Finite Group Databasebeta

Subgroups — #19134007

Order 5504.

176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14583247	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583186	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583095	C₂	1	1	yes	maximal, characteristic
4	#14582964	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582649	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₄₄	—	2	1	no	—
9	C₂×C₈×D₄₃	—	2	1	no	—
10	#13063322	C₂²	1	1	yes	characteristic
11	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
12	#13063256	—	2	1	no	—
13	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	#13063247	—	2	1	no	—
15	#13063245	—	2	1	no	—
16	#13063245	—	2	1	no	—
17	#13063245	—	2	1	no	—
18	(C₂×D₄₃)⋊C₈	—	2	1	no	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	D₄	1	1	yes	characteristic
28	C₂×C₄×D₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	—	2	1	no	—
30	C₂×C₈×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	(C₂×D₄₃)⋊C₄	—	2	1	no	—
35	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
36	C₂×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
39	D₃₄₄	—	4	2	no	—
40	C₈×D₄₃	—	4	2	no	—
41	C₂²×D₄₃	—	2	1	no	—
42	C₂²×D₄₃	—	4	1	no	—
43	Q₈×C₄₃	—	8	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
48	C₂×Dic₄₃	—	2	1	no	—
49	D₁₇₂	—	2	1	no	—
50	D₁₇₂	—	4	1	no	—
51	D₁₇₂	—	4	1	no	—
52	D₁₇₂	—	4	1	no	—
53	D₁₇₂	—	4	1	no	—
54	D₁₇₂	—	8	1	no	—
55	D₁₇₂	SD₁₆	1	2	yes	—
56	C₄×D₄₃	—	4	1	no	—
57	C₄×D₄₃	—	4	1	no	—
58	C₈×C₄₃	—	4	1	no	—
59	C₈×C₄₃	—	4	1	no	—
60	C₄₃⋊C₈	—	2	1	no	—
61	C₄₃⋊C₈	—	2	1	no	—
62	C₄₃⋊C₈	—	4	1	no	—
63	C₂²×C₄₃	#121	1	1	yes	characteristic
64	C₂×D₄₃	—	2	2	no	—
65	C₂×D₄₃	—	4	1	no	—
66	C₂×D₄₃	—	4	1	no	—
67	C₂×D₄₃	—	8	1	no	—
68	C₂×D₄₃	—	8	1	no	—
69	C₂×D₄₃	—	8	1	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	—	8	1	no	—
72	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
73	C₄×C₄₃	#135	1	1	yes	characteristic
74	C₄×C₄₃	#135	1	1	yes	characteristic
75	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
76	Dic₄₃	—	4	1	no	—
77	#1677	—	43	1	no	maximal, Sylow
78	C₂×C₄₃	#463	1	1	yes	characteristic
79	C₂×C₄₃	#465	1	1	yes	characteristic
80	C₂×C₄₃	#472	1	1	yes	characteristic
81	D₄₃	—	4	2	no	—
82	D₄₃	—	16	1	no	—
83	#486	—	43	1	no	—
84	#476	—	43	1	no	—
85	#459	—	43	1	no	—
86	C₈×D₄	—	43	1	no	—
87	#334	—	43	1	no	—
88	#333	D₄₃	1	1	yes	characteristic, complemented
89	#331	—	43	1	no	—
90	C₄₃	#1677	1	1	yes	characteristic, complemented, Sylow
91	C₂×D₈	—	86	1	no	—
92	C₂²×C₈	—	86	1	no	—
93	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
94	#127	—	43	1	no	—
95	C₄×D₄	—	43	1	no	—
96	#106	—	86	1	no	—
97	C₄⋊C₈	—	43	1	no	—
98	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
99	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
100	#102	—	86	1	no	—
101	#102	—	86	1	no	—
102	#102	—	86	1	no	—
103	#102	—	86	1	no	—
104	C₂²⋊C₈	—	86	1	no	—
105	C₄×C₈	—	43	1	no	—
106	C₂×Q₈	—	2	1	no	—
107	C₂×D₄	—	43	1	no	—
108	C₂×D₄	—	86	1	no	—
109	C₂×D₄	—	86	1	no	—
110	C₂×D₄	—	86	1	no	—
111	C₂²×C₄	—	86	1	no	—
112	D₈	—	172	2	no	—
113	C₂×C₈	—	2	1	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	43	1	no	—
116	C₂×C₈	—	43	1	no	—
117	C₂×C₈	—	86	1	no	—
118	C₂×C₈	—	172	2	no	—
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	43	1	no	—
122	C₂²⋊C₄	—	86	1	no	—
123	C₄²	C₂²×D₄₃	1	1	yes	characteristic
124	C₂³	—	86	1	no	—
125	C₂³	—	172	1	no	—
126	Q₈	—	8	1	no	—
127	D₄	—	43	2	no	—
128	D₄	—	86	1	no	—
129	D₄	—	344	1	no	—
130	D₄	—	172	1	no	—
131	D₄	—	172	1	no	—
132	D₄	—	172	1	no	—
133	D₄	—	172	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	86	1	no	—
136	C₂×C₄	—	172	1	no	—
137	C₂×C₄	—	172	1	no	—
138	C₂×C₄	#10621898	1	1	yes	characteristic
139	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
141	C₈	—	4	1	no	—
142	C₈	—	4	1	no	—
143	C₈	—	86	1	no	—
144	C₈	—	86	1	no	—
145	C₈	—	172	1	no	—
146	C₂²	—	86	2	no	—
147	C₂²	—	344	1	no	—
148	C₂²	—	344	1	no	—
149	C₂²	—	344	1	no	—
150	C₂²	—	172	1	no	—
151	C₂²	—	172	1	no	—
152	C₂²	#13063298	1	1	yes	characteristic
153	C₄	—	2	1	no	—
154	C₄	—	8	1	no	—
155	C₄	—	172	1	no	—
156	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
157	C₄	#13063348	1	1	yes	characteristic
158	C₄	#13063348	1	1	yes	characteristic
159	C₄	#13063352	1	1	yes	characteristic
160	C₂	—	172	2	no	—
161	C₂	—	688	1	no	—
162	C₂	#14583117	1	1	yes	characteristic
163	C₂	#14583131	1	1	yes	characteristic
164	C₂	#14583168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#333	C₂
socle	C₂²×C₄₃	#121
hypercenter	#333	D₄₃
hypocenter	C₄₃	#1677
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

Complements

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

N	H ≅ G/N	type
1. #14583247	C₂	semidirect
2. #14583186	C₂	semidirect
4. #14582964	C₂	semidirect
5. #14582649	C₂	semidirect
6. #14582642	C₂	semidirect
7. C₄₃×#333	C₂	semidirect
88. #333	D₄₃	semidirect
90. C₄₃	#1677	semidirect