Subgroups — C₂×C₃×#4554 #11783391

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic
4	C₃×#4554	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#343	—	3	1	no	maximal
6	C₂×#4554	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₂³×C₃×Dic₃	C₄	1	2	yes	—
9	C₂×C₃²×M₁₆	—	2	2	no	—
10	C₂×C₃²×M₁₆	—	2	1	no	—
11	C₂×C₃²×M₁₆	C₄	1	4	yes	complemented
12	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₃²×C₈	—	2	1	no	—
14	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
15	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₃×C₄⋊Dic₃	C₄	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₃×#208	—	2	2	no	—
21	C₂×C₃×#208	—	2	1	no	—
22	C₂×C₃×#208	C₄	1	4	yes	complemented
23	C₂×C₃×#208	C₂²	1	2	yes	—
24	C₂²×C₃×C₃⋊C₈	—	2	1	no	—
25	C₂²×C₃×M₁₆	—	2	1	no	—
26	C₂²×C₃×M₁₆	—	3	1	no	—
27	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic
28	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
29	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
30	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
31	C₂²×#208	C₂×C₃	1	1	yes	characteristic
32	C₃×#343	—	3	4	no	—
33	#4554	C₂×C₃	1	4	yes	direct product factor
34	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
37	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
38	C₂²×C₃²×C₄	D₄	1	2	yes	—
39	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
42	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	Q₈	1	2	yes	—
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	—	2	2	no	—
46	C₂²×C₃×Dic₃	—	2	2	no	—
47	C₂²×C₃×Dic₃	—	4	4	no	—
48	C₂²×C₃×Dic₃	C₂×C₄	1	4	yes	—
49	C₃²×M₁₆	—	2	4	no	—
50	C₃²×M₁₆	—	2	2	no	—
51	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
52	C₂×C₃²×C₈	—	2	4	no	—
53	C₂×C₃²×C₈	—	2	2	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄⋊Dic₃	—	2	2	no	—
56	C₃×C₄⋊Dic₃	—	2	2	no	—
57	C₃×C₄⋊Dic₃	—	2	2	no	—
58	C₃×#208	—	2	4	no	—
59	C₃×#208	—	2	2	no	—
60	C₃×#208	C₂×C₄	1	4	yes	complemented
61	C₂×C₃×C₃⋊C₈	—	2	4	no	—
62	C₂×C₃×C₃⋊C₈	—	2	2	no	—
63	C₂×#343	—	3	1	no	Sylow
64	C₂³×C₃×C₄	—	2	1	no	—
65	C₂³×C₃×C₄	—	3	2	no	—
66	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
67	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂³×Dic₃	C₃×C₄	1	2	yes	—
69	C₂×C₃×M₁₆	—	2	4	no	—
70	C₂×C₃×M₁₆	—	2	2	no	—
71	C₂×C₃×M₁₆	—	2	2	no	—
72	C₂×C₃×M₁₆	—	2	1	no	—
73	C₂×C₃×M₁₆	—	2	2	no	—
74	C₂×C₃×M₁₆	—	2	1	no	—
75	C₂×C₃×M₁₆	—	2	4	no	—
76	C₂×C₃×M₁₆	—	2	2	no	—
77	C₂×C₃×M₁₆	—	3	4	no	—
78	C₂×C₃×M₁₆	—	3	2	no	—
79	C₂×C₃×M₁₆	—	6	1	no	—
80	C₂×C₃×M₁₆	—	6	2	no	—
81	C₂×C₃×M₁₆	Dic₃	1	4	yes	complemented
82	C₂×C₃×M₁₆	C₃×C₄	1	4	yes	complemented
83	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
84	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
85	C₂²×C₃×C₈	—	2	2	no	—
86	C₂²×C₃×C₈	—	2	1	no	—
87	C₂²×C₃×C₈	—	2	1	no	—
88	C₂²×C₃×C₈	—	6	1	no	—
89	C₂×C₃×C₄⋊C₄	—	3	2	no	—
90	C₂×C₃×C₄⋊C₄	—	3	2	no	—
91	C₂×C₃×C₄⋊C₄	—	6	1	no	—
92	C₂×C₃×C₄⋊C₄	—	6	1	no	—
93	C₂×C₃×C₄⋊C₄	—	6	1	no	—
94	C₂×C₃×C₄⋊C₄	—	6	1	no	—
95	C₂×C₄⋊Dic₃	—	2	1	no	—
96	C₂×C₄⋊Dic₃	—	2	1	no	—
97	C₂×C₄⋊Dic₃	—	2	1	no	—
98	C₂×C₄⋊Dic₃	—	2	1	no	—
99	C₂×C₄⋊Dic₃	C₃×C₄	1	2	yes	—
100	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
101	C₂×#208	—	2	1	no	—
102	C₂×#208	—	2	2	no	—
103	C₂×#208	C₃×C₄	1	4	yes	complemented
104	C₂×#208	C₂²×C₃	1	2	yes	—
105	C₂²×C₃⋊C₈	—	2	1	no	—
106	C₂³×C₃²	—	2	2	no	—
107	C₂³×C₃²	—	2	2	no	—
108	C₂³×C₃²	C₄²	1	2	yes	—
109	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
111	C₂³×C₃²	C₄⋊C₄	1	2	yes	—
112	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₄²	1	2	yes	—
114	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
117	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
118	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
119	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
120	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
121	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
122	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
123	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
