Finite Group Databasebeta

← #14666766

Subgroups — #14666766

Order 2816.

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

normal subgroups only

This group has 558 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#13069961C211yesmaximal, characteristic, complemented
2#13067555C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2537C211yesmaximal, characteristic
6C2×C11×#121—22no—
7C2×C4×D4×C11—21no—
8#10623031C2211yescharacteristic
9C11×#394—21no—
10C11×#394C2212yes—
11C11×#384C2211yescharacteristic
12C11×#380—22no—
13#10622831—22no—
14#10622577—21no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×D4×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11D412yes—
22C23×C4×C11—22no—
23C11×#121—48no—
24C4×D4×C11—42no—
25C4×D4×C11—42no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C42×C11D411yescharacteristic
34C2×#4324—42no—
35#66979—21no—
36#66977—22no—
37C2×#4318—21no—
38#66943—41no—
39#66941—41no—
40C11×#95—21no—
41C11×#95D412yes—
42#66896—42no—
43C22⋊(C11⋊C8)—22no—
44#66872—41no—
45#66871—41no—
46#12246—111nomaximal, Sylow
47C24×C11—22no—
48C2×D4×C11—24no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—44no—
53C2×D4×C11—44no—
54C2×D4×C11—81no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—21no—
58C22×C4×C11—44no—
59C22×C4×C11—44no—
60C22×C4×C11—44no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D412yes—
63C2×Dic22—22no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—44no—
67C11×C4⋊C4—41no—
68C11×C22⋊C4—44no—
69C11×C22⋊C4—44no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—42no—
72C42×C11—21no—
73C42×C11SD1612yescomplemented
74C22⋊Dic11—41no—
75#4324—84no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11—22no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81#4318—22no—
82#4318—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—42no—
85#2537D1111yescharacteristic
86#2060—111no—
87#1599—112no—
88#1345—112no—
89#1325—111no—
90C23×C11—24no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11#12011yescharacteristic
98D4×C11—48no—
99D4×C11—44no—
100D4×C11—82no—
101D4×C11—84no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—88no—
115C2×C4×C11C2×SD1611yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×Dic11—41no—
118C2×Dic11—41no—
119Dic22—82no—
120C11⋊C8—42no—
121C11⋊C8—82no—
122#544—111no—
123C2×#121—22no—
124C2×C4×D4—21no—
125#450—222no—
126#428—221no—
127#394—21no—
128#394C2×D1112yes—
129#384C2×D1111yescharacteristic
130#380—22no—
131#343—111no—
132#339—221no—
133#328—222no—
134#324—112no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11—44no—
138C22×C11—44no—
139C22×C11—44no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11—82no—
144C22×C11#45011yescharacteristic
145C22×C11#45611yescharacteristic
146C22×C11B(4,𝔽2)11yescharacteristic
147C4×C11—24no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—42no—
151C4×C11—82no—
152C4×C11—81no—
153Dic11—81no—
154Dic11—81no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4C22⋊D1112yes—
158C23×C4—22no—
159C2×SD16—442no—
160C2×M16—221no—
161C4⋊Q8—441no—
162#125—441no—
163C22⋊Q8—222no—
164#121—48no—
165C4×D4—42no—
166C4×D4—42no—
167#117—221no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C22⋊D1111yescharacteristic
171C2×C4⋊C4C22×D1111yescharacteristic
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C42C22⋊D1111yescharacteristic
176#107—441no—
177#106—441no—
178#102—442no—
179C22⋊C8—222no—
180#95—21no—
181#95C22⋊D1112yes—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11—84no—
185C2×C11#160411yescharacteristic
186C2×C11#219611yescharacteristic
187C2×C11#220411yescharacteristic
188C24—22no—
189C2×Q8—222no—
190C2×D4—24no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—44no—
195C2×D4—44no—
196C2×D4—81no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—44no—
201C22×C4—44no—
202C22×C4—44no—
203C22×C4C2×C22⋊D1111yescharacteristic
204C22×C4C2×C22⋊D1112yes—
205SD16—884no—
206M16—222no—
207M16—441no—
208C2×C8—441no—
209C2×C8—442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—44no—
214C4⋊C4—222no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—442no—
218C22⋊C4—44no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—441no—
223C42—21no—
224C42—441no—
225C42#432412yescomplemented
226C11#1224611yescharacteristic, complemented, Sylow
227C23—24no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#6700611yescharacteristic
235Q8—882no—
236D4—48no—
237D4—44no—
238D4—82no—
239D4—84no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—88no—
253C2×C4—441no—
254C2×C4—441no—
255C2×C4#6698511yescharacteristic
256C2×C4C2×#432411yescharacteristic
257C8—442no—
258C8—882no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22—44no—
263C22—44no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#1062283111yescharacteristic
269C22#1062285711yescharacteristic
270C22#1062285911yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—82no—
276C4—81no—
277C4—881no—
278C4—881no—
279C2—21no—
280C2—21no—
281C2—84no—
282C2#1306758511yescharacteristic
283C2#1307060011yescharacteristic
284C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2537C2
socleC22×C11B(4,𝔽2)
hypercenter#2537D11
hypocenterC11#12246
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13069961C2semidirect
2. #13067555C2semidirect
3. #13066619C2semidirect
4. #13066562C2semidirect
73. C42×C11SD16semidirect
225. C42#4324semidirect
226. C11#12246semidirect

Maximal subgroups

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

subgroupindex
#130699612
#130675552
#130666192
#130665622
C11×#25372
#1224611