Subgroups — C₂²×C₃²×#235 #13181713

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×#235	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃²×C₄×D₃	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃²×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃²×#41	—	3	1	no	maximal
8	C₂²×C₃×#235	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃²×D₃	C₂²	1	2	yes	—
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	C₂²	1	12	yes	complemented
14	C₂×C₃²×#67	C₂²	1	24	yes	complemented
15	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
16	C₃²×#235	C₂²	1	64	yes	direct product factor
17	C₂×C₃²×D₁₂	C₂²	1	12	yes	complemented
18	C₂×C₃²×C₄×D₃	C₂²	1	24	yes	complemented
19	C₂×C₃²×Dic₆	C₂²	1	12	yes	complemented
20	C₂×C₃²×#41	—	3	24	no	—
21	C₂²×C₃²×Q₈	—	3	1	no	—
22	C₂²×C₃²×D₄	—	3	1	no	—
23	C₂²×C₃²×D₄	—	3	2	no	—
24	C₂³×C₃²×C₄	—	2	4	no	—
25	C₂³×C₃²×C₄	—	3	2	no	—
26	C₂³×C₃²×C₄	D₃	1	1	yes	characteristic, complemented
27	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	complemented
28	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
29	C₂×C₃×#235	C₂×C₃	1	96	yes	direct product factor
30	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
31	C₂²×C₃×C₄×D₃	C₂×C₃	1	8	yes	complemented
32	C₂²×C₃×Dic₆	C₂×C₃	1	4	yes	complemented
33	C₂³×C₃³	—	2	4	no	—
34	C₂³×C₃³	C₂³	1	6	yes	—
35	C₂³×C₃³	C₂³	1	1	yes	characteristic
36	C₂²×C₃²×D₃	—	2	8	no	—
37	C₂²×C₃²×D₃	C₂³	1	12	yes	—
38	C₂×C₃³×C₄	C₂³	1	6	yes	—
39	C₂×C₃³×C₄	C₂³	1	6	yes	—
40	C₂×C₃³×C₄	C₂³	1	16	yes	complemented
41	C₃²×#67	C₂³	1	32	yes	complemented
42	C₂×C₃²×Dic₃	C₂³	1	12	yes	—
43	C₃²×D₁₂	C₂³	1	16	yes	complemented
44	C₃²×C₄×D₃	C₂³	1	32	yes	complemented
45	C₃²×Dic₆	C₂³	1	16	yes	complemented
46	C₂²×C₃×#41	—	3	4	no	—
47	C₂²×#235	C₃²	1	1	yes	characteristic, direct product factor
48	C₂⁴×C₃²	—	2	4	no	—
49	C₂⁴×C₃²	—	3	2	no	—
50	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
51	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
52	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
53	C₃²×#41	—	3	64	no	—
54	C₂×C₃²×Q₈	—	3	12	no	—
55	C₂×C₃²×D₄	—	3	24	no	—
56	C₂×C₃²×D₄	—	3	12	no	—
57	C₂²×C₃²×C₄	—	2	4	no	—
58	C₂²×C₃²×C₄	—	2	4	no	—
59	C₂²×C₃²×C₄	—	2	48	no	—
60	C₂²×C₃²×C₄	—	3	2	no	—
