Finite Group Databasebeta

← #14673633

Subgroups — #14673633

Order 2816.

342 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622127C211yesmaximal, characteristic, complemented
2C2×(C2×D11)⋊C16C211yesmaximal, characteristic
3#13068642C211yesmaximal, characteristic
4#13068642C211yesmaximal, characteristic
5#13066708C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D11C2211yescharacteristic
9C22×C11×C16C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13C2×#66882C2211yescharacteristic
14C22×C11⋊C16C2211yescharacteristic
15#10622600—21no—
16#10622600—21no—
17#10622167—21no—
18#10622167—21no—
19(C2×D11)⋊C16—22no—
20#10622127—22no—
21C22×C4×D11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—21no—
25C2×(C2×D11)⋊C4—41no—
26C2×(C2×D11)⋊C4—41no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11—21no—
29C22×C11⋊C8D411yescharacteristic
30C2×C8×D11—21no—
31C2×C8×D11—21no—
32C2×C8×D11—21no—
33C2×C8×D11—21no—
34C2×C8×D11—21no—
35C2×C8×D11—21no—
36C2×C11×C16—21no—
37C2×C11×C16—21no—
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#107—21no—
43C11⋊#95—41no—
44C11⋊#95—41no—
45#66882—21no—
46#66882—21no—
47#66882—21no—
48#66882—21no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16D412yes—
52#13492—111nomaximal, Sylow
53C23×D11D811yescharacteristic
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C22×Dic11—41no—
59C22×Dic11D811yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11#4111yescharacteristic
68C2×C8×C11#4111yescharacteristic
69C2×C8×C11#4111yescharacteristic
70C2×C8×C11#4111yescharacteristic
71C2×C8×C11#4111yescharacteristic
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76(C2×D11)⋊C4—82no—
77(C2×D11)⋊C4—82no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—21no—
85C8×D11—41no—
86C8×D11—41no—
87C8×D11—41no—
88C8×D11—41no—
89C11×C16—41no—
90C11⋊C16—22no—
91C2×#366—111no—
92C2×C22⋊C16—111no—
93#1808—111no—
94#1808—111no—
95#1380—111no—
96#1380—111no—
97#1380D1111yescharacteristic, complemented
98C23×C11C2×D811yescharacteristic
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11D1612yes—
106C2×C4×C11—81no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11#13511yescharacteristic
116C2×C4×C11#13711yescharacteristic
117C2×C4×C11#13711yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—81no—
122C2×Dic11—81no—
123C2×Dic11—81no—
124C2×Dic11—81no—
125C2×Dic11—81no—
126C2×Dic11—81no—
127C4×D11—41no—
128C4×D11—41no—
129C4×D11—41no—
130C4×D11—41no—
131C8×C11#12311yescharacteristic
132C8×C11#12411yescharacteristic
133C8×C11#12611yescharacteristic
134C8×C11#12611yescharacteristic
135C11⋊C8—41no—
136C23×C8—111no—
137C22×C16—111no—
138C22×C16C2×D1111yescharacteristic
139C2×#107—111no—
140C2×#107—111no—
141C2×#107C2×D1111yescharacteristic
142C2×#107C2×D1111yescharacteristic
143#380—221no—
144#380—221no—
145#366—222no—
146C22⋊C16—222no—
147#340—221no—
148#340—221no—
149C22×C11#46611yescharacteristic
150C22×C11#48011yescharacteristic
151C22×C11#48011yescharacteristic
152C22×C11C2×D1611yescharacteristic
153C22×C11#50811yescharacteristic
154C22×C11#51011yescharacteristic
155C22×C11#51011yescharacteristic
156C2×D11—22no—
157C2×D11—22no—
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C4×C11—161no—
164C4×C11—161no—
165C4×C11#39711yescharacteristic
166C4×C11#47011yescharacteristic
167C4×C11#48511yescharacteristic
168C4×C11#48511yescharacteristic
169Dic11—41no—
170Dic11—161no—
171Dic11—161no—
172C23×C4—111no—
173C22×C8—111no—
174C22×C8—221no—
175C22×C8—221no—
176C22×C8—221no—
177C22×C8—221no—
178C22×C8—221no—
179C22×C8—221no—
180C22×C8C22×D1111yescharacteristic
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C22⋊C4—441no—
186C2×C22⋊C4—441no—
187C2×C16—21no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16—112no—
191C2×C16—221no—
192C2×C16—221no—
193#107—21no—
194#107—21no—
195#107—21no—
196#107—21no—
197#107—221no—
198#107—221no—
199#107—221no—
200#107—221no—
201#95—441no—
202#95—441no—
203C2×C11#207511yescharacteristic
204C2×C11#221511yescharacteristic
205C2×C11#221911yescharacteristic
206C2×C11#223211yescharacteristic
207C2×C11#223211yescharacteristic
208C2×C11#223711yescharacteristic
209C2×C11#223711yescharacteristic
210D11—42no—
211C24—111no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—111no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—441no—
222C22×C4—441no—
223C22×C4D4×D1111yescharacteristic
224C2×C8—221no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—441no—
228C2×C8—441no—
229C2×C8—441no—
230C2×C8—441no—
231C2×C8#433911yescharacteristic
232C2×C8#433911yescharacteristic
233C2×C8#433911yescharacteristic
234C2×C8D4×D1111yescharacteristic
235C2×C8#434111yescharacteristic
236C2×C8#434311yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C22⋊C4—882no—
246C22⋊C4—882no—
247C16—41no—
248C16—222no—
249C11#1349211yescharacteristic, complemented, Sylow
250C23—112no—
251C23—221no—
252C23—221no—
253C23—221no—
254C23—221no—
255C23—221no—
256C23—221no—
257C23D8×D1111yescharacteristic
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—881no—
272C2×C4—881no—
273C2×C4—881no—
274C2×C4—881no—
275C2×C4—881no—
276C2×C4—881no—
277C2×C4#6693611yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4#6694711yescharacteristic
280C2×C4#6696811yescharacteristic
281C2×C4#6696911yescharacteristic
282C2×C4#6697111yescharacteristic
283C8—441no—
284C8#6692911yescharacteristic
285C8#6693811yescharacteristic
286C8#6694711yescharacteristic
287C8#6695111yescharacteristic
288C22—222no—
289C22—222no—
290C22—222no—
291C22—441no—
292C22—441no—
293C22—441no—
294C22—441no—
295C22#1062238711yescharacteristic
296C22#1062238811yescharacteristic
297C22#1062249511yescharacteristic
298C22D11×D1611yescharacteristic
299C22#1062252811yescharacteristic
300C22#1062252911yescharacteristic
301C22#1062253111yescharacteristic
302C4—161no—
303C4—161no—
304C4—441no—
305C4—1761no—
306C4—1761no—
307C4#1062228811yescharacteristic
308C4#1062242811yescharacteristic
309C4#1062242911yescharacteristic
310C4#1062248011yescharacteristic
311C2—442no—
312C2#1307004311yescharacteristic
313C2#1307070111yescharacteristic
314C2#1307072311yescharacteristic
315C2#1307079511yescharacteristic
316C2#1307079811yescharacteristic
317C2#1307082211yescharacteristic
318C2#1307082711yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC23×D11D8
hypercenter#1380D11
hypocenterC11#13492
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C2×#10622127C2semidirect
5. #13066708C2semidirect
6. #13066707C2semidirect
7. C11×#1380C2semidirect
97. #1380D11semidirect
249. C11#13492semidirect

Maximal subgroups

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

subgroupindex
C2×#106221272
C2×(C2×D11)⋊C162
#130686422
#130667082
#130667072
C11×#13802
#1349211