Finite Group Databasebeta

← #13080241

Subgroups — #13080241

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
1C2×C11×#137C211yesmaximal, characteristic, complemented
2#10623360C211yesmaximal, characteristic, complemented
3#10623348C211yesmaximal, characteristic, complemented
4C2×#66967C211yesmaximal, characteristic, complemented
5#10622851C211yesmaximal, characteristic, complemented
6#10622840C211yesmaximal, characteristic, complemented
7#10622804C211yesmaximal, characteristic, complemented
8#10622802C211yesmaximal, characteristic, complemented
9#10622800C211yesmaximal, characteristic, complemented
10#10622798C211yesmaximal, characteristic, complemented
11#10622782C211yesmaximal, characteristic, complemented
12#10622778C211yesmaximal, characteristic, complemented
13SD16×Dic11C211yesmaximal, characteristic, complemented
14#10622748C211yesmaximal, characteristic, complemented
15#10622741C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18C2×#4343C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C11×#137—24no—
21C2×C11×Q16C2211yescharacteristic, complemented
22C2×C11×Q16C2211yescharacteristic, complemented
23C2×C11×SD16C2211yescharacteristic
24C2×C11×SD16C2211yescharacteristic
25C2×C11×M16C2211yescharacteristic, complemented
26#67000—21no—
27#67000C2211yescharacteristic
28#67000C2211yescharacteristic, complemented
29#66999—21no—
30#66999C2211yescharacteristic
31#66999C2211yescharacteristic
32Q8×Dic11C2211yescharacteristic, complemented
33C2×#4325C2211yescharacteristic
34C2×#4325C2211yescharacteristic
35C2×#4325C2211yescharacteristic, complemented
36#66992—21no—
37#66990—21no—
38D4×Dic11C2211yescharacteristic
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#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55#66885C2211yescharacteristic
56#66885C2211yescharacteristic, complemented
57(C2×D11)⋊C8C2211yescharacteristic
58#66881C2211yescharacteristic, complemented
59Dic11⋊C8C2211yescharacteristic, complemented
60C8×Dic11C2211yescharacteristic, complemented
61C23×D11—21no—
62C11×#41—22no—
63C11×#41—41no—
64C2×Q8×C11—21no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11C2311yescharacteristic
68C2×Q8×C11C2311yescharacteristic
69C2×Q8×C11C2311yescharacteristic
70C2×D4×C11—21no—
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⋊D11D411yescharacteristic
79C22×Dic11—21no—
80#4343—22no—
81#4343—41no—
82D4×D11—22no—
83D4×D11—41no—
84C2×D44—21no—
85C2×D44C2311yescharacteristic
86C2×D44C2311yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11C2311yescharacteristic
89C11×Q16—22no—
90C11×Q16—22no—
91C11×SD16—22no—
92C11×SD16D414yescomplemented
93C11×M16—22no—
94C2×C8×C11C2311yescharacteristic
95C2×C8×C11C2311yescharacteristic
96C22⋊Dic11—21no—
97C22⋊Dic11D411yescharacteristic
98#4325—22no—
99#4325—41no—
100#4325—41no—
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)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4D411yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11C2311yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4D411yescharacteristic
117C4×Dic11—21no—
118C4×Dic11C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121D88—22no—
122#4313—22no—
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136Q8×C11—21no—
137Q8×C11—42no—
138Q8×C11C2×D412yes—
139D4×C11—21no—
140D4×C11—42no—
141D4×C11C2×D412yes—
142C2×C4×C11—21no—
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—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—81no—
158C2×Dic11C2×D411yescharacteristic
159C2×Dic11C2×D411yescharacteristic
160C2×Dic11C2×D411yescharacteristic
161D44—21no—
162D44—21no—
163D44—21no—
164D44—21no—
165D44—42no—
166C4×D11—21no—
167C4×D11—21no—
168C4×D11—42no—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#137D1111yescharacteristic, complemented
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#449—111no—
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×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—84no—
