Finite Group Databasebeta

← #14673537

Subgroups — #14673537

Order 2816.

382 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×#10622128C211yesmaximal, characteristic, complemented
2C2×C4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
3C2×#10622129C211yesmaximal, characteristic
4C2×#10622129C211yesmaximal, characteristic
5#13069482C211yesmaximal, characteristic
6#13066707C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C2×C11×#107C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#389—21no—
13C2×#66885—21no—
14C2×#66882C2211yescharacteristic
15C22×C11⋊C16C2211yescharacteristic
16C22×C11⋊C16C2211yescharacteristic
17#10622552—21no—
18C11×#340—21no—
19#10622129—22no—
20#10622129—22no—
21#10622128—22no—
22C4⋊(C11⋊C16)—22no—
23C22×D44—21no—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—41no—
29C2×C42×C11D411yescharacteristic
30C2×(C2×D11)⋊C4—41no—
31C2×(C2×D11)⋊C4—41no—
32C2×C4⋊Dic11—21no—
33C2×D88—21no—
34C2×D88—21no—
35C2×D88—21no—
36C2×D88—21no—
37C2×D88—21no—
38C2×D88Q812yes—
39C11×#107—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#107D412yes—
43C4×C8×C11—21no—
44C4×C8×C11—21no—
45C11×#95—41no—
46#66885—42no—
47#66882—21no—
48#66882—21no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54C2×C11⋊C16D412yes—
55#13476—111nomaximal, Sylow
56C23×D11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11D811yescharacteristic
60C22×C4×C11D811yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—41no—
63C2×D44—22no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—41no—
68C2×D44—41no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×Q811yescharacteristic
75C2×C8×C11#4111yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C2×C8×C11#4111yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—82no—
83C42×C11—21no—
84C42×C11—21no—
85(C2×D11)⋊C4—82no—
86(C2×D11)⋊C4—82no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89D88—22no—
90D88—22no—
91D88—41no—
92D88—41no—
93C11⋊C16—22no—
94C11⋊C16—41no—
95C2×#367—111no—
96C2×C4⋊C16—111no—
97C2×#357—111no—
98C2×#357—111no—
99#1970—111no—
100#1942D1111yescharacteristic, complemented
101#1380—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—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—42no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11SD3212yes—
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131D44—42no—
132D44—42no—
133D44—81no—
134D44—81no—
135C8×C11—41no—
136C8×C11#12111yescharacteristic
137C8×C11C22⋊Q811yescharacteristic
138C8×C11C22⋊Q811yescharacteristic
139C8×C11#12611yescharacteristic
140C22×D8—111no—
141C22×C16—111no—
142C22×C16—111no—
143C2×#107—111no—
144C2×#107C2×D1111yescharacteristic
145C2×#107C2×D1111yescharacteristic
146C2×#102—221no—
147C2×C4×C8C2×D1111yescharacteristic
148#390—221no—
149#389—21no—
150#367—222no—
151C4⋊C16—222no—
152#357—222no—
153#357—222no—
154#340—21no—
155C22×C11#45911yescharacteristic
156C22×C11#46611yescharacteristic
157C22×C11#47411yescharacteristic
158C22×C11C2×SD3211yescharacteristic
159C22×C11#50811yescharacteristic
160C22×C11#50911yescharacteristic
161C22×C11#50911yescharacteristic
162C2×D11—82no—
163C2×D11—82no—
164C2×D11—82no—
165C2×D11—161no—
166C2×D11—161no—
167C2×D11—161no—
168C2×D11—161no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—82no—
172C4×C11—161no—
173C4×C11#39611yescharacteristic
174C4×C11#46411yescharacteristic
175C4×C11#46811yescharacteristic
176C4×C11#47811yescharacteristic
177Dic11—161no—
178C22×D4—221no—
179C2×D8—112no—
180C2×D8—221no—
181C2×D8—221no—
182C2×D8—221no—
