Subgroups — C₃×#10589627 #13152486

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 388 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×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63457	C₂	1	4	yes	maximal, complemented
5	C₃×#63444	C₂	1	4	yes	maximal, complemented
6	C₃×#63437	C₂	1	2	yes	maximal, complemented
7	C₃×#63436	C₂	1	2	yes	maximal, complemented
8	C₃×#5525	—	3	1	no	maximal
9	#10589627	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂³×C₃×D₉	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×#611	C₂²	1	2	yes	—
13	C₃×#3697	—	2	4	no	—
14	C₂×C₃×D₃₆	—	2	4	no	—
15	C₂×C₃×D₃₆	C₂²	1	2	yes	—
16	C₂×C₃×D₃₆	C₂²	1	2	yes	—
17	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×D₃₆	C₂²	1	8	yes	complemented
19	C₂×C₃×C₄×D₉	C₂²	1	2	yes	complemented
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	8	yes	complemented
25	C₂×C₃×#235	—	3	1	no	—
26	C₂²×C₃×D₁₂	—	3	1	no	—
27	C₃²×#117	D₃	1	1	yes	characteristic
28	C₃×#895	—	3	4	no	—
29	C₃×#882	—	3	4	no	—
30	C₃×#875	—	3	2	no	—
31	C₃×#874	—	3	2	no	—
32	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₉×#117	—	2	1	no	—
35	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
36	#63457	C₂×C₃	1	4	yes	complemented
37	#63444	C₂×C₃	1	4	yes	complemented
38	#63437	C₂×C₃	1	2	yes	complemented
39	#63436	C₂×C₃	1	2	yes	complemented
40	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
41	C₂²×C₃×D₉	—	2	4	no	—
42	C₂²×C₃×D₉	—	4	4	no	—
43	C₂²×C₃×D₉	C₂³	1	4	yes	—
44	C₂²×C₃×D₉	C₂³	1	2	yes	—
45	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₃×#611	—	2	4	no	—
50	C₂×C₃×Dic₉	C₂³	1	2	yes	—
51	C₃×D₃₆	—	2	4	no	—
52	C₃×D₃₆	—	2	4	no	—
53	C₃×D₃₆	—	2	2	no	—
54	C₃×D₃₆	—	4	8	no	—
55	C₃×C₄×D₉	—	2	4	no	—
56	C₃×Dic₁₈	—	2	2	no	—
57	C₃×#535	—	9	1	no	—
58	#5525	—	3	1	no	—
59	C₂³×C₃×D₃	—	3	2	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×#67	—	3	2	no	—
62	C₃×#235	—	6	4	no	—
63	C₂×C₃×D₁₂	—	3	2	no	—
64	C₂×C₃×D₁₂	—	3	2	no	—
65	C₂×C₃×D₁₂	—	3	1	no	—
66	C₂×C₃×D₁₂	—	3	8	no	—
67	C₂×C₃×D₁₂	—	6	4	no	—
68	C₂×C₃×C₄×D₃	—	3	2	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₂³×D₉	C₂²×C₃	1	2	yes	—
71	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
73	C₃²×C₄²	C₂×D₃	1	2	yes	—
74	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
75	C₂²×C₄×C₉	—	2	1	no	—
76	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
77	C₂×#611	C₂²×C₃	1	2	yes	—
78	#3697	—	2	4	no	—
79	C₂×D₃₆	—	2	4	no	—
80	C₂×D₃₆	C₂²×C₃	1	2	yes	—
81	C₂×D₃₆	C₂²×C₃	1	2	yes	—
82	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂×D₃₆	C₂²×C₃	1	8	yes	complemented
84	C₂×C₄×D₉	C₂²×C₃	1	2	yes	complemented
85	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₉×C₄⋊C₄	—	2	2	no	—
87	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₄²×C₉	—	2	2	no	—
91	C₄²×C₉	C₂²×C₃	1	2	yes	complemented
92	(C₂×D₉)⋊C₄	C₂²×C₃	1	8	yes	complemented
93	C₂²×C₃×C₉	—	2	2	no	—
94	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×D₉	—	2	2	no	—
97	C₂×C₃×D₉	—	2	4	no	—
98	C₂×C₃×D₉	—	2	4	no	—
99	C₂×C₃×D₉	—	2	8	no	—
100	C₂×C₃×D₉	—	4	8	no	—
101	C₃×C₄×C₉	—	2	4	no	—
102	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
