Subgroups — C₂×C₃×#5012 #11859267

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#208	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#830	C₂	1	2	yes	maximal, complemented
4	C₃×#5012	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#436	—	3	1	no	maximal
8	C₂×#5012	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×D₄	C₄	1	1	yes	characteristic
10	C₂³×C₃²×C₄	C₂²	1	2	yes	—
11	C₃²×C₄×D₄	C₄	1	4	yes	—
12	C₃²×C₄×D₄	C₂²	1	4	yes	—
13	C₂×C₃²×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₃²×C₂²⋊C₄	C₄	1	2	yes	—
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	—	2	8	no	—
17	C₂×C₃×#208	C₂²	1	8	yes	complemented
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
20	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#830	C₂²	1	8	yes	complemented
22	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
23	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	complemented
24	C₂²×C₃×M₁₆	—	3	2	no	—
25	C₂×C₃×C₄×D₄	—	2	1	no	—
26	C₂×C₃×C₄×D₄	D₃	1	1	yes	characteristic
27	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
28	C₂²×#208	C₂×C₃	1	2	yes	complemented
29	C₃×#436	—	3	8	no	—
30	C₂×C₃×C₄⋊C₈	—	3	1	no	—
31	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
32	C₂×C₃×C₄×C₈	—	3	1	no	—
33	C₂×#830	C₂×C₃	1	2	yes	complemented
34	#5012	C₂×C₃	1	8	yes	direct product factor
35	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃²	C₂×C₄	1	2	yes	—
38	C₂×C₃²×D₄	—	2	4	no	—
39	C₂×C₃²×D₄	C₂×C₄	1	4	yes	—
40	C₂²×C₃²×C₄	—	2	4	no	—
41	C₂²×C₃²×C₄	—	2	4	no	—
42	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
44	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃²×C₄	C₂³	1	4	yes	—
47	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
48	C₃²×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₃²×C₂²⋊C₄	C₂×C₄	1	8	yes	—
50	C₃²×C₄²	C₂×C₄	1	2	yes	—
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₃×#208	—	2	16	no	—
53	C₂×C₃×C₃⋊C₈	—	2	4	no	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
56	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
59	C₂×#436	—	3	1	no	Sylow
60	C₂²×C₃×D₄	—	2	1	no	—
61	C₂²×C₃×D₄	Dic₃	1	1	yes	characteristic
62	C₂²×C₃×D₄	C₃×C₄	1	1	yes	characteristic
63	C₂³×C₃×C₄	—	2	2	no	—
64	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
65	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₃×M₁₆	—	3	8	no	—
67	C₂×C₃×M₁₆	—	6	8	no	—
68	C₂²×C₃×C₈	—	3	1	no	—
69	C₂²×C₃×C₈	—	3	2	no	—
70	C₂²×C₃×C₈	—	3	1	no	—
71	C₃×C₄×D₄	—	2	4	no	—
72	C₃×C₄×D₄	—	2	4	no	—
73	C₃×C₄×D₄	Dic₃	1	4	yes	—
74	C₃×C₄×D₄	C₃×C₄	1	4	yes	—
75	C₃×C₄×D₄	C₂×D₃	1	4	yes	—
76	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
77	C₂×C₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₃×C₄⋊C₄	Dic₃	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
80	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₃×C₂²⋊C₄	Dic₃	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₂×#208	—	2	8	no	—
87	C₂×#208	C₂²×C₃	1	8	yes	complemented
88	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
90	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
91	C₃×C₄⋊C₈	—	3	4	no	—
92	C₃×C₂²⋊C₈	—	3	8	no	—
93	C₃×C₄×C₈	—	3	4	no	—
94	#830	C₂²×C₃	1	8	yes	complemented
95	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
96	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
97	C₂³×C₃²	—	2	4	no	—
98	C₂³×C₃²	—	2	4	no	—
99	C₂³×C₃²	—	2	4	no	—
100	C₂³×C₃²	C₂²×C₄	1	4	yes	—
101	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
102	C₃²×D₄	—	2	8	no	—
103	C₂×C₃²×C₄	—	2	4	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	2	8	no	—
106	C₂×C₃²×C₄	—	2	4	no	—
107	C₂×C₃²×C₄	—	2	4	no	—
108	C₂×C₃²×C₄	M₁₆	1	4	yes	complemented
109	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
110	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
111	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
113	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
114	C₂×C₃²×C₄	#41	1	2	yes	—
115	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
116	C₃×C₃⋊C₈	—	2	4	no	—
117	C₃×C₃⋊C₈	—	2	2	no	—
118	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
119	C₂²×M₁₆	—	3	2	no	—
120	C₂×C₄×D₄	C₃×D₃	1	1	yes	characteristic
121	#436	—	3	8	no	—
122	C₂×C₄⋊C₈	—	3	1	no	—
123	C₂×C₂²⋊C₈	—	3	2	no	—
124	C₂×C₄×C₈	—	3	1	no	—
125	C₂⁴×C₃	—	2	2	no	—
126	C₂⁴×C₃	C₂×Dic₃	1	2	yes	—
127	C₂⁴×C₃	C₂×C₃×C₄	1	2	yes	—
128	C₂×C₃×D₄	—	2	8	no	—
129	C₂×C₃×D₄	—	2	4	no	—
130	C₂×C₃×D₄	—	2	4	no	—
131	C₂×C₃×D₄	—	2	4	no	—
132	C₂×C₃×D₄	C₂×Dic₃	1	4	yes	—
133	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
134	C₂²×C₃×C₄	—	2	4	no	—
