Finite Group Databasebeta

← #14642958

Subgroups — #14642958

Order 2816.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070159C211yesmaximal, characteristic, complemented
2#13070019C212yesmaximal, complemented
3#13066442C211yesmaximal, characteristic, complemented
4#13066437C212yesmaximal, complemented
5C11×#2733C211yesmaximal, characteristic
6C2×C11×#124—21no—
7C11×#394—21no—
8C11×#392—22no—
9C11×#391C2211yescharacteristic
10C11×#390C2212yes—
11C11×#388—22no—
12C2×#66899—21no—
13C2×#66896—22no—
14C2×#66872—21no—
15#10622548C2211yescharacteristic
16#10622167—22no—
17#10622162C2211yescharacteristic
18#10622162C2212yes—
19C22×Q8×C11D411yescharacteristic
20C22×D4×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11D412yes—
23C11×#124—42no—
24C11×#124—42no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4D412yes—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C22×C11⋊C8—21no—
36C22×C11⋊C8—22no—
37C11×#95—21no—
38C11×#95—22no—
39#66899—42no—
40#66896—44no—
41#66872—42no—
42#7810—111nomaximal, Sylow
43C24×C11—22no—
44C2×Q8×C11—21no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11SD1612yes—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—81no—
54C2×D4×C11—81no—
55C2×D4×C11—81no—
56C2×D4×C11—82no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C22×Dic11—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—44no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—42no—
70C11×C22⋊C4—82no—
71C42×C11—41no—
72C42×C11—42no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—42no—
83#2733D1111yescharacteristic
84#2096—111no—
85#2071—112no—
86#1272—111no—
87#1270—112no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11#12011yescharacteristic
96Q8×C11—42no—
97Q8×C11—81no—
98D4×C11—44no—
99D4×C11—82no—
100D4×C11—84no—
101D4×C11—84no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11#13512yes—
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)12yes—
118C2×Dic11—82no—
119C2×Dic11—81no—
120C11⋊C8—42no—
121C11⋊C8—82no—
122C2×#124—21no—
123C2×#106—221no—
124C2×#103—221no—
125C2×#102—222no—
126#394—21no—
127#392—22no—
128#391C2×D1111yescharacteristic
129#390C2×D1112yes—
130#388—22no—
131#384—111no—
132#340—222no—
133#336—112no—
134#336—111no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11#44912yes—
143C22×C11#45011yescharacteristic
144C22×C11#45311yescharacteristic
145C22×C11#45512yes—
146C22×C11#45811yescharacteristic
147C4×C11—22no—
148C4×C11—22no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—82no—
153C4×C11—81no—
154Dic11—161no—
155C22×Q8C22⋊D1111yescharacteristic
156C22×D4—21no—
157C22×D4—21no—
158C22×D4C22⋊D1112yes—
159C22×C8—221no—
160C22×C8—222no—
161#124—42no—
162#124—42no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4C22⋊D1112yes—
166C2×C4⋊C4C22⋊D1111yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C42—21no—
172C2×C42C22×D1111yescharacteristic
173#106—442no—
174#103—442no—
175#102—444no—
176#95—21no—
177#95—22no—
178C2×C11—162no—
179C2×C11#161212yes—
180C2×C11#161311yescharacteristic
181C2×C11#162411yescharacteristic
182C2×C11#164212yes—
183C2×C11#165911yescharacteristic
184C24—22no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#432412yes—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—81no—
195C2×D4—81no—
196C2×D4—81no—
197C2×D4—82no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—441no—
202C22×C4C2×C22⋊D1111yescharacteristic
203C22×C4C2×C22⋊D1112yes—
204C2×C8—222no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—442no—
208C2×C8—442no—
209C2×C8—442no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4—442no—
215C4⋊C4—442no—
216C22⋊C4—44no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—82no—
222C42—41no—
223C42—42no—
224C11#781011yescharacteristic, complemented, Sylow
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23#6700611yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—44no—
236D4—82no—
237D4—84no—
238D4—84no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—882no—
252C2×C4—881no—
253C2×C4#6698511yescharacteristic
254C2×C4C2×#432411yescharacteristic
255C2×C4#6700212yes—
256C2×C4#6700312yes—
257C8—442no—
258C8—882no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22#1062283111yescharacteristic
267C22#1062285112yes—
268C22#1062285411yescharacteristic
269C22#1062285512yes—
270C22#1062285611yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—82no—
277C4—81no—
278C4—1761no—
279C2—162no—
280C2#1306763012yes—
281C2#1306763611yescharacteristic
282C2#1306769911yescharacteristic
283C2#1306781612yes—
284C2#1306792211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2733C2
socleC23×C11#120
hypercenter#2733D11
hypocenterC11#7810
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #13070159C2semidirect
2. #13070019C2semidirect
3. #13066442C2semidirect
4. #13066437C2semidirect
224. C11#7810semidirect

Maximal subgroups

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

subgroupindex
#130701592
#130700192
#130664422
#130664372
C11×#27332
#781011