Finite Group Databasebeta

← #13080156

Subgroups — #13080156

Order 1408.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#135C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623360C211yesmaximal, characteristic, complemented
4C2×#66967C211yesmaximal, characteristic, complemented
5#10622851C211yesmaximal, characteristic, complemented
6#10622851C211yesmaximal, characteristic, complemented
7#10622800C211yesmaximal, characteristic, complemented
8#10622798C211yesmaximal, characteristic, complemented
9#10622789C211yesmaximal, characteristic, complemented
10#10622787C211yesmaximal, characteristic, complemented
11#10622777C211yesmaximal, characteristic, complemented
12#10622769C211yesmaximal, characteristic, complemented
13#10622763C211yesmaximal, characteristic, complemented
14#10622728C211yesmaximal, characteristic, complemented
15#10622724C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic, complemented
18C2×#4343C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C11×#135—24no—
21C2×C11×Q16C2211yescharacteristic, complemented
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic, complemented
24C2×C11×D8C2211yescharacteristic
25C22×C8×C11C2211yescharacteristic, complemented
26#67000C2211yescharacteristic
27#66999C2211yescharacteristic
28Q8×Dic11C2211yescharacteristic, complemented
29C2×#4325C2211yescharacteristic
30C2×#4325C2211yescharacteristic, complemented
31#66993—21no—
32#66993C2211yescharacteristic, complemented
33#66992—21no—
34#66991—21no—
35#66991C2211yescharacteristic
36#66990—21no—
37D4×Dic11C2211yescharacteristic
38C2×#4323C2211yescharacteristic
39C2×#4323C2211yescharacteristic
40#66983—21no—
41#66983C2211yescharacteristic
42#66983C2211yescharacteristic, complemented
43#66982—21no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11C2211yescharacteristic
46C2×(C2×D11)⋊C4—21no—
47#66967—24no—
48C2×D88C2211yescharacteristic
49C2×#4313C2211yescharacteristic
50#66899C2211yescharacteristic, complemented
51#66899C2211yescharacteristic, complemented
52#66896C2211yescharacteristic
53#66896C2211yescharacteristic, complemented
54C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55#66885C2211yescharacteristic
56#66885C2211yescharacteristic, complemented
57(C2×D11)⋊C8C2211yescharacteristic
58#66882C2211yescharacteristic, complemented
59#66879C2211yescharacteristic, complemented
60Dic11⋊C8C2211yescharacteristic, complemented
61C23×D11—21no—
62C11×#41—22no—
63C11×#41—22no—
64C11×#41—41no—
65C11×#41—41no—
66C2×Q8×C11C2311yescharacteristic
67C2×Q8×C11C2311yescharacteristic
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11C2311yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C2×C22⋊D11—21no—
81C2×C22⋊D11D411yescharacteristic
82C22×Dic11—21no—
83#4343—22no—
84#4343—41no—
85D4×D11—22no—
86D4×D11—41no—
87C2×D44—21no—
88C2×D44C2311yescharacteristic
89C2×D44C2311yescharacteristic
90C2×C4×D11—21no—
91C2×C4×D11C2311yescharacteristic
92C11×Q16—22no—
93C11×SD16—22no—
94C11×SD16D414yescomplemented
95C11×D8—22no—
96C2×C8×C11—22no—
97C2×C8×C11C2311yescharacteristic
98C2×C8×C11C2311yescharacteristic
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11D411yescharacteristic
102#4325—22no—
103#4325—41no—
104#4323—22no—
105#4323—41no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4D411yescharacteristic
112C4⋊Dic11—21no—
113C4⋊Dic11C2311yescharacteristic
114C4⋊Dic11C2311yescharacteristic
115Dic11⋊C4—21no—
116Dic11⋊C4D411yescharacteristic
117C4×Dic11—21no—
118C4×Dic11C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121D88—22no—
122#4313—22no—
123#3268—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×D411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—81no—
132C22×D11C2×D411yescharacteristic
133Q8×C11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136Q8×C11C2×D412yes—
137D4×C11—21no—
138D4×C11—21no—
139D4×C11—21no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11C2×D412yes—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11C2×D411yescharacteristic
150C2×C4×C11C2411yescharacteristic
151C22⋊D11—41no—
152C22⋊D11—42no—
153C22⋊D11—42no—
154C22⋊D11—81no—
155C22⋊D11—81no—
156C22⋊D11—81no—
157C22⋊D11—81no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—81no—
161C2×Dic11C2×D411yescharacteristic
162C2×Dic11C2×D411yescharacteristic
163C2×Dic11C2×D411yescharacteristic
164D44—21no—
165D44—21no—
166D44—21no—
167D44—21no—
168D44—42no—
169C4×D11—21no—
170C4×D11—21no—
171C4×D11—42no—
172C8×C11—21no—
173C8×C11C2×D412yes—
174C11⋊C8—21no—
175C11⋊C8—21no—
176C2×AGL(1,ℤ/8)—111no—
177C2×#135D1111yescharacteristic, complemented
178#550—111no—
179#546—111no—
180#496—111no—
181#468—111no—
182#466—111no—
183#464—111no—
184#459—111no—
185#452—111no—
186#449—111no—
187#449—111no—
188#447—111no—
189#440—111no—
190#435—111no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11C22×D411yescharacteristic
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—84no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—41no—