103	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
104	C₃×Dic₉	—	2	2	no	—
105	C₂×C₃×#41	—	9	1	no	—
106	C₂²×C₃×D₄	—	9	1	no	—
107	C₂×#235	—	3	1	no	—
108	C₂²×D₁₂	—	3	1	no	—
109	C₃×#127	—	9	2	no	—
110	C₃×#124	—	9	2	no	—
111	C₃×#121	—	9	4	no	—
112	C₃×#120	—	9	4	no	—
113	C₃×#117	—	2	1	no	—
114	C₃×#117	D₉	1	1	yes	characteristic, complemented
115	C₃×#117	C₃×D₃	1	1	yes	characteristic
116	#895	—	3	4	no	—
117	#882	—	3	4	no	—
118	#875	—	3	2	no	—
119	#874	—	3	2	no	—
120	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	3	4	no	—
122	C₂²×C₃×D₃	—	3	2	no	—
123	C₂²×C₃×D₃	—	6	4	no	—
124	C₂²×C₃×D₃	—	12	4	no	—
125	C₂×C₃²×C₄	D₁₂	1	4	yes	—
126	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₃×#67	—	6	4	no	—
130	C₂×C₃×Dic₃	—	3	2	no	—
131	C₃×D₁₂	—	6	4	no	—
132	C₃×D₁₂	—	6	4	no	—
133	C₃×D₁₂	—	6	2	no	—
134	C₃×D₁₂	—	12	8	no	—
135	C₃×C₄×D₃	—	6	4	no	—
136	C₃×Dic₆	—	6	2	no	—
137	C₂³×C₉	—	2	1	no	—
138	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
139	C₂²×D₉	—	2	4	no	—
140	C₂²×D₉	—	4	4	no	—
141	C₂²×D₉	C₂³×C₃	1	4	yes	—
142	C₂²×D₉	C₂³×C₃	1	2	yes	—
143	C₂×C₄×C₉	—	2	4	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	4	no	—
147	C₂×C₄×C₉	C₃×D₄	1	4	yes	complemented
148	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
149	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
151	#611	—	2	4	no	—
152	C₂×Dic₉	C₂³×C₃	1	2	yes	—
153	D₃₆	—	2	4	no	—
154	D₃₆	—	2	4	no	—
155	D₃₆	—	2	2	no	—
156	D₃₆	—	4	8	no	—
157	C₄×D₉	—	2	4	no	—
158	Dic₁₈	—	2	2	no	—
159	#535	—	9	1	no	Sylow
160	C₂×C₃×C₉	—	2	2	no	—
161	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
163	C₃×D₉	—	4	2	no	—
164	C₃×D₉	—	4	4	no	—
165	C₂⁴×C₃	—	9	2	no	—
166	C₂³×D₃	—	3	2	no	—
167	C₃×#41	—	18	4	no	—
168	C₂×C₃×Q₈	—	9	1	no	—
169	C₂×C₃×D₄	—	9	2	no	—
170	C₂×C₃×D₄	—	9	2	no	—
171	C₂×C₃×D₄	—	9	2	no	—
172	C₂×C₃×D₄	—	9	1	no	—
173	C₂×C₃×D₄	—	9	8	no	—
174	C₂×C₃×D₄	—	18	4	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	9	2	no	—
177	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
179	C₂×#67	—	3	2	no	—
180	#235	—	6	4	no	—
181	C₂×D₁₂	—	3	1	no	—
182	C₂×D₁₂	—	3	2	no	—
183	C₂×D₁₂	—	3	2	no	—
184	C₂×D₁₂	—	3	8	no	—
185	C₂×D₁₂	—	6	4	no	—
186	C₂×C₄×D₃	—	3	2	no	—
187	C₂×Dic₆	—	3	1	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	complemented
190	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
191	C₃×C₂²⋊C₄	—	2	2	no	—
192	C₃×C₂²⋊C₄	—	9	8	no	—
193	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	C₂×D₉	1	2	yes	complemented
197	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
198	(C₂×D₃)⋊C₄	—	3	8	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	C₂×D₁₂	1	2	yes	—
201	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
202	C₂×C₃×D₃	—	6	2	no	—
203	C₂×C₃×D₃	—	6	4	no	—
204	C₂×C₃×D₃	—	6	4	no	—
205	C₂×C₃×D₃	—	6	8	no	—
206	C₂×C₃×D₃	—	12	8	no	—
207	C₃²×C₄	—	2	4	no	—
208	C₃²×C₄	C₂×D₁₂	1	2	yes	—
209	C₃²×C₄	C₂×D₁₂	1	2	yes	—
210	C₃×Dic₃	—	6	2	no	—
211	C₂²×C₉	—	2	2	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	2	no	—
214	C₂²×C₉	—	4	2	no	—
215	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
