Subgroups — C₂×C₃×#63512 #13153680

Order 1728.

1058 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63512	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3675	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3673	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#949	—	3	1	no	maximal
8	C₂×#63512	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃×D₉	—	2	1	no	—
10	C₃×C₉×#41	—	2	2	no	—
11	C₃×C₉×#41	C₂²	1	4	yes	complemented
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×D₄×C₉	—	2	1	no	—
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₉	—	2	1	no	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₃₆	—	2	2	no	—
18	C₂×C₃×D₃₆	—	2	1	no	—
19	C₂×C₃×D₃₆	C₂²	1	2	yes	—
20	C₂×C₃×D₃₆	C₂²	1	4	yes	complemented
21	C₃×#3675	C₂²	1	8	yes	complemented
22	C₃×#3673	C₂²	1	8	yes	complemented
23	C₃×#3667	C₂²	1	4	yes	complemented
24	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	D₃	1	1	yes	characteristic
26	C₂²×C₃×D₁₂	—	3	1	no	—
27	C₃×#949	—	3	8	no	—
28	C₂×C₃×#215	—	3	2	no	—
29	C₂×C₃×#213	—	3	2	no	—
30	C₂×C₃×#208	—	3	1	no	—
31	C₂×C₉×#41	—	2	1	no	—
32	C₂×C₉×#41	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
34	#63512	C₂×C₃	1	8	yes	direct product factor
35	C₂×#3675	C₂×C₃	1	2	yes	complemented
36	C₂×#3673	C₂×C₃	1	2	yes	complemented
37	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
40	C₂²×C₃×D₉	—	2	2	no	—
41	C₂²×C₃×D₉	—	2	4	no	—
42	C₂²×C₃×D₉	—	4	4	no	—
43	C₃×Q₈×C₉	—	2	1	no	—
44	C₃×Q₈×C₉	C₂³	1	2	yes	complemented
45	C₃×D₄×C₉	—	2	4	no	—
46	C₃×D₄×C₉	—	2	1	no	—
47	C₃×D₄×C₉	C₂³	1	2	yes	complemented
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	—	2	4	no	—
50	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
52	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
54	C₃×D₃₆	—	2	2	no	—
55	C₃×D₃₆	—	2	4	no	—
56	C₃×D₃₆	C₂³	1	4	yes	—
57	C₃×C₉⋊C₈	C₂³	1	4	yes	complemented
58	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
59	C₂×#949	—	3	1	no	—
60	C₂³×C₃×D₃	—	6	1	no	—
61	C₃²×#41	—	2	2	no	—
62	C₃²×#41	C₂×D₃	1	4	yes	—
63	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃²×D₄	—	2	1	no	—
65	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	—	2	1	no	—
67	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×D₁₂	—	3	2	no	—
69	C₂×C₃×D₁₂	—	3	4	no	—
70	C₂×C₃×D₁₂	—	6	1	no	—
71	C₂×C₃×D₁₂	—	6	2	no	—
72	C₂³×D₉	—	2	1	no	—
73	C₃×#215	—	3	8	no	—
74	C₃×#213	—	3	8	no	—
75	C₃×#208	—	3	4	no	—
76	C₂×C₃×C₃⋊C₈	—	3	2	no	—
77	C₉×#41	—	2	4	no	—
78	C₉×#41	—	2	4	no	—
79	C₉×#41	—	2	2	no	—
80	C₉×#41	C₂²×C₃	1	4	yes	complemented
81	C₂×Q₈×C₉	—	2	1	no	—
82	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂×D₄×C₉	—	2	2	no	—
84	C₂×D₄×C₉	—	2	1	no	—
85	C₂×D₄×C₉	—	2	1	no	—
86	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂²×C₄×C₉	—	2	2	no	—
88	C₂²×C₄×C₉	—	2	1	no	—
89	C₂²×C₄×C₉	—	2	1	no	—
90	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