61	C₂²×C₃²×C₄	—	3	24	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂×D₃	1	12	yes	complemented
65	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
66	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
67	C₂²×C₃²×C₄	C₂²×C₃	1	48	yes	complemented
68	C₂×C₃×#67	C₂²×C₃	1	96	yes	complemented
69	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
70	C₃×#235	C₂²×C₃	1	256	yes	direct product factor
71	C₂×C₃×D₁₂	C₂²×C₃	1	48	yes	complemented
72	C₂×C₃×C₄×D₃	C₂²×C₃	1	96	yes	complemented
73	C₂×C₃×Dic₆	C₂²×C₃	1	48	yes	complemented
74	C₂²×C₃³	—	2	12	no	—
75	C₂²×C₃³	#41	1	4	yes	complemented
76	C₂²×C₃³	C₂⁴	1	4	yes	—
77	C₂²×C₃³	C₂⁴	1	3	yes	—
78	C₂×C₃²×D₃	—	2	24	no	—
79	C₂×C₃²×D₃	C₂⁴	1	8	yes	—
80	C₃³×C₄	C₂⁴	1	4	yes	—
81	C₃³×C₄	C₂⁴	1	4	yes	—
82	C₃²×Dic₃	C₂⁴	1	8	yes	—
83	C₂×C₃×#41	—	3	96	no	—
84	C₂²×C₃×Q₈	—	3	4	no	—
85	C₂²×C₃×D₄	—	3	8	no	—
86	C₂²×C₃×D₄	—	3	4	no	—
87	C₂³×C₃×C₄	—	2	4	no	—
88	C₂³×C₃×C₄	—	3	8	no	—
89	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
90	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
91	C₂²×#67	C₂×C₃²	1	2	yes	complemented
92	C₂×#235	C₂×C₃²	1	24	yes	direct product factor
93	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
94	C₂²×C₄×D₃	C₂×C₃²	1	2	yes	complemented
95	C₂²×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
96	C₂³×C₃²	—	2	32	no	—
97	C₂³×C₃²	—	2	4	no	—
98	C₂³×C₃²	—	2	16	no	—
99	C₂³×C₃²	—	2	24	no	—
100	C₂³×C₃²	—	2	4	no	—
101	C₂³×C₃²	—	3	12	no	—
102	C₂³×C₃²	—	6	8	no	—
103	C₂³×C₃²	C₂²×D₃	1	6	yes	—
104	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
105	C₂³×C₃²	C₂³×C₃	1	24	yes	—
106	C₂³×C₃²	C₂³×C₃	1	4	yes	—
107	C₂²×C₃×D₃	—	2	32	no	—
108	C₂²×C₃×D₃	C₂³×C₃	1	48	yes	—
109	C₃²×Q₈	—	3	16	no	—
110	C₃²×D₄	—	3	32	no	—
111	C₃²×D₄	—	3	16	no	—
112	C₂×C₃²×C₄	—	2	24	no	—
113	C₂×C₃²×C₄	—	2	24	no	—
114	C₂×C₃²×C₄	—	2	64	no	—
115	C₂×C₃²×C₄	—	3	12	no	—
116	C₂×C₃²×C₄	—	3	32	no	—
117	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	—
118	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	—
119	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	complemented
120	C₂×C₃²×C₄	C₂³×C₃	1	24	yes	—
121	C₂×C₃²×C₄	C₂³×C₃	1	24	yes	—
122	C₂×C₃²×C₄	C₂³×C₃	1	64	yes	complemented
123	C₃×#67	C₂³×C₃	1	128	yes	complemented
