Finite Group Databasebeta

← #15682660

Subgroups — #15682660

Order 2944.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625155C211yesmaximal, characteristic, complemented
2C2×#10625082C211yesmaximal, characteristic, complemented
3C2×D8×D23C211yesmaximal, characteristic, complemented
4#13092983C211yesmaximal, characteristic, complemented
5#13092564C211yesmaximal, characteristic, complemented
6#13092563C211yesmaximal, characteristic, complemented
7#13092560C211yesmaximal, characteristic, complemented
8#13092559C211yesmaximal, characteristic, complemented
9#13092552C211yesmaximal, characteristic, complemented
10#13092551C211yesmaximal, characteristic, complemented
11#13092549C211yesmaximal, characteristic, complemented
12#13092420C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14#13092382C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic, complemented
17C22×C22⋊D23—21no—
18C22×C22⋊D23—21no—
19#10625155—24no—
20#10625155—24no—
21C2×#67290—21no—
22C2×#67290C2211yescharacteristic
23C2×#67290C2211yescharacteristic, complemented
24C2×D4×D23—21no—
25C2×D4×D23C2211yescharacteristic
26C2×D4×D23C2211yescharacteristic, complemented
27C2×D4×D23C2211yescharacteristic, complemented
28C2×#67288C2211yescharacteristic
29C2×#67288C2211yescharacteristic, complemented
30C2×D8×C23C2211yescharacteristic, complemented
31C2×D8×C23C2211yescharacteristic, complemented
32C23×#121C2211yescharacteristic, complemented
33#10625111—21no—
34#10625109C2211yescharacteristic, complemented
35#10625108—21no—
36C2×#67273C2211yescharacteristic, complemented
37C2×#67272C2211yescharacteristic, complemented
38C2×#67272C2211yescharacteristic, complemented
39C2×#67272C2211yescharacteristic, complemented
40#10625101C2211yescharacteristic, complemented
41#10625082—24no—
42D8×D23—24no—
43C2×D184C2211yescharacteristic, complemented
44C2×#67263C2211yescharacteristic, complemented
45C2×#67262C2211yescharacteristic, complemented
46C2×C8×D23C2211yescharacteristic, complemented
47#10625066C2211yescharacteristic, complemented
48#10625063C2211yescharacteristic, complemented
49#10625056—21no—
50#10625053—21no—
51C23×#102C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53C23×C22⋊C8C2211yescharacteristic, complemented
54#10625014C2211yescharacteristic, complemented
55#10625014C2211yescharacteristic, complemented
56C22⋊(C23⋊C8)C2211yescharacteristic, complemented
57#10625003C2211yescharacteristic, complemented
58(C2×D23)⋊C8C2211yescharacteristic, complemented
59(C2×D23)⋊C8C2211yescharacteristic, complemented
60#10624998C2211yescharacteristic, complemented
61#10624992C2211yescharacteristic, complemented
62#10624991C2211yescharacteristic, complemented
63C24×C23—21no—
64C23×D23—21no—
65C23×D23—21no—
66C23×D23—21no—
67C2×D4×C23—22no—
68C2×D4×C23—22no—
69C2×D4×C23—21no—
70C2×D4×C23—21no—
71C2×D4×C23C2311yescharacteristic
72C2×D4×C23C2311yescharacteristic
73C2×D4×C23C2311yescharacteristic
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—28no—
76C2×C22⋊D23—28no—
77C2×C22⋊D23—21no—
78C2×C22⋊D23—21no—
79C2×C22⋊D23—21no—
80C2×C22⋊D23—21no—
81C2×C22⋊D23—21no—
82C2×C22⋊D23—21no—
83C2×C22⋊D23—21no—
84C2×C22⋊D23—21no—
