Finite Group Databasebeta

← #13080245

Subgroups — #13080245

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623360C211yesmaximal, characteristic, complemented
2C2×#67004C211yesmaximal, characteristic, complemented
3C2×#66964C211yesmaximal, characteristic, complemented
4#10623129C211yesmaximal, characteristic, complemented
5C11×#449C211yesmaximal, characteristic, complemented
6#10622786C211yesmaximal, characteristic, complemented
7#10622781C211yesmaximal, characteristic, complemented
8#10622766C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622411C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622351C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic, complemented
20C2×C11×SD16C2211yescharacteristic, complemented
21C2×C11×D8C2211yescharacteristic
22C11×#121C2211yescharacteristic, complemented
23#67004—24no—
24#67000C2211yescharacteristic
25#66999C2211yescharacteristic
26C2×#4326C2211yescharacteristic, complemented
27C2×#4326C2211yescharacteristic, complemented
28#66992—21no—
29#66992—21no—
30#66990—21no—
31#66989C2211yescharacteristic, complemented
32D4×Dic11—21no—
33D4×Dic11C2211yescharacteristic
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4323C2211yescharacteristic
37#66983C2211yescharacteristic
38#66982—21no—
39C4×C22⋊D11C2211yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×#4318C2211yescharacteristic, complemented
42#66964—24no—
43C2×#4314C2211yescharacteristic
44C2×#4314C2211yescharacteristic
45C2×#4313C2211yescharacteristic
46#66950C2211yescharacteristic
47#66940C2211yescharacteristic, complemented
48#66938—21no—
49#66931—21no—
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66873C2211yescharacteristic
60#66872C2211yescharacteristic, complemented
61C23×D11—21no—
62C11×#41—22no—
63C11×#41—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11C2311yescharacteristic
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11C2311yescharacteristic
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78#4341—22no—
79#4341—41no—
80D4×D11—22no—
81D4×D11—41no—
82C2×D44C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C2×Dic22—22no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×SD16—41no—
90C11×D8—22no—
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11D411yescharacteristic
99#4326—22no—
100#4326—22no—
101#4324—22no—
102#4324D414yescomplemented
103#4323—22no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11C2311yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4D411yescharacteristic
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117#4318—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120#4314—22no—
121#4314—41no—
122#4313—22no—
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×D411yescharacteristic
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11—21no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11C2×D412yes—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—42no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—41no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—81no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—81no—
157C2×Dic11C2×D411yescharacteristic
158C2×Dic11C2×D411yescharacteristic
159C2×Dic11C2×D411yescharacteristic
160D44—21no—
161D44—21no—
162C4×D11—21no—
163C4×D11—21no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#137—111no—
174C2×AGL(1,ℤ/8)—111no—
175#548—111no—
176#546—111no—
177#495—111no—
178#470—111no—
179#469—111no—
180#464—111no—
181#463—111no—
182#452—111no—
183#450—111no—
184#449D1111yescharacteristic, complemented
185#448—111no—
186C4×SD16—111no—
187#436—111no—
188C22×C11—21no—
189C22×C11—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—84no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11C22×D411yescharacteristic
209C4×C11H(5,𝔽2)11yescharacteristic
210Dic11—22no—
211Dic11—21no—
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic
218C22×Q8—111no—
219C22×D4—111no—
220#137—224no—
221AGL(1,ℤ/8)—224no—
222C2×Q16—111no—
223C2×Q16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—111no—
228C2×SD16C2×D1111yescharacteristic, complemented
229C2×D8—111no—
230C2×D8C2×D1111yescharacteristic
231C2×M16—111no—
232C2×M16—111no—
233#124—111no—
234#124—111no—
235#124—221no—
236#123—221no—
237C22⋊Q8—111no—
238C22⋊Q8—111no—
239C22⋊Q8—221no—
240#121—111no—
241#121—221no—
242#121—221no—
243#121C2×D1111yescharacteristic, complemented
244#120—221no—
245C4×Q8—111no—
246C4×D4—111no—
247C4×D4—111no—
248C4×D4—221no—
249C2×C22⋊C4—221no—
250#106—111no—
251C4⋊C8—111no—
252#103—111no—
253#103—111no—
254#103C2×D1111yescharacteristic, complemented
255#102—111no—
256#102—111no—
257#102C2×D1111yescharacteristic
258C22⋊C8—111no—
259C22⋊C8C2×D1111yescharacteristic, complemented
260C4×C8—111no—
261C2×C11—42no—
262C2×C11—41no—
263C2×C11—81no—
264C2×C11D4211yescharacteristic
265C2×C11#57511yescharacteristic
266C2×C11#57711yescharacteristic
267D11—41no—
268D11—81no—
269C24—221no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—111no—
276C2×Q8—222no—
277C2×Q8—221no—
278C2×Q8—441no—
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—222no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—222no—
298Q16—222no—
299SD16—41no—
300SD16—114no—
301SD16—222no—
302SD16—222no—
303SD16—441no—
304D8—22no—
305D8—222no—
306M16—222no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—111no—
313C4⋊C4—111no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4C22×D1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—111no—
320C22⋊C4—111no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C22⋊C4—221no—
329C42—111no—
330C42—221no—
331C11#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—111no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—881no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—112no—
343Q8—221no—
344Q8—221no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—221no—
353D4—221no—
354D4—441no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4D4×D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—881no—
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—21no—
379C8—112no—
380C8—221no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—221no—
391C22—221no—
392C22—221no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—221no—
402C4—221no—
403C4—221no—
404C4—222no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—441no—
413C2—881no—
414C2#1062312111yescharacteristic
415C2#1062330111yescharacteristic
416C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623360C2semidirect
2. C2×#67004C2semidirect
3. C2×#66964C2semidirect
4. #10623129C2semidirect
5. C11×#449C2semidirect
6. #10622786C2semidirect
7. #10622781C2semidirect
8. #10622766C2semidirect
9. #10622652C2semidirect
10. #10622429C2semidirect
11. #10622411C2semidirect
12. #10622389C2semidirect
13. #10622371C2semidirect
14. #10622351C2semidirect
15. #10622342C2semidirect
19. C22×Dic22C22semidirect
20. C2×C11×SD16C22semidirect
22. C11×#121C22semidirect
26. C2×#4326C22semidirect
27. C2×#4326C22semidirect
31. #66989C22semidirect
41. C2×#4318C22semidirect
47. #66940C22semidirect
50. C11×#103C22semidirect
52. C11×C22⋊C8C22semidirect
53. #66896C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
60. #66872C22semidirect
102. #4324D4semidirect
184. #449D11semidirect
228. C2×SD16C2×D11semidirect
243. #121C2×D11semidirect
254. #103C2×D11semidirect
259. C22⋊C8C2×D11semidirect
331. C11#3275semidirect

Maximal subgroups

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

subgroupindex
#106233602
C2×#670042
C2×#669642
#106231292
C11×#4492
#106227862
#106227812
#106227662
#106226522
#106224292
#106224112
#106223892
#106223712
#106223512
#106223422
#327511