Subgroups — C₄×#63467 #11859981

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63467	C₂	1	1	yes	maximal, characteristic
2	C₄×#3697	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588794	C₂	1	2	yes	maximal, complemented
5	#10588787	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×D₇₂	C₂	1	2	yes	maximal, complemented
7	C₄×#3664	C₂	1	4	yes	maximal, complemented
8	C₄×Dic₃₆	C₂	1	2	yes	maximal, complemented
9	C₄×#904	—	3	1	no	maximal
10	C₂×#3697	C₂²	1	2	yes	—
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₄×#611	—	2	4	no	—
15	#63488	C₂²	1	2	yes	—
16	#63467	C₄	1	8	yes	direct product factor
17	C₂×D₇₂	C₂²	1	1	yes	characteristic
18	C₂×#3664	C₂²	1	2	yes	—
19	C₂×Dic₃₆	C₂²	1	1	yes	characteristic
20	C₄×D₃₆	C₂²	1	4	yes	—
21	#63434	—	2	2	no	—
22	C₄²×D₉	—	2	2	no	—
23	C₄×Dic₁₈	C₂²	1	4	yes	—
24	C₄×C₈×C₉	C₂²	1	2	yes	—
25	C₄×C₈×C₉	C₂²	1	2	yes	—
26	#63380	C₂²	1	4	yes	—
27	#63378	C₂²	1	2	yes	—
28	#63377	C₂²	1	2	yes	—
29	#63376	C₂²	1	4	yes	—
30	C₂×#904	—	3	1	no	—
31	C₄×#235	—	3	2	no	—
32	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
33	#5113	—	3	2	no	—
34	#5106	—	3	1	no	—
35	C₄×Dic₁₂	—	3	2	no	—
36	C₄×D₂₄	—	3	2	no	—
37	C₄×#204	—	3	4	no	—
38	C₂²×C₄×C₉	D₄	1	2	yes	—
39	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
40	C₂×#611	—	2	2	no	—
41	#3697	—	2	4	no	—
42	#3697	C₂×C₄	1	8	yes	complemented
43	C₂×D₃₆	C₂³	1	2	yes	—
44	C₂×C₄×D₉	—	2	2	no	—
45	C₂×C₄×D₉	—	2	4	no	—
46	C₂×Dic₁₈	C₂³	1	2	yes	—
47	C₂×C₈×C₉	—	2	2	no	—
48	C₂×C₈×C₉	C₂×C₄	1	4	yes	complemented
49	C₂×C₈×C₉	C₂³	1	2	yes	—
50	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
52	C₄²×C₉	D₄	1	1	yes	characteristic
53	C₄²×C₉	D₄	1	1	yes	characteristic
54	C₄²×C₉	C₂³	1	2	yes	—
55	#3676	—	2	2	no	—
56	(C₂×D₉)⋊C₄	—	2	4	no	—
57	C₄⋊Dic₉	C₂³	1	4	yes	—
58	Dic₉⋊C₄	—	2	4	no	—
59	C₄×Dic₉	—	2	2	no	—
60	C₄×Dic₉	—	2	4	no	—
61	D₇₂	C₂×C₄	1	4	yes	complemented
62	#3664	C₂×C₄	1	8	yes	complemented
63	Dic₃₆	C₂×C₄	1	4	yes	complemented
64	C₄×#135	—	9	1	no	Sylow
65	C₂×#235	—	3	2	no	—
66	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₄×#67	—	6	4	no	—
70	#926	—	3	2	no	—
71	C₂×Dic₁₂	—	3	1	no	—
72	#904	—	3	8	no	—
73	C₂×D₂₄	—	3	1	no	—
74	C₂×#204	—	3	2	no	—
75	C₄×D₁₂	—	3	4	no	—
76	#872	—	6	2	no	—
77	C₄²×D₃	—	6	2	no	—
78	C₄×Dic₆	—	3	4	no	—
79	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
80	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
81	#821	—	3	4	no	—
82	#818	—	3	2	no	—
83	#817	—	3	2	no	—
84	#816	—	3	4	no	—
85	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×D₉	—	2	2	no	—
87	C₂×C₄×C₉	—	2	4	no	—
88	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
89	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
90	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
92	C₂×C₄×C₉	#41	1	2	yes	—
93	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
94	#611	—	2	8	no	—
95	C₂×Dic₉	—	2	2	no	—
96	C₂×Dic₉	—	2	4	no	—
97	D₃₆	—	2	2	no	—
98	D₃₆	C₂²×C₄	1	4	yes	—
99	C₄×D₉	—	2	8	no	—
100	C₄×D₉	—	4	8	no	—
101	Dic₁₈	—	2	2	no	—
102	Dic₁₈	C₂²×C₄	1	4	yes	—
103	C₈×C₉	—	2	2	no	—
104	C₈×C₉	C₂²×C₄	1	2	yes	—
105	C₈×C₉	C₂²×C₄	1	2	yes	—
106	C₂×#135	—	9	1	no	—
