Subgroups — C₃×#70800 #11774789

Order 1152.

515 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃²×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4484	C₂	1	2	yes	maximal, complemented
5	C₃×#4483	C₂	1	2	yes	maximal, complemented
6	C₃×#1494	—	3	1	no	maximal
7	#70800	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₃×#930	C₄	1	1	yes	characteristic
10	C₃×#929	—	2	1	no	—
11	C₃×C₄×#67	—	2	1	no	—
12	C₃×#924	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊C₈	—	2	1	no	—
14	C₃×#876	—	2	1	no	—
15	C₃×#875	C₄	1	1	yes	characteristic
16	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
17	C₃×#872	—	2	1	no	—
18	C₃×#870	C₄	1	1	yes	characteristic
19	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
20	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
21	C₃²×C₂²⋊C₈	—	2	1	no	—
22	C₃²×#97	—	2	1	no	—
23	C₃×C₄×C₃⋊C₈	—	2	1	no	—
24	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
25	C₃×#529	—	3	1	no	—
26	#5479	C₂×C₃	1	1	yes	characteristic
27	C₃×#432	—	2	1	no	—
28	C₃×#432	D₃	1	1	yes	characteristic, complemented
29	C₃×#432	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×C₈	—	3	1	no	—
31	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₃×Q₈⋊C₈	—	3	2	no	—
33	C₃×D₄⋊C₈	—	3	2	no	—
34	#4484	C₂×C₃	1	2	yes	complemented
35	#4483	C₂×C₃	1	2	yes	complemented
36	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
39	C₂×C₃×#67	—	2	1	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	—	2	1	no	—
42	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	—	2	2	no	—
44	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
45	C₃²×C₄²	D₄	1	1	yes	characteristic
46	C₃²×C₄²	D₄	1	1	yes	characteristic
47	C₃²×C₄²	C₂³	1	1	yes	characteristic
48	C₃×#217	—	2	1	no	—
49	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₃×Dic₃⋊C₄	—	2	1	no	—
56	C₃×Dic₃⋊C₄	—	2	1	no	—
57	C₃×Dic₃⋊C₄	—	2	1	no	—
58	C₃×Dic₃⋊C₄	—	2	1	no	—
59	C₃×C₄×Dic₃	—	2	1	no	—
60	C₂×C₃×C₃⋊C₈	—	2	4	no	—
61	C₂×C₃×C₃⋊C₈	—	2	2	no	—
62	#1494	—	3	1	no	Sylow
63	C₂²×C₃×C₈	—	6	1	no	—
64	C₃×#126	—	6	1	no	—
65	C₃×#125	—	3	1	no	—
66	C₃×#124	—	3	1	no	—
67	C₃×#123	—	6	1	no	—
68	C₃×C₂²⋊Q₈	—	3	1	no	—
69	C₃×#121	—	3	1	no	—
70	C₃×C₄×Q₈	—	3	1	no	—
71	C₃×C₄×D₄	—	3	1	no	—
72	C₃×C₄×D₄	—	6	1	no	—
73	C₃×#117	—	6	1	no	—
74	C₂×C₃×C₄²	—	2	1	no	—
75	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	#930	C₃×C₄	1	1	yes	characteristic
78	#929	—	2	1	no	—
79	C₄×#67	—	2	1	no	—
80	#924	C₃×C₄	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	—	2	1	no	—
82	#876	—	2	1	no	—
83	#875	C₃×C₄	1	1	yes	characteristic
84	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
85	#872	—	2	1	no	—
86	#870	C₃×C₄	1	1	yes	characteristic
87	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄⋊C₈	—	2	2	no	—
89	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
90	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
91	C₃×C₂²⋊C₈	—	2	2	no	—
92	C₃×C₂²⋊C₈	—	2	1	no	—
93	C₃×C₂²⋊C₈	—	2	1	no	—
94	C₃×#97	—	2	2	no	—
95	C₃×#97	—	2	1	no	—
96	C₃×#97	—	2	1	no	—
97	C₃×C₄×C₈	—	3	2	no	—
98	C₃×C₄×C₈	—	6	1	no	—
99	C₄×C₃⋊C₈	—	2	1	no	—
100	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
101	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₃×D₃	—	2	1	no	—
103	C₂×C₃²×C₄	—	2	2	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	2	2	no	—
106	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₃×#67	—	4	2	no	—
113	C₂×C₃×Dic₃	—	2	1	no	—
114	C₂×C₃×Dic₃	—	2	1	no	—
115	C₂×C₃×Dic₃	—	2	1	no	—
116	C₃×D₁₂	—	2	2	no	—
117	C₃×C₄×D₃	—	4	2	no	—
118	C₃×Dic₆	—	2	2	no	—
119	C₃²×C₈	—	4	2	no	—
120	C₃×C₃⋊C₈	—	2	4	no	—
121	#529	—	3	1	no	—
122	#432	C₃×D₃	1	1	yes	characteristic, complemented
123	C₂×C₄×C₈	—	3	1	no	—
124	Q₈⋊C₈	—	3	2	no	—
125	D₄⋊C₈	—	3	2	no	—
