Finite Group Databasebeta

← #15684883

Subgroups — #15684883

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
4D4×D92C211yesmaximal, characteristic, complemented
5#13092807C211yesmaximal, characteristic, complemented
6#13092669C211yesmaximal, characteristic, complemented
7#13092649C211yesmaximal, characteristic, complemented
8#13092613C211yesmaximal, characteristic, complemented
9#13092566C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092552C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092487C211yesmaximal, characteristic, complemented
15C23×#463C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic, complemented
17C2×D4×D23C2211yescharacteristic
18C2×D4×D23C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic, complemented
20C22×D92—21no—
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×D8×C23C2211yescharacteristic
23C23×#124C2211yescharacteristic, complemented
24C4×D4×C23C2211yescharacteristic, complemented
25#10625117C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic, complemented
27C2×#67274C2211yescharacteristic, complemented
28#10625109C2211yescharacteristic, complemented
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic, complemented
31C2×#67272C2211yescharacteristic, complemented
32#10625101—21no—
33#10625085—24no—
34D8×D23—24no—
35C2×D184C2211yescharacteristic, complemented
36C2×D184C2211yescharacteristic, complemented
37C2×#67262C2211yescharacteristic, complemented
38C2×C8×D23C2211yescharacteristic, complemented
39#10625066C2211yescharacteristic
40#10625066C2211yescharacteristic, complemented
41#10625055—21no—
42#10625054—21no—
43#10625053—21no—
44#10625053—21no—
45#10625053—21no—
46C22⋊C4×D23—21no—
47#10625045C2211yescharacteristic, complemented
48C4×D92C2211yescharacteristic
49C4×D92C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624990C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72#67292—22no—
73#67292—41no—
74D4×D23—22no—
75D4×D23—22no—
76D4×D23—22no—
77D4×D23—41no—
78D4×D23—41no—
79D4×D23—41no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—21no—
84C2×D92—21no—
85C2×D92—44no—
86C2×D92D411yescharacteristic
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×C4×D23C2311yescharacteristic
94SD16×C23—22no—
95D8×C23—22no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C42×C23C2311yescharacteristic
103C22⋊Dic23—21no—
104#67274—22no—
105#67274—41no—
106#67272—22no—
107#67272—41no—
108#67272D414yescomplemented
109(C2×D23)⋊C4—21no—
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
117Dic23⋊C4—21no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—22no—
121D184—22no—
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C22×D23—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×C23C2×D412yes—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—42no—
149C2×C4×C23C2×D411yescharacteristic
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2411yescharacteristic
152C22⋊D23—42no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—81no—
156C2×Dic23—21no—
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—22no—
160D92—21no—
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—42no—
166D92—42no—
167D92—42no—
168D92—42no—
169D92—81no—
170D92C2×D412yescomplemented
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—21no—
174C4×D23—21no—
175C4×D23—42no—
176C4×D23—81no—
177C8×C23—21no—
178C8×C23—21no—
179C23⋊C8—21no—
180C23⋊C8C2×D412yescomplemented
181#3264—231nomaximal, Sylow
182C22×C23—22no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23C22×D411yescharacteristic
189C2×D23—21no—
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—22no—
193C2×D23—21no—
194C2×D23—21no—
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—84no—
204C2×D23—84no—
205C2×D23—84no—
206C2×D23AGL(1,ℤ/8)12yescomplemented
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—41no—
210C4×C23—41no—
211C4×C23C22×D411yescharacteristic
212C4×C23H(5,𝔽2)11yescharacteristic
213Dic23—21no—
214Dic23—21no—
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#463D2311yescharacteristic, complemented
224#459—231no—
225#450—231no—
226#449—231no—
227#447—231no—
228#447—231no—
229#442—231no—
230#435—231no—
231C2×C23—42no—
232C2×C23—81no—
233C2×C23D4211yescharacteristic
234C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C23#57611yescharacteristic
236D23—22no—
237D23—41no—
238D23—42no—
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×SD16C2×D2311yescharacteristic, complemented
250C2×D8—231no—
