Subgroups — C₂²×#63367 #11858373

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#63367	C₂	1	12	yes	maximal, direct product factor
5	C₂²×#808	—	3	1	no	maximal
6	C₂³×C₄×C₉	—	2	1	no	—
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂³×Dic₉	—	2	1	no	—
9	C₂×C₉×C₄⋊C₄	—	2	3	no	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	6	yes	—
11	C₂×C₄⋊Dic₉	—	2	3	no	—
12	C₂×C₄⋊Dic₉	C₂²	1	6	yes	—
13	C₂²×C₉⋊C₈	C₄	1	8	yes	complemented
14	C₂²×C₉⋊C₈	C₂²	1	6	yes	—
15	#63367	C₂²	1	16	yes	direct product factor
16	C₂²×C₃×C₄⋊C₄	D₃	1	1	yes	characteristic
17	C₂²×C₄⋊Dic₃	—	3	1	no	—
18	C₂³×C₃⋊C₈	—	3	1	no	—
19	C₂×#808	—	3	12	no	—
20	C₂⁴×C₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₉	—	2	6	no	—
22	C₂²×C₄×C₉	—	4	4	no	—
23	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₉	D₄	1	3	yes	—
25	C₂²×C₄×C₉	Q₈	1	4	yes	—
26	C₂²×C₄×C₉	C₂³	1	3	yes	—
27	C₂²×Dic₉	—	2	6	no	—
28	C₂²×Dic₉	—	4	4	no	—
29	C₉×C₄⋊C₄	—	2	6	no	—
30	C₉×C₄⋊C₄	C₂³	1	4	yes	—
31	C₄⋊Dic₉	—	2	6	no	—
32	C₄⋊Dic₉	C₂³	1	4	yes	—
33	C₂×C₉⋊C₈	C₂×C₄	1	24	yes	complemented
34	C₂×C₉⋊C₈	C₂³	1	4	yes	—
35	C₂²×#106	—	9	1	no	Sylow
36	C₂³×C₃×C₄	—	2	1	no	—
37	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂³×Dic₃	—	6	1	no	—
39	C₂×C₃×C₄⋊C₄	—	2	3	no	—
40	C₂×C₃×C₄⋊C₄	C₂×D₃	1	6	yes	—
41	C₂×C₄⋊Dic₃	—	3	6	no	—
42	C₂×C₄⋊Dic₃	—	6	3	no	—
43	C₂²×C₃⋊C₈	—	3	8	no	—
44	C₂²×C₃⋊C₈	—	3	6	no	—
45	#808	—	3	16	no	—
46	C₂³×C₉	C₄⋊C₄	1	4	yes	—
47	C₂³×C₉	SD₁₆	1	4	yes	—
48	C₂³×C₉	SD₁₆	1	4	yes	—
49	C₂³×C₉	C₂×D₄	1	3	yes	—
50	C₂×C₄×C₉	—	2	4	no	—
51	C₂×C₄×C₉	—	4	12	no	—
52	C₂×C₄×C₉	C₄⋊C₄	1	12	yes	—
53	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
54	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
55	C₂×C₄×C₉	C₂×Q₈	1	6	yes	—
56	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₉	—	2	4	no	—
58	C₂×Dic₉	—	4	12	no	—
59	C₉⋊C₈	C₂²×C₄	1	8	yes	complemented
60	C₂³×C₈	—	9	1	no	—
61	C₂²×C₄⋊C₄	—	9	1	no	—
62	C₂²×C₄⋊C₄	D₉	1	1	yes	characteristic
63	C₂×#106	—	9	12	no	—
64	C₂⁴×C₃	#67	1	1	yes	characteristic
65	C₂²×C₃×C₄	—	2	6	no	—
66	C₂²×C₃×C₄	—	4	4	no	—
67	C₂²×C₃×C₄	Dic₆	1	4	yes	—
68	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
69	C₂²×C₃×C₄	#67	1	3	yes	—
70	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
71	C₂²×Dic₃	—	6	6	no	—
72	C₂²×Dic₃	—	12	4	no	—
73	C₃×C₄⋊C₄	—	2	6	no	—
74	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
75	C₄⋊Dic₃	—	3	4	no	—
76	C₄⋊Dic₃	—	6	6	no	—
77	C₂×C₃⋊C₈	—	3	24	no	—
78	C₂×C₃⋊C₈	—	3	4	no	—
79	C₂²×C₉	#106	1	16	yes	complemented
80	C₂²×C₉	C₂×C₄⋊C₄	1	6	yes	—
81	C₂²×C₉	C₂×SD₁₆	1	6	yes	—
82	C₂²×C₉	C₂×SD₁₆	1	6	yes	—
83	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
84	C₄×C₉	—	4	4	no	—
85	C₄×C₉	C₂×C₄⋊C₄	1	6	yes	—
86	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
87	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
88	Dic₉	—	4	4	no	—
89	C₂³×C₄	—	2	1	no	—
90	C₂³×C₄	—	18	1	no	—
91	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
92	C₂²×C₈	—	9	8	no	—
93	C₂²×C₈	—	9	6	no	—
94	C₂×C₄⋊C₄	—	2	3	no	—
95	C₂×C₄⋊C₄	—	9	6	no	—
96	C₂×C₄⋊C₄	—	18	3	no	—
97	C₂×C₄⋊C₄	C₂×D₉	1	6	yes	—
98	#106	—	9	16	no	—
99	C₂³×C₃	Dic₃⋊C₄	1	4	yes	—
100	C₂³×C₃	#214	1	4	yes	—
101	C₂³×C₃	#215	1	4	yes	—
102	C₂³×C₃	C₂×#67	1	3	yes	—
103	C₂×C₃×C₄	—	2	4	no	—
104	C₂×C₃×C₄	—	4	12	no	—
