Finite Group Databasebeta

← #13080113

Subgroups — #13080113

Order 1408.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66967C211yesmaximal, characteristic, complemented
2C2×SD16×D11C211yesmaximal, characteristic, complemented
3#10623107C211yesmaximal, characteristic, complemented
4D4×D44C211yesmaximal, characteristic, complemented
5C11×#440C211yesmaximal, characteristic, complemented
6#10622640C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic, complemented
8#10622499C211yesmaximal, characteristic, complemented
9#10622496C211yesmaximal, characteristic, complemented
10#10622424C211yesmaximal, characteristic, complemented
11#10622419C211yesmaximal, characteristic, complemented
12#10622389C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622325C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic, complemented
17C2×Q8×D11C2211yescharacteristic, complemented
18C2×D4×D11C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C22×D44—21no—
21C2×C11×SD16C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic, complemented
23C4×D4×C11C2211yescharacteristic
24C2×#4325C2211yescharacteristic, complemented
25C2×#4325C2211yescharacteristic, complemented
26C2×#4324C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983—21no—
29#66967—24no—
30SD16×D11—24no—
31C2×D88C2211yescharacteristic, complemented
32C2×D88C2211yescharacteristic, complemented
33C2×#4314C2211yescharacteristic, complemented
34C2×#4314C2211yescharacteristic, complemented
35C2×#4313C2211yescharacteristic, complemented
36C2×C8×D11C2211yescharacteristic, complemented
37#66950—21no—
38#66950C2211yescharacteristic, complemented
39#66948—21no—
40#66948C2211yescharacteristic
41#66948C2211yescharacteristic
42#66948C2211yescharacteristic, complemented
43#66935—21no—
44#66935—21no—
45#66928—21no—
46#66928C2211yescharacteristic, complemented
47#66927C2211yescharacteristic
48C4×D44—21no—
49C4×D44C2211yescharacteristic
50C11×#107C2211yescharacteristic, complemented
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic
53C11×#97C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic, complemented
55(C2×D11)⋊C8C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic, complemented
58#66873C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68#4343—22no—
69#4343—41no—
70Q8×D11—22no—
71Q8×D11—41no—
72D4×D11—22no—
73D4×D11—22no—
74D4×D11—41no—
75D4×D11—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—44no—
83C2×D44D411yescharacteristic
84C2×D44C2311yescharacteristic
85C2×D44C2311yescharacteristic
86C2×D44C2311yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11C2311yescharacteristic
90C2×C4×D11C2311yescharacteristic
91C2×Dic22—21no—
92C2×Dic22C2311yescharacteristic
93C11×SD16D414yescomplemented
94C2×C8×C11C2311yescharacteristic
95C2×C8×C11C2311yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4C2311yescharacteristic
98C11×C4⋊C4C2311yescharacteristic
99C11×C22⋊C4—21no—
100C42×C11—21no—
101C42×C11C2311yescharacteristic
102#4325—22no—
103#4325—22no—
104#4324—22no—
105#4323—22no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4D411yescharacteristic
113(C2×D11)⋊C4D411yescharacteristic
114C4⋊Dic11—21no—
115C4⋊Dic11D411yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117C2×C11⋊C8C2311yescharacteristic
118D88—22no—
119D88—41no—
120#4314—22no—
121#4314—41no—
122#4313—22no—
123C8×D11—22no—
