Subgroups — C₃²×#4836 #13162275

Order 1728.

896 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₃³×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#435	—	3	1	no	maximal
9	C₃×#4836	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃²×D₁₂	C₄	1	1	yes	characteristic
11	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
15	C₃³×C₄²	C₂²	1	1	yes	characteristic
16	C₃²×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
17	C₃²×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
18	C₃²×C₄⋊Dic₃	C₄	1	1	yes	characteristic
19	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃²×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₃²×D₃×C₈	—	2	2	no	—
23	C₂×C₃²×M₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	3	1	no	—
25	C₃²×C₄×D₄	—	3	1	no	—
26	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	complemented
27	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	complemented
28	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	—
29	C₃²×C₄⋊C₈	—	2	4	no	—
30	C₃²×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
31	C₃²×C₄⋊C₈	C₂×C₃	1	4	yes	complemented
32	C₃²×C₂²⋊C₈	—	3	1	no	—
33	C₃²×C₂²⋊C₈	—	3	1	no	—
34	C₃²×#97	—	3	1	no	—
35	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	4	yes	complemented
36	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	4	yes	complemented
37	C₃×#803	C₂×C₃	1	4	yes	complemented
38	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
43	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₃²×D₁₂	—	2	2	no	—
46	C₃²×C₄×D₃	—	2	1	no	—
47	C₃²×C₄×D₃	—	2	1	no	—
48	C₃²×C₄×D₃	—	2	1	no	—
49	C₃²×C₄×D₃	—	2	1	no	—
50	C₃³×C₈	—	2	1	no	—
51	C₃³×C₈	—	2	1	no	—
52	C₃²×C₃⋊C₈	—	2	1	no	—
53	C₃²×C₃⋊C₈	D₄	1	2	yes	complemented
54	C₃×#435	—	3	4	no	—
55	#4836	C₃²	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×D₄	—	3	1	no	—
57	C₂²×C₃²×C₄	—	3	1	no	—
58	C₂²×C₃²×C₄	—	3	1	no	—
59	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	—
60	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
61	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
62	C₃²×M₁₆	—	6	2	no	—
63	C₂×C₃²×C₈	—	2	4	no	—
64	C₂×C₃²×C₈	—	2	4	no	—
65	C₂×C₃²×C₈	—	3	1	no	—
66	C₂×C₃²×C₈	—	3	1	no	—
67	C₂×C₃²×C₈	—	6	2	no	—
68	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
69	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
71	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
72	C₃²×C₄⋊C₄	—	3	1	no	—
73	C₃²×C₂²⋊C₄	—	3	1	no	—
74	C₃²×C₂²⋊C₄	—	3	1	no	—
75	C₃²×C₄²	—	2	4	no	—
76	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
77	C₃²×C₄²	C₂²×C₃	1	4	yes	—
78	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
79	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
80	C₃×C₄⋊Dic₃	C₃×C₄	1	4	yes	—
81	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
82	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
83	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
84	C₃×D₃×C₈	—	2	8	no	—
85	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃²×D₃	—	2	1	no	—
87	C₂×C₃²×D₃	—	2	1	no	—
88	C₂×C₃²×D₃	—	2	1	no	—
89	C₂×C₃²×D₃	—	2	1	no	—
90	C₂×C₃²×D₃	—	2	1	no	—
91	C₂×C₃²×D₃	M₁₆	1	2	yes	complemented
92	C₃³×C₄	—	2	1	no	—
93	C₃³×C₄	—	2	1	no	—
94	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₃³×C₄	#41	1	1	yes	characteristic
96	C₃²×Dic₃	—	2	1	no	—
97	C₃²×Dic₃	—	2	1	no	—
