Subgroups — C₃²×#4803 #13162238

Order 1728.

1140 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#239	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃³×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#417	—	3	1	no	maximal
9	C₃×#4803	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₃²×#239	—	2	2	no	—
12	C₃²×#239	C₄	1	4	yes	complemented
13	C₂×C₃²×D₁₂	—	2	1	no	—
14	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄×D₃	—	2	1	no	—
16	C₂×C₃²×C₄×D₃	—	2	1	no	—
17	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₃²×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×ΓL(1,𝔽₂₅)	—	2	2	no	—
24	C₂×C₃²×#41	—	3	1	no	—
25	C₂×C₃×#239	C₂×C₃	1	4	yes	—
26	C₂×C₃²×M₁₆	—	3	1	no	—
27	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
28	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	complemented
29	C₃×D₃×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
30	C₃²×#103	—	2	4	no	—
31	C₃²×#103	—	3	1	no	—
32	C₃²×#103	D₃	1	1	yes	characteristic, complemented
33	C₃²×#103	C₂×C₃	1	4	yes	complemented
34	C₃²×#102	—	3	1	no	—
35	C₃²×#102	—	3	1	no	—
36	C₃×#835	C₂×C₃	1	4	yes	complemented
37	C₃×#821	C₂×C₃	1	4	yes	complemented
38	C₃×#809	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃²×D₃	—	2	1	no	—
40	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
41	C₃³×Q₈	—	2	1	no	—
42	C₃³×Q₈	C₂×C₄	1	2	yes	complemented
43	C₂×C₃³×C₄	—	2	1	no	—
44	C₂×C₃³×C₄	—	2	1	no	—
45	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃²×Dic₃	—	2	1	no	—
47	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
48	C₃²×D₁₂	—	2	4	no	—
49	C₃²×D₁₂	—	2	1	no	—
50	C₃²×D₁₂	C₂×C₄	1	2	yes	complemented
51	C₃²×C₄×D₃	—	2	4	no	—
52	C₃²×C₄×D₃	—	4	2	no	—
53	C₃²×C₄×D₃	C₂×C₄	1	2	yes	—
54	C₃²×C₄×D₃	D₄	1	2	yes	—
55	C₃³×C₈	—	2	1	no	—
56	C₃²×C₃⋊C₈	—	2	1	no	—
57	C₃×#417	—	3	4	no	—
58	#4803	C₃²	1	1	yes	characteristic, direct product factor
59	C₃²×#41	—	3	4	no	—
60	C₃²×#41	—	6	2	no	—
61	C₂×C₃²×Q₈	—	2	4	no	—
62	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
64	C₂×C₃²×D₄	—	3	1	no	—
65	C₂×C₃²×D₄	—	6	1	no	—
66	C₂²×C₃²×C₄	—	3	1	no	—
67	C₂²×C₃²×C₄	—	6	1	no	—
68	C₂²×C₃²×C₄	—	6	1	no	—
69	C₃×#239	—	2	8	no	—
70	C₃×#239	C₃×C₄	1	16	yes	complemented
71	C₂×C₃×D₁₂	—	2	4	no	—
72	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
73	C₂×C₃×C₄×D₃	—	2	4	no	—
74	C₂×C₃×C₄×D₃	—	2	4	no	—
75	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
76	C₃²×M₁₆	—	6	2	no	—
77	C₂×C₃²×C₈	—	2	4	no	—
78	C₂×C₃²×C₈	—	3	1	no	—
79	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
81	C₃²×C₄⋊C₄	—	2	4	no	—
82	C₃²×C₄⋊C₄	—	3	1	no	—
83	C₃²×C₄⋊C₄	—	6	1	no	—
84	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
87	C₃×Dic₃⋊C₄	—	2	4	no	—
88	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
89	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
90	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×D₃	—	2	1	no	—
92	C₂×C₃²×D₃	—	2	1	no	—
93	C₂×C₃²×D₃	—	2	2	no	—
94	C₂×C₃²×D₃	—	4	1	no	—
95	C₂×C₃²×D₃	—	4	1	no	—
96	C₂×C₃²×D₃	C₂²⋊C₄	1	2	yes	—
97	C₃³×C₄	—	2	2	no	—
98	C₃³×C₄	—	4	1	no	—
99	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
100	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
101	C₃²×Dic₃	—	4	1	no	—
102	C₃²×Dic₃	C₂²⋊C₄	1	2	yes	—
103	C₂×C₃×#41	—	3	4	no	—
104	C₂×#239	C₂×C₃²	1	1	yes	characteristic
105	C₂×C₃×M₁₆	—	3	4	no	—
106	C₂×C₃×C₄⋊C₄	—	3	4	no	—
107	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic, complemented
108	D₃×C₄⋊C₄	C₂×C₃²	1	1	yes	characteristic, complemented