126	C₂×C₃×Q₈	—	3	1	no	—
127	C₂×C₃×D₄	—	3	1	no	—
128	C₂×C₃×D₄	—	6	1	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	6	1	no	—
133	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
134	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
135	C₂²×C₃×C₄	#67	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
139	C₂×#67	—	2	1	no	—
140	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
141	C₂×C₄×D₃	—	2	1	no	—
142	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂×C₃×C₈	—	2	4	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	6	4	no	—
147	C₂×C₃×C₈	—	6	2	no	—
148	C₃×C₄⋊C₄	—	3	1	no	—
149	C₃×C₄⋊C₄	—	3	1	no	—
150	C₃×C₄⋊C₄	—	6	1	no	—
151	C₃×C₄⋊C₄	—	6	1	no	—
152	C₃×C₄⋊C₄	—	6	1	no	—
153	C₃×C₄⋊C₄	—	6	1	no	—
154	C₃×C₂²⋊C₄	—	6	1	no	—
155	C₃×C₂²⋊C₄	—	6	1	no	—
156	C₃×C₂²⋊C₄	—	6	1	no	—
157	C₃×C₂²⋊C₄	—	6	1	no	—
158	C₃×C₂²⋊C₄	—	6	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	1	no	—
161	C₃×C₄²	—	2	1	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₃×C₄²	—	6	1	no	—
164	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
165	C₃×C₄²	D₁₂	1	1	yes	characteristic
166	C₃×C₄²	#67	1	1	yes	characteristic
167	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
168	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
169	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
170	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
171	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
172	#217	—	2	1	no	—
173	(C₂×D₃)⋊C₄	—	2	1	no	—
174	(C₂×D₃)⋊C₄	—	2	1	no	—
175	(C₂×D₃)⋊C₄	—	2	1	no	—
176	(C₂×D₃)⋊C₄	—	2	1	no	—
177	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
178	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
179	Dic₃⋊C₄	—	2	1	no	—
180	Dic₃⋊C₄	—	2	1	no	—
181	Dic₃⋊C₄	—	2	1	no	—
182	Dic₃⋊C₄	—	2	1	no	—
183	C₄×Dic₃	—	2	1	no	—
184	C₂×C₃⋊C₈	—	2	4	no	—
185	C₂×C₃⋊C₈	—	2	2	no	—
186	C₂²×C₃²	—	2	1	no	—
187	C₂²×C₃²	—	2	1	no	—
188	C₂²×C₃²	#104	1	2	yes	—
189	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₃×D₃	—	4	1	no	—
191	C₂×C₃×D₃	—	4	1	no	—
192	C₂×C₃×D₃	—	4	1	no	—
193	C₃²×C₄	—	2	1	no	—
194	C₃²×C₄	—	2	1	no	—
195	C₃²×C₄	—	2	1	no	—
196	C₃²×C₄	—	2	1	no	—
197	C₃²×C₄	#131	1	2	yes	—
198	C₃²×C₄	#135	1	2	yes	—
199	C₃×Dic₃	—	4	1	no	—
200	C₃×Dic₃	—	4	1	no	—
201	C₃×Dic₃	—	4	1	no	—
202	C₂²×C₈	—	6	1	no	—
203	#126	—	6	1	no	—
204	#125	—	3	1	no	—
205	#124	—	3	1	no	—
206	#123	—	6	1	no	—
207	C₂²⋊Q₈	—	3	1	no	—
208	#121	—	3	1	no	—
209	C₄×Q₈	—	3	1	no	—
210	C₄×D₄	—	3	1	no	—
211	C₄×D₄	—	6	1	no	—
212	#117	—	6	1	no	—
213	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
214	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
215	C₂²⋊C₈	—	2	1	no	—
216	#97	—	2	1	no	—
217	C₄×C₈	—	3	2	no	—
218	C₄×C₈	—	6	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	6	1	no	—
221	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
222	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×D₃	—	2	1	no	—
224	C₃×Q₈	—	6	2	no	—
225	C₃×D₄	—	6	2	no	—
226	C₃×D₄	—	12	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	6	1	no	—
243	C₂×C₃×C₄	—	6	1	no	—
244	C₂×C₃×C₄	—	6	1	no	—
245	C₂×C₃×C₄	—	12	2	no	—
246	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
258	#67	—	4	2	no	—
259	C₂×Dic₃	—	2	1	no	—
260	C₂×Dic₃	—	2	1	no	—
261	C₂×Dic₃	—	2	1	no	—
262	D₁₂	—	2	2	no	—
263	C₄×D₃	—	4	2	no	—
264	Dic₆	—	2	2	no	—
265	C₃×C₈	—	4	4	no	—
266	C₃×C₈	—	4	2	no	—
267	C₃×C₈	—	4	2	no	—
268	C₃×C₈	—	6	4	no	—
269	C₃⋊C₈	—	2	4	no	—
270	C₂×C₃²	—	2	2	no	—
271	C₂×C₃²	#408	1	1	yes	characteristic
272	C₂×C₃²	#416	1	1	yes	characteristic
273	C₂×C₃²	C₂×#104	1	1	yes	characteristic
274	C₃×D₃	—	8	1	no	—
275	C₂×Q₈	—	3	1	no	—
276	C₂×D₄	—	3	1	no	—
277	C₂×D₄	—	6	1	no	—
278	C₂²×C₄	—	6	1	no	—
279	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
