Subgroups — C₃×#60618 #10679225

Order 768.

2170 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₃×#3142	C₂	1	4	yes	maximal, complemented
4	C₃×#3141	C₂	1	4	yes	maximal, complemented
5	C₃×#3140	C₂	1	4	yes	maximal, complemented
6	C₃×#3139	C₂	1	2	yes	maximal, complemented
7	C₃×#3138	C₂	1	2	yes	maximal, complemented
8	C₃×#3135	C₂	1	4	yes	maximal, complemented
9	C₃×#3131	C₂	1	4	yes	maximal, complemented
10	C₃×#2896	C₂	1	4	yes	maximal, complemented
11	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#60618	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×#41	C₂²	1	2	yes	—
14	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
15	C₃×#533	—	2	2	no	—
16	C₃×#533	—	2	2	no	—
17	C₃×#533	C₂²	1	2	yes	—
18	C₃×#533	C₂²	1	2	yes	—
19	C₃×#533	C₂²	1	2	yes	complemented
20	C₃×#533	C₂²	1	2	yes	complemented
21	C₃×#532	—	2	2	no	—
22	C₃×#532	—	2	2	no	—
23	C₃×#532	C₂²	1	2	yes	—
24	C₃×#532	C₂²	1	2	yes	—
25	C₃×#532	C₂²	1	2	yes	—
26	C₃×#532	C₂²	1	2	yes	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₃×#125	C₂²	1	2	yes	complemented
31	C₂×C₃×#124	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
33	C₂×C₃×#121	—	2	2	no	—
34	C₂×C₃×C₄×Q₈	—	2	2	no	—
35	C₂×C₃×C₄×D₄	—	2	2	no	—
36	C₂×C₃×#117	C₂²	1	2	yes	—
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₃×#491	C₂²	1	8	yes	complemented
39	C₃×#490	C₂²	1	8	yes	complemented
40	C₃×#489	C₂²	1	16	yes	complemented
41	C₃×#488	C₂²	1	16	yes	complemented
42	C₃×#487	C₂²	1	8	yes	complemented
43	C₃×#486	C₂²	1	8	yes	complemented
44	C₃×#419	C₂²	1	8	yes	—
45	C₃×#418	C₂²	1	8	yes	—
46	C₃×#417	C₂²	1	16	yes	complemented
47	C₃×#416	C₂²	1	16	yes	complemented
48	C₃×C₄×M₁₆	C₂²	1	2	yes	—
49	C₃×C₄×M₁₆	C₂²	1	2	yes	—
50	C₃×C₄×M₁₆	C₂²	1	2	yes	complemented
51	C₃×C₄×M₁₆	C₂²	1	2	yes	complemented
52	C₂×C₃×#97	C₂²	1	2	yes	complemented
53	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
54	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#532	C₂×C₃	1	1	yes	characteristic
56	#3142	C₂×C₃	1	4	yes	complemented
57	#3141	C₂×C₃	1	4	yes	complemented
58	#3140	C₂×C₃	1	4	yes	complemented
59	#3139	C₂×C₃	1	2	yes	complemented
60	#3138	C₂×C₃	1	2	yes	complemented
61	#3135	C₂×C₃	1	4	yes	complemented
62	#3131	C₂×C₃	1	4	yes	complemented
63	#2896	C₂×C₃	1	4	yes	complemented
64	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×C₃×#41	—	2	2	no	—
66	C₂×C₃×#41	—	2	2	no	—
67	C₂×C₃×#41	—	2	16	no	—
68	C₂×C₃×#41	C₂³	1	4	yes	—
69	C₂×C₃×#41	C₂³	1	4	yes	—
70	C₂²×C₃×Q₈	—	2	2	no	—
71	C₂²×C₃×Q₈	C₂³	1	2	yes	—
72	C₂²×C₃×D₄	—	2	2	no	—
73	C₂²×C₃×D₄	—	2	2	no	—
74	C₂²×C₃×D₄	C₂³	1	2	yes	—
75	C₂³×C₃×C₄	—	2	2	no	—
76	C₂³×C₃×C₄	D₄	1	2	yes	—
77	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×M₁₆	—	2	8	no	—
79	C₂×C₃×M₁₆	C₂³	1	4	yes	—
80	C₂×C₃×M₁₆	C₂³	1	4	yes	—
81	C₂²×C₃×C₈	C₂³	1	4	yes	—
82	C₃×C₄⋊Q₈	—	2	2	no	—
83	C₃×C₄⋊Q₈	—	2	2	no	—
84	C₃×C₄⋊Q₈	—	2	2	no	—
85	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
88	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
89	C₃×#127	—	2	2	no	—
90	C₃×#127	C₂³	1	2	yes	—
91	C₃×#127	C₂³	1	2	yes	—
92	C₃×#125	—	2	4	no	—
93	C₃×#125	C₂³	1	4	yes	—
94	C₃×#125	C₂³	1	4	yes	—
95	C₃×#124	—	2	4	no	—