109	C₃×#103	—	2	4	no	—
110	C₃×#103	—	3	4	no	—
111	C₃×#103	C₃×D₃	1	4	yes	complemented
112	C₃×#103	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₃×#102	—	3	4	no	—
114	C₃×#102	—	3	4	no	—
115	#835	C₂×C₃²	1	1	yes	characteristic, complemented
116	#821	C₂×C₃²	1	1	yes	characteristic, complemented
117	#809	C₂×C₃²	1	1	yes	characteristic, complemented
118	C₂³×C₃²	—	3	1	no	—
119	C₂³×C₃²	—	6	1	no	—
120	C₂²×C₃×D₃	—	2	4	no	—
121	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
122	C₃²×Q₈	—	2	1	no	—
123	C₃²×Q₈	—	2	8	no	—
124	C₃²×Q₈	—	2	4	no	—
125	C₃²×Q₈	—	4	4	no	—
126	C₃²×Q₈	C₄×D₃	1	2	yes	complemented
127	C₃²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
128	C₃²×D₄	—	3	2	no	—
129	C₃²×D₄	—	6	4	no	—
130	C₃²×D₄	—	6	1	no	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	—	2	1	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	3	1	no	—
137	C₂×C₃²×C₄	—	3	2	no	—
138	C₂×C₃²×C₄	—	3	2	no	—
139	C₂×C₃²×C₄	—	4	4	no	—
140	C₂×C₃²×C₄	—	4	4	no	—
141	C₂×C₃²×C₄	—	6	4	no	—
142	C₂×C₃²×C₄	—	6	1	no	—
143	C₂×C₃²×C₄	—	12	2	no	—
144	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
146	C₂×C₃×Dic₃	—	2	4	no	—
147	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
148	C₃×D₁₂	—	2	16	no	—
149	C₃×D₁₂	—	2	4	no	—
150	C₃×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
151	C₃×C₄×D₃	—	2	16	no	—
152	C₃×C₄×D₃	—	4	8	no	—
153	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
154	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
155	C₃²×C₈	—	2	1	no	—
156	C₃²×C₈	—	2	4	no	—
157	C₃²×C₈	—	4	4	no	—
158	C₃²×C₈	—	6	1	no	—
159	C₃×C₃⋊C₈	—	2	4	no	—
160	#417	—	3	1	no	Sylow
161	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₃³	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₃³	#137	1	1	yes	characteristic
164	C₃²×D₃	—	2	2	no	—
165	C₃²×D₃	—	4	2	no	—
166	C₃×#41	—	3	16	no	—
167	C₃×#41	—	6	8	no	—
168	C₂×C₃×Q₈	—	2	4	no	—
169	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
170	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
171	C₂×C₃×D₄	—	3	4	no	—
172	C₂×C₃×D₄	—	6	4	no	—
173	C₂²×C₃×C₄	—	3	4	no	—
174	C₂²×C₃×C₄	—	6	4	no	—
175	C₂²×C₃×C₄	—	6	4	no	—
176	#239	—	2	2	no	—
177	#239	C₃²×C₄	1	4	yes	complemented
178	C₂×D₁₂	—	2	1	no	—
179	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×C₄×D₃	—	2	1	no	—
182	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
183	C₃×M₁₆	—	6	8	no	—
184	C₂×C₃×C₈	—	2	4	no	—
185	C₂×C₃×C₈	—	3	4	no	—
186	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
187	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	3	4	no	—
190	C₃×C₄⋊C₄	—	6	4	no	—
191	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
192	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
193	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
194	Dic₃⋊C₄	—	2	1	no	—
195	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
196	ΓL(1,𝔽₂₅)	—	2	2	no	—
197	C₂²×C₃²	—	2	4	no	—
198	C₂²×C₃²	—	3	2	no	—
199	C₂²×C₃²	—	6	1	no	—
200	C₂²×C₃²	—	6	1	no	—
201	C₂²×C₃²	—	6	2	no	—
202	C₂²×C₃²	—	12	1	no	—
203	C₂²×C₃²	—	12	1	no	—
204	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
205	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
206	C₂×C₃×D₃	—	2	4	no	—
207	C₂×C₃×D₃	—	2	4	no	—
208	C₂×C₃×D₃	—	2	8	no	—
209	C₂×C₃×D₃	—	4	4	no	—
210	C₂×C₃×D₃	—	4	4	no	—
211	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	8	yes	—
212	C₃²×C₄	—	2	2	no	—
213	C₃²×C₄	—	2	4	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	8	no	—
