Finite Group Databasebeta

← #14911143

Subgroups — #14911143

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081010C211yesmaximal, characteristic, complemented
2#13080963C211yesmaximal, characteristic
3#13070896C211yesmaximal, characteristic, complemented
4#13070812C212yesmaximal, complemented
5#13070803C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070715C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10D11×#367C212yesmaximal, complemented
11C11×#2225C211yesmaximal, characteristic, complemented
12#10623257—21no—
13#10623110—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622801C2212yes—
17C2×#66892C2211yescharacteristic
18#10622700—21no—
19#10622634—21no—
20C2×C16×D11C2212yes—
21#10622496C2212yes—
22#10622495—22no—
23D11×#107C2212yes—
24D11×#107C2212yes—
25#10622422—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622143C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2212yes—
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×C11×Q16C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×Q8×C11—21no—
45#66999—22no—
46#66999—41no—
47C2×D88C2311yescharacteristic
48C2×C8×D11C2312yes—
49#66949—42no—
50#66948—22no—
51#66947—42no—
52C4⋊C4×D11—22no—
53C4⋊C4×D11—22no—
54C4×D44—21no—
55C4×D44—41no—
56C4×D44D411yescharacteristic
57#66923—41no—
58#66922—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#103—21no—
64C4×C8×C11C2311yescharacteristic
65#66899—22no—
66#66892—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66871—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33902—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82#4343—84no—
83C2×D44—21no—
84C2×D44—42no—
85C2×D44D811yescharacteristic
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×C4×D11—41no—
89C2×C4×D11C2×D412yes—
90C2×Dic22—41no—
91C11×Q16—21no—
92C11×Q16—21no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C2×C11⋊C8C2×D412yes—
113D88—21no—
114D88—21no—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—22no—
118C11⋊C16—21no—
119C11⋊C16#4112yescomplemented
120#3338—111no—
121#3334—111no—
122#2254—111no—
123#2235—112no—
124#2233—112no—
125#2226—111no—
126#2225D1111yescharacteristic, complemented
127#2217—112no—
128C4×SD32—111no—
129D4×C16—111no—
130C2×#367—112no—
131C22×D11—41no—
132C22×D11C2×D812yes—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—82no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145D44—41no—
146D44—41no—
147D44—84no—
148D44SD3214yescomplemented
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—84no—
152C4×D11—82no—
153C4×D11—162no—
154Dic22—161no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158C11⋊C8—22no—
159#554—221no—
160#547—221no—
161C2×SD32—111no—
162C22×C16—112no—
163#500—111no—
164#500C2×D1111yescharacteristic
165#484—222no—
166#480—222no—
167#477—221no—
168#474—221no—
169#467—112no—
170#466—112no—
171C4×Q16C2×D1111yescharacteristic
172C4×D8—111no—
173C8×D4—111no—
174C2×#107—112no—
175C2×#107—112no—
176#367—112no—
177#367—111no—
178#367—112no—
179#367—112no—
180#367C2×D1112yes—
181C4⋊C16C2×D1111yescharacteristic
182#358—111no—
183#358C2×D1112yes—
184#357—112no—
185#357—111no—
186C22⋊C16—112no—
187C4×C16—111no—
188C22×C11C22×D811yescharacteristic
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11C2×SD3214yes—
195C4×C11—21no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11—81no—
199C4×C11C2×SD3212yes—
200C4×C11#54711yescharacteristic
201C4×C11#57811yescharacteristic
202Dic11—22no—
203Dic11—81no—
204Dic11—82no—
205C2×#41—441no—
206C2×Q16C22×D1111yescharacteristic
207C2×D8—111no—
208C22×C8—112no—
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#125—441no—
212#123—442no—
213C22⋊Q8—222no—
214C22⋊Q8—442no—
215C22⋊Q8—441no—
216#121—222no—
217C4×Q8—21no—
218C4×D4—111no—
219C4×D4—221no—
220C4×D4—441no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223SD32—222no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16—224no—
227C2×C16C22×D1112yes—
228#107—21no—
229#107—112no—
230#107—111no—
231#107—222no—
232#107—222no—
233#107—221no—
234#107C22×D1111yescharacteristic
235#107C22×D1112yes—
236C4⋊C8—111no—
237#103—21no—
238#103—222no—
239#102—222no—
240#102—221no—
241C22⋊C8—112no—
242C4×C8C22×D1111yescharacteristic
243C2×C11#333411yescharacteristic
244C2×C11C22×SD3211yescharacteristic
245C2×C11#341611yescharacteristic
246D11—24no—
247D11—161no—
248#41—884no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—441no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—442no—
255C22×C4—112no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4—441no—
259Q16—21no—
260Q16—21no—
261D8—221no—
262D8—221no—
263C2×C8—112no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8D4×D1111yescharacteristic
267C2×C8C23×D1111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—111no—
273C4⋊C4—221no—
274C4⋊C4—222no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C22⋊C4—112no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—441no—
283C42—41no—
284C42D4×D1111yescharacteristic
285C16—22no—
286C16—112no—
287C16—221no—
288C11#3390211yescharacteristic, complemented, Sylow
289C23—112no—
290C23—441no—
291Q8—41no—
292Q8—41no—
293Q8—82no—
294Q8—1761no—
295D4—114no—
296D4—441no—
297D4—441no—
298D4—884no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—112no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—442no—
306C2×C4—441no—
307C2×C4—884no—
308C2×C4—882no—
309C2×C4—1762no—
310C2×C4D8×D1111yescharacteristic
311C2×C4D8×D1111yescharacteristic
312C2×C4C2×D4×D1111yescharacteristic
313C8—21no—
314C8—222no—
315C8#6704011yescharacteristic
316C8#41×D1111yescharacteristic
317C22—114no—
318C22—222no—
319C22—222no—
320C22—881no—
321C22—881no—
322C22—881no—
323C22C2×D8×D1111yescharacteristic
324C4—21no—
325C4—82no—
326C4—81no—
327C4—81no—
328C4—222no—
329C4—881no—
330C4—882no—
331C4D11×SD3212yes—
332C4#1062316211yescharacteristic
333C4#1062331011yescharacteristic
334C2—224no—
335C2—1761no—
336C2#1308096211yescharacteristic
337C2C2×D11×SD3211yescharacteristic
338C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radical#13080963C2
hypercenter#2225D11
hypocenterC11#33902
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
1. #13081010C2semidirect
3. #13070896C2semidirect
4. #13070812C2semidirect
5. #13070803C2semidirect
6. #13070764C2semidirect
7. #13070715C2semidirect
8. C4×#66892C2semidirect
9. #13070435C2semidirect
10. D11×#367C2semidirect
11. C11×#2225C2semidirect
119. C11⋊C16#41semidirect
126. #2225D11semidirect
148. D44SD32semidirect
288. C11#33902semidirect

Maximal subgroups

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

subgroupindex
#130810102
#130809632
#130708962
#130708122
#130708032
#130707642
#130707152
C4×#668922
#130704352
D11×#3672
C11×#22252
#3390211