Finite Group Databasebeta

← #14908617

Subgroups — #14908617

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078264C211yesmaximal, characteristic
2#13070807C212yesmaximal, complemented
3#13070807C212yesmaximal, complemented
4#13070801C212yesmaximal, complemented
5#13070796C212yesmaximal, complemented
6#13070402C211yesmaximal, characteristic, complemented
7#13070398C211yesmaximal, characteristic, complemented
8#13070331C211yesmaximal, characteristic, complemented
9C2×#10622129C211yesmaximal, characteristic, complemented
10#13070230C211yesmaximal, characteristic, complemented
11C11×#2913C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13C11×#520—21no—
14#10623361—21no—
15C22×D88C2211yescharacteristic
16C11×#428—22no—
17C11×#428—21no—
18C11×#427C2211yescharacteristic
19C11×#427C2212yescomplemented
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2212yescomplemented
22#10622748—22no—
23#10622744—21no—
24#10622728C2212yes—
25#10622728C2212yes—
26#10622719C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C22×C11⋊C16C2211yescharacteristic
29C22⋊(C11⋊C16)C2212yescomplemented
30C22⋊(C11⋊C16)C2212yescomplemented
31#10622129C2212yes—
32#10622129C2212yes—
33#10622129C2212yes—
34#10622129C2212yes—
35#10622128C2211yescharacteristic, complemented
36#10622128C2211yescharacteristic, complemented
37#10622128C2212yescomplemented
38#10622127C2211yescharacteristic, complemented
39#10622127C2211yescharacteristic, complemented
40#10622127C2212yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D44—21no—
43C11×#131—22no—
44C11×#131—22no—
45C2×C11×M16D411yescharacteristic
46C2×C11×M16D412yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—41no—
50C4×D4×C11—42no—
51C4×D4×C11—41no—
52C11×#117—21no—
53C11×#117—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56#67000—41no—
57#66993—41no—
58#66990—42no—
59#66983—22no—
60#66983—22no—
61#66979—21no—
62C2×D88—22no—
63C2×D88—22no—
64C2×D88—21no—
65C2×D88C2312yes—
66C11×#107—21no—
67C11×#107—22no—
68C11×#107C2312yes—
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#106—21no—
72C11×#106—22no—
73#66885—22no—
74#66885—22no—
75#66882C2311yescharacteristic
76#66882C2311yescharacteristic
77#66881—21no—
78#66876—22no—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2312yes—
82C2×C11⋊C16C2311yescharacteristic
83#33650—111nomaximal, Sylow
84C23×D11—41no—
85C11×#41—22no—
86C11×#41—22no—
87C2×Q8×C11D811yescharacteristic
88C2×D4×C11D812yes—
89C2×D4×C11D811yescharacteristic
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C2×D44—22no—
97C2×D44—42no—
98C2×D44—41no—
99C2×D44—42no—
100C11×M16—24no—
101C11×M16—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D412yes—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11#4112yes—
107C2×C8×C11#4112yes—
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C42×C11—42no—
117C42×C11—41no—
118C22⋊Dic11—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4×Dic11—41no—
124D88—22no—
125D88—22no—
126D88—42no—
127C11⋊C16—21no—
128C11⋊C16—21no—
129C11⋊C16—22no—
130#3058—111no—
131#2913D1111yescharacteristic, complemented
132#2234—112no—
133#2234—112no—
134#2233—112no—
135#2232—112no—
136#2159—111no—
137#2158—111no—
138#2140—111no—
139C2×#357—111no—
140#2113—111no—
141C23×C11C2×D812yes—
142C23×C11C2×D811yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—161no—
146C22×D11—161no—
147Q8×C11—22no—
148D4×C11—24no—
149D4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—161no—
156C2×C4×C11—162no—
157C2×C4×C11#12312yes—
158C2×C4×C11C2×D812yes—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—162no—
163C22⋊D11—162no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166D44—42no—
167D44—42no—
168D44—82no—
169C8×C11—22no—
170C8×C11#12312yes—
171C8×C11C2×#4111yescharacteristic
172C8×C11C2×#4111yescharacteristic
173C22×D8—111no—
174C2×#131C2×D1111yescharacteristic
175#535—221no—
176#520—21no—
177C2×M32—111no—
178C22×C16—111no—
179#469—222no—
180#466—112no—
181#466—112no—
182#428—22no—
183#428—21no—
184#427—111no—
185#427C2×D1111yescharacteristic
186#427C2×D1112yescomplemented
187C2×#107C2×D1111yescharacteristic
188C2×#107C2×D1112yescomplemented
189#418—221no—
190#367—111no—
