11#162311yescharacteristic
175C2×C11#162712yes—
176C2×C11#202312yes—
177C2×C11#202711yescharacteristic
178D11—162no—
179C24—441no—
180C2×Q8—448no—
181C2×Q8—882no—
182C2×D4—224no—
183C2×D4—222no—
184C2×D4—442no—
185C2×D4—442no—
186C2×D4—441no—
187C2×D4—442no—
188C2×D4—442no—
189C2×D4—442no—
190C2×D4—442no—
191C2×D4—442no—
192C22×C4—22no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4C2×D4411yescharacteristic
196C22×C4D4×D1112yes—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—222no—
201C2×C8—441no—
202C2×C8—441no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—114no—
207C4⋊C4—114no—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—448no—
211C42—442no—
212C42—442no—
213C42#433912yes—
214C42#434111yescharacteristic
215C42Q8×D1111yescharacteristic
216C11#1034811yescharacteristic, complemented, Sylow
217C23—442no—
218C23—881no—
219C23—881no—
220C23—882no—
221C23—882no—
222C23#6693511yescharacteristic
223Q8—888no—
224D4—444no—
225D4—444no—
226D4—444no—
227D4—882no—
228D4—882no—
229D4—882no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—224no—
235C2×C4—224no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4#6692811yescharacteristic
241C2×C4#6693812yes—
242C2×C4#6694912yes—
243C2×C4#6695011yescharacteristic
244C2×C4D8×D1112yes—
245C2×C4SD16×D1112yes—
246C2×C4#6696712yes—
247C2×C4#6697112yes—
248C8—82no—
249C8—442no—
250C22—884no—
251C22—882no—
252C22—1761no—
253C22—1761no—
254C22—1762no—
255C22#1062228611yescharacteristic
256C22#1062236011yescharacteristic
257C22#1062236611yescharacteristic
258C22#1062238612yes—
259C22#1062241912yes—
260C4—21no—
261C4—21no—
262C4—82no—
263C4—444no—
264C4—444no—
265C4#1062237312yes—
266C4#1062240812yes—
267C4#1062248312yes—
268C4#1062250312yes—
269C2—1762no—
270C2#1306767111yescharacteristic
271C2#1306769511yescharacteristic
272C2#1306772012yes—
273C2#1306975112yes—
274C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1296D11
hypocenterC11#10348
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. #13073645C2semidirect
4. #13066455C2semidirect
5. C11×#1296C2semidirect
33. #66927Q8semidirect
83. #1296D11semidirect
216. C11#10348semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130695422
#130694212
#130664552
C11×#12962
#1034811