Subgroups — C₂²×C₃×D₄×C₃⋊D₃ #13181734

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×C₃×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#638	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×D₄×C₃⋊D₃	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₃×D₄	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	2	yes	complemented
10	C₂³×C₃×C₃⋊D₃	—	2	16	no	—
11	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₃⋊D₃	C₂²	1	24	yes	complemented
13	C₂³×C₃×C₃⋊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×C₃×#638	C₂²	1	24	yes	complemented
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
18	C₃×D₄×C₃⋊D₃	C₂²	1	64	yes	direct product factor
19	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
20	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	12	yes	complemented
21	C₂⁴×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
22	C₂⁴×C₃×D₃	—	3	8	no	—
23	C₂²×C₃²×D₄	—	2	4	no	—
24	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
25	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×#638	C₂×C₃	1	2	yes	complemented
27	C₂×D₄×C₃⋊D₃	C₂×C₃	1	24	yes	direct product factor
28	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₃×#67	—	3	8	no	—
31	C₂×C₃×D₃×D₄	—	3	96	no	—
32	C₂²×C₃×D₁₂	—	3	4	no	—
33	C₂²×C₃×C₄×D₃	—	3	4	no	—
34	C₂³×C₃³	—	2	8	no	—
35	C₂³×C₃³	C₂³	1	1	yes	characteristic
36	C₂³×C₃³	C₂³	1	12	yes	complemented
37	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
38	C₂²×C₃×C₃⋊D₃	—	2	96	no	—
39	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	direct product factor
40	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	—
41	C₂²×C₃×C₃⋊D₃	C₂³	1	32	yes	complemented
42	C₂²×C₃×C₃⋊D₃	C₂³	1	12	yes	complemented
43	C₃³×D₄	C₂³	1	16	yes	complemented
44	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
45	C₃×#638	C₂³	1	32	yes	complemented
46	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	complemented
47	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
48	C₃×C₄×C₃⋊D₃	C₂³	1	16	yes	complemented
49	C₂³×C₃×D₄	—	9	1	no	—
50	C₂²×D₃×D₄	—	3	4	no	—
51	C₂⁴×C₃²	—	2	8	no	—
52	C₂⁴×C₃²	C₂×D₃	1	8	yes	complemented
53	C₂⁴×C₃²	C₂²×C₃	1	2	yes	complemented
54	C₂³×C₃⋊D₃	—	2	16	no	—
55	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
56	C₂³×C₃⋊D₃	C₂²×C₃	1	24	yes	complemented
57	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
58	C₂³×C₃×D₃	—	3	4	no	—
59	C₂³×C₃×D₃	—	3	8	no	—
60	C₂³×C₃×D₃	—	3	96	no	—
61	C₂³×C₃×D₃	—	6	64	no	—
62	C₂×C₃²×D₄	—	2	48	no	—
63	C₂×C₃²×D₄	C₂×D₃	1	48	yes	complemented
64	C₂×C₃²×D₄	C₂²×C₃	1	12	yes	complemented
65	C₂²×C₃²×C₄	—	2	4	no	—
66	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
67	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
68	C₂×#638	C₂²×C₃	1	24	yes	complemented
69	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
70	D₄×C₃⋊D₃	C₂²×C₃	1	64	yes	direct product factor
71	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	12	yes	complemented
72	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	12	yes	complemented
73	C₂×C₃×#67	—	3	96	no	—
74	C₂²×C₃×Dic₃	—	3	4	no	—
75	C₃×D₃×D₄	—	3	256	no	—
76	C₂×C₃×D₁₂	—	3	48	no	—
77	C₂×C₃×C₄×D₃	—	3	48	no	—
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×C₃×C₃⋊D₃	—	2	24	no	—
83	C₂×C₃×C₃⋊D₃	—	2	64	no	—
84	C₂×C₃×C₃⋊D₃	C₂×D₄	1	24	yes	direct product factor
85	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
86	C₂×C₃×C₃⋊D₃	C₂⁴	1	8	yes	complemented
87	C₃³×C₄	C₂⁴	1	4	yes	complemented
88	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	complemented
89	C₂⁵×C₃	—	9	2	no	—
90	C₂⁴×D₃	—	3	8	no	—
