Subgroups — C₂×C₃×#4887 #11866784

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#897	C₂	1	2	yes	maximal
4	C₂×C₃²×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#810	C₂	1	2	yes	maximal, complemented
6	C₃×#4887	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#467	—	3	1	no	maximal
8	C₂×#4887	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₂×C₃×C₄⋊Dic₃	—	2	2	no	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₂	—	2	4	no	—
17	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
18	C₂×C₃×D₃×C₈	—	2	4	no	—
19	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
20	C₃×#897	—	2	4	no	—
21	C₃×#897	C₂²	1	8	yes	—
22	C₃²×#107	C₂²	1	4	yes	complemented
23	C₃×#810	C₂²	1	8	yes	complemented
24	C₂²×C₃×Q₁₆	—	3	1	no	—
25	C₂³×C₃×C₈	—	3	1	no	—
26	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
27	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
29	C₂×#897	C₂×C₃	1	2	yes	—
30	C₃×#467	—	3	8	no	—
31	C₂×C₃×#107	—	2	1	no	—
32	C₂×C₃×#107	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#103	—	3	2	no	—
35	C₂×#810	C₂×C₃	1	2	yes	complemented
36	#4887	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	—	2	2	no	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	—	2	2	no	—
41	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₃	—	2	2	no	—
43	C₂×C₃×C₄×D₃	—	2	2	no	—
44	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₂×C₃×Dic₆	—	2	4	no	—
47	C₂×C₃×Dic₆	—	2	4	no	—
48	C₂×C₃×Dic₆	—	2	2	no	—
49	C₂×C₃×Dic₆	C₂³	1	4	yes	—
50	C₂×C₃²×C₈	D₄	1	4	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	C₃²×C₄⋊C₄	—	2	2	no	—
53	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
54	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
55	C₃×C₄⋊Dic₃	—	2	8	no	—
56	C₂×C₃×C₃⋊C₈	—	2	2	no	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₃×Dic₁₂	—	2	8	no	—
59	C₃×D₃×C₈	—	2	8	no	—
60	C₂×#467	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	3	2	no	—
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
64	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
65	C₂×C₃×Q₁₆	—	3	4	no	—
66	C₂×C₃×Q₁₆	—	6	4	no	—
67	C₂²×C₃×C₈	—	2	1	no	—
68	C₂²×C₃×C₈	—	3	1	no	—
69	C₂²×C₃×C₈	—	3	4	no	—
70	C₂²×C₃×C₈	—	6	4	no	—
71	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃×C₂²⋊Q₈	—	3	8	no	—
74	C₃×C₂²⋊Q₈	—	6	4	no	—
75	C₂×C₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₃×C₄⋊C₄	—	6	2	no	—
77	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
80	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
81	C₂×C₄⋊Dic₃	—	2	2	no	—
82	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×Dic₁₂	—	2	4	no	—
84	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
85	C₂×D₃×C₈	—	2	4	no	—
86	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
87	#897	—	2	4	no	—
88	#897	C₂²×C₃	1	8	yes	—
89	C₃×#107	—	2	4	no	—
90	C₃×#107	C₂×D₃	1	4	yes	complemented
91	C₃×#107	C₂²×C₃	1	4	yes	complemented
92	C₃×#103	—	3	8	no	—
93	#810	C₂²×C₃	1	8	yes	complemented
94	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	2	2	no	—
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	Q₁₆	1	4	yes	complemented
98	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
99	C₂×C₃²×C₄	—	2	4	no	—
100	C₂×C₃²×C₄	—	4	4	no	—
101	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	#41	1	2	yes	—
