Finite Group Databasebeta

← #13080330

Subgroups — #13080330

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
1C2×SD16×D11C211yesmaximal, characteristic, complemented
2C2×#66957C211yesmaximal, characteristic, complemented
3#10623164C211yesmaximal, characteristic, complemented
4#10623143C211yesmaximal, characteristic, complemented
5C11×#465C211yesmaximal, characteristic, complemented
6#10622781C211yesmaximal, characteristic, complemented
7C8×C22⋊D11C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622650C211yesmaximal, characteristic, complemented
10#10622477C211yesmaximal, characteristic, complemented
11#10622465C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622421C211yesmaximal, characteristic, complemented
14#10622386C211yesmaximal, characteristic, complemented
15#10622380C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×#4339C2211yescharacteristic, complemented
20C2×C11×SD16C2211yescharacteristic
21C22×C8×C11C2211yescharacteristic, complemented
22C11×C22⋊Q8C2211yescharacteristic, complemented
23C11×#121C2211yescharacteristic
24#67000C2211yescharacteristic, complemented
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic
27#66991—21no—
28#66990—21no—
29#66989C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4323C2211yescharacteristic
32C4×C22⋊D11C2211yescharacteristic
33SD16×D11—24no—
34C2×Dic44C2211yescharacteristic, complemented
35#66957—24no—
36C2×D88C2211yescharacteristic
37C2×#4314C2211yescharacteristic
38C2×#4314C2211yescharacteristic, complemented
39C2×C8×D11C2211yescharacteristic
40#66950C2211yescharacteristic
41#66949—21no—
42#66948C2211yescharacteristic
43#66946—21no—
44#66946C2211yescharacteristic
45#66940C2211yescharacteristic, complemented
46#66938—21no—
47#66937—21no—
48#66936—21no—
49C22⋊C4×D11—21no—
50C11×#106C2211yescharacteristic, complemented
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic
53C22⋊(C11⋊C8)C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66874C2211yescharacteristic, complemented
59#66873C2211yescharacteristic
60#66873C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70Q8×D11—22no—
71Q8×D11—41no—
72D4×D11—22no—
73D4×D11—41no—
74#4339—22no—
75#4339—22no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44C2311yescharacteristic
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
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—
90C2×C8×C11—22no—
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4C2311yescharacteristic
95C11×C4⋊C4C2311yescharacteristic
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11D411yescharacteristic
101#4326—41no—
102#4325—22no—
103#4324—22no—
104#4323—41no—
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—
112Dic11⋊C4—21no—
113Dic11⋊C4D411yescharacteristic
114C4×Dic11—21no—
115C4×Dic11C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117C2×C11⋊C8C2311yescharacteristic
118Dic44—22no—
119D88—22no—
120#4314—22no—
121#4314D414yescomplemented
122C8×D11—22no—
123#3282—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—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2411yescharacteristic
144C22⋊D11—22no—
145C22⋊D11—42no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152C2×Dic11C2×D411yescharacteristic
153D44—21no—
154D44—21no—
155D44—21no—
156D44—42no—
157D44C2×D412yes—
158C4×D11—21no—
159C4×D11—21no—
160C4×D11—42no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11—81no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#135—111no—
174C22×SD16—111no—
175#548—111no—
176#546—111no—
177#495—111no—
178#465—111no—
179#465D1111yescharacteristic, complemented
180#464—111no—
181#463—111no—
182#452—111no—
183#451—111no—
184#449—111no—
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×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—22no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—84no—
204C2×D11#13512yescomplemented
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11H(5,𝔽2)11yescharacteristic
211Dic11—22no—
212Dic11—21no—
213Dic11—21no—
214Dic11—21no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41—111no—
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×D8—111no—
231C22×C8—111no—
232C22×C8C2×D1111yescharacteristic, complemented
233#124—111no—
234#124—111no—
235#124—221no—
236#123—221no—
237C22⋊Q8—111no—
238C22⋊Q8—221no—
239C22⋊Q8C2×D1111yescharacteristic, complemented
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#106C2×D1111yescharacteristic, complemented
251C4⋊C8—111no—
252#103—111no—
253#103—111no—
254#103C2×D1111yescharacteristic, complemented
255#102—111no—
256#102—111no—
257#102C2×D1111yescharacteristic
258C22⋊C8—111no—
259C22⋊C8—111no—
260C4×C8—111no—
261C2×C11—41no—
262C2×C11—81no—
263C2×C11D4211yescharacteristic
264C2×C11C2×#13511yescharacteristic
265C2×C11#57711yescharacteristic
266D11—22no—
267D11—42no—
268D11—81no—
269C24—221no—
270#41—222no—
271#41—222no—
272#41—441no—
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—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—111no—
292C22×C4—221no—
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—222no—
305D8—441no—
306C2×C8—22no—
307C2×C8—111no—
308C2×C8—111no—
309C2×C8—222no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—111no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4C22×D1111yescharacteristic
317C4⋊C4C22×D1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—111no—
321C22⋊C4—111no—
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—111no—
334C23—221no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—881no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—112no—
343Q8—221no—
344Q8—221no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—112no—
351D4—222no—
352D4—221no—
353D4—221no—
354D4—221no—
355D4—442no—
356D4—442no—
357D4—442no—
358D4—442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
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—221no—
379C8—221no—
380C8D4×D1112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—112no—
388C22—221no—
389C22—221no—
390C22—222no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—221no—
403C4—221no—
404C4—221no—
405C4—222no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6704211yescharacteristic
409C2—41no—
410C2—81no—
411C2—222no—
412C2—442no—
413C2—881no—
414C2#1062314011yescharacteristic
415C2#1062329311yescharacteristic
416C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
hypercenter#465D11
hypocenterC11#3282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D11C2semidirect
2. C2×#66957C2semidirect
3. #10623164C2semidirect
4. #10623143C2semidirect
5. C11×#465C2semidirect
6. #10622781C2semidirect
7. C8×C22⋊D11C2semidirect
8. #10622660C2semidirect
9. #10622650C2semidirect
10. #10622477C2semidirect
11. #10622465C2semidirect
12. #10622432C2semidirect
13. #10622421C2semidirect
14. #10622386C2semidirect
15. #10622380C2semidirect
19. C2×#4339C22semidirect
21. C22×C8×C11C22semidirect
22. C11×C22⋊Q8C22semidirect
24. #67000C22semidirect
25. C2×#4326C22semidirect
34. C2×Dic44C22semidirect
38. C2×#4314C22semidirect
45. #66940C22semidirect
50. C11×#106C22semidirect
51. C11×#103C22semidirect
53. C22⋊(C11⋊C8)C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
57. #66874C22semidirect
58. #66874C22semidirect
60. #66873C22semidirect
121. #4314D4semidirect
179. #465D11semidirect
204. C2×D11#135semidirect
232. C22×C8C2×D11semidirect
239. C22⋊Q8C2×D11semidirect
250. #106C2×D11semidirect
254. #103C2×D11semidirect
331. C11#3282semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D112
C2×#669572
#106231642
#106231432
C11×#4652
#106227812
C8×C22⋊D112
#106226602
#106226502
#106224772
#106224652
#106224322
#106224212
#106223862
#106223802
#328211