Finite Group Databasebeta

← #14656844

Subgroups — #14656844

Order 2816.

484 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 89 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#13069440C212yesmaximal
3#13069439C211yesmaximal, characteristic
4#13066498C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C2×C11×#97C2212yes—
8C11×#382C2211yescharacteristic
9C2×#66885—22no—
10C2×#66885—22no—
11#10622599—21no—
12#10622592—21no—
13C2×#66873—21no—
14C2×#66873—21no—
15#10622549C2212yes—
16C2×#66867C2211yescharacteristic
17#10622273—22no—
18#10622269—22no—
19C22×D44—22no—
20C22×D44—21no—
21C22×Dic22—21no—
22C22×C8×C11—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11D412yes—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—21no—
31#66927—22no—
32#66927—21no—
33#66927Q812yescomplemented
34C11×#97—22no—
35C11×#97—22no—
36C11×#95—22no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42#66885—44no—
43#66885—44no—
44#66873—42no—
45#66873—42no—
46#66867—22no—
47#10358—111nomaximal, Sylow
48C23×D11—41no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C2×D44—24no—
56C2×D44—22no—
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—42no—
60C2×D44—42no—
61C2×D44—41no—
62C2×D44—41no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—41no—
66C2×D44—42no—
67C2×Dic22—82no—
68C2×Dic22—81no—
69C2×C8×C11—24no—
70C2×C8×C11—42no—
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C42×C11C2×Q811yescharacteristic
75C42×C11#4112yes—
76C42×C11#4111yescharacteristic
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—81no—
80Dic11⋊C4—82no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84#2844—111no—
85#1961—112no—
86#1961—111no—
87#1295—112no—
88#1295D1111yescharacteristic, complemented
89C23×C11#12011yescharacteristic
90C22×D11—42no—
91C22×D11—81no—
92C22×D11—82no—
93C22×D11—81no—
94C22×D11—82no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11C22⋊Q812yes—
104C2×C4×C11C22⋊Q811yescharacteristic
105C2×C4×C11#12411yescharacteristic
106C2×C4×C11#12412yes—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113D44—42no—
114D44—42no—
115D44—44no—
116D44—44no—
117D44—81no—
118D44—81no—
119D44—82no—
120D44—82no—
121Dic22—84no—
122C8×C11—44no—
123C11⋊C8—42no—
124C2×#127—111no—
125C2×#102—222no—
126C2×#102—222no—
127C2×#102—221no—
128C2×#102—221no—
129C2×#97—111no—
130C2×#97C2×D1112yes—
131#400—222no—
132#400—221no—
133#395—222no—
134#395—221no—
135#382—112no—
136#382C2×D1111yescharacteristic
137C22×C11#39311yescharacteristic
138C22×C11#45311yescharacteristic
139C22×C11#45312yes—
140C22×C11#45411yescharacteristic
141C22×C11#45412yes—
142C2×D11—84no—
143C2×D11—82no—
144C2×D11—161no—
145C2×D11—161no—
146C2×D11—162no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—22no—
151C4×C11—81no—
152C4×C11—81no—
153Dic11—82no—
154Dic11—82no—
155C22×Q8—221no—
156C22×D4—221no—
157C22×D4—222no—
158C22×C8—22no—
159C22×C8—221no—
160#127—112no—
161#127—222no—
162#127—221no—
163C2×C4⋊C4—112no—
164C2×C4⋊C4—112no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4D4411yescharacteristic
168C2×C4⋊C4D4411yescharacteristic
169C2×C42C22×D1111yescharacteristic
170#102—442no—
171#102—442no—
172#102—444no—
173#102—444no—
174#97—22no—
175#97—22no—
176#97—222no—
177#95—22no—
178#95—222no—
179#95—221no—
180#95—221no—
181#95—222no—
182#95—222no—
183C2×C11#165511yescharacteristic
184C2×C11#165711yescharacteristic
185C2×C11#165712yes—
186C2×C11#202712yes—
187C2×C11#202711yescharacteristic
188D11—162no—
189C24—441no—
190C2×Q8—881no—
191C2×Q8—882no—
192C2×D4—224no—
193C2×D4—222no—
194C2×D4—441no—
195C2×D4—441no—
196C2×D4—442no—
197C2×D4—442no—
198C2×D4—441no—
199C2×D4—441no—
200C2×D4—442no—
201C2×D4—442no—
202C2×D4—441no—
203C2×D4—442no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—222no—
207C22×C4—222no—
208C22×C4C2×D4411yescharacteristic
209C22×C4D4×D1112yes—
210C2×C8—24no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—222no—
214C2×C8—441no—
215C2×C8—441no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—442no—
219C4⋊C4—442no—
220C4⋊C4—882no—
221C4⋊C4—881no—
222C42#433912yes—
223C42#434111yescharacteristic
224C42Q8×D1111yescharacteristic
225C11#1035811yescharacteristic, complemented, Sylow
226C23—442no—
227C23—881no—
228C23—881no—
229C23—882no—
230C23—882no—
231C23#6693511yescharacteristic
232Q8—884no—
233D4—444no—
234D4—444no—
235D4—442no—
236D4—442no—
237D4—882no—
238D4—882no—
239D4—881no—
240D4—881no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4#6692811yescharacteristic
256C2×C4#6693812yes—
257C2×C4#6694912yes—
258C2×C4#6695011yescharacteristic
259C8—44no—
260C8—442no—
261C22—884no—
262C22—882no—
263C22—1761no—
264C22—1761no—
265C22—1762no—
266C22#1062228611yescharacteristic
267C22#1062236011yescharacteristic
268C22#1062236611yescharacteristic
269C22#1062243512yes—
270C22#1062244012yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—81no—
276C4—81no—
277C4—882no—
278C4—882no—
279C2—1762no—
280C2#1306790611yescharacteristic
281C2#1306791511yescharacteristic
282C2#1306791612yes—
283C2#1306977112yes—
284C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1295D11
hypocenterC11#10358
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #13076888C2semidirect
4. #13066498C2semidirect
5. C11×#1295C2semidirect
33. #66927Q8semidirect
88. #1295D11semidirect
225. C11#10358semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130694402
#130694392
#130664982
C11×#12952
#1035811