Finite Group Databasebeta

← #14673577

Subgroups — #14673577

Order 2816.

362 conjugacy classes of subgroups.

The subgroup lattice has 324 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#13068779C211yesmaximal, 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#10622590—21no—
17C2×#66873—21no—
18C2×#66872—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×C4×Dic11D411yescharacteristic
29C22×C11⋊C8D411yescharacteristic
30C2×D88—21no—
31C2×D88—21no—
32C2×D88—21no—
33C2×D88—21no—
34C2×D88—21no—
35C2×D88D412yes—
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—
47C8×Dic11—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66873—42no—
53#66872—42no—
54#13482—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—
82C4×Dic11—21no—
83C4×Dic11—21no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8SD1612yes—
87D88—22no—
88D88—22no—
89D88—41no—
90D88—41no—
91C11×C16—41no—
92C11⋊C16—41no—
93C2×#357—111no—
94C2×#357—111no—
95#1970—111no—
96#1846—111no—
97#1380—111no—
98#1380D1111yescharacteristic, complemented
99#1374—111no—
100C23×C11C2×D811yescharacteristic
101C22×D11—42no—
102C22×D11—81no—
103C22×D11—81no—
104C22×D11—81no—
105C22×D11—81no—
106C22×D11—81no—
107C22×D11—81no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11#12111yescharacteristic
115C2×C4×C11#12311yescharacteristic
116C2×C4×C11#12411yescharacteristic
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C11#13711yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129D44—42no—
130D44—42no—
131D44—81no—
132D44—81no—
133C8×C11#12311yescharacteristic
134C8×C11#12311yescharacteristic
135C8×C11#12611yescharacteristic
136C8×C11#12611yescharacteristic
137C11⋊C8—22no—
138C22×D8—111no—
139C22×C16—111no—
140C22×C16C2×D1111yescharacteristic
141C2×#107—111no—
142C2×#107C2×D1111yescharacteristic
143C2×#107C2×D1111yescharacteristic
144C2×#106—221no—
145C2×#102—221no—
146C2×C4×C8—111no—
147#390—221no—
148#382—221no—
149#357—222no—
150#357—222no—
151C22×C11#45911yescharacteristic
152C22×C11#48011yescharacteristic
153C22×C11#48611yescharacteristic
154C22×C11#50811yescharacteristic
155C22×C11#50811yescharacteristic
156C22×C11#50911yescharacteristic
157C22×C11#50911yescharacteristic
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—161no—
162C2×D11—161no—
163C2×D11—161no—
164C2×D11—161no—
165C4×C11—161no—
166C4×C11—161no—
167C4×C11#39711yescharacteristic
168C4×C11#46111yescharacteristic
169C4×C11#48111yescharacteristic
170C4×C11#48911yescharacteristic
171Dic11—41no—
172Dic11—41no—
173Dic11—161no—
174C22×D4—221no—
175C2×D8—112no—
176C2×D8—221no—
177C2×D8—221no—
178C2×D8—221no—
179C2×D8—221no—
180C2×D8—221no—
181C22×C8—111no—
182C22×C8C22×D1111yescharacteristic
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—221no—
186C2×C22⋊C4—441no—
187C2×C22⋊C4—441no—
188C2×C42—111no—
189C2×C16—21no—
190C2×C16—21no—
191C2×C16—21no—
192C2×C16—221no—
193C2×C16—221no—
194C2×C16—221no—
195#107—21no—
196#107—21no—
197#107—21no—
198#107—21no—
199#107—221no—
200#107—221no—
201#106—442no—
202#102—442no—
203C4×C8—221no—
204C4×C8—221no—
205#95—441no—
206#95—441no—
207C2×C11#207111yescharacteristic
208C2×C11#221011yescharacteristic
209C2×C11#221011yescharacteristic
210C2×C11#223411yescharacteristic
211C2×C11#223411yescharacteristic
212C2×C11#224211yescharacteristic
213C2×C11#224411yescharacteristic
214D11—162no—
215C24—441no—
216C2×D4—222no—
217C2×D4—441no—
218C2×D4—441no—
219C2×D4—441no—
220C2×D4—441no—
221C2×D4—441no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—441no—
227C22×C4D4×D1111yescharacteristic
228D8—222no—
229D8—222no—
230D8—441no—
231D8—441no—
232C2×C8—112no—
233C2×C8—221no—
234C2×C8—221no—
235C2×C8#433911yescharacteristic
236C2×C8#433911yescharacteristic
237C2×C8#433911yescharacteristic
238C2×C8D4×D1111yescharacteristic
239C2×C8#434111yescharacteristic
240C2×C8#434311yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C22⋊C4—882no—
248C22⋊C4—882no—
249C42—221no—
250C42—221no—
251C16—41no—
252C16—441no—
253C11#1348211yescharacteristic, complemented, Sylow
254C23—442no—
255C23—881no—
256C23—881no—
257C23—881no—
258C23—881no—
259C23—881no—
260C23—881no—
261C23D8×D1111yescharacteristic
262D4—442no—
263D4—442no—
264D4—881no—
265D4—881no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—881no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4#6693711yescharacteristic
282C2×C4#6693811yescharacteristic
283C2×C4#6694711yescharacteristic
284C2×C4SD16×D1111yescharacteristic
285C2×C4#6696711yescharacteristic
286C2×C4#6697111yescharacteristic
287C8—222no—
288C8#6692911yescharacteristic
289C8#6693611yescharacteristic
290C8#6694711yescharacteristic
291C8#6695111yescharacteristic
292C22—882no—
293C22—882no—
294C22—882no—
295C22—1761no—
296C22—1761no—
297C22—1761no—
298C22—1761no—
299C22#1062237311yescharacteristic
300C22#1062239911yescharacteristic
301C22#1062249511yescharacteristic
302C22#1062252411yescharacteristic
303C22#1062252711yescharacteristic
304C22#1062252911yescharacteristic
305C22#1062253211yescharacteristic
306C4—161no—
307C4—161no—
308C4—441no—
309C4—441no—
310C4—1761no—
311C4#1062228811yescharacteristic
312C4#1062240811yescharacteristic
313C4#1062243111yescharacteristic
314C4#1062247611yescharacteristic
315C2—1762no—
316C2#1307002311yescharacteristic
317C2#1307067011yescharacteristic
318C2#1307067411yescharacteristic
319C2#1307080911yescharacteristic
320C2#1307081011yescharacteristic
321C2#1307084911yescharacteristic
322C2#1307085611yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenter#1380D11
hypocenterC11#13482
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. #13068779C2semidirect
5. #13066707C2semidirect
6. #13066693C2semidirect
7. C11×#1380C2semidirect
98. #1380D11semidirect
253. C11#13482semidirect

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
#130687792
#130667072
#130666932
C11×#13802
#1348211