Subgroups — C₃×#10589626 #13152485

Order 1728.

1066 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×#3697	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63459	C₂	1	2	yes	maximal, complemented
5	C₃×#63457	C₂	1	2	yes	maximal, complemented
6	C₃×#63448	C₂	1	2	yes	maximal, complemented
7	C₃×#63444	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₃₆	C₂	1	4	yes	maximal, complemented
9	C₃×#5524	—	3	1	no	maximal
10	#10589626	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×#611	C₂²	1	2	yes	—
14	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
15	C₃×#3697	—	2	4	no	—
16	C₂×C₃×D₃₆	C₂²	1	4	yes	—
17	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄×D₉	—	2	4	no	—
19	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
20	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
21	C₂×C₃×C₄×D₉	C₂²	1	2	yes	complemented
22	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
26	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
27	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	complemented
28	C₃×C₄⋊Dic₉	C₂²	1	4	yes	complemented
29	C₂×C₃×#235	—	3	1	no	—
30	C₂²×C₃×C₄×D₃	—	3	1	no	—
31	C₃²×#117	D₃	1	1	yes	characteristic
32	C₃×#897	—	3	2	no	—
33	C₃×#895	—	3	2	no	—
34	C₃×#886	—	3	2	no	—
35	C₃×#882	—	3	2	no	—
36	C₃×C₄×D₁₂	—	3	4	no	—
37	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂²×C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
39	C₉×#117	—	2	1	no	—
40	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
41	#63459	C₂×C₃	1	2	yes	complemented
42	#63457	C₂×C₃	1	2	yes	complemented
43	#63448	C₂×C₃	1	2	yes	complemented
44	#63444	C₂×C₃	1	2	yes	complemented
45	C₄×D₃₆	C₂×C₃	1	4	yes	complemented
46	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
47	C₂²×C₃×D₉	—	2	2	no	—
48	C₂²×C₃×D₉	—	2	4	no	—
49	C₂²×C₃×D₉	C₂³	1	2	yes	—
50	C₂²×C₃×D₉	C₂³	1	2	yes	—
51	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
52	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
53	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₃×#611	—	2	4	no	—
56	C₂×C₃×Dic₉	—	2	2	no	—
57	C₂×C₃×Dic₉	C₂³	1	2	yes	—
58	C₂×C₃×Dic₉	C₂³	1	2	yes	—
59	C₃×D₃₆	—	2	8	no	—
60	C₃×D₃₆	—	2	2	no	—
61	C₃×C₄×D₉	—	2	4	no	—
62	C₃×C₄×D₉	—	2	4	no	—
63	C₃×C₄×D₉	—	2	4	no	—
64	C₃×Dic₁₈	—	2	2	no	—
65	C₃×#525	—	9	1	no	—
66	#5524	—	3	1	no	—
67	C₂³×C₃×D₃	—	3	1	no	—
68	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
69	C₂×C₃×#67	—	3	2	no	—
70	C₂²×C₃×Dic₃	—	3	1	no	—
71	C₃×#235	—	6	4	no	—
72	C₂×C₃×D₁₂	—	3	4	no	—
73	C₂×C₃×D₁₂	—	3	1	no	—
74	C₂×C₃×C₄×D₃	—	3	2	no	—
75	C₂×C₃×C₄×D₃	—	3	2	no	—
76	C₂×C₃×C₄×D₃	—	3	2	no	—
77	C₂×C₃×C₄×D₃	—	6	4	no	—
78	C₂×C₃×Dic₆	—	3	1	no	—
79	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
81	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
82	C₃²×C₄²	C₂×D₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
84	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
