Finite Group Databasebeta

← #14910604

Subgroups — #14910604

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081008C211yesmaximal, characteristic, complemented
2D8×D44C211yesmaximal, characteristic
3#13070841C211yesmaximal, characteristic, complemented
4#13070803C212yesmaximal, complemented
5#13070713C212yesmaximal, complemented
6#13070657C211yesmaximal, characteristic, complemented
7#13070546C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10D11×#357C212yesmaximal, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12C2×D8×D11C2212yes—
13#10623261—21no—
14D4×D44—21no—
15C11×#500C2211yescharacteristic, complemented
16C4×C11×D8C2211yescharacteristic
17C2×#66891C2211yescharacteristic
18#10622704—21no—
19#10622628—21no—
20C2×#66864C2212yescomplemented
21C2×C16×D11C2212yescomplemented
22#10622500C2212yescomplemented
23#10622497—22no—
24#10622496C2212yes—
25D11×#107C2212yescomplemented
26#10622386—22no—
27C4×Dic44C2211yescharacteristic, complemented
28#10622308C2211yescharacteristic
29C8×D44C2211yescharacteristic
30C11×#367C2212yescomplemented
31C11×C4⋊C16C2211yescharacteristic, complemented
32C11×#357C2212yes—
33#10622200C2211yescharacteristic
34#10622147C2212yescomplemented
35(C2×D11)⋊C16C2212yescomplemented
36#10622130C2211yescharacteristic, complemented
37#10622129C2212yescomplemented
38#10622129C2212yescomplemented
39#10622128C2211yescharacteristic, complemented
40C4×C11⋊C16C2211yescharacteristic, complemented
41C2×D4×D11—22no—
42C22×D44—41no—
43C2×C11×D8C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×D4×C11—21no—
46#66999—42no—
47C2×#4323—22no—
48#66983—41no—
49D8×D11—24no—
50D8×D11—42no—
51C2×Dic44C2311yescharacteristic
52C2×D88—21no—
53C2×D88C2312yes—
54C2×C8×D11C2312yes—
55#66950—22no—
56#66948—22no—
57#66946—41no—
58C4⋊C4×D11—22no—
59#66943—41no—
60#66935—42no—
61#66927—21no—
62C4×D44D411yescharacteristic
63C4×Dic22—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#102—21no—
69C4×C8×C11C2311yescharacteristic
70#66891—22no—
71(C2×D11)⋊C8D412yes—
72#66882C2311yescharacteristic
73#66880—21no—
74C2×C11⋊C16C2311yescharacteristic
75C2×C11⋊C16C2311yescharacteristic
76#66874—22no—
77#66873—22no—
78#66871—22no—
79C4⋊(C11⋊C8)D411yescharacteristic
80#66864—42no—
81C16×D11—42no—
82#33862—111nomaximal, Sylow
83C23×D11—42no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C22×C4×C11—41no—
87C2×C22⋊D11—42no—
88D4×D11—44no—
89D4×D11—82no—
90C2×D44—22no—
91C2×D44—42no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—84no—
95C2×D44D811yescharacteristic
96C2×C4×D11—42no—
97C2×C4×D11C2×D412yes—
98C2×Dic22—21no—
99C11×D8—21no—
100C11×D8#4112yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108#4323—44no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4D812yes—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4⋊Dic11D811yescharacteristic
115Dic11⋊C4—42no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118C2×C11⋊C8C2×D412yes—
119Dic44—21no—
120Dic44—21no—
121D88—22no—
122D88—22no—
123D88—81no—
124C8×D11—22no—
125C8×D11—22no—
126C11×C16—22no—
127C11⋊C16—21no—
128C11⋊C16—21no—
129#3338—111no—
130D4×D8—111no—
131#2240—111no—
132#2233—112no—
133#2226D1111yescharacteristic, complemented
134#2217—112no—
135#2207—111no—
136#2187—112no—
137C4×SD32—111no—
138D4×C16—111no—
139C2×#357—112no—
140C23×C11—41no—
141C22×D11—42no—
142C22×D11—84no—
143C22×D11—84no—
144C22×D11—162no—
145C22×D11C2×D812yes—
146Q8×C11—161no—
147D4×C11—22no—
148D4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C22⋊D11—84no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11C2×D812yes—
159D44—42no—
160D44—42no—
161D44—84no—
162D44—82no—
163D44—161no—
164D44SD3214yescomplemented
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—162no—
168Dic22—41no—
169Dic22—41no—
170C8×C11—21no—
171C8×C11C2×#4111yescharacteristic
172C8×C11H(5,𝔽2)11yescharacteristic
173C11⋊C8—22no—
174C22×D8—112no—
175#554—221no—
176D42—221no—
177C2×SD32—111no—
178C2×SD32—112no—
179C22×C16—112no—
180#500C2×D1111yescharacteristic, complemented
181#493—111no—
182#484—222no—
183#477—221no—
184#467—112no—
185#466—112no—
186#459—221no—
187#447—222no—
188C4×Q16—111no—
189C4×D8C2×D1111yescharacteristic
190C8×D4—111no—
191C2×#107—112no—
192#367—111no—
193#367C2×D1112yescomplemented
194C4⋊C16C2×D1111yescharacteristic, complemented
195#358—111no—
196#357—111no—
197#357—112no—
198#357—112no—
