Finite Group Databasebeta

← #15684876

Subgroups — #15684876

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×#10625085C211yesmaximal, characteristic, complemented
2C2×D8×D23C211yesmaximal, characteristic, complemented
3#13093060C211yesmaximal, characteristic, complemented
4#13093052C211yesmaximal, characteristic, complemented
5#13092667C211yesmaximal, characteristic, complemented
6#13092643C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092609C211yesmaximal, characteristic, complemented
9#13092566C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11#13092549C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092530C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#496C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic, complemented
17C2×D4×D23—21no—
18C2×D4×D23C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic, complemented
20C2×D4×D23C2211yescharacteristic, complemented
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×SD16×C23C2211yescharacteristic, complemented
23C2×D8×C23C2211yescharacteristic, complemented
24C2×D8×C23C2211yescharacteristic, complemented
25C23×#127C2211yescharacteristic, complemented
26C23×#124C2211yescharacteristic, complemented
27#10625117C2211yescharacteristic, complemented
28C2×#67274C2211yescharacteristic, complemented
29#10625109—21no—
30#10625109C2211yescharacteristic
31#10625109C2211yescharacteristic, complemented
32#10625109C2211yescharacteristic, complemented
33#10625108—21no—
34#10625108—21no—
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic, complemented
37C2×#67272C2211yescharacteristic, complemented
38#10625085—24no—
39D8×D23—24no—
40C2×D184C2211yescharacteristic
41C2×#67262C2211yescharacteristic, complemented
42C2×C8×D23C2211yescharacteristic, complemented
43#10625055—21no—
44#10625054—21no—
45#10625053—21no—
46C22⋊C4×D23—21no—
47C4×D92C2211yescharacteristic
48C4×D92C2211yescharacteristic, complemented
49C4×D92C2211yescharacteristic, complemented
50C23×#97C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625014C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56#10625003C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58(C2×D23)⋊C8C2211yescharacteristic, complemented
59#10624999C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76#67292—22no—
77#67292—41no—
78D4×D23—22no—
79D4×D23—22no—
80D4×D23—22no—
81D4×D23—41no—
82D4×D23—41no—
83D4×D23—41no—
84D4×D23—44no—
85C2×D92—21no—
86C2×D92D411yescharacteristic
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×C4×D23C2311yescharacteristic
94SD16×C23—22no—
95SD16×C23—41no—
96D8×C23—22no—
97D8×C23—41no—
98C2×C8×C23C2311yescharacteristic
99C2×C8×C23C2311yescharacteristic
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C42×C23C2311yescharacteristic
103C22⋊Dic23—21no—
104C22⋊Dic23—21no—
105C22⋊Dic23—21no—
106#67274—22no—
107#67272—22no—
108#67272—22no—
109#67272—22no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4D411yescharacteristic
114(C2×D23)⋊C4D411yescharacteristic
115C4⋊Dic23D411yescharacteristic
116C4⋊Dic23C2311yescharacteristic
117C4⋊Dic23C2311yescharacteristic
118Dic23⋊C4—21no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121D184D414yescomplemented
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—42no—
135C22×D23—81no—
136C22×D23—81no—
137C22×D23—81no—
138C22×D23C2×D411yescharacteristic
139C22×D23C2×D411yescharacteristic
140Q8×C23—21no—
141Q8×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—21no—
145D4×C23—21no—
146D4×C23—21no—
147D4×C23—21no—
148D4×C23—42no—
149D4×C23—81no—
150C2×C4×C23—21no—
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2×D411yescharacteristic
153C2×C4×C23C2411yescharacteristic
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—42no—
158C22⋊D23—42no—
159C22⋊D23—81no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23C2×D411yescharacteristic
163C2×Dic23C2×D411yescharacteristic
164D92—22no—
165D92—21no—
166D92—21no—
167D92—42no—
168D92C2×D412yes—
169D92C2×D412yescomplemented
170C4×D23—21no—
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—21no—
174C4×D23—42no—
175C4×D23—42no—
176C4×D23—81no—
177C8×C23—21no—
178C8×C23C2×D412yescomplemented
179C23⋊C8—21no—
180C23⋊C8—21no—
181#3264—231nomaximal, Sylow
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23C22×D411yescharacteristic
192C2×D23—21no—
193C2×D23—21no—
194C2×D23—21no—
195C2×D23—22no—
196C2×D23—22no—
197C2×D23—21no—
198C2×D23—21no—
199C2×D23—41no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—84no—
204C2×D23—84no—
205C2×D23—84no—
206C2×D23AGL(1,ℤ/8)12yescomplemented
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23H(5,𝔽2)11yescharacteristic
212Dic23—21no—
213Dic23—21no—
214Dic23—41no—
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546—231no—
219D42—231no—
220#496D2311yescharacteristic, complemented
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—81no—
232C2×C23—81no—
233C2×C23—81no—
234C2×C23D4211yescharacteristic
