Finite Group Databasebeta

← #13079713

Subgroups — #13079713

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#10623264C211yesmaximal, characteristic, complemented
2#10623246C211yesmaximal, characteristic, complemented
3C11×#486C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic, complemented
5#10622687C211yesmaximal, characteristic, complemented
6#10622400C211yesmaximal, characteristic, complemented
7#10622399C211yesmaximal, characteristic, complemented
8#10622396C211yesmaximal, characteristic, complemented
9#10622394C211yesmaximal, characteristic, complemented
10#10622389C211yesmaximal, characteristic, complemented
11#10622386C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic, complemented
14#10622309C211yesmaximal, characteristic, complemented
15#10622303C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic, complemented
19C11×#127C2211yescharacteristic
20#67000—21no—
21#66999—21no—
22#66993C2211yescharacteristic
23#66992—21no—
24#66992—21no—
25#66990—21no—
26#66990—21no—
27#66989C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C2×#4324C2211yescharacteristic, complemented
30C2×#4323C2211yescharacteristic
31C2×#4323C2211yescharacteristic, complemented
32C2×Dic44C2211yescharacteristic, complemented
33C2×D88C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×#4314C2211yescharacteristic, complemented
36#66951—21no—
37#66950C2211yescharacteristic
38#66948C2211yescharacteristic
39#66947—21no—
40#66946C2211yescharacteristic, complemented
41#66940C2211yescharacteristic, complemented
42#66928C2211yescharacteristic
43#66928C2211yescharacteristic, complemented
44#66925C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×#102C2211yescharacteristic, complemented
48C11×#102C2211yescharacteristic, complemented
49C4×C8×C11C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic, complemented
53Dic11⋊C8C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58#66867C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C22×Dic11—21no—
70#4341—41no—
71#4341—41no—
72D4×D11—41no—
73D4×D11—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C2×Dic22C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4324—41no—
90#4324—41no—
91#4323—41no—
92#4323—41no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4D411yescharacteristic
101(C2×D11)⋊C4D411yescharacteristic
102C4⋊Dic11—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105Dic11⋊C4D411yescharacteristic
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44—41no—
111D88—41no—
112#4314—41no—
113#4314—41no—
114#3224—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123Q8×C11—81no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—42no—
136C22⋊D11—42no—
137C22⋊D11—81no—
138C22⋊D11—81no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—42no—
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
147D44—21no—
148D44—21no—
149D44—81no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—81no—
153Dic22—21no—
154Dic22—21no—
155Dic22—21no—
156Dic22—21no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#542—111no—
162#535—111no—
163#496—111no—
164#495—111no—
165#489—111no—
166#486D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—84no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11H(5,𝔽2)11yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C22×D4—111no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×D8—111no—
212C2×D8—111no—
213C2×D8—111no—
214C4⋊Q8C2×D1111yescharacteristic, complemented
215#127—111no—
216#127C2×D1111yescharacteristic
217#126—221no—
218#124—111no—
219#124—111no—
220#124—111no—
221#124—221no—
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#102C2×D1111yescharacteristic
240#102C2×D1111yescharacteristic
241#102C2×D1111yescharacteristic, complemented
242#102C2×D1111yescharacteristic, complemented
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97—111no—
246C4×C8C2×D1111yescharacteristic, complemented
247C2×C11—81no—
248C2×C11—81no—
249C2×C11#53511yescharacteristic
250C2×C11#57611yescharacteristic
251C2×C11#57711yescharacteristic
252D11—41no—
253D11—81no—
254D11—81no—
255C24—221no—
256#41—441no—
257#41—441no—
258C2×Q8—21no—
259C2×Q8—111no—
260C2×Q8—111no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277Q16—441no—
278SD16—441no—
279SD16—441no—
280SD16—441no—
281SD16—441no—
282D8—441no—
283D8—441no—
284D8—441no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8C22×D1111yescharacteristic
288C2×C8C22×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4C22×D1111yescharacteristic
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—111no—
297C22⋊C4—111no—
298C22⋊C4—221no—
299C22⋊C4—221no—
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—111no—
314C23—221no—
315C23—221no—
316C23—442no—
317C23—881no—
318C23—881no—
319Q8—81no—
320Q8—221no—
321Q8—221no—
322Q8—221no—
323Q8—221no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—221no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—442no—
336D4—881no—
337D4—881no—
338D4—881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—111no—
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—221no—
364C22—221no—
365C22—221no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—884no—
373C22C2×D4×D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—221no—
379C4—221no—
380C4—221no—
381C4—441no—
382C4—441no—
383C4#6704211yescharacteristic
384C4#6704211yescharacteristic
385C2—81no—
386C2—81no—
387C2—441no—
388C2—881no—
389C2—881no—
390C2#1062320511yescharacteristic
391C2#1062328811yescharacteristic
392C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
hypercenter#486D11
hypocenterC11#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10623264C2semidirect
2. #10623246C2semidirect
3. C11×#486C2semidirect
4. #10622702C2semidirect
5. #10622687C2semidirect
6. #10622400C2semidirect
7. #10622399C2semidirect
8. #10622396C2semidirect
9. #10622394C2semidirect
10. #10622389C2semidirect
11. #10622386C2semidirect
12. #10622380C2semidirect
13. #10622375C2semidirect
14. #10622309C2semidirect
15. #10622303C2semidirect
18. C11×C4⋊Q8C22semidirect
29. C2×#4324C22semidirect
31. C2×#4323C22semidirect
32. C2×Dic44C22semidirect
35. C2×#4314C22semidirect
40. #66946C22semidirect
41. #66940C22semidirect
43. #66928C22semidirect
47. C11×#102C22semidirect
48. C11×#102C22semidirect
49. C4×C8×C11C22semidirect
52. Dic11⋊C8C22semidirect
53. Dic11⋊C8C22semidirect
54. #66874C22semidirect
55. #66874C22semidirect
58. #66867C22semidirect
166. #486D11semidirect
214. C4⋊Q8C2×D11semidirect
241. #102C2×D11semidirect
242. #102C2×D11semidirect
246. C4×C8C2×D11semidirect
310. C11#3224semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106232462
C11×#4862
#106227022
#106226872
#106224002
#106223992
#106223962
#106223942
#106223892
#106223862
#106223802
#106223752
#106223092
#106223032
#322411