Finite Group Databasebeta

← #14656843

Subgroups — #14656843

Order 2816.

484 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 91 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#13076888C211yesmaximal, characteristic, complemented
2#13069441C212yesmaximal
3#13066498C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#102—21no—
8C2×C11×#102—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66896—22no—
12C2×#66896—22no—
13#10622599—21no—
14#10622592—21no—
15#10622549C2212yes—
16C2×#66867C2212yes—
17#10622273—22no—
18#10622269—22no—
19C22×D4×C11—22no—
20C22×D4×C11—21no—
21C22×Dic22—21no—
22C22×C8×C11—21no—
23C11×#127—21no—
24C11×#127—22no—
25C11×#127Q812yescomplemented
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C22×C11⋊C8—22no—
34C11×#102—42no—
35C11×#102—42no—
36C11×#97—22no—
37C11×#95—22no—
38#66896—44no—
39#66896—44no—
40C11⋊#95—22no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45#66867—22no—
46#66867—22no—
47#10358—111nomaximal, Sylow
48C24×C11—41no—
49C2×D4×C11—24no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—42no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C2×D412yes—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×Dic22—82no—
68C2×Dic22—81no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C42×C11C2×Q811yescharacteristic
75C42×C11#4111yescharacteristic
76C42×C11#4112yes—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—81no—
80Dic11⋊C4—82no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2844—111no—
85#1961—112no—
86#1961D1111yescharacteristic
87#1295—112no—
88#1295—111no—
89C23×C11—42no—
90C23×C11—82no—
91C23×C11—81no—
92C23×C11—82no—
93C23×C11—81no—
94C23×C11#12011yescharacteristic
95D4×C11—44no—
96D4×C11—44no—
97D4×C11—42no—
98D4×C11—42no—
99D4×C11—82no—
100D4×C11—82no—
101D4×C11—81no—
102D4×C11—81no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11C22⋊Q812yes—
112C2×C4×C11C22⋊Q811yescharacteristic
113C2×C4×C11#12412yes—
114C2×C4×C11#12411yescharacteristic
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121Dic22—84no—
122C8×C11—42no—
123C11⋊C8—44no—
124C2×#127C2×D1111yescharacteristic
125C2×#102—21no—
126C2×#102—21no—
127C2×#102—222no—
128C2×#102—222no—
129C2×#97—112no—
130C2×#97C2×D1111yescharacteristic
131#400—222no—
132#400—221no—
133#395—222no—
134#395—221no—
135#382—112no—
136#382C2×D1111yescharacteristic
137C22×C11—84no—
138C22×C11—82no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11—162no—
142C22×C11#39311yescharacteristic
143C22×C11#45312yes—
144C22×C11#45311yescharacteristic
145C22×C11#45412yes—
146C22×C11#45411yescharacteristic
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—22no—
150C4×C11—21no—
151C4×C11—81no—
152C4×C11—81no—
153Dic11—82no—
154Dic11—82no—
155C22×Q8—221no—
156C22×D4—22no—
157C22×D4—21no—
158C22×C8—21no—
159C22×C8—222no—
160#127—21no—
161#127—22no—
162#127Dic2212yescomplemented
163C2×C4⋊C4—112no—
164C2×C4⋊C4—112no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4C22⋊D1111yescharacteristic
168C2×C4⋊C4C22⋊D1111yescharacteristic
169C2×C42C22×D1111yescharacteristic
170#102—42no—
171#102—42no—
172#102—444no—
173#102—444no—
174#97—22no—
175#97—222no—
176#97—222no—
177#95—22no—
178#95—222no—
179#95—221no—
180#95—221no—
181#95—222no—
182#95—222no—
183C2×C11—162no—
184C2×C11#165511yescharacteristic
185C2×C11#165711yescharacteristic
186C2×C11#165712yes—
187C2×C11#202712yes—
188C2×C11#202711yescharacteristic
189C24—41no—
190C2×Q8—882no—
191C2×Q8—881no—
192C2×D4—24no—
193C2×D4—22no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—42no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—42no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—222no—
207C22×C4—222no—
208C22×C4D4×D1112yes—
209C22×C4C2×C22⋊D1111yescharacteristic
210C2×C8—22no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—224no—
214C2×C8—442no—
215C2×C8—442no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—442no—
219C4⋊C4—442no—
220C4⋊C4—882no—
221C4⋊C4—881no—
222C42C2×Dic2211yescharacteristic
223C42#433911yescharacteristic
224C42#434112yes—
225C11#1035811yescharacteristic, complemented, Sylow
226C23—42no—
227C23—82no—
228C23—82no—
229C23—81no—
230C23—81no—
231C23#6699011yescharacteristic
232Q8—884no—
233D4—44no—
234D4—44no—
235D4—42no—
236D4—42no—
237D4—82no—
238D4—82no—
239D4—81no—
240D4—81no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4#6693112yes—
256C2×C4#6693812yes—
257C2×C4#6697711yescharacteristic
258C2×C4#6698911yescharacteristic
259C8—42no—
260C8—444no—
261C22—84no—
262C22—82no—
263C22—161no—
264C22—161no—
265C22—162no—
266C22#1062256011yescharacteristic
267C22#1062267511yescharacteristic
268C22#1062269011yescharacteristic
269C22#1062281112yes—
270C22#1062281412yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—81no—
276C4—81no—
277C4—882no—
278C4—882no—
279C2—162no—
280C2#1306790411yescharacteristic
281C2#1306791211yescharacteristic
282C2#1306791312yes—
283C2#1306977012yes—
284C2#1306977211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1961C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenter#1961D11
hypocenterC11#10358
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #13076888C2semidirect
3. #13066498C2semidirect
4. #13066497C2semidirect
25. C11×#127Q8semidirect
162. #127Dic22semidirect
225. C11#10358semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130694412
#130664982
#130664972
C11×#19612
#1035811