Finite Group Databasebeta

← #15684872

Subgroups — #15684872

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
2C2×D8×D23C211yesmaximal, characteristic, complemented
3#13093062C211yesmaximal, characteristic, complemented
4#13093052C211yesmaximal, characteristic, complemented
5#13092804C211yesmaximal, characteristic, complemented
6#13092669C211yesmaximal, characteristic, complemented
7#13092645C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092569C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic, complemented
11#13092552C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092487C211yesmaximal, characteristic, complemented
15C23×#459C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic, complemented
17C2×D4×D23—21no—
18C2×D4×D23C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic, complemented
20C2×D4×D23C2211yescharacteristic, complemented
21C2×D8×C23C2211yescharacteristic, complemented
22C2×D8×C23C2211yescharacteristic, complemented
23C23×#127C2211yescharacteristic, complemented
24C4×D4×C23C2211yescharacteristic, complemented
25#10625109—21no—
26#10625109C2211yescharacteristic
27#10625109C2211yescharacteristic, complemented
28#10625108—21no—
29#10625108—21no—
30C2×#67273C2211yescharacteristic, complemented
31C2×#67273C2211yescharacteristic, complemented
32C2×#67272C2211yescharacteristic
33C2×#67272C2211yescharacteristic, complemented
34C2×#67272C2211yescharacteristic, complemented
35#10625101—21no—
36C2×(C2×D23)⋊C4—21no—
37#10625082—24no—
38D8×D23—24no—
39C2×D184C2211yescharacteristic
40C2×#67263C2211yescharacteristic, complemented
41C2×#67262C2211yescharacteristic, complemented
42C2×C8×D23C2211yescharacteristic, complemented
43#10625068C2211yescharacteristic, complemented
44#10625066C2211yescharacteristic, complemented
45#10625057—21no—
46#10625053—21no—
47#10625046C2211yescharacteristic, complemented
48C4×D92C2211yescharacteristic
49C4×D92C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624990C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C22×Dic23—21no—
77#67290—22no—
78#67290—41no—
79D4×D23—22no—
80D4×D23—22no—
81D4×D23—22no—
82D4×D23—41no—
83D4×D23—41no—
84D4×D23—41no—
85D4×D23—44no—
86C2×D92—21no—
87C2×D92D411yescharacteristic
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23C2311yescharacteristic
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94D8×C23—22no—
95D8×C23—22no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C42×C23C2311yescharacteristic
101C22⋊Dic23—21no—
102C22⋊Dic23—21no—
103#67273—22no—
104#67273—41no—
105#67272—22no—
106#67272—41no—
107#67272D414yescomplemented
108(C2×D23)⋊C4—21no—
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⋊Dic23—21no—
116C4⋊Dic23D411yescharacteristic
117C4⋊Dic23C2311yescharacteristic
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—22no—
121#67263—22no—
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
140D4×C23—21no—
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—21no—
145D4×C23—42no—
146D4×C23—81no—
147D4×C23C2×D412yescomplemented
148C2×C4×C23—21no—
149C2×C4×C23—81no—
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2411yescharacteristic
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—42no—
158C22⋊D23—42no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—42no—
162C2×Dic23C2×D411yescharacteristic
163C2×Dic23C2×D411yescharacteristic
164D92—22no—
165D92—21no—
166D92—21no—
167D92—21no—
168D92—81no—
169D92C2×D412yes—
170C4×D23—21no—
171C4×D23—21no—
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—22no—
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—21no—
197C2×D23—21no—
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×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#496—231no—
221#469—231no—
222#465—231no—
223#463—231no—
224#459D2311yescharacteristic, complemented
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×C23—81no—
234C2×C23D4211yescharacteristic
235C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C23#57611yescharacteristic
237D23—22no—
238D23—41no—
239D23—42no—
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—464no—
255C2×D8C2×D2311yescharacteristic, complemented
256C2×D8C2×D2311yescharacteristic, complemented
257C2×M16—231no—
258C22×C8—231no—
259#127C2×D2311yescharacteristic, complemented
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, complemented
274C2×C22⋊C4—461no—
275#106—231no—
276C4⋊C8C2×D2311yescharacteristic, complemented
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102C2×D2311yescharacteristic, complemented
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×Q8—231no—
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—21no—
316C22×C4—231no—
317C22×C4—231no—
318C22×C4—461no—
319C22×C4—461no—
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—22no—
324D8—22no—
325D8—234no—
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—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—
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—461no—
367Q8—461no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—232no—
376D4—462no—
377D4—461no—
378D4—461no—
379D4—461no—
380D4—922no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—922no—
386D4—1841no—
387D4D4×D2312yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—231no—
391C2×C4—231no—
392C2×C4—461no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—922no—
399C2×C4—922no—
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—41no—
414C22—41no—
415C22—41no—
416C22—232no—
417C22—461no—
418C22—461no—
419C22—461no—
420C22—461no—
421C22—461no—
422C22—462no—
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—461no—
436C4—461no—
437C4—921no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062516011yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—462no—
445C2—921no—
446C2—922no—
447C2—1841no—
448C2#1309305111yescharacteristic
449C2AGL(1,ℤ/8)×D2311yescharacteristic
450C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#459C2
socleC22×C23C22×D4
hypercenter#459D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×D8×D23C2semidirect
3. #13093062C2semidirect
4. #13093052C2semidirect
5. #13092804C2semidirect
6. #13092669C2semidirect
7. #13092645C2semidirect
8. #13092633C2semidirect
9. #13092569C2semidirect
10. #13092559C2semidirect
11. #13092552C2semidirect
12. #13092549C2semidirect
13. #13092527C2semidirect
14. #13092487C2semidirect
15. C23×#459C2semidirect
16. C2×#67290C22semidirect
19. C2×D4×D23C22semidirect
20. C2×D4×D23C22semidirect
21. C2×D8×C23C22semidirect
22. C2×D8×C23C22semidirect
23. C23×#127C22semidirect
24. C4×D4×C23C22semidirect
27. #10625109C22semidirect
30. C2×#67273C22semidirect
31. C2×#67273C22semidirect
33. C2×#67272C22semidirect
34. C2×#67272C22semidirect
40. C2×#67263C22semidirect
41. C2×#67262C22semidirect
42. C2×C8×D23C22semidirect
43. #10625068C22semidirect
44. #10625066C22semidirect
47. #10625046C22semidirect
49. C4×D92C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×#102C22semidirect
52. C23×#102C22semidirect
53. #10625014C22semidirect
54. #10625003C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624998C22semidirect
58. #10624991C22semidirect
59. #10624990C22semidirect
60. #10624985C22semidirect
107. #67272D4semidirect
147. D4×C23C2×D4semidirect
180. C23⋊C8C2×D4semidirect
206. C2×D23AGL(1,ℤ/8)semidirect
224. #459D23semidirect
255. C2×D8C2×D23semidirect
256. C2×D8C2×D23semidirect
259. #127C2×D23semidirect
273. C4×D4C2×D23semidirect
276. C4⋊C8C2×D23semidirect
281. #102C2×D23semidirect
282. #102C2×D23semidirect
286. C23#3264semidirect
387. D4D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×D8×D232
#130930622
#130930522
#130928042
#130926692
#130926452
#130926332
#130925692
#130925592
#130925522
#130925492
#130925272
#130924872
C23×#4592
#326423