Subgroups — C₂²×C₃²×D₃×D₄ #13181714

Order 1728.

9116 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×D₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
4	C₂×C₃²×D₃×D₄	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₃²×D₄	—	3	1	no	maximal
8	C₂²×C₃×D₃×D₄	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	2	yes	complemented
10	C₂³×C₃²×D₃	—	2	16	no	—
11	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃²×D₃	C₂²	1	24	yes	complemented
13	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
14	C₂×C₃³×D₄	C₂²	1	12	yes	complemented
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃²×#67	C₂²	1	24	yes	complemented
17	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
18	C₃²×D₃×D₄	C₂²	1	64	yes	direct product factor
19	C₂×C₃²×D₁₂	C₂²	1	12	yes	complemented
20	C₂×C₃²×C₄×D₃	C₂²	1	12	yes	complemented
21	C₂⁵×C₃²	—	3	2	no	—
22	C₂⁴×C₃×D₃	C₂×C₃	1	8	yes	complemented
23	C₂²×C₃²×D₄	—	2	4	no	—
24	C₂²×C₃²×D₄	—	3	24	no	—
25	C₂²×C₃²×D₄	—	3	1	no	—
26	C₂²×C₃²×D₄	—	3	2	no	—
27	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, direct product factor
28	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
29	C₂³×C₃²×C₄	—	3	1	no	—
30	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
31	C₂×C₃×D₃×D₄	C₂×C₃	1	96	yes	direct product factor
32	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
33	C₂²×C₃×C₄×D₃	C₂×C₃	1	4	yes	complemented
34	C₂³×C₃³	—	2	8	no	—
35	C₂³×C₃³	C₂³	1	1	yes	characteristic
36	C₂³×C₃³	C₂³	1	12	yes	complemented
37	C₂²×C₃²×D₃	—	2	8	no	—
38	C₂²×C₃²×D₃	—	2	96	no	—
39	C₂²×C₃²×D₃	D₄	1	8	yes	direct product factor
40	C₂²×C₃²×D₃	C₂³	1	6	yes	—
41	C₂²×C₃²×D₃	C₂³	1	32	yes	complemented
42	C₂²×C₃²×D₃	C₂³	1	12	yes	complemented
43	C₃³×D₄	C₂³	1	16	yes	complemented
44	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
45	C₃²×#67	C₂³	1	32	yes	complemented
46	C₂×C₃²×Dic₃	C₂³	1	6	yes	complemented
47	C₃²×D₁₂	C₂³	1	16	yes	complemented
48	C₃²×C₄×D₃	C₂³	1	16	yes	complemented
49	C₂³×C₃×D₄	—	3	4	no	—
50	C₂²×D₃×D₄	C₃²	1	1	yes	characteristic, direct product factor
51	C₂⁴×C₃²	—	2	8	no	—
52	C₂⁴×C₃²	—	3	1	no	—
53	C₂⁴×C₃²	—	3	2	no	—
54	C₂⁴×C₃²	—	3	24	no	—
55	C₂⁴×C₃²	—	6	16	no	—
56	C₂⁴×C₃²	C₂×D₃	1	2	yes	complemented
57	C₂⁴×C₃²	C₂²×C₃	1	8	yes	complemented
58	C₂³×C₃×D₃	—	2	64	no	—
59	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
60	C₂³×C₃×D₃	C₂²×C₃	1	96	yes	complemented
61	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	complemented
62	C₂×C₃²×D₄	—	2	48	no	—