124	C₂×C₃×Dic₃	C₂³×C₃	1	48	yes	—
125	C₃×D₁₂	C₂³×C₃	1	64	yes	complemented
126	C₃×C₄×D₃	C₂³×C₃	1	128	yes	complemented
127	C₃×Dic₆	C₂³×C₃	1	64	yes	complemented
128	C₂²×#41	—	3	1	no	Sylow
129	C₂×C₃³	—	2	4	no	—
130	C₂×C₃³	C₂×#41	1	6	yes	complemented
131	C₂×C₃³	C₂⁵	1	1	yes	characteristic
132	C₃²×D₃	—	2	8	no	—
133	C₂⁴×C₃	—	2	4	no	—
134	C₂⁴×C₃	—	3	8	no	—
135	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
136	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
137	C₂³×D₃	C₂²×C₃²	1	2	yes	—
138	C₃×#41	—	3	256	no	—
139	C₂×C₃×Q₈	—	3	48	no	—
140	C₂×C₃×D₄	—	3	96	no	—
141	C₂×C₃×D₄	—	3	48	no	—
142	C₂²×C₃×C₄	—	2	4	no	—
143	C₂²×C₃×C₄	—	2	4	no	—
144	C₂²×C₃×C₄	—	2	48	no	—
145	C₂²×C₃×C₄	—	3	8	no	—
146	C₂²×C₃×C₄	—	3	96	no	—
147	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
148	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
149	C₂²×C₃×C₄	C₂×C₃×D₃	1	48	yes	complemented
150	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂²×C₃²	1	12	yes	complemented
153	C₂×#67	C₂²×C₃²	1	24	yes	complemented
154	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
155	#235	C₂²×C₃²	1	64	yes	direct product factor
156	C₂×D₁₂	C₂²×C₃²	1	12	yes	complemented
157	C₂×C₄×D₃	C₂²×C₃²	1	24	yes	complemented
158	C₂×Dic₆	C₂²×C₃²	1	12	yes	complemented
159	C₂²×C₃²	—	2	96	no	—
160	C₂²×C₃²	—	2	12	no	—
161	C₂²×C₃²	—	2	48	no	—
162	C₂²×C₃²	—	2	16	no	—
163	C₂²×C₃²	—	2	12	no	—
164	C₂²×C₃²	—	2	16	no	—
165	C₂²×C₃²	—	3	8	no	—
166	C₂²×C₃²	—	6	24	no	—
167	C₂²×C₃²	#235	1	4	yes	direct product factor
168	C₂²×C₃²	C₃×#41	1	16	yes	complemented
169	C₂²×C₃²	C₂³×D₃	1	4	yes	—
170	C₂²×C₃²	C₂³×D₃	1	3	yes	—
171	C₂²×C₃²	C₂⁴×C₃	1	16	yes	—
172	C₂²×C₃²	C₂⁴×C₃	1	12	yes	—
173	C₂×C₃×D₃	—	2	96	no	—
174	C₂×C₃×D₃	C₂⁴×C₃	1	32	yes	—
175	C₃²×C₄	—	2	16	no	—
176	C₃²×C₄	—	2	16	no	—
177	C₃²×C₄	—	3	8	no	—
178	C₃²×C₄	C₂³×D₃	1	4	yes	—
179	C₃²×C₄	C₂³×D₃	1	4	yes	—
180	C₃²×C₄	C₂⁴×C₃	1	16	yes	—
181	C₃²×C₄	C₂⁴×C₃	1	16	yes	—
182	C₃×Dic₃	C₂⁴×C₃	1	32	yes	—
183	C₂×#41	—	3	24	no	—
184	C₂²×Q₈	—	3	1	no	—
185	C₂²×D₄	—	3	2	no	—
186	C₂²×D₄	—	3	1	no	—
187	C₂³×C₄	—	3	2	no	—
188	C₂³×C₄	C₃²×D₃	1	1	yes	characteristic, complemented
189	C₃³	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
190	C₂³×C₃	—	2	32	no	—
191	C₂³×C₃	—	2	16	no	—