216	C₃²×C₄	—	3	2	no	—
217	C₃²×C₄	—	4	8	no	—
218	C₃²×C₄	—	4	1	no	—
219	C₃²×C₄	—	4	4	no	—
220	C₃²×C₄	—	8	4	no	—
221	C₃²×C₄	—	12	1	no	—
222	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
223	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
224	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
225	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
226	C₃×Dic₃	—	4	4	no	—
227	C₃×Dic₃	C₃×C₂²⋊C₄	1	8	yes	—
228	C₂×#41	—	3	1	no	—
229	C₂×M₁₆	—	3	1	no	—
230	C₂×C₄⋊C₄	—	3	1	no	—
231	#103	—	3	1	no	—
232	#103	C₃²×D₃	1	1	yes	characteristic, complemented
233	#102	—	3	1	no	—
234	#102	—	3	1	no	—
235	C₃³	#417	1	1	yes	characteristic, complemented, Sylow
236	C₂³×C₃	—	3	4	no	—
237	C₂³×C₃	—	6	4	no	—
238	C₂²×D₃	—	2	1	no	—
239	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
240	C₃×Q₈	—	2	4	no	—
241	C₃×Q₈	—	2	1	no	—
242	C₃×Q₈	—	2	8	no	—
243	C₃×Q₈	—	4	4	no	—
244	C₃×Q₈	C₃×C₄×D₃	1	8	yes	complemented
245	C₃×Q₈	C₂×C₃²×C₄	1	2	yes	complemented
246	C₃×D₄	—	3	8	no	—
247	C₃×D₄	—	6	16	no	—
248	C₃×D₄	—	6	4	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	3	4	no	—
255	C₂×C₃×C₄	—	3	8	no	—
256	C₂×C₃×C₄	—	3	8	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	4	4	no	—
259	C₂×C₃×C₄	—	6	16	no	—
260	C₂×C₃×C₄	—	6	4	no	—
261	C₂×C₃×C₄	—	12	8	no	—
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
263	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
264	C₂×Dic₃	—	2	1	no	—
265	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
266	D₁₂	—	2	4	no	—
267	D₁₂	—	2	1	no	—
268	D₁₂	C₂×C₃²×C₄	1	2	yes	complemented
269	C₄×D₃	—	2	4	no	—
270	C₄×D₃	—	4	2	no	—
271	C₄×D₃	C₂×C₃²×C₄	1	2	yes	—
272	C₄×D₃	C₃²×D₄	1	2	yes	—
273	C₃×C₈	—	2	4	no	—
274	C₃×C₈	—	2	1	no	—
275	C₃×C₈	—	4	4	no	—
276	C₃×C₈	—	6	4	no	—
277	C₃⋊C₈	—	2	1	no	—
278	C₂×C₃²	—	2	4	no	—
279	C₂×C₃²	—	2	4	no	—
280	C₂×C₃²	—	2	4	no	—
281	C₂×C₃²	—	6	2	no	—
282	C₂×C₃²	—	12	2	no	—
283	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₃²	#914	1	1	yes	characteristic
285	C₂×C₃²	#918	1	1	yes	characteristic
286	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
287	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	4	yes	—
288	C₂×C₃²	C₃×#137	1	4	yes	—
289	C₃×D₃	—	2	8	no	—
290	C₃×D₃	—	4	8	no	—
291	#41	—	3	4	no	—
292	#41	—	6	2	no	—
293	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
294	C₂×D₄	—	3	1	no	—
295	C₂×D₄	—	6	1	no	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	6	1	no	—
298	C₂²×C₄	—	6	1	no	—
299	M₁₆	—	6	2	no	—
300	C₂×C₈	—	3	1	no	—
301	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
302	C₄⋊C₄	—	3	1	no	—
303	C₄⋊C₄	—	6	1	no	—
304	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	3	8	no	—
307	C₂²×C₃	—	6	4	no	—
308	C₂²×C₃	—	6	4	no	—
309	C₂²×C₃	—	6	8	no	—
310	C₂²×C₃	—	12	4	no	—
311	C₂²×C₃	—	12	4	no	—
312	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
313	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
314	C₂×D₃	—	2	1	no	—
315	C₂×D₃	—	2	1	no	—
316	C₂×D₃	—	2	2	no	—
317	C₂×D₃	—	4	1	no	—
318	C₂×D₃	—	4	1	no	—
319	C₂×D₃	C₃²×C₂²⋊C₄	1	2	yes	—
320	C₃×C₄	—	2	8	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	3	8	no	—
325	C₃×C₄	—	4	8	no	—
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	8	4	no	—
329	C₃×C₄	—	12	4	no	—
330	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
331	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
332	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
333	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