135	C₂²×C₃×C₄	—	2	4	no	—
136	C₂²×C₃×C₄	—	2	4	no	—
137	C₂²×C₃×C₄	—	2	4	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	4	no	—
144	C₂²×C₃×C₄	—	4	4	no	—
145	C₂²×C₃×C₄	—	4	4	no	—
146	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
148	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
149	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
152	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
153	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₃×M₁₆	—	6	16	no	—
159	C₂×C₃×C₈	—	3	4	no	—
160	C₂×C₃×C₈	—	3	2	no	—
161	C₂×C₃×C₈	—	3	2	no	—
162	C₂×C₃×C₈	—	3	4	no	—
163	C₂×C₃×C₈	—	6	4	no	—
164	C₂×C₃×C₈	—	6	2	no	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
167	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
168	C₃×C₂²⋊C₄	—	2	8	no	—
169	C₃×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
170	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
171	C₃×C₄²	—	2	2	no	—
172	C₃×C₄²	—	2	2	no	—
173	C₃×C₄²	C₂×Dic₃	1	2	yes	—
174	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
175	C₃×C₄²	C₂²×D₃	1	2	yes	—
176	C₃×C₄²	C₂³×C₃	1	2	yes	—
177	#208	—	2	16	no	—
178	C₂×C₃⋊C₈	—	2	4	no	—
179	C₂×C₃⋊C₈	—	2	2	no	—
180	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
181	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
182	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
183	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
184	C₂²×C₃²	—	2	4	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	—	2	4	no	—
187	C₂²×C₃²	—	4	8	no	—
188	C₂²×C₃²	C₄×D₄	1	2	yes	—
189	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
190	C₂²×C₃²	#131	1	2	yes	—
191	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
192	C₃²×C₄	—	2	4	no	—
193	C₃²×C₄	—	2	2	no	—
194	C₃²×C₄	C₄×D₄	1	2	yes	—
195	C₃²×C₄	C₂×M₁₆	1	4	yes	complemented
196	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
197	C₃²×C₄	C₂×#41	1	1	yes	characteristic
198	C₂²×D₄	C₃×Dic₃	1	1	yes	characteristic
199	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
200	C₂×M₁₆	—	3	8	no	—
201	C₂×M₁₆	—	6	8	no	—
202	C₂²×C₈	—	3	1	no	—
203	C₂²×C₈	—	3	2	no	—
204	C₂²×C₈	—	3	1	no	—
205	C₄×D₄	C₃×Dic₃	1	4	yes	—
206	C₄×D₄	C₂×C₃×D₃	1	4	yes	—
207	C₂×C₄⋊C₄	C₃×Dic₃	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	C₃×Dic₃	1	2	yes	—
209	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
210	C₄⋊C₈	—	3	4	no	—
211	C₂²⋊C₈	—	3	8	no	—
212	C₄×C₈	—	3	4	no	—
213	C₂³×C₃	—	2	8	no	—
214	C₂³×C₃	—	2	4	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	4	4	no	—
223	C₂³×C₃	—	4	4	no	—
224	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
225	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
226	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
227	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₃×D₄	—	2	16	no	—
229	C₃×D₄	—	2	8	no	—
230	C₃×D₄	—	2	8	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	4	8	no	—
250	C₂×C₃×C₄	—	4	4	no	—
251	C₂×C₃×C₄	—	4	4	no	—
252	C₂×C₃×C₄	—	4	2	no	—
253	C₂×C₃×C₄	—	4	4	no	—
254	C₂×C₃×C₄	#208	1	4	yes	complemented
255	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	complemented
256	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
257	C₂×C₃×C₄	#237	1	2	yes	—
258	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
259	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
260	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
261	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₃×C₄	C₃×#41	1	2	yes	—
268	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
270	C₃×C₈	—	3	4	no	—
271	C₃×C₈	—	6	4	no	—
272	C₃×C₈	—	6	2	no	—
273	C₃⋊C₈	—	2	4	no	—
274	C₃⋊C₈	—	2	2	no	—
275	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	complemented
276	C₂×C₃²	—	4	4	no	—
277	C₂×C₃²	#436	1	4	yes	complemented
278	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
280	C₂×C₃²	C₂×#131	1	1	yes	characteristic
281	C₂⁴	C₂×C₃×Dic₃	1	2	yes	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	C₂×C₃×Dic₃	1	4	yes	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
288	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
289	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
291	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
292	M₁₆	—	6	16	no	—
293	C₂×C₈	—	3	2	no	—
294	C₂×C₈	—	3	4	no	—
295	C₂×C₈	—	3	2	no	—
296	C₂×C₈	—	3	4	no	—
297	C₂×C₈	—	6	4	no	—
298	C₂×C₈	—	6	2	no	—
299	C₄⋊C₄	C₂×C₃×Dic₃	1	4	yes	—
300	C₂²⋊C₄	C₂×C₃×Dic₃	1	8	yes	—
301	C₄²	C₂×C₃×Dic₃	1	2	yes	—
302	C₄²	C₂²×C₃×D₃	1	2	yes	—