98	C₂×C₃×M₁₆	—	3	4	no	—
99	C₂²×C₃×C₈	—	3	4	no	—
100	C₃×C₄×D₄	—	3	4	no	—
101	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic, complemented
102	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic
104	C₃×C₄⋊C₈	—	2	4	no	—
105	C₃×C₄⋊C₈	C₃×D₃	1	4	yes	complemented
106	C₃×C₄⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
107	C₃×C₂²⋊C₈	—	3	4	no	—
108	C₃×C₂²⋊C₈	—	3	4	no	—
109	C₃×#97	—	3	4	no	—
110	(C₂×D₃)⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
111	(C₂×D₃)⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
112	#803	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₂³×C₃²	—	3	1	no	—
114	C₂³×C₃²	—	3	1	no	—
115	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
116	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
117	C₃²×D₄	—	6	2	no	—
118	C₂×C₃²×C₄	—	2	4	no	—
119	C₂×C₃²×C₄	—	2	4	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	3	1	no	—
122	C₂×C₃²×C₄	—	3	1	no	—
123	C₂×C₃²×C₄	—	6	1	no	—
124	C₂×C₃²×C₄	—	6	1	no	—
125	C₂×C₃²×C₄	—	6	1	no	—
126	C₂×C₃²×C₄	—	6	1	no	—
127	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
130	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
131	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
133	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
134	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
135	C₃×D₁₂	—	2	8	no	—
136	C₃×C₄×D₃	—	2	4	no	—
137	C₃×C₄×D₃	—	2	4	no	—
138	C₃×C₄×D₃	—	2	4	no	—
139	C₃×C₄×D₃	—	2	4	no	—
140	C₃²×C₈	—	2	1	no	—
141	C₃²×C₈	—	2	1	no	—
142	C₃²×C₈	—	2	4	no	—
143	C₃²×C₈	—	2	4	no	—
144	C₃²×C₈	—	3	2	no	—
145	C₃²×C₈	—	4	4	no	—
146	C₃²×C₈	—	4	4	no	—
147	C₃²×C₈	—	6	1	no	—
148	C₃×C₃⋊C₈	—	2	4	no	—
149	C₃×C₃⋊C₈	C₃×D₄	1	8	yes	complemented
150	#435	—	3	1	no	Sylow
151	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
152	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₃³	#131	1	1	yes	characteristic
154	C₃²×D₃	—	2	2	no	—
155	C₃²×D₃	—	4	1	no	—
156	C₂×C₃×D₄	—	3	4	no	—
157	C₂²×C₃×C₄	—	3	4	no	—
158	C₂²×C₃×C₄	—	3	4	no	—
159	C₂×D₁₂	C₃²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
161	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
162	C₃×M₁₆	—	6	8	no	—
163	C₂×C₃×C₈	—	2	4	no	—
164	C₂×C₃×C₈	—	2	4	no	—
165	C₂×C₃×C₈	—	3	4	no	—
166	C₂×C₃×C₈	—	3	4	no	—
167	C₂×C₃×C₈	—	6	8	no	—
168	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
169	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
170	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	3	4	no	—
173	C₃×C₂²⋊C₄	—	3	4	no	—
174	C₃×C₂²⋊C₄	—	3	4	no	—
175	C₃×C₄²	—	2	4	no	—
176	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
177	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
178	(C₂×D₃)⋊C₄	C₃²×C₄	1	1	yes	characteristic
179	(C₂×D₃)⋊C₄	C₃²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₃	C₃²×C₄	1	1	yes	characteristic
181	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
182	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
183	ΓL(1,𝔽₂₅)	—	2	2	no	—
184	D₃×C₈	—	2	2	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	—	3	2	no	—
187	C₂²×C₃²	—	6	1	no	—
188	C₂²×C₃²	—	6	1	no	—
189	C₂²×C₃²	—	6	1	no	—
190	C₂²×C₃²	—	6	1	no	—
191	C₂²×C₃²	—	6	1	no	—
192	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
193	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
194	C₂×C₃×D₃	—	2	4	no	—
