Finite Group Databasebeta

← #13078117

Subgroups — #13078117

Order 1408.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66967C211yesmaximal, characteristic, complemented
2C2×D8×D11C211yesmaximal, characteristic, complemented
3#10623205C211yesmaximal, characteristic, complemented
4#10623076C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622778C211yesmaximal, characteristic, complemented
7#10622763C211yesmaximal, characteristic, complemented
8#10622670C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622417C211yesmaximal, characteristic, complemented
14#10622399C211yesmaximal, characteristic, complemented
15#10622383C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C2×C11×D8C2211yescharacteristic
21C11×#124C2211yescharacteristic, complemented
22C4×D4×C11C2211yescharacteristic, complemented
23#67000C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic, complemented
25#66993C2211yescharacteristic, complemented
26D4×Dic11C2211yescharacteristic, complemented
27C2×#4323C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×#4323C2211yescharacteristic, complemented
30C4×C22⋊D11—21no—
31C2×(C2×D11)⋊C4—21no—
32#66967—24no—
33D8×D11—24no—
34C2×D88C2211yescharacteristic
35C2×D88C2211yescharacteristic, complemented
36C2×#4313C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38#66946C2211yescharacteristic, complemented
39#66945C2211yescharacteristic
40#66937—21no—
41#66937—21no—
42#66935—21no—
43#66935—21no—
44(C22⋊D11)⋊C4—21no—
45C22⋊C4×D11—21no—
46#66927C2211yescharacteristic, complemented
47C4×D44C2211yescharacteristic, complemented
48#66925C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66885C2211yescharacteristic, complemented
55#66885C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58#66873C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72#4343—22no—
73#4343—22no—
74D4×D11—22no—
75D4×D11—22no—
76D4×D11—22no—
77D4×D11D414yescomplemented
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44C2311yescharacteristic
82C2×D44C2311yescharacteristic
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11C2311yescharacteristic
88C11×SD16—22no—
89C11×D8—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C42×C11C2311yescharacteristic
97C22⋊Dic11—21no—
98#4325—22no—
99#4323—22no—
100#4323—22no—
101#4323—22no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4D411yescharacteristic
108(C2×D11)⋊C4D411yescharacteristic
109C4⋊Dic11C2311yescharacteristic
110Dic11⋊C4D411yescharacteristic
111Dic11⋊C4D411yescharacteristic
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116D88—22no—
117D88—22no—
118#4313—22no—
119C8×D11—22no—
120#3041—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11—21no—
123C22×D11—21no—
124C22×D11—24no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—42no—
128C22×D11—81no—
129C22×D11—81no—
130C22×D11—81no—
131C22×D11—81no—
132C22×D11C2×D411yescharacteristic
133Q8×C11—21no—
134Q8×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11C2×D412yes—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—81no—
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C22⋊D11—24no—
146C22⋊D11—42no—
147C22⋊D11—81no—
148C22⋊D11—81no—
149C2×Dic11—21no—
150C2×Dic11—81no—
151C2×Dic11C2×D411yescharacteristic
152C2×Dic11C2×D411yescharacteristic
153C2×Dic11C2×D411yescharacteristic
154D44—21no—
155D44—21no—
156D44—21no—
157D44—21no—
158D44—21no—
159D44—42no—
160D44—81no—
161D44—81no—
162D44C2×D412yes—
163C4×D11—42no—
164C4×D11—81no—
165C4×D11—81no—
166C4×D11C2×D412yes—
167C4×D11#4112yes—
168C8×C11—21no—
169C8×C11—21no—
170C11⋊C8—21no—
171C11⋊C8—21no—
172C2×AGL(1,ℤ/8)—111no—
173C22×D8—111no—
174#535—111no—
175#518—111no—
176#463—111no—
177#463—111no—
178#463—111no—
179#463D1111yescharacteristic, complemented
180#459—111no—
181#459—111no—
182#459—111no—
183#459—111no—
184#424—111no—
185#418—111no—
186#416—111no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11C22×D411yescharacteristic
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—22no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—84no—
206C2×D11—84no—
207C2×D11#12112yes—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11C22×D411yescharacteristic
213C4×C11C2×#4111yescharacteristic
214Dic11—21no—
215Dic11—21no—
216Dic11—41no—
217Dic11#12112yes—
218C2×#41—111no—
219C22×D4—111no—
220C22×D4—111no—
221AGL(1,ℤ/8)—224no—
222C2×SD16—111no—
223C2×SD16C2×D1111yescharacteristic, complemented
224C2×D8—111no—
225C2×D8—111no—
226C2×D8—111no—
227C2×D8—111no—
228C2×D8—111no—
229C2×D8—224no—
230C2×D8C2×D1111yescharacteristic
231C2×M16—111no—
232C22×C8—111no—