85C2×C22⋊D23D411yescharacteristic
86C2×C22⋊D23D411yescharacteristic
87C22×Dic23—21no—
88C22×Dic23—21no—
89#67290—28no—
90#67290—22no—
91#67290—22no—
92#67290—22no—
93#67290D414yescomplemented
94D4×D23—28no—
95D4×D23—22no—
96D4×D23—22no—
97D4×D23—22no—
98D4×D23—22no—
99D4×D23—22no—
100D4×D23D414yescomplemented
101#67288—22no—
102#67288—22no—
103#67288—22no—
104#67288—22no—
105C2×D92—21no—
106C2×D92D411yescharacteristic
107C2×D92C2311yescharacteristic
108C2×D92C2311yescharacteristic
109C2×C4×D23—21no—
110C2×C4×D23C2311yescharacteristic
111C2×C4×D23C2311yescharacteristic
112C2×Dic46D411yescharacteristic
113C2×Dic46C2311yescharacteristic
114D8×C23—22no—
115D8×C23—22no—
116C2×C8×C23C2311yescharacteristic
117C2×C8×C23C2311yescharacteristic
118C4⋊C4×C23C2311yescharacteristic
119C22⋊C4×C23—21no—
120C22⋊Dic23—21no—
121#67273—22no—
122#67272—22no—
123#67272—22no—
124#67272—22no—
125(C2×D23)⋊C4—21no—
126(C2×D23)⋊C4—21no—
127(C2×D23)⋊C4—21no—
128C4⋊Dic23C2311yescharacteristic
129C4×Dic23—21no—
130C2×C23⋊C8C2311yescharacteristic
131C2×C23⋊C8C2311yescharacteristic
132D184—22no—
133#67263—22no—
134#67262—22no—
135C8×D23—22no—
136C23×C23—24no—
137C23×C23—21no—
138C23×C23—21no—
139C23×C23—21no—
140C23×C23—81no—
141C23×C23—81no—
142C23×C23C2×D411yescharacteristic
143C22×D23—21no—
144C22×D23—24no—
145C22×D23—24no—
146C22×D23—21no—
147C22×D23—42no—
148C22×D23—81no—
149C22×D23—81no—
150C22×D23—81no—
151C22×D23—81no—
152C22×D23—81no—
153C22×D23—81no—
154C22×D23C2×D411yescharacteristic
155C22×D23C2×D411yescharacteristic
156D4×C23—24no—
157D4×C23—21no—
158D4×C23—21no—
159D4×C23—21no—
160D4×C23—21no—
161D4×C23—81no—
162D4×C23C2×D412yes—
163D4×C23C2×D412yes—
164C2×C4×C23—21no—
165C2×C4×C23—21no—
166C2×C4×C23—21no—
167C2×C4×C23C2×D411yescharacteristic
168C2×C4×C23C2411yescharacteristic
169C22⋊D23—24no—
170C22⋊D23—24no—
171C22⋊D23—24no—
172C22⋊D23—22no—
173C22⋊D23—24no—
174C22⋊D23—22no—
175C22⋊D23—24no—
176C22⋊D23—42no—
177C22⋊D23—81no—
178C22⋊D23—81no—
179C2×Dic23—24no—
180C2×Dic23—21no—
181C2×Dic23—24no—
182C2×Dic23—21no—
183C2×Dic23C2×D411yescharacteristic
184C2×Dic23C2×D411yescharacteristic
185D92—22no—
186D92—21no—
187D92—21no—
188D92—21no—
189D92—81no—
190D92C2×D412yes—
191C4×D23—24no—
192C4×D23—21no—
193C4×D23—21no—
194C4×D23C2×D412yes—
195C4×D23C2×D412yes—
196Dic46—21no—
197Dic46—22no—
198Dic46C2×D412yes—
199C8×C23—21no—
200C8×C23—21no—
201C23⋊C8—21no—
202C23⋊C8—21no—
203#3008—231nomaximal, Sylow
204C22×C23—22no—
205C22×C23—22no—
206C22×C23—21no—
207C22×C23—21no—
208C22×C23—21no—
209C22×C23—41no—
210C22×C23—41no—
211C22×C23—41no—
212C22×C23—41no—
213C22×C23—41no—
214C22×C23—41no—
215C22×C23—41no—
216C22×C23—84no—
217C22×C23C22×D411yescharacteristic
218C2×D23—21no—
219C2×D23—21no—
220C2×D23—21no—
221C2×D23—22no—
222C2×D23—21no—
223C2×D23—21no—
224C2×D23—41no—
225C2×D23—41no—
226C2×D23—41no—
227C2×D23—41no—
228C2×D23—41no—
229C2×D23—84no—
230C2×D23—84no—
231C2×D23—84no—
232C2×D23#12012yes—
233C4×C23—21no—
234C4×C23—41no—
235C4×C23C22×D411yescharacteristic
236C4×C23C22×D411yescharacteristic
237Dic23—21no—
238Dic23—22no—
239Dic23—41no—
240Dic23#12012yes—
241C2×H(5,𝔽2)—231no—
242C2×AGL(1,ℤ/8)—231no—
