Subgroups — C₃×#60126 #10678733

Order 768.

2042 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3428	C₂	1	1	yes	maximal, characteristic
2	C₃×#2925	C₂	1	8	yes	maximal, complemented
3	C₃×#2924	C₂	1	8	yes	maximal, complemented
4	C₃×#2923	C₂	1	4	yes	maximal, complemented
5	C₃×#2922	C₂	1	4	yes	maximal, complemented
6	C₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2879	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic
10	C₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	#60126	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
18	C₃×#520	C₄	1	4	yes	—
19	C₃×#520	C₄	1	4	yes	—
20	C₃×#519	C₄	1	2	yes	—
21	C₃×#518	C₄	1	2	yes	—
22	C₃×#518	C₄	1	4	yes	—
23	C₃×C₄×#41	C₂²	1	4	yes	—
24	C₃×C₄×#41	C₂²	1	4	yes	—
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃×#117	C₂²	1	4	yes	—
28	C₃×#433	C₂²	1	16	yes	complemented
29	C₃×#433	C₂²	1	16	yes	complemented
30	C₃×#432	C₂²	1	16	yes	complemented
31	C₃×#431	C₂²	1	16	yes	complemented
32	C₃×#424	C₂²	1	4	yes	—
33	C₃×#424	C₂²	1	4	yes	—
34	C₃×#424	C₂²	1	2	yes	complemented
35	C₃×#424	C₂²	1	2	yes	complemented
36	C₃×#424	C₂²	1	4	yes	complemented
37	C₃×#423	C₂²	1	4	yes	complemented
38	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	complemented
39	C₃×#408	C₂²	1	2	yes	—
40	C₃×#408	C₂²	1	2	yes	—
41	C₃×#408	C₂²	1	4	yes	—
42	C₃×#408	C₂²	1	4	yes	—
43	C₃×#408	C₂²	1	4	yes	—
44	C₃×#407	C₂²	1	4	yes	—
45	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
46	C₃×#405	C₂²	1	4	yes	—
47	C₃×#405	C₂²	1	4	yes	—
48	C₃×#405	C₂²	1	4	yes	complemented
49	C₃×#405	C₂²	1	4	yes	complemented
50	C₃×C₄×M₁₆	C₂²	1	4	yes	complemented
51	C₂×C₃×#97	C₂²	1	2	yes	complemented
52	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
53	#3428	C₂×C₃	1	1	yes	characteristic
54	#2925	C₂×C₃	1	8	yes	complemented
55	#2924	C₂×C₃	1	8	yes	complemented
56	#2923	C₂×C₃	1	4	yes	complemented
57	#2922	C₂×C₃	1	4	yes	complemented
58	#2905	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
60	#2879	C₂×C₃	1	1	yes	characteristic
61	C₂×#408	C₂×C₃	1	1	yes	characteristic
62	#2873	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×#405	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₃×#41	—	2	4	no	—
65	C₂×C₃×#41	—	2	4	no	—
66	C₂×C₃×#41	C₂×C₄	1	2	yes	—
67	C₂×C₃×#41	C₂×C₄	1	2	yes	—
68	C₂×C₃×#41	C₂³	1	2	yes	—
69	C₂×C₃×#41	C₂³	1	2	yes	—
70	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
72	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₃×C₄	C₂³	1	2	yes	—
74	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃×M₁₆	—	2	4	no	—
76	C₂×C₃×M₁₆	—	2	4	no	—
77	C₂×C₃×M₁₆	—	2	4	no	—
78	C₂×C₃×M₁₆	C₂³	1	2	yes	—
79	C₂×C₃×M₁₆	C₂³	1	2	yes	—
80	C₂×C₃×M₁₆	C₂³	1	2	yes	—
81	C₂×C₃×M₁₆	C₂³	1	2	yes	—
82	C₂×C₃×M₁₆	C₂³	1	2	yes	—
83	C₂×C₃×M₁₆	C₂³	1	2	yes	—
84	C₂²×C₃×C₈	—	2	4	no	—
85	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₈	C₂³	1	2	yes	—
88	C₂²×C₃×C₈	C₂³	1	2	yes	—
89	C₂²×C₃×C₈	C₂³	1	2	yes	—
90	C₂²×C₃×C₈	C₂³	1	2	yes	—
91	C₂²×C₃×C₈	C₂³	1	2	yes	—
92	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
93	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
94	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
95	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
96	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
97	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
98	C₃×#117	C₂×C₄	1	8	yes	—
99	C₃×#117	C₂×C₄	1	2	yes	—
100	C₃×#117	C₂×C₄	1	2	yes	—