199#357—112no—
200#357C2×D1112yes—
201C22⋊C16—112no—
202C4×C16—111no—
203C22×C11—42no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11C22×D811yescharacteristic
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—168no—
213C2×D11C2×SD3214yes—
214C4×C11—21no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11C2×SD3212yes—
218C4×C11#54611yescharacteristic
219C4×C11#57711yescharacteristic
220Dic11—22no—
221Dic11—81no—
222Dic11—81no—
223C22×D4—222no—
224C22×D4—441no—
225C2×Q16—111no—
226C2×D8—112no—
227C2×D8—222no—
228C2×D8—224no—
229C2×D8—221no—
230C2×D8—442no—
231C2×D8C22×D1111yescharacteristic
232C22×C8—112no—
233C4⋊Q8—21no—
234#127—221no—
235#125—441no—
236C22⋊Q8—222no—
237C22⋊Q8—442no—
238#121—222no—
239#121—441no—
240#120—442no—
241C4×Q8—221no—
242C4×D4—21no—
243C4×D4—111no—
244C4×D4—441no—
245C2×C4⋊C4—222no—
246SD32—222no—
247SD32—442no—
248C2×C16—111no—
249C2×C16—111no—
250C2×C16—442no—
251C2×C16C22×D1112yes—
252#107—21no—
253#107—111no—
254#107—222no—
255#107C22×D1112yes—
256#107C22×D1111yescharacteristic
257C4⋊C8—111no—
258#103—222no—
259#103—221no—
260#102—21no—
261#102—222no—
262C22⋊C8—112no—
263C4×C8C22×D1111yescharacteristic
264C2×C11—82no—
265C2×C11#329411yescharacteristic
266C2×C11C22×SD3211yescharacteristic
267C2×C11#341511yescharacteristic
268D11—24no—
269D11—162no—
270C24—442no—
271C2×Q8—41no—
272C2×Q8—221no—
273C2×D4—21no—
274C2×D4—111no—
275C2×D4—222no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—444no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—884no—
282C2×D4—882no—
283C22×C4—41no—
284C22×C4—112no—
285C22×C4—442no—
286Q16—221no—
287Q16—221no—
288D8—21no—
289D8—222no—
290D8—222no—
291D8—444no—
292D8—881no—
293D8#434312yes—
294C2×C8—112no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8D4×D1111yescharacteristic
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—111no—
303C4⋊C4—221no—
304C4⋊C4—442no—
305C4⋊C4—442no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—112no—
309C22⋊C4—442no—
310C22⋊C4—442no—
311C42—441no—
312C42D4×D1111yescharacteristic
313C16—22no—
314C16—221no—
315C16—221no—
316C11#3386211yescharacteristic, complemented, Sylow
317C23—41no—
318C23—112no—
319C23—442no—
320C23—884no—
321C23—884no—
322C23—1762no—
323Q8—161no—
324Q8—441no—
325Q8—441no—
326D4—22no—
327D4—41no—
328D4—114no—
329D4—442no—
330D4—442no—
331D4—884no—
332D4—884no—
333D4—882no—
334D4—1761no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—112no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—1762no—
344C2×C4D8×D1111yescharacteristic
345C2×C4D8×D1111yescharacteristic
346C2×C4C2×D4×D1111yescharacteristic
347C8—21no—
348C8—222no—
349C8C2×#434311yescharacteristic
350C8#6704211yescharacteristic
351C22—42no—
352C22—81no—
353C22—81no—
354C22—114no—
355C22—222no—
356C22—222no—
357C22—882no—
358C22—882no—
359C22—882no—
360C22—1768no—
361C22C2×D8×D1111yescharacteristic
362C4—21no—
363C4—81no—
364C4—82no—
365C4—222no—
366C4—881no—
367C4—881no—
368C4D11×SD3212yes—
369C4#1062316111yescharacteristic
370C4#1062330911yescharacteristic
371C2—82no—
372C2—224no—
373C2—1762no—
374C2#1308042611yescharacteristic
375C2C2×D11×SD3211yescharacteristic
376C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radicalD8×D44C2
hypercenter#2226D11
hypocenterC11#33862
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13081008C2semidirect
3. #13070841C2semidirect
4. #13070803C2semidirect
5. #13070713C2semidirect
6. #13070657C2semidirect
7. #13070546C2semidirect
8. C4×#66891C2semidirect
9. #13070435C2semidirect
10. D11×#357C2semidirect
11. C11×#2226C2semidirect
15. C11×#500C22semidirect
20. C2×#66864C22semidirect
21. C2×C16×D11C22semidirect
22. #10622500C22semidirect
25. D11×#107C22semidirect
27. C4×Dic44C22semidirect
30. C11×#367C22semidirect
31. C11×C4⋊C16C22semidirect
34. #10622147C22semidirect
35. (C2×D11)⋊C16C22semidirect
36. #10622130C22semidirect
37. #10622129C22semidirect
38. #10622129C22semidirect
39. #10622128C22semidirect
40. C4×C11⋊C16C22semidirect
133. #2226D11semidirect
164. D44SD32semidirect
180. #500C2×D11semidirect
193. #367C2×D11semidirect
194. C4⋊C16C2×D11semidirect
316. C11#33862semidirect

Maximal subgroups

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

subgroupindex
#130810082
D8×D442
#130708412
#130708032
#130707132
#130706572
#130705462
C4×#668912
#130704352
D11×#3572
C11×#22262
#3386211