85	C₃×C₄⋊Dic₃	—	3	4	no	—
86	C₂²×C₄×C₉	—	2	1	no	—
87	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
88	C₂×#611	C₂²×C₃	1	2	yes	—
89	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
90	#3697	—	2	4	no	—
91	C₂×D₃₆	C₂²×C₃	1	4	yes	—
92	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂×C₄×D₉	—	2	4	no	—
94	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
95	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
96	C₂×C₄×D₉	C₂²×C₃	1	2	yes	complemented
97	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₉×C₂²⋊C₄	—	2	2	no	—
101	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₄²×C₉	—	2	2	no	—
103	C₄²×C₉	C₂²×C₃	1	2	yes	complemented
104	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
105	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	complemented
106	C₄⋊Dic₉	C₂²×C₃	1	4	yes	complemented
107	C₂²×C₃×C₉	—	2	2	no	—
108	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
109	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₃×D₉	—	2	8	no	—
111	C₂×C₃×D₉	—	2	2	no	—
112	C₂×C₃×D₉	—	2	2	no	—
113	C₂×C₃×D₉	—	2	2	no	—
114	C₂×C₃×D₉	—	2	4	no	—
115	C₂×C₃×D₉	#41	1	4	yes	complemented
116	C₃×C₄×C₉	—	2	4	no	—
117	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
118	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
119	C₃×Dic₉	—	2	2	no	—
120	C₃×Dic₉	—	2	2	no	—
121	C₂×C₃×#41	—	9	1	no	—
122	C₂³×C₃×C₄	—	9	1	no	—
123	C₂×#235	—	3	1	no	—
124	C₂²×C₄×D₃	—	3	1	no	—
125	C₃×#123	—	9	2	no	—
126	C₃×C₂²⋊Q₈	—	9	2	no	—
127	C₃×#121	—	9	2	no	—
128	C₃×#120	—	9	2	no	—
129	C₃×C₄×D₄	—	9	4	no	—
130	C₃×#117	—	2	1	no	—
131	C₃×#117	D₉	1	1	yes	characteristic, complemented
132	C₃×#117	C₃×D₃	1	1	yes	characteristic
133	#897	—	3	2	no	—
134	#895	—	3	2	no	—
135	#886	—	3	2	no	—
136	#882	—	3	2	no	—
137	C₄×D₁₂	—	3	4	no	—
138	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×D₃	—	3	2	no	—
140	C₂²×C₃×D₃	—	3	2	no	—
141	C₂²×C₃×D₃	—	6	4	no	—
142	C₂²×C₃×D₃	—	6	2	no	—
143	C₂×C₃²×C₄	D₁₂	1	4	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
145	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₃×#67	—	6	4	no	—
148	C₂×C₃×Dic₃	—	3	2	no	—
149	C₂×C₃×Dic₃	—	3	2	no	—
150	C₂×C₃×Dic₃	—	6	2	no	—
151	C₃×D₁₂	—	6	8	no	—
152	C₃×D₁₂	—	6	2	no	—
153	C₃×C₄×D₃	—	6	4	no	—
154	C₃×C₄×D₃	—	6	4	no	—
155	C₃×C₄×D₃	—	6	4	no	—
156	C₃×Dic₆	—	6	2	no	—
157	C₂³×C₉	—	2	1	no	—
158	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
159	C₂²×D₉	—	2	2	no	—
160	C₂²×D₉	—	2	4	no	—
161	C₂²×D₉	C₂³×C₃	1	2	yes	—
162	C₂²×D₉	C₂³×C₃	1	2	yes	—
163	C₂×C₄×C₉	—	2	4	no	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	4	no	—
167	C₂×C₄×C₉	C₃×D₄	1	4	yes	complemented
168	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
169	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
171	#611	—	2	4	no	—
172	C₂×Dic₉	—	2	2	no	—
173	C₂×Dic₉	C₂³×C₃	1	2	yes	—
174	C₂×Dic₉	C₂³×C₃	1	2	yes	—
175	D₃₆	—	2	8	no	—
176	D₃₆	—	2	2	no	—
