Finite Group Databasebeta

← #14673567

Subgroups — #14673567

Order 2816.

378 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622147C211yesmaximal, characteristic
2C2×#10622129C211yesmaximal, characteristic
3#13069480C211yesmaximal, characteristic
4#13068774C211yesmaximal, characteristic, complemented
5#13066707C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C22×C11×C16C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14C22×C11⋊C16C2211yescharacteristic
15#10622601—21no—
16#10622589—21no—
17C2×#66873—21no—
18C2×#66871—21no—
19#10622147—22no—
20#10622129—22no—
21C22×D44—21no—
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×Dic11⋊C4—41no—
29C2×Dic11⋊C4—41no—
30C2×C4×Dic11D411yescharacteristic
31C22×C11⋊C8D411yescharacteristic
32C2×D88—21no—
33C2×D88—21no—
34C2×D88—21no—
35C2×D88—21no—
36C2×D88—21no—
37C2×D88D412yes—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C11×#107—21no—
42C11×#107—21no—
43C11×#107—21no—
44C11×#107—21no—
45#66882—21no—
46#66882—21no—
47C8×Dic11—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66873—42no—
53#66871—42no—
54#13480—111nomaximal, Sylow
55C23×D11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—41no—
60C22×Dic11D811yescharacteristic
61C22×Dic11D811yescharacteristic
62C2×D44—22no—
63C2×D44—41no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—41no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11#4111yescharacteristic
70C2×C8×C11#4111yescharacteristic
71C2×C8×C11#4111yescharacteristic
72C2×C8×C11#4111yescharacteristic
73C2×C8×C11#4111yescharacteristic
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78(C2×D11)⋊C4—82no—
79(C2×D11)⋊C4—82no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82Dic11⋊C4—82no—
83Dic11⋊C4—82no—
84C4×Dic11—21no—
85C4×Dic11—21no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8SD1612yes—
89D88—22no—
90D88—22no—
91D88—41no—
92D88—41no—
93C11×C16—41no—
94C11⋊C16—41no—
95C2×#357—111no—
96C2×#357—111no—
97#1970—111no—
98#1845—111no—
99#1380—111no—
100#1380D1111yescharacteristic, complemented
101#1374—111no—
102C23×C11C2×D811yescharacteristic
103C22×D11—42no—
104C22×D11—81no—
105C22×D11—81no—
106C22×D11—81no—
107C22×D11—81no—
108C22×D11—81no—
109C22×D11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12311yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11C2×SD1611yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C11#13711yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129C2×Dic11D1612yes—
130C2×Dic11SD3212yes—
131D44—42no—
132D44—42no—
133D44—81no—
134D44—81no—
135C8×C11#12311yescharacteristic
136C8×C11#12311yescharacteristic
137C8×C11#12611yescharacteristic
138C8×C11#12611yescharacteristic
139C11⋊C8—22no—
140C22×D8—111no—
141C22×C16—111no—
142C22×C16C2×D1111yescharacteristic
143C2×#107—111no—
144C2×#107—221no—
145C2×#107C2×D1111yescharacteristic
146C2×#107C2×D1111yescharacteristic
147C2×#102—221no—
148C2×C4×C8—111no—
149#390—221no—
150#384—221no—
151#357—222no—
152#357—222no—
153C22×C11#45911yescharacteristic
154C22×C11#48011yescharacteristic
155C22×C11#48611yescharacteristic
156C22×C11C2×D1611yescharacteristic
157C22×C11C2×SD3211yescharacteristic
158C22×C11#50911yescharacteristic
159C22×C11#51011yescharacteristic
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C2×D11—161no—
164C2×D11—161no—
165C2×D11—161no—
166C2×D11—161no—
167C4×C11—161no—
168C4×C11—161no—
169C4×C11#39711yescharacteristic
170C4×C11#46111yescharacteristic
171C4×C11#48111yescharacteristic
172C4×C11#48911yescharacteristic
