Subgroups — #44470155

Order 29888.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28417975	C₂	1	1	yes	maximal, characteristic
2	#28417959	C₂	1	2	yes	maximal, complemented
3	#28417889	C₂	1	1	yes	maximal, characteristic, complemented
4	#28417881	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#21418743	C₂²	1	2	yes	—
7	Dic₁₈₆₈	C₄	1	1	yes	characteristic, complemented
8	#21418732	C₄	1	2	yes	complemented
9	D₃₇₃₆	C₄	1	1	yes	characteristic, complemented
10	#21418727	C₂²	1	2	yes	—
11	#21418726	—	2	2	no	—
12	C₈×D₄₆₇	—	2	2	no	—
13	C₂×C₈×C₄₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₄₆₇	C₂²	1	1	yes	characteristic
15	C₄²×C₄₆₇	C₂²	1	1	yes	characteristic
16	Dic₉₃₄	C₂×C₄	1	2	yes	—
17	D₁₈₆₈	C₂×C₄	1	2	yes	—
18	C₂²⋊D₄₆₇	—	2	2	no	—
19	C₄×D₄₆₇	—	2	2	no	—
20	C₄₆₇⋊C₈	—	2	2	no	—
21	C₂×C₄×C₄₆₇	—	2	1	no	—
22	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
23	C₈×C₄₆₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₆₇	C₂×C₄	1	1	yes	characteristic
25	C₈×C₄₆₇	D₄	1	1	yes	characteristic
26	C₈×C₄₆₇	D₄	1	1	yes	characteristic
27	C₂²×C₄₆₇	#41	1	1	yes	characteristic
28	C₂×D₄₆₇	—	2	2	no	—
29	C₄×C₄₆₇	—	2	2	no	—
30	C₄×C₄₆₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₆₇	C₂×D₄	1	1	yes	characteristic
32	Dic₄₆₇	—	2	2	no	—
33	C₂×C₄₆₇	—	2	1	no	—
34	C₂×C₄₆₇	C₄×D₄	1	1	yes	characteristic
35	D₄₆₇	—	4	2	no	—
36	C₄₆₇	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	467	1	no	maximal, Sylow
38	#135	—	467	1	no	—
39	#131	—	467	2	no	—
40	#108	—	467	1	no	—
41	#104	—	467	2	no	—
42	C₄×C₈	D₄₆₇	1	1	yes	characteristic, complemented
43	#41	—	467	2	no	—
44	Q₁₆	—	467	1	no	—
45	SD₁₆	—	467	2	no	—
46	D₈	—	467	1	no	—
47	M₁₆	—	934	2	no	—
48	M₁₆	—	467	2	no	—
49	C₂×C₈	—	934	2	no	—
50	C₂×C₈	C₂×D₄₆₇	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₆₇	1	1	yes	characteristic
52	C₄²	C₂×D₄₆₇	1	1	yes	characteristic
53	Q₈	—	467	2	no	—
54	D₄	—	934	2	no	—
55	D₄	—	467	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	934	2	no	—
58	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
59	C₈	—	934	2	no	—
60	C₈	C₄×D₄₆₇	1	1	yes	characteristic
61	C₈	C₄×D₄₆₇	1	1	yes	characteristic
62	C₈	D₁₈₆₈	1	1	yes	characteristic
63	C₈	D₁₈₆₈	1	1	yes	characteristic
64	C₂²	—	934	2	no	—
65	C₂²	#21418743	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	934	2	no	—
68	C₄	C₂×C₄×D₄₆₇	1	1	yes	characteristic
69	C₄	C₂×D₁₈₆₈	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1868	2	no	—
72	C₂	C₄×D₁₈₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₈₆₈
commutator	C₄×C₄₆₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₆₇
Fitting	C₄×C₈×C₄₆₇	C₂
socle	C₂×C₄₆₇	C₄×D₄
prime radical	#28417975	C₂
cosocle	C₂×C₄×C₄₆₇	C₂³
hypercenter	C₄×C₈	D₄₆₇
hypocenter	C₄₆₇	#443
LCS	G ▷ C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #28417959	C₂	semidirect
3. #28417889	C₂	semidirect
4. #28417881	C₂	semidirect
5. C₄×C₈×C₄₆₇	C₂	semidirect
7. Dic₁₈₆₈	C₄	semidirect
8. #21418732	C₄	semidirect
9. D₃₇₃₆	C₄	semidirect
36. C₄₆₇	#443	semidirect
42. C₄×C₈	D₄₆₇	semidirect

Maximal subgroups

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

subgroup	index
#28417975	2
#28417959	2
#28417889	2
#28417881	2
C₄×C₈×C₄₆₇	2
#443	467