Subgroups — C₃×#79048 #11858303

Order 1152.

1031 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×C₃×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic
3	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5118	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4839	C₂	1	8	yes	maximal, complemented
7	C₃×#2905	—	3	1	no	maximal
8	#79048	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
13	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×#208	C₂²	1	2	yes	—
16	C₃×D₃×M₁₆	—	2	8	no	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
19	C₃×#872	C₄	1	2	yes	—
20	C₃×#872	C₄	1	2	yes	—
21	C₃×#872	C₂²	1	4	yes	—
22	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
23	C₃×Dic₃⋊C₈	C₂²	1	8	yes	complemented
24	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂²×C₃×M₁₆	—	3	2	no	—
26	C₂×C₃×#117	—	3	1	no	—
27	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
28	C₂×#872	C₂×C₃	1	1	yes	characteristic
29	C₃×#424	—	3	8	no	—
30	C₃×#423	—	2	1	no	—
31	C₃×#423	—	3	2	no	—
32	C₃×#423	—	3	1	no	—
33	C₃×#423	D₃	1	1	yes	characteristic, complemented
34	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
35	#5118	C₂×C₃	1	2	yes	complemented
36	#4924	C₂×C₃	1	1	yes	characteristic, complemented
37	#4839	C₂×C₃	1	8	yes	complemented
38	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₃	D₄	1	4	yes	—
45	C₂×C₃×C₄×D₃	Q₈	1	4	yes	—
46	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
47	C₃²×M₁₆	—	2	4	no	—
48	C₂×C₃²×C₈	C₂³	1	4	yes	—
49	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
50	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
53	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
54	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
56	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
57	C₃×C₄×Dic₃	C₂³	1	2	yes	—
58	C₃×#208	—	2	4	no	—
59	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
60	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
61	C₃×D₃×C₈	—	2	8	no	—
62	#2905	—	3	1	no	Sylow
63	C₂³×C₃×C₄	—	3	1	no	—
64	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×M₁₆	—	2	2	no	—
66	C₂×C₃×M₁₆	—	3	2	no	—
67	C₂×C₃×M₁₆	—	3	4	no	—
68	C₂×C₃×M₁₆	—	6	8	no	—
69	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
70	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
71	C₂²×C₃×C₈	—	3	4	no	—
72	C₃×#117	—	3	2	no	—
73	C₃×#117	—	3	2	no	—
74	C₃×#117	—	3	4	no	—
75	C₂×C₃×C₄⋊C₄	—	3	2	no	—
76	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
77	C₂×C₃×C₄²	—	2	1	no	—
78	C₂×C₃×C₄²	—	3	1	no	—
79	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
82	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
83	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×#208	C₂²×C₃	1	2	yes	—
85	D₃×M₁₆	—	2	8	no	—
86	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
87	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
88	#872	C₃×C₄	1	2	yes	—
89	#872	C₃×C₄	1	2	yes	—
90	#872	C₂²×C₃	1	4	yes	—
91	C₃×C₄⋊C₈	—	2	4	no	—
92	C₃×C₄⋊C₈	—	3	8	no	—
93	C₃×C₄⋊C₈	—	3	4	no	—
94	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
95	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
96	Dic₃⋊C₈	C₂²×C₃	1	8	yes	complemented
97	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
98	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₃×D₃	—	4	2	no	—
100	C₂²×C₃×D₃	C₄⋊C₄	1	4	yes	—
101	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
102	C₂×C₃²×C₄	—	4	2	no	—
103	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
104	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
107	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
108	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₃	—	4	2	no	—
110	C₂×C₃×Dic₃	C₄⋊C₄	1	4	yes	—
111	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
112	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
113	C₃×C₄×D₃	C₄⋊C₄	1	8	yes	—
114	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
115	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
116	C₃²×C₈	—	2	4	no	—
117	C₃×C₃⋊C₈	—	2	4	no	—
118	C₂²×M₁₆	—	3	2	no	—
119	C₂×#117	—	3	1	no	—
120	#424	—	3	8	no	—
121	#423	—	3	2	no	—
122	#423	—	3	1	no	—
123	#423	C₃×D₃	1	1	yes	characteristic, complemented
124	C₂⁴×C₃	—	3	1	no	—
125	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂²×C₃×C₄	—	2	2	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	3	1	no	—
129	C₂²×C₃×C₄	—	3	2	no	—
