Subgroups — C₃×#10589820 #13153255

Order 1728.

1044 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3699	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63502	C₂	1	2	yes	maximal, complemented
4	C₃×#63501	C₂	1	4	yes	maximal, complemented
5	C₃×#63500	C₂	1	2	yes	maximal, complemented
6	C₃×D₄×Dic₉	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5718	—	3	1	no	maximal
10	#10589820	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
12	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
13	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
14	C₂×C₃×#611	C₂²	1	4	yes	—
15	C₂×C₃×#611	C₂²	1	4	yes	—
16	C₂²×C₃×Dic₉	C₂²	1	4	yes	—
17	C₃×#3699	—	2	8	no	—
18	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×#3676	C₂²	1	4	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
26	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
27	C₃×C₄×Dic₉	C₂²	1	2	yes	—
28	C₂×C₃×#237	—	3	2	no	—
29	C₃²×#127	D₃	1	1	yes	characteristic
30	C₃×#940	—	3	2	no	—
31	C₃×#939	—	3	4	no	—
32	C₃×#938	—	3	2	no	—
33	C₃×D₄×Dic₃	—	3	2	no	—
34	C₃×C₄×D₁₂	—	3	1	no	—
35	C₃×C₄×Dic₆	—	3	1	no	—
36	C₂×#3699	C₂×C₃	1	2	yes	complemented
37	C₉×#127	—	2	1	no	—
38	C₉×#127	C₂×C₃	1	1	yes	characteristic, complemented
39	#63502	C₂×C₃	1	2	yes	complemented
40	#63501	C₂×C₃	1	4	yes	complemented
41	#63500	C₂×C₃	1	2	yes	complemented
42	D₄×Dic₉	C₂×C₃	1	2	yes	complemented
43	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×C₉	C₂³	1	4	yes	—
46	C₂²×C₃×D₉	C₂³	1	2	yes	—
47	C₃×D₄×C₉	—	2	4	no	—
48	C₃×D₄×C₉	—	2	4	no	—
49	C₃×D₄×C₉	—	4	2	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₃×#611	—	2	8	no	—
54	C₃×#611	—	4	4	no	—
55	C₂×C₃×Dic₉	—	2	8	no	—
56	C₂×C₃×Dic₉	C₂³	1	2	yes	—
57	C₂×C₃×Dic₉	C₂³	1	2	yes	—
58	C₂×C₃×Dic₉	C₂³	1	2	yes	—
59	C₃×D₃₆	—	2	2	no	—
60	C₃×C₄×D₉	—	2	4	no	—
61	C₃×Dic₁₈	D₄	1	4	yes	complemented
62	C₃×#550	—	9	1	no	—
63	#5718	—	3	1	no	—
64	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
65	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
66	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
67	C₂×C₃×#67	—	3	4	no	—
68	C₂×C₃×#67	—	3	4	no	—
69	C₂²×C₃×Dic₃	—	3	4	no	—
70	C₃×#237	—	6	8	no	—
71	C₂×C₃×D₁₂	—	3	1	no	—
72	C₂×C₃×C₄×D₃	—	3	2	no	—
73	C₂×C₃×Dic₆	—	3	1	no	—
74	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
75	C₃×#217	—	3	4	no	—
76	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
77	C₃×C₄⋊Dic₃	—	3	1	no	—
78	C₃×C₄⋊Dic₃	—	3	1	no	—
79	C₃×Dic₃⋊C₄	—	3	2	no	—
80	C₃×C₄×Dic₃	—	3	2	no	—
81	C₂×D₄×C₉	—	2	2	no	—
82	C₂×D₄×C₉	—	2	2	no	—
83	C₂×D₄×C₉	—	2	2	no	—
84	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
85	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
86	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
87	C₂×#611	C₂²×C₃	1	4	yes	—
88	C₂×#611	C₂²×C₃	1	4	yes	—
89	C₂²×Dic₉	C₂²×C₃	1	4	yes	—
90	#3699	—	2	8	no	—
91	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
93	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
94	C₄²×C₉	—	2	1	no	—
95	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
96	#3676	C₂²×C₃	1	4	yes	—
97	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
98	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
99	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
