Finite Group Databasebeta

← #15684870

Subgroups — #15684870

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×#10625082C211yesmaximal, characteristic, complemented
2C22×#67272C211yesmaximal, characteristic, complemented
3#13093061C211yesmaximal, characteristic, complemented
4#13093051C211yesmaximal, characteristic, complemented
5#13092805C211yesmaximal, characteristic, complemented
6#13092669C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092631C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092570C211yesmaximal, characteristic, complemented
11#13092563C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092526C211yesmaximal, characteristic, complemented
14#13092485C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic, complemented
17C2×#67290C2211yescharacteristic, complemented
18C2×D4×D23—21no—
19C2×D4×D23C2211yescharacteristic, complemented
20C22×D92C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic, complemented
22C2×D8×C23C2211yescharacteristic, complemented
23C23×#121C2211yescharacteristic
24#10625124—21no—
25C2×C22⋊Dic23—21no—
26#10625111C2211yescharacteristic, complemented
27#10625110—21no—
28#10625109C2211yescharacteristic, complemented
29#10625108—21no—
30#10625107C2211yescharacteristic, complemented
31#10625106—21no—
32D4×Dic23C2211yescharacteristic, complemented
33C2×#67273C2211yescharacteristic, complemented
34C2×#67272—24no—
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37C2×#67272C2211yescharacteristic, complemented
38C2×#67272C2211yescharacteristic, complemented
39C4×C22⋊D23C2211yescharacteristic
40#10625095C2211yescharacteristic, complemented
41C22×C23⋊C8C2211yescharacteristic, complemented
42#10625082—24no—
43C2×#67263C2211yescharacteristic, complemented
44C2×#67263C2211yescharacteristic, complemented
45C2×#67262C2211yescharacteristic, complemented
46#10625066C2211yescharacteristic, complemented
47#10625064C2211yescharacteristic, complemented
48#10625055—21no—
49#10625053—21no—
50C23×#102C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×C22⋊C8C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624992C2211yescharacteristic, complemented
60#10624990C2211yescharacteristic, complemented
61C24×C23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×D4×C23—22no—
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23—41no—
68C2×D4×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×D4×C23C2311yescharacteristic
71C22×C4×C23C2311yescharacteristic
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23D411yescharacteristic
78C22×Dic23—21no—
79C22×Dic23—21no—
80#67290—22no—
81#67290—41no—
82D4×D23—22no—
83D4×D23—41no—
84D4×D23—44no—
85C2×D92—22no—
86C2×D92—21no—
87C2×D92—21no—
88C2×D92—41no—
89C2×D92C2311yescharacteristic
90C2×D92C2311yescharacteristic
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94D8×C23—22no—
95D8×C23—41no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23—21no—
102C22⋊Dic23—21no—
103C22⋊Dic23—21no—
104C22⋊Dic23—21no—
105C22⋊Dic23D411yescharacteristic
106#67273—22no—
107#67272—22no—
108#67272—22no—
109#67272—22no—
110#67272D414yescomplemented
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4D411yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4D411yescharacteristic
117C4×Dic23C2311yescharacteristic
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121#67263—22no—
122#67263—41no—
123#67262—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C23×C23—42no—
128C23×C23—42no—
129C23×C23—81no—
130C23×C23C2×D411yescharacteristic
131C22×D23—21no—
132C22×D23—21no—
133C22×D23—42no—
134C22×D23—42no—
135C22×D23—42no—
136C22×D23—42no—
137C22×D23—81no—
138C22×D23—81no—
139C22×D23C2×D411yescharacteristic
140D4×C23—21no—
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—21no—
145D4×C23—42no—
146D4×C23—42no—
147D4×C23C2×D412yescomplemented
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2411yescharacteristic
153C22⋊D23—22no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—81no—
158C22⋊D23—81no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—42no—
162C2×Dic23—81no—
163C2×Dic23C2×D411yescharacteristic
164C2×Dic23C2×D411yescharacteristic
165C2×Dic23C2×D411yescharacteristic
166D92—21no—
167D92—21no—
168D92—21no—
169D92—42no—
170D92—42no—
171D92C2×D412yes—
172C4×D23—21no—
173C4×D23—21no—
174C4×D23—42no—
175Dic46—21no—
176Dic46—21no—
177C8×C23—21no—
178C8×C23—21no—
179C23⋊C8—21no—
180C23⋊C8C2×D412yescomplemented
181#3264—231nomaximal, Sylow
182C22×C23—21no—
183C22×C23—21no—
184C22×C23—22no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—41no—
193C22×C23—84no—
194C22×C23AGL(1,ℤ/8)12yescomplemented
195C22×C23C22×D411yescharacteristic
196C2×D23—21no—
197C2×D23—22no—
198C2×D23—21no—
199C2×D23—21no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—41no—
204C2×D23—41no—
205C2×D23—84no—
206C2×D23—84no—
207C4×C23—21no—
208C4×C23—41no—
209C4×C23C22×D411yescharacteristic
210C4×C23H(5,𝔽2)11yescharacteristic
211Dic23—21no—
212Dic23—21no—
213Dic23—21no—
214Dic23—41no—
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546—231no—
219D42—231no—
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#447D2311yescharacteristic, complemented
229#442—231no—
230#435—231no—
231C2×C23—22no—