195	C₂×C₃×D₃	—	2	4	no	—
196	C₂×C₃×D₃	—	2	4	no	—
197	C₂×C₃×D₃	—	2	4	no	—
198	C₂×C₃×D₃	—	2	4	no	—
199	C₂×C₃×D₃	C₃×M₁₆	1	8	yes	complemented
200	C₃²×C₄	—	2	8	no	—
201	C₃²×C₄	—	2	1	no	—
202	C₃²×C₄	—	2	1	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	—	2	4	no	—
205	C₃²×C₄	—	2	4	no	—
206	C₃²×C₄	—	2	4	no	—
207	C₃²×C₄	—	4	4	no	—
208	C₃²×C₄	—	6	1	no	—
209	C₃²×C₄	—	6	1	no	—
210	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
211	C₃²×C₄	#239	1	1	yes	characteristic
212	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
213	C₃²×C₄	C₃×#41	1	4	yes	—
214	C₃×Dic₃	—	2	4	no	—
215	C₃×Dic₃	—	2	4	no	—
216	C₂×M₁₆	—	3	1	no	—
217	C₂²×C₈	—	3	1	no	—
218	C₄×D₄	—	3	1	no	—
219	C₄⋊C₈	C₃²×D₃	1	1	yes	characteristic, complemented
220	C₂²⋊C₈	—	3	1	no	—
221	C₂²⋊C₈	—	3	1	no	—
222	#97	—	3	1	no	—
223	C₃³	#435	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₃	—	3	4	no	—
225	C₂³×C₃	—	3	4	no	—
226	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
227	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
228	C₃×D₄	—	6	8	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	3	4	no	—
233	C₂×C₃×C₄	—	3	4	no	—
234	C₂×C₃×C₄	—	6	4	no	—
235	C₂×C₃×C₄	—	6	4	no	—
236	C₂×C₃×C₄	—	6	4	no	—
237	C₂×C₃×C₄	—	6	4	no	—
238	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
239	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
240	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
243	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
244	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
245	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
246	D₁₂	—	2	2	no	—
247	C₄×D₃	—	2	1	no	—
248	C₄×D₃	—	2	1	no	—
249	C₄×D₃	—	2	1	no	—
250	C₄×D₃	—	2	1	no	—
251	C₃×C₈	—	2	4	no	—
252	C₃×C₈	—	2	4	no	—
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	—	2	1	no	—
255	C₃×C₈	—	3	8	no	—
256	C₃×C₈	—	4	4	no	—
257	C₃×C₈	—	4	4	no	—
258	C₃×C₈	—	6	4	no	—
259	C₃⋊C₈	—	2	1	no	—
260	C₃⋊C₈	C₃²×D₄	1	2	yes	complemented
261	C₂×C₃²	—	2	4	no	—
262	C₂×C₃²	—	2	4	no	—
263	C₂×C₃²	—	2	4	no	—
264	C₂×C₃²	—	6	2	no	—
265	C₂×C₃²	—	12	1	no	—
266	C₂×C₃²	#893	1	1	yes	characteristic
267	C₂×C₃²	#901	1	1	yes	characteristic
268	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
269	C₂×C₃²	C₃×C₄×D₄	1	4	yes	—
270	C₂×C₃²	C₂×C₃×M₁₆	1	4	yes	—
271	C₂×C₃²	C₃×#131	1	4	yes	—
272	C₃×D₃	—	2	8	no	—
273	C₃×D₃	—	4	4	no	—
274	C₂×D₄	—	3	1	no	—
275	C₂²×C₄	—	3	1	no	—
276	C₂²×C₄	—	3	1	no	—
277	M₁₆	—	6	2	no	—
278	C₂×C₈	—	3	1	no	—
279	C₂×C₈	—	3	1	no	—
280	C₂×C₈	—	6	2	no	—
281	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
282	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
283	C₄⋊C₄	—	3	1	no	—
284	C₂²⋊C₄	—	3	1	no	—
285	C₂²⋊C₄	—	3	1	no	—
286	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	3	8	no	—
289	C₂²×C₃	—	6	4	no	—
290	C₂²×C₃	—	6	4	no	—
291	C₂²×C₃	—	6	4	no	—
292	C₂²×C₃	—	6	4	no	—
293	C₂²×C₃	—	6	4	no	—
294	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
295	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
296	C₂×D₃	—	2	1	no	—
297	C₂×D₃	—	2	1	no	—
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	—	2	1	no	—
300	C₂×D₃	—	2	1	no	—
301	C₂×D₃	C₃²×M₁₆	1	2	yes	complemented
302	C₃×C₄	—	2	8	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	4	4	no	—
310	C₃×C₄	—	6	4	no	—
311	C₃×C₄	—	6	4	no	—
