Subgroups — C₃×#78574 #11860935

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₃×#5523	C₂	1	2	yes	maximal, complemented
3	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5133	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4716	C₂	1	2	yes	maximal, complemented
7	C₃×#4711	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#204	C₂	1	4	yes	maximal, complemented
9	C₃×#2952	—	3	1	no	maximal
10	#78574	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	2	yes	—
12	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃²×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
17	C₃×#904	C₄	1	8	yes	complemented
18	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×#204	C₂²	1	2	yes	—
20	C₃×#892	—	2	2	no	—
21	C₃×D₃×C₄⋊C₄	—	2	2	no	—
22	C₃×#67⋊C₄	—	2	4	no	—
23	C₃×C₄×D₁₂	C₂²	1	4	yes	—
24	C₃×C₄×Dic₆	C₂²	1	4	yes	—
25	C₃²×#97	C₂²	1	2	yes	—
26	C₃²×C₄×C₈	C₂²	1	2	yes	—
27	C₃×#821	C₂²	1	4	yes	—
28	C₃×#817	C₂²	1	2	yes	—
29	C₃×#817	C₂²	1	2	yes	—
30	C₃×#816	C₂²	1	4	yes	—
31	C₂×C₃×#135	—	3	1	no	—
32	C₃×#520	—	3	2	no	—
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	#5523	C₂×C₃	1	2	yes	complemented
35	C₃×#442	—	3	2	no	—
36	C₃×#441	—	3	2	no	—
37	C₃×C₄×SD₁₆	—	3	4	no	—
38	C₂×C₃×#106	—	3	1	no	—
39	C₃×#417	—	3	2	no	—
40	C₃×#405	—	2	1	no	—
41	C₃×#405	D₃	1	1	yes	characteristic, complemented
42	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
43	#5133	C₂×C₃	1	2	yes	complemented
44	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
45	#4716	C₂×C₃	1	2	yes	complemented
46	#4711	C₂×C₃	1	2	yes	complemented
47	C₄×#204	C₂×C₃	1	4	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	2	no	—
50	C₂²×C₃×Dic₃	—	2	2	no	—
51	C₃×#235	—	2	4	no	—
52	C₃×#235	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×D₁₂	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₃	—	2	2	no	—
55	C₂×C₃×C₄×D₃	—	2	4	no	—
56	C₂×C₃×Dic₆	C₂³	1	2	yes	—
57	C₃²×M₁₆	—	2	2	no	—
58	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
59	C₂×C₃²×C₈	C₂³	1	2	yes	—
60	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
62	C₃²×C₄⋊C₄	D₄	1	2	yes	—
63	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
64	C₃²×C₄²	C₂³	1	2	yes	—
65	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
66	C₃×C₄⋊Dic₃	—	2	2	no	—
67	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
68	C₃×Dic₃⋊C₄	—	2	4	no	—
69	C₃×C₄×Dic₃	—	2	4	no	—
70	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
71	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
72	C₃×#204	C₂×C₄	1	8	yes	complemented
73	#2952	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	2	no	—
75	C₂×#235	C₂²×C₃	1	2	yes	—
76	C₃×#135	—	3	8	no	—
77	C₂×C₃×Q₁₆	—	3	1	no	—
78	C₂×C₃×SD₁₆	—	3	2	no	—
79	C₂×C₃×D₈	—	3	1	no	—
80	C₂×C₃×M₁₆	—	2	1	no	—
81	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×C₈	—	2	1	no	—
84	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₃×C₄×Q₈	—	3	4	no	—
87	C₃×C₄×D₄	—	3	4	no	—
88	C₃×C₄×D₄	—	6	4	no	—
89	C₃×#117	—	2	1	no	—
90	C₃×#117	—	6	2	no	—
91	C₃×#117	C₂×D₃	1	1	yes	characteristic
92	C₃×#117	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	—	3	2	no	—
94	C₂×C₃×C₄⋊C₄	—	6	2	no	—
95	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
96	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
97	#904	C₃×C₄	1	8	yes	complemented
