Finite Group Databasebeta

← #14643032

Subgroups — #14643032

Order 2816.

698 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 87 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#13074951C211yesmaximal, characteristic
2#13070149C211yesmaximal, characteristic, complemented
3#13070148C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C11×#1270C211yesmaximal, characteristic, complemented
6C2×#66990—21no—
7C2×#66935—22no—
8C11×#390C2211yescharacteristic
9C2×#66896—21no—
10C2×#66885—22no—
11C2×#66881—22no—
12#10622604—21no—
13C2×#66872—21no—
14#10622574—22no—
15#10622552C2212yes—
16#10622548C2211yescharacteristic, complemented
17C11×#336C2212yescomplemented
18#10622162C2211yescharacteristic, complemented
19C24×D11—21no—
20C22×D4×C11D411yescharacteristic
21C22×C22⋊D11—22no—
22C22×D44—21no—
23C22×D44D412yes—
24C22×C8×C11—22no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C22⋊C4—22no—
27C2×C42×C11C2311yescharacteristic
28C2×C22⋊Dic11—21no—
29#66990—42no—
30#66990—42no—
31C2×(C2×D11)⋊C4—22no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D412yes—
37C22×C11⋊C8—21no—
38#66935—44no—
39#66935—44no—
40#66896—42no—
41C11⋊#95—21no—
42#66885—44no—
43#66881—44no—
44#66872—42no—
45#7822—111nomaximal, Sylow
46C24×C11—21no—
47C23×D11—22no—
48C23×D11—44no—
49C23×D11—42no—
50C23×D11—82no—
51C23×D11—81no—
52C23×D11—81no—
53C2×D4×C11—21no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11SD1612yes—
57C22×C4×C11—21no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D412yes—
60C2×C22⋊D11—44no—
61C2×C22⋊D11—44no—
62C2×C22⋊D11—82no—
63C22×Dic11—22no—
64C22×Dic11—41no—
65C2×D44—22no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—44no—
69C2×D44—81no—
70C2×D44SD1614yes—
71C2×C8×C11—24no—
72C2×C8×C11—42no—
73C2×C8×C11—42no—
74C11×C4⋊C4—41no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C42×C11—41no—
78C22⋊Dic11—42no—
79(C2×D11)⋊C4—44no—
80(C2×D11)⋊C4—42no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—42no—
83(C2×D11)⋊C4—42no—
84C4⋊Dic11—42no—
85C4⋊Dic11—41no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92#2679—111no—
93#2094—111no—
94#2094—112no—
95#1270—112no—
96#1270D1111yescharacteristic, complemented
97C23×C11—22no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11#12011yescharacteristic
103C22×D11—24no—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—42no—
107C22×D11—42no—
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—84no—
111C22×D11—88no—
112C22×D11—88no—
113C22×D11—84no—
114C22×D11—84no—
115D4×C11—42no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11C2×SD1612yes—
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)12yes—
127C22⋊D11—88no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—81no—
132C2×Dic11—82no—
133D44—44no—
134D44—82no—
135D44—84no—
136C8×C11—44no—
137C11⋊C8—42no—
138C2×#120—222no—
139C2×#120—221no—
140C2×#106—222no—
141C2×#106—221no—
142C2×#102—222no—
143C2×#102—221no—
144#394—222no—
145#394—221no—
146#390—112no—
147#390C2×D1111yescharacteristic
148#384—111no—
149#336—111no—
150#336C2×D1112yescomplemented
151C22×C11—42no—
152C22×C11—44no—
153C22×C11—82no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11#45011yescharacteristic
157C22×C11#45012yes—
158C22×C11#45311yescharacteristic
159C22×C11#45312yes—
160C22×C11#45811yescharacteristic
161C2×D11—44no—
162C2×D11—44no—
163C2×D11—44no—
164C2×D11—816no—