101	C₃×#117	C₂×C₄	1	8	yes	—
102	C₃×#117	C₂×C₄	1	2	yes	—
103	C₃×#117	C₂×C₄	1	2	yes	—
104	C₃×#117	C₂³	1	2	yes	—
105	C₃×#117	C₂³	1	2	yes	—
106	C₃×#117	C₂³	1	2	yes	—
107	C₃×#117	C₂³	1	2	yes	—
108	C₃×#117	C₂³	1	8	yes	—
109	C₂×C₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
110	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
115	C₂×C₃×C₄²	C₂³	1	2	yes	—
116	C₂×C₃×C₄²	C₂³	1	2	yes	—
117	C₂×C₃×C₄²	C₂³	1	8	yes	—
118	C₃×C₄⋊C₈	C₂³	1	8	yes	—
119	C₃×C₄⋊C₈	C₂³	1	8	yes	—
120	C₃×C₄⋊C₈	C₂³	1	16	yes	—
121	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
123	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
124	C₃×#97	C₂³	1	8	yes	—
125	C₃×#97	C₂³	1	8	yes	—
126	C₃×C₄×C₈	C₂³	1	8	yes	—
127	C₃×C₄×C₈	C₂³	1	8	yes	—
128	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
129	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
130	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
131	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
132	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
133	#520	C₃×C₄	1	4	yes	—
134	#520	C₃×C₄	1	4	yes	—
135	#519	C₃×C₄	1	2	yes	—
136	#518	C₃×C₄	1	2	yes	—
137	#518	C₃×C₄	1	4	yes	—
138	C₄×#41	C₂²×C₃	1	4	yes	—
139	C₄×#41	C₂²×C₃	1	4	yes	—
140	C₂×#117	C₂²×C₃	1	1	yes	characteristic
141	C₂×#117	C₂²×C₃	1	1	yes	characteristic
142	C₂×#117	C₂²×C₃	1	4	yes	—
143	#433	C₂²×C₃	1	16	yes	complemented
144	#433	C₂²×C₃	1	16	yes	complemented
145	#432	C₂²×C₃	1	16	yes	complemented
146	#431	C₂²×C₃	1	16	yes	complemented
147	#424	C₂²×C₃	1	4	yes	—
148	#424	C₂²×C₃	1	4	yes	—
149	#424	C₂²×C₃	1	2	yes	complemented
150	#424	C₂²×C₃	1	2	yes	complemented
151	#424	C₂²×C₃	1	4	yes	complemented
152	#423	C₂²×C₃	1	4	yes	complemented
153	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
154	#408	C₂²×C₃	1	2	yes	—
155	#408	C₂²×C₃	1	2	yes	—
156	#408	C₂²×C₃	1	4	yes	—
157	#408	C₂²×C₃	1	4	yes	—
158	#408	C₂²×C₃	1	4	yes	—
159	#407	C₂²×C₃	1	4	yes	—
160	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
161	#405	C₂²×C₃	1	4	yes	—
162	#405	C₂²×C₃	1	4	yes	—
163	#405	C₂²×C₃	1	4	yes	complemented
164	#405	C₂²×C₃	1	4	yes	complemented
165	C₄×M₁₆	C₂²×C₃	1	4	yes	complemented
166	C₂×#97	C₂²×C₃	1	2	yes	complemented
167	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
168	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
169	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
170	C₃×#41	—	2	8	no	—
171	C₃×#41	—	2	8	no	—
172	C₃×#41	—	2	4	no	—
173	C₃×#41	—	2	4	no	—
174	C₃×#41	—	2	4	no	—
175	C₃×#41	—	2	4	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
178	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	2	4	no	—
181	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
182	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
183	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
184	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
185	C₂²×C₃×C₄	—	2	4	no	—
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
188	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
189	C₂²×C₃×C₄	C₂²×C₄	1	16	yes	—
190	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
191	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
192	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₃×C₄	#41	1	4	yes	—
196	C₂²×C₃×C₄	#41	1	4	yes	—
197	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
198	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
201	C₃×M₁₆	—	2	4	no	—
