Finite Group Databasebeta

← C₂×#17989486 #22626172

Subgroups — C₂×#17989486 #22626172

Order 9344.

224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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	C₂×#14556665	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989486	C₂	1	4	yes	maximal, direct product factor
4	C₂×#14556599	C₂	1	1	yes	maximal, characteristic
5	#14556665	—	2	1	no	—
6	#14556665	C₂²	1	2	yes	complemented
7	C₂×#11924031	—	2	1	no	—
8	C₂×#11924031	—	2	1	no	—
9	C₂×#11924031	—	2	1	no	—
10	C₂×#11924031	C₂²	1	2	yes	complemented
11	C₂×#11924028	C₄	1	1	yes	characteristic
12	#14556599	—	2	1	no	—
13	#14556599	—	2	1	no	—
14	#14556599	C₄	1	2	yes	—
15	#14556599	C₂²	1	2	yes	—
16	C₂×#11924011	—	2	1	no	—
17	C₂²×#10596831	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₇₃	—	2	1	no	—
19	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
20	#11924031	—	2	2	no	—
21	#11924031	—	2	2	no	—
22	#11924028	—	2	1	no	—
23	#11924028	—	2	1	no	—
24	#11924028	C₈	1	2	yes	—
25	#11924028	C₂×C₄	1	2	yes	—
26	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
27	C₂×D₂₉₂	C₈	1	1	yes	characteristic
28	C₂×C₂²⋊D₇₃	—	2	1	no	—
29	C₂×C₄×D₇₃	—	2	1	no	—
30	#11924011	—	2	2	no	—
31	#11924011	—	2	2	no	—
32	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
33	C₂×#10596831	D₄	1	1	yes	characteristic
34	C₂×#10596831	D₄	1	1	yes	characteristic
35	C₂×#10596831	D₄	1	1	yes	characteristic
36	C₂×#10596831	D₄	1	1	yes	characteristic
37	C₂×#10596831	C₂³	1	1	yes	characteristic
38	C₈×D₇₃	—	2	2	no	—
39	C₈×D₇₃	—	2	2	no	—
40	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
41	M₁₆×C₇₃	—	2	1	no	—
42	M₁₆×C₇₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×C₇₃	—	2	1	no	—
44	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
45	C₂²×D₇₃	—	2	1	no	—
46	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
49	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
50	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²⋊D₇₃	—	2	2	no	—
53	C₂²⋊D₇₃	—	2	2	no	—
54	C₂×Dic₇₃	—	2	1	no	—
55	D₂₉₂	—	2	1	no	—
56	D₂₉₂	C₂×C₈	1	2	yes	—
57	C₄×D₇₃	—	2	2	no	—
58	C₄×D₇₃	—	2	2	no	—
59	Dic₁₄₆	—	2	1	no	—
60	Dic₁₄₆	C₂×C₈	1	2	yes	—
61	C₈×C₇₃	—	2	2	no	—
62	#10596831	C₂²⋊C₄	1	1	yes	characteristic
63	#10596831	C₂²⋊C₄	1	1	yes	characteristic
64	#10596831	C₂×D₄	1	1	yes	characteristic
65	#10596831	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₇₃	—	2	2	no	—
67	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
68	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
69	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
70	C₂×D₇₃	—	2	2	no	—
71	C₂×D₇₃	—	4	2	no	—
72	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
73	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
74	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
76	Dic₇₃	—	2	2	no	—
