Finite Group Databasebeta

← #15684873

Subgroups — #15684873

Order 2944.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625103C211yesmaximal, characteristic, complemented
2C22×#67272C211yesmaximal, characteristic, complemented
3#13093063C211yesmaximal, characteristic, complemented
4#13092804C211yesmaximal, characteristic, complemented
5#13092668C211yesmaximal, characteristic, complemented
6#13092644C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092609C211yesmaximal, characteristic, complemented
9#13092568C211yesmaximal, characteristic, complemented
10#13092560C211yesmaximal, characteristic, complemented
11#13092551C211yesmaximal, characteristic, complemented
12#13092550C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15D42×C23C211yesmaximal, characteristic, complemented
16C22×D4×C23—21no—
17C22×D4×C23C2211yescharacteristic
18C22×D4×C23C2211yescharacteristic, complemented
19C2×#67288C2211yescharacteristic, complemented
20C22×D92C2211yescharacteristic, complemented
21C23×#127C2211yescharacteristic, complemented
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C23×#121C2211yescharacteristic, complemented
25C23×#120—21no—
26C23×#120—21no—
27C4×D4×C23C2211yescharacteristic
28C4×D4×C23C2211yescharacteristic, complemented
29#10625108—21no—
30C2×#67273C2211yescharacteristic, complemented
31C2×#67273C2211yescharacteristic, complemented
32C2×#67273C2211yescharacteristic, complemented
33#10625103—24no—
34C2×#67272—24no—
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37C2×#67272C2211yescharacteristic, complemented
38C2×#67272C2211yescharacteristic, complemented
39C2×#67272C2211yescharacteristic, complemented
40C2×#67272C2211yescharacteristic, complemented
41#10625101C2211yescharacteristic, complemented
42#10625095C2211yescharacteristic, complemented
43C2×#67267C2211yescharacteristic, complemented
44C22×C23⋊C8C2211yescharacteristic, complemented
45#10625065—21no—
46#10625055—21no—
47C22⋊C4×D23—21no—
48#10625046C2211yescharacteristic, complemented
49C4×D92C2211yescharacteristic, complemented
50#10625014C2211yescharacteristic, complemented
51#10625014C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624990C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C24×C23—21no—
62C24×C23—21no—
63C23×D23—21no—
64C2×D4×C23—22no—
65C2×D4×C23—22no—
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23—21no—
71C2×D4×C23—21no—
72C2×D4×C23—41no—
73C2×D4×C23—41no—
74C2×D4×C23—44no—
75C2×D4×C23D411yescharacteristic
76C2×D4×C23C2311yescharacteristic
77C2×D4×C23C2311yescharacteristic
78C2×D4×C23C2311yescharacteristic
79C22×C4×C23—21no—
80C22×C4×C23C2311yescharacteristic
81C22×C4×C23C2311yescharacteristic
82C2×C22⋊D23—21no—
83C2×C22⋊D23—21no—
84#67288—22no—
85#67288—41no—
86C2×D92—22no—
87C2×D92—21no—
88C2×D92—41no—
89C2×D92C2311yescharacteristic
90C2×D92C2311yescharacteristic
91C2×C4×D23—21no—
92C2×C4×D23—21no—
93C2×Dic46C2311yescharacteristic
94C4⋊C4×C23D411yescharacteristic
95C4⋊C4×C23C2311yescharacteristic
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊C4×C23—21no—
99C22⋊C4×C23D411yescharacteristic
100C22⋊C4×C23D411yescharacteristic
101C42×C23C2311yescharacteristic
102C22⋊Dic23—21no—
103#67273—22no—
104#67273—22no—
105#67273—41no—
106#67272—22no—
107#67272—22no—
108#67272—22no—
109#67272—22no—
110#67272—41no—
111#67272D414yescomplemented
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4—21no—
114(C2×D23)⋊C4—21no—
115(C2×D23)⋊C4—21no—
116C4⋊Dic23C2311yescharacteristic
117Dic23⋊C4—21no—
118#67267—22no—
119C2×C23⋊C8—22no—
