Finite Group Databasebeta

← #13080408

Subgroups — #13080408

Order 1408.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623309C211yesmaximal, characteristic, complemented
2#10623306C211yesmaximal, characteristic, complemented
3#10623293C211yesmaximal, characteristic, complemented
4#10623282C211yesmaximal, characteristic, complemented
5C11×#471C211yesmaximal, characteristic, complemented
6#10622818C211yesmaximal, characteristic, complemented
7#10622811C211yesmaximal, characteristic, complemented
8#10622788C211yesmaximal, characteristic, complemented
9#10622757C211yesmaximal, characteristic, complemented
10#10622511C211yesmaximal, characteristic, complemented
11#10622508C211yesmaximal, characteristic, complemented
12#10622367C211yesmaximal, characteristic, complemented
13#10622365C211yesmaximal, characteristic, complemented
14#10622361C211yesmaximal, characteristic, complemented
15#10622360C211yesmaximal, characteristic, complemented
16#67043C2211yescharacteristic
17#67042C2211yescharacteristic, complemented
18#67040C2211yescharacteristic
19#67037C2211yescharacteristic, complemented
20C11×#137C2211yescharacteristic, complemented
21C11×AGL(1,ℤ/8)C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic, complemented
23C11×#131C2211yescharacteristic, complemented
24#67003C2211yescharacteristic
25#66997C2211yescharacteristic, complemented
26#66995C2211yescharacteristic, complemented
27C2×#4325C2211yescharacteristic, complemented
28#66993C2211yescharacteristic
29C2×#4324C2211yescharacteristic, complemented
30#66985C2211yescharacteristic
31#66972—21no—
32#66971—21no—
33#66969—21no—
34#66968—21no—
35#66968—21no—
36#66967—21no—
37#66967—21no—
38SD16×D11—21no—
39SD16×D11—21no—
40SD16×D11—21no—
41#66965—21no—
42#66964—21no—
43#66962—21no—
44#66962C2211yescharacteristic, complemented
45#66962C2211yescharacteristic, complemented
46#66961—21no—
47#66961C2211yescharacteristic
48#66961C2211yescharacteristic
49#66960C2211yescharacteristic, complemented
50#66960C2211yescharacteristic, complemented
51#66957—21no—
52#66957C2211yescharacteristic
53C2×#4314—21no—
54C2×#4314C2211yescharacteristic, complemented
55#66954C2211yescharacteristic, complemented
56C11×#108C2211yescharacteristic, complemented
57C11×#101C2211yescharacteristic, complemented
58C11×#100C2211yescharacteristic, complemented
59#66901C2211yescharacteristic, complemented
60#66889C2211yescharacteristic, complemented
61#66889C2211yescharacteristic, complemented
62#66889C2211yescharacteristic, complemented
63#66888C2211yescharacteristic, complemented
64#66887C2211yescharacteristic, complemented
65#66886C2211yescharacteristic, complemented
66C8×Dic11C2211yescharacteristic, complemented
67C11×#41C2311yescharacteristic
68C2×Q8×C11C2311yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72#4343—21no—
73#4343—21no—
74#4343—21no—
75Q8×D11—21no—
76Q8×D11—21no—
77Q8×D11—21no—
78#4341—21no—
79#4341—21no—
80#4341—21no—
81#4341—41no—
82D4×D11—21no—
83D4×D11—21no—
84D4×D11—21no—
85D4×D11—41no—
86#4339—21no—
87#4339—21no—
88#4339—41no—
89#4339C2311yescharacteristic
90#4339C2311yescharacteristic
91#4339C2311yescharacteristic
92C2×D44—21no—
93C2×D44C2311yescharacteristic
94C2×Dic22—21no—
95C2×Dic22C2311yescharacteristic
96C11×Q16—21no—
97C11×SD16—21no—
98C11×SD16—21no—
99C11×SD16—21no—
100C11×SD16—21no—
101C11×D8—21no—
102C11×M16—21no—
103C11×M16C2311yescharacteristic
104C11×M16C2311yescharacteristic
105C11×M16C2311yescharacteristic
106C2×C8×C11—21no—
107C2×C8×C11C2311yescharacteristic
108#4326—21no—
109#4326D411yescharacteristic, complemented
110#4325—21no—
111#4325—21no—
112#4325—21no—
113#4325D411yescharacteristic, complemented
114#4324—21no—
115#4324—21no—
116#4324—21no—
117#4324D411yescharacteristic, complemented
118#4323—21no—
119#4323D411yescharacteristic, complemented
120Dic11⋊C4—41no—
121C4×Dic11C2311yescharacteristic