91	C₂×D₃₆	—	2	2	no	—
92	C₂×D₃₆	—	2	1	no	—
93	C₂×D₃₆	C₂²×C₃	1	2	yes	—
94	C₂×D₃₆	C₂²×C₃	1	4	yes	complemented
95	#3675	C₂²×C₃	1	8	yes	complemented
96	#3673	C₂²×C₃	1	8	yes	complemented
97	#3667	C₂²×C₃	1	4	yes	complemented
98	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	complemented
99	C₂²×C₃×C₉	—	2	2	no	—
100	C₂²×C₃×C₉	—	2	2	no	—
101	C₂²×C₃×C₉	—	4	2	no	—
102	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
103	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×D₉	—	2	4	no	—
105	C₂×C₃×D₉	—	4	8	no	—
106	C₂×C₃×D₉	—	4	4	no	—
107	C₃×C₄×C₉	—	2	2	no	—
108	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
109	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
110	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×#41	—	2	1	no	—
112	C₂×C₃×#41	D₉	1	1	yes	characteristic, complemented
113	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
114	C₂²×C₃×D₄	—	9	1	no	—
115	C₂²×D₁₂	—	3	1	no	—
116	C₃×AGL(1,ℤ/8)	—	9	8	no	—
117	C₂×C₃×SD₁₆	—	9	2	no	—
118	C₂×C₃×D₈	—	9	2	no	—
119	C₂×C₃×M₁₆	—	9	1	no	—
120	#949	—	3	8	no	—
121	C₂×#215	—	3	2	no	—
122	C₂×#213	—	3	2	no	—
123	C₂×#208	—	3	1	no	—
124	C₂³×C₃²	—	2	1	no	—
125	C₂³×C₃²	#67	1	1	yes	characteristic
126	C₂²×C₃×D₃	—	6	4	no	—
127	C₂²×C₃×D₃	—	6	2	no	—
128	C₂²×C₃×D₃	—	12	4	no	—
129	C₃²×Q₈	—	2	1	no	—
130	C₃²×Q₈	C₂²×D₃	1	2	yes	—
131	C₃²×D₄	—	2	4	no	—
132	C₃²×D₄	—	2	1	no	—
133	C₃²×D₄	C₂²×D₃	1	2	yes	—
134	C₂×C₃²×C₄	—	2	1	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	#67	1	1	yes	characteristic
137	C₂×C₃²×C₄	#67	1	2	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
140	C₃×D₁₂	—	3	4	no	—
141	C₃×D₁₂	—	6	4	no	—
142	C₃×D₁₂	—	6	2	no	—
143	C₂³×C₉	—	2	2	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	—	2	1	no	—
146	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
147	C₂²×D₉	—	2	2	no	—
148	C₂²×D₉	—	2	4	no	—
149	C₂²×D₉	—	4	4	no	—
150	C₃×C₃⋊C₈	—	3	4	no	—
151	Q₈×C₉	—	2	2	no	—
152	Q₈×C₉	—	2	1	no	—
153	Q₈×C₉	—	2	2	no	—
154	Q₈×C₉	C₂³×C₃	1	2	yes	complemented
155	D₄×C₉	—	2	8	no	—
156	D₄×C₉	—	2	2	no	—
157	D₄×C₉	—	2	4	no	—
158	D₄×C₉	—	2	1	no	—
159	D₄×C₉	—	2	2	no	—
160	D₄×C₉	C₂³×C₃	1	2	yes	complemented
161	C₂×C₄×C₉	—	2	2	no	—
162	C₂×C₄×C₉	—	2	8	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	4	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	2	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	2	no	—
169	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
170	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
171	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
173	D₃₆	—	2	2	no	—
174	D₃₆	—	2	4	no	—
175	D₃₆	C₂³×C₃	1	4	yes	—
176	C₉⋊C₈	C₂³×C₃	1	4	yes	complemented
177	C₂×AGL(1,ℤ/8)	—	9	1	no	Sylow
178	C₂×C₃×C₉	—	2	2	no	—
179	C₂×C₃×C₉	—	4	2	no	—
180	C₂×C₃×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
181	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
182	C₃×D₉	—	4	4	no	—