251C2×D8—231no—
252C2×D8—231no—
253C2×D8—231no—
254C2×D8—231no—
255C2×D8—464no—
256C2×D8C2×D2311yescharacteristic
257C2×M16—231no—
258C22×C8—231no—
259#127—231no—
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×D4C2×D2311yescharacteristic, complemented
274C2×C22⋊C4—461no—
275#106—231no—
276C4⋊C8C2×D2311yescharacteristic, complemented
277#103C2×D2311yescharacteristic, complemented
278#102—231no—
279#102—231no—
280#102—231no—
281#102—231no—
282#102C2×D2311yescharacteristic, complemented
283C22⋊C8—231no—
284C22⋊C8—231no—
285#97—231no—
286C23#326411yescharacteristic, complemented, Sylow
287C24—461no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8C22×D2311yescharacteristic
293C2×D4—231no—
294C2×D4—231no—
295C2×D4—231no—
296C2×D4—231no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—462no—
304C2×D4—462no—
305C2×D4—462no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—924no—
310C2×D4—921no—
311C2×D4—921no—
312C2×D4—921no—
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—21no—
316C22×C4—231no—
317C22×C4—231no—
318C22×C4—461no—
319C22×C4—461no—
320SD16—22no—
321SD16—462no—
322SD16—921no—
323D8—22no—
324D8—234no—
325D8—462no—
326D8—462no—
327D8—462no—
328D8—921no—
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—21no—
341C22⋊C4—21no—
342C22⋊C4—231no—
343C22⋊C4—231no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4—461no—
348C22⋊C4—461no—
349C42C22×D2311yescharacteristic
350C23—21no—
351C23—21no—
352C23—231no—
353C23—231no—
354C23—461no—
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—232no—
372D4—462no—
373D4—461no—
374D4—461no—
375D4—461no—
376D4—461no—
377D4—461no—
378D4—922no—
379D4—922no—
380D4—922no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—1841no—
386D4—1841no—
387D4D4×D2312yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—231no—
392C2×C4—231no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—922no—
399C2×C4—1841no—
400C2×C4D4×D2311yescharacteristic
401C2×C4D4×D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—21no—
405C8—232no—
406C8—461no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—232no—
414C22—461no—
415C22—461no—
416C22—461no—
417C22—461no—
418C22—461no—
419C22—462no—
420C22—921no—
421C22—921no—
422C22—921no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—1844no—
429C22—1844no—
430C22—1844no—
431C22C2×D4×D2311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—461no—
437C4—461no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062516011yescharacteristic
441C2—42no—
442C2—81no—
443C2—462no—
444C2—921no—
445C2—922no—
446C2—1841no—
447C2—1841no—
448C2#1309305111yescharacteristic
449C2AGL(1,ℤ/8)×D2311yescharacteristic
450C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#463C2
socleC22×C23C22×D4
hypercenter#463D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×D8×D23C2semidirect
3. #13093060C2semidirect
4. D4×D92C2semidirect
5. #13092807C2semidirect
6. #13092669C2semidirect
7. #13092649C2semidirect
8. #13092613C2semidirect
9. #13092566C2semidirect
10. #13092565C2semidirect
11. #13092552C2semidirect
12. #13092549C2semidirect
13. #13092527C2semidirect
14. #13092487C2semidirect
15. C23×#463C2semidirect
16. C2×#67292C22semidirect
18. C2×D4×D23C22semidirect
19. C2×D4×D23C22semidirect
21. C2×SD16×C23C22semidirect
23. C23×#124C22semidirect
24. C4×D4×C23C22semidirect
25. #10625117C22semidirect
26. C2×#67274C22semidirect
27. C2×#67274C22semidirect
28. #10625109C22semidirect
30. C2×#67272C22semidirect
31. C2×#67272C22semidirect
35. C2×D184C22semidirect
36. C2×D184C22semidirect
37. C2×#67262C22semidirect
38. C2×C8×D23C22semidirect
40. #10625066C22semidirect
47. #10625045C22semidirect
49. C4×D92C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×#103C22semidirect
52. C23×#102C22semidirect
53. #10625014C22semidirect
54. #10625003C22semidirect
55. #10625003C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10624991C22semidirect
59. #10624990C22semidirect
60. #10624985C22semidirect
108. #67272D4semidirect
170. D92C2×D4semidirect
180. C23⋊C8C2×D4semidirect
206. C2×D23AGL(1,ℤ/8)semidirect
223. #463D23semidirect
249. C2×SD16C2×D23semidirect
260. #124C2×D23semidirect
273. C4×D4C2×D23semidirect
276. C4⋊C8C2×D23semidirect
277. #103C2×D23semidirect
282. #102C2×D23semidirect
286. C23#3264semidirect

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
D4×D922
#130928072
#130926692
#130926492
#130926132
#130925662
#130925652
#130925522
#130925492
#130925272
#130924872
C23×#4632
#326423