63	C₂×C₃²×D₄	—	3	24	no	—
64	C₂×C₃²×D₄	—	3	64	no	—
65	C₂×C₃²×D₄	—	3	12	no	—
66	C₂×C₃²×D₄	C₂×D₃	1	12	yes	direct product factor
67	C₂×C₃²×D₄	C₂²×C₃	1	48	yes	complemented
68	C₂²×C₃²×C₄	—	2	4	no	—
69	C₂²×C₃²×C₄	—	3	1	no	—
70	C₂²×C₃²×C₄	—	3	12	no	—
71	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
72	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
73	C₂×C₃×#67	C₂²×C₃	1	96	yes	complemented
74	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	complemented
75	C₃×D₃×D₄	C₂²×C₃	1	256	yes	direct product factor
76	C₂×C₃×D₁₂	C₂²×C₃	1	48	yes	complemented
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	48	yes	complemented
78	C₂²×C₃³	—	2	24	no	—
79	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
80	C₂²×C₃³	C₂⁴	1	3	yes	—
81	C₂²×C₃³	C₂⁴	1	8	yes	complemented
82	C₂×C₃²×D₃	—	2	24	no	—
83	C₂×C₃²×D₃	—	2	64	no	—
84	C₂×C₃²×D₃	C₂×D₄	1	24	yes	direct product factor
85	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
86	C₂×C₃²×D₃	C₂⁴	1	8	yes	complemented
87	C₃³×C₄	C₂⁴	1	4	yes	complemented
88	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
89	C₂⁵×C₃	—	3	8	no	—
90	C₂⁴×D₃	C₂×C₃²	1	2	yes	complemented
91	C₂²×C₃×D₄	—	2	4	no	—
92	C₂²×C₃×D₄	—	3	8	no	—
93	C₂²×C₃×D₄	—	3	96	no	—
94	C₂²×C₃×D₄	—	3	4	no	—
95	C₂²×C₃×D₄	C₃×D₃	1	4	yes	direct product factor
96	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
97	C₂³×C₃×C₄	—	3	4	no	—
98	C₂²×#67	C₂×C₃²	1	2	yes	complemented
99	C₂×D₃×D₄	C₂×C₃²	1	24	yes	direct product factor
100	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
101	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
102	C₂³×C₃²	—	2	8	no	—
103	C₂³×C₃²	—	2	4	no	—
104	C₂³×C₃²	—	2	48	no	—
105	C₂³×C₃²	—	2	32	no	—
106	C₂³×C₃²	—	3	8	no	—
107	C₂³×C₃²	—	3	6	no	—
108	C₂³×C₃²	—	3	12	no	—
109	C₂³×C₃²	—	3	32	no	—
110	C₂³×C₃²	—	4	32	no	—
111	C₂³×C₃²	—	6	96	no	—
112	C₂³×C₃²	—	6	8	no	—
113	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
114	C₂³×C₃²	C₂²×D₃	1	12	yes	complemented
115	C₂³×C₃²	C₂³×C₃	1	4	yes	—
116	C₂³×C₃²	C₂³×C₃	1	48	yes	complemented
117	C₂²×C₃×D₃	—	2	32	no	—
118	C₂²×C₃×D₃	—	2	384	no	—
119	C₂²×C₃×D₃	C₃×D₄	1	32	yes	direct product factor
120	C₂²×C₃×D₃	C₂³×C₃	1	24	yes	—
121	C₂²×C₃×D₃	C₂³×C₃	1	128	yes	complemented
122	C₂²×C₃×D₃	C₂³×C₃	1	48	yes	complemented
123	C₃²×D₄	—	2	64	no	—
124	C₃²×D₄	—	3	32	no	—
125	C₃²×D₄	—	3	16	no	—
126	C₃²×D₄	C₂²×D₃	1	16	yes	direct product factor
127	C₃²×D₄	C₂³×C₃	1	64	yes	complemented
128	C₂×C₃²×C₄	—	2	24	no	—