104	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×Dic₃	—	2	2	no	—
106	C₂×C₃×Dic₃	—	2	4	no	—
107	C₂×C₃×Dic₃	—	4	4	no	—
108	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
109	C₃×C₄×D₃	—	2	4	no	—
110	C₃×C₄×D₃	—	2	2	no	—
111	C₃×C₄×D₃	—	2	2	no	—
112	C₃×Dic₆	—	2	4	no	—
113	C₃×Dic₆	—	2	4	no	—
114	C₃×Dic₆	—	4	4	no	—
115	C₃²×C₈	C₂×D₄	1	4	yes	—
116	C₃×C₃⋊C₈	—	2	2	no	—
117	C₂²×Q₁₆	—	3	1	no	—
118	C₂³×C₈	—	3	1	no	—
119	C₂×C₂²⋊Q₈	—	3	2	no	—
120	#467	—	3	8	no	—
121	C₂×#107	C₃×D₃	1	1	yes	characteristic, complemented
122	C₂×#103	—	3	2	no	—
123	C₂⁴×C₃	—	3	1	no	—
124	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
125	C₂×C₃×Q₈	—	3	4	no	—
126	C₂×C₃×Q₈	—	6	2	no	—
127	C₂×C₃×Q₈	—	6	4	no	—
128	C₂×C₃×Q₈	—	6	4	no	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	3	1	no	—
133	C₂²×C₃×C₄	—	3	2	no	—
134	C₂²×C₃×C₄	—	3	2	no	—
135	C₂²×C₃×C₄	—	4	2	no	—
136	C₂²×C₃×C₄	—	6	2	no	—
137	C₂²×C₃×C₄	—	6	2	no	—
138	C₂²×C₃×C₄	—	6	2	no	—
139	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₂²×Dic₃	—	2	2	no	—
142	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
143	C₂×C₄×D₃	—	2	2	no	—
144	C₂×C₄×D₃	—	2	2	no	—
145	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
146	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
147	C₂×Dic₆	—	2	4	no	—
148	C₂×Dic₆	—	2	4	no	—
149	C₂×Dic₆	—	2	2	no	—
150	C₂×Dic₆	C₂³×C₃	1	4	yes	—
151	C₃×Q₁₆	—	6	8	no	—
152	C₂×C₃×C₈	—	2	4	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	3	2	no	—
155	C₂×C₃×C₈	—	6	2	no	—
156	C₂×C₃×C₈	—	6	8	no	—
157	C₂×C₃×C₈	D₁₂	1	4	yes	—
158	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
159	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
160	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
161	C₃×C₄⋊C₄	—	2	2	no	—
162	C₃×C₄⋊C₄	—	2	2	no	—
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	—	4	2	no	—
165	C₃×C₄⋊C₄	—	6	8	no	—
166	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
167	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
168	C₃×C₂²⋊C₄	—	6	8	no	—
169	(C₂×D₃)⋊C₄	—	2	8	no	—
170	C₄⋊Dic₃	—	2	8	no	—
171	C₂×C₃⋊C₈	—	2	2	no	—
172	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
173	Dic₁₂	—	2	8	no	—
174	D₃×C₈	—	2	8	no	—
175	C₂²×C₃²	#121	1	2	yes	—
176	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
177	C₂²×C₃²	#135	1	2	yes	—
178	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₃×D₃	—	2	2	no	—
180	C₂×C₃×D₃	—	2	2	no	—
181	C₂×C₃×D₃	—	2	8	no	—
182	C₂×C₃×D₃	C₂×Q₁₆	1	4	yes	complemented
183	C₃²×C₄	—	4	4	no	—
184	C₃²×C₄	#121	1	2	yes	—
185	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
186	C₃²×C₄	C₂×#41	1	1	yes	characteristic
187	C₃×Dic₃	—	2	2	no	—
188	C₃×Dic₃	—	4	4	no	—
189	C₂²×Q₈	—	3	2	no	—
190	C₂³×C₄	—	3	1	no	—
191	C₂×Q₁₆	—	3	4	no	—
192	C₂×Q₁₆	—	6	4	no	—
193	C₂²×C₈	—	3	1	no	—
194	C₂²×C₈	—	3	4	no	—
195	C₂²×C₈	—	6	4	no	—
196	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
197	C₂²⋊Q₈	—	3	8	no	—
198	C₂²⋊Q₈	—	6	4	no	—
199	C₂×C₄⋊C₄	—	6	2	no	—
200	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
201	C₂×C₂²⋊C₄	—	6	2	no	—
202	#107	C₂×C₃×D₃	1	4	yes	complemented
203	#103	—	3	8	no	—
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	3	4	no	—
206	C₂³×C₃	—	3	2	no	—
207	C₂³×C₃	—	6	2	no	—