130	C₂²×C₃×C₄	—	3	4	no	—
131	C₂²×C₃×C₄	—	3	4	no	—
132	C₂²×C₃×C₄	—	3	2	no	—
133	C₂²×C₃×C₄	—	3	2	no	—
134	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
135	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
136	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
138	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
139	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₄×D₃	C₃×D₄	1	4	yes	—
142	C₂×C₄×D₃	C₃×Q₈	1	4	yes	—
143	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
144	C₃×M₁₆	—	2	4	no	—
145	C₃×M₁₆	—	2	4	no	—
146	C₃×M₁₆	—	4	4	no	—
147	C₃×M₁₆	—	6	8	no	—
148	C₃×M₁₆	—	6	4	no	—
149	C₂×C₃×C₈	—	2	4	no	—
150	C₂×C₃×C₈	—	3	4	no	—
151	C₂×C₃×C₈	—	6	8	no	—
152	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
153	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
154	C₃×C₄⋊C₄	—	3	4	no	—
155	C₃×C₄⋊C₄	—	3	4	no	—
156	C₃×C₂²⋊C₄	—	3	4	no	—
157	C₃×C₂²⋊C₄	—	3	4	no	—
158	C₃×C₄²	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	—	3	2	no	—
162	C₃×C₄²	—	3	2	no	—
163	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
164	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
165	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
166	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
167	C₃×C₄²	C₂²×D₃	1	2	yes	—
168	C₃×C₄²	C₂³×C₃	1	2	yes	—
169	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
170	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
171	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
172	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
173	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
174	C₄×Dic₃	C₂³×C₃	1	2	yes	—
175	#208	—	2	4	no	—
176	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
177	ΓL(1,𝔽₂₅)	—	2	8	no	—
178	D₃×C₈	—	2	8	no	—
179	C₂²×C₃²	—	2	2	no	—
180	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
181	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₃×D₃	—	2	4	no	—
183	C₂×C₃×D₃	—	4	4	no	—
184	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
185	C₃²×C₄	—	2	2	no	—
186	C₃²×C₄	—	2	2	no	—
187	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
188	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
189	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
190	C₃×Dic₃	—	2	4	no	—
191	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
192	C₂³×C₄	—	3	1	no	—
193	C₂×M₁₆	—	3	2	no	—
194	C₂×M₁₆	—	3	4	no	—
195	C₂×M₁₆	—	6	8	no	—
196	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
197	C₂²×C₈	—	3	4	no	—
198	#117	—	3	2	no	—
199	#117	—	3	2	no	—
200	#117	—	3	4	no	—
201	C₂×C₄⋊C₄	—	3	2	no	—
202	C₂×C₂²⋊C₄	—	3	2	no	—
203	C₂×C₄²	—	3	1	no	—
204	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
205	C₄⋊C₈	—	3	8	no	—
206	C₄⋊C₈	—	3	4	no	—
207	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
208	C₂³×C₃	—	2	1	no	—
209	C₂³×C₃	—	3	2	no	—
210	C₂³×C₃	—	3	4	no	—
211	C₂³×C₃	—	12	2	no	—
212	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
213	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₂²×D₃	—	4	2	no	—
215	C₂²×D₃	C₃×C₄⋊C₄	1	4	yes	—
216	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	3	4	no	—
224	C₂×C₃×C₄	—	3	2	no	—
225	C₂×C₃×C₄	—	3	8	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	3	4	no	—
228	C₂×C₃×C₄	—	3	4	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	—	4	4	no	—
232	C₂×C₃×C₄	—	12	2	no	—
233	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
237	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
238	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
239	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
240	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
243	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
245	C₂×Dic₃	—	4	2	no	—
246	C₂×Dic₃	C₃×C₄⋊C₄	1	4	yes	—
247	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
248	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
249	C₄×D₃	C₃×C₄⋊C₄	1	8	yes	—
250	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
251	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
252	C₃×C₈	—	2	4	no	—
253	C₃×C₈	—	2	4	no	—
254	C₃×C₈	—	4	4	no	—
255	C₃×C₈	—	6	4	no	—
256	C₃⋊C₈	—	2	4	no	—
257	C₂×C₃²	—	2	2	no	—
258	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₃²	#568	1	2	yes	—
260	C₃×D₃	—	2	4	no	—
261	C₂⁴	—	3	1	no	—
262	C₂²×C₄	—	3	1	no	—
263	C₂²×C₄	—	3	2	no	—
264	C₂²×C₄	—	3	2	no	—
