Subgroups — C₄×#63432 #11802472

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63432	C₂	1	1	yes	maximal, characteristic
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
3	#10588616	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Dic₉	C₂	1	2	yes	maximal
5	#10588613	C₂	1	4	yes	maximal
6	C₄×Dic₉⋊C₄	C₂	1	4	yes	maximal
7	#10588608	C₂	1	2	yes	maximal
8	C₄×#870	—	3	1	no	maximal
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
16	C₂×Dic₉⋊C₄	C₂²	1	4	yes	—
17	C₂×Dic₉⋊C₄	C₂²	1	4	yes	—
18	C₂×C₄×Dic₉	C₂²	1	4	yes	—
19	#63432	C₄	1	8	yes	direct product factor
20	C₉⋊#95	C₂²	1	4	yes	—
21	C₉⋊#95	C₂²	1	4	yes	—
22	C₉⋊#95	C₂²	1	4	yes	—
23	C₂×#870	—	3	1	no	—
24	C₃×C₄³	D₃	1	1	yes	characteristic
25	#4936	—	3	1	no	—
26	C₄×C₄⋊Dic₃	—	3	2	no	—
27	#4933	—	3	4	no	—
28	C₄×Dic₃⋊C₄	—	3	4	no	—
29	#4928	—	3	2	no	—
30	C₂²×C₄×C₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₉	C₂³	1	2	yes	—
33	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₉	C₂³	1	4	yes	—
36	C₂²×Dic₉	C₂³	1	4	yes	—
37	C₄²×C₉	—	2	4	no	—
38	C₄²×C₉	—	2	2	no	—
39	C₄²×C₉	—	2	4	no	—
40	C₄²×C₉	C₂×C₄	1	4	yes	—
41	C₄²×C₉	Q₈	1	4	yes	—
42	C₄⋊Dic₉	—	2	4	no	—
43	C₄⋊Dic₉	C₂×C₄	1	8	yes	—
44	Dic₉⋊C₄	—	2	8	no	—
45	Dic₉⋊C₄	C₂×C₄	1	16	yes	—
46	C₄×Dic₉	—	2	8	no	—
47	C₄×#125	—	9	1	no	Sylow
48	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
49	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
50	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
51	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
53	C₂×C₄⋊Dic₃	—	3	2	no	—
54	C₂×C₄⋊Dic₃	—	3	2	no	—
55	C₂×Dic₃⋊C₄	—	3	4	no	—
56	C₂×Dic₃⋊C₄	—	3	4	no	—
57	C₂×C₄×Dic₃	—	3	4	no	—
58	#870	—	3	8	no	—
59	C₃⋊#95	—	3	4	no	—
60	C₃⋊#95	—	3	4	no	—
61	C₃⋊#95	—	3	4	no	—
62	C₂³×C₉	C₂⁴	1	1	yes	characteristic
63	C₂×C₄×C₉	—	2	2	no	—
64	C₂×C₄×C₉	—	2	2	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	—	2	2	no	—
67	C₂×C₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
69	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
71	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
72	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
73	C₂×C₄×C₉	#41	1	4	yes	—
74	C₂×C₄×C₉	#41	1	2	yes	—
75	C₂×C₄×C₉	#41	1	4	yes	—
76	C₂×Dic₉	—	2	4	no	—
77	C₂×Dic₉	—	2	4	no	—
78	C₂×Dic₉	—	2	4	no	—
79	C₂×Dic₉	—	2	4	no	—
80	C₂×Dic₉	—	2	4	no	—
81	C₂×Dic₉	C₂²×C₄	1	8	yes	—
82	C₂×#125	—	9	1	no	—
83	#389	—	9	2	no	—
84	#387	—	9	4	no	—
85	#382	—	9	1	no	—
86	C₄×C₄⋊C₄	—	9	4	no	—
87	C₄×C₄⋊C₄	—	9	2	no	—
88	C₄³	D₉	1	1	yes	characteristic
89	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
91	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
92	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
94	C₂²×Dic₃	—	3	4	no	—
95	C₂²×Dic₃	—	3	4	no	—
96	C₃×C₄²	—	2	4	no	—
97	C₃×C₄²	—	2	2	no	—
98	C₃×C₄²	—	2	4	no	—
99	C₃×C₄²	Dic₆	1	4	yes	—
100	C₃×C₄²	C₄×D₃	1	4	yes	—
101	C₄⋊Dic₃	—	3	8	no	—
102	C₄⋊Dic₃	—	6	4	no	—
103	Dic₃⋊C₄	—	3	16	no	—
104	Dic₃⋊C₄	—	6	8	no	—
105	C₄×Dic₃	—	6	8	no	—
106	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
107	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
108	C₂²×C₉	C₂×#41	1	1	yes	characteristic
109	C₂²×C₉	C₂×#41	1	2	yes	—
110	C₂²×C₉	C₂×#41	1	2	yes	—
111	C₄×C₉	—	2	4	no	—
112	C₄×C₉	—	2	4	no	—
113	C₄×C₉	—	2	2	no	—
114	C₄×C₉	C₄×Q₈	1	4	yes	—
115	C₄×C₉	#125	1	4	yes	complemented
116	Dic₉	—	2	8	no	—
117	Dic₉	—	4	4	no	—
118	#125	—	9	8	no	—
119	C₂×C₄⋊C₄	—	9	4	no	—
120	C₂×C₄⋊C₄	—	9	2	no	—
121	C₂×C₄⋊C₄	—	9	2	no	—
122	C₂×C₄⋊C₄	—	9	4	no	—
123	C₂×C₄²	—	9	4	no	—
124	C₂×C₄²	C₂×D₉	1	2	yes	—
125	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
126	C₂×C₄²	C₂×D₉	1	2	yes	—
127	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
128	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
129	#95	—	9	4	no	—