77	C₂×C₇₃	—	2	1	no	—
78	C₂×C₇₃	—	2	1	no	—
79	C₂×C₇₃	#350	1	2	yes	complemented
80	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
81	D₇₃	—	4	2	no	—
82	C₂×#350	—	73	1	no	maximal, Sylow
83	C₇₃	C₂×#350	1	1	yes	characteristic, complemented, Sylow
84	C₂×#131	—	73	1	no	—
85	C₂×M₃₂	—	73	1	no	—
86	C₂²×C₁₆	—	73	1	no	—
87	#350	—	73	4	no	—
88	C₂×#41	—	73	1	no	—
89	#131	—	73	2	no	—
90	#131	—	73	2	no	—
91	#131	—	146	1	no	—
92	#131	—	146	1	no	—
93	C₂×M₁₆	—	146	1	no	—
94	C₂×M₁₆	#64408	1	1	yes	characteristic
95	C₂²×C₈	—	73	1	no	—
96	C₂²×C₈	—	146	1	no	—
97	M₃₂	—	73	2	no	—
98	M₃₂	—	146	1	no	—
99	C₂×C₁₆	—	73	2	no	—
100	C₂×C₁₆	—	146	1	no	—
101	C₂×C₁₆	—	146	1	no	—
102	C₂×C₁₆	—	146	1	no	—
103	#41	—	73	2	no	—
104	#41	—	73	2	no	—
105	#41	—	146	1	no	—
106	#41	—	146	1	no	—
107	C₂×Q₈	—	73	1	no	—
108	C₂×D₄	—	73	1	no	—
109	C₂×D₄	—	146	1	no	—
110	C₂²×C₄	—	146	1	no	—
111	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
112	M₁₆	—	2	1	no	—
113	M₁₆	—	146	2	no	—
114	M₁₆	—	146	2	no	—
115	M₁₆	C₂×#64408	1	2	yes	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	73	1	no	—
118	C₂×C₈	—	73	1	no	—
119	C₂×C₈	—	73	1	no	—
120	C₂×C₈	—	73	1	no	—
121	C₂×C₈	—	73	1	no	—
122	C₂×C₈	—	73	1	no	—
123	C₂×C₈	—	146	2	no	—
124	C₂×C₈	—	146	2	no	—
125	C₁₆	—	146	2	no	—
126	C₁₆	—	146	2	no	—
127	C₂³	—	146	1	no	—
128	C₂³	#11924038	1	1	yes	characteristic
129	Q₈	—	73	2	no	—
130	Q₈	—	146	1	no	—
131	D₄	—	73	2	no	—
132	D₄	—	146	2	no	—
133	D₄	—	146	2	no	—
134	D₄	—	146	1	no	—
135	C₂×C₄	—	146	1	no	—
136	C₂×C₄	—	146	2	no	—
137	C₂×C₄	—	146	2	no	—
138	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
139	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
140	C₂×C₄	#11924036	1	1	yes	characteristic
141	C₂×C₄	#11924036	1	1	yes	characteristic
142	C₂×C₄	#11924038	1	1	yes	characteristic
143	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	73	1	no	—
146	C₈	—	73	1	no	—
147	C₈	—	73	1	no	—
148	C₈	—	73	1	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	292	2	no	—
151	C₂²	—	146	2	no	—
152	C₂²	#14556648	1	1	yes	characteristic
153	C₂²	#14556648	1	1	yes	characteristic
154	C₂²	C₂×#11924038	1	1	yes	characteristic
155	C₄	—	146	2	no	—
156	C₄	#14556648	1	1	yes	characteristic
157	C₄	#14556648	1	1	yes	characteristic
158	C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
159	C₄	C₂×#11924036	1	1	yes	characteristic
160	C₂	—	2	1	no	—
161	C₂	—	2	1	no	—
162	C₂	—	292	2	no	—
163	C₂	#17989486	1	2	yes	direct product factor
164	C₂	C₂×#14556648	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	C₂×#350
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#14556665	C₂	semidirect
2. C₂²×#11924031	C₂	semidirect
3. #17989486	C₂	direct (N × H)
6. #14556665	C₂²	semidirect
10. C₂×#11924031	C₂²	semidirect
79. C₂×C₇₃	#350	semidirect
83. C₇₃	C₂×#350	semidirect
163. C₂	#17989486	direct (N × H)