192	C₂³×C₃	—	2	4	no	—
193	C₂³×C₃	—	2	24	no	—
194	C₂³×C₃	—	2	4	no	—
195	C₂³×C₃	—	3	48	no	—
196	C₂³×C₃	—	6	32	no	—
197	C₂³×C₃	C₂²×C₃×D₃	1	24	yes	—
198	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
199	C₂³×C₃	C₂³×C₃²	1	6	yes	—
200	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
201	C₂²×D₃	—	2	8	no	—
202	C₂²×D₃	C₂³×C₃²	1	12	yes	—
203	C₃×Q₈	—	3	64	no	—
204	C₃×D₄	—	3	128	no	—
205	C₃×D₄	—	3	64	no	—
206	C₂×C₃×C₄	—	2	24	no	—
207	C₂×C₃×C₄	—	2	24	no	—
208	C₂×C₃×C₄	—	2	64	no	—
209	C₂×C₃×C₄	—	3	48	no	—
210	C₂×C₃×C₄	—	3	128	no	—
211	C₂×C₃×C₄	C₂²×C₃×D₃	1	24	yes	—
212	C₂×C₃×C₄	C₂²×C₃×D₃	1	24	yes	—
213	C₂×C₃×C₄	C₂²×C₃×D₃	1	64	yes	complemented
214	C₂×C₃×C₄	C₂³×C₃²	1	6	yes	—
215	C₂×C₃×C₄	C₂³×C₃²	1	6	yes	—
216	C₂×C₃×C₄	C₂³×C₃²	1	16	yes	complemented
217	#67	C₂³×C₃²	1	32	yes	complemented
218	C₂×Dic₃	C₂³×C₃²	1	12	yes	—
219	D₁₂	C₂³×C₃²	1	16	yes	complemented
220	C₄×D₃	C₂³×C₃²	1	32	yes	complemented
221	Dic₆	C₂³×C₃²	1	16	yes	complemented
222	C₂×C₃²	—	2	32	no	—
223	C₂×C₃²	—	2	4	no	—
224	C₂×C₃²	—	2	16	no	—
225	C₂×C₃²	—	2	24	no	—
226	C₂×C₃²	—	2	4	no	—
227	C₂×C₃²	—	6	8	no	—
228	C₂×C₃²	C₂×#235	1	6	yes	direct product factor
229	C₂×C₃²	C₂×C₃×#41	1	24	yes	complemented
230	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
231	C₂×C₃²	C₂⁵×C₃	1	4	yes	—
232	C₃×D₃	—	2	32	no	—
233	C₂⁴	—	3	2	no	—
234	C₂⁴	C₂×C₃²×D₃	1	1	yes	characteristic
235	#41	—	3	64	no	—
236	C₂×Q₈	—	3	12	no	—
237	C₂×D₄	—	3	24	no	—
238	C₂×D₄	—	3	12	no	—
239	C₂²×C₄	—	3	2	no	—
240	C₂²×C₄	—	3	24	no	—
241	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₃²×D₃	1	12	yes	complemented
244	C₂²×C₃	—	2	96	no	—
245	C₂²×C₃	—	2	48	no	—
246	C₂²×C₃	—	2	12	no	—
247	C₂²×C₃	—	2	16	no	—
248	C₂²×C₃	—	2	12	no	—
249	C₂²×C₃	—	2	16	no	—
250	C₂²×C₃	—	3	32	no	—
251	C₂²×C₃	—	6	96	no	—
252	C₂²×C₃	C₃×#235	1	16	yes	direct product factor
253	C₂²×C₃	C₃²×#41	1	4	yes	complemented
254	C₂²×C₃	C₂³×C₃×D₃	1	16	yes	—
255	C₂²×C₃	C₂³×C₃×D₃	1	12	yes	—
256	C₂²×C₃	C₂⁴×C₃²	1	4	yes	—
257	C₂²×C₃	C₂⁴×C₃²	1	3	yes	—
258	C₂×D₃	—	2	24	no	—
259	C₂×D₃	C₂⁴×C₃²	1	8	yes	—
260	C₃×C₄	—	2	16	no	—
261	C₃×C₄	—	2	16	no	—
262	C₃×C₄	—	3	32	no	—
263	C₃×C₄	C₂³×C₃×D₃	1	16	yes	—
264	C₃×C₄	C₂³×C₃×D₃	1	16	yes	—
265	C₃×C₄	C₂⁴×C₃²	1	4	yes	—
266	C₃×C₄	C₂⁴×C₃²	1	4	yes	—