129	C₂×C₃²×C₄	—	3	6	no	—
130	C₂×C₃²×C₄	—	3	16	no	—
131	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	complemented
132	C₂×C₃²×C₄	C₂³×C₃	1	24	yes	complemented
133	C₃×#67	C₂³×C₃	1	128	yes	complemented
134	C₂×C₃×Dic₃	C₂³×C₃	1	24	yes	complemented
135	C₃×D₁₂	C₂³×C₃	1	64	yes	complemented
136	C₃×C₄×D₃	C₂³×C₃	1	64	yes	complemented
137	C₂³×D₄	—	3	1	no	Sylow
138	C₂×C₃³	—	2	8	no	—
139	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
140	C₂×C₃³	C₂⁵	1	1	yes	characteristic
141	C₃²×D₃	—	2	8	no	—
142	C₃²×D₃	C₂²×D₄	1	8	yes	direct product factor
143	C₂⁴×C₃	—	2	8	no	—
144	C₂⁴×C₃	—	3	4	no	—
145	C₂⁴×C₃	—	3	8	no	—
146	C₂⁴×C₃	—	3	96	no	—
147	C₂⁴×C₃	—	6	64	no	—
148	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	complemented
149	C₂⁴×C₃	C₂²×C₃²	1	2	yes	complemented
150	C₂³×D₃	—	2	16	no	—
151	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
152	C₂³×D₃	C₂²×C₃²	1	24	yes	complemented
153	C₂³×D₃	C₂²×C₃²	1	2	yes	complemented
154	C₂×C₃×D₄	—	2	48	no	—
155	C₂×C₃×D₄	—	3	96	no	—
156	C₂×C₃×D₄	—	3	256	no	—
157	C₂×C₃×D₄	—	3	48	no	—
158	C₂×C₃×D₄	C₂×C₃×D₃	1	48	yes	direct product factor
159	C₂×C₃×D₄	C₂²×C₃²	1	12	yes	complemented
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	3	4	no	—
162	C₂²×C₃×C₄	—	3	48	no	—
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
164	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
165	C₂×#67	C₂²×C₃²	1	24	yes	complemented
166	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
167	D₃×D₄	C₂²×C₃²	1	64	yes	direct product factor
168	C₂×D₁₂	C₂²×C₃²	1	12	yes	complemented
169	C₂×C₄×D₃	C₂²×C₃²	1	12	yes	complemented
170	C₂²×C₃²	—	2	24	no	—
171	C₂²×C₃²	—	2	12	no	—
172	C₂²×C₃²	—	2	32	no	—
173	C₂²×C₃²	—	2	16	no	—
174	C₂²×C₃²	—	2	96	no	—
175	C₂²×C₃²	—	3	24	no	—
176	C₂²×C₃²	—	3	4	no	—
177	C₂²×C₃²	—	3	8	no	—
178	C₂²×C₃²	—	4	96	no	—
179	C₂²×C₃²	—	6	64	no	—
180	C₂²×C₃²	—	6	24	no	—
181	C₂²×C₃²	D₃×D₄	1	4	yes	direct product factor
182	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	complemented
183	C₂²×C₃²	C₂³×D₃	1	3	yes	—
184	C₂²×C₃²	C₂³×D₃	1	8	yes	complemented
185	C₂²×C₃²	C₂⁴×C₃	1	12	yes	—
186	C₂²×C₃²	C₂⁴×C₃	1	32	yes	complemented
187	C₂×C₃×D₃	—	2	96	no	—
188	C₂×C₃×D₃	—	2	256	no	—
189	C₂×C₃×D₃	C₂×C₃×D₄	1	96	yes	direct product factor
190	C₂×C₃×D₃	C₂⁴×C₃	1	16	yes	—
191	C₂×C₃×D₃	C₂⁴×C₃	1	32	yes	complemented
192	C₃²×C₄	—	2	16	no	—
193	C₃²×C₄	—	3	4	no	—
194	C₃²×C₄	C₂³×D₃	1	4	yes	complemented
195	C₃²×C₄	C₂⁴×C₃	1	16	yes	complemented
196	C₃×Dic₃	C₂⁴×C₃	1	16	yes	complemented