107	C₄×#41	—	9	2	no	—
108	C₄×Q₁₆	—	9	2	no	—
109	C₄×SD₁₆	—	9	4	no	—
110	C₄×D₈	—	9	2	no	—
111	#427	—	9	1	no	—
112	#416	—	9	2	no	—
113	C₂×C₄×C₈	D₉	1	1	yes	characteristic, complemented
114	C₂²×C₃×C₄	D₁₂	1	2	yes	—
115	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
116	C₂×#67	—	6	2	no	—
117	#235	—	3	8	no	—
118	#235	—	6	4	no	—
119	C₂×D₁₂	—	3	2	no	—
120	C₂×C₄×D₃	—	6	2	no	—
121	C₂×C₄×D₃	—	6	4	no	—
122	C₂×Dic₆	—	3	2	no	—
123	C₂×C₃×C₈	—	2	2	no	—
124	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
125	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
126	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
127	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
128	C₃×C₄²	D₁₂	1	1	yes	characteristic
129	C₃×C₄²	D₁₂	1	1	yes	characteristic
130	C₃×C₄²	C₂²×D₃	1	2	yes	—
131	#217	—	6	2	no	—
132	(C₂×D₃)⋊C₄	—	6	4	no	—
133	C₄⋊Dic₃	—	3	4	no	—
134	Dic₃⋊C₄	—	6	4	no	—
135	C₄×Dic₃	—	6	4	no	—
136	C₄×Dic₃	—	6	2	no	—
137	Dic₁₂	—	3	4	no	—
138	D₂₄	—	3	4	no	—
139	#204	—	3	8	no	—
140	C₂²×C₉	—	2	2	no	—
141	C₂²×C₉	C₄×D₄	1	2	yes	—
142	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×D₉	—	2	4	no	—
144	C₂×D₉	—	4	4	no	—
145	C₄×C₉	—	2	2	no	—
146	C₄×C₉	C₄×D₄	1	2	yes	—
147	C₄×C₉	#135	1	4	yes	complemented
148	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
149	C₄×C₉	C₂×#41	1	1	yes	characteristic
150	Dic₉	—	2	4	no	—
151	Dic₉	—	4	4	no	—
152	C₂×#41	—	9	2	no	—
153	#135	—	9	8	no	—
154	C₂×Q₁₆	—	9	1	no	—
155	C₂×SD₁₆	—	9	2	no	—
156	C₂×D₈	—	9	1	no	—
157	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
158	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
159	C₄×Q₈	—	9	4	no	—
160	C₄×D₄	—	9	4	no	—
161	C₄×D₄	—	18	4	no	—
162	#117	—	9	2	no	—
163	#117	—	18	2	no	—
164	C₂×C₄²	—	18	2	no	—
165	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
166	#107	—	9	2	no	—
167	#106	—	9	2	no	—
168	#103	—	9	4	no	—
169	#102	—	9	4	no	—
170	C₄×C₈	C₂×D₉	1	2	yes	—
171	C₄×C₈	C₂×D₉	1	2	yes	—
172	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
173	C₂²×D₃	—	6	2	no	—
174	C₂×C₃×C₄	—	2	4	no	—
175	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
176	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
177	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
178	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
179	C₂×C₃×C₄	#235	1	2	yes	—
180	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
181	#67	—	6	8	no	—
182	C₂×Dic₃	—	6	2	no	—
183	C₂×Dic₃	—	6	4	no	—
184	D₁₂	—	3	4	no	—
185	D₁₂	—	6	2	no	—
186	C₄×D₃	—	6	8	no	—
187	C₄×D₃	—	12	8	no	—
188	Dic₆	—	3	4	no	—
189	Dic₆	—	6	2	no	—
190	C₃×C₈	—	2	2	no	—
191	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
192	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
193	C₂×C₉	—	2	2	no	—
194	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×C₉	C₂×#135	1	2	yes	—
196	D₉	—	4	4	no	—
197	#41	—	9	8	no	—
198	#41	—	18	4	no	—
199	C₂×Q₈	—	9	2	no	—
200	C₂×D₄	—	9	2	no	—
201	C₂×D₄	—	18	2	no	—
202	C₂²×C₄	—	18	2	no	—
203	C₂²×C₄	—	18	4	no	—
204	C₂²×C₄	D₃₆	1	2	yes	—
205	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
206	Q₁₆	—	9	4	no	—
207	SD₁₆	—	9	8	no	—