124	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
125	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
131	C₂×C₃×Dic₃	—	2	4	no	—
132	C₂×C₃×Dic₃	—	4	4	no	—
133	C₂×C₃×Dic₃	—	4	4	no	—
134	C₂×C₃×Dic₃	—	4	4	no	—
135	C₃²×C₈	—	2	4	no	—
136	C₃×C₃⋊C₈	—	2	4	no	—
137	C₂²×M₁₆	—	3	1	no	—
138	C₂²×M₁₆	C₃×D₃	1	1	yes	characteristic
139	C₂²×C₄⋊C₄	—	3	1	no	—
140	#343	—	3	4	no	—
141	C₂⁴×C₃	—	2	1	no	—
142	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
143	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	2	1	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	3	4	no	—
155	C₂²×C₃×C₄	—	6	2	no	—
156	C₂²×C₃×C₄	—	6	2	no	—
157	C₂²×C₃×C₄	—	12	4	no	—
158	C₂²×C₃×C₄	Dic₆	1	2	yes	—
159	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
161	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
162	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
164	C₂²×C₃×C₄	#67	1	1	yes	characteristic
165	C₂²×C₃×C₄	#67	1	1	yes	characteristic
166	C₂²×C₃×C₄	#67	1	2	yes	—
167	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
169	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
170	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
173	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₃×Q₈	1	2	yes	—
176	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×Dic₃	—	2	2	no	—
179	C₂²×Dic₃	—	2	2	no	—
180	C₂²×Dic₃	—	4	4	no	—
181	C₂²×Dic₃	C₂×C₃×C₄	1	4	yes	—
182	C₃×M₁₆	—	2	8	no	—
183	C₃×M₁₆	—	2	4	no	—
184	C₃×M₁₆	—	2	4	no	—
185	C₃×M₁₆	—	2	4	no	—
186	C₃×M₁₆	—	2	2	no	—
187	C₃×M₁₆	—	2	2	no	—
188	C₃×M₁₆	—	2	4	no	—
189	C₃×M₁₆	—	3	4	no	—
190	C₃×M₁₆	—	6	4	no	—
191	C₃×M₁₆	—	6	2	no	—
192	C₃×M₁₆	C₂×Dic₃	1	4	yes	complemented
193	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
194	C₂×C₃×C₈	—	2	8	no	—
195	C₂×C₃×C₈	—	2	4	no	—
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	—	2	4	no	—
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	2	2	no	—
200	C₂×C₃×C₈	—	6	4	no	—
201	C₂×C₃×C₈	—	6	2	no	—
202	C₃×C₄⋊C₄	—	6	2	no	—
203	C₃×C₄⋊C₄	—	6	2	no	—
204	C₃×C₄⋊C₄	—	6	2	no	—
205	C₃×C₄⋊C₄	—	6	2	no	—
206	C₄⋊Dic₃	—	2	2	no	—
207	C₄⋊Dic₃	—	2	2	no	—
208	C₄⋊Dic₃	—	2	2	no	—
209	C₄⋊Dic₃	—	2	2	no	—
210	#208	—	2	4	no	—
211	#208	—	2	2	no	—
212	#208	C₂×C₃×C₄	1	4	yes	complemented
213	C₂×C₃⋊C₈	—	2	4	no	—
214	C₂×C₃⋊C₈	—	2	2	no	—
215	C₂²×C₃²	—	2	4	no	—
216	C₂²×C₃²	—	2	4	no	—
217	C₂²×C₃²	—	2	1	no	—
218	C₂²×C₃²	—	2	1	no	—
219	C₂²×C₃²	—	2	1	no	—
220	C₂²×C₃²	—	2	1	no	—
221	C₂²×C₃²	#95	1	2	yes	—
222	C₂²×C₃²	#95	1	2	yes	—
223	C₂²×C₃²	#100	1	2	yes	—
224	C₂²×C₃²	#101	1	2	yes	—
225	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
226	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₃²×C₄	#95	1	2	yes	—
229	C₃²×C₄	#95	1	2	yes	—
230	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₃×Dic₃	—	4	4	no	—
235	C₂³×C₄	—	3	2	no	—
236	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	3	4	no	—
240	C₂×M₁₆	—	3	2	no	—
241	C₂×M₁₆	—	6	1	no	—
242	C₂×M₁₆	—	6	2	no	—
243	C₂×M₁₆	C₃×Dic₃	1	4	yes	complemented
244	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	6	1	no	—
247	C₂×C₄⋊C₄	—	3	2	no	—
248	C₂×C₄⋊C₄	—	3	2	no	—
249	C₂×C₄⋊C₄	—	6	1	no	—
250	C₂×C₄⋊C₄	—	6	1	no	—
251	C₂×C₄⋊C₄	—	6	1	no	—
252	C₂×C₄⋊C₄	—	6	1	no	—
253	C₂³×C₃	—	2	2	no	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	1	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	4	2	no	—
263	C₂³×C₃	—	4	2	no	—
264	C₂³×C₃	C₄×Dic₃	1	2	yes	—
265	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
266	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
267	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
268	C₂³×C₃	C₃×C₄²	1	2	yes	—
269	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
271	C₂³×C₃	C₃×C₄⋊C₄	1	2	yes	—
272	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	6	4	no	—
293	C₂×C₃×C₄	—	12	4	no	—
294	C₂×C₃×C₄	—	12	4	no	—
295	C₂×C₃×C₄	—	12	4	no	—
296	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
297	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
298	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