122#4318C2311yescharacteristic
123C2×C11⋊C8C2311yescharacteristic
124Dic44—21no—
125Dic44—21no—
126Dic44D411yescharacteristic, complemented
127D88—21no—
128D88—21no—
129D88D411yescharacteristic, complemented
130#4314—21no—
131#4314—21no—
132#4314—21no—
133#4314—21no—
134#4314—21no—
135#4314—21no—
136#4314D411yescharacteristic, complemented
137#4314D411yescharacteristic, complemented
138#4313—21no—
139#4313—21no—
140#4313—21no—
141C8×D11—21no—
142C8×D11—21no—
143C8×D11—21no—
144#3291—111nomaximal, Sylow
145C23×C11—21no—
146C22×D11—21no—
147C22×D11—41no—
148C22×D11—41no—
149Q8×C11—21no—
150Q8×C11—21no—
151Q8×C11C2×D411yescharacteristic
152D4×C11—21no—
153D4×C11—21no—
154D4×C11—21no—
155D4×C11C2×D411yescharacteristic
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11C2411yescharacteristic
159C22⋊D11—21no—
160C22⋊D11—21no—
161C22⋊D11—21no—
162C22⋊D11—41no—
163C22⋊D11—41no—
164C22⋊D11—41no—
165C22⋊D11—41no—
166C22⋊D11—82no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171D44—21no—
172D44—21no—
173D44—41no—
174D44—41no—
175D44C2×D411yescharacteristic
176D44C2×D411yescharacteristic
177D44C2×D411yescharacteristic
178C4×D11—21no—
179C4×D11—21no—
180C4×D11—21no—
181C4×D11—41no—
182C4×D11—41no—
183C4×D11—41no—
184C4×D11—41no—
185Dic22—21no—
186Dic22—21no—
187Dic22—41no—
188Dic22—41no—
189Dic22C2×D411yescharacteristic
190Dic22C2×D411yescharacteristic
191Dic22C2×D411yescharacteristic
192C8×C11—21no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11C2×D411yescharacteristic
196C8×C11C2×D411yescharacteristic
197C11⋊C8—21no—
198C11⋊C8C2×D411yescharacteristic
199C11⋊C8C2×D411yescharacteristic
200#577—111no—
201#577—111no—
202#577—111no—
203#577—111no—
204#492—111no—
205#471—111no—
206#471—111no—
207#471—111no—
208#471D1111yescharacteristic, complemented
209#456—111no—
210#456—111no—
211#453—111no—
212#453—111no—
213#443—111no—
214#443—111no—
215C22×C11—21no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11H(5,𝔽2)11yescharacteristic
219C2×D11—21no—
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—41no—
223C2×D11—81no—
224C2×D11—161no—
225C2×D11—161no—
226C4×C11—21no—
227C4×C11—41no—
228C4×C11C22×D411yescharacteristic
229C4×C11C22×D411yescharacteristic
230Dic11—22no—
231Dic11—21no—
232Dic11—21no—
233Dic11—21no—
234Dic11—41no—
2352−1+4—111no—
2362−1+4—111no—
237H(5,𝔽2)—111no—
238H(5,𝔽2)—111no—
239#137—111no—
240#137—111no—
241#137—111no—
242#137—221no—
243#137—221no—
244#137—221no—
245#137—221no—
246#137C2×D1111yescharacteristic, complemented
247AGL(1,ℤ/8)—111no—
248AGL(1,ℤ/8)—111no—
249AGL(1,ℤ/8)—111no—
250AGL(1,ℤ/8)—221no—
251AGL(1,ℤ/8)—221no—
252AGL(1,ℤ/8)—221no—
253AGL(1,ℤ/8)—221no—
254AGL(1,ℤ/8)C2×D1111yescharacteristic
255#135—111no—
256#135—111no—
257#135—221no—
258#135—221no—
259#135—221no—
260#135—221no—
261C2×SD16—111no—
262C2×SD16—111no—
263C2×SD16—111no—
264C2×SD16—221no—
265C2×SD16—221no—
266C2×SD16—221no—
267C2×SD16—221no—
268C2×SD16C2×D1111yescharacteristic, complemented
269#131—111no—
270#131—111no—
271#131—111no—
272#131C2×D1111yescharacteristic, complemented
273C4⋊Q8—111no—
274#127—111no—
275#108—111no—
276#108C2×D1111yescharacteristic, complemented
277#104—111no—
278#104—111no—
279#104—111no—
280#104—111no—
281#101—111no—
282#101C2×D1111yescharacteristic, complemented
283#100—111no—
284#100C2×D1111yescharacteristic, complemented
285C4×C8—111no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—81no—
289C2×C11D4211yescharacteristic
290D11—41no—
291D11—41no—
292D11—41no—
293D11—81no—
294#41—111no—
295#41—111no—
296#41—111no—
297#41—221no—
298#41—221no—
299#41—221no—
300#41—221no—
301#41—221no—
302#41—221no—
303#41—221no—
304#41—221no—
305#41—441no—
306#41—441no—
307#41C22×D1111yescharacteristic
308C2×Q8—111no—
309C2×Q8—221no—
310C2×Q8—221no—
311C2×Q8—221no—
312C2×Q8—221no—
313C2×Q8C22×D1111yescharacteristic
314C2×D4—111no—
315C2×D4—221no—