98	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×#204	C₂²×C₃	1	2	yes	—
100	#892	—	2	2	no	—
101	D₃×C₄⋊C₄	—	2	2	no	—
102	#67⋊C₄	—	2	4	no	—
103	C₄×D₁₂	C₂²×C₃	1	4	yes	—
104	C₄×Dic₆	C₂²×C₃	1	4	yes	—
105	C₃×#106	—	3	2	no	—
106	C₃×#106	—	3	2	no	—
107	C₃×#103	—	3	4	no	—
108	C₃×#102	—	3	4	no	—
109	C₃×#97	—	2	2	no	—
110	C₃×#97	C₂×D₃	1	2	yes	—
111	C₃×#97	C₂²×C₃	1	2	yes	—
112	C₃×C₄×C₈	—	2	2	no	—
113	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
114	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
115	#821	C₂²×C₃	1	4	yes	—
116	#817	C₂²×C₃	1	2	yes	—
117	#817	C₂²×C₃	1	2	yes	—
118	#816	C₂²×C₃	1	4	yes	—
119	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×D₃	—	2	2	no	—
121	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
122	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	#41	1	2	yes	—
125	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
126	C₃×#67	—	2	8	no	—
127	C₂×C₃×Dic₃	—	2	2	no	—
128	C₂×C₃×Dic₃	—	2	4	no	—
129	C₂×C₃×Dic₃	—	8	2	no	—
130	C₃×D₁₂	—	2	2	no	—
131	C₃×D₁₂	C₂²×C₄	1	4	yes	—
132	C₃×C₄×D₃	—	2	8	no	—
133	C₃×C₄×D₃	—	8	4	no	—
134	C₃×Dic₆	—	2	2	no	—
135	C₃×Dic₆	C₂²×C₄	1	4	yes	—
136	C₃²×C₈	—	2	2	no	—
137	C₃²×C₈	C₂²×C₄	1	2	yes	—
138	C₃²×C₈	C₂²×C₄	1	2	yes	—
139	C₂×#135	—	3	1	no	—
140	#520	—	3	2	no	—
141	#442	—	3	2	no	—
142	#441	—	3	2	no	—
143	C₄×SD₁₆	—	3	4	no	—
144	C₂×#106	—	3	1	no	—
145	#417	—	3	2	no	—
146	#405	C₃×D₃	1	1	yes	characteristic, complemented
147	C₃×#41	—	3	8	no	—
148	C₃×#41	—	6	4	no	—
149	C₂×C₃×Q₈	—	3	2	no	—
150	C₂×C₃×D₄	—	3	2	no	—
151	C₂×C₃×D₄	—	6	2	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	6	2	no	—
154	C₂²×C₃×C₄	—	6	2	no	—
155	C₂²×C₃×C₄	—	6	4	no	—
156	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂×#67	—	2	2	no	—
159	C₂²×Dic₃	—	2	2	no	—
160	#235	—	2	4	no	—
161	#235	C₂×C₃×C₄	1	8	yes	complemented
162	C₂×D₁₂	C₂³×C₃	1	2	yes	—
163	C₂×C₄×D₃	—	2	2	no	—
164	C₂×C₄×D₃	—	2	4	no	—
165	C₂×Dic₆	C₂³×C₃	1	2	yes	—
166	C₃×Q₁₆	—	3	4	no	—
167	C₃×SD₁₆	—	3	8	no	—
168	C₃×D₈	—	3	4	no	—
169	C₃×M₁₆	—	2	4	no	—
170	C₃×M₁₆	—	2	2	no	—
171	C₃×M₁₆	—	2	2	no	—
172	C₂×C₃×C₈	—	2	4	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
177	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
178	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
179	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
182	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	3	4	no	—
186	C₃×C₄⋊C₄	—	6	4	no	—
187	C₃×C₄⋊C₄	—	6	2	no	—
188	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
189	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	—	6	4	no	—
192	C₃×C₂²⋊C₄	D₁₂	1	2	yes	—
193	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	—	6	4	no	—
196	C₃×C₄²	C₂²×D₃	1	2	yes	—
197	C₃×C₄²	C₂³×C₃	1	2	yes	—
198	(C₂×D₃)⋊C₄	—	2	4	no	—
199	C₄⋊Dic₃	—	2	2	no	—
200	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
201	Dic₃⋊C₄	—	2	4	no	—
202	C₄×Dic₃	—	2	4	no	—
203	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
204	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
205	#204	C₂×C₃×C₄	1	8	yes	complemented
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	C₄×D₄	1	2	yes	—
208	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₃×D₃	—	2	4	no	—
210	C₂×C₃×D₃	—	4	2	no	—
211	C₂×C₃×D₃	—	4	2	no	—
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	C₄×D₄	1	2	yes	—