100	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
101	C₄×Dic₉	C₂²×C₃	1	2	yes	—
102	C₂²×C₃×C₉	—	2	4	no	—
103	C₂²×C₃×C₉	—	2	4	no	—
104	C₂²×C₃×C₉	—	2	4	no	—
105	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×D₉	—	2	2	no	—
107	C₂×C₃×D₉	—	2	2	no	—
108	C₂×C₃×D₉	—	2	2	no	—
109	C₃×C₄×C₉	—	2	1	no	—
110	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
111	C₃×C₄×C₉	#41	1	2	yes	complemented
112	C₃×Dic₉	—	2	2	no	—
113	C₃×Dic₉	—	2	2	no	—
114	C₃×Dic₉	C₂×D₄	1	4	yes	—
115	C₂×C₃×#41	—	9	2	no	—
116	C₂×#237	—	3	2	no	—
117	C₃×#127	—	2	1	no	—
118	C₃×#127	—	9	2	no	—
119	C₃×#127	D₉	1	1	yes	characteristic, complemented
120	C₃×#127	C₃×D₃	1	1	yes	characteristic
121	C₃×#121	—	9	2	no	—
122	C₃×#121	—	9	4	no	—
123	C₃×C₄×Q₈	—	9	1	no	—
124	C₃×C₄×D₄	—	9	2	no	—
125	C₃×C₄×D₄	—	9	1	no	—
126	#940	—	3	2	no	—
127	#939	—	3	4	no	—
128	#938	—	3	2	no	—
129	D₄×Dic₃	—	3	2	no	—
130	C₄×D₁₂	—	3	1	no	—
131	C₄×Dic₆	—	3	1	no	—
132	C₂³×C₃²	C₂²×D₃	1	4	yes	—
133	C₂²×C₃×D₃	—	3	2	no	—
134	C₃²×D₄	—	2	4	no	—
135	C₃²×D₄	—	2	4	no	—
136	C₃²×D₄	—	4	2	no	—
137	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
140	C₃×#67	—	6	8	no	—
141	C₃×#67	—	12	4	no	—
142	C₂×C₃×Dic₃	—	3	2	no	—
143	C₂×C₃×Dic₃	—	3	2	no	—
144	C₂×C₃×Dic₃	—	3	2	no	—
145	C₂×C₃×Dic₃	—	6	8	no	—
146	C₃×D₁₂	—	6	2	no	—
147	C₃×C₄×D₃	—	6	4	no	—
148	C₃×Dic₆	—	3	4	no	—
149	C₂³×C₉	—	2	4	no	—
150	C₂³×C₉	C₂³×C₃	1	4	yes	—
151	C₂²×D₉	C₂³×C₃	1	2	yes	—
152	D₄×C₉	—	2	4	no	—
153	D₄×C₉	—	2	4	no	—
154	D₄×C₉	—	4	4	no	—
155	D₄×C₉	—	4	4	no	—
156	D₄×C₉	—	4	2	no	—
157	D₄×C₉	—	4	4	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
164	#611	—	2	8	no	—
165	#611	—	4	4	no	—
166	C₂×Dic₉	—	2	8	no	—
167	C₂×Dic₉	C₂³×C₃	1	2	yes	—
168	C₂×Dic₉	C₂³×C₃	1	2	yes	—
169	C₂×Dic₉	C₂³×C₃	1	2	yes	—
170	D₃₆	—	2	2	no	—
171	C₄×D₉	—	2	4	no	—
172	Dic₁₈	C₃×D₄	1	4	yes	complemented
173	#550	—	9	1	no	Sylow
174	C₂×C₃×C₉	—	4	4	no	—
175	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₃×D₉	—	4	2	no	—
179	C₃×#41	—	18	8	no	—
180	C₂×C₃×Q₈	—	9	1	no	—
181	C₂×C₃×D₄	—	2	2	no	—
182	C₂×C₃×D₄	—	2	2	no	—
183	C₂×C₃×D₄	—	2	2	no	—
184	C₂×C₃×D₄	—	9	4	no	—
185	C₂×C₃×D₄	—	9	4	no	—
186	C₂×C₃×D₄	—	9	1	no	—
187	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
188	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
189	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
190	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
191	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
192	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
193	C₂²×C₃×C₄	—	9	4	no	—
194	C₂²×C₃×C₄	—	9	2	no	—
195	C₂×#67	—	3	4	no	—
196	C₂×#67	—	3	4	no	—
197	C₂²×Dic₃	—	3	4	no	—
198	#237	—	6	8	no	—
199	C₂×D₁₂	—	3	1	no	—
200	C₂×C₄×D₃	—	3	2	no	—
201	C₂×Dic₆	—	3	1	no	—
202	C₃×C₄⋊C₄	—	9	2	no	—
203	C₃×C₄⋊C₄	—	9	1	no	—
204	C₃×C₄⋊C₄	—	9	1	no	—
205	C₃×C₂²⋊C₄	—	9	4	no	—
206	C₃×C₂²⋊C₄	—	9	2	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	—	9	2	no	—
209	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
210	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
211	#217	—	3	4	no	—
212	(C₂×D₃)⋊C₄	—	3	2	no	—
213	C₄⋊Dic₃	—	3	1	no	—
214	C₄⋊Dic₃	—	3	1	no	—
215	Dic₃⋊C₄	—	3	2	no	—
216	C₄×Dic₃	—	3	2	no	—
217	C₂²×C₃²	—	2	4	no	—