233#127—111no—
234#127—111no—
235#124—111no—
236#124C2×D1111yescharacteristic, complemented
237#121—221no—
238#121—221no—
239#120—221no—
240#120—221no—
241C4×D4—111no—
242C4×D4—111no—
243C4×D4—111no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4C2×D1111yescharacteristic, complemented
247#117—111no—
248#117—111no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C4⋊C8—111no—
252C4⋊C8—111no—
253C4⋊C8—111no—
254C4⋊C8C2×D1111yescharacteristic, complemented
255#103—111no—
256#103C2×D1111yescharacteristic, complemented
257#102—111no—
258#102—111no—
259#102—111no—
260#102—111no—
261#102—111no—
262#102C2×D1111yescharacteristic, complemented
263C2×C11—42no—
264C2×C11—81no—
265C2×C11C2×#12111yescharacteristic
266C2×C11#57611yescharacteristic
267C2×C11#57611yescharacteristic
268D11—22no—
269D11—42no—
270D11—81no—
271D11—81no—
272C24—221no—
273C24—221no—
274#41—222no—
275#41—222no—
276C2×Q8C22×D1111yescharacteristic
277C2×D4—114no—
278C2×D4—111no—
279C2×D4—111no—
280C2×D4—111no—
281C2×D4—221no—
282C2×D4—222no—
283C2×D4—222no—
284C2×D4—222no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4C22×D1111yescharacteristic
292C2×D4C22×D1111yescharacteristic
293C22×C4—21no—
294C22×C4—111no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299SD16—22no—
300SD16—222no—
301D8—22no—
302D8—222no—
303D8—222no—
304D8—222no—
305D8—222no—
306D8—222no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—222no—
311C2×C8C22×D1111yescharacteristic
312C2×C8C22×D1111yescharacteristic
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—111no—
316C4⋊C4C22×D1111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—111no—
321C22⋊C4—111no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C42—111no—
329C42—221no—
330C42C22×D1111yescharacteristic
331C11#304111yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—111no—
335C23—224no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23—442no—
340C23—881no—
341C23—881no—
342C23—881no—
343C23—881no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—112no—
350D4—224no—
351D4—221no—
352D4—221no—
353D4—221no—
354D4—221no—
355D4—221no—
356D4—442no—
357D4—442no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362D4D4×D1112yes—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—81no—
366C2×C4—111no—
367C2×C4—112no—
368C2×C4—112no—
369C2×C4—111no—
370C2×C4—111no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4D4×D1111yescharacteristic
377C2×C4D4×D1111yescharacteristic
378C2×C4C23×D1111yescharacteristic
379C8—21no—
380C8—21no—
381C8—221no—
382C8—221no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—112no—
390C22—221no—
391C22—221no—
392C22—222no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—884no—
402C22—884no—
403C22C2×D4×D1111yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—112no—
409C4—221no—
410C4—221no—
411C4—441no—
412C4C2×D4×D1111yescharacteristic
413C4#41×D1111yescharacteristic
414C2—42no—
415C2—81no—
416C2—222no—
417C2—442no—
418C2—881no—
419C2—881no—
420C2D11×#12111yescharacteristic
421C2#1062330011yescharacteristic
422C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#66967C2semidirect
2. C2×D8×D11C2semidirect
3. #10623205C2semidirect
4. #10623076C2semidirect
5. C11×#463C2semidirect
6. #10622778C2semidirect
7. #10622763C2semidirect
8. #10622670C2semidirect
9. #10622628C2semidirect
10. #10622456C2semidirect
11. #10622452C2semidirect
12. #10622432C2semidirect
13. #10622417C2semidirect
14. #10622399C2semidirect
15. #10622383C2semidirect
19. C2×C11×SD16C22semidirect
21. C11×#124C22semidirect
22. C4×D4×C11C22semidirect
23. #67000C22semidirect
24. C2×#4325C22semidirect
25. #66993C22semidirect
26. D4×Dic11C22semidirect
29. C2×#4323C22semidirect
35. C2×D88C22semidirect
38. #66946C22semidirect
46. #66927C22semidirect
47. C4×D44C22semidirect
49. C11×C4⋊C8C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. #66899C22semidirect
53. #66896C22semidirect
54. #66885C22semidirect
55. #66885C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
58. #66873C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
77. D4×D11D4semidirect
179. #463D11semidirect
223. C2×SD16C2×D11semidirect
236. #124C2×D11semidirect
246. C4×D4C2×D11semidirect
254. C4⋊C8C2×D11semidirect
256. #103C2×D11semidirect
262. #102C2×D11semidirect
331. C11#3041semidirect

Maximal subgroups

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

subgroupindex
C2×#669672
C2×D8×D112
#106232052
#106230762
C11×#4632
#106227782
#106227632
#106226702
#106226282
#106224562
#106224522
#106224322
#106224172
#106223992
#106223832
#304111