Finite Group Databasebeta

← #14909766

Subgroups — #14909766

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622308C211yesmaximal, characteristic, complemented
2#13070883C212yesmaximal, complemented
3#13070859C212yesmaximal, complemented
4#13070656C212yesmaximal, complemented
5#13070651C212yesmaximal, complemented
6#13070544C212yesmaximal, complemented
7#13070527C212yesmaximal, complemented
8#13070419C211yesmaximal, characteristic, complemented
9C11×#3168C211yesmaximal, characteristic, complemented
10C11×#529—21no—
11C22×D88—21no—
12C22×D88C2212yes—
13C2×#66927—21no—
14C11×#499C2211yescharacteristic, complemented
15C11×#495C2211yescharacteristic, complemented
16C11×#488—21no—
17C11×#467C2211yescharacteristic
18C11×#466C2211yescharacteristic
19C11×#465—21no—
20C4×C11×Q16C2211yescharacteristic, complemented
21C4×C11×SD16—21no—
22C4×C11×D8C2211yescharacteristic, complemented
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66892C2214yescomplemented
25C2×#66890C2214yescomplemented
26#10622308—21no—
27#10622308—21no—
28#10622308C2212yes—
29#10622308C2212yes—
30C22⋊(C11⋊C16)C2212yes—
31#10622129C2214yescomplemented
32#10622129C2214yescomplemented
33C4⋊(C11⋊C16)C2212yescomplemented
34#10622099C2212yescomplemented
35C22×D44—22no—
36C22×D44—41no—
37C22×D44—41no—
38C2×C11×Q16C2311yescharacteristic
39C2×C11×SD16—21no—
40C2×C11×D8C2311yescharacteristic
41C22×C8×C11D411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C11×#126—41no—
44C11×#125—21no—
45C11×#124—21no—
46C11×#123—41no—
47C11×C22⋊Q8—21no—
48C11×#121—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—41no—
52C11×#117—41no—
53C2×C42×C11D411yescharacteristic
54C2×D88—22no—
55C2×D88—22no—
56C2×D88—22no—
57C2×D88—44no—
58C2×D88—44no—
59C2×D88C2314yes—
60#66927—22no—
61#66927—22no—
62#66927—41no—
63#66927—41no—
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#106—21no—
67C11×#103—21no—
68C11×#103—21no—
69C11×#102—21no—
70C11×#102—21no—
71C4×C8×C11D411yescharacteristic
72C4×C8×C11D411yescharacteristic
73C4×C8×C11C2311yescharacteristic
74C4×C8×C11C2311yescharacteristic
75#66892—44no—
76#66890—44no—
77C2×C11⋊C16C2314yes—
78#33783—111nomaximal, Sylow
79C23×D11—42no—
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11D811yescharacteristic
85C22×C4×C11D811yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×D44—24no—
88C2×D44—44no—
89C2×D44—44no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—84no—
96C2×D44—84no—
97C11×Q16—22no—
98C11×SD16—42no—
99C11×D8—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2411yescharacteristic
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11D811yescharacteristic
119C42×C11D811yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122D88—24no—
123D88—24no—
124D88—44no—
125D88—44no—
126D88—44no—
127C11⋊C16—24no—
128#3168D1111yescharacteristic, complemented
129C2×#493—111no—
130#2250—112no—
131#2244—112no—
132#2207—112no—
133#2206—112no—
134#2187—112no—
135#2184—112no—
136#2163—111no—
137C23×C11—41no—
138C23×C11C2×D811yescharacteristic
139C22×D11—44no—
140C22×D11—84no—
141C22×D11—84no—
142C22×D11—84no—
143Q8×C11—41no—
144Q8×C11—41no—
145D4×C11—41no—
146D4×C11—41no—
147D4×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—82no—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162D44—44no—
163D44—44no—
164D44—84no—
165D44—84no—
166D44—84no—
167D44—84no—
168D44—84no—
169C8×C11—21no—
170C8×C11—21no—
171C8×C11AGL(1,ℤ/8)12yes—
172C8×C11H(5,𝔽2)12yes—
173C22×D8—112no—
174C22×D8—221no—
175C2×#127—221no—
176#529—21no—
177C2×SD32—114no—
178C2×D16—114no—
179#499C2×D1111yescharacteristic, complemented
180#495C2×D1111yescharacteristic, complemented
181#493—112no—
182#493—112no—
183#493—221no—
184#493—221no—
185#488—21no—
186#467C2×D1111yescharacteristic
187#466C2×D1111yescharacteristic
188#465—21no—
189C4×Q16C2×D1111yescharacteristic, complemented
190C4×SD16—21no—
191C4×D8C2×D1111yescharacteristic, complemented