177	C₄×D₉	—	2	4	no	—
178	C₄×D₉	—	2	4	no	—
179	C₄×D₉	—	2	4	no	—
180	Dic₁₈	—	2	2	no	—
181	#525	—	9	1	no	Sylow
182	C₂×C₃×C₉	—	2	2	no	—
183	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₉	C₂×#41	1	2	yes	—
185	C₃×D₉	—	2	4	no	—
186	C₃×D₉	—	4	2	no	—
187	C₂⁴×C₃	—	9	1	no	—
188	C₂³×D₃	—	3	1	no	—
189	C₃×#41	—	18	4	no	—
190	C₂×C₃×Q₈	—	9	1	no	—
191	C₂×C₃×D₄	—	9	2	no	—
192	C₂×C₃×D₄	—	9	4	no	—
193	C₂×C₃×D₄	—	9	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	9	1	no	—
196	C₂²×C₃×C₄	—	9	2	no	—
197	C₂²×C₃×C₄	—	9	2	no	—
198	C₂²×C₃×C₄	—	9	2	no	—
199	C₂²×C₃×C₄	—	18	4	no	—
200	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
202	C₂×#67	—	3	2	no	—
203	C₂²×Dic₃	—	3	1	no	—
204	#235	—	6	4	no	—
205	C₂×D₁₂	—	3	4	no	—
206	C₂×D₁₂	—	3	1	no	—
207	C₂×C₄×D₃	—	3	2	no	—
208	C₂×C₄×D₃	—	3	2	no	—
209	C₂×C₄×D₃	—	3	2	no	—
210	C₂×C₄×D₃	—	6	4	no	—
211	C₂×Dic₆	—	3	1	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	—	9	4	no	—
214	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	complemented
215	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	9	4	no	—
218	C₃×C₂²⋊C₄	—	9	4	no	—
219	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
221	C₃×C₄²	—	2	2	no	—
222	C₃×C₄²	C₂×D₉	1	2	yes	complemented
223	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
224	(C₂×D₃)⋊C₄	—	3	4	no	—
225	(C₂×D₃)⋊C₄	—	3	4	no	—
226	C₄⋊Dic₃	—	3	4	no	—
227	C₂²×C₃²	—	2	2	no	—
228	C₂²×C₃²	C₂×D₁₂	1	2	yes	—
229	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
230	C₂×C₃×D₃	—	3	4	no	—
231	C₂×C₃×D₃	—	6	8	no	—
232	C₂×C₃×D₃	—	6	2	no	—
233	C₂×C₃×D₃	—	6	2	no	—
234	C₂×C₃×D₃	—	6	2	no	—
235	C₂×C₃×D₃	—	6	4	no	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	C₂×D₁₂	1	2	yes	—
238	C₃²×C₄	C₂×D₁₂	1	2	yes	—
239	C₃×Dic₃	—	6	2	no	—
240	C₃×Dic₃	—	6	2	no	—
241	C₂²×C₉	—	2	2	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	2	2	no	—
244	C₂²×C₉	—	4	2	no	—
245	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
246	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
247	C₂×D₉	—	2	8	no	—
248	C₂×D₉	—	2	2	no	—
249	C₂×D₉	—	2	2	no	—
250	C₂×D₉	—	2	2	no	—
251	C₂×D₉	—	2	4	no	—
252	C₂×D₉	C₃×#41	1	4	yes	complemented
253	C₄×C₉	—	2	4	no	—
254	C₄×C₉	—	2	2	no	—
255	C₄×C₉	—	2	2	no	—
256	C₄×C₉	—	4	4	no	—
257	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
258	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
259	Dic₉	—	2	2	no	—
260	Dic₉	—	2	2	no	—
261	C₂×#41	—	9	1	no	—
262	C₂³×C₄	—	9	1	no	—
263	#123	—	9	2	no	—
264	C₂²⋊Q₈	—	9	2	no	—
265	#121	—	9	2	no	—
266	#120	—	9	2	no	—
267	C₄×D₄	—	9	4	no	—
268	#117	C₃×D₉	1	1	yes	characteristic, complemented
269	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	9	2	no	—
272	C₂³×C₃	—	9	2	no	—
273	C₂³×C₃	—	18	4	no	—
274	C₂³×C₃	—	18	2	no	—
275	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
276	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂²×D₃	—	3	2	no	—
278	C₂²×D₃	—	3	2	no	—