165C2×D11—82no—
166C2×D11—82no—
167C2×D11—82no—
168C2×D11—82no—
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—81no—
174Dic11—82no—
175Dic11—161no—
176C25—221no—
177C22×D4—112no—
178C22×D4—221no—
179C22×D4—222no—
180C22×D4D4411yescharacteristic
181C22×C8—22no—
182C22×C8—221no—
183#120—444no—
184#120—444no—
185#120—442no—
186#120—442no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—222no—
190C2×C4⋊C4D4411yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4—222no—
195C2×C22⋊C4—222no—
196C2×C42C22×D1111yescharacteristic
197#106—442no—
198#106—444no—
199#102—444no—
200#102—442no—
201#95—221no—
202C2×C11—82no—
203C2×C11#161312yes—
204C2×C11#161311yescharacteristic
205C2×C11#162911yescharacteristic
206C2×C11#162912yes—
207C2×C11#165511yescharacteristic
208D11—84no—
209C24—21no—
210C24—222no—
211C24—442no—
212C24—444no—
213C24—881no—
214C24—881no—
215C24—882no—
216C2×D4—21no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—114no—
220C2×D4—222no—
221C2×D4—442no—
222C2×D4—442no—
223C2×D4—444no—
224C2×D4—444no—
225C2×D4—444no—
226C2×D4—881no—
227C2×D4—882no—
228C2×D4#431412yes—
229C22×C4—21no—
230C22×C4—222no—
231C22×C4—441no—
232C22×C4C2×D4411yescharacteristic
233C22×C4D4×D1112yes—
234C2×C8—24no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—222no—
238C2×C8—441no—
239C2×C8—441no—
240C4⋊C4—41no—
241C4⋊C4—442no—
242C4⋊C4—441no—
243C4⋊C4—442no—
244C4⋊C4—441no—
245C4⋊C4—442no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—444no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C22⋊C4—442no—
252C22⋊C4—442no—
253C22⋊C4—442no—
254C42—41no—
255C11#782211yescharacteristic, complemented, Sylow
256C23—22no—
257C23—41no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—224no—
262C23—442no—
263C23—442no—
264C23—442no—
265C23—442no—
266C23—442no—
267C23—442no—
268C23—888no—
269C23—884no—
270C23—884no—
271C23—888no—
272C23—884no—
273C23#6693511yescharacteristic
274D4—42no—
275D4—81no—
276D4—444no—
277D4—882no—
278D4—884no—
279D4—888no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—881no—
290C2×C4—882no—
291C2×C4C2×#431411yescharacteristic
292C2×C4#6696111yescharacteristic
293C2×C4#6696412yes—
294C2×C4SD16×D1112yes—
295C8—44no—
296C8—442no—
297C22—42no—
298C22—44no—
299C22—82no—
300C22—81no—
301C22—81no—
302C22—444no—
303C22—444no—
304C22—444no—
305C22—8816no—
306C22—882no—
307C22—882no—
308C22—882no—
309C22—882no—
310C22#1062234411yescharacteristic
311C22#1062235511yescharacteristic
312C22#1062236011yescharacteristic
313C22#1062238912yes—
314C22#1062243512yes—
315C4—22no—
316C4—22no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—882no—
321C4—1761no—
322C2—82no—
323C2—884no—
324C2#1306763712yes—
325C2#1306763811yescharacteristic
326C2#1306773311yescharacteristic
327C2#1306773412yes—
328C2#1306790611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radical#13074951C2
hypercenter#1270D11
hypocenterC11#7822
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070149C2semidirect
3. #13070148C2semidirect
4. #13066436C2semidirect
5. C11×#1270C2semidirect
16. #10622548C22semidirect
17. C11×#336C22semidirect
18. #10622162C22semidirect
96. #1270D11semidirect
150. #336C2×D11semidirect
255. C11#7822semidirect

Maximal subgroups

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

subgroupindex
#130749512
#130701492
#130701482
#130664362
C11×#12702
#782211