183C2×D8—221no—
184C2×D8—221no—
185C22×C8C22⋊D1111yescharacteristic
186C22×C8C22×D1111yescharacteristic
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—221no—
191C2×C22⋊C4—441no—
192C2×C22⋊C4—441no—
193C2×C42C22⋊D1111yescharacteristic
194C2×C16—112no—
195C2×C16—221no—
196C2×C16—221no—
197C2×C16—221no—
198C2×C16—221no—
199C2×C16—221no—
200#107—21no—
201#107—21no—
202#107—21no—
203#107—221no—
204#107—221no—
205#107D4412yes—
206#102—442no—
207C4×C8—21no—
208C4×C8—21no—
209#95—41no—
210C2×C11#206711yescharacteristic
211C2×C11#220711yescharacteristic
212C2×C11#221011yescharacteristic
213C2×C11#221711yescharacteristic
214C2×C11#221811yescharacteristic
215C2×C11#222611yescharacteristic
216C2×C11#222811yescharacteristic
217D11—162no—
218C24—441no—
219C2×D4—222no—
220C2×D4—441no—
221C2×D4—441no—
222C2×D4—441no—
223C2×D4—441no—
224C2×D4—441no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—441no—
228C22×C4#432311yescharacteristic
229C22×C4#432311yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231D8—222no—
232D8—222no—
233D8—441no—
234D8—441no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8C2×D4411yescharacteristic
239C2×C8#433911yescharacteristic
240C2×C8D4×D1111yescharacteristic
241C2×C8#434111yescharacteristic
242C2×C8Q8×D1111yescharacteristic
243C2×C8#434311yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—82no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—882no—
252C22⋊C4—882no—
253C42—21no—
254C42—21no—
255C16—222no—
256C16—441no—
257C11#1347611yescharacteristic, complemented, Sylow
258C23—442no—
259C23—881no—
260C23—881no—
261C23—881no—
262C23—881no—
263C23—881no—
264C23—881no—
265C23C2×#432311yescharacteristic
266D4—442no—
267D4—442no—
268D4—881no—
269D4—881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—881no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4#6689212yes—
285C2×C4#6698311yescharacteristic
286C2×C4#6699211yescharacteristic
287C2×C4#6699511yescharacteristic
288C2×C4#6699911yescharacteristic
289C2×C4#6700211yescharacteristic
290C2×C4#6700311yescharacteristic
291C8—41no—
292C8#6694811yescharacteristic
293C8#6694911yescharacteristic
294C8#6695011yescharacteristic
295C8#6695111yescharacteristic
296C22—882no—
297C22—882no—
298C22—882no—
299C22—1761no—
300C22—1761no—
301C22—1761no—
302C22—1761no—
303C22#1062262811yescharacteristic
304C22#1062265111yescharacteristic
305C22#1062270011yescharacteristic
306C22#1062276011yescharacteristic
307C22C2×#6689211yescharacteristic
308C22#1062280611yescharacteristic
309C22#1062280711yescharacteristic
310C4—22no—
311C4—41no—
312C4—82no—
313C4—161no—
314C4—1761no—
315C4#1062260711yescharacteristic
316C4#1062264111yescharacteristic
317C4#1062266211yescharacteristic
318C4#1062267911yescharacteristic
319C2—1762no—
320C2#1307000111yescharacteristic
321C2#1307065611yescharacteristic
322C2#1307067111yescharacteristic
323C2#1307071411yescharacteristic
324C2#1307071711yescharacteristic
325C2#1307076011yescharacteristic
326C2#1307077011yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1942C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenter#1942D11
hypocenterC11#13476
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
1. C2×#10622128C2semidirect
2. C2×C4⋊(C11⋊C16)C2semidirect
6. #13066707C2semidirect
7. C11×#1942C2semidirect
100. #1942D11semidirect
257. C11#13476semidirect

Maximal subgroups

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

subgroupindex
C2×#106221282
C2×C4⋊(C11⋊C16)2
C2×#106221292
#130694822
#130667072
C11×#19422
#1347611