Finite Group Databasebeta

← #15684882

Subgroups — #15684882

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×#10625079C211yesmaximal, characteristic, complemented
2C22×D184C211yesmaximal, characteristic, complemented
3#13093063C211yesmaximal, characteristic, complemented
4D4×D92C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092670C211yesmaximal, characteristic, complemented
7#13092646C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092613C211yesmaximal, characteristic, complemented
10#13092570C211yesmaximal, characteristic, complemented
11#13092564C211yesmaximal, characteristic, complemented
12#13092553C211yesmaximal, characteristic, complemented
13#13092553C211yesmaximal, characteristic, complemented
14#13092530C211yesmaximal, characteristic, complemented
15C23×#435C211yesmaximal, characteristic, complemented
16C2×D4×D23—21no—
17C2×#67288C2211yescharacteristic, complemented
18C22×D92C2211yescharacteristic
19C22×D92C2211yescharacteristic, complemented
20C22×D92C2211yescharacteristic, complemented
21C2×M16×C23C2211yescharacteristic, complemented
22C22×C8×C23C2211yescharacteristic, complemented
23C4×D4×C23C2211yescharacteristic
24#10625108—21no—
25#10625101C2211yescharacteristic
26#10625101C2211yescharacteristic, complemented
27#10625101C2211yescharacteristic, complemented
28#10625095C2211yescharacteristic, complemented
29#10625079—24no—
30C2×D184—24no—
31C2×D184C2211yescharacteristic
32C2×D184C2211yescharacteristic
33C2×D184C2211yescharacteristic, complemented
34C2×D184C2211yescharacteristic, complemented
35C2×D184C2211yescharacteristic, complemented
36C2×D184C2211yescharacteristic, complemented
37C2×#67263C2211yescharacteristic, complemented
38C2×#67263C2211yescharacteristic, complemented
39C2×#67263C2211yescharacteristic, complemented
40#10625066—21no—
41#10625065—21no—
42#10625055—21no—
43#10625053—21no—
44#10625053—21no—
45C22⋊C4×D23—21no—
46#10625046C2211yescharacteristic, complemented
47#10625045C2211yescharacteristic, complemented
48C4×D92C2211yescharacteristic, complemented
49C4×D92C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×C22⋊C8C2211yescharacteristic, complemented
52C23×C22⋊C8C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56#10625003C2211yescharacteristic, complemented
57#10625003C2211yescharacteristic, complemented
58#10625003C2211yescharacteristic, complemented
59#10624999C2211yescharacteristic, complemented
60#10624998C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×D4×C23D411yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71D4×D23—44no—
72#67288—22no—
73#67288—41no—
74C2×D92—22no—
75C2×D92—22no—
76C2×D92—22no—
77C2×D92—21no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—41no—
83C2×D92—41no—
84C2×D92—41no—
85C2×D92C2311yescharacteristic
86C2×D92C2311yescharacteristic
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23—21no—
93C2×Dic46C2311yescharacteristic
94M16×C23—22no—
95C2×C8×C23—22no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C2×C8×C23C2311yescharacteristic
99C2×C8×C23C2311yescharacteristic
100C4⋊C4×C23D411yescharacteristic
101C22⋊C4×C23D411yescharacteristic
102C22⋊C4×C23D411yescharacteristic
103C42×C23C2311yescharacteristic
104C22⋊Dic23—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112C4⋊Dic23C2311yescharacteristic
113C4⋊Dic23C2311yescharacteristic
114Dic23⋊C4—21no—
115D184—22no—
116D184—22no—
117D184—22no—
118D184—22no—
119D184—41no—
120D184D414yescomplemented
121#67263—22no—
122#67263—22no—
123#67263—41no—
124C23×C23C2×D411yescharacteristic
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23—42no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—42no—
135C22×D23—42no—
136C22×D23—42no—
137C22×D23—81no—
138C22×D23—81no—
139C22×D23—81no—
140D4×C23—22no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23C2×D411yescharacteristic
146C2×C4×C23C2×D411yescharacteristic
147C2×C4×C23C2×D411yescharacteristic
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2411yescharacteristic
150C22⋊D23—42no—
151C22⋊D23—42no—
152C22⋊D23—42no—
153C22⋊D23—81no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157D92—21no—
158D92—21no—
159D92—21no—
160D92—21no—
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—42no—
166D92—42no—
167D92—42no—
168D92—42no—
169D92—81no—
170D92C2×D412yes—
171D92C2×D412yescomplemented
172C4×D23—42no—
173C4×D23—42no—
174C4×D23—81no—
175Dic46—21no—
176Dic46—21no—
177C8×C23—21no—
178C8×C23—21no—
179C8×C23—21no—
180C8×C23C2×D412yescomplemented
181#3264—231nomaximal, Sylow
182C22×C23—21no—
183C22×C23—21no—
184C22×C23—21no—
185C22×C23—21no—
186C22×C23—21no—
187C22×C23AGL(1,ℤ/8)12yescomplemented
188C22×C23C22×D411yescharacteristic
189C2×D23—22no—
190C2×D23—22no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—41no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—41no—
204C2×D23—84no—
205C2×D23—84no—
206C2×D23—84no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—21no—
211C4×C23C22×D411yescharacteristic
212C4×C23H(5,𝔽2)11yescharacteristic
213Dic23—41no—
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#447—231no—
229#442—231no—
230#435D2311yescharacteristic, complemented
231C2×C23—22no—
232C2×C23—41no—
233C2×C23D4211yescharacteristic