124#3265—111nomaximal, Sylow
125C23×C11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—81no—
134C22×D11—81no—
135C22×D11C2×D411yescharacteristic
136C22×D11C2×D411yescharacteristic
137Q8×C11—21no—
138Q8×C11C2×D412yescomplemented
139D4×C11—21no—
140D4×C11C2×D412yes—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—42no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2411yescharacteristic
148C22⋊D11—42no—
149C22⋊D11—42no—
150C2×Dic11—21no—
151C2×Dic11C2×D411yescharacteristic
152C2×Dic11C2×D411yescharacteristic
153D44—22no—
154D44—21no—
155D44—21no—
156D44—21no—
157D44—21no—
158D44—21no—
159D44—21no—
160D44—42no—
161D44—42no—
162D44—42no—
163D44—42no—
164D44—42no—
165D44—81no—
166C4×D11—21no—
167C4×D11—21no—
168C4×D11—21no—
169C4×D11—21no—
170C4×D11—42no—
171C4×D11—42no—
172Dic22—21no—
173Dic22—21no—
174Dic22—42no—
175C8×C11—21no—
176C8×C11C2×D412yescomplemented
177C11⋊C8—21no—
178C11⋊C8—21no—
179C2×AGL(1,ℤ/8)—111no—
180C22×SD16—111no—
181#548—111no—
182D42—111no—
183#496—111no—
184#468—111no—
185#466—111no—
186#463—111no—
187#460—111no—
188#450—111no—
189#449—111no—
190#448—111no—
191#447—111no—
192#440D1111yescharacteristic, complemented
193#435—111no—
194C22×C11—22no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—84no—
213C2×D11—84no—
214C2×D11AGL(1,ℤ/8)12yescomplemented
215C4×C11—22no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11C22×D411yescharacteristic
221C4×C11H(5,𝔽2)11yescharacteristic
222Dic11—21no—
223Dic11—21no—
224Dic11—41no—
225C2×#41—111no—
226C22×Q8—111no—
227C22×D4—111no—
228C22×D4—111no—
229C22×D4—221no—
230AGL(1,ℤ/8)—224no—
231C2×SD16—111no—
232C2×SD16—111no—
233C2×SD16—111no—
234C2×SD16—111no—
235C2×SD16—111no—
236C2×SD16—224no—
237C2×SD16C2×D1111yescharacteristic
238C2×D8—111no—
239C2×D8—111no—
240C2×D8—111no—
241C2×M16—111no—
242C22×C8—111no—
243#127—111no—
244#124—111no—
245#124—221no—
246C22⋊Q8—111no—
247C22⋊Q8—221no—
248#121—111no—
249#121—111no—
250#121—111no—
251#121—221no—
252#121—221no—
253#120—221no—
254#120—221no—
255C4×Q8C2×D1111yescharacteristic, complemented
256C4×D4—111no—
257C4×D4—221no—
258C4×D4C2×D1111yescharacteristic
259#107C2×D1111yescharacteristic, complemented
260C4⋊C8—111no—
261#103—111no—
262#103C2×D1111yescharacteristic, complemented
263#102—111no—
264#102—111no—
265#102—111no—
266#102C2×D1111yescharacteristic
267C22⋊C8—111no—
268C22⋊C8—111no—
269#97C2×D1111yescharacteristic, complemented
270C2×C11—42no—
271C2×C11D4211yescharacteristic
272C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C2×C11#57711yescharacteristic
274D11—22no—
275D11—41no—
276D11—81no—
277D11—81no—
278D11—81no—
279C24—221no—
280C24—221no—
281#41—222no—
282#41—441no—
283C2×Q8—111no—
284C2×Q8—221no—
285C2×Q8—222no—
286C2×Q8—441no—
287C2×Q8C22×D1111yescharacteristic
288C2×D4—111no—
289C2×D4—111no—
290C2×D4—111no—
291C2×D4—111no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—444no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4C22×D1111yescharacteristic
306C22×C4—21no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—221no—
310C22×C4—221no—
311SD16—222no—
312SD16—222no—
313SD16—222no—
314SD16—222no—
315SD16—441no—
316SD16D4414yescomplemented
317D8—222no—
318D8—222no—
319D8—441no—
320M16—222no—
321C2×C8—111no—
322C2×C8—111no—
323C2×C8—222no—
324C2×C8C22×D1111yescharacteristic
325C2×C8C22×D1111yescharacteristic