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	4	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	—	4	4	no	—
316	C₂²×C₃	—	4	16	no	—
317	C₂²×C₃	—	4	8	no	—
318	C₂²×C₃	—	4	8	no	—
319	C₂²×C₃	C₂×#208	1	2	yes	—
320	C₂²×C₃	D₄×Dic₃	1	2	yes	—
321	C₂²×C₃	#948	1	2	yes	—
322	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
323	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
324	C₂²×C₃	C₃×#131	1	2	yes	—
325	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
326	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	4	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	4	4	no	—
336	C₃×C₄	—	4	2	no	—
337	C₃×C₄	C₂×#208	1	4	yes	complemented
338	C₃×C₄	D₄×Dic₃	1	2	yes	—
339	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
340	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	complemented
341	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
342	C₃×C₄	C₂×#237	1	1	yes	characteristic
343	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
345	C₃²	C₂×#436	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	4	no	—
349	C₂³	C₂²×C₃×Dic₃	1	4	yes	—
350	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
351	D₄	—	2	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	C₃×#208	1	4	yes	complemented
358	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
359	C₂×C₄	C₃×#237	1	2	yes	—
360	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
361	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
362	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
363	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
365	C₈	—	3	4	no	—
366	C₈	—	6	4	no	—
367	C₈	—	6	2	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	4	8	no	—
373	C₂×C₃	—	4	4	no	—
374	C₂×C₃	—	4	4	no	—
375	C₂×C₃	#5012	1	4	yes	direct product factor
376	C₂×C₃	C₃×#436	1	4	yes	complemented
377	C₂×C₃	C₂²×#208	1	1	yes	characteristic
378	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
379	C₂×C₃	C₂×#948	1	1	yes	characteristic
380	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
381	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
382	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	C₂×C₃×#208	1	2	yes	—
388	C₂²	C₃×D₄×Dic₃	1	2	yes	—
389	C₂²	C₃×#948	1	2	yes	—
390	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	2	no	—
393	C₄	C₂×C₃×#208	1	4	yes	complemented
394	C₄	C₃×D₄×Dic₃	1	2	yes	—
395	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
396	C₄	C₂×C₃×#237	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×#5012	1	1	yes	characteristic, direct product factor
399	C₃	C₂×C₃×#436	1	1	yes	characteristic, complemented
400	C₂	—	4	4	no	—
401	C₂	C₃×#5012	1	4	yes	direct product factor
402	C₂	C₂²×C₃×#208	1	1	yes	characteristic
403	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic
404	C₂	C₂×C₃×#948	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×D₄	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂²×C₃²×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₃
hypocenter	C₃	C₂×C₃×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#208	C₂	semidirect
3. C₂×C₃×#830	C₂	semidirect
4. C₃×#5012	C₂	direct (N × H)
5. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
8. C₂×#5012	C₃	direct (N × H)
17. C₂×C₃×#208	C₂²	semidirect
21. C₃×#830	C₂²	semidirect
22. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
23. C₃×C₄×C₃⋊C₈	C₂²	semidirect
28. C₂²×#208	C₂×C₃	semidirect
33. C₂×#830	C₂×C₃	semidirect
34. #5012	C₂×C₃	direct (N × H)
35. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
36. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
55. C₂×C₃×C₃⋊C₈	D₄	semidirect
87. C₂×#208	C₂²×C₃	semidirect
94. #830	C₂²×C₃	semidirect
95. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
96. C₄×C₃⋊C₈	C₂²×C₃	semidirect
108. C₂×C₃²×C₄	M₁₆	semidirect
118. C₃×C₃⋊C₈	C₂×D₄	semidirect
180. C₂×C₃⋊C₈	C₃×D₄	semidirect
195. C₃²×C₄	C₂×M₁₆	semidirect
254. C₂×C₃×C₄	#208	semidirect
255. C₂×C₃×C₄	C₃×M₁₆	semidirect
275. C₃⋊C₈	C₂×C₃×D₄	semidirect
277. C₂×C₃²	#436	semidirect
337. C₃×C₄	C₂×#208	semidirect
340. C₃×C₄	C₂×C₃×M₁₆	semidirect
345. C₃²	C₂×#436	semidirect
357. C₂×C₄	C₃×#208	semidirect
375. C₂×C₃	#5012	direct (N × H)
376. C₂×C₃	C₃×#436	semidirect
393. C₄	C₂×C₃×#208	semidirect
398. C₃	C₂×#5012	direct (N × H)
399. C₃	C₂×C₃×#436	semidirect
401. C₂	C₃×#5012	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×D₄	2
C₂²×C₃×#208	2
C₂×C₃×#830	2
C₃×#5012	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×C₃×#436	3
C₂×#5012	3

Subgroups — C2×C3×#5012 #11859267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5012 #11859267