234C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C23#57611yescharacteristic
236D23—42no—
237D23—42no—
238D23—81no—
239D23—81no—
240D23—81no—
241C2×#41—231no—
242C22×D4—231no—
243C22×D4—231no—
244C22×D4—231no—
245C22×D4—461no—
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×M16C2×D2311yescharacteristic, complemented
258C22×C8C2×D2311yescharacteristic, complemented
259#127—231no—
260#124—231no—
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×D4C2×D2311yescharacteristic
274C2×C22⋊C4—461no—
275#106—231no—
276C4⋊C8C2×D2311yescharacteristic, complemented
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102—231no—
282#102—231no—
283C22⋊C8C2×D2311yescharacteristic, complemented
284C22⋊C8C2×D2311yescharacteristic, complemented
285#97C2×D2311yescharacteristic, complemented
286C23#326411yescharacteristic, complemented, Sylow
287C24—461no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8—231no—
293C2×D4—231no—
294C2×D4—231no—
295C2×D4—231no—
296C2×D4—231no—
297C2×D4—231no—
298C2×D4—462no—
299C2×D4—462no—
300C2×D4—462no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—461no—
304C2×D4—461no—
305C2×D4—461no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—461no—
310C2×D4—921no—
311C2×D4—921no—
312C2×D4—921no—
313C2×D4—924no—
314C2×D4D9211yescharacteristic
315C22×C4—461no—
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—22no—
330C2×C8—22no—
331C2×C8C22×D2311yescharacteristic
332C2×C8C22×D2311yescharacteristic
333C2×C8C22×D2311yescharacteristic
334C2×C8C22×D2311yescharacteristic
335C4⋊C4—231no—
336C4⋊C4—231no—
337C4⋊C4—461no—
338C4⋊C4D9211yescharacteristic
339C22⋊C4—461no—
340C22⋊C4—461no—
341C22⋊C4—461no—
342C22⋊C4—461no—
343C22⋊C4—461no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4D9211yescharacteristic
348C22⋊C4D9211yescharacteristic
349C42C22×D2311yescharacteristic
350C23—461no—
351C23—461no—
352C23—461no—
353C23—461no—
354C23—461no—
355C23—922no—
356C23—922no—
357C23—922no—
358C23—922no—
359C23—922no—
360C23—922no—
361C23—1841no—
362C23—1841no—
363C23—1841no—
364C23C2×D9211yescharacteristic
365C23C2×D9211yescharacteristic
366Q8—461no—
367Q8—461no—
368D4—22no—
369D4—232no—
370D4—232no—
371D4—461no—
372D4—461no—
373D4—461no—
374D4—461no—
375D4—461no—
376D4—461no—
377D4—461no—
378D4—461no—
379D4—922no—
380D4—922no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—922no—
386D4—1841no—
387D4—1841no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—461no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—922no—
396C2×C4—922no—
397C2×C4—1841no—
398C2×C4C2×D9211yescharacteristic
399C2×C4C2×D9211yescharacteristic
400C2×C4C2×D9211yescharacteristic
401C2×C4C2×D9211yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D2312yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—462no—
413C22—462no—
414C22—921no—
415C22—921no—
416C22—921no—
417C22—921no—
418C22—921no—
419C22—921no—
420C22—921no—
421C22—921no—
422C22—921no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—1844no—
428C22—1844no—
429C22—1844no—
430C22#1062507912yescomplemented
431C22C22×D9211yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—921no—
437C4—921no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062516011yescharacteristic
441C2—22no—
442C2—41no—
443C2—922no—
444C2—922no—
445C2—1841no—
446C2—1841no—
447C2—1841no—
448C2D4×D9211yescharacteristic
449C2C2×#1062507911yescharacteristic
450C2#1309322211yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#435C2
socleC22×C23C22×D4
hypercenter#435D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C22×D184C2semidirect
3. #13093063C2semidirect
4. D4×D92C2semidirect
5. #13092806C2semidirect
6. #13092670C2semidirect
7. #13092646C2semidirect
8. #13092633C2semidirect
9. #13092613C2semidirect
10. #13092570C2semidirect
11. #13092564C2semidirect
12. #13092553C2semidirect
13. #13092553C2semidirect
14. #13092530C2semidirect
15. C23×#435C2semidirect
17. C2×#67288C22semidirect
19. C22×D92C22semidirect
20. C22×D92C22semidirect
21. C2×M16×C23C22semidirect
22. C22×C8×C23C22semidirect
26. #10625101C22semidirect
27. #10625101C22semidirect
28. #10625095C22semidirect
33. C2×D184C22semidirect
34. C2×D184C22semidirect
35. C2×D184C22semidirect
36. C2×D184C22semidirect
37. C2×#67263C22semidirect
38. C2×#67263C22semidirect
39. C2×#67263C22semidirect
46. #10625046C22semidirect
47. #10625045C22semidirect
48. C4×D92C22semidirect
49. C4×D92C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×C22⋊C8C22semidirect
52. C23×C22⋊C8C22semidirect
53. C23×#97C22semidirect
54. #10625003C22semidirect
55. #10625003C22semidirect
56. #10625003C22semidirect
57. #10625003C22semidirect
58. #10625003C22semidirect
59. #10624999C22semidirect
60. #10624998C22semidirect
120. D184D4semidirect
171. D92C2×D4semidirect
180. C8×C23C2×D4semidirect
187. C22×C23AGL(1,ℤ/8)semidirect
230. #435D23semidirect
257. C2×M16C2×D23semidirect
258. C22×C8C2×D23semidirect
276. C4⋊C8C2×D23semidirect
283. C22⋊C8C2×D23semidirect
284. C22⋊C8C2×D23semidirect
285. #97C2×D23semidirect
286. C23#3264semidirect
406. C8D4×D23semidirect
430. C22#10625079semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C22×D1842
#130930632
D4×D922
#130928062
#130926702
#130926462
#130926332
#130926132
#130925702
#130925642
#130925532
#130925302
C23×#4352
#326423