312	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
313	C₃×C₄	C₃×#239	1	4	yes	—
314	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
315	C₃×C₄	C₃²×#41	1	1	yes	characteristic
316	Dic₃	—	2	1	no	—
317	Dic₃	—	2	1	no	—
318	C₃²	—	2	4	no	—
319	C₃²	#4836	1	1	yes	characteristic, direct product factor
320	C₃²	C₃×#435	1	4	yes	complemented
321	C₂³	—	3	1	no	—
322	C₂³	—	3	1	no	—
323	D₄	—	6	2	no	—
324	C₂×C₄	—	3	1	no	—
325	C₂×C₄	—	3	1	no	—
326	C₂×C₄	—	6	1	no	—
327	C₂×C₄	—	6	1	no	—
328	C₂×C₄	—	6	1	no	—
329	C₂×C₄	—	6	1	no	—
330	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
331	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	3	2	no	—
336	C₈	—	6	1	no	—
337	C₂×C₃	—	2	4	no	—
338	C₂×C₃	—	2	4	no	—
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	6	8	no	—
341	C₂×C₃	—	12	4	no	—
342	C₂×C₃	C₃×#893	1	4	yes	—
343	C₂×C₃	C₃×#901	1	4	yes	—
344	C₂×C₃	C₃×D₃×M₁₆	1	4	yes	—
345	C₂×C₃	C₃²×C₄×D₄	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃²×M₁₆	1	1	yes	characteristic
347	C₂×C₃	C₃²×#131	1	1	yes	characteristic
348	D₃	—	2	2	no	—
349	D₃	—	4	1	no	—
350	C₂²	—	3	2	no	—
351	C₂²	—	6	1	no	—
352	C₂²	—	6	1	no	—
353	C₂²	—	6	1	no	—
354	C₂²	—	6	1	no	—
355	C₂²	—	6	1	no	—
356	C₂²	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	6	1	no	—
360	C₄	—	6	1	no	—
361	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
362	C₄	C₃²×#239	1	1	yes	characteristic
363	C₃	—	2	4	no	—
364	C₃	C₃×#4836	1	4	yes	direct product factor
365	C₃	C₃²×#435	1	1	yes	characteristic, complemented
366	C₂	—	6	2	no	—
367	C₂	—	12	1	no	—
368	C₂	C₃²×#893	1	1	yes	characteristic
369	C₂	C₃²×#901	1	1	yes	characteristic
370	C₂	C₃²×D₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×C₄⋊C₈	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃²×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₃²×C₄⋊C₈	D₃
hypocenter	C₃	C₃²×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
2. C₂×C₃²×D₃×C₈	C₂	semidirect
4. C₃³×C₄⋊C₈	C₂	semidirect
5. C₃²×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₃²×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₃²×#803	C₂	semidirect
9. C₃×#4836	C₃	direct (N × H)
26. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
27. C₂×C₃×D₃×C₈	C₂×C₃	semidirect
30. C₃²×C₄⋊C₈	D₃	semidirect
31. C₃²×C₄⋊C₈	C₂×C₃	semidirect
35. C₃×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
36. C₃×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
37. C₃×#803	C₂×C₃	semidirect
53. C₃²×C₃⋊C₈	D₄	semidirect
55. #4836	C₃²	direct (N × H)
91. C₂×C₃²×D₃	M₁₆	semidirect
101. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
102. C₂×D₃×C₈	C₂×C₃²	semidirect
105. C₃×C₄⋊C₈	C₃×D₃	semidirect
106. C₃×C₄⋊C₈	C₂×C₃²	semidirect
110. (C₂×D₃)⋊C₈	C₂×C₃²	semidirect
111. (C₂×D₃)⋊C₈	C₂×C₃²	semidirect
112. #803	C₂×C₃²	semidirect
149. C₃×C₃⋊C₈	C₃×D₄	semidirect
199. C₂×C₃×D₃	C₃×M₁₆	semidirect
219. C₄⋊C₈	C₃²×D₃	semidirect
223. C₃³	#435	semidirect
260. C₃⋊C₈	C₃²×D₄	semidirect
301. C₂×D₃	C₃²×M₁₆	semidirect
319. C₃²	#4836	direct (N × H)
320. C₃²	C₃×#435	semidirect
364. C₃	C₃×#4836	direct (N × H)
365. C₃	C₃²×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×D₃×C₈	2
C₃²×C₄×D₁₂	2
C₃³×C₄⋊C₈	2
C₃²×(C₂×D₃)⋊C₈	2
C₃²×#803	2
C₃²×#435	3
C₃×#4836	3

Subgroups — C32×#4836 #13162275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4836 #13162275