183	C₂⁴×C₃	—	18	1	no	—
184	C₂³×D₃	—	6	1	no	—
185	C₃×#41	—	2	4	no	—
186	C₃×#41	—	2	2	no	—
187	C₃×#41	—	2	2	no	—
188	C₃×#41	—	2	4	no	—
189	C₃×#41	C₂×D₉	1	4	yes	complemented
190	C₃×#41	C₂×C₃×D₃	1	4	yes	—
191	C₂×C₃×Q₈	—	2	1	no	—
192	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
193	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
194	C₂×C₃×D₄	—	2	2	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	—	2	1	no	—
198	C₂×C₃×D₄	—	9	2	no	—
199	C₂×C₃×D₄	—	9	4	no	—
200	C₂×C₃×D₄	—	18	2	no	—
201	C₂×C₃×D₄	—	18	1	no	—
202	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic, complemented
203	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	2	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
210	C₂×D₁₂	—	3	2	no	—
211	C₂×D₁₂	—	3	4	no	—
212	C₂×D₁₂	—	6	1	no	—
213	C₂×D₁₂	—	6	2	no	—
214	C₃×SD₁₆	—	9	8	no	—
215	C₃×D₈	—	9	8	no	—
216	C₃×M₁₆	—	9	4	no	—
217	C₂×C₃×C₈	—	9	2	no	—
218	#215	—	3	8	no	—
219	#213	—	3	8	no	—
220	#208	—	3	4	no	—
221	C₂×C₃⋊C₈	—	3	2	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	2	2	no	—
224	C₂²×C₃²	—	4	2	no	—
225	C₂²×C₃²	C₂×#67	1	2	yes	—
226	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
227	C₂×C₃×D₃	—	6	4	no	—
228	C₂×C₃×D₃	—	12	8	no	—
229	C₂×C₃×D₃	—	12	4	no	—
230	C₃²×C₄	—	2	2	no	—
231	C₃²×C₄	C₂×#67	1	2	yes	—
232	C₃²×C₄	C₂×#67	1	1	yes	characteristic
233	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
234	C₂²×C₉	—	2	2	no	—
235	C₂²×C₉	—	2	4	no	—
236	C₂²×C₉	—	2	2	no	—
237	C₂²×C₉	—	2	1	no	—
238	C₂²×C₉	—	2	2	no	—
239	C₂²×C₉	—	4	2	no	—
240	C₂²×C₉	—	4	4	no	—
241	C₂²×C₉	—	4	2	no	—
242	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
243	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×D₉	—	2	4	no	—
245	C₂×D₉	—	4	8	no	—
246	C₂×D₉	—	4	4	no	—
247	C₄×C₉	—	2	4	no	—
248	C₄×C₉	—	2	2	no	—
249	C₄×C₉	—	2	1	no	—
250	C₄×C₉	—	2	2	no	—
251	C₄×C₉	—	2	1	no	—
252	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
253	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
254	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
255	C₂×#41	C₃×D₉	1	1	yes	characteristic, complemented
256	C₂²×D₄	—	9	1	no	—
257	AGL(1,ℤ/8)	—	9	8	no	—
258	C₂×SD₁₆	—	9	2	no	—
259	C₂×D₈	—	9	2	no	—
260	C₂×M₁₆	—	9	1	no	—
261	C₃×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	—	18	4	no	—
267	C₂³×C₃	—	18	2	no	—
268	C₂³×C₃	—	36	4	no	—
269	C₂³×C₃	#611	1	1	yes	characteristic
270	C₂³×C₃	C₃×#67	1	1	yes	characteristic
271	C₂²×D₃	—	6	4	no	—
272	C₂²×D₃	—	6	2	no	—
273	C₂²×D₃	—	12	4	no	—
274	C₃×Q₈	—	2	2	no	—
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	—	2	1	no	—
277	C₃×Q₈	—	2	2	no	—
278	C₃×Q₈	C₂²×D₉	1	2	yes	complemented
279	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
280	C₃×D₄	—	2	8	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	4	no	—
283	C₃×D₄	—	2	4	no	—
284	C₃×D₄	—	2	1	no	—
285	C₃×D₄	—	2	1	no	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	9	4	no	—