202	C₃×M₁₆	—	2	4	no	—
203	C₃×M₁₆	—	2	4	no	—
204	C₃×M₁₆	—	2	4	no	—
205	C₃×M₁₆	—	2	4	no	—
206	C₃×M₁₆	—	2	4	no	—
207	C₂×C₃×C₈	—	2	4	no	—
208	C₂×C₃×C₈	—	2	4	no	—
209	C₂×C₃×C₈	—	2	2	no	—
210	C₂×C₃×C₈	—	2	2	no	—
211	C₂×C₃×C₈	—	2	4	no	—
212	C₂×C₃×C₈	—	2	4	no	—
213	C₂×C₃×C₈	—	2	4	no	—
214	C₂×C₃×C₈	C₂⁴	1	2	yes	—
215	C₂×C₃×C₈	C₂⁴	1	4	yes	—
216	C₂×C₃×C₈	C₂⁴	1	4	yes	—
217	C₂×C₃×C₈	C₂⁴	1	4	yes	—
218	C₂×C₃×C₈	C₂⁴	1	2	yes	—
219	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
220	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
221	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
222	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
223	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
224	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
225	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
226	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
227	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
228	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
229	C₃×C₄²	C₂²×C₄	1	16	yes	—
230	C₃×C₄²	C₂²×C₄	1	4	yes	—
231	C₃×C₄²	C₂²×C₄	1	4	yes	—
232	C₃×C₄²	C₂⁴	1	4	yes	—
233	C₃×C₄²	C₂⁴	1	4	yes	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	C₂×C₃×C₄	1	2	yes	—
237	C₂×#41	C₂×C₃×C₄	1	2	yes	—
238	C₂×#41	C₂³×C₃	1	2	yes	—
239	C₂×#41	C₂³×C₃	1	2	yes	—
240	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
242	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	C₂³×C₃	1	2	yes	—
249	C₂×M₁₆	C₂³×C₃	1	2	yes	—
250	C₂×M₁₆	C₂³×C₃	1	2	yes	—
251	C₂×M₁₆	C₂³×C₃	1	2	yes	—
252	C₂×M₁₆	C₂³×C₃	1	2	yes	—
253	C₂×M₁₆	C₂³×C₃	1	2	yes	—
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₃	1	2	yes	—
259	C₂²×C₈	C₂³×C₃	1	2	yes	—
260	C₂²×C₈	C₂³×C₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₃	1	2	yes	—
262	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
263	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
264	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
265	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
266	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
267	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
268	#117	C₂×C₃×C₄	1	8	yes	—
269	#117	C₂×C₃×C₄	1	2	yes	—
270	#117	C₂×C₃×C₄	1	2	yes	—
271	#117	C₂×C₃×C₄	1	8	yes	—
272	#117	C₂×C₃×C₄	1	2	yes	—
273	#117	C₂×C₃×C₄	1	2	yes	—
274	#117	C₂³×C₃	1	2	yes	—
275	#117	C₂³×C₃	1	2	yes	—
276	#117	C₂³×C₃	1	2	yes	—
277	#117	C₂³×C₃	1	2	yes	—
278	#117	C₂³×C₃	1	8	yes	—
279	C₂×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
280	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
285	C₂×C₄²	C₂³×C₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₃	1	8	yes	—
288	C₄⋊C₈	C₂³×C₃	1	8	yes	—
289	C₄⋊C₈	C₂³×C₃	1	8	yes	—
290	C₄⋊C₈	C₂³×C₃	1	16	yes	—
291	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
292	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
293	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
294	#97	C₂³×C₃	1	8	yes	—
295	#97	C₂³×C₃	1	8	yes	—
296	C₄×C₈	C₂³×C₃	1	8	yes	—
297	C₄×C₈	C₂³×C₃	1	8	yes	—
298	C₂³×C₃	—	2	4	no	—
299	C₂³×C₃	—	4	2	no	—
300	C₂³×C₃	—	4	4	no	—
301	C₂³×C₃	#117	1	4	yes	—
302	C₂³×C₃	C₂³×C₄	1	4	yes	—
303	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
304	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
305	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
306	C₃×Q₈	—	2	4	no	—
307	C₃×Q₈	—	2	4	no	—
308	C₃×D₄	—	2	8	no	—
309	C₃×D₄	—	2	8	no	—