267	Dic₃	C₂⁴×C₃²	1	8	yes	—
268	C₃²	—	2	4	no	—
269	C₃²	C₂²×#235	1	1	yes	characteristic, direct product factor
270	C₃²	C₂²×C₃×#41	1	4	yes	complemented
271	C₂³	—	2	4	no	—
272	C₂³	—	3	12	no	—
273	C₂³	—	6	8	no	—
274	C₂³	C₂²×C₃²×D₃	1	6	yes	—
275	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
276	Q₈	—	3	16	no	—
277	D₄	—	3	32	no	—
278	D₄	—	3	16	no	—
279	C₂×C₄	—	3	12	no	—
280	C₂×C₄	—	3	32	no	—
281	C₂×C₄	C₂²×C₃²×D₃	1	6	yes	—
282	C₂×C₄	C₂²×C₃²×D₃	1	6	yes	—
283	C₂×C₄	C₂²×C₃²×D₃	1	16	yes	complemented
284	C₂×C₃	—	2	32	no	—
285	C₂×C₃	—	2	16	no	—
286	C₂×C₃	—	2	4	no	—
287	C₂×C₃	—	2	24	no	—
288	C₂×C₃	—	2	4	no	—
289	C₂×C₃	—	6	32	no	—
290	C₂×C₃	C₂×C₃×#235	1	24	yes	direct product factor
291	C₂×C₃	C₂×C₃²×#41	1	6	yes	complemented
292	C₂×C₃	C₂⁴×C₃×D₃	1	4	yes	—
293	C₂×C₃	C₂⁵×C₃²	1	1	yes	characteristic
294	D₃	—	2	8	no	—
295	C₂²	—	2	12	no	—
296	C₂²	—	3	8	no	—
297	C₂²	—	6	24	no	—
298	C₂²	C₃²×#235	1	4	yes	direct product factor
299	C₂²	C₂³×C₃²×D₃	1	4	yes	—
300	C₂²	C₂³×C₃²×D₃	1	3	yes	—
301	C₄	—	3	8	no	—
302	C₄	C₂³×C₃²×D₃	1	4	yes	—
303	C₄	C₂³×C₃²×D₃	1	4	yes	—
304	C₃	—	2	4	no	—
305	C₃	C₂²×C₃×#235	1	4	yes	direct product factor
306	C₃	C₂²×C₃²×#41	1	1	yes	characteristic, complemented
307	C₂	—	2	4	no	—
308	C₂	—	6	8	no	—
309	C₂	C₂×C₃²×#235	1	6	yes	direct product factor
310	C₂	C₂⁴×C₃²×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁵×C₃²
Frattini	C₂	C₂⁴×C₃²×D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂³×C₃²×C₄	D₃
hypocenter	C₃	C₂²×C₃²×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ C₂³×C₃²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂×C₃²×#235	C₂	direct (N × H)
4. C₂²×C₃²×D₁₂	C₂	semidirect
5. C₂²×C₃²×C₄×D₃	C₂	semidirect
6. C₂²×C₃²×Dic₆	C₂	semidirect
8. C₂²×C₃×#235	C₃	direct (N × H)
13. C₂²×C₃³×C₄	C₂²	semidirect
14. C₂×C₃²×#67	C₂²	semidirect
16. C₃²×#235	C₂²	direct (N × H)
17. C₂×C₃²×D₁₂	C₂²	semidirect
18. C₂×C₃²×C₄×D₃	C₂²	semidirect
19. C₂×C₃²×Dic₆	C₂²	semidirect
26. C₂³×C₃²×C₄	D₃	semidirect
27. C₂³×C₃²×C₄	C₂×C₃	semidirect
28. C₂²×C₃×#67	C₂×C₃	semidirect
29. C₂×C₃×#235	C₂×C₃	direct (N × H)
30. C₂²×C₃×D₁₂	C₂×C₃	semidirect
31. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
32. C₂²×C₃×Dic₆	C₂×C₃	semidirect
40. C₂×C₃³×C₄	C₂³	semidirect