279	C₂²×D₃	—	6	4	no	—
280	C₂²×D₃	—	6	2	no	—
281	C₃×Q₈	—	18	2	no	—
282	C₃×D₄	—	18	8	no	—
283	C₃×D₄	—	18	4	no	—
284	C₃×D₄	—	18	2	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	9	2	no	—
290	C₂×C₃×C₄	—	9	2	no	—
291	C₂×C₃×C₄	—	18	2	no	—
292	C₂×C₃×C₄	—	18	4	no	—
293	C₂×C₃×C₄	—	18	4	no	—
294	C₂×C₃×C₄	—	18	4	no	—
295	C₂×C₃×C₄	D₃₆	1	4	yes	complemented
296	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
297	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
299	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
300	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
303	#67	—	6	4	no	—
304	C₂×Dic₃	—	3	2	no	—
305	C₂×Dic₃	—	3	2	no	—
306	C₂×Dic₃	—	6	2	no	—
307	D₁₂	—	6	8	no	—
308	D₁₂	—	6	2	no	—
309	C₄×D₃	—	6	4	no	—
310	C₄×D₃	—	6	4	no	—
311	C₄×D₃	—	6	4	no	—
312	Dic₆	—	6	2	no	—
313	C₂×C₃²	—	2	2	no	—
314	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
315	C₂×C₃²	D₃×#41	1	2	yes	—
316	C₃×D₃	—	6	4	no	—
317	C₃×D₃	—	12	2	no	—
318	C₂×C₉	—	2	2	no	—
319	C₂×C₉	—	2	1	no	—
320	C₂×C₉	—	2	2	no	—
321	C₂×C₉	—	4	2	no	—
322	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
323	C₂×C₉	C₂×C₃×#41	1	2	yes	—
324	D₉	—	2	4	no	—
325	D₉	—	4	2	no	—
326	C₂⁴	—	9	1	no	—
327	#41	—	18	4	no	—
328	C₂×Q₈	—	9	1	no	—
329	C₂×D₄	—	9	2	no	—
330	C₂×D₄	—	9	4	no	—
331	C₂×D₄	—	9	1	no	—
332	C₂²×C₄	—	9	1	no	—
333	C₂²×C₄	—	9	2	no	—
334	C₂²×C₄	—	9	2	no	—
335	C₂²×C₄	—	9	2	no	—
336	C₂²×C₄	—	18	4	no	—
337	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
338	C₄⋊C₄	—	9	4	no	—
339	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	complemented
340	C₂²⋊C₄	—	9	4	no	—
341	C₂²⋊C₄	—	9	4	no	—
342	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
343	C₄²	C₂×C₃×D₉	1	2	yes	complemented
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	9	4	no	—
350	C₂²×C₃	—	18	8	no	—
351	C₂²×C₃	—	18	2	no	—
352	C₂²×C₃	—	18	2	no	—
353	C₂²×C₃	—	18	2	no	—
354	C₂²×C₃	—	18	4	no	—
355	C₂²×C₃	C₂×D₃₆	1	2	yes	—
356	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
358	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
359	C₂×D₃	—	3	4	no	—
360	C₂×D₃	—	6	8	no	—
361	C₂×D₃	—	6	2	no	—
362	C₂×D₃	—	6	2	no	—
363	C₂×D₃	—	6	2	no	—
364	C₂×D₃	—	6	4	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	4	4	no	—
370	C₃×C₄	—	18	2	no	—
371	C₃×C₄	—	18	2	no	—
372	C₃×C₄	C₂×D₃₆	1	2	yes	—
373	C₃×C₄	C₂×D₃₆	1	2	yes	—
374	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
375	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
376	Dic₃	—	6	2	no	—
377	Dic₃	—	6	2	no	—
378	C₃²	#5524	1	1	yes	characteristic
379	C₉	—	2	1	no	—
380	C₉	C₃×#525	1	1	yes	characteristic, complemented
381	C₂³	—	9	2	no	—
382	C₂³	—	9	2	no	—
383	C₂³	—	18	4	no	—
384	C₂³	—	18	2	no	—
385	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
386	Q₈	—	18	2	no	—
387	D₄	—	18	8	no	—
388	D₄	—	18	4	no	—
389	D₄	—	18	2	no	—
390	C₂×C₄	—	9	2	no	—
391	C₂×C₄	—	9	2	no	—
392	C₂×C₄	—	18	2	no	—
