Subgroups — #42122786

Order 27712.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294107	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20294105	C₂	1	1	yes	maximal, characteristic, complemented
3	#28357277	C₂	1	4	yes	maximal, complemented
4	C₂×#20294098	C₂	1	1	yes	maximal, characteristic
5	#20294107	—	2	2	no	—
6	#20294105	—	2	2	no	—
7	C₂×#16812365	C₂²	1	2	yes	—
8	C₂×#16812365	C₂²	1	2	yes	—
9	#20294098	—	2	2	no	—
10	#20294098	—	2	2	no	—
11	C₂×D₁₇₃₂	C₄	1	2	yes	—
12	C₂×D₁₇₃₂	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄₃₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄₃₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₃₃	C₄	1	1	yes	characteristic
16	#16812365	—	2	2	no	—
17	#16812365	—	2	2	no	—
18	C₂²×D₄₃₃	C₂×C₄	1	2	yes	—
19	C₂²×D₄₃₃	C₂×C₄	1	1	yes	characteristic
20	D₁₇₃₂	—	2	4	no	—
21	D₁₇₃₂	—	2	2	no	—
22	C₂×Dic₄₃₃	C₂³	1	1	yes	characteristic
23	C₄×D₄₃₃	—	2	2	no	—
24	C₄×D₄₃₃	—	2	2	no	—
25	C₄×D₄₃₃	D₄	1	2	yes	—
26	C₄×D₄₃₃	D₄	1	2	yes	—
27	Q₈×C₄₃₃	—	2	2	no	—
28	C₂×C₄×C₄₃₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₄₃₃	—	2	2	no	—
32	C₂×D₄₃₃	—	2	2	no	—
33	C₂×D₄₃₃	—	2	4	no	—
34	C₂×D₄₃₃	C₂²⋊C₄	1	2	yes	—
35	C₄×C₄₃₃	—	2	2	no	—
36	C₄×C₄₃₃	C₂²⋊C₄	1	2	yes	—
37	Dic₄₃₃	C₂×D₄	1	1	yes	characteristic
38	Dic₄₃₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄₃₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄₃₃	#131	1	2	yes	—
41	D₄₃₃	—	2	2	no	—
42	D₄₃₃	—	4	2	no	—
43	C₄₃₃	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	433	1	no	maximal, Sylow
45	C₂×#41	—	433	1	no	—
46	C₂×M₁₆	—	433	1	no	—
47	C₂²×C₈	—	433	1	no	—
48	C₂²⋊C₈	—	433	4	no	—
49	#41	—	866	2	no	—
50	#41	—	866	2	no	—
51	C₂×Q₈	#13181884	1	1	yes	characteristic
52	C₂×D₄	—	433	2	no	—
53	C₂×D₄	—	433	1	no	—
54	C₂²×C₄	—	433	2	no	—
55	C₂²×C₄	—	433	1	no	—
56	M₁₆	—	866	2	no	—
57	C₂×C₈	—	866	2	no	—
58	C₂×C₈	—	433	2	no	—
59	C₂×C₈	—	433	2	no	—
60	C₂³	—	433	2	no	—
61	C₂³	—	433	1	no	—
62	Q₈	—	2	2	no	—
63	D₄	—	866	4	no	—
64	D₄	—	866	2	no	—
65	C₂×C₄	—	866	2	no	—
66	C₂×C₄	—	866	2	no	—
67	C₂×C₄	—	433	1	no	—
68	C₂×C₄	—	433	2	no	—
69	C₂×C₄	—	433	2	no	—
70	C₂×C₄	C₂×#13181884	1	2	yes	—
71	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
72	C₈	—	866	2	no	—
73	C₈	—	866	2	no	—
74	C₂²	—	866	2	no	—
75	C₂²	—	866	2	no	—
76	C₂²	—	866	4	no	—
77	C₂²	—	433	2	no	—
78	C₂²	C₂²×#13181884	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	433	1	no	—
81	C₄	—	433	1	no	—
82	C₄	C₂²⋊#13181884	1	2	yes	—
83	C₂	—	866	2	no	—
84	C₂	—	1732	2	no	—
85	C₂	C₂×C₂²⋊#13181884	1	1	yes	characteristic
86	C₂	#28357308	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13181884
commutator, socle	C₂²×C₄₃₃	C₂²×C₄
Fitting	C₂×Q₈×C₄₃₃	C₄
prime radical	C₂×#20294098	C₂
cosocle	C₂×Dic₄₃₃	C₂³
hypercenter	C₂×Q₈	#13181884
hypocenter	C₄₃₃	#408
LCS	G ▷ C₂²×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#20294107	C₂	semidirect
2. C₂×#20294105	C₂	semidirect
3. #28357277	C₂	semidirect
43. C₄₃₃	#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20294107	2
C₂×#20294105	2
#28357277	2
C₂×#20294098	2
#408	433