173Dic11—22no—
174Dic11—22no—
175Dic11—161no—
176C22×D4—221no—
177C2×D8—112no—
178C2×D8—221no—
179C2×D8—221no—
180C2×D8—221no—
181C2×D8—221no—
182C2×D8—221no—
183C22×C8—111no—
184C22×C8C22×D1111yescharacteristic
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—441no—
189C2×C4⋊C4—441no—
190C2×C22⋊C4—441no—
191C2×C22⋊C4—441no—
192C2×C42—111no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—21no—
196C2×C16—221no—
197C2×C16—221no—
198C2×C16—221no—
199#107—21no—
200#107—21no—
201#107—21no—
202#107—21no—
203#107—221no—
204#107—221no—
205#107—442no—
206#102—442no—
207C4×C8—221no—
208C4×C8—221no—
209C2×C11#207111yescharacteristic
210C2×C11#220611yescharacteristic
211C2×C11#220811yescharacteristic
212C2×C11#223211yescharacteristic
213C2×C11#223311yescharacteristic
214C2×C11#224011yescharacteristic
215C2×C11#224311yescharacteristic
216D11—162no—
217C24—441no—
218C2×D4—222no—
219C2×D4—441no—
220C2×D4—441no—
221C2×D4—441no—
222C2×D4—441no—
223C2×D4—441no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—441no—
229C22×C4D4×D1111yescharacteristic
230D8—222no—
231D8—222no—
232D8—441no—
233D8—441no—
234C2×C8—112no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8#433911yescharacteristic
238C2×C8#433911yescharacteristic
239C2×C8#433911yescharacteristic
240C2×C8D4×D1111yescharacteristic
241C2×C8#434111yescharacteristic
242C2×C8#434311yescharacteristic
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—882no—
250C4⋊C4—882no—
251C22⋊C4—882no—
252C22⋊C4—882no—
253C42—221no—
254C42—221no—
255C16—41no—
256C16—441no—
257C11#1348011yescharacteristic, complemented, Sylow
258C23—442no—
259C23—881no—
260C23—881no—
261C23—881no—
262C23—881no—
263C23—881no—
264C23—881no—
265C23D8×D1111yescharacteristic
266D4—442no—
267D4—442no—
268D4—881no—
269D4—881no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—112no—
277C2×C4—112no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6693711yescharacteristic
286C2×C4#6693811yescharacteristic
287C2×C4#6694711yescharacteristic
288C2×C4SD16×D1111yescharacteristic
289C2×C4#6696711yescharacteristic
290C2×C4#6697111yescharacteristic
291C8—222no—
292C8#6692911yescharacteristic
293C8#6693611yescharacteristic
294C8#6694711yescharacteristic
295C8#6695111yescharacteristic
296C22—882no—
297C22—882no—
298C22—882no—
299C22—1761no—
300C22—1761no—
301C22—1761no—
302C22—1761no—
303C22#1062237311yescharacteristic
304C22#1062239911yescharacteristic
305C22#1062249511yescharacteristic
306C22D11×D1611yescharacteristic
307C22D11×SD3211yescharacteristic
308C22#1062252711yescharacteristic
309C22#1062253111yescharacteristic
310C4—161no—
311C4—161no—
312C4—222no—
313C4—222no—
314C4—1761no—
315C4#1062228811yescharacteristic
316C4#1062240811yescharacteristic
317C4#1062243111yescharacteristic
318C4#1062247611yescharacteristic
319C2—1762no—
320C2#1307002311yescharacteristic
321C2#1307065011yescharacteristic
322C2#1307066011yescharacteristic
323C2#1307079811yescharacteristic
324C2#1307080311yescharacteristic
325C2#1307083811yescharacteristic
326C2#1307085411yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenter#1380D11
hypocenterC11#13480
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
4. #13068774C2semidirect
5. #13066707C2semidirect
6. #13066693C2semidirect
7. C11×#1380C2semidirect
100. #1380D11semidirect
257. C11#13480semidirect

Maximal subgroups

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

subgroupindex
C2×#106221472
C2×#106221292
#130694802
#130687742
#130667072
#130666932
C11×#13802
#1348011