235C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C23#57611yescharacteristic
237D23—22no—
238D23—41no—
239D23—42no—
240D23—42no—
241C2×#41—231no—
242C22×D4—231no—
243C22×D4—231no—
244C22×D4—231no—
245C22×D4—461no—
246AGL(1,ℤ/8)—464no—
247C2×SD16—231no—
248C2×SD16C2×D2311yescharacteristic, complemented
249C2×SD16C2×D2311yescharacteristic, complemented
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#127C2×D2311yescharacteristic, complemented
260#124C2×D2311yescharacteristic, complemented
261#123—461no—
262C22⋊Q8—231no—
263#121—231no—
264#121—231no—
265#121—231no—
266#121—461no—
267#121—461no—
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#102—231no—
282#102—231no—
283C22⋊C8—231no—
284C22⋊C8—231no—
285#97C2×D2311yescharacteristic, complemented
286C23#326411yescharacteristic, complemented, Sylow
287C24—461no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8C22×D2311yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—231no—
296C2×D4—231no—
297C2×D4—231no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—462no—
303C2×D4—462no—
304C2×D4—462no—
305C2×D4—461no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—921no—
309C2×D4—921no—
310C2×D4—921no—
311C2×D4—924no—
312C2×D4C22×D2311yescharacteristic
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—231no—
316C22×C4—231no—
317C22×C4—461no—
318C22×C4—461no—
319C22×C4—461no—
320SD16—22no—
321SD16—41no—
322SD16—462no—
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—231no—
338C4⋊C4—461no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—231no—
342C22⋊C4—231no—
343C22⋊C4—461no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4—461no—
348C22⋊C4—461no—
349C42C22×D2311yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—231no—
354C23—231no—
355C23—461no—
356C23—461no—
357C23—922no—
358C23—922no—
359C23—922no—
360C23—922no—
361C23—922no—
362C23—922no—
363C23—1841no—
364C23—1841no—
365C23—1841no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—81no—
376D4—232no—
377D4—232no—
378D4—462no—
379D4—461no—
380D4—461no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—922no—
386D4—922no—
387D4—1841no—
388C2×C4—21no—
389C2×C4—231no—
390C2×C4—231no—
391C2×C4—461no—
392C2×C4—461no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—922no—
398C2×C4—922no—
399C2×C4—1841no—
400C2×C4D4×D2311yescharacteristic
401C2×C4D4×D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—461no—
405C8—461no—
406C8D4×D2312yescomplemented
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—232no—
417C22—461no—
418C22—461no—
419C22—461no—
420C22—461no—
421C22—461no—
422C22—462no—
423C22—462no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—1844no—
429C22—1844no—
430C22—1844no—
431C22C2×D4×D2311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—461no—
436C4—461no—
437C4—921no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062515511yescharacteristic
441C2—81no—
442C2—81no—
443C2—81no—
444C2—462no—
445C2—921no—
446C2—922no—
447C2—922no—
448C2#1309305211yescharacteristic
449C2AGL(1,ℤ/8)×D2311yescharacteristic
450C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC22×C23C22×D4
hypercenter#496D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×D8×D23C2semidirect
3. #13093060C2semidirect
4. #13093052C2semidirect
5. #13092667C2semidirect
6. #13092643C2semidirect
7. #13092629C2semidirect
8. #13092609C2semidirect
9. #13092566C2semidirect
10. #13092561C2semidirect
11. #13092549C2semidirect
12. #13092549C2semidirect
13. #13092530C2semidirect
14. #13092490C2semidirect
15. C23×#496C2semidirect
16. C2×#67292C22semidirect
19. C2×D4×D23C22semidirect
20. C2×D4×D23C22semidirect
21. C2×SD16×C23C22semidirect
22. C2×SD16×C23C22semidirect
23. C2×D8×C23C22semidirect
24. C2×D8×C23C22semidirect
25. C23×#127C22semidirect
26. C23×#124C22semidirect
27. #10625117C22semidirect
28. C2×#67274C22semidirect
31. #10625109C22semidirect
32. #10625109C22semidirect
36. C2×#67272C22semidirect
37. C2×#67272C22semidirect
41. C2×#67262C22semidirect
42. C2×C8×D23C22semidirect
48. C4×D92C22semidirect
49. C4×D92C22semidirect
50. C23×#97C22semidirect
51. #10625017C22semidirect
52. #10625014C22semidirect
53. #10625014C22semidirect
54. #10625014C22semidirect
55. #10625003C22semidirect
56. #10625003C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. (C2×D23)⋊C8C22semidirect
59. #10624999C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
121. D184D4semidirect
169. D92C2×D4semidirect
178. C8×C23C2×D4semidirect
206. C2×D23AGL(1,ℤ/8)semidirect
220. #496D23semidirect
248. C2×SD16C2×D23semidirect
249. C2×SD16C2×D23semidirect
255. C2×D8C2×D23semidirect
256. C2×D8C2×D23semidirect
259. #127C2×D23semidirect
260. #124C2×D23semidirect
285. #97C2×D23semidirect
286. C23#3264semidirect
406. C8D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×D8×D232
#130930602
#130930522
#130926672
#130926432
#130926292
#130926092
#130925662
#130925612
#130925492
#130925302
#130924902
C23×#4962
#326423