Finite Group Databasebeta

← #14666032

Subgroups — #14666032

Order 2816.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076609C211yesmaximal, characteristic, complemented
2#13069662C211yesmaximal, characteristic
3#13067587C212yesmaximal
4#13066647C212yesmaximal, complemented
5C11×#1319C211yesmaximal, characteristic, complemented
6C2×#66995—21no—
7#10623041C2211yescharacteristic
8C11×#391C2211yescharacteristic
9#10622843—21no—
10#10622592C2212yes—
11#10622542—21no—
12C2×#66869—21no—
13#10622351—22no—
14#10622269—22no—
15#10622259—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C22×Q8×C11D411yescharacteristic
20C2×#4339—21no—
21C22×Dic22—21no—
22C22×Dic22D412yes—
23C2×C11×C4⋊C4C2311yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×#4326—41no—
26#66995—42no—
27#66995—42no—
28C2×#4325—41no—
29#66983—22no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—21no—
34C2×#4318—21no—
35C2×#4314—42no—
36#66950—41no—
37#66948—41no—
38C11×C22⋊C8—22no—
39C11×#95—22no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44#66880—42no—
45#66869—42no—
46#12130—111nomaximal, Sylow
47C2×Q8×C11—21no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11SD1612yescomplemented
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C2×C22⋊D11—41no—
56C22×Dic11—22no—
57C22×Dic11—22no—
58#4339—41no—
59#4339—41no—
60#4339—41no—
61#4339—41no—
62C2×D44—21no—
63C2×D44—22no—
64C2×C4×D11—41no—
65C2×Dic22—21no—
66C2×Dic22—24no—
67C2×Dic22—42no—
68C2×Dic22—82no—
69C2×Dic22—81no—
70C2×Dic22—81no—
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C42×C11—41no—
74#4326—44no—
75#4325—44no—
76(C2×D11)⋊C4—42no—
77C4⋊Dic11—22no—
78C4⋊Dic11—81no—
79C4⋊Dic11—81no—
80Dic11⋊C4—82no—
81C4×Dic11—81no—
82#4318—22no—
83#4318—41no—
84C2×C11⋊C8—41no—
85#4314—84no—
86#2811—111no—
87#2007—111no—
88#1604—112no—
89#1354—112no—
90#1319D1111yescharacteristic, complemented
91C23×C11#12011yescharacteristic
92C22×D11—41no—
93Q8×C11—42no—
94Q8×C11—81no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11C2×SD1611yescharacteristic
106C2×C4×C11#13711yescharacteristic
107C22⋊D11—81no—
108C22⋊D11—81no—
109C2×Dic11—24no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—41no—
115C2×Dic11—42no—
116D44—41no—
117D44—41no—
118D44—82no—
119C4×D11—81no—
120C4×D11—81no—
121Dic22—41no—
122Dic22—41no—
123Dic22—44no—
124Dic22—84no—
125Dic22—82no—
126C8×C11—82no—
127C11⋊C8—42no—
128C2×#137—221no—
129#537—111no—
130#448—222no—
131C2×#104—221no—
132#395—112no—
133#395—222no—
134#391—222no—
135#391—221no—
136#391—221no—
137#391C2×D1111yescharacteristic
138#343—111no—
139#327—222no—
140#324C2×D1112yes—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#44811yescharacteristic
144C22×C11#45311yescharacteristic
145C22×C11B(4,𝔽2)11yescharacteristic
146C2×D11—81no—
147C2×D11—81no—
148C2×D11—81no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—42no—
154Dic11—44no—
155Dic11—81no—
156Dic11—82no—
157C2×#41—221no—
158C22×Q8—112no—
159C22×Q8—221no—
160C22×Q8D4411yescharacteristic
161#137—442no—
162#137—442no—
163C2×Q16—441no—
164C2×SD16—442no—
165C2×SD16—441no—
166C2×M16—221no—
167C22⋊Q8—441no—
168#121—222no—
169#121—441no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—222no—
173C2×C4⋊C4C22×D1111yescharacteristic
174C2×C42—221no—
175C2×C42D4411yescharacteristic
176#104—442no—
177#103—442no—
178C22⋊C8—22no—
179#95—22no—
180#95—112no—
181#95—222no—
182#95—222no—
183#95—222no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#159611yescharacteristic
187C2×C11#219911yescharacteristic
188C2×C11#220511yescharacteristic
189D11—161no—
190#41—441no—
191#41—441no—
192#41—441no—
193#41—441no—
194C2×Q8—21no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—224no—
198C2×Q8—221no—
199C2×Q8—442no—
200C2×Q8—882no—
201C2×Q8—881no—
202C2×Q8—881no—
203C2×Q8#431412yescomplemented
204C2×D4—221no—
205C2×D4—222no—
206C2×D4—441no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—441no—
212C22×C4C2×D4411yescharacteristic
213C22×C4D4×D1112yes—
214Q16—444no—
215SD16—444no—
216SD16—884no—
217M16—222no—
218M16—441no—
219C2×C8—42no—
220C2×C8—441no—
221C4⋊C4—41no—
222C4⋊C4—222no—
223C4⋊C4—882no—
224C4⋊C4—881no—
225C4⋊C4—881no—
226C22⋊C4—442no—
227C42—41no—
228C42—881no—
229C11#1213011yescharacteristic, complemented, Sylow
230C23—441no—
231C23#6693511yescharacteristic
232Q8—42no—
233Q8—81no—
234Q8—441no—
235Q8—441no—
236Q8—444no—
237Q8—884no—
238Q8—882no—
239D4—441no—
240D4—441no—
241D4—882no—
242D4—881no—
243D4—881no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—224no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—441no—
260C2×C4—442no—
261C2×C4—881no—
262C2×C4—881no—
263C2×C4C2×#431411yescharacteristic
264C2×C4#6696211yescharacteristic
265C8—82no—
266C8—442no—
267C22—21no—
268C22—21no—
269C22—881no—
270C22—881no—
271C22—881no—
272C22#1062235111yescharacteristic
273C22#1062235411yescharacteristic
274C22#1062236011yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—444no—
281C4—881no—
282C4—882no—
283C2—21no—
284C2—21no—
285C2—1761no—
286C2#1306754111yescharacteristic
287C2#1307061911yescharacteristic
288C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1319D11
hypocenterC11#12130
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
1. #13076609C2semidirect
4. #13066647C2semidirect
5. C11×#1319C2semidirect
50. C2×Q8×C11SD16semidirect
90. #1319D11semidirect
203. C2×Q8#4314semidirect
229. C11#12130semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130696622
#130675872
#130666472
C11×#13192
#1213011