Subgroups — C₃×#78514 #11857220

Order 1152.

1199 conjugacy classes of subgroups.

The subgroup lattice has 375 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×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×M₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4708	C₂	1	4	yes	maximal, complemented
7	C₃×#4689	C₂	1	4	yes	maximal, complemented
8	C₃×#2873	—	3	1	no	maximal
9	#78514	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	2	yes	—
17	C₃×D₃×M₁₆	C₄	1	16	yes	complemented
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
20	C₃×#872	C₄	1	4	yes	—
21	C₃×#872	C₂²	1	2	yes	—
22	C₃×#872	C₂²	1	2	yes	—
23	C₃²×#97	C₂²	1	2	yes	complemented
24	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
25	C₃×#815	C₂²	1	4	yes	complemented
26	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
27	C₃×#803	C₂²	1	2	yes	complemented
28	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
29	C₂²×C₃×M₁₆	—	3	2	no	—
30	C₂×C₃×#117	—	3	1	no	—
31	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
32	C₂×#872	C₂×C₃	1	1	yes	characteristic
33	C₃×#405	—	3	4	no	—
34	C₃×#405	—	3	4	no	—
35	C₃×C₄×M₁₆	—	2	1	no	—
36	C₃×C₄×M₁₆	—	3	2	no	—
37	C₃×C₄×M₁₆	—	3	1	no	—
38	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
39	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
40	Dic₃×M₁₆	C₂×C₃	1	2	yes	complemented
41	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
42	#4708	C₂×C₃	1	4	yes	complemented
43	#4689	C₂×C₃	1	4	yes	complemented
44	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
46	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
48	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	8	yes	—
51	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
52	C₃²×M₁₆	C₂×C₄	1	8	yes	—
53	C₂×C₃²×C₈	C₂³	1	4	yes	—
54	C₃²×C₄²	C₂×C₄	1	2	yes	—
55	C₃²×C₄²	C₂³	1	1	yes	characteristic
56	C₃²×C₄²	C₂³	1	1	yes	characteristic
57	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
58	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
59	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
60	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
61	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
62	C₃×C₄×Dic₃	C₂³	1	2	yes	—
63	C₃×#208	C₂×C₄	1	8	yes	—
64	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
65	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
66	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
67	#2873	—	3	1	no	Sylow
68	C₂³×C₃×C₄	—	3	1	no	—
69	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×M₁₆	—	2	2	no	—
71	C₂×C₃×M₁₆	—	3	2	no	—
72	C₂×C₃×M₁₆	—	3	16	no	—
73	C₂×C₃×M₁₆	—	3	4	no	—
74	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
75	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
76	C₂²×C₃×C₈	—	3	4	no	—
77	C₃×#117	—	3	4	no	—
78	C₃×#117	—	3	2	no	—
79	C₃×#117	—	3	2	no	—
80	C₂×C₃×C₄⋊C₄	—	3	2	no	—
81	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
82	C₂×C₃×C₄²	—	2	1	no	—
83	C₂×C₃×C₄²	—	3	1	no	—
84	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
87	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
88	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₂×#208	C₂²×C₃	1	2	yes	—
90	D₃×M₁₆	C₃×C₄	1	16	yes	complemented
91	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
92	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
93	#872	C₃×C₄	1	4	yes	—
94	#872	C₂²×C₃	1	2	yes	—
95	#872	C₂²×C₃	1	2	yes	—
96	C₃×#97	—	2	2	no	—
97	C₃×#97	—	3	4	no	—
98	C₃×#97	—	3	2	no	—
99	C₃×#97	C₂×D₃	1	2	yes	complemented
100	C₃×#97	C₂²×C₃	1	2	yes	complemented
101	C₃×C₄×C₈	—	2	2	no	—
102	C₃×C₄×C₈	—	3	4	no	—
103	C₃×C₄×C₈	—	3	2	no	—
104	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
105	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
106	#815	C₂²×C₃	1	4	yes	complemented
107	C₈×Dic₃	C₂²×C₃	1	4	yes	complemented
108	#803	C₂²×C₃	1	2	yes	complemented
109	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
110	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₃×D₃	—	4	2	no	—
112	C₂²×C₃×D₃	C₄²	1	4	yes	—
113	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
114	C₂×C₃²×C₄	—	4	2	no	—
115	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
116	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
117	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
119	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
120	C₂×C₃×Dic₃	—	4	2	no	—
121	C₂×C₃×Dic₃	C₄²	1	4	yes	—
122	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
123	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