41. C₃²×#67	C₂³	semidirect
43. C₃²×D₁₂	C₂³	semidirect
44. C₃²×C₄×D₃	C₂³	semidirect
45. C₃²×Dic₆	C₂³	semidirect
47. C₂²×#235	C₃²	direct (N × H)
64. C₂²×C₃²×C₄	C₂×D₃	semidirect
67. C₂²×C₃²×C₄	C₂²×C₃	semidirect
68. C₂×C₃×#67	C₂²×C₃	semidirect
70. C₃×#235	C₂²×C₃	direct (N × H)
71. C₂×C₃×D₁₂	C₂²×C₃	semidirect
72. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
73. C₂×C₃×Dic₆	C₂²×C₃	semidirect
75. C₂²×C₃³	#41	semidirect
89. C₂³×C₃×C₄	C₃×D₃	semidirect
90. C₂³×C₃×C₄	C₂×C₃²	semidirect
91. C₂²×#67	C₂×C₃²	semidirect
92. C₂×#235	C₂×C₃²	direct (N × H)
93. C₂²×D₁₂	C₂×C₃²	semidirect
94. C₂²×C₄×D₃	C₂×C₃²	semidirect
95. C₂²×Dic₆	C₂×C₃²	semidirect
119. C₂×C₃²×C₄	C₂²×D₃	semidirect
122. C₂×C₃²×C₄	C₂³×C₃	semidirect
123. C₃×#67	C₂³×C₃	semidirect
125. C₃×D₁₂	C₂³×C₃	semidirect
126. C₃×C₄×D₃	C₂³×C₃	semidirect
127. C₃×Dic₆	C₂³×C₃	semidirect
130. C₂×C₃³	C₂×#41	semidirect
149. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
152. C₂²×C₃×C₄	C₂²×C₃²	semidirect
153. C₂×#67	C₂²×C₃²	semidirect
155. #235	C₂²×C₃²	direct (N × H)
156. C₂×D₁₂	C₂²×C₃²	semidirect
157. C₂×C₄×D₃	C₂²×C₃²	semidirect
158. C₂×Dic₆	C₂²×C₃²	semidirect
167. C₂²×C₃²	#235	direct (N × H)
168. C₂²×C₃²	C₃×#41	semidirect
188. C₂³×C₄	C₃²×D₃	semidirect
189. C₃³	C₂²×#41	semidirect
213. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
216. C₂×C₃×C₄	C₂³×C₃²	semidirect
217. #67	C₂³×C₃²	semidirect
219. D₁₂	C₂³×C₃²	semidirect
220. C₄×D₃	C₂³×C₃²	semidirect
221. Dic₆	C₂³×C₃²	semidirect
228. C₂×C₃²	C₂×#235	direct (N × H)
229. C₂×C₃²	C₂×C₃×#41	semidirect
243. C₂²×C₄	C₂×C₃²×D₃	semidirect
252. C₂²×C₃	C₃×#235	direct (N × H)
253. C₂²×C₃	C₃²×#41	semidirect
269. C₃²	C₂²×#235	direct (N × H)
270. C₃²	C₂²×C₃×#41	semidirect
283. C₂×C₄	C₂²×C₃²×D₃	semidirect
290. C₂×C₃	C₂×C₃×#235	direct (N × H)
291. C₂×C₃	C₂×C₃²×#41	semidirect
298. C₂²	C₃²×#235	direct (N × H)
305. C₃	C₂²×C₃×#235	direct (N × H)
306. C₃	C₂²×C₃²×#41	semidirect
309. C₂	C₂×C₃²×#235	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃³×C₄	2
C₂²×C₃²×#67	2
C₂×C₃²×#235	2
C₂²×C₃²×D₁₂	2
C₂²×C₃²×C₄×D₃	2
C₂²×C₃²×Dic₆	2
C₂²×C₃²×#41	3
C₂²×C₃×#235	3

Subgroups — C22×C32×#235 #13181713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×#235 #13181713