105	C₂×C₃×C₄	Dic₃⋊C₄	1	12	yes	—
106	C₂×C₃×C₄	C₂×Dic₆	1	6	yes	—
107	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
108	C₂×C₃×C₄	C₂×#67	1	3	yes	—
109	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
110	C₂×Dic₃	—	6	4	no	—
111	C₂×Dic₃	—	12	12	no	—
112	C₃⋊C₈	—	3	8	no	—
113	C₂×C₉	C₂×#106	1	12	yes	complemented
114	C₂×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
116	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
117	C₂⁴	#611	1	1	yes	characteristic
118	C₂²×C₄	—	2	6	no	—
119	C₂²×C₄	—	4	4	no	—
120	C₂²×C₄	—	18	6	no	—
121	C₂²×C₄	—	36	4	no	—
122	C₂²×C₄	Dic₁₈	1	4	yes	—
123	C₂²×C₄	C₄×D₉	1	4	yes	—
124	C₂²×C₄	#611	1	3	yes	—
125	C₂²×C₄	C₂²×D₉	1	3	yes	—
126	C₂×C₈	—	9	24	no	—
127	C₂×C₈	—	9	4	no	—
128	C₄⋊C₄	—	2	6	no	—
129	C₄⋊C₄	—	9	4	no	—
130	C₄⋊C₄	—	18	6	no	—
131	C₄⋊C₄	C₂²×D₉	1	4	yes	—
132	C₂²×C₃	#808	1	16	yes	—
133	C₂²×C₃	C₂×Dic₃⋊C₄	1	6	yes	—
134	C₂²×C₃	C₂×#214	1	6	yes	—
135	C₂²×C₃	C₂×#215	1	6	yes	—
136	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
137	C₃×C₄	—	4	4	no	—
138	C₃×C₄	C₂×Dic₃⋊C₄	1	6	yes	—
139	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
140	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
141	Dic₃	—	12	4	no	—
142	C₉	C₂²×#106	1	1	yes	characteristic, complemented, Sylow
143	C₂³	Dic₉⋊C₄	1	4	yes	—
144	C₂³	#3672	1	4	yes	—
145	C₂³	#3675	1	4	yes	—
146	C₂³	C₂×#611	1	3	yes	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	4	12	no	—
149	C₂×C₄	—	18	4	no	—
150	C₂×C₄	—	36	12	no	—
151	C₂×C₄	Dic₉⋊C₄	1	12	yes	—
152	C₂×C₄	C₂×Dic₁₈	1	6	yes	—
153	C₂×C₄	C₂×C₄×D₉	1	6	yes	—
154	C₂×C₄	C₂×#611	1	3	yes	—
155	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
156	C₈	—	9	8	no	—
157	C₂×C₃	C₂×#808	1	12	yes	—
158	C₂×C₃	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
159	C₂×C₃	C₂²×#214	1	1	yes	characteristic
160	C₂×C₃	C₂²×#215	1	1	yes	characteristic
161	C₂²	#63367	1	16	yes	direct product factor
162	C₂²	C₂×Dic₉⋊C₄	1	6	yes	—
163	C₂²	C₂×#3672	1	6	yes	—
164	C₂²	C₂×#3675	1	6	yes	—
165	C₂²	C₂²×#611	1	1	yes	characteristic
166	C₄	—	4	4	no	—
167	C₄	—	36	4	no	—
168	C₄	C₂×Dic₉⋊C₄	1	6	yes	—
169	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
170	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
171	C₃	C₂²×#808	1	1	yes	characteristic
172	C₂	C₂×#63367	1	12	yes	direct product factor
173	C₂	C₂²×Dic₉⋊C₄	1	1	yes	characteristic
174	C₂	C₂²×#3672	1	1	yes	characteristic
175	C₂	C₂²×#3675	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	#611
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂²×C₉×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₃	#67
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂²×C₄⋊C₄	D₉
hypocenter	C₉	C₂²×#106
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₂×#63367	C₂	direct (N × H)
13. C₂²×C₉⋊C₈	C₄	semidirect
15. #63367	C₂²	direct (N × H)
33. C₂×C₉⋊C₈	C₂×C₄	semidirect
59. C₉⋊C₈	C₂²×C₄	semidirect
79. C₂²×C₉	#106	semidirect
113. C₂×C₉	C₂×#106	semidirect
142. C₉	C₂²×#106	semidirect
161. C₂²	#63367	direct (N × H)
172. C₂	C₂×#63367	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×C₄⋊C₄	2
C₂²×C₄⋊Dic₉	2
C₂³×C₉⋊C₈	2
C₂×#63367	2
C₂²×#808	3

Subgroups — C22×#63367 #11858373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#63367 #11858373