216	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
217	C₂×D₉	—	2	2	no	—
218	C₂×D₉	—	2	4	no	—
219	C₂×D₉	—	2	4	no	—
220	C₂×D₉	—	2	8	no	—
221	C₂×D₉	—	4	8	no	—
222	C₄×C₉	—	2	4	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	2	no	—
225	C₄×C₉	—	4	4	no	—
226	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
227	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
228	Dic₉	—	2	2	no	—
229	C₂×#41	—	9	1	no	—
230	C₂²×D₄	—	9	1	no	—
231	#127	—	9	2	no	—
232	#124	—	9	2	no	—
233	#121	—	9	4	no	—
234	#120	—	9	4	no	—
235	#117	C₃×D₉	1	1	yes	characteristic, complemented
236	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	9	4	no	—
239	C₂³×C₃	—	9	2	no	—
240	C₂³×C₃	—	18	4	no	—
241	C₂³×C₃	—	36	4	no	—
242	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
243	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
244	C₂²×D₃	—	3	4	no	—
245	C₂²×D₃	—	3	2	no	—
246	C₂²×D₃	—	6	4	no	—
247	C₂²×D₃	—	12	4	no	—
248	C₃×Q₈	—	18	2	no	—
249	C₃×D₄	—	18	4	no	—
250	C₃×D₄	—	18	4	no	—
251	C₃×D₄	—	18	4	no	—
252	C₃×D₄	—	18	2	no	—
253	C₃×D₄	—	36	8	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	9	2	no	—
259	C₂×C₃×C₄	—	18	4	no	—
260	C₂×C₃×C₄	D₃₆	1	4	yes	complemented
261	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
262	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	#67	—	6	4	no	—
269	C₂×Dic₃	—	3	2	no	—
270	D₁₂	—	6	4	no	—
271	D₁₂	—	6	4	no	—
272	D₁₂	—	6	2	no	—
273	D₁₂	—	12	8	no	—
274	C₄×D₃	—	6	4	no	—
275	Dic₆	—	6	2	no	—
276	C₂×C₃²	—	2	2	no	—
277	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
278	C₂×C₃²	#1009	1	2	yes	—
279	C₃×D₃	—	12	2	no	—
280	C₃×D₃	—	12	4	no	—
281	C₂×C₉	—	2	2	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	2	2	no	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
286	C₂×C₉	C₃×H(5,𝔽₂)	1	2	yes	—
287	D₉	—	4	2	no	—
288	D₉	—	4	4	no	—
289	C₂⁴	—	9	2	no	—
290	#41	—	18	4	no	—
291	C₂×Q₈	—	9	1	no	—
292	C₂×D₄	—	9	2	no	—
293	C₂×D₄	—	9	2	no	—
294	C₂×D₄	—	9	2	no	—
295	C₂×D₄	—	9	1	no	—
296	C₂×D₄	—	9	8	no	—
297	C₂×D₄	—	18	4	no	—
298	C₂²×C₄	—	9	2	no	—
299	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
300	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	complemented
301	C₂²⋊C₄	—	9	8	no	—
302	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
303	C₄²	C₂×C₃×D₉	1	2	yes	complemented
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	18	2	no	—
310	C₂²×C₃	—	18	4	no	—
311	C₂²×C₃	—	18	4	no	—
312	C₂²×C₃	—	18	8	no	—
313	C₂²×C₃	—	36	8	no	—
314	C₂²×C₃	C₂×D₃₆	1	2	yes	—
315	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
317	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
318	C₂×D₃	—	6	2	no	—
319	C₂×D₃	—	6	4	no	—
320	C₂×D₃	—	6	4	no	—
321	C₂×D₃	—	6	8	no	—
322	C₂×D₃	—	12	8	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	—	18	2	no	—
329	C₃×C₄	C₂×D₃₆	1	2	yes	—
330	C₃×C₄	C₂×D₃₆	1	2	yes	—
331	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
332	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
333	Dic₃	—	6	2	no	—
334	C₃²	#5525	1	1	yes	characteristic
335	C₉	—	2	1	no	—
336	C₉	C₃×#535	1	1	yes	characteristic, complemented
