Subgroups — C₃×#72038 #11791033

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#5221	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#832	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1970	—	3	1	no	maximal
7	#72038	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×D₄	C₂²	1	2	yes	—
9	C₂×C₃²×D₈	—	2	2	no	—
10	C₂×C₃²×D₈	—	2	2	no	—
11	C₂×C₃²×D₈	C₄	1	4	yes	complemented
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#217	—	2	4	no	—
14	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×#832	—	2	4	no	—
18	C₃×#818	—	2	2	no	—
19	C₃×C₈×Dic₃	—	2	2	no	—
20	C₂²×C₃×D₈	—	2	1	no	—
21	C₂²×C₃×D₈	D₃	1	1	yes	characteristic
22	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×#107	—	3	1	no	—
24	C₂×C₃×#102	—	3	2	no	—
25	C₂×C₃×C₄×C₈	—	3	1	no	—
26	C₃×#390	—	3	2	no	—
27	#5221	C₂×C₃	1	2	yes	complemented
28	C₂×#832	C₂×C₃	1	2	yes	complemented
29	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃²	—	2	2	no	—
32	C₂×C₃²×D₄	—	2	2	no	—
33	C₂×C₃²×D₄	—	2	2	no	—
34	C₂×C₃²×D₄	—	2	2	no	—
35	C₂×C₃²×D₄	—	2	2	no	—
36	C₂×C₃²×D₄	—	2	2	no	—
37	C₂×C₃²×D₄	C₂×C₄	1	4	yes	—
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	—	2	2	no	—
40	C₂²×C₃×Dic₃	D₄	1	2	yes	—
41	C₃²×D₈	—	2	8	no	—
42	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
43	C₂×C₃²×C₈	D₄	1	2	yes	—
44	C₂×C₃²×C₈	D₄	1	2	yes	—
45	C₃×#217	—	4	8	no	—
46	C₃×C₄⋊Dic₃	—	2	2	no	—
47	C₃×C₄⋊Dic₃	—	2	2	no	—
48	C₃×C₄×Dic₃	—	2	1	no	—
49	C₃×C₄×Dic₃	—	2	1	no	—
50	C₂×C₃×C₃⋊C₈	—	2	1	no	—
51	C₂×C₃×C₃⋊C₈	—	2	1	no	—
52	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
53	#1970	—	3	1	no	Sylow
54	C₂²×C₃×D₄	—	2	2	no	—
55	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
56	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
57	C₂×C₃×D₈	—	2	4	no	—
58	C₂×C₃×D₈	—	2	4	no	—
59	C₂×C₃×D₈	—	2	2	no	—
60	C₂×C₃×D₈	—	2	2	no	—
61	C₂×C₃×D₈	—	2	2	no	—
62	C₂×C₃×D₈	—	2	2	no	—
63	C₂×C₃×D₈	—	2	4	no	—
64	C₂×C₃×D₈	Dic₃	1	4	yes	complemented
65	C₂×C₃×D₈	C₃×C₄	1	4	yes	complemented
66	C₂²×C₃×C₈	—	2	1	no	—
67	C₂²×C₃×C₈	—	3	1	no	—
68	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×C₄⋊C₄	—	3	2	no	—
71	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
72	C₂×C₃×C₄²	—	3	1	no	—
73	C₂×#217	—	2	4	no	—
74	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
75	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
77	C₃×#107	—	6	2	no	—
78	C₃×#102	—	6	4	no	—
79	C₃×C₄×C₈	—	6	2	no	—
80	#832	—	2	4	no	—
81	#818	—	2	2	no	—
82	C₈×Dic₃	—	2	2	no	—
83	C₂³×C₃²	—	2	4	no	—
84	C₂³×C₃²	—	4	2	no	—
85	C₂³×C₃²	—	4	2	no	—
86	C₂³×C₃²	—	4	4	no	—
87	C₂³×C₃²	—	4	4	no	—
88	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
89	C₃²×D₄	—	2	4	no	—
90	C₃²×D₄	—	2	4	no	—
91	C₃²×D₄	—	4	2	no	—
92	C₃²×D₄	—	4	2	no	—
93	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	#41	1	1	yes	characteristic
98	C₂×C₃²×C₄	#41	1	1	yes	characteristic
99	C₂×C₃×Dic₃	—	2	2	no	—
100	C₂×C₃×Dic₃	—	2	2	no	—
101	C₂×C₃×Dic₃	—	4	2	no	—
102	C₂×C₃×Dic₃	—	4	4	no	—
103	C₂×C₃×Dic₃	D₈	1	4	yes	complemented
