Subgroups — C₂×C₃×#4523 #11783172

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic
4	C₃×#4523	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#339	—	3	1	no	maximal
6	C₂×#4523	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²×C₄	—	2	1	no	—
8	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃²×C₄²	—	2	1	no	—
10	C₂×C₃²×C₄²	—	2	2	no	—
11	C₂×C₃²×C₄²	C₄	1	4	yes	complemented
12	C₂×C₃²×C₄²	C₂²	1	2	yes	—
13	C₂×C₃×#217	—	2	1	no	—
14	C₃×#926	—	2	1	no	—
15	C₃×#926	—	2	1	no	—
16	C₃×#926	C₄	1	2	yes	complemented
17	C₃×#926	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₃	C₄	1	2	yes	complemented
19	C₂×C₃×C₄×Dic₃	—	2	1	no	—
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	—	3	1	no	—
26	C₂×C₃×#117	—	3	1	no	—
27	C₂²×C₃×C₄²	—	2	1	no	—
28	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
29	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
30	C₂×#926	C₂×C₃	1	1	yes	characteristic
31	C₂²×#208	C₂×C₃	1	1	yes	characteristic
32	C₃×#339	—	3	4	no	—
33	#4523	C₂×C₃	1	4	yes	direct product factor
34	C₂⁴×C₃²	D₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	—	2	8	no	—
36	C₂²×C₃²×C₄	—	2	4	no	—
37	C₂²×C₃²×C₄	—	2	2	no	—
38	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
42	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	D₄	1	2	yes	—
46	C₂²×C₃²×C₄	Q₈	1	2	yes	—
47	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₃	—	2	2	no	—
49	C₃²×C₄²	—	2	4	no	—
50	C₃²×C₄²	—	2	2	no	—
51	C₃²×C₄²	C₂×C₄	1	4	yes	complemented
52	C₃×#217	—	2	2	no	—
53	C₃×#217	—	2	2	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
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×#339	—	3	1	no	Sylow
64	C₂³×C₃×C₄	—	2	2	no	—
65	C₂³×C₃×C₄	—	2	1	no	—
66	C₂³×C₃×C₄	—	2	1	no	—
67	C₂³×C₃×C₄	—	2	1	no	—
68	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
69	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×M₁₆	—	3	4	no	—
71	C₂×C₃×M₁₆	—	3	2	no	—
72	C₂×C₃×M₁₆	—	6	1	no	—
73	C₂×C₃×M₁₆	—	6	2	no	—
74	C₂²×C₃×C₈	—	6	1	no	—
75	C₃×#117	—	3	2	no	—
76	C₃×#117	—	3	2	no	—
77	C₃×#117	—	6	1	no	—
78	C₃×#117	—	6	1	no	—
79	C₂×C₃×C₄⋊C₄	—	3	2	no	—
80	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
81	C₂×C₃×C₄²	—	2	2	no	—
82	C₂×C₃×C₄²	—	2	4	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	—	2	2	no	—
85	C₂×C₃×C₄²	—	2	1	no	—
86	C₂×C₃×C₄²	—	2	2	no	—
87	C₂×C₃×C₄²	—	2	4	no	—
88	C₂×C₃×C₄²	—	2	2	no	—
89	C₂×C₃×C₄²	—	6	1	no	—
90	C₂×C₃×C₄²	Dic₃	1	4	yes	complemented
91	C₂×C₃×C₄²	C₃×C₄	1	4	yes	complemented
92	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
93	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
94	C₂×#217	—	2	1	no	—
95	#926	—	2	1	no	—
96	#926	—	2	1	no	—
97	#926	C₃×C₄	1	2	yes	complemented
98	#926	C₂²×C₃	1	2	yes	—
99	C₂×C₄⋊Dic₃	C₃×C₄	1	2	yes	complemented
100	C₂×C₄×Dic₃	—	2	1	no	—
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	4	no	—
107	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×C₃²	C₂²⋊C₄	1	2	yes	—
110	C₂³×C₃²	C₄⋊C₄	1	2	yes	—
111	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	—	2	16	no	—
113	C₂×C₃²×C₄	—	2	8	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	C₄²	1	2	yes	—
116	C₂×C₃²×C₄	C₄²	1	2	yes	—
117	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
120	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
121	C₂×C₃²×C₄	C₂²⋊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	C₄⋊C₄	1	2	yes	—
126	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
127	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
133	C₂×C₃×Dic₃	—	2	4	no	—
134	C₂×C₃×Dic₃	—	4	4	no	—
135	C₃×C₃⋊C₈	—	2	4	no	—
136	C₂²×M₁₆	—	3	1	no	—
137	C₂×#117	—	3	1	no	—
138	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic
139	#339	—	3	4	no	—