337	C₂³	—	9	4	no	—
338	C₂³	—	9	2	no	—
339	C₂³	—	18	4	no	—
340	C₂³	—	36	4	no	—
341	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
342	Q₈	—	18	2	no	—
343	D₄	—	18	4	no	—
344	D₄	—	18	4	no	—
345	D₄	—	18	4	no	—
346	D₄	—	18	2	no	—
347	D₄	—	36	8	no	—
348	C₂×C₄	—	9	2	no	—
349	C₂×C₄	—	18	4	no	—
350	C₂×C₄	C₃×D₃₆	1	4	yes	complemented
351	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
352	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
354	C₂×C₃	—	2	2	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	2	no	—
359	C₂×C₃	—	36	4	no	—
360	C₂×C₃	—	36	2	no	—
361	C₂×C₃	C₂²×D₃₆	1	1	yes	characteristic
362	C₂×C₃	#63715	1	2	yes	—
363	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
364	C₂×C₃	C₃×#1009	1	2	yes	—
365	D₃	—	12	4	no	—
366	D₃	—	12	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	18	2	no	—
369	C₂²	—	18	4	no	—
370	C₂²	—	18	4	no	—
371	C₂²	—	18	8	no	—
372	C₂²	—	36	8	no	—
373	C₂²	C₂×C₃×D₃₆	1	2	yes	—
374	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	18	2	no	—
377	C₄	C₂×C₃×D₃₆	1	2	yes	—
378	C₄	C₂×C₃×D₃₆	1	2	yes	—
379	C₃	—	2	1	no	—
380	C₃	#10589627	1	1	yes	characteristic, direct product factor
381	C₃	C₃×#5525	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	36	4	no	—
384	C₂	—	36	2	no	—
385	C₂	C₂²×C₃×D₃₆	1	1	yes	characteristic
386	C₂	C₃×#63715	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×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×#535
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ 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×D₃₆	C₂	semidirect
3. C₃×C₉×#117	C₂	semidirect
4. C₃×#63457	C₂	semidirect
5. C₃×#63444	C₂	semidirect
6. C₃×#63437	C₂	semidirect
7. C₃×#63436	C₂	semidirect
9. #10589627	C₃	direct (N × H)
17. C₂×C₃×D₃₆	C₂²	semidirect
18. C₂×C₃×D₃₆	C₂²	semidirect
19. C₂×C₃×C₄×D₉	C₂²	semidirect
20. C₂×C₃×Dic₁₈	C₂²	semidirect
21. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₃×C₄²×C₉	C₂²	semidirect
24. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
32. C₂×#3697	C₂×C₃	semidirect
33. C₂²×D₃₆	C₂×C₃	semidirect
35. C₉×#117	C₂×C₃	semidirect
36. #63457	C₂×C₃	semidirect
37. #63444	C₂×C₃	semidirect
38. #63437	C₂×C₃	semidirect
39. #63436	C₂×C₃	semidirect
45. C₂×C₃×C₄×C₉	D₄	semidirect
82. C₂×D₃₆	C₂²×C₃	semidirect
83. C₂×D₃₆	C₂²×C₃	semidirect
84. C₂×C₄×D₉	C₂²×C₃	semidirect
85. C₂×Dic₁₈	C₂²×C₃	semidirect
87. C₉×C₄⋊C₄	C₂²×C₃	semidirect
91. C₄²×C₉	C₂²×C₃	semidirect
92. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
114. C₃×#117	D₉	semidirect
147. C₂×C₄×C₉	C₃×D₄	semidirect
189. C₃×C₄⋊C₄	C₂×D₉	semidirect
196. C₃×C₄²	C₂×D₉	semidirect
235. #117	C₃×D₉	semidirect
236. C₃×C₉	#535	semidirect
260. C₂×C₃×C₄	D₃₆	semidirect
300. C₄⋊C₄	C₂×C₃×D₉	semidirect
303. C₄²	C₂×C₃×D₉	semidirect
336. C₉	C₃×#535	semidirect
350. C₂×C₄	C₃×D₃₆	semidirect
380. C₃	#10589627	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×D₃₆	2
C₃×C₉×#117	2
C₃×#63457	2
C₃×#63444	2
C₃×#63437	2
C₃×#63436	2
C₃×#5525	3
#10589627	3

Subgroups — C3×#10589627 #13152486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589627 #13152486