96	C₃×#124	C₂³	1	4	yes	—
97	C₃×#124	C₂³	1	4	yes	—
98	C₃×C₂²⋊Q₈	—	2	4	no	—
99	C₃×C₂²⋊Q₈	—	2	4	no	—
100	C₃×C₂²⋊Q₈	—	2	4	no	—
101	C₃×C₂²⋊Q₈	—	2	4	no	—
102	C₃×#121	—	2	4	no	—
103	C₃×#121	—	2	4	no	—
104	C₃×#121	—	2	4	no	—
105	C₃×#121	—	2	4	no	—
106	C₃×C₄×Q₈	—	2	4	no	—
107	C₃×C₄×Q₈	—	2	4	no	—
108	C₃×C₄×Q₈	—	2	4	no	—
109	C₃×C₄×Q₈	—	2	4	no	—
110	C₃×C₄×D₄	—	2	4	no	—
111	C₃×C₄×D₄	—	2	4	no	—
112	C₃×C₄×D₄	—	2	4	no	—
113	C₃×C₄×D₄	—	2	4	no	—
114	C₃×#117	—	2	2	no	—
115	C₃×#117	—	2	2	no	—
116	C₃×#117	C₂³	1	4	yes	—
117	C₃×#117	C₂³	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	—	2	2	no	—
119	C₂×C₃×C₄⋊C₄	—	2	4	no	—
120	C₂×C₃×C₄⋊C₄	—	2	2	no	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
124	C₂×C₃×C₄²	—	2	2	no	—
125	C₂×C₃×C₄²	D₄	1	2	yes	—
126	C₂×C₃×C₄²	D₄	1	2	yes	—
127	C₂×C₃×C₄²	D₄	1	2	yes	—
128	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
134	C₃×#103	C₂³	1	32	yes	—
135	C₃×#102	C₂³	1	32	yes	—
136	C₃×#97	C₂³	1	4	yes	—
137	C₃×#97	C₂³	1	4	yes	—
138	C₃×C₄×C₈	C₂³	1	4	yes	—
139	C₃×C₄×C₈	C₂³	1	4	yes	—
140	C₂²×#41	C₂²×C₃	1	2	yes	—
141	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
142	#533	—	2	2	no	—
143	#533	—	2	2	no	—
144	#533	C₂²×C₃	1	2	yes	—
145	#533	C₂²×C₃	1	2	yes	—
146	#533	C₂²×C₃	1	2	yes	complemented
147	#533	C₂²×C₃	1	2	yes	complemented
148	#532	—	2	2	no	—
149	#532	—	2	2	no	—
150	#532	C₂²×C₃	1	2	yes	—
151	#532	C₂²×C₃	1	2	yes	—
152	#532	C₂²×C₃	1	2	yes	—
153	#532	C₂²×C₃	1	2	yes	—
154	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
156	C₂×#127	C₂²×C₃	1	1	yes	characteristic
157	C₂×#125	C₂²×C₃	1	2	yes	complemented
158	C₂×#124	C₂²×C₃	1	2	yes	—
159	C₂×C₂²⋊Q₈	—	2	2	no	—
160	C₂×#121	—	2	2	no	—
161	C₂×C₄×Q₈	—	2	2	no	—
162	C₂×C₄×D₄	—	2	2	no	—
163	C₂×#117	C₂²×C₃	1	2	yes	—
164	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
165	#491	C₂²×C₃	1	8	yes	complemented
166	#490	C₂²×C₃	1	8	yes	complemented
167	#489	C₂²×C₃	1	16	yes	complemented
168	#488	C₂²×C₃	1	16	yes	complemented
169	#487	C₂²×C₃	1	8	yes	complemented
170	#486	C₂²×C₃	1	8	yes	complemented
171	#419	C₂²×C₃	1	8	yes	—
172	#418	C₂²×C₃	1	8	yes	—
173	#417	C₂²×C₃	1	16	yes	complemented
174	#416	C₂²×C₃	1	16	yes	complemented
175	C₄×M₁₆	C₂²×C₃	1	2	yes	—
176	C₄×M₁₆	C₂²×C₃	1	2	yes	—
177	C₄×M₁₆	C₂²×C₃	1	2	yes	complemented
178	C₄×M₁₆	C₂²×C₃	1	2	yes	complemented
179	C₂×#97	C₂²×C₃	1	2	yes	complemented
180	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
181	C₂⁴×C₃	—	2	2	no	—
182	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
183	C₃×#41	—	2	16	no	—
184	C₃×#41	—	2	16	no	—
185	C₃×#41	—	4	8	no	—
186	C₃×#41	—	4	8	no	—
187	C₂×C₃×Q₈	—	2	4	no	—
188	C₂×C₃×Q₈	—	2	4	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	2	8	no	—
191	C₂×C₃×Q₈	—	4	8	no	—
192	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
193	C₂×C₃×D₄	—	2	4	no	—
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	—	2	4	no	—
196	C₂×C₃×D₄	—	2	4	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	2	8	no	—
199	C₂×C₃×D₄	—	4	8	no	—
200	C₂×C₃×D₄	—	4	8	no	—
201	C₂×C₃×D₄	C₂⁴	1	4	yes	—
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	2	4	no	—
205	C₂²×C₃×C₄	—	2	4	no	—
206	C₂²×C₃×C₄	—	4	4	no	—
207	C₂²×C₃×C₄	—	4	8	no	—