197	C₂⁵	—	3	2	no	—
198	C₂²×D₄	—	3	2	no	—
199	C₂²×D₄	—	3	24	no	—
200	C₂²×D₄	—	3	1	no	—
201	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, direct product factor
202	C₂³×C₄	—	3	1	no	—
203	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₃	—	2	32	no	—
205	C₂³×C₃	—	2	8	no	—
206	C₂³×C₃	—	2	4	no	—
207	C₂³×C₃	—	2	48	no	—
208	C₂³×C₃	—	3	24	no	—
209	C₂³×C₃	—	3	32	no	—
210	C₂³×C₃	—	3	48	no	—
211	C₂³×C₃	—	3	128	no	—
212	C₂³×C₃	—	4	32	no	—
213	C₂³×C₃	—	6	384	no	—
214	C₂³×C₃	—	6	32	no	—
215	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
216	C₂³×C₃	C₂²×C₃×D₃	1	48	yes	complemented
217	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
218	C₂³×C₃	C₂³×C₃²	1	12	yes	complemented
219	C₂²×D₃	—	2	8	no	—
220	C₂²×D₃	—	2	96	no	—
221	C₂²×D₃	C₃²×D₄	1	8	yes	direct product factor
222	C₂²×D₃	C₂³×C₃²	1	6	yes	—
223	C₂²×D₃	C₂³×C₃²	1	32	yes	complemented
224	C₂²×D₃	C₂³×C₃²	1	12	yes	complemented
225	C₃×D₄	—	2	64	no	—
226	C₃×D₄	—	3	128	no	—
227	C₃×D₄	—	3	64	no	—
228	C₃×D₄	C₂²×C₃×D₃	1	64	yes	direct product factor
229	C₃×D₄	C₂³×C₃²	1	16	yes	complemented
230	C₂×C₃×C₄	—	2	24	no	—
231	C₂×C₃×C₄	—	3	24	no	—
232	C₂×C₃×C₄	—	3	64	no	—
233	C₂×C₃×C₄	C₂²×C₃×D₃	1	24	yes	complemented
234	C₂×C₃×C₄	C₂³×C₃²	1	6	yes	complemented
235	#67	C₂³×C₃²	1	32	yes	complemented
236	C₂×Dic₃	C₂³×C₃²	1	6	yes	complemented
237	D₁₂	C₂³×C₃²	1	16	yes	complemented
238	C₄×D₃	C₂³×C₃²	1	16	yes	complemented
239	C₂×C₃²	—	2	8	no	—
240	C₂×C₃²	—	2	24	no	—
241	C₂×C₃²	—	2	4	no	—
242	C₂×C₃²	—	2	32	no	—
243	C₂×C₃²	—	3	8	no	—
244	C₂×C₃²	—	4	32	no	—
245	C₂×C₃²	—	6	8	no	—
246	C₂×C₃²	C₂×D₃×D₄	1	6	yes	direct product factor
247	C₂×C₃²	C₂²×C₃×D₄	1	24	yes	complemented
248	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
249	C₂×C₃²	C₂⁵×C₃	1	4	yes	—
250	C₃×D₃	—	2	32	no	—
251	C₃×D₃	C₂²×C₃×D₄	1	32	yes	direct product factor
252	C₂⁴	—	3	1	no	—
253	C₂⁴	—	3	2	no	—
254	C₂⁴	—	3	24	no	—
255	C₂⁴	—	6	16	no	—
256	C₂⁴	C₂×C₃²×D₃	1	2	yes	complemented
257	C₂×D₄	—	3	24	no	—
258	C₂×D₄	—	3	64	no	—
259	C₂×D₄	—	3	12	no	—
260	C₂×D₄	C₂×C₃²×D₃	1	12	yes	direct product factor
261	C₂²×C₄	—	3	1	no	—
262	C₂²×C₄	—	3	12	no	—
263	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
264	C₂²×C₃	—	2	96	no	—
265	C₂²×C₃	—	2	24	no	—
266	C₂²×C₃	—	2	12	no	—
267	C₂²×C₃	—	2	32	no	—
268	C₂²×C₃	—	2	16	no	—
269	C₂²×C₃	—	3	96	no	—
270	C₂²×C₃	—	3	16	no	—
271	C₂²×C₃	—	3	32	no	—
272	C₂²×C₃	—	4	96	no	—
273	C₂²×C₃	—	6	256	no	—
274	C₂²×C₃	—	6	96	no	—