218	C₂²×C₃²	—	2	4	no	—
219	C₂²×C₃²	—	2	4	no	—
220	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
221	C₂×C₃×D₃	—	6	2	no	—
222	C₂×C₃×D₃	—	6	2	no	—
223	C₂×C₃×D₃	—	6	2	no	—
224	C₃²×C₄	—	2	1	no	—
225	C₃²×C₄	D₃×D₄	1	2	yes	—
226	C₃²×C₄	#237	1	2	yes	—
227	C₃×Dic₃	—	3	4	no	—
228	C₃×Dic₃	—	6	2	no	—
229	C₃×Dic₃	—	6	2	no	—
230	C₂²×C₉	—	2	4	no	—
231	C₂²×C₉	—	2	4	no	—
232	C₂²×C₉	—	2	4	no	—
233	C₂²×C₉	—	2	1	no	—
234	C₂²×C₉	—	4	4	no	—
235	C₂²×C₉	—	4	4	no	—
236	C₂²×C₉	—	4	4	no	—
237	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
238	C₂×D₉	—	2	2	no	—
239	C₂×D₉	—	2	2	no	—
240	C₂×D₉	—	2	2	no	—
241	C₄×C₉	—	2	2	no	—
242	C₄×C₉	—	2	1	no	—
243	C₄×C₉	—	2	2	no	—
244	C₄×C₉	—	2	2	no	—
245	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
246	C₄×C₉	C₃×#41	1	2	yes	complemented
247	Dic₉	—	2	2	no	—
248	Dic₉	—	2	2	no	—
249	Dic₉	C₂×C₃×D₄	1	4	yes	—
250	C₂×#41	—	9	2	no	—
251	#127	—	9	2	no	—
252	#127	C₃×D₉	1	1	yes	characteristic, complemented
253	#121	—	9	2	no	—
254	#121	—	9	4	no	—
255	C₄×Q₈	—	9	1	no	—
256	C₄×D₄	—	9	2	no	—
257	C₄×D₄	—	9	1	no	—
258	C₃×C₉	#550	1	1	yes	characteristic, complemented, Sylow
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	9	2	no	—
261	C₂³×C₃	C₂²×D₉	1	4	yes	—
262	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
263	C₂²×D₃	—	3	2	no	—
264	C₃×Q₈	—	9	4	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	4	no	—
268	C₃×D₄	—	2	4	no	—
269	C₃×D₄	—	4	4	no	—
270	C₃×D₄	—	4	4	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	4	2	no	—
273	C₃×D₄	—	4	4	no	—
274	C₃×D₄	—	18	8	no	—
275	C₃×D₄	—	18	2	no	—
276	C₃×D₄	—	36	4	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	9	2	no	—
281	C₂×C₃×C₄	—	9	2	no	—
282	C₂×C₃×C₄	—	9	2	no	—
283	C₂×C₃×C₄	—	18	8	no	—
284	C₂×C₃×C₄	—	18	4	no	—
285	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
291	#67	—	6	8	no	—
292	#67	—	12	4	no	—
293	C₂×Dic₃	—	3	2	no	—
294	C₂×Dic₃	—	3	2	no	—
295	C₂×Dic₃	—	3	2	no	—
296	C₂×Dic₃	—	6	8	no	—
297	D₁₂	—	6	2	no	—
298	C₄×D₃	—	6	4	no	—
299	Dic₆	—	3	4	no	—
300	C₂×C₃²	—	4	4	no	—
301	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
302	C₂×C₃²	C₂×#237	1	1	yes	characteristic
303	C₂×C₃²	#1004	1	1	yes	characteristic
304	C₃×D₃	—	12	2	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	—	2	1	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	4	4	no	—
309	C₂×C₉	—	8	4	no	—
310	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
311	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
312	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
313	D₉	—	4	2	no	—
314	#41	—	18	8	no	—
315	C₂×Q₈	—	9	1	no	—
316	C₂×D₄	—	9	4	no	—
317	C₂×D₄	—	9	4	no	—
318	C₂×D₄	—	9	1	no	—
319	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
320	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
321	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
322	C₂²×C₄	—	9	4	no	—
323	C₂²×C₄	—	9	2	no	—
324	C₄⋊C₄	—	9	1	no	—
325	C₄⋊C₄	—	9	2	no	—
326	C₄⋊C₄	—	9	1	no	—
327	C₂²⋊C₄	—	9	4	no	—
328	C₂²⋊C₄	—	9	2	no	—
329	C₄²	—	9	2	no	—
330	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	4	no	—
335	C₂²×C₃	—	2	4	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	4	4	no	—
339	C₂²×C₃	—	4	4	no	—
340	C₂²×C₃	—	4	4	no	—
341	C₂²×C₃	—	18	2	no	—