191#367—111no—
192#367—112no—
193#366—111no—
194#366—111no—
195#366—112no—
196#357—112no—
197#357—112no—
198#357—112no—
199#357—112no—
200C22⋊C16—112no—
201C22⋊C16—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11#48012yes—
208C22×C11C22×D811yescharacteristic
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—164no—
213C4×C11—22no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#48012yes—
218C4×C11C2×#12311yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—81no—
221Dic11—81no—
222C2×#41C22⋊D1111yescharacteristic
223C22×D4—221no—
224C2×D8—112no—
225C2×D8—222no—
226C2×D8—222no—
227C2×D8—221no—
228#131—22no—
229#131—22no—
230C2×M16C22⋊D1111yescharacteristic
231C2×M16C22⋊D1112yes—
232C22×C8C22×D1112yes—
233C22×C8C22×D1111yescharacteristic
234#127—441no—
235#124—441no—
236#121—222no—
237#121—222no—
238#120—442no—
239C4×Q8—41no—
240C4×D4—42no—
241C4×D4—41no—
242#117—21no—
243#117—22no—
244#117—221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247M32—222no—
248C2×C16—111no—
249C2×C16—112no—
250C2×C16—111no—
251C2×C16—222no—
252#107—21no—
253#107—22no—
254#107—111no—
255#107—111no—
256#107C22×D1112yes—
257#107C22×D1111yescharacteristic
258#107C22×D1111yescharacteristic
259#106—21no—
260#106—22no—
261#106—221no—
262#102—222no—
263#102—222no—
264C2×C11—22no—
265C2×C11—42no—
266C2×C11C2×#48011yescharacteristic
267C2×C11#341511yescharacteristic
268C2×C11#341611yescharacteristic
269D11—162no—
270C24—441no—
271#41—22no—
272#41—22no—
273C2×Q8#432311yescharacteristic
274C2×D4—222no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—441no—
279C2×D4—442no—
280C2×D4#432312yes—
281C2×D4#432311yescharacteristic
282C22×C4—42no—
283C22×C4—41no—
284C22×C4C2×C22⋊D1112yes—
285C22×C4C2×C22⋊D1111yescharacteristic
286D8—222no—
287D8—222no—
288D8—442no—
289M16—22no—
290M16—24no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8#433912yes—
294C2×C8#433912yes—
295C2×C8C2×C22⋊D1112yes—
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—441no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C42—42no—
311C42—41no—
312C42—441no—
313C16—221no—
314C16—221no—
315C16—222no—
316C11#3365011yescharacteristic, complemented, Sylow
317C23—442no—
318C23—882no—
319C23—1761no—
320C23—1761no—
321C23C2×#432312yes—
322C23C2×#432311yescharacteristic
323Q8—22no—
324D4—24no—
325D4—22no—
326D4—442no—
327D4—442no—
328D4—882no—
329D4—1762no—
330D4—1762no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—161no—
337C2×C4—162no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4#6698212yes—
341C2×C4C2×#432312yes—
342C2×C4C2×#432311yescharacteristic
343C2×C4#6699512yes—
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—22no—
346C8#6698212yes—
347C8C2×#433911yescharacteristic
348C8C2×#433911yescharacteristic
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22—1764no—
358C22#1062258012yes—
359C22C22×#432311yescharacteristic
360C4—22no—
361C4—82no—
362C4—81no—
363C4—81no—
364C4—881no—
365C4—881no—
366C4#1062258012yes—
367C4C2×#6698211yescharacteristic
368C4C2×#6699511yescharacteristic
369C2—22no—
370C2—42no—
371C2—1762no—
372C2C2×#1062258011yescharacteristic
373C2#1308175511yescharacteristic
374C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2913C2
socleC22×C11C22×D8
prime radical#13078264C2
hypercenter#2913D11
hypocenterC11#33650
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #13070807C2semidirect
3. #13070807C2semidirect
4. #13070801C2semidirect
5. #13070796C2semidirect
6. #13070402C2semidirect
7. #13070398C2semidirect
8. #13070331C2semidirect
9. C2×#10622129C2semidirect
10. #13070230C2semidirect
11. C11×#2913C2semidirect
19. C11×#427C22semidirect
21. C2×C11×#107C22semidirect
29. C22⋊(C11⋊C16)C22semidirect
30. C22⋊(C11⋊C16)C22semidirect
35. #10622128C22semidirect
36. #10622128C22semidirect
37. #10622128C22semidirect
38. #10622127C22semidirect
39. #10622127C22semidirect
40. #10622127C22semidirect
131. #2913D11semidirect
186. #427C2×D11semidirect
188. C2×#107C2×D11semidirect
316. C11#33650semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130708072
#130708012
#130707962
#130704022
#130703982
#130703312
C2×#106221292
#130702302
C11×#29132
#3365011