316C2×D4—221no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4C22×D1111yescharacteristic
323Q16—21no—
324Q16—111no—
325Q16—111no—
326Q16—221no—
327Q16—221no—
328Q16—221no—
329SD16—21no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—111no—
334SD16—111no—
335SD16—111no—
336SD16—111no—
337SD16—221no—
338SD16—221no—
339SD16—221no—
340SD16—221no—
341SD16—221no—
342SD16—221no—
343SD16—221no—
344SD16—221no—
345SD16—221no—
346SD16—221no—
347SD16—221no—
348SD16—221no—
349D8—21no—
350D8—111no—
351D8—111no—
352D8—221no—
353D8—221no—
354D8—221no—
355M16—21no—
356M16—111no—
357M16—221no—
358M16—221no—
359M16—221no—
360M16C22×D1111yescharacteristic
361M16C22×D1111yescharacteristic
362M16C22×D1111yescharacteristic
363C2×C8—21no—
364C2×C8—111no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8C22×D1111yescharacteristic
369C4⋊C4—441no—
370C42—111no—
371C11#329111yescharacteristic, complemented, Sylow
372C23—21no—
373C23—221no—
374C23—441no—
375C23—441no—
376Q8—21no—
377Q8—21no—
378Q8—111no—
379Q8—111no—
380Q8—111no—
381Q8—221no—
382Q8—221no—
383Q8—441no—
384Q8—441no—
385Q8D4×D1111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—111no—
390D4—111no—
391D4—111no—
392D4—221no—
393D4—221no—
394D4—221no—
395D4—221no—
396D4—221no—
397D4—441no—
398D4—441no—
399D4—441no—
400D4—441no—
401D4—441no—
402D4—441no—
403D4—882no—
404D4D4×D1111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4C23×D1111yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—111no—
423C8—111no—
424C8—221no—
425C8D4×D1111yescharacteristic
426C8D4×D1111yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—221no—
431C22—221no—
432C22—221no—
433C22—441no—
434C22—881no—
435C22—1761no—
436C22—1761no—
437C22#6704211yescharacteristic
438C4—21no—
439C4—41no—
440C4—222no—
441C4—221no—
442C4—221no—
443C4—221no—
444C4—441no—
445C4C2×D4×D1111yescharacteristic
446C4C2×D4×D1111yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—441no—
451C2—441no—
452C2—441no—
453C2—881no—
454C2#1062314011yescharacteristic
subgroupG/H
centerC2#10623140
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#471C2
socleC2×C11D42
hypercenter#471D11
hypocenterC11#3291
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #10623309C2semidirect
2. #10623306C2semidirect
3. #10623293C2semidirect
4. #10623282C2semidirect
5. C11×#471C2semidirect
6. #10622818C2semidirect
7. #10622811C2semidirect
8. #10622788C2semidirect
9. #10622757C2semidirect
10. #10622511C2semidirect
11. #10622508C2semidirect
12. #10622367C2semidirect
13. #10622365C2semidirect
14. #10622361C2semidirect
15. #10622360C2semidirect
17. #67042C22semidirect
19. #67037C22semidirect
20. C11×#137C22semidirect
22. C2×C11×SD16C22semidirect
23. C11×#131C22semidirect
25. #66997C22semidirect
26. #66995C22semidirect
27. C2×#4325C22semidirect
29. C2×#4324C22semidirect
44. #66962C22semidirect
45. #66962C22semidirect
49. #66960C22semidirect
50. #66960C22semidirect
54. C2×#4314C22semidirect
55. #66954C22semidirect
56. C11×#108C22semidirect
57. C11×#101C22semidirect
58. C11×#100C22semidirect
59. #66901C22semidirect
60. #66889C22semidirect
61. #66889C22semidirect
62. #66889C22semidirect
63. #66888C22semidirect
64. #66887C22semidirect
65. #66886C22semidirect
66. C8×Dic11C22semidirect
109. #4326D4semidirect
113. #4325D4semidirect
117. #4324D4semidirect
119. #4323D4semidirect
126. Dic44D4semidirect
129. D88D4semidirect
136. #4314D4semidirect
137. #4314D4semidirect
208. #471D11semidirect
246. #137C2×D11semidirect
268. C2×SD16C2×D11semidirect
272. #131C2×D11semidirect
276. #108C2×D11semidirect
282. #101C2×D11semidirect
284. #100C2×D11semidirect
371. C11#3291semidirect

Maximal subgroups

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

subgroupindex
#106233092
#106233062
#106232932
#106232822
C11×#4712
#106228182
#106228112
#106227882
#106227572
#106225112
#106225082
#106223672
#106223652
#106223612
#106223602
#329111