214	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
215	C₃²×C₄	C₂×#41	1	1	yes	characteristic
216	C₃×Dic₃	—	2	4	no	—
217	C₃×Dic₃	—	4	4	no	—
218	C₂×#41	—	3	2	no	—
219	#135	—	3	8	no	—
220	C₂×Q₁₆	—	3	1	no	—
221	C₂×SD₁₆	—	3	2	no	—
222	C₂×D₈	—	3	1	no	—
223	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
225	C₄×Q₈	—	3	4	no	—
226	C₄×D₄	—	3	4	no	—
227	C₄×D₄	—	6	4	no	—
228	#117	—	6	2	no	—
229	#117	C₂×C₃×D₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	—	3	2	no	—
231	C₂×C₄⋊C₄	—	6	2	no	—
232	#106	—	3	2	no	—
233	#106	—	3	2	no	—
234	#103	—	3	4	no	—
235	#102	—	3	4	no	—
236	#97	C₂×C₃×D₃	1	2	yes	—
237	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	—	6	2	no	—
240	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
241	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂²×D₃	—	2	2	no	—
243	C₃×Q₈	—	3	4	no	—
244	C₃×Q₈	—	6	2	no	—
245	C₃×D₄	—	3	4	no	—
246	C₃×D₄	—	6	8	no	—
247	C₃×D₄	—	6	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	6	2	no	—
254	C₂×C₃×C₄	—	6	8	no	—
255	C₂×C₃×C₄	—	6	4	no	—
256	C₂×C₃×C₄	—	24	4	no	—
257	C₂×C₃×C₄	—	24	2	no	—
258	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
259	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
260	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
261	C₂×C₃×C₄	#235	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×#41	1	2	yes	—
266	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
268	#67	—	2	8	no	—
269	C₂×Dic₃	—	2	2	no	—
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	—	8	2	no	—
272	D₁₂	—	2	2	no	—
273	D₁₂	C₂²×C₃×C₄	1	4	yes	—
274	C₄×D₃	—	2	8	no	—
275	C₄×D₃	—	8	4	no	—
276	Dic₆	—	2	2	no	—
277	Dic₆	C₂²×C₃×C₄	1	4	yes	—
278	C₃×C₈	—	2	4	no	—
279	C₃×C₈	—	2	2	no	—
280	C₃×C₈	—	2	2	no	—
281	C₃×C₈	—	2	2	no	—
282	C₃×C₈	—	2	2	no	—
283	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
284	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
285	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
286	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
287	C₂×C₃²	—	2	2	no	—
288	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂×C₃²	#577	1	2	yes	—
290	C₃×D₃	—	4	4	no	—
291	#41	—	3	8	no	—
292	#41	—	6	4	no	—
293	C₂×Q₈	—	3	2	no	—
294	C₂×D₄	—	3	2	no	—
295	C₂×D₄	—	6	2	no	—
296	C₂²×C₄	—	6	2	no	—
297	C₂²×C₄	—	6	2	no	—
298	C₂²×C₄	—	6	4	no	—
299	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
300	Q₁₆	—	3	4	no	—
301	SD₁₆	—	3	8	no	—
302	D₈	—	3	4	no	—
303	M₁₆	—	2	2	no	—
304	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
305	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
306	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
307	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
308	C₄⋊C₄	—	3	4	no	—
309	C₄⋊C₄	—	6	2	no	—
310	C₄⋊C₄	—	6	4	no	—
311	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
312	C₂²⋊C₄	—	6	4	no	—
313	C₂²⋊C₄	C₃×D₁₂	1	2	yes	—
314	C₄²	—	6	4	no	—
315	C₄²	C₂²×C₃×D₃	1	2	yes	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	6	4	no	—
322	C₂²×C₃	—	12	2	no	—
323	C₂²×C₃	—	12	2	no	—
324	C₂²×C₃	C₄×D₁₂	1	2	yes	—
325	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
326	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
327	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
328	C₂×D₃	—	2	4	no	—
329	C₂×D₃	—	4	2	no	—
330	C₂×D₃	—	4	2	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	6	4	no	—