124	C₃×C₄×D₃	C₄²	1	8	yes	—
125	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
126	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
127	C₃²×C₈	C₂²×C₄	1	8	yes	—
128	C₃×C₃⋊C₈	C₂²×C₄	1	8	yes	—
129	C₂²×M₁₆	—	3	2	no	—
130	C₂×#117	—	3	1	no	—
131	#405	—	3	4	no	—
132	#405	—	3	4	no	—
133	C₄×M₁₆	—	3	2	no	—
134	C₄×M₁₆	—	3	1	no	—
135	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
136	C₂⁴×C₃	—	3	1	no	—
137	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	3	1	no	—
141	C₂²×C₃×C₄	—	3	2	no	—
142	C₂²×C₃×C₄	—	3	8	no	—
143	C₂²×C₃×C₄	—	3	2	no	—
144	C₂²×C₃×C₄	—	3	2	no	—
145	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
146	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
147	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
150	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
153	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
154	C₃×M₁₆	—	2	8	no	—
155	C₃×M₁₆	—	3	8	no	—
156	C₃×M₁₆	—	3	16	no	—
157	C₃×M₁₆	C₄×D₃	1	8	yes	—
158	C₃×M₁₆	C₂×C₃×C₄	1	8	yes	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	3	4	no	—
161	C₂×C₃×C₈	—	3	16	no	—
162	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
163	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
164	C₃×C₄⋊C₄	—	3	4	no	—
165	C₃×C₄⋊C₄	—	3	4	no	—
166	C₃×C₂²⋊C₄	—	3	4	no	—
167	C₃×C₂²⋊C₄	—	3	4	no	—
168	C₃×C₄²	—	2	2	no	—
169	C₃×C₄²	—	2	1	no	—
170	C₃×C₄²	—	2	1	no	—
171	C₃×C₄²	—	3	2	no	—
172	C₃×C₄²	—	3	2	no	—
173	C₃×C₄²	C₄×D₃	1	2	yes	—
174	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
175	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
176	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
177	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
178	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
179	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
180	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
181	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
182	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
183	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
184	C₄×Dic₃	C₂³×C₃	1	2	yes	—
185	#208	C₂×C₃×C₄	1	8	yes	—
186	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
187	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	16	yes	complemented
188	D₃×C₈	C₂×C₃×C₄	1	16	yes	complemented
189	C₂²×C₃²	—	2	2	no	—
190	C₂²×C₃²	C₂×C₄²	1	2	yes	—
191	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₃×D₃	—	2	4	no	—
193	C₂×C₃×D₃	—	4	4	no	—
194	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
195	C₃²×C₄	—	2	2	no	—
196	C₃²×C₄	—	2	2	no	—
197	C₃²×C₄	C₂×C₄²	1	2	yes	—
198	C₃²×C₄	C₂³×C₄	1	2	yes	—
199	C₃×Dic₃	—	2	4	no	—
200	C₃×Dic₃	C₂×C₄²	1	4	yes	—
201	C₂³×C₄	—	3	1	no	—
202	C₂×M₁₆	—	3	2	no	—
203	C₂×M₁₆	—	3	16	no	—
204	C₂×M₁₆	—	3	4	no	—
205	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
206	C₂²×C₈	—	3	4	no	—
207	#117	—	3	4	no	—
208	#117	—	3	2	no	—
209	#117	—	3	2	no	—
210	C₂×C₄⋊C₄	—	3	2	no	—
211	C₂×C₂²⋊C₄	—	3	2	no	—
212	C₂×C₄²	—	3	1	no	—
213	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
214	#97	—	3	4	no	—
215	#97	—	3	2	no	—
216	#97	C₂×C₃×D₃	1	2	yes	complemented
217	C₄×C₈	—	3	4	no	—
218	C₄×C₈	—	3	2	no	—
219	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	—	3	2	no	—
222	C₂³×C₃	—	3	4	no	—
223	C₂³×C₃	—	12	2	no	—
224	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
225	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂²×D₃	—	4	2	no	—
227	C₂²×D₃	C₃×C₄²	1	4	yes	—
228	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	3	4	no	—
235	C₂×C₃×C₄	—	3	2	no	—
236	C₂×C₃×C₄	—	3	8	no	—
237	C₂×C₃×C₄	—	3	4	no	—
238	C₂×C₃×C₄	—	3	4	no	—
239	C₂×C₃×C₄	—	3	4	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	4	4	no	—
243	C₂×C₃×C₄	—	12	2	no	—
244	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
245	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
250	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
252	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
254	C₂×Dic₃	—	4	2	no	—
255	C₂×Dic₃	C₃×C₄²	1	4	yes	—
256	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
257	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
258	C₄×D₃	C₃×C₄²	1	8	yes	—
259	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
260	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
261	C₃×C₈	—	2	8	no	—
262	C₃×C₈	—	3	8	no	—
263	C₃×C₈	C₂×C₄×D₃	1	8	yes	—
264	C₃×C₈	C₂²×C₃×C₄	1	8	yes	—
265	C₃⋊C₈	C₂²×C₃×C₄	1	8	yes	—
266	C₂×C₃²	—	2	2	no	—
267	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