299	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
300	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
301	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
302	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
303	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
304	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
305	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
306	C₂×C₃×C₄	#217	1	2	yes	—
307	C₂×C₃×C₄	#217	1	2	yes	—
308	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
309	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
312	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
313	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
314	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
315	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
316	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
317	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
318	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
319	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
320	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
332	C₂×Dic₃	—	2	4	no	—
333	C₂×Dic₃	—	4	4	no	—
334	C₂×Dic₃	—	4	4	no	—
335	C₂×Dic₃	—	4	4	no	—
336	C₃×C₈	—	2	8	no	—
337	C₃×C₈	—	2	4	no	—
338	C₃×C₈	—	2	4	no	—
339	C₃×C₈	—	6	4	no	—
340	C₃⋊C₈	—	2	4	no	—
341	C₂×C₃²	—	2	2	no	—
342	C₂×C₃²	—	2	1	no	—
343	C₂×C₃²	—	2	1	no	—
344	C₂×C₃²	#343	1	4	yes	complemented
345	C₂×C₃²	C₂×#95	1	1	yes	characteristic
346	C₂×C₃²	C₂×#100	1	1	yes	characteristic
347	C₂×C₃²	C₂×#101	1	1	yes	characteristic
348	C₂⁴	C₃×C₄×D₃	1	1	yes	characteristic
349	C₂²×C₄	—	3	4	no	—
350	C₂²×C₄	—	6	2	no	—
351	C₂²×C₄	—	6	2	no	—
352	C₂²×C₄	—	12	4	no	—
353	C₂²×C₄	C₃×Dic₆	1	2	yes	—
354	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
355	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
356	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
357	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
359	C₂²×C₄	C₃×#67	1	1	yes	characteristic
360	C₂²×C₄	C₃×#67	1	1	yes	characteristic
361	C₂²×C₄	C₃×#67	1	2	yes	—
362	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	3	4	no	—
366	M₁₆	—	6	4	no	—
367	M₁₆	—	6	2	no	—
368	M₁₆	C₂×C₃×Dic₃	1	4	yes	complemented
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	6	4	no	—
372	C₂×C₈	—	6	2	no	—
373	C₄⋊C₄	—	6	2	no	—
374	C₄⋊C₄	—	6	2	no	—
375	C₄⋊C₄	—	6	2	no	—
376	C₄⋊C₄	—	6	2	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	4	no	—
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	—	2	4	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	2	no	—
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	2	no	—
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	4	4	no	—
398	C₂²×C₃	—	4	1	no	—
399	C₂²×C₃	—	4	1	no	—
400	C₂²×C₃	—	4	1	no	—
401	C₂²×C₃	—	4	1	no	—
402	C₂²×C₃	#823	1	2	yes	—
403	C₂²×C₃	#824	1	2	yes	—
404	C₂²×C₃	C₃⋊#95	1	2	yes	—
405	C₂²×C₃	C₃⋊#95	1	2	yes	—
406	C₂²×C₃	C₃×#95	1	2	yes	—
407	C₂²×C₃	C₃×#95	1	2	yes	—
408	C₂²×C₃	C₃×#100	1	2	yes	—
409	C₂²×C₃	C₃×#101	1	2	yes	—
410	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
411	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
412	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
413	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
414	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	1	no	—
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	12	4	no	—
423	C₃×C₄	C₃⋊#95	1	2	yes	—
424	C₃×C₄	C₃⋊#95	1	2	yes	—
425	C₃×C₄	C₃×#95	1	2	yes	—
426	C₃×C₄	C₃×#95	1	2	yes	—
427	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
428	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
429	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
430	C₃×C₄	C₂×#217	1	1	yes	characteristic
431	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
433	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
434	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
435	Dic₃	—	4	4	no	—
436	C₃²	C₂×#343	1	1	yes	characteristic, complemented, Sylow
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₃×C₄×Dic₃	1	2	yes	—