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C23×C23—42no—
128C23×C23—42no—
129C23×C23—42no—
130C23×C23—42no—
131C23×C23—81no—
132C23×C23—81no—
133C23×C23C2×D411yescharacteristic
134C23×C23C2×D411yescharacteristic
135C22×D23—21no—
136C22×D23—21no—
137C22×D23—42no—
138C22×D23—42no—
139C22×D23—81no—
140D4×C23—22no—
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—21no—
145D4×C23—21no—
146D4×C23—42no—
147D4×C23—42no—
148D4×C23—42no—
149D4×C23—42no—
150D4×C23—42no—
151D4×C23—81no—
152D4×C23C2×D412yes—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23—21no—
158C2×C4×C23—42no—
159C2×C4×C23C2×D411yescharacteristic
160C2×C4×C23C2×D411yescharacteristic
161C2×C4×C23C2×D411yescharacteristic
162C2×C4×C23C2×D411yescharacteristic
163C2×C4×C23C2411yescharacteristic
164C22⋊D23—42no—
165C22⋊D23—81no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168D92—21no—
169D92—21no—
170D92—21no—
171D92—42no—
172D92C2×D412yescomplemented
173C4×D23—42no—
174C4×D23—81no—
175Dic46—21no—
176Dic46—21no—
177C23⋊C8—21no—
178C23⋊C8—21no—
179C23⋊C8—21no—
180C23⋊C8C2×D412yescomplemented
181#3264—231nomaximal, Sylow
182C22×C23—21no—
183C22×C23—21no—
184C22×C23—21no—
185C22×C23—22no—
186C22×C23—21no—
187C22×C23—21no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—41no—
193C22×C23—41no—
194C22×C23—41no—
195C22×C23—41no—
196C22×C23—84no—
197C22×C23—84no—
198C22×C23AGL(1,ℤ/8)12yescomplemented
199C22×C23C22×D411yescharacteristic
200C2×D23—22no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—41no—
204C2×D23—41no—
205C2×D23—41no—
206C2×D23—84no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—21no—
211C4×C23—41no—
212C4×C23C22×D411yescharacteristic
213C4×C23H(5,𝔽2)11yescharacteristic
214Dic23—41no—
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546—231no—
219D42D2311yescharacteristic, complemented
220#496—231no—
221#469—231no—
222#465—231no—
223#463—231no—
224#459—231no—
225#450—231no—
226#449—231no—
227#447—231no—
228#447—231no—
229#442—231no—
230#435—231no—
231C2×C23—22no—
232C2×C23—41no—
233C2×C23—42no—
234C2×C23—81no—
235C2×C23—81no—
236C2×C23D4211yescharacteristic
237C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
238C2×C23#57611yescharacteristic
239D23—42no—
240D23—81no—
241C2×#41—231no—
242C22×D4—21no—
243C22×D4—231no—
244C22×D4C2×D2311yescharacteristic
245C22×D4C2×D2311yescharacteristic, complemented
246AGL(1,ℤ/8)—464no—
247C2×SD16—231no—
248C2×SD16—231no—
249C2×SD16—231no—
250C2×D8—231no—
251C2×D8—231no—
252C2×D8—231no—
253C2×D8—231no—
254C2×D8—231no—
255C2×D8—231no—
256C2×D8—464no—
257C2×M16—231no—
258C22×C8—231no—
259#127C2×D2311yescharacteristic, complemented
260#124—231no—
261#123—461no—
262C22⋊Q8—231no—
263#121—21no—
264#121—231no—
265#121—461no—
266#121C2×D2311yescharacteristic
267#121C2×D2311yescharacteristic, complemented
268#120—21no—
269#120—21no—
270#120—461no—
271C4×D4—231no—
272C4×D4C2×D2311yescharacteristic
273C4×D4C2×D2311yescharacteristic, complemented
274C2×C22⋊C4—461no—
275#106—231no—
276C4⋊C8—231no—
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102—231no—
282#102—231no—
283C22⋊C8—231no—
284C22⋊C8—231no—
285#97—231no—
286C23#326411yescharacteristic, complemented, Sylow
287C24—21no—
288C24—21no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8—231no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—231no—
305C2×D4—231no—
306C2×D4—462no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—461no—
310C2×D4—921no—
311C2×D4C22⋊D2311yescharacteristic
312C2×D4C22×D2311yescharacteristic
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—21no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4C22×D2311yescharacteristic