275	C₂²×C₃	C₃×D₃×D₄	1	16	yes	direct product factor
276	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	complemented
277	C₂²×C₃	C₂³×C₃×D₃	1	12	yes	—
278	C₂²×C₃	C₂³×C₃×D₃	1	32	yes	complemented
279	C₂²×C₃	C₂⁴×C₃²	1	3	yes	—
280	C₂²×C₃	C₂⁴×C₃²	1	8	yes	complemented
281	C₂×D₃	—	2	24	no	—
282	C₂×D₃	—	2	64	no	—
283	C₂×D₃	C₂×C₃²×D₄	1	24	yes	direct product factor
284	C₂×D₃	C₂⁴×C₃²	1	4	yes	—
285	C₂×D₃	C₂⁴×C₃²	1	8	yes	complemented
286	C₃×C₄	—	2	16	no	—
287	C₃×C₄	—	3	16	no	—
288	C₃×C₄	C₂³×C₃×D₃	1	16	yes	complemented
289	C₃×C₄	C₂⁴×C₃²	1	4	yes	complemented
290	Dic₃	C₂⁴×C₃²	1	4	yes	complemented
291	C₃²	—	2	4	no	—
292	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic, direct product factor
293	C₃²	C₂³×C₃×D₄	1	4	yes	complemented
294	C₂³	—	2	8	no	—
295	C₂³	—	3	6	no	—
296	C₂³	—	3	8	no	—
297	C₂³	—	3	12	no	—
298	C₂³	—	3	32	no	—
299	C₂³	—	6	96	no	—
300	C₂³	—	6	8	no	—
301	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
302	C₂³	C₂²×C₃²×D₃	1	12	yes	complemented
303	D₄	—	3	32	no	—
304	D₄	—	3	16	no	—
305	D₄	C₂²×C₃²×D₃	1	16	yes	direct product factor
306	C₂×C₄	—	3	6	no	—
307	C₂×C₄	—	3	16	no	—
308	C₂×C₄	C₂²×C₃²×D₃	1	6	yes	complemented
309	C₂×C₃	—	2	32	no	—
310	C₂×C₃	—	2	8	no	—
311	C₂×C₃	—	2	24	no	—
312	C₂×C₃	—	2	4	no	—
313	C₂×C₃	—	3	32	no	—
314	C₂×C₃	—	4	32	no	—
315	C₂×C₃	—	6	32	no	—
316	C₂×C₃	C₂×C₃×D₃×D₄	1	24	yes	direct product factor
317	C₂×C₃	C₂²×C₃²×D₄	1	6	yes	complemented
318	C₂×C₃	C₂⁴×C₃×D₃	1	4	yes	—
319	C₂×C₃	C₂⁵×C₃²	1	1	yes	characteristic
320	D₃	—	2	8	no	—
321	D₃	C₂²×C₃²×D₄	1	8	yes	direct product factor
322	C₂²	—	2	24	no	—
323	C₂²	—	3	24	no	—
324	C₂²	—	3	4	no	—
325	C₂²	—	3	8	no	—
326	C₂²	—	6	64	no	—
327	C₂²	—	6	24	no	—
328	C₂²	C₃²×D₃×D₄	1	4	yes	direct product factor
329	C₂²	C₂³×C₃²×D₃	1	3	yes	—
330	C₂²	C₂³×C₃²×D₃	1	8	yes	complemented
331	C₄	—	3	4	no	—
332	C₄	C₂³×C₃²×D₃	1	4	yes	complemented
333	C₃	—	2	4	no	—
334	C₃	C₂²×C₃×D₃×D₄	1	4	yes	direct product factor
335	C₃	C₂³×C₃²×D₄	1	1	yes	characteristic, complemented
336	C₂	—	2	8	no	—
337	C₂	—	3	8	no	—
338	C₂	—	6	8	no	—
339	C₂	C₂×C₃²×D₃×D₄	1	6	yes	direct product factor
340	C₂	C₂⁴×C₃²×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃²	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂⁵×C₃²
Frattini	C₂	C₂⁴×C₃²×D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₂³×C₃²×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃² ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃²×D₃	C₂	semidirect
2. C₂²×C₃³×D₄	C₂	semidirect