208	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
209	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
210	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
211	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
212	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
213	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
214	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	#41	1	8	yes	—
218	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
221	C₃×M₁₆	—	2	8	no	—
222	C₃×M₁₆	—	2	8	no	—
223	C₂×C₃×C₈	—	2	8	no	—
224	C₂×C₃×C₈	C₂⁴	1	8	yes	—
225	C₃×C₄⋊C₄	—	2	4	no	—
226	C₃×C₄⋊C₄	—	2	4	no	—
227	C₃×C₄⋊C₄	—	2	8	no	—
228	C₃×C₄⋊C₄	—	2	8	no	—
229	C₃×C₄⋊C₄	—	2	4	no	—
230	C₃×C₄⋊C₄	—	2	4	no	—
231	C₃×C₄⋊C₄	—	2	4	no	—
232	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
233	C₃×C₂²⋊C₄	—	2	4	no	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₂²⋊C₄	—	2	8	no	—
236	C₃×C₂²⋊C₄	—	2	8	no	—
237	C₃×C₄²	—	2	4	no	—
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	C₂×D₄	1	2	yes	—
240	C₃×C₄²	C₂×D₄	1	2	yes	—
241	C₃×C₄²	C₂×D₄	1	2	yes	—
242	C₃×C₄²	C₂×D₄	1	2	yes	—
243	C₃×C₄²	C₂×D₄	1	2	yes	—
244	C₃×C₄²	C₂×D₄	1	2	yes	—
245	C₃×C₄²	C₂⁴	1	1	yes	characteristic
246	C₃×C₄²	C₂⁴	1	1	yes	characteristic
247	C₃×C₄²	C₂⁴	1	1	yes	characteristic
248	C₃×C₄²	C₂⁴	1	1	yes	characteristic
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	16	no	—
252	C₂×#41	C₂³×C₃	1	4	yes	—
253	C₂×#41	C₂³×C₃	1	4	yes	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	C₂³×C₃	1	2	yes	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	C₂³×C₃	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₃×D₄	1	2	yes	—
261	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂×M₁₆	—	2	8	no	—
263	C₂×M₁₆	C₂³×C₃	1	4	yes	—
264	C₂×M₁₆	C₂³×C₃	1	4	yes	—
265	C₂²×C₈	C₂³×C₃	1	4	yes	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
272	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
273	#127	—	2	2	no	—
274	#127	C₂³×C₃	1	2	yes	—
275	#127	C₂³×C₃	1	2	yes	—
276	#125	—	2	4	no	—
277	#125	C₂³×C₃	1	4	yes	—
278	#125	C₂³×C₃	1	4	yes	—
279	#124	—	2	4	no	—
280	#124	C₂³×C₃	1	4	yes	—
281	#124	C₂³×C₃	1	4	yes	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	—	2	4	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	C₂³×C₃	1	4	yes	—
301	#117	C₂³×C₃	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₃×D₄	1	2	yes	—
310	C₂×C₄²	C₃×D₄	1	2	yes	—
311	C₂×C₄²	C₃×D₄	1	2	yes	—
312	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
318	#103	C₂³×C₃	1	32	yes	—
319	#102	C₂³×C₃	1	32	yes	—
320	#97	C₂³×C₃	1	4	yes	—
321	#97	C₂³×C₃	1	4	yes	—
322	C₄×C₈	C₂³×C₃	1	4	yes	—
323	C₄×C₈	C₂³×C₃	1	4	yes	—
324	C₂³×C₃	—	2	4	no	—
325	C₂³×C₃	—	4	2	no	—
326	C₂³×C₃	—	4	8	no	—
327	C₂³×C₃	—	4	4	no	—
328	C₂³×C₃	#124	1	4	yes	—
329	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
330	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
331	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
332	C₃×Q₈	—	2	8	no	—
333	C₃×Q₈	—	4	8	no	—
334	C₃×Q₈	—	4	4	no	—
335	C₃×Q₈	—	4	8	no	—
336	C₃×D₄	—	2	8	no	—
337	C₃×D₄	—	4	8	no	—
338	C₃×D₄	—	4	8	no	—
339	C₃×D₄	—	4	8	no	—
340	C₃×D₄	—	4	4	no	—