214C4×C11C22×D411yescharacteristic
215C4×C11H(5,𝔽2)11yescharacteristic
216Dic11—21no—
217Dic11—21no—
218Dic11—21no—
219Dic11—41no—
220Dic11—41no—
221C2×#41—111no—
222C2×#41C2×D1111yescharacteristic
223C2×#41C2×D1111yescharacteristic, complemented
224C22×D4—111no—
225AGL(1,ℤ/8)—224no—
226#135—24no—
227C2×Q16C2×D1111yescharacteristic, complemented
228C2×SD16—111no—
229C2×SD16—111no—
230C2×SD16C2×D1111yescharacteristic
231C2×SD16C2×D1111yescharacteristic, complemented
232C2×D8—111no—
233C2×D8—111no—
234C2×D8—111no—
235C2×D8C2×D1111yescharacteristic
236C2×M16—111no—
237C22×C8C2×D1111yescharacteristic, complemented
238#127—111no—
239#127—221no—
240#124—111no—
241#123—221no—
242C22⋊Q8—111no—
243#121—111no—
244#121—111no—
245#121—111no—
246#121—221no—
247#121—221no—
248#121—221no—
249#120—221no—
250C4×Q8—111no—
251C4×D4—111no—
252C4×D4—111no—
253C4×D4—221no—
254C2×C22⋊C4—221no—
255#107—111no—
256C4⋊C8—111no—
257#103—111no—
258#103—111no—
259#102—111no—
260#102—111no—
261#102—111no—
262#102—111no—
263C22⋊C8—111no—
264C22⋊C8—111no—
265#97—111no—
266C2×C11—42no—
267C2×C11—41no—
268C2×C11—81no—
269C2×C11D4211yescharacteristic
270C2×C11#57511yescharacteristic
271C2×C11#57611yescharacteristic
272D11—41no—
273D11—81no—
274D11—81no—
275C24—221no—
276#41—22no—
277#41—22no—
278#41—41no—
279#41—41no—
280#41—222no—
281#41—441no—
282C2×Q8C22×D1111yescharacteristic
283C2×Q8C22×D1111yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—111no—
287C2×D4—111no—
288C2×D4—111no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—222no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C2×D4C22×D1111yescharacteristic
299C2×D4C22×D1111yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4C22×D1111yescharacteristic
306Q16—22no—
307SD16—22no—
308SD16—222no—
309SD16—441no—
310SD16C22⋊D1114yescomplemented
311D8—22no—
312D8—222no—
313D8—222no—
314D8—441no—
315M16—222no—
316C2×C8—22no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8C22×D1111yescharacteristic
320C2×C8C22×D1111yescharacteristic
321C4⋊C4—111no—
322C4⋊C4—111no—
323C4⋊C4—111no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C22⋊C4—111no—
327C22⋊C4—111no—
328C22⋊C4—221no—
329C22⋊C4—221no—
330C22⋊C4—221no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C42—111no—
336C42—221no—
337C11#326811yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—111no—
341C23—221no—
342C23—221no—
343C23—442no—
344C23—442no—
345C23—881no—
346C23D4×D1111yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×C22⋊D1112yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—42no—
356D4—221no—
357D4—221no—
358D4—221no—
359D4—221no—
360D4—442no—
361D4—441no—
362D4—442no—
363D4—442no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368D4C2×C22⋊D1112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—111no—
376C2×C4—111no—
377C2×C4—111no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—442no—
383C2×C4—881no—
384C2×C4D4×D1111yescharacteristic
385C2×C4C23×D1111yescharacteristic
386C8—21no—
387C8—221no—
388C8—221no—
389C8C2×C22⋊D1112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—221no—
400C22—221no—
401C22—221no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—884no—
409C22C2×D4×D1111yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—221no—
414C4—221no—
415C4—221no—
416C4—441no—
417C4—441no—
418C4#6703711yescharacteristic
419C4C22×C22⋊D1111yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—441no—
424C2—881no—
425C2—881no—
426C2#1062329911yescharacteristic
427C2#1062330011yescharacteristic
428C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#135C2
socleC22×C11C22×D4
hypercenterC2×#135D11
hypocenterC11#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C11×#135C2semidirect
2. #10623365C2semidirect
3. #10623360C2semidirect
4. C2×#66967C2semidirect
5. #10622851C2semidirect
6. #10622851C2semidirect
7. #10622800C2semidirect
8. #10622798C2semidirect
9. #10622789C2semidirect
10. #10622787C2semidirect
11. #10622777C2semidirect
12. #10622769C2semidirect
13. #10622763C2semidirect
14. #10622728C2semidirect
15. #10622724C2semidirect
17. C2×C11×#41C22semidirect
21. C2×C11×Q16C22semidirect
23. C2×C11×SD16C22semidirect
25. C22×C8×C11C22semidirect
28. Q8×Dic11C22semidirect
30. C2×#4325C22semidirect
32. #66993C22semidirect
42. #66983C22semidirect
50. #66899C22semidirect
51. #66899C22semidirect
53. #66896C22semidirect
54. C22⋊(C11⋊C8)C22semidirect
56. #66885C22semidirect
58. #66882C22semidirect
59. #66879C22semidirect
60. Dic11⋊C8C22semidirect
94. C11×SD16D4semidirect
177. C2×#135D11semidirect
223. C2×#41C2×D11semidirect
227. C2×Q16C2×D11semidirect
231. C2×SD16C2×D11semidirect
237. C22×C8C2×D11semidirect
310. SD16C22⋊D11semidirect
337. C11#3268semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1352
#106233652
#106233602
C2×#669672
#106228512
#106228002
#106227982
#106227892
#106227872
#106227772
#106227692
#106227632
#106227282
#106227242
#326811