104	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
105	C₃×C₃⋊C₈	—	2	2	no	—
106	C₂²×D₈	C₃×D₃	1	1	yes	characteristic
107	C₂×#107	—	3	1	no	—
108	C₂×#102	—	3	2	no	—
109	C₂×C₄×C₈	—	3	1	no	—
110	#390	—	3	2	no	—
111	C₂⁴×C₃	—	2	2	no	—
112	C₂⁴×C₃	—	2	2	no	—
113	C₂⁴×C₃	—	4	2	no	—
114	C₂×C₃×D₄	—	2	4	no	—
115	C₂×C₃×D₄	—	2	4	no	—
116	C₂×C₃×D₄	—	2	2	no	—
117	C₂×C₃×D₄	—	2	2	no	—
118	C₂×C₃×D₄	—	2	2	no	—
119	C₂×C₃×D₄	—	2	2	no	—
120	C₂×C₃×D₄	—	2	2	no	—
121	C₂×C₃×D₄	—	2	2	no	—
122	C₂×C₃×D₄	—	2	2	no	—
123	C₂×C₃×D₄	—	2	2	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	2	2	no	—
126	C₂×C₃×D₄	—	2	4	no	—
127	C₂×C₃×D₄	—	4	2	no	—
128	C₂×C₃×D₄	—	4	2	no	—
129	C₂×C₃×D₄	—	4	2	no	—
130	C₂×C₃×D₄	C₂×Dic₃	1	4	yes	—
131	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	3	2	no	—
134	C₂²×C₃×C₄	—	6	2	no	—
135	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₃	—	2	2	no	—
138	C₂²×Dic₃	C₃×D₄	1	2	yes	—
139	C₃×D₈	—	2	16	no	—
140	C₃×D₈	—	2	8	no	—
141	C₃×D₈	—	2	8	no	—
142	C₂×C₃×C₈	—	2	2	no	—
143	C₂×C₃×C₈	—	2	2	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	3	2	no	—
146	C₂×C₃×C₈	—	6	1	no	—
147	C₂×C₃×C₈	—	6	1	no	—
148	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
149	C₂×C₃×C₈	#67	1	2	yes	—
150	C₂×C₃×C₈	#67	1	2	yes	—
151	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
153	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
154	C₃×C₄⋊C₄	—	6	2	no	—
155	C₃×C₄⋊C₄	—	6	2	no	—
156	C₃×C₂²⋊C₄	—	12	8	no	—
157	C₃×C₄²	—	6	1	no	—
158	C₃×C₄²	—	6	1	no	—
159	#217	—	4	8	no	—
160	C₄⋊Dic₃	—	2	2	no	—
161	C₄⋊Dic₃	—	2	2	no	—
162	C₄×Dic₃	—	2	1	no	—
163	C₄×Dic₃	—	2	1	no	—
164	C₂×C₃⋊C₈	—	2	1	no	—
165	C₂×C₃⋊C₈	—	2	1	no	—
166	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
167	C₂²×C₃²	—	4	4	no	—
168	C₂²×C₃²	—	4	8	no	—
169	C₂²×C₃²	—	8	4	no	—
170	C₂²×C₃²	—	8	2	no	—
171	C₂²×C₃²	—	8	2	no	—
172	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
173	C₂²×C₃²	#121	1	1	yes	characteristic
174	C₂²×C₃²	#127	1	1	yes	characteristic
175	C₂²×C₃²	C₂×D₈	1	2	yes	—
176	C₂²×C₃²	#135	1	2	yes	—
177	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
179	C₃²×C₄	#121	1	1	yes	characteristic
180	C₃²×C₄	#124	1	1	yes	characteristic
181	C₃×Dic₃	—	2	4	no	—
182	C₃×Dic₃	—	8	2	no	—
183	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
184	C₂×D₈	—	2	2	no	—
185	C₂×D₈	—	2	2	no	—
186	C₂×D₈	C₃×Dic₃	1	4	yes	complemented
187	C₂²×C₈	—	3	1	no	—
188	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
189	C₂×C₄⋊C₄	—	3	2	no	—
190	C₂×C₂²⋊C₄	—	6	4	no	—
191	C₂×C₄²	—	3	1	no	—
192	#107	—	6	2	no	—
193	#102	—	6	4	no	—
194	C₄×C₈	—	6	2	no	—
195	C₂³×C₃	—	2	4	no	—
196	C₂³×C₃	—	2	4	no	—
197	C₂³×C₃	—	2	1	no	—
198	C₂³×C₃	—	4	4	no	—
199	C₂³×C₃	—	4	4	no	—
200	C₂³×C₃	—	4	4	no	—
201	C₂³×C₃	—	4	4	no	—
202	C₂³×C₃	—	4	4	no	—
203	C₂³×C₃	—	4	2	no	—
204	C₂³×C₃	—	4	2	no	—
205	C₂³×C₃	—	4	2	no	—
206	C₂³×C₃	—	4	2	no	—
207	C₂³×C₃	—	4	4	no	—
208	C₂³×C₃	—	4	4	no	—
209	C₂³×C₃	—	8	4	no	—
210	C₂³×C₃	—	8	4	no	—