288	C₃×D₄	—	18	4	no	—
289	C₃×D₄	—	18	2	no	—
290	C₃×D₄	C₂²×D₉	1	2	yes	complemented
291	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	#611	1	2	yes	—
303	C₂×C₃×C₄	#611	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
305	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
306	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
307	C₂×C₃×C₄	C₃×#67	1	2	yes	—
308	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
310	D₁₂	—	3	4	no	—
311	D₁₂	—	6	4	no	—
312	D₁₂	—	6	2	no	—
313	C₃×C₈	—	9	4	no	—
314	C₃⋊C₈	—	3	4	no	—
315	C₂×C₃²	—	2	2	no	—
316	C₂×C₃²	—	4	2	no	—
317	C₂×C₃²	#949	1	2	yes	—
318	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
319	C₃×D₃	—	12	4	no	—
320	C₂×C₉	—	2	2	no	—
321	C₂×C₉	—	2	2	no	—
322	C₂×C₉	—	2	1	no	—
323	C₂×C₉	—	4	2	no	—
324	C₂×C₉	—	4	4	no	—
325	C₂×C₉	—	4	2	no	—
326	C₂×C₉	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
327	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
328	D₉	—	4	4	no	—
329	C₂⁴	—	18	1	no	—
330	#41	—	2	2	no	—
331	#41	C₂×C₃×D₉	1	4	yes	complemented
332	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	9	2	no	—
335	C₂×D₄	—	9	4	no	—
336	C₂×D₄	—	18	1	no	—
337	C₂×D₄	—	18	2	no	—
338	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
341	SD₁₆	—	9	8	no	—
342	D₈	—	9	8	no	—
343	M₁₆	—	9	4	no	—
344	C₂×C₈	—	9	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	18	4	no	—
357	C₂²×C₃	—	36	8	no	—
358	C₂²×C₃	—	36	4	no	—
359	C₂²×C₃	C₂×#611	1	2	yes	—
360	C₂²×C₃	C₂×#611	1	1	yes	characteristic
361	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
362	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
363	C₂×D₃	—	6	4	no	—
364	C₂×D₃	—	12	8	no	—
365	C₂×D₃	—	12	4	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	C₂×#611	1	2	yes	—
373	C₃×C₄	C₂×#611	1	1	yes	characteristic
374	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
375	C₃×C₄	C₂×C₃×#67	1	2	yes	—
376	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
377	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
378	C₃²	C₂×#949	1	1	yes	characteristic
379	C₉	—	2	1	no	—
380	C₉	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
381	C₂³	—	2	1	no	—
382	C₂³	—	18	4	no	—
383	C₂³	—	18	2	no	—
384	C₂³	—	36	4	no	—
385	C₂³	C₃×#611	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	C₂²×C₃×D₉	1	2	yes	complemented
388	D₄	—	2	4	no	—
389	D₄	—	2	1	no	—
390	D₄	—	9	4	no	—
391	D₄	—	18	4	no	—
392	D₄	—	18	2	no	—
393	D₄	C₂²×C₃×D₉	1	2	yes	complemented
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	C₃×#611	1	1	yes	characteristic
397	C₂×C₄	C₃×#611	1	2	yes	—
398	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
400	C₈	—	9	4	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	2	no	—
405	C₂×C₃	—	4	2	no	—
406	C₂×C₃	—	4	4	no	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	—	4	2	no	—
409	C₂×C₃	—	36	4	no	—
