Finite Group Databasebeta

← #13079705

Subgroups — #13079705

Order 1408.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623246C211yesmaximal, characteristic, complemented
2#10623213C211yesmaximal, characteristic, complemented
3C11×#496C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic, complemented
5#10622782C211yesmaximal, characteristic, complemented
6#10622779C211yesmaximal, characteristic, complemented
7#10622776C211yesmaximal, characteristic, complemented
8#10622771C211yesmaximal, characteristic, complemented
9#10622769C211yesmaximal, characteristic, complemented
10#10622766C211yesmaximal, characteristic, complemented
11#10622763C211yesmaximal, characteristic, complemented
12#10622683C211yesmaximal, characteristic, complemented
13#10622672C211yesmaximal, characteristic, complemented
14#10622327C211yesmaximal, characteristic, complemented
15#10622322C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C2×C11×D8C2211yescharacteristic
21C2×C11×D8C2211yescharacteristic, complemented
22C11×#127C2211yescharacteristic
23C11×#124C2211yescharacteristic, complemented
24#66999C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic, complemented
26C2×#4326C2211yescharacteristic, complemented
27C2×#4325C2211yescharacteristic
28#66993C2211yescharacteristic
29#66992—21no—
30#66992—21no—
31#66991C2211yescharacteristic
32#66990—21no—
33#66990—21no—
34#66989C2211yescharacteristic
35D4×Dic11C2211yescharacteristic, complemented
36C2×#4324C2211yescharacteristic, complemented
37C2×#4323C2211yescharacteristic
38#66939—21no—
39#66938—21no—
40#66932—21no—
41#66931—21no—
42#66928C2211yescharacteristic
43#66925C2211yescharacteristic
44#66922C2211yescharacteristic, complemented
45C11×#97C2211yescharacteristic, complemented
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic
54#66880C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73#4341—41no—
74#4341—41no—
75D4×D11—41no—
76D4×D11—41no—
77C2×D44C2311yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×SD16—41no—
82C11×SD16—41no—
83C11×D8—41no—
84C11×D8—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C42×C11C2311yescharacteristic
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94#4326—41no—
95#4325—41no—
96#4324—41no—
97#4323—41no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4D411yescharacteristic
102(C2×D11)⋊C4D411yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4D411yescharacteristic
109Dic11⋊C4D411yescharacteristic
110C4×Dic11—21no—
111C4×Dic11C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3224—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—21no—
131D4×C11—81no—
132D4×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—42no—
138C22⋊D11—42no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11—81no—
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150D44—21no—
151D44—21no—
152C4×D11—21no—
153C4×D11—21no—
154Dic22—21no—
155Dic22—21no—
156Dic22—81no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#542—111no—
162#535—111no—
163#496D1111yescharacteristic, complemented
164#495—111no—
165#489—111no—
166#486—111no—
167#464—111no—
168#463—111no—
169#460—111no—
170#459—111no—
171#452—111no—
172#450—111no—
173#449—111no—
174#447—111no—
175#433—111no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11C22×D411yescharacteristic
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—84no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11H(5,𝔽2)11yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—21no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C22×D4—111no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×SD16C2×D1111yescharacteristic
210C2×SD16C2×D1111yescharacteristic, complemented
211C2×D8—111no—
212C2×D8C2×D1111yescharacteristic
213C2×D8C2×D1111yescharacteristic, complemented
214C4⋊Q8—111no—
215#127—111no—
216#127C2×D1111yescharacteristic
217#126—221no—
218#124—111no—
219#124—111no—
220#124—221no—
221#124C2×D1111yescharacteristic, complemented
222#123—221no—
223C22⋊Q8—111no—
224C22⋊Q8—221no—
225#121—111no—
226#121—221no—
227#121—221no—
228#120—221no—
229#120—221no—
230C4×Q8—111no—
231C4×D4—111no—
232#117—111no—
233C4⋊C8—111no—
234C4⋊C8—111no—
235#103—111no—
236#103—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97C2×D1111yescharacteristic, complemented
246C4×C8—111no—
247C2×C11—81no—
248C2×C11—81no—
249C2×C11—81no—
250C2×C11#53511yescharacteristic
251C2×C11#57611yescharacteristic
252C2×C11#57711yescharacteristic
253D11—41no—
254D11—81no—
255C24—221no—
256#41—441no—
257#41—441no—
258C2×Q8—111no—
259C2×Q8—221no—
260C2×Q8C22×D1111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4C22×D1111yescharacteristic
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277Q16—441no—
278SD16—41no—
279SD16—41no—
280SD16—441no—
281SD16—441no—
282D8—41no—
283D8—41no—
284D8—441no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8C22×D1111yescharacteristic
288C2×C8C22×D1111yescharacteristic
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—111no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—111no—
299C22⋊C4—111no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—221no—
309C42C22×D1111yescharacteristic
310C11#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—111no—
315C23—221no—
316C23—442no—
317C23—881no—
318C23—881no—
319Q8—21no—
320Q8—21no—
321Q8—221no—
322Q8—221no—
323Q8—881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—442no—
336D4—881no—
337D4—881no—
338D4—881no—
339C2×C4—21no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—881no—
350C2×C4D4×D1111yescharacteristic
351C2×C4D4×D1111yescharacteristic
352C2×C4C23×D1111yescharacteristic
353C8—21no—
354C8—21no—
355C8—221no—
356C8—221no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—884no—
373C22C2×D4×D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—221no—
378C4—221no—
379C4—221no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6703711yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—441no—
389C2—881no—
390C2#1062324611yescharacteristic
391C2#1062330511yescharacteristic
392C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#496C2
socleC22×C11C22×D4
hypercenter#496D11
hypocenterC11#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #10623246C2semidirect
2. #10623213C2semidirect
3. C11×#496C2semidirect
4. #10622786C2semidirect
5. #10622782C2semidirect
6. #10622779C2semidirect
7. #10622776C2semidirect
8. #10622771C2semidirect
9. #10622769C2semidirect
10. #10622766C2semidirect
11. #10622763C2semidirect
12. #10622683C2semidirect
13. #10622672C2semidirect
14. #10622327C2semidirect
15. #10622322C2semidirect
19. C2×C11×SD16C22semidirect
21. C2×C11×D8C22semidirect
23. C11×#124C22semidirect
25. Q8×Dic11C22semidirect
26. C2×#4326C22semidirect
35. D4×Dic11C22semidirect
36. C2×#4324C22semidirect
44. #66922C22semidirect
45. C11×#97C22semidirect
48. #66896C22semidirect
49. #66896C22semidirect
54. #66880C22semidirect
55. #66880C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
58. C4×C11⋊C8C22semidirect
163. #496D11semidirect
210. C2×SD16C2×D11semidirect
213. C2×D8C2×D11semidirect
221. #124C2×D11semidirect
245. #97C2×D11semidirect
310. C11#3224semidirect

Maximal subgroups

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

subgroupindex
#106232462
#106232132
C11×#4962
#106227862
#106227822
#106227792
#106227762
#106227712
#106227692
#106227662
#106227632
#106226832
#106226722
#106223272
#106223222
#322411