243C22×D8—231no—
244#535—231no—
245#449—231no—
246#449—231no—
247#449—231no—
248#449—231no—
249#447—231no—
250#447—231no—
251#447—231no—
252#447D2311yescharacteristic, complemented
253#418—231no—
254#416—231no—
255#408—231no—
256C2×C23—42no—
257C2×C23—42no—
258C2×C23—41no—
259C2×C23—81no—
260C2×C23C2×#12011yescharacteristic
261C2×C23#57611yescharacteristic
262C2×C23#57611yescharacteristic
263D23—22no—
264D23—41no—
265D23—42no—
266D23—81no—
267H(5,𝔽2)—464no—
268H(5,𝔽2)—464no—
269C2×#41—231no—
270C2×#41—231no—
271C2×#41—231no—
272C2×#41—231no—
273C2×#41—461no—
274C22×D4—231no—
275C22×D4—231no—
276C22×D4—231no—
277C22×D4—461no—
278C22×D4—461no—
279C22×D4—461no—
280C22×D4C2×D2311yescharacteristic, complemented
281AGL(1,ℤ/8)—464no—
282C2×SD16—231no—
283C2×SD16—231no—
284C2×D8—231no—
285C2×D8—231no—
286C2×D8—231no—
287C2×D8—231no—
288C2×D8—464no—
289C2×D8C2×D2311yescharacteristic, complemented
290C2×D8C2×D2311yescharacteristic, complemented
291C2×M16—231no—
292C22×C8—231no—
293#127—461no—
294#124—461no—
295#121—231no—
296#121—231no—
297#121—231no—
298#121C2×D2311yescharacteristic, complemented
299#120—461no—
300#120—461no—
301#117—231no—
302#103—231no—
303#103—231no—
304#102—231no—
305#102—231no—
306#102—231no—
307#102—231no—
308#102C2×D2311yescharacteristic, complemented
309#102C2×D2311yescharacteristic, complemented
310C22⋊C8—231no—
311C22⋊C8—231no—
312C22⋊C8—231no—
313C22⋊C8C2×D2311yescharacteristic, complemented
314C23#300811yescharacteristic, complemented, Sylow
315C24—21no—
316C24—461no—
317C24—461no—
318C24—461no—
319#41—234no—
320#41—462no—
321#41—462no—
322#41—462no—
323#41—462no—
324#41—462no—
325#41—462no—
326#41—468no—
327#41—462no—
328C2×Q8—231no—
329C2×Q8—231no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—234no—
335C2×D4—231no—
336C2×D4—231no—
337C2×D4—231no—
338C2×D4—231no—
339C2×D4—231no—
340C2×D4—461no—
341C2×D4—462no—
342C2×D4—462no—
343C2×D4—462no—
344C2×D4—461no—
345C2×D4—461no—
346C2×D4—461no—
347C2×D4—462no—
348C2×D4—468no—
349C2×D4—461no—
350C2×D4—461no—
351C2×D4—468no—
352C2×D4—468no—
353C2×D4—461no—
354C2×D4—462no—
355C2×D4—461no—
356C2×D4—461no—
357C2×D4C22×D2311yescharacteristic
358C2×D4C22×D2311yescharacteristic
359C2×D4C22×D2311yescharacteristic
360C22×C4—231no—
361C22×C4—231no—
362C22×C4—461no—
363C22×C4—461no—
364C22×C4—461no—
365C22×C4C22×D2311yescharacteristic
366SD16—462no—
367SD16—462no—
368D8—22no—
369D8—22no—
370D8—462no—
371D8—462no—
372D8—462no—
373D8—462no—
374M16—462no—
375C2×C8—231no—
376C2×C8—231no—
377C2×C8—462no—
378C2×C8C22×D2311yescharacteristic
379C2×C8C22×D2311yescharacteristic
380C4⋊C4—231no—
381C4⋊C4C22×D2311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—461no—
384C22⋊C4—461no—
385C22⋊C4—461no—
386C22⋊C4—461no—
387C42—461no—
388C23—24no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—81no—
393C23—81no—
394C23—231no—
395C23—231no—
396C23—464no—
397C23—464no—
398C23—461no—
399C23—461no—
400C23—922no—
401C23—1841no—
402C23—1841no—
403C23—1841no—
404C23—1841no—
405C23—1841no—
406C23—1841no—
407C23D4×D2311yescharacteristic
408Q8—232no—
409Q8—462no—
410Q8—461no—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—21no—