410	C₂×C₃	#63512	1	2	yes	direct product factor
411	C₂×C₃	C₂²×#611	1	1	yes	characteristic
412	C₂×C₃	C₃×#949	1	2	yes	—
413	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
414	D₃	—	12	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	18	4	no	—
419	C₂²	—	36	8	no	—
420	C₂²	—	36	4	no	—
421	C₂²	C₂×C₃×#611	1	2	yes	—
422	C₂²	C₂×C₃×#611	1	1	yes	characteristic
423	C₄	—	2	2	no	—
424	C₄	C₂×C₃×#611	1	2	yes	—
425	C₄	C₂×C₃×#611	1	1	yes	characteristic
426	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
427	C₃	—	2	1	no	—
428	C₃	C₂×#63512	1	1	yes	characteristic, direct product factor
429	C₃	C₂×C₃×#949	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	36	4	no	—
433	C₂	C₃×#63512	1	2	yes	direct product factor
434	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#611
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle	C₂²×C₃²	C₂×#67
hypercenter	C₂×C₃×#41	D₉
hypocenter	C₉	C₂×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂²×C₃×D₃₆	C₂	semidirect
3. C₃×#63512	C₂	direct (N × H)
4. C₂×C₃×#3675	C₂	semidirect
5. C₂×C₃×#3673	C₂	semidirect
6. C₂×C₃×#3667	C₂	semidirect
8. C₂×#63512	C₃	direct (N × H)
11. C₃×C₉×#41	C₂²	semidirect
12. C₂×C₃×Q₈×C₉	C₂²	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
20. C₂×C₃×D₃₆	C₂²	semidirect
21. C₃×#3675	C₂²	semidirect
22. C₃×#3673	C₂²	semidirect
23. C₃×#3667	C₂²	semidirect
24. C₂×C₃×C₉⋊C₈	C₂²	semidirect
32. C₂×C₉×#41	C₂×C₃	semidirect
33. C₂²×D₃₆	C₂×C₃	semidirect
34. #63512	C₂×C₃	direct (N × H)
35. C₂×#3675	C₂×C₃	semidirect
36. C₂×#3673	C₂×C₃	semidirect
37. C₂×#3667	C₂×C₃	semidirect
44. C₃×Q₈×C₉	C₂³	semidirect
47. C₃×D₄×C₉	C₂³	semidirect
57. C₃×C₉⋊C₈	C₂³	semidirect
80. C₉×#41	C₂²×C₃	semidirect
82. C₂×Q₈×C₉	C₂²×C₃	semidirect
86. C₂×D₄×C₉	C₂²×C₃	semidirect
94. C₂×D₃₆	C₂²×C₃	semidirect
95. #3675	C₂²×C₃	semidirect
96. #3673	C₂²×C₃	semidirect
97. #3667	C₂²×C₃	semidirect
98. C₂×C₉⋊C₈	C₂²×C₃	semidirect
112. C₂×C₃×#41	D₉	semidirect
154. Q₈×C₉	C₂³×C₃	semidirect
160. D₄×C₉	C₂³×C₃	semidirect
176. C₉⋊C₈	C₂³×C₃	semidirect
180. C₂×C₃×C₉	AGL(1,ℤ/8)	semidirect
189. C₃×#41	C₂×D₉	semidirect
192. C₂×C₃×Q₈	C₂×D₉	semidirect
202. C₂×C₃×D₄	C₂×D₉	semidirect
255. C₂×#41	C₃×D₉	semidirect
261. C₃×C₉	C₂×AGL(1,ℤ/8)	semidirect
278. C₃×Q₈	C₂²×D₉	semidirect
290. C₃×D₄	C₂²×D₉	semidirect
326. C₂×C₉	C₃×AGL(1,ℤ/8)	semidirect
331. #41	C₂×C₃×D₉	semidirect
332. C₂×Q₈	C₂×C₃×D₉	semidirect
338. C₂×D₄	C₂×C₃×D₉	semidirect
380. C₉	C₂×C₃×AGL(1,ℤ/8)	semidirect
387. Q₈	C₂²×C₃×D₉	semidirect
393. D₄	C₂²×C₃×D₉	semidirect
410. C₂×C₃	#63512	direct (N × H)
428. C₃	C₂×#63512	direct (N × H)
433. C₂	C₃×#63512	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×C₉×#41	2
C₂²×C₃×D₃₆	2
C₃×#63512	2
C₂×C₃×#3675	2
C₂×C₃×#3673	2
C₂×C₃×#3667	2
C₂×C₃×#949	3
C₂×#63512	3

Subgroups — C2×C3×#63512 #13153680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63512 #13153680