310	C₃×D₄	—	2	4	no	—
311	C₃×D₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	4	4	no	—
317	C₂×C₃×C₄	—	4	4	no	—
318	C₂×C₃×C₄	—	4	16	no	—
319	C₂×C₃×C₄	#117	1	4	yes	—
320	C₂×C₃×C₄	#117	1	4	yes	—
321	C₂×C₃×C₄	#117	1	4	yes	—
322	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
323	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
324	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
325	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×#41	1	2	yes	—
329	C₂×C₃×C₄	C₂×#41	1	2	yes	—
330	C₂×C₃×C₄	C₂×#41	1	2	yes	—
331	C₂×C₃×C₄	C₂×#41	1	2	yes	—
332	C₂×C₃×C₄	C₂×#41	1	2	yes	—
333	C₂×C₃×C₄	C₂×#41	1	2	yes	—
334	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
335	C₃×C₈	—	2	2	no	—
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	—	2	4	no	—
338	C₃×C₈	—	2	4	no	—
339	C₃×C₈	—	2	4	no	—
340	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
341	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
342	#41	—	2	8	no	—
343	#41	—	2	8	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
350	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
354	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
355	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
356	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
360	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
361	C₂²×C₄	C₂²×C₃×C₄	1	16	yes	—
362	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
363	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
364	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
367	C₂²×C₄	C₃×#41	1	4	yes	—
368	C₂²×C₄	C₃×#41	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
373	M₁₆	—	2	4	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	4	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	C₂⁴×C₃	1	2	yes	—
387	C₂×C₈	C₂⁴×C₃	1	4	yes	—
388	C₂×C₈	C₂⁴×C₃	1	4	yes	—
389	C₂×C₈	C₂⁴×C₃	1	4	yes	—
390	C₂×C₈	C₂⁴×C₃	1	2	yes	—
391	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
392	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
393	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
394	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
395	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
396	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
397	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
398	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
399	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
400	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
401	C₄²	C₂²×C₃×C₄	1	16	yes	—
402	C₄²	C₂²×C₃×C₄	1	4	yes	—
403	C₄²	C₂²×C₃×C₄	1	4	yes	—
404	C₄²	C₂⁴×C₃	1	4	yes	—
405	C₄²	C₂⁴×C₃	1	4	yes	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	2	8	no	—
411	C₂²×C₃	—	4	4	no	—
412	C₂²×C₃	—	8	4	no	—
413	C₂²×C₃	C₂×#117	1	2	yes	—
414	C₂²×C₃	C₂×#117	1	2	yes	—
415	C₂²×C₃	C₂×#117	1	2	yes	—
416	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
417	C₃×C₄	—	2	4	no	—
418	C₃×C₄	—	2	8	no	—
419	C₃×C₄	—	2	8	no	—
420	C₃×C₄	C₂×#117	1	2	yes	—
421	C₃×C₄	C₂×#117	1	2	yes	—
422	C₃×C₄	C₂×#117	1	2	yes	—
423	C₃×C₄	C₂²×#41	1	1	yes	characteristic
424	C₃×C₄	C₂²×#41	1	1	yes	characteristic
425	C₂³	—	2	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	4	no	—
428	C₂³	C₃×#117	1	4	yes	—
429	C₂³	C₂³×C₃×C₄	1	4	yes	—
430	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
431	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