342	C₂²×C₃	—	18	2	no	—
343	C₂²×C₃	—	18	2	no	—
344	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
345	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
346	C₂×D₃	—	6	2	no	—
347	C₂×D₃	—	6	2	no	—
348	C₂×D₃	—	6	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	9	4	no	—
355	C₃×C₄	—	18	2	no	—
356	C₃×C₄	—	18	2	no	—
357	C₃×C₄	D₄×D₉	1	2	yes	—
358	C₃×C₄	#3699	1	2	yes	complemented
359	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
360	C₃×C₄	C₃×#237	1	2	yes	—
361	Dic₃	—	3	4	no	—
362	Dic₃	—	6	2	no	—
363	Dic₃	—	6	2	no	—
364	C₃²	#5718	1	1	yes	characteristic
365	C₉	—	2	1	no	—
366	C₉	C₃×#550	1	1	yes	characteristic, complemented
367	C₂³	—	9	2	no	—
368	C₂³	C₂²×C₃×D₉	1	4	yes	—
369	Q₈	—	9	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	2	no	—
373	D₄	—	18	8	no	—
374	D₄	—	18	2	no	—
375	D₄	—	36	4	no	—
376	C₂×C₄	—	9	2	no	—
377	C₂×C₄	—	9	2	no	—
378	C₂×C₄	—	9	2	no	—
379	C₂×C₄	—	18	8	no	—
380	C₂×C₄	—	18	4	no	—
381	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	—	4	4	no	—
389	C₂×C₃	—	8	4	no	—
390	C₂×C₃	—	36	2	no	—
391	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
392	C₂×C₃	C₂×#3699	1	1	yes	characteristic
393	C₂×C₃	#63710	1	1	yes	characteristic
394	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
395	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
396	C₂×C₃	C₃×#1004	1	1	yes	characteristic
397	D₃	—	12	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	18	2	no	—
402	C₂²	—	18	2	no	—
403	C₂²	—	18	2	no	—
404	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	9	4	no	—
407	C₄	—	18	2	no	—
408	C₄	—	18	2	no	—
409	C₄	C₃×D₄×D₉	1	2	yes	—
410	C₄	C₃×#3699	1	2	yes	complemented
411	C₃	—	2	1	no	—
412	C₃	#10589820	1	1	yes	characteristic, direct product factor
413	C₃	C₃×#5718	1	1	yes	characteristic
414	C₂	—	4	4	no	—
415	C₂	—	36	2	no	—
416	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
417	C₂	C₂×C₃×#3699	1	1	yes	characteristic
418	C₂	C₃×#63710	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#127	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#127	D₉
hypocenter	C₉	C₃×#550
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3699	C₂	semidirect
2. C₃×C₉×#127	C₂	semidirect
3. C₃×#63502	C₂	semidirect
4. C₃×#63501	C₂	semidirect
5. C₃×#63500	C₂	semidirect
6. C₃×D₄×Dic₉	C₂	semidirect
7. C₃×C₄×D₃₆	C₂	semidirect
8. C₃×C₄×Dic₁₈	C₂	semidirect
10. #10589820	C₃	direct (N × H)
36. C₂×#3699	C₂×C₃	semidirect
38. C₉×#127	C₂×C₃	semidirect
39. #63502	C₂×C₃	semidirect
40. #63501	C₂×C₃	semidirect
41. #63500	C₂×C₃	semidirect
42. D₄×Dic₉	C₂×C₃	semidirect
43. C₄×D₃₆	C₂×C₃	semidirect
44. C₄×Dic₁₈	C₂×C₃	semidirect
61. C₃×Dic₁₈	D₄	semidirect
111. C₃×C₄×C₉	#41	semidirect
119. C₃×#127	D₉	semidirect
172. Dic₁₈	C₃×D₄	semidirect
246. C₄×C₉	C₃×#41	semidirect
252. #127	C₃×D₉	semidirect
258. C₃×C₉	#550	semidirect
358. C₃×C₄	#3699	semidirect
366. C₉	C₃×#550	semidirect
410. C₄	C₃×#3699	semidirect
412. C₃	#10589820	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×#3699	2
C₃×C₉×#127	2
C₃×#63502	2
C₃×#63501	2
C₃×#63500	2
C₃×D₄×Dic₉	2
C₃×C₄×D₃₆	2
C₃×C₄×Dic₁₈	2
C₃×#5718	3
#10589820	3

Subgroups — C3×#10589820 #13153255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589820 #13153255