130	#95	—	9	4	no	—
131	#95	—	9	4	no	—
132	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
133	C₂×C₃×C₄	—	2	2	no	—
134	C₂×C₃×C₄	—	2	2	no	—
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	2	no	—
138	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
139	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
140	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
141	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
142	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
143	C₂×C₃×C₄	#235	1	4	yes	—
144	C₂×C₃×C₄	#235	1	2	yes	—
145	C₂×C₃×C₄	#235	1	4	yes	—
146	C₂×Dic₃	—	3	8	no	—
147	C₂×Dic₃	—	6	4	no	—
148	C₂×Dic₃	—	6	4	no	—
149	C₂×Dic₃	—	6	4	no	—
150	C₂×Dic₃	—	6	4	no	—
151	C₂×Dic₃	—	6	4	no	—
152	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
153	C₂×C₉	C₄×#41	1	2	yes	—
154	C₂×C₉	C₂×#125	1	1	yes	characteristic
155	C₂×C₉	#529	1	2	yes	—
156	C₂×C₉	#533	1	1	yes	characteristic
157	C₂²×C₄	—	9	4	no	—
158	C₂²×C₄	—	9	4	no	—
159	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
160	C₂²×C₄	C₂²×D₉	1	2	yes	—
161	C₂²×C₄	C₂²×D₉	1	2	yes	—
162	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
163	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
164	C₄⋊C₄	—	9	16	no	—
165	C₄⋊C₄	—	9	8	no	—
166	C₄⋊C₄	—	18	8	no	—
167	C₄⋊C₄	—	18	4	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	2	4	no	—
171	C₄²	—	18	8	no	—
172	C₄²	Dic₁₈	1	4	yes	—
173	C₄²	C₄×D₉	1	4	yes	—
174	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
175	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
176	C₂²×C₃	C₂×#235	1	1	yes	characteristic
177	C₂²×C₃	C₂×#235	1	2	yes	—
178	C₂²×C₃	C₂×#235	1	2	yes	—
179	C₃×C₄	—	2	2	no	—
180	C₃×C₄	—	2	4	no	—
181	C₃×C₄	—	2	4	no	—
182	C₃×C₄	C₄×Dic₆	1	4	yes	—
183	C₃×C₄	#870	1	4	yes	—
184	Dic₃	—	6	8	no	—
185	Dic₃	—	12	4	no	—
186	C₉	C₄×#125	1	1	yes	characteristic, complemented, Sylow
187	C₂³	C₂³×D₉	1	1	yes	characteristic
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	9	8	no	—
194	C₂×C₄	—	18	4	no	—
195	C₂×C₄	—	18	4	no	—
196	C₂×C₄	—	18	4	no	—
197	C₂×C₄	—	18	4	no	—
198	C₂×C₄	—	18	4	no	—
199	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
200	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
201	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
202	C₂×C₄	C₂×C₄×D₉	1	4	yes	—
203	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
204	C₂×C₄	#3697	1	4	yes	—
205	C₂×C₄	#3697	1	2	yes	—
206	C₂×C₄	#3697	1	4	yes	—
207	C₂×C₃	C₂×C₄×Dic₆	1	1	yes	characteristic
208	C₂×C₃	C₂×#870	1	1	yes	characteristic
209	C₂×C₃	#5470	1	1	yes	characteristic
210	C₂×C₃	C₄×#235	1	2	yes	—
211	C₂×C₃	#5479	1	2	yes	—
212	C₂²	C₂²×Dic₁₈	1	1	yes	characteristic
213	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
214	C₂²	C₂×#3697	1	1	yes	characteristic
215	C₂²	C₂×#3697	1	2	yes	—
216	C₂²	C₂×#3697	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	4	no	—
219	C₄	—	2	4	no	—
220	C₄	—	18	8	no	—
221	C₄	—	36	4	no	—
222	C₄	C₄×Dic₁₈	1	4	yes	—
223	C₄	#63432	1	4	yes	direct product factor
224	C₃	C₄×#870	1	1	yes	characteristic
225	C₂	C₂×C₄×Dic₁₈	1	1	yes	characteristic
226	C₂	C₂×#63432	1	1	yes	characteristic
227	C₂	#10589572	1	1	yes	characteristic
228	C₂	C₄×#3697	1	2	yes	—
229	C₂	#10589581	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₄³×C₉	C₂
cosocle	C₂³×C₉	C₂⁴
hypercenter	C₄³	D₉
hypocenter	C₉	C₄×#125
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
19. #63432	C₄	direct (N × H)
115. C₄×C₉	#125	semidirect
186. C₉	C₄×#125	semidirect
223. C₄	#63432	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#63432	2
C₄³×C₉	2
#10588616	2
C₄×C₄⋊Dic₉	2
#10588613	2
C₄×Dic₉⋊C₄	2
#10588608	2
C₄×#870	3

Subgroups — C4×#63432 #11802472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63432 #11802472