Finite Group Databasebeta

← #14673541

Subgroups — #14673541

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×Dic11⋊C16C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic
4C2×#10622129C211yesmaximal, characteristic
5#13069480C211yesmaximal, characteristic
6#13069347C211yesmaximal, 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#10622586—21no—
17C2×#66873—21no—
18#10622167—21no—
19#10622147—22no—
20Dic11⋊C16—22no—
21#10622129—22no—
22#10622128—22no—
23C22×D44—21no—
24C22×C8×C11C2311yescharacteristic
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×(C2×D11)⋊C4—41no—
28C2×(C2×D11)⋊C4—41no—
29C2×C4⋊Dic11—21no—
30C2×Dic11⋊C4—41no—
31C2×C4×Dic11D411yescharacteristic
32C22×C11⋊C8D411yescharacteristic
33C2×D88—21no—
34C2×D88—21no—
35C2×D88—21no—
36C2×D88—21no—
37C2×D88—21no—
38C2×D88Q812yes—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C2×C11×C16—21no—
42C11×#107—21no—
43C11×#107—21no—
44C11×#107—21no—
45C11×#107—21no—
46C11⋊#95—41no—
47#66882—21no—
48#66882D412yes—
49C8×Dic11—21no—
50C8×Dic11—21no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16D412yes—
54#66873—42no—
55#13476—111nomaximal, Sylow
56C23×D11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—41no—
61C22×Dic11D811yescharacteristic
62C22×Dic11D811yescharacteristic
63C2×D44—22no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—41no—
68C2×D44—41no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×Q811yescharacteristic
72C2×C8×C11#4111yescharacteristic
73C2×C8×C11#4111yescharacteristic
74C2×C8×C11#4111yescharacteristic
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79(C2×D11)⋊C4—82no—
80(C2×D11)⋊C4—82no—
81C4⋊Dic11—22no—
82C4⋊Dic11—41no—
83Dic11⋊C4—82no—
84C4×Dic11—21no—
85C4×Dic11—21no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89D88—22no—
90D88—22no—
91D88—41no—
92D88—41no—
93C11×C16—41no—
94C11⋊C16—22no—
95C2×#367—111no—
96C2×C4⋊C16—111no—
97C2×#357—111no—
98C2×#357—111no—
99#1970—111no—
100#1942—111no—
101#1380D1111yescharacteristic, complemented
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#12111yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11#13511yescharacteristic
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—21no—
127C2×Dic11—42no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11SD3212yes—
131D44—42no—
132D44—42no—
133D44—81no—
134D44—81no—
135C8×C11#12111yescharacteristic
136C8×C11C22⋊Q811yescharacteristic
137C8×C11C22⋊Q811yescharacteristic
138C8×C11#12611yescharacteristic
139C11⋊C8—41no—
140C22×D8—111no—
141C22×C16—111no—
142C22×C16C2×D1111yescharacteristic
143C2×#107—111no—
144C2×#107C2×D1111yescharacteristic
145C2×#107C2×D1111yescharacteristic
146C2×#102—221no—
147C2×C4×C8—111no—
148#390—221no—
149#389—221no—
150#367—222no—
151C4⋊C16—222no—
152#357—222no—
153#357—222no—
154#340—221no—
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—161no—
170C4×C11—161no—
171C4×C11#39611yescharacteristic
172C4×C11#46411yescharacteristic
173C4×C11#46811yescharacteristic
174C4×C11#47811yescharacteristic
175Dic11—22no—
176Dic11—41no—
177Dic11—82no—
178C22×D4—221no—
179C2×D8—112no—
180C2×D8—221no—
181C2×D8—221no—
182C2×D8—221no—
183C2×D8—221no—
184C2×D8—221no—
185C22×C8—111no—
186C22×C8C22×D1111yescharacteristic
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—441no—
191C2×C22⋊C4—441no—
192C2×C22⋊C4—441no—
193C2×C42—111no—
194C2×C16—21no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—112no—
198C2×C16—221no—
199C2×C16—221no—
200#107—21no—
201#107—21no—
202#107—21no—
203#107—21no—
204#107—112no—
205#107—221no—
206#102—442no—
207C4×C8—221no—
208C4×C8—221no—
209#95—441no—
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—111no—
228C22×C4—111no—
229C22×C4—441no—
230C22×C4D4×D1111yescharacteristic
231D8—222no—
232D8—222no—
233D8—441no—
234D8—441no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8#433911yescharacteristic
239C2×C8#433911yescharacteristic
240C2×C8#433911yescharacteristic
241C2×C8D4×D1111yescharacteristic
242C2×C8D4×D1111yescharacteristic
243C2×C8Q8×D1111yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—222no—
249C4⋊C4—441no—
250C4⋊C4—882no—
251C22⋊C4—882no—
252C22⋊C4—882no—
253C42—221no—
254C42—221no—
255C16—41no—
256C16—222no—
257C11#1347611yescharacteristic, 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—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6693711yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6694911yescharacteristic
288C2×C4#6696711yescharacteristic
289C2×C4#6696911yescharacteristic
290C2×C4#6697111yescharacteristic
291C8—441no—
292C8#6692911yescharacteristic
293C8#6693711yescharacteristic
294C8#6694911yescharacteristic
295C8#6694911yescharacteristic
296C22—882no—
297C22—882no—
298C22—882no—
299C22—1761no—
300C22—1761no—
301C22—1761no—
302C22—1761no—
303C22#1062238811yescharacteristic
304C22#1062239911yescharacteristic
305C22#1062250311yescharacteristic
306C22#1062252411yescharacteristic
307C22D11×SD3211yescharacteristic
308C22#1062252711yescharacteristic
309C22#1062253211yescharacteristic
310C4—161no—
311C4—161no—
312C4—222no—
313C4—441no—
314C4—882no—
315C4#1062228911yescharacteristic
316C4#1062241111yescharacteristic
317C4#1062242511yescharacteristic
318C4#1062248411yescharacteristic
319C2—1762no—
320C2#1307000511yescharacteristic
321C2#1307065511yescharacteristic
322C2#1307067411yescharacteristic
323C2#1307071511yescharacteristic
324C2#1307071811yescharacteristic
325C2#1307076211yescharacteristic
326C2#1307077611yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenter#1380D11
hypocenterC11#13476
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×#10622128C2semidirect
2. C2×Dic11⋊C16C2semidirect
6. #13069347C2semidirect
7. C11×#1380C2semidirect
101. #1380D11semidirect
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×Dic11⋊C162
C2×#106221472
C2×#106221292
#130694802
#130693472
C11×#13802
#1347611