208	C₂³×C₃	—	6	2	no	—
209	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
210	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂²×D₃	—	2	2	no	—
212	C₂²×D₃	—	2	2	no	—
213	C₂²×D₃	C₃×Q₁₆	1	4	yes	complemented
214	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
215	C₃×Q₈	—	6	4	no	—
216	C₃×Q₈	—	6	4	no	—
217	C₃×Q₈	—	12	4	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	3	2	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	—	4	4	no	—
227	C₂×C₃×C₄	—	4	4	no	—
228	C₂×C₃×C₄	—	6	2	no	—
229	C₂×C₃×C₄	—	6	4	no	—
230	C₂×C₃×C₄	—	6	2	no	—
231	C₂×C₃×C₄	—	6	2	no	—
232	C₂×C₃×C₄	—	6	4	no	—
233	C₂×C₃×C₄	—	8	4	no	—
234	C₂×C₃×C₄	—	12	4	no	—
235	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
236	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	#239	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₃×#41	1	2	yes	—
241	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
243	C₂×Dic₃	—	2	2	no	—
244	C₂×Dic₃	—	2	4	no	—
245	C₂×Dic₃	—	4	4	no	—
246	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
247	C₄×D₃	—	2	4	no	—
248	C₄×D₃	—	2	2	no	—
249	C₄×D₃	—	2	2	no	—
250	Dic₆	—	2	4	no	—
251	Dic₆	—	2	4	no	—
252	Dic₆	—	4	4	no	—
253	C₃×C₈	—	2	4	no	—
254	C₃×C₈	—	6	2	no	—
255	C₃×C₈	C₂×D₁₂	1	4	yes	—
256	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
257	C₃⋊C₈	—	2	2	no	—
258	C₂×C₃²	#467	1	4	yes	complemented
259	C₂×C₃²	C₂×#121	1	1	yes	characteristic
260	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
261	C₂×C₃²	C₂×#135	1	1	yes	characteristic
262	C₃×D₃	—	2	4	no	—
263	C₂⁴	—	3	1	no	—
264	C₂×Q₈	—	3	4	no	—
265	C₂×Q₈	—	6	2	no	—
266	C₂×Q₈	—	6	4	no	—
267	C₂×Q₈	—	6	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	3	1	no	—
270	C₂²×C₄	—	3	2	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	—	6	2	no	—
273	C₂²×C₄	—	6	2	no	—
274	C₂²×C₄	—	6	2	no	—
275	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
276	Q₁₆	—	6	8	no	—
277	C₂×C₈	—	3	2	no	—
278	C₂×C₈	—	6	2	no	—
279	C₂×C₈	—	6	8	no	—
280	C₂×C₈	C₃×D₁₂	1	4	yes	—
281	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	6	8	no	—
284	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
285	C₂²⋊C₄	—	6	8	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	3	4	no	—
291	C₂²×C₃	—	6	8	no	—
292	C₂²×C₃	—	6	2	no	—
293	C₂²×C₃	—	6	2	no	—
294	C₂²×C₃	#895	1	2	yes	—
295	C₂²×C₃	#912	1	2	yes	—
296	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
297	C₂²×C₃	C₃×#121	1	2	yes	—
298	C₂²×C₃	C₂×C₃×Q₁₆	1	2	yes	—
299	C₂²×C₃	C₃×#135	1	2	yes	—
300	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
301	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
302	C₂×D₃	—	2	2	no	—
303	C₂×D₃	—	2	2	no	—
304	C₂×D₃	—	2	8	no	—
305	C₂×D₃	C₂×C₃×Q₁₆	1	4	yes	complemented
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	4	4	no	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	—	6	2	no	—
312	C₃×C₄	—	8	4	no	—
313	C₃×C₄	—	12	4	no	—
314	C₃×C₄	#895	1	2	yes	—
315	C₃×C₄	C₃×#121	1	2	yes	—
316	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
317	C₃×C₄	C₂×#239	1	1	yes	characteristic
318	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
319	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
320	Dic₃	—	2	2	no	—
321	Dic₃	—	4	4	no	—
322	C₃²	C₂×#467	1	1	yes	characteristic, complemented, Sylow