334	Dic₃	—	4	1	no	—
335	Dic₃	C₃²×C₂²⋊C₄	1	2	yes	—
336	C₃²	—	2	4	no	—
337	C₃²	#4803	1	1	yes	characteristic, direct product factor
338	C₃²	C₃×#417	1	4	yes	complemented
339	C₂³	—	3	1	no	—
340	C₂³	—	6	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	C₃²×C₄×D₃	1	2	yes	complemented
343	D₄	—	3	2	no	—
344	D₄	—	6	4	no	—
345	D₄	—	6	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	3	1	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	3	2	no	—
351	C₂×C₄	—	6	4	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	6	1	no	—
357	C₂×C₃	—	2	4	no	—
358	C₂×C₃	—	2	4	no	—
359	C₂×C₃	—	2	4	no	—
360	C₂×C₃	—	6	8	no	—
361	C₂×C₃	—	12	8	no	—
362	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	4	yes	—
363	C₂×C₃	C₃×#914	1	4	yes	—
364	C₂×C₃	C₃×#918	1	4	yes	—
365	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
366	C₂×C₃	C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic
367	C₂×C₃	C₃²×#137	1	1	yes	characteristic
368	D₃	—	2	2	no	—
369	D₃	—	4	2	no	—
370	C₂²	—	3	2	no	—
371	C₂²	—	6	1	no	—
372	C₂²	—	6	1	no	—
373	C₂²	—	6	2	no	—
374	C₂²	—	12	1	no	—
375	C₂²	—	12	1	no	—
376	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	3	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	12	1	no	—
381	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
382	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
383	C₃	—	2	4	no	—
384	C₃	C₃×#4803	1	4	yes	direct product factor
385	C₃	C₃²×#417	1	1	yes	characteristic, complemented
386	C₂	—	6	2	no	—
387	C₂	—	12	2	no	—
388	C₂	C₃²×D₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂	C₃²×#914	1	1	yes	characteristic
390	C₂	C₃²×#918	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×#103	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃²×#239	C₂
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₃²×#103	D₃
hypocenter	C₃	C₃²×#417
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₃²×#103

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₃²×D₃×C₄⋊C₄	C₂	semidirect
4. C₃³×#103	C₂	semidirect
5. C₃²×#835	C₂	semidirect
6. C₃²×#821	C₂	semidirect
7. C₃²×#809	C₂	semidirect
9. C₃×#4803	C₃	direct (N × H)
12. C₃²×#239	C₄	semidirect
28. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
29. C₃×D₃×C₄⋊C₄	C₂×C₃	semidirect
32. C₃²×#103	D₃	semidirect
33. C₃²×#103	C₂×C₃	semidirect
36. C₃×#835	C₂×C₃	semidirect
37. C₃×#821	C₂×C₃	semidirect
38. C₃×#809	C₂×C₃	semidirect
42. C₃³×Q₈	C₂×C₄	semidirect
50. C₃²×D₁₂	C₂×C₄	semidirect
58. #4803	C₃²	direct (N × H)
70. C₃×#239	C₃×C₄	semidirect
107. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
108. D₃×C₄⋊C₄	C₂×C₃²	semidirect
111. C₃×#103	C₃×D₃	semidirect
112. C₃×#103	C₂×C₃²	semidirect
115. #835	C₂×C₃²	semidirect
116. #821	C₂×C₃²	semidirect
117. #809	C₂×C₃²	semidirect
126. C₃²×Q₈	C₄×D₃	semidirect
127. C₃²×Q₈	C₂×C₃×C₄	semidirect
150. C₃×D₁₂	C₂×C₃×C₄	semidirect
177. #239	C₃²×C₄	semidirect
232. #103	C₃²×D₃	semidirect
235. C₃³	#417	semidirect
244. C₃×Q₈	C₃×C₄×D₃	semidirect
245. C₃×Q₈	C₂×C₃²×C₄	semidirect
268. D₁₂	C₂×C₃²×C₄	semidirect
337. C₃²	#4803	direct (N × H)
338. C₃²	C₃×#417	semidirect
342. Q₈	C₃²×C₄×D₃	semidirect
384. C₃	C₃×#4803	direct (N × H)
385. C₃	C₃²×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#239	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₃²×D₃×C₄⋊C₄	2
C₃³×#103	2
C₃²×#835	2
C₃²×#821	2
C₃²×#809	2
C₃²×#417	3
C₃×#4803	3

Subgroups — C32×#4803 #13162238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4803 #13162238