393	C₂×C₄	—	18	4	no	—
394	C₂×C₄	—	18	4	no	—
395	C₂×C₄	—	18	4	no	—
396	C₂×C₄	C₃×D₃₆	1	4	yes	complemented
397	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
398	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	—	18	4	no	—
406	C₂×C₃	—	36	2	no	—
407	C₂×C₃	C₂²×D₃₆	1	1	yes	characteristic
408	C₂×C₃	#41×D₉	1	2	yes	—
409	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
410	C₂×C₃	C₃×D₃×#41	1	2	yes	—
411	D₃	—	6	4	no	—
412	D₃	—	12	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	9	4	no	—
415	C₂²	—	18	8	no	—
416	C₂²	—	18	2	no	—
417	C₂²	—	18	2	no	—
418	C₂²	—	18	2	no	—
419	C₂²	—	18	4	no	—
420	C₂²	C₂×C₃×D₃₆	1	2	yes	—
421	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	18	2	no	—
424	C₄	—	18	2	no	—
425	C₄	C₂×C₃×D₃₆	1	2	yes	—
426	C₄	C₂×C₃×D₃₆	1	2	yes	—
427	C₃	—	2	1	no	—
428	C₃	#10589626	1	1	yes	characteristic, direct product factor
429	C₃	C₃×#5524	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	18	4	no	—
432	C₂	—	36	2	no	—
433	C₂	C₂²×C₃×D₃₆	1	1	yes	characteristic
434	C₂	C₃×#41×D₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#117	D₉
hypocenter	C₉	C₃×#525
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3697	C₂	semidirect
2. C₂²×C₃×C₄×D₉	C₂	semidirect
3. C₃×C₉×#117	C₂	semidirect
4. C₃×#63459	C₂	semidirect
5. C₃×#63457	C₂	semidirect
6. C₃×#63448	C₂	semidirect
7. C₃×#63444	C₂	semidirect
8. C₃×C₄×D₃₆	C₂	semidirect
10. #10589626	C₃	direct (N × H)
17. C₂×C₃×D₃₆	C₂²	semidirect
21. C₂×C₃×C₄×D₉	C₂²	semidirect
22. C₂×C₃×Dic₁₈	C₂²	semidirect
23. C₃×C₉×C₄⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₉	C₂²	semidirect
27. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
28. C₃×C₄⋊Dic₉	C₂²	semidirect
37. C₂×#3697	C₂×C₃	semidirect
38. C₂²×C₄×D₉	C₂×C₃	semidirect
40. C₉×#117	C₂×C₃	semidirect
41. #63459	C₂×C₃	semidirect
42. #63457	C₂×C₃	semidirect
43. #63448	C₂×C₃	semidirect
44. #63444	C₂×C₃	semidirect
45. C₄×D₃₆	C₂×C₃	semidirect
51. C₂×C₃×C₄×C₉	D₄	semidirect
92. C₂×D₃₆	C₂²×C₃	semidirect
96. C₂×C₄×D₉	C₂²×C₃	semidirect
97. C₂×Dic₁₈	C₂²×C₃	semidirect
99. C₉×C₄⋊C₄	C₂²×C₃	semidirect
103. C₄²×C₉	C₂²×C₃	semidirect
105. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
106. C₄⋊Dic₉	C₂²×C₃	semidirect
115. C₂×C₃×D₉	#41	semidirect
131. C₃×#117	D₉	semidirect
167. C₂×C₄×C₉	C₃×D₄	semidirect
214. C₃×C₄⋊C₄	C₂×D₉	semidirect
222. C₃×C₄²	C₂×D₉	semidirect
252. C₂×D₉	C₃×#41	semidirect
268. #117	C₃×D₉	semidirect
269. C₃×C₉	#525	semidirect
295. C₂×C₃×C₄	D₃₆	semidirect
339. C₄⋊C₄	C₂×C₃×D₉	semidirect
343. C₄²	C₂×C₃×D₉	semidirect
380. C₉	C₃×#525	semidirect
396. C₂×C₄	C₃×D₃₆	semidirect
428. C₃	#10589626	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×#3697	2
C₂²×C₃×C₄×D₉	2
C₃×C₉×#117	2
C₃×#63459	2
C₃×#63457	2
C₃×#63448	2
C₃×#63444	2
C₃×C₄×D₃₆	2
C₃×#5524	3
#10589626	3

Subgroups — C3×#10589626 #13152485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589626 #13152485