432	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	2	4	no	—
435	D₄	—	2	8	no	—
436	D₄	—	2	8	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	C₃×#117	1	4	yes	—
447	C₂×C₄	C₃×#117	1	4	yes	—
448	C₂×C₄	C₃×#117	1	4	yes	—
449	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
450	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
451	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
452	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
453	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
454	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
455	C₂×C₄	C₂×C₃×#41	1	2	yes	—
456	C₂×C₄	C₂×C₃×#41	1	2	yes	—
457	C₂×C₄	C₂×C₃×#41	1	2	yes	—
458	C₂×C₄	C₂×C₃×#41	1	2	yes	—
459	C₂×C₄	C₂×C₃×#41	1	2	yes	—
460	C₂×C₄	C₂×C₃×#41	1	2	yes	—
461	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	4	no	—
465	C₈	—	2	4	no	—
466	C₈	—	2	4	no	—
467	C₂×C₃	—	2	2	no	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	C₂²×#117	1	1	yes	characteristic
472	C₂×C₃	#3573	1	2	yes	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	8	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₂×C₃×#117	1	2	yes	—
481	C₂²	C₂×C₃×#117	1	2	yes	—
482	C₂²	C₂×C₃×#117	1	2	yes	—
483	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
484	C₄	—	2	4	no	—
485	C₄	—	2	8	no	—
486	C₄	—	2	8	no	—
487	C₄	C₂×C₃×#117	1	2	yes	—
488	C₄	C₂×C₃×#117	1	2	yes	—
489	C₄	C₂×C₃×#117	1	2	yes	—
490	C₄	C₂²×C₃×#41	1	1	yes	characteristic
491	C₄	C₂²×C₃×#41	1	1	yes	characteristic
492	C₃	#60126	1	1	yes	characteristic, direct product factor, Sylow
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	2	no	—
496	C₂	—	4	4	no	—
497	C₂	C₂²×C₃×#117	1	1	yes	characteristic
498	C₂	C₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂⁴×C₄
prime radical	C₂²×C₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2925	C₂	semidirect
3. C₃×#2924	C₂	semidirect
4. C₃×#2923	C₂	semidirect
5. C₃×#2922	C₂	semidirect
6. C₃×#2905	C₂	semidirect
7. C₂×C₃×#424	C₂	semidirect
10. C₃×#2873	C₂	semidirect
11. C₂×C₃×#405	C₂	semidirect
12. #60126	C₃	direct (N × H)
28. C₃×#433	C₂²	semidirect
29. C₃×#433	C₂²	semidirect
30. C₃×#432	C₂²	semidirect
31. C₃×#431	C₂²	semidirect
34. C₃×#424	C₂²	semidirect
35. C₃×#424	C₂²	semidirect
36. C₃×#424	C₂²	semidirect
37. C₃×#423	C₂²	semidirect
38. C₂×C₃×C₄⋊C₈	C₂²	semidirect
48. C₃×#405	C₂²	semidirect
49. C₃×#405	C₂²	semidirect
50. C₃×C₄×M₁₆	C₂²	semidirect
51. C₂×C₃×#97	C₂²	semidirect
52. C₂×C₃×C₄×C₈	C₂²	semidirect
54. #2925	C₂×C₃	semidirect
55. #2924	C₂×C₃	semidirect
56. #2923	C₂×C₃	semidirect
57. #2922	C₂×C₃	semidirect
58. #2905	C₂×C₃	semidirect
59. C₂×#424	C₂×C₃	semidirect
62. #2873	C₂×C₃	semidirect
63. C₂×#405	C₂×C₃	semidirect
143. #433	C₂²×C₃	semidirect
144. #433	C₂²×C₃	semidirect
145. #432	C₂²×C₃	semidirect
146. #431	C₂²×C₃	semidirect
149. #424	C₂²×C₃	semidirect
150. #424	C₂²×C₃	semidirect
151. #424	C₂²×C₃	semidirect
152. #423	C₂²×C₃	semidirect
153. C₂×C₄⋊C₈	C₂²×C₃	semidirect
163. #405	C₂²×C₃	semidirect
164. #405	C₂²×C₃	semidirect
165. C₄×M₁₆	C₂²×C₃	semidirect
166. C₂×#97	C₂²×C₃	semidirect
167. C₂×C₄×C₈	C₂²×C₃	semidirect
492. C₃	#60126	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3428	2
C₃×#2925	2
C₃×#2924	2
C₃×#2923	2
C₃×#2922	2
C₃×#2905	2
C₂×C₃×#424	2
C₃×#2879	2
C₂×C₃×#408	2
C₃×#2873	2
C₂×C₃×#405	2
#60126	3

Subgroups — C3×#60126 #10678733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60126 #10678733