323	C₂³	—	3	4	no	—
324	C₂³	—	3	2	no	—
325	C₂³	—	6	2	no	—
326	C₂³	—	6	2	no	—
327	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
328	Q₈	—	6	4	no	—
329	Q₈	—	6	4	no	—
330	Q₈	—	12	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	3	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	6	4	no	—
336	C₂×C₄	—	6	2	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	12	4	no	—
340	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
341	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
342	C₂×C₄	C₃×#239	1	2	yes	—
343	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
344	C₈	—	6	2	no	—
345	C₈	C₂×C₃×D₁₂	1	4	yes	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	6	4	no	—
351	C₂×C₃	#4887	1	4	yes	direct product factor
352	C₂×C₃	C₃×#467	1	4	yes	complemented
353	C₂×C₃	C₂×#895	1	1	yes	characteristic
354	C₂×C₃	C₂×#912	1	1	yes	characteristic
355	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
356	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
357	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
358	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
359	D₃	—	2	4	no	—
360	C₂²	—	3	4	no	—
361	C₂²	—	6	2	no	—
362	C₂²	—	6	2	no	—
363	C₂²	—	6	8	no	—
364	C₂²	C₃×#895	1	2	yes	—
365	C₂²	C₃×#912	1	2	yes	—
366	C₂²	C₃×D₃×Q₁₆	1	2	yes	—
367	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
368	C₄	—	4	4	no	—
369	C₄	—	6	2	no	—
370	C₄	—	12	4	no	—
371	C₄	C₃×#895	1	2	yes	—
372	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
373	C₄	C₂×C₃×#239	1	1	yes	characteristic
374	C₃	—	2	1	no	—
375	C₃	C₂×#4887	1	1	yes	characteristic, direct product factor
376	C₃	C₂×C₃×#467	1	1	yes	characteristic, complemented
377	C₂	—	6	4	no	—
378	C₂	C₃×#4887	1	4	yes	direct product factor
379	C₂	C₂×C₃×#895	1	1	yes	characteristic
380	C₂	C₂×C₃×#912	1	1	yes	characteristic
381	C₂	C₂×C₃×D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#107	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
hypercenter	C₂×C₃×#107	D₃
hypocenter	C₃	C₂×C₃×#467
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₂×C₃²×#107	C₂	semidirect
5. C₂×C₃×#810	C₂	semidirect
6. C₃×#4887	C₂	direct (N × H)
8. C₂×#4887	C₃	direct (N × H)
17. C₂×C₃×Dic₁₂	C₂²	semidirect
22. C₃²×#107	C₂²	semidirect
23. C₃×#810	C₂²	semidirect
27. C₂²×Dic₁₂	C₂×C₃	semidirect
32. C₂×C₃×#107	D₃	semidirect
33. C₂×C₃×#107	C₂×C₃	semidirect
35. C₂×#810	C₂×C₃	semidirect
36. #4887	C₂×C₃	direct (N × H)
84. C₂×Dic₁₂	C₂²×C₃	semidirect
90. C₃×#107	C₂×D₃	semidirect
91. C₃×#107	C₂²×C₃	semidirect
93. #810	C₂²×C₃	semidirect
97. C₂²×C₃×D₃	Q₁₆	semidirect
121. C₂×#107	C₃×D₃	semidirect
182. C₂×C₃×D₃	C₂×Q₁₆	semidirect
202. #107	C₂×C₃×D₃	semidirect
213. C₂²×D₃	C₃×Q₁₆	semidirect
258. C₂×C₃²	#467	semidirect
305. C₂×D₃	C₂×C₃×Q₁₆	semidirect
322. C₃²	C₂×#467	semidirect
351. C₂×C₃	#4887	direct (N × H)
352. C₂×C₃	C₃×#467	semidirect
375. C₃	C₂×#4887	direct (N × H)
376. C₃	C₂×C₃×#467	semidirect
378. C₂	C₃×#4887	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₂	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#897	2
C₂×C₃²×#107	2
C₂×C₃×#810	2
C₃×#4887	2
C₂×C₃×#467	3
C₂×#4887	3

Subgroups — C2×C3×#4887 #11866784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4887 #11866784