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11H(5,𝔽2)11yescharacteristic
211Dic11—21no—
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic
218C22×Q8C2×D1111yescharacteristic, complemented
219C22×D4—111no—
220#137—24no—
221AGL(1,ℤ/8)—224no—
222C2×Q16C2×D1111yescharacteristic, complemented
223C2×Q16C2×D1111yescharacteristic, complemented
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16C2×D1111yescharacteristic
228C2×SD16C2×D1111yescharacteristic
229C2×D8—111no—
230C2×D8—111no—
231C2×M16—111no—
232C2×M16C2×D1111yescharacteristic, complemented
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—111no—
242#121—221no—
243#121—221no—
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#103—111no—
255#102—111no—
256#102—111no—
257#102—111no—
258C22⋊C8—111no—
259C22⋊C8—111no—
260C4×C8—111no—
261C2×C11—42no—
262C2×C11—41no—
263C2×C11D4211yescharacteristic
264C2×C11#57511yescharacteristic
265C2×C11#57711yescharacteristic
266D11—41no—
267D11—81no—
268D11—81no—
269C24—221no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8C22×D1111yescharacteristic
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—222no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—111no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—22no—
298Q16—22no—
299SD16—22no—
300SD16—222no—
301SD16—441no—
302SD16—441no—
303SD16C22⋊D1114yescomplemented
304D8—222no—
305D8—222no—
306M16—22no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—111no—
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C22⋊C4—111no—
319C22⋊C4—111no—
320C22⋊C4—221no—
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—111no—
334C23—221no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—881no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D1112yes—
347D4—21no—
348D4—42no—
349D4—221no—
350D4—221no—
351D4—221no—
352D4—221no—
353D4—442no—
354D4—441no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4C2×C22⋊D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—111no—
367C2×C4—111no—
368C2×C4—111no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—442no—
374C2×C4—881no—
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—221no—
379C8—221no—
380C8C2×C22⋊D1112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—221no—
388C22—221no—
389C22—221no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—221no—
403C4—221no—
404C4—221no—
405C4—441no—
406C4—441no—
407C4#6703711yescharacteristic
408C4C22×C22⋊D1111yescharacteristic
409C2—41no—
410C2—42no—
411C2—441no—
412C2—881no—
413C2—881no—
414C2#1062330811yescharacteristic
415C2#1062330911yescharacteristic
416C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#137C2
socleC22×C11C22×D4
hypercenterC2×#137D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C11×#137C2semidirect
2. #10623360C2semidirect
3. #10623348C2semidirect
4. C2×#66967C2semidirect
5. #10622851C2semidirect
6. #10622840C2semidirect
7. #10622804C2semidirect
8. #10622802C2semidirect
9. #10622800C2semidirect
10. #10622798C2semidirect
11. #10622782C2semidirect
12. #10622778C2semidirect
13. SD16×Dic11C2semidirect
14. #10622748C2semidirect
15. #10622741C2semidirect
17. C22×Q8×C11C22semidirect
21. C2×C11×Q16C22semidirect
22. C2×C11×Q16C22semidirect
25. C2×C11×M16C22semidirect
28. #67000C22semidirect
32. Q8×Dic11C22semidirect
35. C2×#4325C22semidirect
42. #66983C22semidirect
50. #66899C22semidirect
51. #66899C22semidirect
52. #66899C22semidirect
54. C22⋊(C11⋊C8)C22semidirect
56. #66885C22semidirect
58. #66881C22semidirect
59. Dic11⋊C8C22semidirect
60. C8×Dic11C22semidirect
92. C11×SD16D4semidirect
173. C2×#137D11semidirect
218. C22×Q8C2×D11semidirect
222. C2×Q16C2×D11semidirect
223. C2×Q16C2×D11semidirect
232. C2×M16C2×D11semidirect
303. SD16C22⋊D11semidirect
331. C11#3275semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1372
#106233602
#106233482
C2×#669672
#106228512
#106228402
#106228042
#106228022
#106228002
#106227982
#106227822
#106227782
SD16×Dic112
#106227482
#106227412
#327511