208	D₈	—	9	4	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	C₄×D₉	1	4	yes	complemented
211	C₂×C₈	C₂²×D₉	1	2	yes	—
212	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
213	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
214	C₄⋊C₄	—	9	4	no	—
215	C₄⋊C₄	—	18	4	no	—
216	C₂²⋊C₄	—	18	2	no	—
217	C₂²⋊C₄	—	18	4	no	—
218	C₄²	—	18	2	no	—
219	C₄²	—	18	4	no	—
220	C₄²	D₃₆	1	1	yes	characteristic
221	C₄²	D₃₆	1	1	yes	characteristic
222	C₄²	C₂²×D₉	1	2	yes	—
223	C₂²×C₃	—	2	2	no	—
224	C₂²×C₃	C₄×D₁₂	1	2	yes	—
225	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
226	C₂×D₃	—	6	4	no	—
227	C₂×D₃	—	12	4	no	—
228	C₃×C₄	—	2	2	no	—
229	C₃×C₄	C₄×D₁₂	1	2	yes	—
230	C₃×C₄	#904	1	4	yes	—
231	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
232	C₃×C₄	C₂×#235	1	1	yes	characteristic
233	Dic₃	—	6	4	no	—
234	Dic₃	—	12	4	no	—
235	C₉	C₄×#135	1	1	yes	characteristic, complemented, Sylow
236	C₂³	—	18	2	no	—
237	C₂³	C₂×D₃₆	1	1	yes	characteristic
238	Q₈	—	9	4	no	—
239	Q₈	—	18	2	no	—
240	D₄	—	9	4	no	—
241	D₄	—	18	8	no	—
242	D₄	—	18	2	no	—
243	C₂×C₄	—	2	4	no	—
244	C₂×C₄	—	18	2	no	—
245	C₂×C₄	—	18	8	no	—
246	C₂×C₄	—	18	4	no	—
247	C₂×C₄	—	36	8	no	—
248	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
249	C₂×C₄	C₂×D₃₆	1	2	yes	—
250	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
251	C₂×C₄	C₂×D₃₆	1	2	yes	—
252	C₂×C₄	#3697	1	2	yes	—
253	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
254	C₈	—	2	2	no	—
255	C₈	C₂×C₄×D₉	1	2	yes	—
256	C₈	C₂×C₄×D₉	1	2	yes	—
257	C₂×C₃	—	2	2	no	—
258	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
259	C₂×C₃	C₂×#904	1	2	yes	—
260	D₃	—	12	4	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	18	4	no	—
263	C₂²	—	36	4	no	—
264	C₂²	C₄×D₃₆	1	2	yes	—
265	C₂²	C₂²×D₃₆	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	18	4	no	—
268	C₄	—	36	4	no	—
269	C₄	C₄×D₃₆	1	2	yes	—
270	C₄	#63467	1	4	yes	direct product factor
271	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
272	C₄	C₂×#3697	1	1	yes	characteristic
273	C₃	C₄×#904	1	1	yes	characteristic
274	C₂	—	2	2	no	—
275	C₂	—	36	4	no	—
276	C₂	C₂×C₄×D₃₆	1	1	yes	characteristic
277	C₂	C₂×#63467	1	2	yes	—

	subgroup	G/H
center	C₄²	D₃₆
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle	C₂²×C₃	C₂²×D₁₂
prime radical	C₂×#63467	C₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	C₄×#135
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×#3697	C₂	semidirect
3. C₂×C₄×C₈×C₉	C₂	semidirect
4. #10588794	C₂	semidirect
5. #10588787	C₂	semidirect
6. C₄×D₇₂	C₂	semidirect
7. C₄×#3664	C₂	semidirect
8. C₄×Dic₃₆	C₂	semidirect
16. #63467	C₄	direct (N × H)
42. #3697	C₂×C₄	semidirect
48. C₂×C₈×C₉	C₂×C₄	semidirect
61. D₇₂	C₂×C₄	semidirect
62. #3664	C₂×C₄	semidirect
63. Dic₃₆	C₂×C₄	semidirect
113. C₂×C₄×C₈	D₉	semidirect
147. C₄×C₉	#135	semidirect
210. C₂×C₈	C₄×D₉	semidirect
235. C₉	C₄×#135	semidirect
270. C₄	#63467	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×#63467	2
C₄×#3697	2
C₂×C₄×C₈×C₉	2
#10588794	2
#10588787	2
C₄×D₇₂	2
C₄×#3664	2
C₄×Dic₃₆	2
C₄×#904	3

Subgroups — C4×#63467 #11859981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63467 #11859981