Subgroups — #44470378

Order 29888.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28417932	C₂	1	1	yes	maximal, characteristic
2	#28417886	C₂	1	1	yes	maximal, characteristic, complemented
3	#28417884	C₂	1	1	yes	maximal, characteristic, complemented
4	#28417876	C₂	1	1	yes	maximal, characteristic, complemented
5	#28417876	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²⋊(C₄₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	#117×C₄₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₃₄	C₂²	1	1	yes	characteristic
9	C₂×C₄₆₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄₆₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₆₇	C₂²	1	1	yes	characteristic
12	Dic₄₆₇⋊C₄	—	2	1	no	—
13	C₂²⋊Dic₄₆₇	—	2	1	no	—
14	C₂²×C₄×C₄₆₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₄₆₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₄₆₇	C₂²	1	1	yes	characteristic
17	C₂²⋊C₄×C₄₆₇	—	2	1	no	—
18	C₄²×C₄₆₇	—	2	1	no	—
19	Dic₉₃₄	—	2	1	no	—
20	Dic₉₃₄	—	2	1	no	—
21	C₂×Dic₄₆₇	—	2	1	no	—
22	C₂×Dic₄₆₇	—	2	1	no	—
23	C₄₆₇⋊C₈	—	2	1	no	—
24	C₄₆₇⋊C₈	—	2	1	no	—
25	C₂³×C₄₆₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₄₆₇	—	2	1	no	—
27	C₂×C₄×C₄₆₇	—	2	1	no	—
28	C₂×C₄×C₄₆₇	—	2	1	no	—
29	C₂×C₄×C₄₆₇	—	2	1	no	—
30	C₂×C₄×C₄₆₇	D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
32	C₂²×C₄₆₇	—	2	1	no	—
33	C₂²×C₄₆₇	—	2	1	no	—
34	C₂²×C₄₆₇	—	2	1	no	—
35	C₂²×C₄₆₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₆₇	—	2	1	no	—
37	C₄×C₄₆₇	—	4	1	no	—
38	C₄×C₄₆₇	—	4	1	no	—
39	C₄×C₄₆₇	#41	1	1	yes	characteristic
40	C₄×C₄₆₇	#41	1	1	yes	characteristic
41	Dic₄₆₇	—	4	1	no	—
42	Dic₄₆₇	—	4	1	no	—
43	C₂×C₄₆₇	—	4	1	no	—
44	C₂×C₄₆₇	#123	1	1	yes	characteristic
45	C₂×C₄₆₇	#135	1	1	yes	characteristic
46	C₂×C₄₆₇	#137	1	1	yes	characteristic
47	C₄₆₇	#485	1	1	yes	characteristic, complemented, Sylow
48	#485	—	467	1	no	maximal, Sylow
49	C₂²⋊Q₈	—	467	1	no	—
50	#117	D₄₆₇	1	1	yes	characteristic
51	#107	—	467	1	no	—
52	#106	—	467	1	no	—
53	#103	—	467	1	no	—
54	#103	—	467	1	no	—
55	C₂²⋊C₈	—	467	1	no	—
56	C₂×Q₈	—	467	1	no	—
57	C₂²×C₄	C₂×D₄₆₇	1	1	yes	characteristic
58	C₂×C₈	—	467	1	no	—
59	C₂×C₈	—	467	1	no	—
60	C₄⋊C₄	—	934	1	no	—
61	C₄⋊C₄	—	467	1	no	—
62	C₄⋊C₄	C₂×D₄₆₇	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₄₆₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	2	1	no	—
65	C₂²⋊C₄	—	934	1	no	—
66	C₄²	—	2	1	no	—
67	C₂³	C₂²⋊D₄₆₇	1	1	yes	characteristic
68	Q₈	—	934	1	no	—
69	Q₈	—	934	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	934	1	no	—
75	C₂×C₄	—	934	1	no	—
76	C₂×C₄	C₂²⋊D₄₆₇	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
78	C₈	—	934	1	no	—
79	C₈	—	934	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂×C₂²⋊D₄₆₇	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	1868	1	no	—
88	C₄	—	1868	1	no	—
89	C₄	#21418743	1	1	yes	characteristic
90	C₄	#21418743	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	#28417936	1	1	yes	characteristic
93	C₂	#28417973	1	1	yes	characteristic
94	C₂	#28417983	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₆₇
commutator, cosocle	C₂×C₄×C₄₆₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₆₇
Fitting	#117×C₄₆₇	C₂
socle	C₂²×C₄₆₇	C₂×D₄
prime radical	C₂³×C₄₆₇	D₄
hypercenter	#117	D₄₆₇
hypocenter	C₄₆₇	#485
LCS	G ▷ C₂×C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #28417886	C₂	semidirect
3. #28417884	C₂	semidirect
4. #28417876	C₂	semidirect
5. #28417876	C₂	semidirect
47. C₄₆₇	#485	semidirect

Maximal subgroups

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

subgroup	index
#28417932	2
#28417886	2
#28417884	2
#28417876	2
C₂²⋊(C₄₆₇⋊C₈)	2
#117×C₄₆₇	2
#485	467