Subgroups — #44470313

Order 29888.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28417986	C₂	1	2	yes	maximal
2	C₂×Dic₁₈₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#28417959	C₂	1	1	yes	maximal, characteristic
4	#28417871	C₂	1	2	yes	maximal, complemented
5	#108×C₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#21418743	C₂²	1	1	yes	characteristic
7	C₂×Dic₉₃₄	C₂²	1	2	yes	—
8	Dic₁₈₆₈	—	2	2	no	—
9	Dic₁₈₆₈	—	2	1	no	—
10	Dic₁₈₆₈	—	2	1	no	—
11	#21418732	—	2	2	no	—
12	#21418727	C₂²	1	1	yes	characteristic
13	#21418726	—	2	1	no	—
14	C₈×D₄₆₇	—	2	1	no	—
15	M₁₆×C₄₆₇	C₂²	1	2	yes	—
16	C₂×C₈×C₄₆₇	C₂²	1	1	yes	characteristic
17	Dic₉₃₄	—	2	2	no	—
18	Dic₉₃₄	—	2	2	no	—
19	Dic₉₃₄	D₄	1	1	yes	characteristic
20	D₁₈₆₈	D₄	1	1	yes	characteristic
21	C₂²⋊D₄₆₇	—	2	1	no	—
22	C₂×Dic₄₆₇	—	2	2	no	—
23	C₄×D₄₆₇	—	2	1	no	—
24	C₄₆₇⋊C₈	—	2	1	no	—
25	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
26	C₈×C₄₆₇	—	2	2	no	—
27	C₈×C₄₆₇	D₄	1	1	yes	characteristic
28	C₈×C₄₆₇	D₄	1	1	yes	characteristic
29	C₂²×C₄₆₇	#41	1	1	yes	characteristic
30	C₂×D₄₆₇	—	2	1	no	—
31	C₄×C₄₆₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₆₇	C₂×D₄	1	1	yes	characteristic
33	Dic₄₆₇	—	2	1	no	—
34	Dic₄₆₇	—	4	2	no	—
35	C₂×C₄₆₇	—	2	1	no	—
36	C₂×C₄₆₇	#121	1	1	yes	characteristic
37	D₄₆₇	—	4	1	no	—
38	C₄₆₇	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	467	1	no	maximal, Sylow
40	#137	—	467	2	no	—
41	C₂×Q₁₆	—	467	1	no	—
42	#131	—	467	1	no	—
43	#108	D₄₆₇	1	1	yes	characteristic, complemented
44	#101	—	467	2	no	—
45	#41	—	467	1	no	—
46	C₂×Q₈	—	467	2	no	—
47	Q₁₆	—	934	2	no	—
48	Q₁₆	—	934	1	no	—
49	Q₁₆	—	934	1	no	—
50	SD₁₆	—	934	2	no	—
51	M₁₆	—	934	1	no	—
52	M₁₆	—	467	1	no	—
53	M₁₆	C₂×D₄₆₇	1	2	yes	—
54	C₂×C₈	—	934	1	no	—
55	C₂×C₈	C₂×D₄₆₇	1	1	yes	characteristic
56	Q₈	—	934	2	no	—
57	Q₈	—	934	2	no	—
58	Q₈	—	467	1	no	—
59	D₄	—	934	1	no	—
60	D₄	—	467	1	no	—
61	C₂×C₄	—	934	2	no	—
62	C₂×C₄	—	934	1	no	—
63	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	934	1	no	—
66	C₈	D₁₈₆₈	1	1	yes	characteristic
67	C₈	D₁₈₆₈	1	1	yes	characteristic
68	C₂²	—	934	1	no	—
69	C₂²	#21418744	1	1	yes	characteristic
70	C₄	—	1868	2	no	—
71	C₄	—	934	1	no	—
72	C₄	D₄×D₄₆₇	1	1	yes	characteristic
73	C₄	C₂×D₁₈₆₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	1868	1	no	—
76	C₂	#28417928	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28417928
commutator, cosocle	C₂×C₄×C₄₆₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₆₇
Fitting	#108×C₄₆₇	C₂
socle	C₂×C₄₆₇	#121
prime radical	#21418743	C₂²
hypercenter	#108	D₄₆₇
hypocenter	C₄₆₇	#473
LCS	G ▷ C₂×C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₈₆₈	C₂	semidirect
4. #28417871	C₂	semidirect
5. #108×C₄₆₇	C₂	semidirect
38. C₄₆₇	#473	semidirect
43. #108	D₄₆₇	semidirect

Maximal subgroups

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

subgroup	index
#28417986	2
C₂×Dic₁₈₆₈	2
#28417959	2
#28417871	2
#108×C₄₆₇	2
#473	467