326C4⋊C4—21no—
327C4⋊C4—111no—
328C4⋊C4—221no—
329C4⋊C4C22×D1111yescharacteristic
330C4⋊C4C22×D1111yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—111no—
333C22⋊C4—111no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C42—21no—
341C42C22×D1111yescharacteristic
342C11#326511yescharacteristic, complemented, Sylow
343C23—21no—
344C23—111no—
345C23—111no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—442no—
350C23—442no—
351C23—442no—
352C23—442no—
353C23—881no—
354C23—881no—
355Q8—21no—
356Q8—221no—
357Q8—221no—
358Q8—442no—
359Q8C2×D4412yescomplemented
360D4—21no—
361D4—222no—
362D4—221no—
363D4—221no—
364D4—221no—
365D4—221no—
366D4—221no—
367D4—221no—
368D4—442no—
369D4—442no—
370D4—442no—
371D4—442no—
372D4—442no—
373D4—442no—
374D4—442no—
375D4—881no—
376D4C2×D4412yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—111no—
382C2×C4—111no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4D4×D1111yescharacteristic
391C2×C4D4×D1111yescharacteristic
392C2×C4C23×D1111yescharacteristic
393C8—21no—
394C8—221no—
395C8—221no—
396C8C2×D4412yescomplemented
397C22—22no—
398C22—41no—
399C22—41no—
400C22—112no—
401C22—221no—
402C22—221no—
403C22—221no—
404C22—221no—
405C22—221no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—441no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22—441no—
414C22—441no—
415C22—884no—
416C22—884no—
417C22C2×D4×D1111yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—221no—
424C4—221no—
425C4—441no—
426C4C22×D4411yescharacteristic
427C4#6704211yescharacteristic
428C2—42no—
429C2—222no—
430C2—441no—
431C2—881no—
432C2—881no—
433C2—881no—
434C2D4×D4411yescharacteristic
435C2D11×AGL(1,ℤ/8)11yescharacteristic
436C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3265
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#66967C2semidirect
2. C2×SD16×D11C2semidirect
3. #10623107C2semidirect
4. D4×D44C2semidirect
5. C11×#440C2semidirect
6. #10622640C2semidirect
7. #10622629C2semidirect
8. #10622499C2semidirect
9. #10622496C2semidirect
10. #10622424C2semidirect
11. #10622419C2semidirect
12. #10622389C2semidirect
13. #10622386C2semidirect
14. #10622325C2semidirect
15. #10622319C2semidirect
16. C2×#4343C22semidirect
17. C2×Q8×D11C22semidirect
22. C4×Q8×C11C22semidirect
24. C2×#4325C22semidirect
25. C2×#4325C22semidirect
31. C2×D88C22semidirect
32. C2×D88C22semidirect
33. C2×#4314C22semidirect
34. C2×#4314C22semidirect
35. C2×#4313C22semidirect
36. C2×C8×D11C22semidirect
38. #66950C22semidirect
42. #66948C22semidirect
46. #66928C22semidirect
50. C11×#107C22semidirect
51. C11×#103C22semidirect
53. C11×#97C22semidirect
54. (C2×D11)⋊C8C22semidirect
55. (C2×D11)⋊C8C22semidirect
56. #66874C22semidirect
57. #66873C22semidirect
58. #66873C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
93. C11×SD16D4semidirect
138. Q8×C11C2×D4semidirect
176. C8×C11C2×D4semidirect
192. #440D11semidirect
214. C2×D11AGL(1,ℤ/8)semidirect
255. C4×Q8C2×D11semidirect
259. #107C2×D11semidirect
262. #103C2×D11semidirect
269. #97C2×D11semidirect
316. SD16D44semidirect
342. C11#3265semidirect
359. Q8C2×D44semidirect
396. C8C2×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#669672
C2×SD16×D112
#106231072
D4×D442
C11×#4402
#106226402
#106226292
#106224992
#106224962
#106224242
#106224192
#106223892
#106223862
#106223252
#106223192
#326511