211	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
212	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
213	C₃×D₄	—	2	8	no	—
214	C₃×D₄	—	2	4	no	—
215	C₃×D₄	—	2	4	no	—
216	C₃×D₄	—	2	4	no	—
217	C₃×D₄	—	2	4	no	—
218	C₃×D₄	—	4	4	no	—
219	C₃×D₄	—	4	4	no	—
220	C₃×D₄	—	4	4	no	—
221	C₃×D₄	—	4	2	no	—
222	C₃×D₄	—	4	2	no	—
223	C₃×D₄	—	4	2	no	—
224	C₃×D₄	—	4	2	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	3	4	no	—
232	C₂×C₃×C₄	—	6	2	no	—
233	C₂×C₃×C₄	—	6	2	no	—
234	C₂×C₃×C₄	—	12	4	no	—
235	C₂×C₃×C₄	—	12	2	no	—
236	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	#237	1	1	yes	characteristic
238	C₂×C₃×C₄	#237	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
247	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
248	C₂×Dic₃	—	2	2	no	—
249	C₂×Dic₃	—	2	2	no	—
250	C₂×Dic₃	—	4	2	no	—
251	C₂×Dic₃	—	4	4	no	—
252	C₂×Dic₃	C₃×D₈	1	4	yes	complemented
253	C₃×C₈	—	2	4	no	—
254	C₃×C₈	—	6	2	no	—
255	C₃×C₈	#217	1	4	yes	complemented
256	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
257	C₃⋊C₈	—	2	2	no	—
258	C₂×C₃²	—	8	4	no	—
259	C₂×C₃²	#390	1	1	yes	characteristic
260	C₂×C₃²	C₄×D₈	1	2	yes	—
261	C₂×C₃²	#466	1	2	yes	—
262	C₂×C₃²	#493	1	1	yes	characteristic
263	C₂×C₃²	#495	1	1	yes	characteristic
264	C₂⁴	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₂×C₃×Dic₃	1	4	yes	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	—	6	2	no	—
273	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
274	D₈	—	2	8	no	—
275	C₂×C₈	—	3	2	no	—
276	C₂×C₈	—	6	1	no	—
277	C₂×C₈	—	6	1	no	—
278	C₂×C₈	C₂×C₃×Dic₃	1	2	yes	—
279	C₂×C₈	C₃×#67	1	2	yes	—
280	C₂×C₈	C₃×#67	1	2	yes	—
281	C₄⋊C₄	—	6	2	no	—
282	C₄⋊C₄	—	6	2	no	—
283	C₂²⋊C₄	—	12	8	no	—
284	C₄²	—	6	1	no	—
285	C₄²	—	6	1	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	4	8	no	—
292	C₂²×C₃	—	4	8	no	—
293	C₂²×C₃	—	4	4	no	—
294	C₂²×C₃	—	4	4	no	—
295	C₂²×C₃	—	4	8	no	—
296	C₂²×C₃	—	8	8	no	—
297	C₂²×C₃	—	8	4	no	—
298	C₂²×C₃	—	8	4	no	—
299	C₂²×C₃	—	8	8	no	—
300	C₂²×C₃	—	8	2	no	—
301	C₂²×C₃	—	8	2	no	—
302	C₂²×C₃	—	8	4	no	—
303	C₂²×C₃	—	8	4	no	—
304	C₂²×C₃	—	8	2	no	—
305	C₂²×C₃	—	8	2	no	—
306	C₂²×C₃	D₃×D₈	1	2	yes	—
307	C₂²×C₃	#912	1	2	yes	—
308	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
309	C₂²×C₃	#938	1	1	yes	characteristic
310	C₂²×C₃	#940	1	1	yes	characteristic
311	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₃	C₃×#121	1	1	yes	characteristic
313	C₂²×C₃	C₃×#127	1	1	yes	characteristic
314	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
315	C₂²×C₃	C₃×#135	1	2	yes	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	6	4	no	—
321	C₃×C₄	—	24	2	no	—
322	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
323	C₃×C₄	#936	1	1	yes	characteristic
324	C₃×C₄	#938	1	1	yes	characteristic
325	C₃×C₄	C₂×#217	1	1	yes	characteristic
326	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
327	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
328	C₃×C₄	C₃×#121	1	1	yes	characteristic
329	C₃×C₄	C₃×#124	1	1	yes	characteristic
