Finite Group Databasebeta

← #14666524

Subgroups — #14666524

Order 2816.

664 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069772C211yesmaximal, characteristic, complemented
2#13067555C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066548C211yesmaximal, characteristic, complemented
5C11×#2679C211yesmaximal, characteristic
6C2×C11×#120—22no—
7C2×C11×#120—21no—
8#10623031C2211yescharacteristic, complemented
9C11×#394—22no—
10C11×#394C2212yes—
11C11×#390—21no—
12C11×#390C2211yescharacteristic
13#10622831—22no—
14#10622828—21no—
15#10622168C2211yescharacteristic, complemented
16#10622166C2212yescomplemented
17#10622161—21no—
18#10622090—22no—
19C25×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—22no—
22C22×D4×C11D411yescharacteristic
23C22×D4×C11D412yes—
24C11×#120—48no—
25C11×#120—42no—
26C11×#120—42no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11D411yescharacteristic
35C2×#4324—42no—
36#66979—21no—
37#66977—22no—
38C2×#4318—21no—
39#66943—41no—
40#66941—41no—
41C11×#95D412yes—
42#66896—41no—
43#66896—41no—
44#66896—42no—
45C22⋊(C11⋊C8)—22no—
46#12208—111nomaximal, Sylow
47C24×C11—22no—
48C24×C11—21no—
49C24×C11—44no—
50C24×C11—42no—
51C24×C11—82no—
52C24×C11—81no—
53C24×C11—81no—
54C2×D4×C11—24no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11—42no—
58C2×D4×C11—41no—
59C2×D4×C11—44no—
60C2×D4×C11—44no—
61C2×D4×C11—44no—
62C2×D4×C11—81no—
63C2×D4×C11—81no—
64C2×D4×C11—82no—
65C2×D4×C11SD1612yescomplemented
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D412yes—
70C2×Dic22—22no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—81no—
73C11×C22⋊C4—44no—
74C11×C22⋊C4—44no—
75C11×C22⋊C4—44no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C42×C11—41no—
80C22⋊Dic11—41no—
81#4324—84no—
82C4⋊Dic11—21no—
83C4⋊Dic11—22no—
84C4⋊Dic11—21no—
85Dic11⋊C4—42no—
86C4×Dic11—41no—
87#4318—41no—
88#4318—41no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—41no—
91#2679D1111yescharacteristic
92#2027—111no—
93#1599—112no—
94#1345—112no—
95#1318—111no—
96C23×C11—24no—
97C23×C11—22no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—41no—
105C23×C11—42no—
106C23×C11—41no—
107C23×C11—42no—
108C23×C11—88no—
109C23×C11—84no—
110C23×C11—88no—
111C23×C11—84no—
112C23×C11—84no—
113C23×C11#12011yescharacteristic
114D4×C11—42no—
115D4×C11—44no—
116D4×C11—81no—
117D4×C11—84no—
118D4×C11—82no—
119D4×C11—88no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×Dic11—41no—
133C2×Dic11—41no—
134Dic22—82no—
135C11⋊C8—81no—
136C11⋊C8—82no—
137#544—111no—
138C2×#120—22no—
139C2×#120—21no—
140#450—222no—
141#418—221no—
142#394—22no—
143#394C2×D1112yes—
144#390—21no—
145#390C2×D1111yescharacteristic
146#343—111no—
147#339—221no—
148#328—222no—
149#324—112no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—44no—
153C22×C11—44no—
154C22×C11—44no—
155C22×C11—42no—
156C22×C11—44no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11—816no—
161C22×C11—82no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11—82no—
165C22×C11#45011yescharacteristic
166C22×C11#45511yescharacteristic
167C22×C11B(4,𝔽2)11yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—42no—
172C4×C11—82no—
173Dic11—81no—
174Dic11—81no—
175C25—21no—
176C22×D4—21no—
177C22×D4—22no—
178C22×D4C22⋊D1111yescharacteristic
179C22×D4C22⋊D1112yes—
180C2×SD16—442no—
181C2×M16—221no—
182C4⋊Q8—441no—
183#125—441no—
184C22⋊Q8—222no—
185#120—48no—
186#120—42no—
187#120—42no—
188#117—221no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C22×D1111yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C42C22⋊D1111yescharacteristic
197#102—441no—
198#102—441no—
199#102—442no—
200C22⋊C8—222no—
201#95C22⋊D1112yes—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11—82no—
205C2×C11—84no—
206C2×C11#160111yescharacteristic
207C2×C11#219611yescharacteristic
208C2×C11#220211yescharacteristic
209C24—22no—
210C24—21no—
211C24—44no—
212C24—42no—
213C24—82no—
214C24—81no—
215C24—81no—
216C2×Q8—222no—
217C2×D4—24no—
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—44no—
225C2×D4—81no—
226C2×D4—81no—
227C2×D4—82no—
228C2×D4#432412yescomplemented
229C22×C4—21no—
230C22×C4—22no—
231C22×C4C2×C22⋊D1111yescharacteristic
232C22×C4C2×C22⋊D1112yes—
233SD16—884no—
234M16—441no—
235M16—441no—
236C2×C8—442no—
237C2×C8—441no—
238C4⋊C4—41no—
239C4⋊C4—81no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—222no—
243C4⋊C4—442no—
244C22⋊C4—44no—
245C22⋊C4—44no—
246C22⋊C4—44no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—441no—
251C42—41no—
252C42—441no—
253C11#1220811yescharacteristic, complemented, Sylow
254C23—24no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—41no—
263C23—42no—
264C23—42no—
265C23—41no—
266C23—88no—
267C23—84no—
268C23—88no—
269C23—84no—
270C23—84no—
271C23#6700611yescharacteristic
272Q8—882no—
273D4—42no—
274D4—44no—
275D4—81no—
276D4—84no—
277D4—82no—
278D4—88no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4#6698511yescharacteristic
292C2×C4C2×#432411yescharacteristic
293C8—881no—
294C8—882no—
295C22—21no—
296C22—21no—
297C22—44no—
298C22—44no—
299C22—44no—
300C22—44no—
301C22—42no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22—816no—
306C22—81no—
307C22—82no—
308C22—81no—
309C22—82no—
310C22#1062283111yescharacteristic
311C22#1062285511yescharacteristic
312C22#1062285711yescharacteristic
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4—881no—
319C4—881no—
320C2—21no—
321C2—21no—
322C2—84no—
323C2—82no—
324C2#1306756811yescharacteristic
325C2#1307060011yescharacteristic
326C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2679C2
socleC22×C11B(4,𝔽2)
hypercenter#2679D11
hypocenterC11#12208
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #13069772C2semidirect
2. #13067555C2semidirect
3. #13066619C2semidirect
4. #13066548C2semidirect
8. #10623031C22semidirect
15. #10622168C22semidirect
16. #10622166C22semidirect
65. C2×D4×C11SD16semidirect
228. C2×D4#4324semidirect
253. C11#12208semidirect

Maximal subgroups

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

subgroupindex
#130697722
#130675552
#130666192
#130665482
C11×#26792
#1220811