Finite Group Databasebeta

← #14656902

Subgroups — #14656902

Order 2816.

454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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#13071909C211yesmaximal, characteristic, complemented
2#13069448C211yesmaximal, characteristic
3#13067112C212yesmaximal
4#13066518C212yesmaximal, complemented
5C11×#1274C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#431C2212yes—
9C11×#376C2211yescharacteristic
10C4×C4⋊Dic11—21no—
11C4×C4⋊Dic11C2212yes—
12C2×#66869—21no—
13C2×#66869—21no—
14#10622537C2211yescharacteristic
15#10622274—22no—
16#10622269—22no—
17#10622108—22no—
18#10622108—22no—
19C2×#4339—21no—
20C22×Dic22—21no—
21C2×C42×C11D411yescharacteristic
22C2×C42×C11D411yescharacteristic
23C2×C42×C11C2311yescharacteristic
24#66983—22no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×Dic11⋊C4—22no—
29C2×C4×Dic11—22no—
30C2×#4318—21no—
31#66928—21no—
32#66927Q811yescharacteristic, complemented
33C4×D44—22no—
34#66922Q811yescharacteristic, complemented
35C4×Dic22—42no—
36C4×Dic22—42no—
37C11×C4⋊C8—22no—
38C11×C22⋊C8—22no—
39C4×C8×C11—22no—
40C11×#95—22no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95D412yes—
44C11⋊#95D412yes—
45#66869—42no—
46#66869—42no—
47C4⋊(C11⋊C8)—22no—
48#10370—111nomaximal, Sylow
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D412yes—
52C22×C4×C11C2×D411yescharacteristic
53C2×C22⋊D11—41no—
54C22×Dic11—22no—
55C22×Dic11—22no—
56#4339—41no—
57#4339—41no—
58#4339—41no—
59#4339—41no—
60C2×D44—21no—
61C2×D44—22no—
62C2×C4×D11—41no—
63C2×Dic22—21no—
64C2×Dic22—42no—
65C2×Dic22—44no—
66C2×C8×C11—42no—
67C42×C11—21no—
68C42×C11—21no—
69C42×C11D812yes—
70C42×C11SD1612yes—
71C42×C11C2×Q811yescharacteristic
72C42×C11#4112yes—
73C42×C11#4111yescharacteristic
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—22no—
76C4⋊Dic11—42no—
77C4⋊Dic11—44no—
78C4⋊Dic11—44no—
79Dic11⋊C4—44no—
80C4×Dic11—42no—
81C4×Dic11—42no—
82#4318—41no—
83#4318—41no—
84C2×C11⋊C8—41no—
85#2399—111no—
86#1963—111no—
87#1502—112no—
88#1303—112no—
89#1274D1111yescharacteristic, complemented
90C23×C11#12011yescharacteristic
91C22×D11—41no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11C22⋊Q812yes—
98C2×C4×C11C22⋊Q811yescharacteristic
99C2×C4×C11#12411yescharacteristic
100C2×C4×C11#12412yes—
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11C2×SD1611yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C11#13711yescharacteristic
105C22⋊D11—81no—
106C22⋊D11—81no—
107C2×Dic11—24no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—41no—
113C2×Dic11—42no—
114D44—41no—
115D44—41no—
116D44—82no—
117C4×D11—81no—
118C4×D11—81no—
119Dic22—48no—
120Dic22—41no—
121Dic22—41no—
122C8×C11—82no—
123C11⋊C8—81no—
124#532—111no—
125C2×C4×Q8—221no—
126#431C2×D1112yes—
127#423—111no—
128C2×#104—221no—
129C2×#104—221no—
130#398—222no—
131#395—222no—
132C4×C4⋊C4—112no—
133C4×C4⋊C4—221no—
134#376C2×D1111yescharacteristic
135#327—222no—
136#327—222no—
137C22×C11—22no—
138C22×C11#39311yescharacteristic
139C22×C11#44711yescharacteristic
140C22×C11#44811yescharacteristic
141C2×D11—81no—
142C2×D11—82no—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11#47411yescharacteristic
148C4×C11#47611yescharacteristic
149C4×C11#48611yescharacteristic
150C4×C11#48911yescharacteristic
151Dic11—44no—
152Dic11—82no—
153Dic11—81no—
154C2×#41—221no—
155C22×Q8—221no—
156C2×M16—221no—
157C4⋊Q8—111no—
158#127—111no—
159#124—221no—
160#121—222no—
161C4×Q8—442no—
162C4×Q8—442no—
163C4×D4—222no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—222no—
167C2×C4⋊C4—222no—
168C2×C42—222no—
169C2×C42D4411yescharacteristic
170C2×C42D4411yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—222no—
174#104—442no—
175#104—442no—
176C22⋊C8—22no—
177C4×C8—22no—
178#95—22no—
179#95—112no—
180#95—112no—
181#95—221no—
182#95—221no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#202311yescharacteristic
186C2×C11#203112yes—
187D11—161no—
188#41—441no—
189#41—441no—
190#41—441no—
191#41—441no—
192C2×Q8—221no—
193C2×Q8—442no—
194C2×Q8—444no—
195C2×D4—222no—
196C2×D4—221no—
197C2×D4—441no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—222no—
201C22×C4—222no—
202C22×C4—441no—
203C22×C4C2×D4411yescharacteristic
204C22×C4D4×D1112yes—
205M16—441no—
206M16—441no—
207C2×C8—42no—
208C2×C8—441no—
209C4⋊C4—222no—
210C4⋊C4—444no—
211C4⋊C4—442no—
212C4⋊C4—444no—
213C4⋊C4—444no—
214C22⋊C4—442no—
215C42—21no—
216C42—21no—
217C42—442no—
218C42—442no—
219C42#431412yes—
220C42D8812yes—
221C42#433912yes—
222C42#434111yescharacteristic
223C42Q8×D1111yescharacteristic
224C11#1037011yescharacteristic, complemented, Sylow
225C23—441no—
226C23#6693511yescharacteristic
227Q8—448no—
228Q8—441no—
229Q8—441no—
230D4—441no—
231D4—441no—
232D4—882no—
233D4—881no—
234D4—881no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—224no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—441no—
246C2×C4—442no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4#6692811yescharacteristic
250C2×C4#6693812yes—
251C2×C4#6694912yes—
252C2×C4#6695011yescharacteristic
253C2×C4C2×#431411yescharacteristic
254C2×C4C2×D8811yescharacteristic
255C2×C4#6696111yescharacteristic
256C2×C4#6696211yescharacteristic
257C8—82no—
258C8—881no—
259C22—22no—
260C22—881no—
261C22—882no—
262C22#1062228611yescharacteristic
263C22#1062234511yescharacteristic
264C22#1062235111yescharacteristic
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—444no—
270C4—882no—
271C4—881no—
272C4#1062230711yescharacteristic
273C4#1062232711yescharacteristic
274C4#1062245511yescharacteristic
275C4#1062245911yescharacteristic
276C2—21no—
277C2—21no—
278C2—1761no—
279C2#1306975311yescharacteristic
280C2#1306978712yes—
subgroupG/H
centerC2×C4#66928
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1274D11
hypocenterC11#10370
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
1. #13071909C2semidirect
4. #13066518C2semidirect
5. C11×#1274C2semidirect
32. #66927Q8semidirect
34. #66922Q8semidirect
89. #1274D11semidirect
224. C11#10370semidirect

Maximal subgroups

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

subgroupindex
#130719092
#130694482
#130671122
#130665182
C11×#12742
#1037011