232C2×C23—42no—
233C2×C23—81no—
234C2×C23—81no—
235C2×C23D4211yescharacteristic
236C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C23#57611yescharacteristic
238D23—41no—
239D23—42no—
240D23—81no—
241C2×#41—231no—
242C22×D4—231no—
243C22×D4—231no—
244C22×D4—461no—
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—464no—
255C2×D8C2×D2311yescharacteristic, complemented
256C2×D8C2×D2311yescharacteristic, complemented
257C2×M16—231no—
258C22×C8—231no—
259#127—231no—
260#124—231no—
261#123—461no—
262C22⋊Q8—231no—
263#121—231no—
264#121—231no—
265#121—461no—
266#121—461no—
267#121C2×D2311yescharacteristic
268#120—461no—
269#120—461no—
270#120—461no—
271C4×D4—231no—
272C4×D4—231no—
273C4×D4—231no—
274C2×C22⋊C4—461no—
275#106—231no—
276C4⋊C8—231no—
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102C2×D2311yescharacteristic, complemented
282#102C2×D2311yescharacteristic, complemented
283C22⋊C8—231no—
284C22⋊C8C2×D2311yescharacteristic, complemented
285#97—231no—
286C23#326411yescharacteristic, complemented, Sylow
287C24—21no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8—231no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—231no—
298C2×D4—231no—
299C2×D4—231no—
300C2×D4—462no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—461no—
304C2×D4—461no—
305C2×D4—462no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—921no—
310C2×D4—921no—
311C2×D4—924no—
312C2×D4C22×D2311yescharacteristic
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—231no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4—461no—
319C22×C4C22×D2311yescharacteristic
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—22no—
324D8—41no—
325D8—234no—
326D8—462no—
327D8—462no—
328D8—462no—
329M16—462no—
330C2×C8—231no—
331C2×C8—231no—
332C2×C8—462no—
333C2×C8C22×D2311yescharacteristic
334C2×C8C22×D2311yescharacteristic
335C4⋊C4—231no—
336C4⋊C4—231no—
337C4⋊C4—461no—
338C4⋊C4C22×D2311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—231no—
341C22⋊C4—231no—
342C22⋊C4—461no—
343C22⋊C4—461no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4—461no—
348C22⋊C4—461no—
349C42—231no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—81no—
356C23—231no—
357C23—461no—
358C23—461no—
359C23—922no—
360C23—922no—
361C23—922no—
362C23—922no—
363C23—1841no—
364C23—1841no—
365C23D4×D2311yescharacteristic
366Q8—461no—
367Q8—461no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—42no—
375D4—232no—
376D4—462no—
377D4—461no—
378D4—461no—
379D4—461no—
380D4—922no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—1841no—
386D4—1841no—
387D4D4×D2312yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—231no—
392C2×C4—231no—
393C2×C4—231no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—922no—
399C2×C4—922no—
400C2×C4—1841no—
401C2×C4D4×D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—21no—
405C8—232no—
406C8—461no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—461no—
420C22—461no—
421C22—461no—
422C22—462no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—1844no—
429C22—1844no—
430C22#1062508212yescomplemented
431C22C2×D4×D2311yescharacteristic
432C4—21no—
433C4—41no—
434C4—461no—
435C4—461no—
436C4—461no—
437C4—921no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062515511yescharacteristic
441C2—22no—
442C2—42no—
443C2—81no—
444C2—81no—
445C2—921no—
446C2—922no—
447C2—1841no—
448C2#1309304911yescharacteristic
449C2C2×#1062508211yescharacteristic
450C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C22×#67272C2semidirect
3. #13093061C2semidirect
4. #13093051C2semidirect
5. #13092805C2semidirect
6. #13092669C2semidirect
7. #13092644C2semidirect
8. #13092631C2semidirect
9. #13092610C2semidirect
10. #13092570C2semidirect
11. #13092563C2semidirect
12. #13092549C2semidirect
13. #13092526C2semidirect
14. #13092485C2semidirect
15. C23×#447C2semidirect
16. C22×D4×C23C22semidirect
17. C2×#67290C22semidirect
19. C2×D4×D23C22semidirect
21. C2×D8×C23C22semidirect
22. C2×D8×C23C22semidirect
26. #10625111C22semidirect
28. #10625109C22semidirect
30. #10625107C22semidirect
32. D4×Dic23C22semidirect
33. C2×#67273C22semidirect
37. C2×#67272C22semidirect
38. C2×#67272C22semidirect
40. #10625095C22semidirect
41. C22×C23⋊C8C22semidirect
43. C2×#67263C22semidirect
44. C2×#67263C22semidirect
45. C2×#67262C22semidirect
46. #10625066C22semidirect
47. #10625064C22semidirect
50. C23×#102C22semidirect
51. C23×#102C22semidirect
52. C23×C22⋊C8C22semidirect
53. #10625014C22semidirect
54. #10625003C22semidirect
55. #10625003C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624992C22semidirect
60. #10624990C22semidirect
110. #67272D4semidirect
147. D4×C23C2×D4semidirect
180. C23⋊C8C2×D4semidirect
194. C22×C23AGL(1,ℤ/8)semidirect
228. #447D23semidirect
245. C22×D4C2×D23semidirect
255. C2×D8C2×D23semidirect
256. C2×D8C2×D23semidirect
281. #102C2×D23semidirect
282. #102C2×D23semidirect
284. C22⋊C8C2×D23semidirect
286. C23#3264semidirect
387. D4D4×D23semidirect
430. C22#10625082semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C22×#672722
#130930612
#130930512
#130928052
#130926692
#130926442
#130926312
#130926102
#130925702
#130925632
#130925492
#130925262
#130924852
C23×#4472
#326423