265	C₂²×C₄	—	3	4	no	—
266	C₂²×C₄	—	3	4	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
269	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
270	M₁₆	—	2	4	no	—
271	M₁₆	—	6	8	no	—
272	M₁₆	—	6	4	no	—
273	C₂×C₈	—	3	4	no	—
274	C₂×C₈	—	6	8	no	—
275	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
276	C₄⋊C₄	—	3	4	no	—
277	C₄⋊C₄	—	3	4	no	—
278	C₂²⋊C₄	—	3	4	no	—
279	C₂²⋊C₄	—	3	4	no	—
280	C₄²	—	3	2	no	—
281	C₄²	—	3	2	no	—
282	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
283	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
284	C₄²	C₂²×C₃×D₃	1	2	yes	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	3	4	no	—
290	C₂²×C₃	—	4	2	no	—
291	C₂²×C₃	—	6	4	no	—
292	C₂²×C₃	—	12	4	no	—
293	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
294	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
295	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
296	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
297	C₂×D₃	—	2	4	no	—
298	C₂×D₃	—	4	4	no	—
299	C₂×D₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
300	C₃×C₄	—	2	4	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	3	4	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	6	4	no	—
311	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
312	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
313	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
314	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
315	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
317	Dic₃	—	2	4	no	—
318	Dic₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
319	C₃²	#2905	1	1	yes	characteristic, complemented, Sylow
320	C₂³	—	3	2	no	—
321	C₂³	—	3	4	no	—
322	C₂³	—	12	2	no	—
323	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
324	C₂×C₄	—	3	4	no	—
325	C₂×C₄	—	3	2	no	—
326	C₂×C₄	—	3	8	no	—
327	C₂×C₄	—	3	4	no	—
328	C₂×C₄	—	3	4	no	—
329	C₂×C₄	—	3	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	12	2	no	—
332	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
333	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
335	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
336	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
337	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
338	C₈	—	2	4	no	—
339	C₈	—	6	4	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	—	2	2	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	4	2	no	—
345	C₂×C₃	—	6	4	no	—
346	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₃	#5745	1	2	yes	—
348	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
349	C₂×C₃	C₃×#568	1	2	yes	—
350	D₃	—	2	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	3	4	no	—
353	C₂²	—	6	4	no	—
354	C₂²	—	12	4	no	—
355	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
356	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	3	4	no	—
360	C₄	—	6	4	no	—
361	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
362	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
363	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
364	C₃	—	2	1	no	—
365	C₃	#79048	1	1	yes	characteristic, direct product factor
366	C₃	C₃×#2905	1	1	yes	characteristic, complemented
367	C₂	—	2	2	no	—
368	C₂	—	6	4	no	—
369	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
370	C₂	C₃×#5745	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#2905
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
3. C₃²×#423	C₂	semidirect
4. C₃×#5118	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4839	C₂	semidirect
8. #79048	C₃	direct (N × H)
22. C₃²×C₄⋊C₈	C₂²	semidirect
23. C₃×Dic₃⋊C₈	C₂²	semidirect
24. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
33. C₃×#423	D₃	semidirect
34. C₃×#423	C₂×C₃	semidirect
35. #5118	C₂×C₃	semidirect
36. #4924	C₂×C₃	semidirect
37. #4839	C₂×C₃	semidirect
94. C₃×C₄⋊C₈	C₂×D₃	semidirect
95. C₃×C₄⋊C₈	C₂²×C₃	semidirect
96. Dic₃⋊C₈	C₂²×C₃	semidirect
97. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
123. #423	C₃×D₃	semidirect
207. C₄⋊C₈	C₂×C₃×D₃	semidirect
319. C₃²	#2905	semidirect
365. C₃	#79048	direct (N × H)
366. C₃	C₃×#2905	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×M₁₆	2
C₂×C₃×#872	2
C₃²×#423	2
C₃×#5118	2
C₃×#4924	2
C₃×#4839	2
C₃×#2905	3
#79048	3

Subgroups — C3×#79048 #11858303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79048 #11858303