341	C₃×D₄	—	4	8	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	4	no	—
344	C₂×C₃×C₄	—	2	4	no	—
345	C₂×C₃×C₄	—	2	8	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	4	2	no	—
348	C₂×C₃×C₄	—	4	2	no	—
349	C₂×C₃×C₄	—	4	2	no	—
350	C₂×C₃×C₄	—	4	8	no	—
351	C₂×C₃×C₄	—	4	4	no	—
352	C₂×C₃×C₄	—	4	8	no	—
353	C₂×C₃×C₄	—	4	8	no	—
354	C₂×C₃×C₄	#124	1	4	yes	—
355	C₂×C₃×C₄	#124	1	4	yes	—
356	C₂×C₃×C₄	#124	1	4	yes	—
357	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
358	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
359	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
360	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
363	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×#41	1	4	yes	—
365	C₂×C₃×C₄	C₂×#41	1	4	yes	—
366	C₂×C₃×C₄	C₂×#41	1	4	yes	—
367	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
368	C₃×C₈	—	2	8	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
371	#41	—	2	16	no	—
372	#41	—	2	16	no	—
373	#41	—	4	8	no	—
374	#41	—	4	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	C₂⁴×C₃	1	4	yes	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	8	no	—
396	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
397	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
398	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
399	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
400	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
401	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
402	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
405	C₂²×C₄	C₃×#41	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	M₁₆	—	2	8	no	—
410	M₁₆	—	2	8	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	C₂⁴×C₃	1	8	yes	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₄²	—	2	4	no	—
426	C₄²	—	2	4	no	—
427	C₄²	C₂×C₃×D₄	1	2	yes	—
428	C₄²	C₂×C₃×D₄	1	2	yes	—
429	C₄²	C₂×C₃×D₄	1	2	yes	—
430	C₄²	C₂×C₃×D₄	1	2	yes	—
431	C₄²	C₂×C₃×D₄	1	2	yes	—
432	C₄²	C₂×C₃×D₄	1	2	yes	—
433	C₄²	C₂⁴×C₃	1	1	yes	characteristic
434	C₄²	C₂⁴×C₃	1	1	yes	characteristic
435	C₄²	C₂⁴×C₃	1	1	yes	characteristic
436	C₄²	C₂⁴×C₃	1	1	yes	characteristic
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	4	4	no	—
441	C₂²×C₃	—	4	4	no	—
442	C₂²×C₃	—	4	8	no	—
443	C₂²×C₃	—	8	8	no	—
444	C₂²×C₃	C₂×#124	1	2	yes	—
445	C₂²×C₃	C₂×#124	1	2	yes	—
446	C₂²×C₃	C₂×#124	1	2	yes	—
447	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	4	4	no	—
452	C₃×C₄	—	4	8	no	—
453	C₃×C₄	C₂×#124	1	2	yes	—
454	C₃×C₄	C₂×#124	1	2	yes	—
455	C₃×C₄	C₂×#124	1	2	yes	—
456	C₃×C₄	#575	1	4	yes	—
457	C₃×C₄	C₂²×#41	1	2	yes	—
458	C₂³	—	2	4	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	4	no	—
462	C₂³	C₃×#124	1	4	yes	—
463	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
464	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
465	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
466	Q₈	—	2	8	no	—
467	Q₈	—	4	8	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	4	no	—
470	D₄	—	2	8	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	C₃×#124	1	4	yes	—
489	C₂×C₄	C₃×#124	1	4	yes	—
490	C₂×C₄	C₃×#124	1	4	yes	—
491	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