140	C₂⁴×C₃	—	2	1	no	—
141	C₂⁴×C₃	#67	1	1	yes	characteristic
142	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	—	2	8	no	—
144	C₂²×C₃×C₄	—	2	4	no	—
145	C₂²×C₃×C₄	—	2	16	no	—
146	C₂²×C₃×C₄	—	2	8	no	—
147	C₂²×C₃×C₄	—	2	8	no	—
148	C₂²×C₃×C₄	—	2	4	no	—
149	C₂²×C₃×C₄	—	2	4	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	2	1	no	—
157	C₂²×C₃×C₄	—	2	1	no	—
158	C₂²×C₃×C₄	—	2	2	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	2	2	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	6	2	no	—
163	C₂²×C₃×C₄	Dic₆	1	2	yes	—
164	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
167	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
168	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
170	C₂²×C₃×C₄	#67	1	1	yes	characteristic
171	C₂²×C₃×C₄	#67	1	2	yes	—
172	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
173	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
176	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
180	C₂²×C₃×C₄	C₃×Q₈	1	2	yes	—
181	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×Dic₃	—	2	2	no	—
184	C₃×M₁₆	—	3	4	no	—
185	C₃×M₁₆	—	6	4	no	—
186	C₃×M₁₆	—	6	2	no	—
187	C₂×C₃×C₈	—	6	4	no	—
188	C₂×C₃×C₈	—	6	2	no	—
189	C₃×C₄⋊C₄	—	3	4	no	—
190	C₃×C₄⋊C₄	—	6	2	no	—
191	C₃×C₂²⋊C₄	—	6	2	no	—
192	C₃×C₂²⋊C₄	—	6	2	no	—
193	C₃×C₄²	—	2	8	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	—	2	4	no	—
197	C₃×C₄²	—	2	2	no	—
198	C₃×C₄²	—	2	2	no	—
199	C₃×C₄²	—	2	4	no	—
200	C₃×C₄²	—	6	2	no	—
201	C₃×C₄²	—	6	2	no	—
202	C₃×C₄²	C₂×Dic₃	1	4	yes	complemented
203	C₃×C₄²	C₂×C₃×C₄	1	4	yes	complemented
204	#217	—	2	2	no	—
205	#217	—	2	2	no	—
206	C₄⋊Dic₃	—	2	2	no	—
207	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	complemented
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	2	no	—
218	C₂²×C₃²	—	2	2	no	—
219	C₂²×C₃²	#95	1	2	yes	—
220	C₂²×C₃²	#95	1	2	yes	—
221	C₂²×C₃²	#104	1	4	yes	—
222	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₃²×C₄	—	2	8	no	—
226	C₃²×C₄	#95	1	2	yes	—
227	C₃²×C₄	#95	1	2	yes	—
228	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
229	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₃×Dic₃	—	4	4	no	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
235	C₂×M₁₆	—	3	4	no	—
236	C₂×M₁₆	—	3	2	no	—
237	C₂×M₁₆	—	6	1	no	—
238	C₂×M₁₆	—	6	2	no	—
239	C₂²×C₈	—	6	1	no	—
240	#117	—	3	2	no	—
241	#117	—	3	2	no	—
242	#117	—	6	1	no	—
243	#117	—	6	1	no	—
244	C₂×C₄⋊C₄	—	3	2	no	—
245	C₂×C₂²⋊C₄	—	6	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	6	1	no	—
249	C₂×C₄²	C₃×Dic₃	1	4	yes	complemented
250	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
251	C₂³×C₃	—	2	8	no	—
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
260	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
261	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
262	C₂³×C₃	#217	1	2	yes	—
263	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
264	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
265	C₂³×C₃	C₃×C₂²⋊C₄	1	2	yes	—
266	C₂³×C₃	C₃×C₄⋊C₄	1	2	yes	—
267	C₂³×C₃	C₂×#67	1	1	yes	characteristic
268	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	—	2	8	no	—
270	C₂×C₃×C₄	—	2	16	no	—
271	C₂×C₃×C₄	—	2	32	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	16	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	16	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	4	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	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	6	4	no	—
297	C₂×C₃×C₄	—	12	4	no	—
298	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
299	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
300	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
301	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