440	C₂³	C₃×Dic₃⋊C₄	1	2	yes	—
441	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
442	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
443	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
444	C₂×C₄	—	6	4	no	—
445	C₂×C₄	—	12	4	no	—
446	C₂×C₄	—	12	4	no	—
447	C₂×C₄	—	12	4	no	—
448	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
449	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
450	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
451	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
452	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
453	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
454	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
455	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
456	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₃×#217	1	2	yes	—
459	C₂×C₄	C₃×#217	1	2	yes	—
460	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
461	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
462	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
464	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
465	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	6	4	no	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	2	2	no	—
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	2	1	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	2	4	no	—
476	C₂×C₃	—	2	1	no	—
477	C₂×C₃	—	2	1	no	—
478	C₂×C₃	—	4	1	no	—
479	C₂×C₃	—	4	1	no	—
480	C₂×C₃	—	4	2	no	—
481	C₂×C₃	#4554	1	4	yes	direct product factor
482	C₂×C₃	C₃×#343	1	4	yes	complemented
483	C₂×C₃	C₂×#823	1	1	yes	characteristic
484	C₂×C₃	C₂×#824	1	1	yes	characteristic
485	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
486	C₂×C₃	C₂×C₃×#95	1	1	yes	characteristic
487	C₂×C₃	C₂×C₃×#100	1	1	yes	characteristic
488	C₂×C₃	C₂×C₃×#101	1	1	yes	characteristic
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	C₃×#823	1	2	yes	—
496	C₂²	C₃×#824	1	2	yes	—
497	C₂²	C₃×C₃⋊#95	1	2	yes	—
498	C₂²	C₃×C₃⋊#95	1	2	yes	—
499	C₂²	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
500	C₂²	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
501	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
502	C₄	—	12	4	no	—
503	C₄	C₃×C₃⋊#95	1	2	yes	—
504	C₄	C₃×C₃⋊#95	1	2	yes	—
505	C₄	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
506	C₄	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
507	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
508	C₄	C₂×C₃×#217	1	1	yes	characteristic
509	C₃	—	2	1	no	—
510	C₃	C₂×#4554	1	1	yes	characteristic, direct product factor
511	C₃	C₂×C₃×#343	1	1	yes	characteristic, complemented
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	2	no	—
515	C₂	C₃×#4554	1	4	yes	direct product factor
516	C₂	C₂×C₃×#823	1	1	yes	characteristic
517	C₂	C₂×C₃×#824	1	1	yes	characteristic
518	C₂	C₂×C₃×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂²×C₃²×M₁₆	C₂
socle	C₂³×C₃²	C₂²⋊C₄
prime radical	C₂⁴×C₃²	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂²×C₃×M₁₆	D₃
hypocenter	C₃	C₂×C₃×#343
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#4554	C₂	direct (N × H)
6. C₂×#4554	C₃	direct (N × H)
11. C₂×C₃²×M₁₆	C₄	semidirect
22. C₂×C₃×#208	C₄	semidirect
33. #4554	C₂×C₃	direct (N × H)
51. C₃²×M₁₆	C₂×C₄	semidirect
60. C₃×#208	C₂×C₄	semidirect
81. C₂×C₃×M₁₆	Dic₃	semidirect
82. C₂×C₃×M₁₆	C₃×C₄	semidirect
103. C₂×#208	C₃×C₄	semidirect
192. C₃×M₁₆	C₂×Dic₃	semidirect
193. C₃×M₁₆	C₂×C₃×C₄	semidirect
212. #208	C₂×C₃×C₄	semidirect
243. C₂×M₁₆	C₃×Dic₃	semidirect
344. C₂×C₃²	#343	semidirect
368. M₁₆	C₂×C₃×Dic₃	semidirect
436. C₃²	C₂×#343	semidirect
481. C₂×C₃	#4554	direct (N × H)
482. C₂×C₃	C₃×#343	semidirect
510. C₃	C₂×#4554	direct (N × H)
511. C₃	C₂×C₃×#343	semidirect
515. C₂	C₃×#4554	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×C₃²×M₁₆	2
C₂²×C₃×C₄⋊Dic₃	2
C₂²×C₃×#208	2
C₃×#4554	2
C₂×C₃×#343	3
C₂×#4554	3

Subgroups — C2×C3×#4554 #11783391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4554 #11783391