492	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
493	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
494	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
495	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
498	C₂×C₄	C₂×C₃×#41	1	4	yes	—
499	C₂×C₄	C₂×C₃×#41	1	4	yes	—
500	C₂×C₄	C₂×C₃×#41	1	4	yes	—
501	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
502	C₈	—	2	8	no	—
503	C₂×C₃	—	2	2	no	—
504	C₂×C₃	—	2	2	no	—
505	C₂×C₃	—	2	2	no	—
506	C₂×C₃	—	8	4	no	—
507	C₂×C₃	C₂²×#124	1	1	yes	characteristic
508	C₂×C₃	C₂×#575	1	2	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	8	no	—
515	C₂²	—	8	8	no	—
516	C₂²	C₂×C₃×#124	1	2	yes	—
517	C₂²	C₂×C₃×#124	1	2	yes	—
518	C₂²	C₂×C₃×#124	1	2	yes	—
519	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	8	no	—
525	C₄	C₂×C₃×#124	1	2	yes	—
526	C₄	C₂×C₃×#124	1	2	yes	—
527	C₄	C₂×C₃×#124	1	2	yes	—
528	C₄	C₃×#575	1	4	yes	—
529	C₄	C₂²×C₃×#41	1	2	yes	—
530	C₃	#60618	1	1	yes	characteristic, direct product factor, Sylow
531	C₂	—	2	2	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	2	no	—
534	C₂	—	8	4	no	—
535	C₂	C₂²×C₃×#124	1	1	yes	characteristic
536	C₂	C₂×C₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
prime radical	C₂×C₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3142	C₂	semidirect
4. C₃×#3141	C₂	semidirect
5. C₃×#3140	C₂	semidirect
6. C₃×#3139	C₂	semidirect
7. C₃×#3138	C₂	semidirect
8. C₃×#3135	C₂	semidirect
9. C₃×#3131	C₂	semidirect
10. C₃×#2896	C₂	semidirect
11. C₂×C₃×C₄×M₁₆	C₂	semidirect
12. #60618	C₃	direct (N × H)
19. C₃×#533	C₂²	semidirect
20. C₃×#533	C₂²	semidirect
28. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×#125	C₂²	semidirect
38. C₃×#491	C₂²	semidirect
39. C₃×#490	C₂²	semidirect
40. C₃×#489	C₂²	semidirect
41. C₃×#488	C₂²	semidirect
42. C₃×#487	C₂²	semidirect
43. C₃×#486	C₂²	semidirect
46. C₃×#417	C₂²	semidirect
47. C₃×#416	C₂²	semidirect
50. C₃×C₄×M₁₆	C₂²	semidirect
51. C₃×C₄×M₁₆	C₂²	semidirect
52. C₂×C₃×#97	C₂²	semidirect
53. C₂×C₃×C₄×C₈	C₂²	semidirect
54. C₂×#533	C₂×C₃	semidirect
56. #3142	C₂×C₃	semidirect
57. #3141	C₂×C₃	semidirect
58. #3140	C₂×C₃	semidirect
59. #3139	C₂×C₃	semidirect
60. #3138	C₂×C₃	semidirect
61. #3135	C₂×C₃	semidirect
62. #3131	C₂×C₃	semidirect
63. #2896	C₂×C₃	semidirect
64. C₂×C₄×M₁₆	C₂×C₃	semidirect
146. #533	C₂²×C₃	semidirect
147. #533	C₂²×C₃	semidirect
155. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
157. C₂×#125	C₂²×C₃	semidirect
165. #491	C₂²×C₃	semidirect
166. #490	C₂²×C₃	semidirect
167. #489	C₂²×C₃	semidirect
168. #488	C₂²×C₃	semidirect
169. #487	C₂²×C₃	semidirect
170. #486	C₂²×C₃	semidirect
173. #417	C₂²×C₃	semidirect
174. #416	C₂²×C₃	semidirect
177. C₄×M₁₆	C₂²×C₃	semidirect
178. C₄×M₁₆	C₂²×C₃	semidirect
179. C₂×#97	C₂²×C₃	semidirect
180. C₂×C₄×C₈	C₂²×C₃	semidirect
530. C₃	#60618	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×C₃×#533	2
C₂×C₃×#532	2
C₃×#3142	2
C₃×#3141	2
C₃×#3140	2
C₃×#3139	2
C₃×#3138	2
C₃×#3135	2
C₃×#3131	2
C₃×#2896	2
C₂×C₃×C₄×M₁₆	2
#60618	3

Subgroups — C3×#60618 #10679225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60618 #10679225