302	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
303	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
304	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
305	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
306	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
307	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
308	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
309	C₂×C₃×C₄	#217	1	2	yes	—
310	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
311	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
312	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
315	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
316	C₂×C₃×C₄	C₃×C₂²⋊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	C₃×C₄⋊C₄	1	2	yes	—
321	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
334	C₂×Dic₃	—	2	4	no	—
335	C₂×Dic₃	—	4	4	no	—
336	C₃×C₈	—	6	4	no	—
337	C₃⋊C₈	—	2	4	no	—
338	C₂×C₃²	—	2	1	no	—
339	C₂×C₃²	—	2	2	no	—
340	C₂×C₃²	—	2	1	no	—
341	C₂×C₃²	#339	1	4	yes	complemented
342	C₂×C₃²	C₂×#95	1	1	yes	characteristic
343	C₂×C₃²	C₂×#104	1	2	yes	—
344	C₂⁴	C₃×#67	1	1	yes	characteristic
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	6	2	no	—
349	C₂²×C₄	C₃×Dic₆	1	2	yes	—
350	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
351	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
352	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
353	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
354	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
356	C₂²×C₄	C₃×#67	1	1	yes	characteristic
357	C₂²×C₄	C₃×#67	1	2	yes	—
358	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
359	M₁₆	—	3	4	no	—
360	M₁₆	—	6	4	no	—
361	M₁₆	—	6	2	no	—
362	C₂×C₈	—	6	4	no	—
363	C₂×C₈	—	6	2	no	—
364	C₄⋊C₄	—	3	4	no	—
365	C₄⋊C₄	—	6	2	no	—
366	C₂²⋊C₄	—	6	2	no	—
367	C₂²⋊C₄	—	6	2	no	—
368	C₄²	—	2	4	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	6	2	no	—
371	C₄²	—	6	2	no	—
372	C₄²	C₂×C₃×Dic₃	1	4	yes	complemented
373	C₂²×C₃	—	2	4	no	—
374	C₂²×C₃	—	2	8	no	—
375	C₂²×C₃	—	2	4	no	—
376	C₂²×C₃	—	2	8	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	#805	1	4	yes	—
392	C₂²×C₃	C₃⋊#95	1	2	yes	—
393	C₂²×C₃	C₃⋊#95	1	2	yes	—
394	C₂²×C₃	C₃×#95	1	2	yes	—
395	C₂²×C₃	C₃×#95	1	2	yes	—
396	C₂²×C₃	C₃×#104	1	4	yes	—
397	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
398	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
399	C₂²×C₃	C₂×#217	1	1	yes	characteristic
400	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
401	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
402	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
403	C₃×C₄	—	2	16	no	—
404	C₃×C₄	—	2	8	no	—
405	C₃×C₄	—	2	8	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	12	4	no	—
413	C₃×C₄	C₃⋊#95	1	2	yes	—
414	C₃×C₄	C₃⋊#95	1	2	yes	—
415	C₃×C₄	C₃×#95	1	2	yes	—
416	C₃×C₄	C₃×#95	1	2	yes	—
417	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
418	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
419	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
420	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
421	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
422	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
423	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
424	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
425	Dic₃	—	4	4	no	—
426	C₃²	C₂×#339	1	1	yes	characteristic, complemented, Sylow
427	C₂³	—	2	4	no	—
428	C₂³	C₃×Dic₃⋊C₄	1	2	yes	—
429	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
430	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
431	C₂³	C₃×#217	1	2	yes	—
432	C₂³	C₂×C₃×#67	1	1	yes	characteristic