338	C₃×C₄	—	12	4	no	—
339	C₃×C₄	C₄×D₁₂	1	2	yes	—
340	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
341	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
342	C₃×C₄	C₂×#235	1	1	yes	characteristic
343	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
345	Dic₃	—	2	4	no	—
346	Dic₃	—	4	4	no	—
347	C₃²	#2952	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	6	2	no	—
349	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
350	Q₈	—	3	4	no	—
351	Q₈	—	6	2	no	—
352	D₄	—	3	4	no	—
353	D₄	—	6	8	no	—
354	D₄	—	6	2	no	—
355	C₂×C₄	—	6	2	no	—
356	C₂×C₄	—	6	8	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	24	4	no	—
359	C₂×C₄	—	24	2	no	—
360	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
361	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
362	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
363	C₂×C₄	C₃×#235	1	2	yes	—
364	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
367	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
368	C₂×C₃	—	2	2	no	—
369	C₂×C₃	—	2	2	no	—
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	4	2	no	—
373	C₂×C₃	—	12	4	no	—
374	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
375	C₂×C₃	#5751	1	2	yes	—
376	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
377	C₂×C₃	C₃×#577	1	2	yes	—
378	D₃	—	4	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	6	4	no	—
381	C₂²	—	12	2	no	—
382	C₂²	—	12	2	no	—
383	C₂²	C₃×C₄×D₁₂	1	2	yes	—
384	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	6	4	no	—
387	C₄	—	12	4	no	—
388	C₄	C₃×C₄×D₁₂	1	2	yes	—
389	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
390	C₄	C₂×C₃×#235	1	1	yes	characteristic
391	C₃	—	2	1	no	—
392	C₃	#78574	1	1	yes	characteristic, direct product factor
393	C₃	C₃×#2952	1	1	yes	characteristic, complemented
394	C₂	—	2	2	no	—
395	C₂	—	12	4	no	—
396	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
397	C₂	C₃×#5751	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2952
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₃×#5523	C₂	semidirect
3. C₃²×#405	C₂	semidirect
4. C₃×#5133	C₂	semidirect
5. C₂×C₃×#817	C₂	semidirect
6. C₃×#4716	C₂	semidirect
7. C₃×#4711	C₂	semidirect
8. C₃×C₄×#204	C₂	semidirect
10. #78574	C₃	direct (N × H)
17. C₃×#904	C₄	semidirect
34. #5523	C₂×C₃	semidirect
41. C₃×#405	D₃	semidirect
42. C₃×#405	C₂×C₃	semidirect
43. #5133	C₂×C₃	semidirect
44. C₂×#817	C₂×C₃	semidirect
45. #4716	C₂×C₃	semidirect
46. #4711	C₂×C₃	semidirect
47. C₄×#204	C₂×C₃	semidirect
52. C₃×#235	C₂×C₄	semidirect
58. C₂×C₃²×C₈	C₂×C₄	semidirect
70. C₃×Dic₁₂	C₂×C₄	semidirect
71. C₃×D₂₄	C₂×C₄	semidirect
72. C₃×#204	C₂×C₄	semidirect
97. #904	C₃×C₄	semidirect
146. #405	C₃×D₃	semidirect
161. #235	C₂×C₃×C₄	semidirect
176. C₂×C₃×C₈	C₄×D₃	semidirect
177. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
203. Dic₁₂	C₂×C₃×C₄	semidirect
204. D₂₄	C₂×C₃×C₄	semidirect
205. #204	C₂×C₃×C₄	semidirect
304. C₂×C₈	C₃×C₄×D₃	semidirect
347. C₃²	#2952	semidirect
392. C₃	#78574	direct (N × H)
393. C₃	C₃×#2952	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#904	2
C₃×#5523	2
C₃²×#405	2
C₃×#5133	2
C₂×C₃×#817	2
C₃×#4716	2
C₃×#4711	2
C₃×C₄×#204	2
C₃×#2952	3
#78574	3

Subgroups — C3×#78574 #11860935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78574 #11860935