Finite Group Databasebeta

← #13078156

Subgroups — #13078156

Order 1408.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66969C211yesmaximal, characteristic, complemented
2C2×#66964C211yesmaximal, characteristic, complemented
3#10623205C211yesmaximal, characteristic, complemented
4#10623077C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622778C211yesmaximal, characteristic, complemented
7#10622763C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622416C211yesmaximal, characteristic, complemented
13#10622411C211yesmaximal, characteristic, complemented
14D11×#102C211yesmaximal, characteristic, complemented
15#10622375C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic, complemented
20C2×C11×D8C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C4×D4×C11C2211yescharacteristic, complemented
23#67000C2211yescharacteristic
24C2×#4326C2211yescharacteristic, complemented
25#66993C2211yescharacteristic
26D4×Dic11C2211yescharacteristic, complemented
27C2×#4324C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×#4323C2211yescharacteristic, complemented
30C4×C22⋊D11—21no—
31C2×Dic11⋊C4—21no—
32#66969—24no—
33#66964—24no—
34C2×#4314C2211yescharacteristic
35C2×#4314C2211yescharacteristic, complemented
36C2×#4313C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic
39#66940C2211yescharacteristic, complemented
40#66937—21no—
41#66937—21no—
42#66935—21no—
43#66935—21no—
44(C22⋊D11)⋊C4—21no—
45#66930—21no—
46#66927C2211yescharacteristic
47#66925C2211yescharacteristic
48C4×Dic22C2211yescharacteristic, complemented
49C11×C4⋊C8C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54#66885C2211yescharacteristic
55#66885C2211yescharacteristic, complemented
56Dic11⋊C8C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58#66873C2211yescharacteristic
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72#4343—22no—
73#4343—22no—
74#4341—22no—
75#4341D414yescomplemented
76D4×D11—22no—
77D4×D11—22no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44C2311yescharacteristic
82C2×D44C2311yescharacteristic
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×Dic22C2311yescharacteristic
87C11×SD16—22no—
88C11×D8—22no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C42×C11C2311yescharacteristic
96C22⋊Dic11—21no—
97#4326—22no—
98#4324—22no—
99#4323—22no—
100#4323—22no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4D411yescharacteristic
104(C2×D11)⋊C4D411yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4D411yescharacteristic
110Dic11⋊C4D411yescharacteristic
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116#4314—22no—
117#4314—22no—
118#4313—22no—
119C8×D11—22no—
120#3045—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—42no—
126C22×D11—81no—
127C22×D11—81no—
128C22×D11C2×D411yescharacteristic
129Q8×C11—21no—
130Q8×C11—21no—
131D4×C11—21no—
132D4×C11—21no—
133D4×C11—21no—
134D4×C11C2×D412yes—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—81no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C22⋊D11—24no—
142C22⋊D11—42no—
143C22⋊D11—81no—
144C22⋊D11—81no—
145C2×Dic11—21no—
146C2×Dic11—24no—
147C2×Dic11—21no—
148C2×Dic11—81no—
149C2×Dic11C2×D411yescharacteristic
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—21no—
153D44—21no—
154D44—21no—
155D44—21no—
156D44—42no—
157D44—81no—
158D44—81no—
159C4×D11—42no—
160C4×D11—81no—
161C4×D11C2×D412yes—
162C4×D11#4112yes—
163Dic22—21no—
164Dic22C2×D412yes—
165C8×C11—21no—
166C8×C11—21no—
167C11⋊C8—21no—
168C11⋊C8—21no—
169C2×AGL(1,ℤ/8)—111no—
170C2×#135—111no—
171#535—111no—
172#520—111no—
173#464—111no—
174#464—111no—
175#463—111no—
176#463D1111yescharacteristic, complemented
177#460—111no—
178#460—111no—
179#459—111no—
180#459—111no—
181#424—111no—
182#417—111no—
183C2×#102—111no—
184C22×C11—22no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11C22×D411yescharacteristic
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—84no—
200C2×D11#12112yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11C22×D411yescharacteristic
206C4×C11C2×#4111yescharacteristic
207Dic11—22no—
208Dic11—21no—
209Dic11—21no—
210Dic11—41no—
211Dic11#12112yes—
212C2×#41—111no—
213C2×#41—111no—
214C22×D4—111no—
215AGL(1,ℤ/8)—224no—
216#135—224no—
217C2×Q16—111no—
218C2×SD16—111no—
219C2×SD16—111no—
220C2×SD16—111no—
221C2×SD16C2×D1111yescharacteristic, complemented
