Finite Group Databasebeta

← #13080326

Subgroups — #13080326

Order 1408.

504 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
1#10623362C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic, complemented
3C2×SD16×D11C211yesmaximal, characteristic, complemented
4#10623143C211yesmaximal, characteristic, complemented
5C11×#449C211yesmaximal, characteristic, complemented
6#10622779C211yesmaximal, characteristic, complemented
7#10622769C211yesmaximal, characteristic, complemented
8#10622768C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622421C211yesmaximal, characteristic, complemented
11#10622401C211yesmaximal, characteristic, complemented
12#10622400C211yesmaximal, characteristic, complemented
13#10622391C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C2×Q8×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×#4339C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C2×C11×D8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23#67003—24no—
24Q8×Dic11C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic
27#66991—21no—
28#66991—21no—
29#66991C2211yescharacteristic
30#66990—21no—
31#66989—21no—
32#66989C2211yescharacteristic
33#66989C2211yescharacteristic, complemented
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic, complemented
36C2×#4323C2211yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11C2211yescharacteristic
39#66977—21no—
40#66977C2211yescharacteristic, complemented
41C22×C11⋊C8C2211yescharacteristic, complemented
42SD16×D11—24no—
43C2×Dic44C2211yescharacteristic, complemented
44C2×#4314C2211yescharacteristic
45C2×C8×D11C2211yescharacteristic
46#66950C2211yescharacteristic
47#66946C2211yescharacteristic
48#66936—21no—
49C22⋊C4×D11—21no—
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic, complemented
52C11×C22⋊C8C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54#66885C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56#66880C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66874C2211yescharacteristic, complemented
60#66872C2211yescharacteristic, complemented
61C23×D11—21no—
62C11×#41—22no—
63C11×#41—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11C2311yescharacteristic
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11C2311yescharacteristic
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11D411yescharacteristic
75Q8×D11—22no—
76Q8×D11—41no—
77D4×D11—22no—
78D4×D11—41no—
79#4339—22no—
80#4339—41no—
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×Dic22—21no—
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×SD16—22no—
90C11×D8—41no—
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11D411yescharacteristic
102#4326—22no—
103#4325D414yescomplemented
104#4324—22no—
105#4324—22no—
106#4323—22no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11C2311yescharacteristic
113Dic11⋊C4—21no—
114Dic11⋊C4D411yescharacteristic
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117C2×C11⋊C8—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120Dic44—41no—
121#4314—22no—
122C8×D11—22no—
123#3282—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×D411yescharacteristic
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11C2×D412yes—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—42no—
139D4×C11—81no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—42no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—22no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—42no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11C2×D411yescharacteristic
155C2×Dic11C2×D411yescharacteristic
156C2×Dic11C2×D411yescharacteristic
157D44—21no—
158D44C2×D412yes—
159C4×D11—21no—
160C4×D11—21no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11—81no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—21no—
168Dic22—42no—
169C8×C11—21no—
170C8×C11—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#135—111no—
174C22×SD16—111no—
175#548—111no—
176#546—111no—
177#495—111no—
178#465—111no—
179#465—111no—
180#464—111no—
181#463—111no—
182#452—111no—
183#451—111no—
184#449D1111yescharacteristic, complemented
185#447—111no—
186C4×SD16—111no—
187C8×D4—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—84no—
204C2×D11#13512yescomplemented
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—41no—
208C4×C11C22×D411yescharacteristic
209C4×C11H(5,𝔽2)11yescharacteristic
210Dic11—21no—
211Dic11—21no—
212Dic11—21no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic, complemented
218C22×Q8—111no—
219C22×D4—111no—
220#135—224no—
221C2×Q16—111no—
222C2×Q16—111no—
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—224no—
228C2×SD16C2×D1111yescharacteristic
229C2×D8—111no—
230C2×D8C2×D1111yescharacteristic
231C22×C8—111no—
232C22×C8—111no—
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—221no—
242#121—221no—
243#121C2×D1111yescharacteristic
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#103C2×D1111yescharacteristic, complemented
255#102—111no—
256#102—111no—
257#102C2×D1111yescharacteristic, complemented
258C22⋊C8—111no—
259C22⋊C8C2×D1111yescharacteristic, complemented
260C4×C8—111no—
261C2×C11—41no—
262C2×C11—81no—
263C2×C11—81no—
264C2×C11D4211yescharacteristic
265C2×C11C2×#13511yescharacteristic
266C2×C11#57711yescharacteristic
267D11—22no—
268D11—42no—
269C24—221no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—111no—
276C2×Q8—221no—
277C2×Q8—222no—
278C2×Q8—441no—
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—222no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—222no—
298Q16—441no—
299SD16—22no—
300SD16—114no—
301SD16—222no—
302SD16—222no—
303SD16—222no—
304D8—41no—
305D8—222no—
306C2×C8—111no—
307C2×C8—111no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—111no—
313C4⋊C4—111no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4C22×D1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—111no—
320C22⋊C4—111no—
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#328211yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—111no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—881no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—221no—
342Q8—221no—
343Q8—221no—
344Q8—221no—
345Q8—442no—
346Q8D4×D1112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—112no—
354D4—222no—
355D4—221no—
356D4—442no—
357D4—442no—
358D4—442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—881no—
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—21no—
379C8—112no—
380C8—221no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—112no—
391C22—221no—
392C22—221no—
393C22—222no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—221no—
402C4—221no—
403C4—221no—
404C4—441no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—222no—
413C2—442no—
414C2#1062312111yescharacteristic
415C2D11×#13511yescharacteristic
416C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623362C2semidirect
2. C2×#67003C2semidirect
3. C2×SD16×D11C2semidirect
4. #10623143C2semidirect
5. C11×#449C2semidirect
6. #10622779C2semidirect
7. #10622769C2semidirect
8. #10622768C2semidirect
9. #10622654C2semidirect
10. #10622421C2semidirect
11. #10622401C2semidirect
12. #10622400C2semidirect
13. #10622391C2semidirect
14. #10622346C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
16. C2×C11×#41C22semidirect
24. Q8×Dic11C22semidirect
25. C2×#4326C22semidirect
33. #66989C22semidirect
35. C2×#4324C22semidirect
40. #66977C22semidirect
41. C22×C11⋊C8C22semidirect
43. C2×Dic44C22semidirect
50. C11×#103C22semidirect
51. C11×#102C22semidirect
52. C11×C22⋊C8C22semidirect
56. #66880C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
59. #66874C22semidirect
60. #66872C22semidirect
103. #4325D4semidirect
184. #449D11semidirect
204. C2×D11#135semidirect
217. C2×#41C2×D11semidirect
254. #103C2×D11semidirect
257. #102C2×D11semidirect
259. C22⋊C8C2×D11semidirect
331. C11#3282semidirect

Maximal subgroups

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

subgroupindex
#106233622
C2×#670032
C2×SD16×D112
#106231432
C11×#4492
#106227792
#106227692
#106227682
#106226542
#106224212
#106224012
#106224002
#106223912
#106223462
(C22⋊D11)⋊C82
#328211