3. C₂²×C₃²×#67	C₂	semidirect
4. C₂×C₃²×D₃×D₄	C₂	direct (N × H)
5. C₂²×C₃²×D₁₂	C₂	semidirect
6. C₂²×C₃²×C₄×D₃	C₂	semidirect
8. C₂²×C₃×D₃×D₄	C₃	direct (N × H)
9. C₂⁴×C₃³	C₂²	semidirect
12. C₂³×C₃²×D₃	C₂²	semidirect
13. C₂³×C₃²×D₃	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
15. C₂²×C₃³×C₄	C₂²	semidirect
16. C₂×C₃²×#67	C₂²	semidirect
17. C₂²×C₃²×Dic₃	C₂²	semidirect
18. C₃²×D₃×D₄	C₂²	direct (N × H)
19. C₂×C₃²×D₁₂	C₂²	semidirect
20. C₂×C₃²×C₄×D₃	C₂²	semidirect
22. C₂⁴×C₃×D₃	C₂×C₃	semidirect
27. C₂²×C₃²×D₄	D₃	direct (N × H)
28. C₂²×C₃²×D₄	C₂×C₃	semidirect
30. C₂²×C₃×#67	C₂×C₃	semidirect
31. C₂×C₃×D₃×D₄	C₂×C₃	direct (N × H)
32. C₂²×C₃×D₁₂	C₂×C₃	semidirect
33. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
36. C₂³×C₃³	C₂³	semidirect
39. C₂²×C₃²×D₃	D₄	direct (N × H)
41. C₂²×C₃²×D₃	C₂³	semidirect
42. C₂²×C₃²×D₃	C₂³	semidirect
43. C₃³×D₄	C₂³	semidirect
44. C₂×C₃³×C₄	C₂³	semidirect
45. C₃²×#67	C₂³	semidirect
46. C₂×C₃²×Dic₃	C₂³	semidirect
47. C₃²×D₁₂	C₂³	semidirect
48. C₃²×C₄×D₃	C₂³	semidirect
50. C₂²×D₃×D₄	C₃²	direct (N × H)
56. C₂⁴×C₃²	C₂×D₃	semidirect
57. C₂⁴×C₃²	C₂²×C₃	semidirect
60. C₂³×C₃×D₃	C₂²×C₃	semidirect
61. C₂³×C₃×D₃	C₂²×C₃	semidirect
66. C₂×C₃²×D₄	C₂×D₃	direct (N × H)
67. C₂×C₃²×D₄	C₂²×C₃	semidirect
71. C₂²×C₃²×C₄	C₂×D₃	semidirect
72. C₂²×C₃²×C₄	C₂²×C₃	semidirect
73. C₂×C₃×#67	C₂²×C₃	semidirect
74. C₂²×C₃×Dic₃	C₂²×C₃	semidirect
75. C₃×D₃×D₄	C₂²×C₃	direct (N × H)
76. C₂×C₃×D₁₂	C₂²×C₃	semidirect
77. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
79. C₂²×C₃³	C₂×D₄	semidirect
81. C₂²×C₃³	C₂⁴	semidirect
84. C₂×C₃²×D₃	C₂×D₄	direct (N × H)
86. C₂×C₃²×D₃	C₂⁴	semidirect
87. C₃³×C₄	C₂⁴	semidirect
88. C₃²×Dic₃	C₂⁴	semidirect
90. C₂⁴×D₃	C₂×C₃²	semidirect
95. C₂²×C₃×D₄	C₃×D₃	direct (N × H)
96. C₂²×C₃×D₄	C₂×C₃²	semidirect
98. C₂²×#67	C₂×C₃²	semidirect
99. C₂×D₃×D₄	C₂×C₃²	direct (N × H)
100. C₂²×D₁₂	C₂×C₃²	semidirect
101. C₂²×C₄×D₃	C₂×C₃²	semidirect
114. C₂³×C₃²	C₂²×D₃	semidirect
116. C₂³×C₃²	C₂³×C₃	semidirect
119. C₂²×C₃×D₃	C₃×D₄	direct (N × H)
121. C₂²×C₃×D₃	C₂³×C₃	semidirect
122. C₂²×C₃×D₃	C₂³×C₃	semidirect
126. C₃²×D₄	C₂²×D₃	direct (N × H)
127. C₃²×D₄	C₂³×C₃	semidirect
131. C₂×C₃²×C₄	C₂²×D₃	semidirect
132. C₂×C₃²×C₄	C₂³×C₃	semidirect
133. C₃×#67	C₂³×C₃	semidirect
134. C₂×C₃×Dic₃	C₂³×C₃	semidirect
135. C₃×D₁₂	C₂³×C₃	semidirect
136. C₃×C₄×D₃	C₂³×C₃	semidirect
139. C₂×C₃³	C₂²×D₄	semidirect
142. C₃²×D₃	C₂²×D₄	direct (N × H)
148. C₂⁴×C₃	C₂×C₃×D₃	semidirect