192C2×C4×C8C2×D1111yescharacteristic
193C4⋊C16—112no—
194#357—114no—
195#357—114no—
196C22⋊C16—112no—
197#346—112no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#50912yes—
204C22×C11C22×D811yescharacteristic
205C2×D11—84no—
206C2×D11—84no—
207C2×D11—84no—
208C2×D11—168no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11#50912yes—
217C4×C11#53511yescharacteristic
218C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
219C22×D4—222no—
220C22×D4—441no—
221C22×D4—441no—
222C2×Q16C22×D1111yescharacteristic
223C2×SD16—21no—
224C2×D8—114no—
225C2×D8—222no—
226C2×D8—222no—
227C2×D8—222no—
228C2×D8—444no—
229C2×D8—444no—
230C2×D8C22×D1111yescharacteristic
231C22×C8C22⋊D1111yescharacteristic
232C22×C8C22×D1111yescharacteristic
233#127—222no—
234#127—222no—
235#127—441no—
236#127—441no—
237#126—41no—
238#125—21no—
239#124—21no—
240#123—41no—
241C22⋊Q8—21no—
242#121—21no—
243C4×Q8—21no—
244C4×D4—21no—
245C4×D4—41no—
246#117—41no—
247C2×C42C22⋊D1111yescharacteristic
248SD32—444no—
249D16—444no—
250C2×C16—114no—
251#107C22×D1111yescharacteristic
252#107C22×D1111yescharacteristic
253#106—21no—
254#103—21no—
255#103—21no—
256#102—21no—
257#102—21no—
258C4×C8C22⋊D1111yescharacteristic
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11—161no—
264C2×C11#320511yescharacteristic
265C2×C11C2×#50911yescharacteristic
266C2×C11C2×#50911yescharacteristic
267D11—164no—
268C24—442no—
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—224no—
273C2×D4—444no—
274C2×D4—444no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—884no—
281C2×D4—884no—
282C22×C4—41no—
283C22×C4#432311yescharacteristic
284C22×C4#432311yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286Q16—22no—
287SD16—42no—
288D8—22no—
289D8—224no—
290D8—224no—
291D8—444no—
292D8—444no—
293D8—444no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—41no—
312C42#432311yescharacteristic
313C42#432311yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C16—224no—
317C11#3378311yescharacteristic, complemented, Sylow
318C23—41no—
319C23—444no—
320C23—884no—
321C23—884no—
322C23—884no—
323C23C2×#432311yescharacteristic
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—82no—
329D4—444no—
330D4—444no—
331D4—884no—
332D4—884no—
333D4—884no—
334D4—884no—
335D4—884no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4C2×#432311yescharacteristic
345C2×C4C2×#432311yescharacteristic
346C2×C4C2×#432311yescharacteristic
347C2×C4C2×#432311yescharacteristic
348C2×C4C2×#432311yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8#6700212yes—
353C8#6704212yes—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—884no—
360C22—884no—
361C22—884no—
362C22—1768no—
363C22#1062280612yes—
364C22C22×#432311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4#1062280612yes—
373C4C2×#6700211yescharacteristic
374C4#1062336111yescharacteristic
375C2—22no—
376C2—161no—
377C2—1764no—
378C2#1307953111yescharacteristic
379C2C2×#1062280611yescharacteristic
380C2C2×#1062280611yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
hypercenter#3168D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. C2×#10622308C2semidirect
2. #13070883C2semidirect
3. #13070859C2semidirect
4. #13070656C2semidirect
5. #13070651C2semidirect
6. #13070544C2semidirect
7. #13070527C2semidirect
8. #13070419C2semidirect
9. C11×#3168C2semidirect
14. C11×#499C22semidirect
15. C11×#495C22semidirect
20. C4×C11×Q16C22semidirect
22. C4×C11×D8C22semidirect
24. C2×#66892C22semidirect
25. C2×#66890C22semidirect
31. #10622129C22semidirect
32. #10622129C22semidirect
33. C4⋊(C11⋊C16)C22semidirect
34. #10622099C22semidirect
128. #3168D11semidirect
179. #499C2×D11semidirect
180. #495C2×D11semidirect
189. C4×Q16C2×D11semidirect
191. C4×D8C2×D11semidirect
317. C11#33783semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
#130708832
#130708592
#130706562
#130706512
#130705442
#130705272
#130704192
C11×#31682
#3378311