319C22×C4C22×D2311yescharacteristic
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—234no—
324D8—462no—
325D8—462no—
326D8—462no—
327D8—462no—
328D8—921no—
329M16—462no—
330C2×C8—231no—
331C2×C8—231no—
332C2×C8—231no—
333C2×C8—231no—
334C2×C8—462no—
335C4⋊C4—231no—
336C4⋊C4—461no—
337C4⋊C4C22⋊D2311yescharacteristic
338C4⋊C4C22×D2311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—461no—
343C22⋊C4—461no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4C22⋊D2311yescharacteristic
348C22⋊C4C22⋊D2311yescharacteristic
349C42C22×D2311yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—461no—
360C23—461no—
361C23—922no—
362C23—922no—
363C23—1841no—
364C23C2×C22⋊D2311yescharacteristic
365C23C2×C22⋊D2311yescharacteristic
366Q8—461no—
367Q8—461no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—232no—
381D4—461no—
382D4—461no—
383D4—461no—
384D4—922no—
385D4—922no—
386D4—1841no—
387D4D4×D2312yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—922no—
397C2×C4—1841no—
398C2×C4C2×C22⋊D2311yescharacteristic
399C2×C4C2×C22⋊D2311yescharacteristic
400C2×C4C2×C22⋊D2311yescharacteristic
401C2×C4C2×C22⋊D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—232no—
404C8—461no—
405C8—461no—
406C8—461no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—462no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—921no—
429C22—1844no—
430C22#1062510312yescomplemented
431C22C22×C22⋊D2311yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—921no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062515511yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—922no—
447C2—1841no—
448C2D4×C22⋊D2311yescharacteristic
449C2C2×#1062510311yescharacteristic
450C2#1309322011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingD42×C23C2
socleC22×C23C22×D4
hypercenterD42D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C22×#67272C2semidirect
3. #13093063C2semidirect
4. #13092804C2semidirect
5. #13092668C2semidirect
6. #13092644C2semidirect
7. #13092632C2semidirect
8. #13092609C2semidirect
9. #13092568C2semidirect
10. #13092560C2semidirect
11. #13092551C2semidirect
12. #13092550C2semidirect
13. #13092527C2semidirect
14. #13092489C2semidirect
15. D42×C23C2semidirect
18. C22×D4×C23C22semidirect
19. C2×#67288C22semidirect
20. C22×D92C22semidirect
21. C23×#127C22semidirect
24. C23×#121C22semidirect
28. C4×D4×C23C22semidirect
30. C2×#67273C22semidirect
31. C2×#67273C22semidirect
32. C2×#67273C22semidirect
37. C2×#67272C22semidirect
38. C2×#67272C22semidirect
39. C2×#67272C22semidirect
40. C2×#67272C22semidirect
41. #10625101C22semidirect
42. #10625095C22semidirect
43. C2×#67267C22semidirect
44. C22×C23⋊C8C22semidirect
48. #10625046C22semidirect
49. C4×D92C22semidirect
50. #10625014C22semidirect
51. #10625014C22semidirect
52. #10625014C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624992C22semidirect
56. #10624991C22semidirect
57. #10624991C22semidirect
58. #10624990C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
111. #67272D4semidirect
172. D92C2×D4semidirect
180. C23⋊C8C2×D4semidirect
198. C22×C23AGL(1,ℤ/8)semidirect
219. D42D23semidirect
245. C22×D4C2×D23semidirect
259. #127C2×D23semidirect
267. #121C2×D23semidirect
273. C4×D4C2×D23semidirect
286. C23#3264semidirect
430. C22#10625103semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C22×#672722
#130930632
#130928042
#130926682
#130926442
#130926322
#130926092
#130925682
#130925602
#130925512
#130925502
#130925272
#130924892
D42×C232
#326423