Finite Group Databasebeta

Subgroups — #49094860

Order 35968.

146 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823815	C₂	1	1	yes	maximal, characteristic
2	#31823749	C₂	1	1	yes	maximal, characteristic
3	#31823670	C₂	1	1	yes	maximal, characteristic
4	#31823590	C₂	1	1	yes	maximal, characteristic
5	#31823215	C₂	1	1	yes	maximal, characteristic
6	#31823210	C₂	1	1	yes	maximal, characteristic
7	#332×C₂₈₁	C₂	1	1	yes	maximal, characteristic
8	C₂×#17985128	—	2	1	no	—
9	#22582879	C₂²	1	1	yes	characteristic
10	C₄×Dic₅₆₂	C₂²	1	1	yes	characteristic
11	#22582811	—	2	1	no	—
12	C₄⋊#14555886	C₂²	1	1	yes	characteristic
13	#22582808	—	2	1	no	—
14	#22582804	—	2	1	no	—
15	#22582803	—	2	1	no	—
16	#22582802	—	2	1	no	—
17	#22582802	—	2	1	no	—
18	#22582789	—	2	1	no	—
19	C₄×#14555886	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₂₈₁	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₂₈₁	C₂²	1	1	yes	characteristic
23	C₂×Dic₅₆₂	—	2	1	no	—
24	C₂×Dic₅₆₂	D₄	1	1	yes	characteristic
25	#17985128	—	4	2	no	—
26	C₂×#14555886	—	2	1	no	—
27	C₂×#14555886	D₄	1	1	yes	characteristic
28	C₂×#14555886	D₄	1	1	yes	characteristic
29	C₄⋊Dic₂₈₁	—	2	1	no	—
30	C₄⋊Dic₂₈₁	—	2	1	no	—
31	C₄⋊Dic₂₈₁	D₄	1	1	yes	characteristic
32	#17985117	—	2	1	no	—
33	C₄×Dic₂₈₁	—	2	1	no	—
34	C₂×Q₈×C₂₈₁	—	2	1	no	—
35	C₂×C₈×C₂₈₁	—	2	1	no	—
36	C₂×C₈×C₂₈₁	—	2	1	no	—
37	C₄⋊C₄×C₂₈₁	—	2	1	no	—
38	C₄⋊C₄×C₂₈₁	—	2	1	no	—
39	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
40	Dic₅₆₂	—	2	1	no	—
41	Dic₅₆₂	—	2	1	no	—
42	Dic₅₆₂	—	4	1	no	—
43	Dic₅₆₂	—	4	1	no	—
44	C₂×Dic₂₈₁	—	2	1	no	—
45	C₂×Dic₂₈₁	—	2	1	no	—
46	C₂×Dic₂₈₁	—	4	1	no	—
47	#14555886	—	2	1	no	—
48	#14555886	—	2	1	no	—
49	#14555886	—	4	1	no	—
50	Q₈×C₂₈₁	—	4	1	no	—
51	Q₈×C₂₈₁	—	4	1	no	—
52	C₂×C₄×C₂₈₁	—	4	1	no	—
53	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₂₈₁	#41	1	1	yes	characteristic
56	C₈×C₂₈₁	—	4	1	no	—
57	C₈×C₂₈₁	—	4	1	no	—
58	C₂²×C₂₈₁	#121	1	1	yes	characteristic
59	C₄×C₂₈₁	—	2	1	no	—
60	C₄×C₂₈₁	—	8	1	no	—
61	C₄×C₂₈₁	#135	1	1	yes	characteristic
62	C₄×C₂₈₁	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₄×C₂₈₁	#137	1	1	yes	characteristic
64	C₄×C₂₈₁	#137	1	1	yes	characteristic
65	Dic₂₈₁	—	4	1	no	—
66	Dic₂₈₁	—	4	1	no	—
67	Dic₂₈₁	—	8	1	no	—
68	C₂×C₂₈₁	#464	1	1	yes	characteristic
69	C₂×C₂₈₁	#468	1	1	yes	characteristic
70	C₂×C₂₈₁	#473	1	1	yes	characteristic
71	C₂₈₁	#1700	1	1	yes	characteristic, complemented, Sylow
72	#1700	—	281	1	no	maximal, Sylow
73	#487	—	281	1	no	—
74	#475	—	281	1	no	—
75	#462	—	281	1	no	—
76	#446	—	281	1	no	—
77	#335	—	281	1	no	—
78	#332	—	281	1	no	—
79	#332	D₂₈₁	1	1	yes	characteristic
80	C₂×Q₁₆	—	562	1	no	—
81	C₄⋊Q₈	—	281	1	no	—
82	C₄⋊Q₈	C₂×D₂₈₁	1	1	yes	characteristic
83	C₄×Q₈	—	281	1	no	—
84	#106	—	562	1	no	—
85	C₄⋊C₈	—	281	1	no	—
86	C₄⋊C₈	—	562	1	no	—
87	C₄⋊C₈	C₂×D₂₈₁	1	1	yes	characteristic
88	C₄⋊C₈	C₂×D₂₈₁	1	1	yes	characteristic
89	#103	—	562	1	no	—
90	#103	—	562	1	no	—
91	#103	—	562	1	no	—
92	#103	—	562	1	no	—
93	#97	—	562	1	no	—
94	C₄×C₈	—	281	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	281	1	no	—
97	C₂×Q₈	—	562	1	no	—
98	Q₁₆	—	1124	2	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	281	1	no	—
102	C₂×C₈	—	281	1	no	—
103	C₂×C₈	—	562	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	281	1	no	—
107	C₄⋊C₄	—	562	1	no	—
108	C₄⋊C₄	—	562	1	no	—
109	C₄⋊C₄	—	562	1	no	—
110	C₄²	—	562	1	no	—
111	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
112	Q₈	—	4	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	562	1	no	—
115	Q₈	—	562	1	no	—
116	Q₈	—	1124	1	no	—
117	Q₈	—	1124	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	562	1	no	—
120	C₂×C₄	—	562	1	no	—
121	C₂×C₄	—	1124	1	no	—
122	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
123	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
124	C₂×C₄	#17985138	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	4	1	no	—
127	C₈	—	562	1	no	—
128	C₈	—	562	1	no	—
129	C₈	—	1124	1	no	—
130	C₂²	#22582852	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	8	1	no	—
133	C₄	—	1124	1	no	—
134	C₄	—	1124	1	no	—
135	C₄	—	2248	1	no	—
136	C₄	#22582900	1	1	yes	characteristic
137	C₄	#22582903	1	1	yes	characteristic
138	C₄	#22582908	1	1	yes	characteristic
139	C₄	#22582911	1	1	yes	characteristic
140	C₂	#31823688	1	1	yes	characteristic
141	C₂	#31823708	1	1	yes	characteristic
142	C₂	#31823737	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22582852
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	#332×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	#121
hypercenter	#332	D₂₈₁
hypocenter	C₂₈₁	#1700
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

Complements

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

N	H ≅ G/N	type
71. C₂₈₁	#1700	semidirect

Maximal subgroups

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

subgroup	index
#31823815	2
#31823749	2
#31823670	2
#31823590	2
#31823215	2
#31823210	2
#332×C₂₈₁	2
#1700	281