Finite Group Databasebeta

← #13080249

Subgroups — #13080249

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×#66968C211yesmaximal, characteristic, complemented
2C2×#66967C211yesmaximal, characteristic, complemented
3#10623107C211yesmaximal, characteristic, complemented
4#10623085C211yesmaximal, characteristic, complemented
5C4×C11×SD16C211yesmaximal, characteristic, complemented
6#10622641C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic, complemented
8#10622481C211yesmaximal, characteristic, complemented
9#10622478C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622419C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622389C211yesmaximal, characteristic, complemented
14#10622309C211yesmaximal, characteristic, complemented
15#10622301C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic, complemented
18C2×#4341C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic, complemented
22C4×D4×C11C2211yescharacteristic
23C2×#4326C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66983—21no—
28C2×(C2×D11)⋊C4—21no—
29#66968—24no—
30#66967—24no—
31C2×Dic44C2211yescharacteristic, complemented
32C2×D88C2211yescharacteristic
33C2×#4314C2211yescharacteristic
34C2×#4314C2211yescharacteristic, complemented
35C2×#4313C2211yescharacteristic
36C2×#4313C2211yescharacteristic, complemented
37#66950—21no—
38#66950C2211yescharacteristic
39#66950C2211yescharacteristic
40#66948—21no—
41#66948C2211yescharacteristic
42#66948C2211yescharacteristic, complemented
43#66939—21no—
44#66935—21no—
45#66928—21no—
46#66928C2211yescharacteristic
47#66928C2211yescharacteristic, complemented
48C4×D44—21no—
49C4×D44C2211yescharacteristic
50C11×#106C2211yescharacteristic, complemented
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic
53C4×C8×C11C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66873C2211yescharacteristic
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68#4343—22no—
69#4343—41no—
70Q8×D11—22no—
71Q8×D11—41no—
72#4341—22no—
73#4341—41no—
74D4×D11—22no—
75D4×D11—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44D411yescharacteristic
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11C2311yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22—21no—
87C2×Dic22C2311yescharacteristic
88C2×Dic22C2311yescharacteristic
89C11×SD16D414yescomplemented
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4C2311yescharacteristic
94C11×C4⋊C4C2311yescharacteristic
95C11×C22⋊C4—21no—
96C42×C11—21no—
97C42×C11C2311yescharacteristic
98#4326—22no—
99#4325—22no—
100#4324—22no—
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
111(C2×D11)⋊C4D411yescharacteristic
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11D411yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117Dic44—22no—
118D88—22no—
119#4314—41no—
120#4314—41no—
121#4313—22no—
122#4313—22no—
123#3275—111nomaximal, Sylow
124C23×C11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—81no—
130C22×D11C2×D411yescharacteristic
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11C2×D412yes—
134D4×C11—21no—
135D4×C11C2×D412yes—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—81no—
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2411yescharacteristic
143C22⋊D11—42no—
144C22⋊D11—42no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—42no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150D44—21no—
151D44—21no—
152D44—21no—
153D44—21no—
154D44—41no—
155D44—42no—
156D44—42no—
157D44—81no—
158C4×D11—21no—
159C4×D11—21no—
160C4×D11—21no—
161C4×D11—21no—
162C4×D11—42no—
163C4×D11—42no—
164Dic22—21no—
165Dic22—21no—
166Dic22—21no—
167Dic22—21no—
168Dic22—42no—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#137—111no—
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×SD16D1111yescharacteristic, complemented
187#436—111no—
188C22×C11—22no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11C22×D411yescharacteristic
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
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—22no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11C22×D411yescharacteristic
211C4×C11H(5,𝔽2)11yescharacteristic
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41—111no—
218C22×Q8—111no—
219C22×D4—111no—
220#137—224no—
221AGL(1,ℤ/8)—224no—
222C2×Q16—111no—
223C2×Q16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—111no—
228C2×SD16C2×D1111yescharacteristic
229C2×D8—111no—
230C2×D8—111no—
231C2×M16—111no—
232C2×M16—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—111no—
242#121—221no—
243#121—221no—
244#120—221no—
245C4×Q8C2×D1111yescharacteristic, complemented
246C4×D4—111no—
247C4×D4—221no—
248C4×D4C2×D1111yescharacteristic
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×C8C2×D1111yescharacteristic, complemented
261C2×C11—42no—
262C2×C11D4211yescharacteristic
263C2×C11#57511yescharacteristic
264C2×C11#57711yescharacteristic
265D11—41no—
266D11—41no—
267D11—81no—
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—111no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—222no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297Q16—222no—
298Q16—222no—
299SD16—222no—
300SD16—222no—
301SD16—441no—
302SD16—441no—
303SD16D4414yescomplemented
304D8—222no—
305D8—222no—
306M16—222no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
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—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—21no—
330C42C22×D1111yescharacteristic
331C11#327511yescharacteristic, complemented, Sylow
332C23—21no—
333C23—111no—
334C23—111no—
335C23—221no—
336C23—221no—
337C23—442no—
338C23—442no—
339C23—881no—
340Q8—21no—
341Q8—221no—
342Q8—221no—
343Q8—221no—
344Q8—221no—
345Q8—442no—
346Q8C2×D4412yes—
347D4—21no—
348D4—221no—
349D4—221no—
350D4—221no—
351D4—221no—
352D4—441no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4C2×D4412yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—81no—
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×C4D4×D1111yescharacteristic
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—221no—
379C8—221no—
380C8C2×D4412yes—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—221no—
385C22—221no—
386C22—221no—
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—21no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—221no—
404C4—221no—
405C4—441no—
406C4—441no—
407C4C22×D4411yescharacteristic
408C4#6704211yescharacteristic
409C2—42no—
410C2—441no—
411C2—441no—
412C2—881no—
413C2—881no—
414C2D4×D4411yescharacteristic
415C2#1062329311yescharacteristic
416C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
hypercenterC4×SD16D11
hypocenterC11#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#66968C2semidirect
2. C2×#66967C2semidirect
3. #10623107C2semidirect
4. #10623085C2semidirect
5. C4×C11×SD16C2semidirect
6. #10622641C2semidirect
7. #10622629C2semidirect
8. #10622481C2semidirect
9. #10622478C2semidirect
10. #10622423C2semidirect
11. #10622419C2semidirect
12. #10622394C2semidirect
13. #10622389C2semidirect
14. #10622309C2semidirect
15. #10622301C2semidirect
17. C2×Q8×D11C22semidirect
21. C4×Q8×C11C22semidirect
23. C2×#4326C22semidirect
31. C2×Dic44C22semidirect
34. C2×#4314C22semidirect
36. C2×#4313C22semidirect
42. #66948C22semidirect
47. #66928C22semidirect
50. C11×#106C22semidirect
51. C11×#103C22semidirect
53. C4×C8×C11C22semidirect
55. (C2×D11)⋊C8C22semidirect
56. #66874C22semidirect
57. #66874C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
89. C11×SD16D4semidirect
186. C4×SD16D11semidirect
245. C4×Q8C2×D11semidirect
250. #106C2×D11semidirect
254. #103C2×D11semidirect
260. C4×C8C2×D11semidirect
303. SD16D44semidirect
331. C11#3275semidirect

Maximal subgroups

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

subgroupindex
C2×#669682
C2×#669672
#106231072
#106230852
C4×C11×SD162
#106226412
#106226292
#106224812
#106224782
#106224232
#106224192
#106223942
#106223892
#106223092
#106223012
#327511