280	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
281	C₂²×C₄	C₃×#67	1	1	yes	characteristic
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	6	4	no	—
284	C₂×C₈	—	6	2	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	1	no	—
287	C₄⋊C₄	—	6	1	no	—
288	C₄⋊C₄	—	6	1	no	—
289	C₄⋊C₄	—	6	1	no	—
290	C₄⋊C₄	—	6	1	no	—
291	C₂²⋊C₄	—	6	1	no	—
292	C₂²⋊C₄	—	6	1	no	—
293	C₂²⋊C₄	—	6	1	no	—
294	C₂²⋊C₄	—	6	1	no	—
295	C₂²⋊C₄	—	6	1	no	—
296	C₄²	—	6	1	no	—
297	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
298	C₄²	C₃×D₁₂	1	1	yes	characteristic
299	C₄²	C₃×#67	1	1	yes	characteristic
300	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	12	1	no	—
310	C₂²×C₃	—	12	1	no	—
311	C₂²×C₃	—	12	1	no	—
312	C₂²×C₃	#825	1	2	yes	—
313	C₂²×C₃	C₃×#104	1	2	yes	—
314	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×D₃	—	4	1	no	—
317	C₂×D₃	—	4	1	no	—
318	C₂×D₃	—	4	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	—	4	1	no	—
332	C₃×C₄	—	4	1	no	—
333	C₃×C₄	—	12	1	no	—
334	C₃×C₄	—	12	1	no	—
335	C₃×C₄	—	12	1	no	—
336	C₃×C₄	#907	1	2	yes	—
337	C₃×C₄	#950	1	2	yes	—
338	C₃×C₄	C₃×#131	1	2	yes	—
339	C₃×C₄	C₃×#135	1	2	yes	—
340	Dic₃	—	4	1	no	—
341	Dic₃	—	4	1	no	—
342	Dic₃	—	4	1	no	—
343	C₃²	#1494	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	6	1	no	—
345	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
346	Q₈	—	6	2	no	—
347	D₄	—	6	2	no	—
348	D₄	—	12	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	—	6	1	no	—
354	C₂×C₄	—	6	1	no	—
355	C₂×C₄	—	12	2	no	—
356	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
361	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	6	4	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	2	2	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	4	2	no	—
370	C₂×C₃	—	24	1	no	—
371	C₂×C₃	#5002	1	1	yes	characteristic
372	C₂×C₃	#5129	1	1	yes	characteristic
373	C₂×C₃	C₂×#825	1	1	yes	characteristic
374	C₂×C₃	C₃×#408	1	1	yes	characteristic
375	C₂×C₃	C₃×#416	1	1	yes	characteristic
376	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
377	D₃	—	8	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	12	1	no	—
381	C₂²	—	12	1	no	—
382	C₂²	—	12	1	no	—
383	C₂²	C₃×#825	1	2	yes	—
384	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	12	1	no	—
390	C₄	—	12	1	no	—
391	C₄	—	12	1	no	—
392	C₄	C₃×#907	1	2	yes	—
393	C₄	C₃×#950	1	2	yes	—
394	C₃	—	2	1	no	—
395	C₃	#70800	1	1	yes	characteristic, direct product factor
396	C₃	C₃×#1494	1	1	yes	characteristic, complemented
397	C₂	—	2	2	no	—
398	C₂	—	24	1	no	—
399	C₂	C₃×#5002	1	1	yes	characteristic
400	C₂	C₃×#5129	1	1	yes	characteristic
401	C₂	C₂×C₃×#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×#432	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#930	C₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×#432	D₃
hypocenter	C₃	C₃×#1494
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#432

Complements

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

N	H ≅ G/N	type
2. C₃²×#432	C₂	semidirect
3. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
4. C₃×#4484	C₂	semidirect
5. C₃×#4483	C₂	semidirect
7. #70800	C₃	direct (N × H)
28. C₃×#432	D₃	semidirect
29. C₃×#432	C₂×C₃	semidirect
31. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
34. #4484	C₂×C₃	semidirect
35. #4483	C₂×C₃	semidirect
122. #432	C₃×D₃	semidirect
343. C₃²	#1494	semidirect
395. C₃	#70800	direct (N × H)
396. C₃	C₃×#1494	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5479	2
C₃²×#432	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4484	2
C₃×#4483	2
C₃×#1494	3
#70800	3

Subgroups — C3×#70800 #11774789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70800 #11774789