330	Dic₃	—	2	4	no	—
331	Dic₃	—	8	2	no	—
332	C₃²	#1970	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	2	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
339	D₄	—	2	4	no	—
340	D₄	—	2	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	3	4	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	6	2	no	—
346	C₂×C₄	—	12	4	no	—
347	C₂×C₄	—	12	2	no	—
348	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
349	C₂×C₄	C₃×#237	1	1	yes	characteristic
350	C₂×C₄	C₃×#237	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
354	C₈	—	6	2	no	—
355	C₈	C₃×#217	1	4	yes	complemented
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	8	8	no	—
362	C₂×C₃	—	8	4	no	—
363	C₂×C₃	—	8	4	no	—
364	C₂×C₃	Dic₃×D₈	1	2	yes	—
365	C₂×C₃	#5151	1	1	yes	characteristic
366	C₂×C₃	#5155	1	1	yes	characteristic
367	C₂×C₃	#5157	1	2	yes	—
368	C₂×C₃	#5221	1	1	yes	characteristic
369	C₂×C₃	C₃×#390	1	1	yes	characteristic
370	C₂×C₃	C₃×C₄×D₈	1	2	yes	—
371	C₂×C₃	C₃×#466	1	2	yes	—
372	C₂×C₃	C₃×#493	1	1	yes	characteristic
373	C₂×C₃	C₃×#495	1	1	yes	characteristic
374	C₂²	—	4	4	no	—
375	C₂²	—	4	8	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	4	no	—
379	C₂²	C₃×D₃×D₈	1	2	yes	—
380	C₂²	C₃×#912	1	2	yes	—
381	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
382	C₂²	C₃×#938	1	1	yes	characteristic
383	C₂²	C₃×#940	1	1	yes	characteristic
384	C₄	—	6	4	no	—
385	C₄	—	24	2	no	—
386	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
387	C₄	C₃×#936	1	1	yes	characteristic
388	C₄	C₃×#938	1	1	yes	characteristic
389	C₄	C₂×C₃×#217	1	1	yes	characteristic
390	C₃	—	2	1	no	—
391	C₃	#72038	1	1	yes	characteristic, direct product factor
392	C₃	C₃×#1970	1	1	yes	characteristic, complemented
393	C₂	—	8	4	no	—
394	C₂	C₃×Dic₃×D₈	1	2	yes	—
395	C₂	C₃×#5151	1	1	yes	characteristic
396	C₂	C₃×#5155	1	1	yes	characteristic
397	C₂	C₃×#5157	1	2	yes	—
398	C₂	C₃×#5221	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting, prime radical	C₂²×C₃²×D₈	C₂
socle	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₃×#1970
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×#5221	C₂	semidirect
3. C₂×C₃×#832	C₂	semidirect
4. C₂×C₃×#818	C₂	semidirect
5. C₂×C₃×C₈×Dic₃	C₂	semidirect
7. #72038	C₃	direct (N × H)
11. C₂×C₃²×D₈	C₄	semidirect
27. #5221	C₂×C₃	semidirect
28. C₂×#832	C₂×C₃	semidirect
29. C₂×#818	C₂×C₃	semidirect
30. C₂×C₈×Dic₃	C₂×C₃	semidirect
64. C₂×C₃×D₈	Dic₃	semidirect
65. C₂×C₃×D₈	C₃×C₄	semidirect
103. C₂×C₃×Dic₃	D₈	semidirect
104. C₃²×C₈	C₂²⋊C₄	semidirect
186. C₂×D₈	C₃×Dic₃	semidirect
252. C₂×Dic₃	C₃×D₈	semidirect
255. C₃×C₈	#217	semidirect
256. C₃×C₈	C₃×C₂²⋊C₄	semidirect
332. C₃²	#1970	semidirect
355. C₈	C₃×#217	semidirect
391. C₃	#72038	direct (N × H)
392. C₃	C₃×#1970	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×D₈	2
C₃×#5221	2
C₂×C₃×#832	2
C₂×C₃×#818	2
C₂×C₃×C₈×Dic₃	2
C₃×#1970	3
#72038	3

Subgroups — C3×#72038 #11791033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#72038 #11791033