149. C₂⁴×C₃	C₂²×C₃²	semidirect
152. C₂³×D₃	C₂²×C₃²	semidirect
153. C₂³×D₃	C₂²×C₃²	semidirect
158. C₂×C₃×D₄	C₂×C₃×D₃	direct (N × H)
159. C₂×C₃×D₄	C₂²×C₃²	semidirect
163. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
164. C₂²×C₃×C₄	C₂²×C₃²	semidirect
165. C₂×#67	C₂²×C₃²	semidirect
166. C₂²×Dic₃	C₂²×C₃²	semidirect
167. D₃×D₄	C₂²×C₃²	direct (N × H)
168. C₂×D₁₂	C₂²×C₃²	semidirect
169. C₂×C₄×D₃	C₂²×C₃²	semidirect
181. C₂²×C₃²	D₃×D₄	direct (N × H)
182. C₂²×C₃²	C₂×C₃×D₄	semidirect
184. C₂²×C₃²	C₂³×D₃	semidirect
186. C₂²×C₃²	C₂⁴×C₃	semidirect
189. C₂×C₃×D₃	C₂×C₃×D₄	direct (N × H)
191. C₂×C₃×D₃	C₂⁴×C₃	semidirect
194. C₃²×C₄	C₂³×D₃	semidirect
195. C₃²×C₄	C₂⁴×C₃	semidirect
196. C₃×Dic₃	C₂⁴×C₃	semidirect
201. C₂²×D₄	C₃²×D₃	direct (N × H)
203. C₃³	C₂³×D₄	semidirect
216. C₂³×C₃	C₂²×C₃×D₃	semidirect
218. C₂³×C₃	C₂³×C₃²	semidirect
221. C₂²×D₃	C₃²×D₄	direct (N × H)
223. C₂²×D₃	C₂³×C₃²	semidirect
224. C₂²×D₃	C₂³×C₃²	semidirect
228. C₃×D₄	C₂²×C₃×D₃	direct (N × H)
229. C₃×D₄	C₂³×C₃²	semidirect
233. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
234. C₂×C₃×C₄	C₂³×C₃²	semidirect
235. #67	C₂³×C₃²	semidirect
236. C₂×Dic₃	C₂³×C₃²	semidirect
237. D₁₂	C₂³×C₃²	semidirect
238. C₄×D₃	C₂³×C₃²	semidirect
246. C₂×C₃²	C₂×D₃×D₄	direct (N × H)
247. C₂×C₃²	C₂²×C₃×D₄	semidirect
251. C₃×D₃	C₂²×C₃×D₄	direct (N × H)
256. C₂⁴	C₂×C₃²×D₃	semidirect
260. C₂×D₄	C₂×C₃²×D₃	direct (N × H)
263. C₂²×C₄	C₂×C₃²×D₃	semidirect
275. C₂²×C₃	C₃×D₃×D₄	direct (N × H)
276. C₂²×C₃	C₂×C₃²×D₄	semidirect
278. C₂²×C₃	C₂³×C₃×D₃	semidirect
280. C₂²×C₃	C₂⁴×C₃²	semidirect
283. C₂×D₃	C₂×C₃²×D₄	direct (N × H)
285. C₂×D₃	C₂⁴×C₃²	semidirect
288. C₃×C₄	C₂³×C₃×D₃	semidirect
289. C₃×C₄	C₂⁴×C₃²	semidirect
290. Dic₃	C₂⁴×C₃²	semidirect
292. C₃²	C₂²×D₃×D₄	direct (N × H)
293. C₃²	C₂³×C₃×D₄	semidirect
302. C₂³	C₂²×C₃²×D₃	semidirect
305. D₄	C₂²×C₃²×D₃	direct (N × H)
308. C₂×C₄	C₂²×C₃²×D₃	semidirect
316. C₂×C₃	C₂×C₃×D₃×D₄	direct (N × H)
317. C₂×C₃	C₂²×C₃²×D₄	semidirect
321. D₃	C₂²×C₃²×D₄	direct (N × H)
328. C₂²	C₃²×D₃×D₄	direct (N × H)
330. C₂²	C₂³×C₃²×D₃	semidirect
332. C₄	C₂³×C₃²×D₃	semidirect
334. C₃	C₂²×C₃×D₃×D₄	direct (N × H)
335. C₃	C₂³×C₃²×D₄	semidirect
339. C₂	C₂×C₃²×D₃×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×D₃	2
C₂²×C₃³×D₄	2
C₂²×C₃²×#67	2
C₂×C₃²×D₃×D₄	2
C₂²×C₃²×D₁₂	2
C₂²×C₃²×C₄×D₃	2
C₂³×C₃²×D₄	3
C₂²×C₃×D₃×D₄	3

Subgroups — C22×C32×D3×D4 #13181714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×D₃×D₄ #13181714