Finite Group Databasebeta

← #13080327

Subgroups — #13080327

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#10623337C211yesmaximal, characteristic, complemented
2C22×#4324C211yesmaximal, characteristic, complemented
3C2×#66965C211yesmaximal, characteristic, complemented
4#10623129C211yesmaximal, characteristic, complemented
5C11×#447C211yesmaximal, characteristic, complemented
6#10622771C211yesmaximal, characteristic, complemented
7#10622768C211yesmaximal, characteristic, complemented
8#10622766C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622396C211yesmaximal, characteristic, complemented
11#10622391C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×#4341C2211yescharacteristic, complemented
19C22×Dic22C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C2×C11×D8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23#67006—21no—
24C2×C22⋊Dic11—21no—
25#66992—21no—
26#66992—21no—
27#66991C2211yescharacteristic
28#66989C2211yescharacteristic
29#66989C2211yescharacteristic, complemented
30#66988—21no—
31D4×Dic11—21no—
32D4×Dic11C2211yescharacteristic
33C2×#4324—24no—
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4324C2211yescharacteristic
37C2×#4324C2211yescharacteristic
38C2×#4324C2211yescharacteristic, complemented
39C4×C22⋊D11C2211yescharacteristic
40#66977C2211yescharacteristic
41C22×C11⋊C8C2211yescharacteristic
42#66965—24no—
43C2×Dic44C2211yescharacteristic, complemented
44C2×Dic44C2211yescharacteristic, complemented
45C2×C8×D11C2211yescharacteristic, complemented
46#66950C2211yescharacteristic, complemented
47#66940C2211yescharacteristic, complemented
48#66938—21no—
49#66931—21no—
50C11×#102C2211yescharacteristic
51C11×#102C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic
53#66896C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66874C2211yescharacteristic, complemented
60#66872C2211yescharacteristic, complemented
61C24×C11—21no—
62C2×D4×C11—22no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—41no—
66C2×D4×C11C2311yescharacteristic
67C2×D4×C11C2311yescharacteristic
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78#4341—22no—
79#4341—22no—
80#4341—41no—
81#4341—41no—
82C2×C4×D11C2311yescharacteristic
83C2×Dic22—22no—
84C2×Dic22—21no—
85C2×Dic22—41no—
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×D8—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⋊Dic11—21no—
102C22⋊Dic11D411yescharacteristic
103#4324—22no—
104#4324—22no—
105#4324—22no—
106#4324—22no—
107#4324D414yescomplemented
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11C2311yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4D411yescharacteristic
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117C2×C11⋊C8—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120Dic44—22no—
121Dic44—41no—
122C8×D11—22no—
123#3282—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11C2×D411yescharacteristic
131C22×D11C2×D411yescharacteristic
132D4×C11—21no—
133D4×C11—21no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11C2×D412yes—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C22⋊D11—22no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C22⋊D11—81no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—81no—
157C2×Dic11C2×D411yescharacteristic
158C2×Dic11C2×D411yescharacteristic
159C2×Dic11C2×D411yescharacteristic
160C4×D11—21no—
161C4×D11—21no—
162Dic22—21no—
163Dic22—21no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
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#449—111no—
185#447D1111yescharacteristic, complemented
186C4×SD16—111no—
187C8×D4—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—22no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—84no—
200C22×C11#13512yescomplemented
201C22×C11C22×D411yescharacteristic
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—21no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11C22×D411yescharacteristic
208C4×C11H(5,𝔽2)11yescharacteristic
209Dic11—22no—
210Dic11—21no—
211Dic11—21no—
212Dic11—21no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41—111no—
218C22×Q8—111no—
219C22×D4C2×D1111yescharacteristic
220#135—224no—
221C2×Q16—111no—
222C2×Q16—111no—
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—111no—
228C2×SD16—224no—
229C2×D8C2×D1111yescharacteristic
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#103—111no—
255#102—111no—
256#102C2×D1111yescharacteristic
257#102C2×D1111yescharacteristic
258C22⋊C8—111no—
259C22⋊C8C2×D1111yescharacteristic
260C4×C8—111no—
261C2×C11—22no—
262C2×C11—42no—
263C2×C11—81no—
264C2×C11—81no—
265C2×C11D4211yescharacteristic
266C2×C11C2×#13511yescharacteristic
267C2×C11#57711yescharacteristic
268D11—41no—
269C24—21no—
270#41—222no—
271#41—222no—
272#41—441no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—111no—
276C2×Q8—111no—
277C2×Q8—222no—
278C2×Q8—221no—
279C2×Q8—441no—
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—111no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4C22×D1111yescharacteristic
289C2×D4C22×D1111yescharacteristic
290C2×D4C22×D1111yescharacteristic
291C22×C4—111no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—222no—
298Q16—441no—
299SD16—114no—
300SD16—222no—
301SD16—222no—
302SD16—222no—
303SD16—222no—
304D8—22no—
305D8—41no—
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—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—111no—
339C23D4×D1111yescharacteristic
340Q8—112no—
341Q8—221no—
342Q8—221no—
343Q8—221no—
344Q8—221no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—222no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4D4×D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—111no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—442no—
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—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—84no—
393C22—221no—
394C22—221no—
395C22—221no—
396C22#6696512yescomplemented
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—41no—
400C4—221no—
401C4—221no—
402C4—221no—
403C4—222no—
404C4—441no—
405C4—441no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—441no—
414C2#1062312111yescharacteristic
415C2C2×#6696511yescharacteristic
416C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10623337C2semidirect
2. C22×#4324C2semidirect
3. C2×#66965C2semidirect
4. #10623129C2semidirect
5. C11×#447C2semidirect
6. #10622771C2semidirect
7. #10622768C2semidirect
8. #10622766C2semidirect
9. #10622654C2semidirect
10. #10622396C2semidirect
11. #10622391C2semidirect
12. #10622380C2semidirect
13. #10622371C2semidirect
14. #10622352C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
18. C2×#4341C22semidirect
29. #66989C22semidirect
38. C2×#4324C22semidirect
43. C2×Dic44C22semidirect
44. C2×Dic44C22semidirect
45. C2×C8×D11C22semidirect
46. #66950C22semidirect
47. #66940C22semidirect
53. #66896C22semidirect
54. (C2×D11)⋊C8C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
59. #66874C22semidirect
60. #66872C22semidirect
107. #4324D4semidirect
185. #447D11semidirect
200. C22×C11#135semidirect
331. C11#3282semidirect
396. C22#66965semidirect

Maximal subgroups

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

subgroupindex
#106233372
C22×#43242
C2×#669652
#106231292
C11×#4472
#106227712
#106227682
#106227662
#106226542
#106223962
#106223912
#106223802
#106223712
#106223522
(C22⋊D11)⋊C82
#328211