416D4—81no—
417D4—232no—
418D4—462no—
419D4—462no—
420D4—464no—
421D4—462no—
422D4—464no—
423D4—464no—
424D4—464no—
425D4—464no—
426D4—461no—
427D4—461no—
428D4—461no—
429D4—922no—
430D4—1841no—
431D4—1841no—
432D4—1841no—
433D4D4×D2312yes—
434D4D4×D2312yes—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—231no—
439C2×C4—232no—
440C2×C4—232no—
441C2×C4—231no—
442C2×C4—464no—
443C2×C4—464no—
444C2×C4—464no—
445C2×C4—461no—
446C2×C4—461no—
447C2×C4—461no—
448C2×C4—461no—
449C2×C4D4×D2311yescharacteristic
450C2×C4C23×D2311yescharacteristic
451C8—21no—
452C8—21no—
453C8—461no—
454C8—461no—
455C22—21no—
456C22—22no—
457C22—22no—
458C22—21no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—84no—
468C22—232no—
469C22—461no—
470C22—461no—
471C22—462no—
472C22—461no—
473C22—461no—
474C22—461no—
475C22—921no—
476C22—921no—
477C22—921no—
478C22—921no—
479C22—921no—
480C22—1844no—
481C22—1844no—
482C22—1844no—
483C22C2×D4×D2311yescharacteristic
484C4—21no—
485C4—41no—
486C4—232no—
487C4—461no—
488C4—462no—
489C4—921no—
490C4C2×D4×D2311yescharacteristic
491C4C2×D4×D2311yescharacteristic
492C2—41no—
493C2—42no—
494C2—42no—
495C2—81no—
496C2—462no—
497C2—921no—
498C2—922no—
499C2—1841no—
500C2#120×D2311yescharacteristic
501C2#1309321811yescharacteristic
502C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3008
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×#10625155C2semidirect
2. C2×#10625082C2semidirect
3. C2×D8×D23C2semidirect
4. #13092983C2semidirect
5. #13092564C2semidirect
6. #13092563C2semidirect
7. #13092560C2semidirect
8. #13092559C2semidirect
9. #13092552C2semidirect
10. #13092551C2semidirect
11. #13092549C2semidirect
12. #13092420C2semidirect
13. #13092410C2semidirect
14. #13092382C2semidirect
15. C23×#447C2semidirect
16. C22×D4×C23C22semidirect
23. C2×#67290C22semidirect
26. C2×D4×D23C22semidirect
27. C2×D4×D23C22semidirect
29. C2×#67288C22semidirect
30. C2×D8×C23C22semidirect
31. C2×D8×C23C22semidirect
32. C23×#121C22semidirect
34. #10625109C22semidirect
36. C2×#67273C22semidirect
37. C2×#67272C22semidirect
38. C2×#67272C22semidirect
39. C2×#67272C22semidirect
40. #10625101C22semidirect
43. C2×D184C22semidirect
44. C2×#67263C22semidirect
45. C2×#67262C22semidirect
46. C2×C8×D23C22semidirect
47. #10625066C22semidirect
48. #10625063C22semidirect
51. C23×#102C22semidirect
52. C23×#102C22semidirect
53. C23×C22⋊C8C22semidirect
54. #10625014C22semidirect
55. #10625014C22semidirect
56. C22⋊(C23⋊C8)C22semidirect
57. #10625003C22semidirect
58. (C2×D23)⋊C8C22semidirect
59. (C2×D23)⋊C8C22semidirect
60. #10624998C22semidirect
61. #10624992C22semidirect
62. #10624991C22semidirect
93. #67290D4semidirect
100. D4×D23D4semidirect
252. #447D23semidirect
280. C22×D4C2×D23semidirect
289. C2×D8C2×D23semidirect
290. C2×D8C2×D23semidirect
298. #121C2×D23semidirect
308. #102C2×D23semidirect
309. #102C2×D23semidirect
313. C22⋊C8C2×D23semidirect
314. C23#3008semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
C2×#106250822
C2×D8×D232
#130929832
#130925642
#130925632
#130925602
#130925592
#130925522
#130925512
#130925492
#130924202
#130924102
#130923822
C23×#4472
#300823