222C2×D8—111no—
223C2×D8—111no—
224C2×D8C2×D1111yescharacteristic
225C2×M16—111no—
226C22×C8—111no—
227#127—111no—
228#127—111no—
229#124—111no—
230#124C2×D1111yescharacteristic
231#121—221no—
232#121—221no—
233#120—221no—
234#120—221no—
235C4×Q8—111no—
236C4×Q8—111no—
237C4×D4—111no—
238C4×D4—221no—
239C4×D4—221no—
240C4×D4C2×D1111yescharacteristic, complemented
241#117—111no—
242#117—221no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C4⋊C8—111no—
246C4⋊C8—111no—
247C4⋊C8—111no—
248C4⋊C8C2×D1111yescharacteristic, complemented
249#103—111no—
250#103C2×D1111yescharacteristic, complemented
251#102—111no—
252#102—111no—
253#102—111no—
254#102—111no—
255#102—111no—
256#102C2×D1111yescharacteristic
257C2×C11—42no—
258C2×C11—81no—
259C2×C11C2×#12111yescharacteristic
260C2×C11#57611yescharacteristic
261C2×C11#57711yescharacteristic
262D11—22no—
263D11—81no—
264D11—81no—
265C24—221no—
266#41—114no—
267#41—222no—
268#41—222no—
269#41—222no—
270C2×Q8—111no—
271C2×Q8C22×D1111yescharacteristic
272C2×D4—111no—
273C2×D4—111no—
274C2×D4—221no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—21no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291Q16—222no—
292SD16—22no—
293SD16—222no—
294SD16—222no—
295SD16—222no—
296D8—22no—
297D8—222no—
298D8—222no—
299M16—222no—
300C2×C8—111no—
301C2×C8—111no—
302C2×C8—222no—
303C2×C8C22×D1111yescharacteristic
304C2×C8C22×D1111yescharacteristic
305C4⋊C4—111no—
306C4⋊C4—111no—
307C4⋊C4—111no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4C22×D1111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—111no—
316C22⋊C4—111no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C42—111no—
321C42—221no—
322C42—221no—
323C42C22×D1111yescharacteristic
324C11#304511yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—111no—
328C23—221no—
329C23—221no—
330C23—442no—
331C23—881no—
332C23—881no—
333Q8—21no—
334Q8—21no—
335Q8—112no—
336Q8—221no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—224no—
341D4—221no—
342D4—221no—
343D4—221no—
344D4—221no—
345D4—442no—
346D4—442no—
347D4—881no—
348D4—881no—
349D4—881no—
350D4—881no—
351D4D4×D1112yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—111no—
356C2×C4—112no—
357C2×C4—112no—
358C2×C4—111no—
359C2×C4—111no—
360C2×C4—224no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—442no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4D4×D1111yescharacteristic
367C2×C4D4×D1111yescharacteristic
368C2×C4C23×D1111yescharacteristic
369C8—21no—
370C8—21no—
371C8—221no—
372C8—221no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—112no—
380C22—221no—
381C22—221no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22—441no—
388C22—884no—
389C22C2×D4×D1111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—112no—
395C4—221no—
396C4—221no—
397C4—222no—
398C4—441no—
399C4C2×D4×D1111yescharacteristic
400C4#41×D1111yescharacteristic
401C2—42no—
402C2—81no—
403C2—222no—
404C2—881no—
405C2—881no—
406C2D11×#12111yescharacteristic
407C2#1062330111yescharacteristic
408C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3045
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×#66969C2semidirect
2. C2×#66964C2semidirect
3. #10623205C2semidirect
4. #10623077C2semidirect
5. C11×#463C2semidirect
6. #10622778C2semidirect
7. #10622763C2semidirect
8. #10622667C2semidirect
9. #10622628C2semidirect
10. #10622461C2semidirect
11. #10622452C2semidirect
12. #10622416C2semidirect
13. #10622411C2semidirect
14. D11×#102C2semidirect
15. #10622375C2semidirect
19. C2×C11×SD16C22semidirect
22. C4×D4×C11C22semidirect
24. C2×#4326C22semidirect
26. D4×Dic11C22semidirect
29. C2×#4323C22semidirect
35. C2×#4314C22semidirect
39. #66940C22semidirect
48. C4×Dic22C22semidirect
49. C11×C4⋊C8C22semidirect
50. C11×#103C22semidirect
52. #66899C22semidirect
55. #66885C22semidirect
56. Dic11⋊C8C22semidirect
57. Dic11⋊C8C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
75. #4341D4semidirect
176. #463D11semidirect
221. C2×SD16C2×D11semidirect
240. C4×D4C2×D11semidirect
248. C4⋊C8C2×D11semidirect
250. #103C2×D11semidirect
324. C11#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
C2×#669642
#106232052
#106230772
C11×#4632
#106227782
#106227632
#106226672
#106226282
#106224612
#106224522
#106224162
#106224112
D11×#1022
#106223752
#304511