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	16	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	6	4	no	—
437	C₂×C₄	—	12	4	no	—
438	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
439	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
440	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
441	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
442	C₂×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
443	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
444	C₂×C₄	C₃×C₄⋊Dic₃	1	2	yes	—
445	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
446	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
447	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
448	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₃×#217	1	2	yes	—
450	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
456	C₈	—	6	4	no	—
457	C₂×C₃	—	2	2	no	—
458	C₂×C₃	—	2	2	no	—
459	C₂×C₃	—	2	4	no	—
460	C₂×C₃	—	2	1	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	1	no	—
463	C₂×C₃	—	2	1	no	—
464	C₂×C₃	—	2	2	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	2	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	4	no	—
469	C₂×C₃	#4523	1	4	yes	direct product factor
470	C₂×C₃	C₃×#339	1	4	yes	complemented
471	C₂×C₃	C₂×#805	1	2	yes	—
472	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
473	C₂×C₃	C₂×C₃×#95	1	1	yes	characteristic
474	C₂×C₃	C₂×C₃×#104	1	2	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	C₃×#805	1	4	yes	—
480	C₂²	C₃×C₃⋊#95	1	2	yes	—
481	C₂²	C₃×C₃⋊#95	1	2	yes	—
482	C₂²	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
483	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
484	C₂²	C₂×C₃×#217	1	1	yes	characteristic
485	C₄	—	2	8	no	—
486	C₄	—	12	4	no	—
487	C₄	C₃×C₃⋊#95	1	2	yes	—
488	C₄	C₃×C₃⋊#95	1	2	yes	—
489	C₄	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
490	C₄	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
491	C₄	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
492	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
493	C₃	—	2	1	no	—
494	C₃	C₂×#4523	1	1	yes	characteristic, direct product factor
495	C₃	C₂×C₃×#339	1	1	yes	characteristic, complemented
496	C₂	—	2	1	no	—
497	C₂	—	2	1	no	—
498	C₂	—	2	2	no	—
499	C₂	C₃×#4523	1	4	yes	direct product factor
500	C₂	C₂×C₃×#805	1	2	yes	—
501	C₂	C₂×C₃×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	D₁₂
commutator	C₃×C₄	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₄²	C₂
socle	C₂³×C₃²	C₂²⋊C₄
prime radical	C₂⁴×C₃²	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×#339
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. C₃×#4523	C₂	direct (N × H)
6. C₂×#4523	C₃	direct (N × H)
11. C₂×C₃²×C₄²	C₄	semidirect
16. C₃×#926	C₄	semidirect
18. C₂×C₃×C₄⋊Dic₃	C₄	semidirect
22. C₂×C₃×#208	C₄	semidirect
33. #4523	C₂×C₃	direct (N × H)
51. C₃²×C₄²	C₂×C₄	semidirect
55. C₃×C₄⋊Dic₃	C₂×C₄	semidirect
60. C₃×#208	C₂×C₄	semidirect
90. C₂×C₃×C₄²	Dic₃	semidirect
91. C₂×C₃×C₄²	C₃×C₄	semidirect
97. #926	C₃×C₄	semidirect
99. C₂×C₄⋊Dic₃	C₃×C₄	semidirect
103. C₂×#208	C₃×C₄	semidirect
202. C₃×C₄²	C₂×Dic₃	semidirect
203. C₃×C₄²	C₂×C₃×C₄	semidirect
207. C₄⋊Dic₃	C₂×C₃×C₄	semidirect
212. #208	C₂×C₃×C₄	semidirect
249. C₂×C₄²	C₃×Dic₃	semidirect
341. C₂×C₃²	#339	semidirect
372. C₄²	C₂×C₃×Dic₃	semidirect
426. C₃²	C₂×#339	semidirect
469. C₂×C₃	#4523	direct (N × H)
470. C₂×C₃	C₃×#339	semidirect
494. C₃	C₂×#4523	direct (N × H)
495. C₃	C₂×C₃×#339	semidirect
499. C₂	C₃×#4523	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×C₄²	2
C₂×C₃×#926	2
C₂²×C₃×#208	2
C₃×#4523	2
C₂×C₃×#339	3
C₂×#4523	3

Subgroups — C2×C3×#4523 #11783172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4523 #11783172