268	C₂×C₃²	#568	1	2	yes	—
269	C₃×D₃	—	2	4	no	—
270	C₂⁴	—	3	1	no	—
271	C₂²×C₄	—	3	1	no	—
272	C₂²×C₄	—	3	2	no	—
273	C₂²×C₄	—	3	2	no	—
274	C₂²×C₄	—	3	8	no	—
275	C₂²×C₄	—	3	2	no	—
276	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
277	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
278	M₁₆	—	3	8	no	—
279	M₁₆	—	3	16	no	—
280	M₁₆	C₃×C₄×D₃	1	8	yes	—
281	C₂×C₈	—	3	4	no	—
282	C₂×C₈	—	3	16	no	—
283	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
284	C₄⋊C₄	—	3	4	no	—
285	C₄⋊C₄	—	3	4	no	—
286	C₂²⋊C₄	—	3	4	no	—
287	C₂²⋊C₄	—	3	4	no	—
288	C₄²	—	3	2	no	—
289	C₄²	—	3	2	no	—
290	C₄²	C₃×C₄×D₃	1	2	yes	—
291	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
292	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	3	4	no	—
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	6	4	no	—
300	C₂²×C₃	—	12	4	no	—
301	C₂²×C₃	C₄²×D₃	1	2	yes	—
302	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
303	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
305	C₂×D₃	—	2	4	no	—
306	C₂×D₃	—	4	4	no	—
307	C₂×D₃	C₂×C₃×C₄²	1	4	yes	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	2	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	3	4	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	6	4	no	—
318	C₃×C₄	C₄²×D₃	1	2	yes	—
319	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
320	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
321	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
322	Dic₃	—	2	4	no	—
323	Dic₃	C₂×C₃×C₄²	1	4	yes	—
324	C₃²	#2873	1	1	yes	characteristic, complemented, Sylow
325	C₂³	—	3	2	no	—
326	C₂³	—	3	4	no	—
327	C₂³	—	12	2	no	—
328	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	4	no	—
331	C₂×C₄	—	3	4	no	—
332	C₂×C₄	—	3	4	no	—
333	C₂×C₄	—	3	8	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	12	2	no	—
337	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
338	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
339	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
340	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
341	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
342	C₈	—	3	8	no	—
343	C₈	C₂×C₃×C₄×D₃	1	8	yes	—
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	4	2	no	—
349	C₂×C₃	—	6	4	no	—
350	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
351	C₂×C₃	#5745	1	2	yes	—
352	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
353	C₂×C₃	C₃×#568	1	2	yes	—
354	D₃	—	2	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	3	4	no	—
357	C₂²	—	6	4	no	—
358	C₂²	—	12	4	no	—
359	C₂²	C₃×C₄²×D₃	1	2	yes	—
360	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	3	4	no	—
364	C₄	—	6	4	no	—
365	C₄	C₃×C₄²×D₃	1	2	yes	—
366	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
367	C₃	—	2	1	no	—
368	C₃	#78514	1	1	yes	characteristic, direct product factor
369	C₃	C₃×#2873	1	1	yes	characteristic, complemented
370	C₂	—	2	2	no	—
371	C₂	—	6	4	no	—
372	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
373	C₂	C₃×#5745	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×#2873
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃²×C₄×M₁₆	C₂	semidirect
4. C₃×Dic₃×M₁₆	C₂	semidirect
5. C₃×C₄×#208	C₂	semidirect
6. C₃×#4708	C₂	semidirect
7. C₃×#4689	C₂	semidirect
9. #78514	C₃	direct (N × H)
17. C₃×D₃×M₁₆	C₄	semidirect
23. C₃²×#97	C₂²	semidirect
24. C₃²×C₄×C₈	C₂²	semidirect
25. C₃×#815	C₂²	semidirect
26. C₃×C₈×Dic₃	C₂²	semidirect
27. C₃×#803	C₂²	semidirect
28. C₃×C₄×C₃⋊C₈	C₂²	semidirect
38. C₃×C₄×M₁₆	D₃	semidirect
39. C₃×C₄×M₁₆	C₂×C₃	semidirect
40. Dic₃×M₁₆	C₂×C₃	semidirect
41. C₄×#208	C₂×C₃	semidirect
42. #4708	C₂×C₃	semidirect
43. #4689	C₂×C₃	semidirect
65. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
66. C₃×D₃×C₈	C₂×C₄	semidirect
90. D₃×M₁₆	C₃×C₄	semidirect
99. C₃×#97	C₂×D₃	semidirect
100. C₃×#97	C₂²×C₃	semidirect
104. C₃×C₄×C₈	C₂×D₃	semidirect
105. C₃×C₄×C₈	C₂²×C₃	semidirect
106. #815	C₂²×C₃	semidirect
107. C₈×Dic₃	C₂²×C₃	semidirect
108. #803	C₂²×C₃	semidirect
109. C₄×C₃⋊C₈	C₂²×C₃	semidirect
135. C₄×M₁₆	C₃×D₃	semidirect
187. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
188. D₃×C₈	C₂×C₃×C₄	semidirect
216. #97	C₂×C₃×D₃	semidirect
219. C₄×C₈	C₂×C₃×D₃	semidirect
324. C₃²	#2873	semidirect
368. C₃	#78514	direct (N × H)
369. C₃	C₃×#2873	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×C₄×M₁₆	2
C₃×Dic₃×M₁₆	2
C₃×C₄×#208	2
C₃×#4708	2
C₃×#4689	2
C₃×#2873	3
#78514	3

Subgroups — C3×#78514 #11857220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78514 #11857220