91	C₂²×C₃×D₄	—	2	4	no	—
92	C₂²×C₃×D₄	—	9	2	no	—
93	C₂²×C₃×D₄	—	9	24	no	—
94	C₂²×C₃×D₄	—	9	1	no	—
95	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
96	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, direct product factor
97	C₂³×C₃×C₄	—	9	1	no	—
98	C₂²×#67	—	3	8	no	—
99	C₂×D₃×D₄	—	3	96	no	—
100	C₂²×D₁₂	—	3	4	no	—
101	C₂²×C₄×D₃	—	3	4	no	—
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	—	4	32	no	—
107	C₂³×C₃²	C₂²×D₃	1	4	yes	—
108	C₂³×C₃²	C₂²×D₃	1	48	yes	complemented
109	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
110	C₂³×C₃²	C₂³×C₃	1	12	yes	complemented
111	C₂²×C₃⋊D₃	—	2	8	no	—
112	C₂²×C₃⋊D₃	—	2	96	no	—
113	C₂²×C₃⋊D₃	C₃×D₄	1	8	yes	direct product factor
114	C₂²×C₃⋊D₃	C₂³×C₃	1	6	yes	—
115	C₂²×C₃⋊D₃	C₂³×C₃	1	32	yes	complemented
116	C₂²×C₃⋊D₃	C₂³×C₃	1	12	yes	complemented
117	C₂²×C₃×D₃	—	3	32	no	—
118	C₂²×C₃×D₃	—	3	24	no	—
119	C₂²×C₃×D₃	—	3	48	no	—
120	C₂²×C₃×D₃	—	3	128	no	—
121	C₂²×C₃×D₃	—	6	384	no	—
122	C₂²×C₃×D₃	—	6	32	no	—
123	C₃²×D₄	—	2	64	no	—
124	C₃²×D₄	C₂²×D₃	1	64	yes	complemented
125	C₃²×D₄	C₂³×C₃	1	16	yes	complemented
126	C₂×C₃²×C₄	—	2	24	no	—
127	C₂×C₃²×C₄	C₂²×D₃	1	24	yes	complemented
128	C₂×C₃²×C₄	C₂³×C₃	1	6	yes	complemented
129	#638	C₂³×C₃	1	32	yes	complemented
130	C₂×C₃⋊Dic₃	C₂³×C₃	1	6	yes	complemented
131	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	16	yes	complemented
132	C₄×C₃⋊D₃	C₂³×C₃	1	16	yes	complemented
133	C₃×#67	—	3	128	no	—
134	C₂×C₃×Dic₃	—	3	24	no	—
135	C₃×D₁₂	—	3	64	no	—
136	C₃×C₄×D₃	—	3	64	no	—
137	C₂³×D₄	—	9	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	C₃×C₃⋊D₃	—	2	8	no	—
142	C₃×C₃⋊D₃	C₂²×D₄	1	8	yes	direct product factor
143	C₂⁴×C₃	—	2	8	no	—
144	C₂⁴×C₃	—	9	1	no	—
145	C₂⁴×C₃	—	9	2	no	—
146	C₂⁴×C₃	—	9	24	no	—
147	C₂⁴×C₃	—	18	16	no	—
148	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	complemented
149	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	complemented
150	C₂³×D₃	—	3	4	no	—
151	C₂³×D₃	—	3	8	no	—
152	C₂³×D₃	—	3	96	no	—
153	C₂³×D₃	—	6	64	no	—
154	C₂×C₃×D₄	—	2	48	no	—
155	C₂×C₃×D₄	—	9	24	no	—
156	C₂×C₃×D₄	—	9	64	no	—
157	C₂×C₃×D₄	—	9	12	no	—
158	C₂×C₃×D₄	C₂×C₃×D₃	1	48	yes	complemented
159	C₂×C₃×D₄	C₂×C₃⋊D₃	1	12	yes	direct product factor
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	9	1	no	—
162	C₂²×C₃×C₄	—	9	12	no	—
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
164	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
165	C₂×#67	—	3	96	no	—
166	C₂²×Dic₃	—	3	4	no	—
167	D₃×D₄	—	3	256	no	—
168	C₂×D₁₂	—	3	48	no	—
169	C₂×C₄×D₃	—	3	48	no	—
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	—	4	96	no	—
176	C₂²×C₃²	D₃×D₄	1	16	yes	complemented
177	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
178	C₂²×C₃²	C₂³×D₃	1	12	yes	—
179	C₂²×C₃²	C₂³×D₃	1	32	yes	complemented
180	C₂²×C₃²	C₂⁴×C₃	1	3	yes	—
181	C₂²×C₃²	C₂⁴×C₃	1	8	yes	complemented
182	C₂×C₃⋊D₃	—	2	24	no	—
183	C₂×C₃⋊D₃	—	2	64	no	—
184	C₂×C₃⋊D₃	C₂×C₃×D₄	1	24	yes	direct product factor
185	C₂×C₃⋊D₃	C₂⁴×C₃	1	4	yes	—
186	C₂×C₃⋊D₃	C₂⁴×C₃	1	8	yes	complemented
187	C₂×C₃×D₃	—	3	96	no	—
188	C₂×C₃×D₃	—	3	16	no	—
189	C₂×C₃×D₃	—	3	32	no	—
190	C₂×C₃×D₃	—	6	256	no	—
191	C₂×C₃×D₃	—	6	96	no	—
192	C₃²×C₄	—	2	16	no	—
193	C₃²×C₄	C₂³×D₃	1	16	yes	complemented
194	C₃²×C₄	C₂⁴×C₃	1	4	yes	complemented
195	C₃⋊Dic₃	C₂⁴×C₃	1	4	yes	complemented
196	C₃×Dic₃	—	3	16	no	—
197	C₂⁵	—	9	2	no	—
198	C₂²×D₄	—	9	2	no	—
199	C₂²×D₄	—	9	24	no	—
200	C₂²×D₄	—	9	1	no	—
201	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
202	C₂³×C₄	—	9	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	—	4	32	no	—
209	C₂³×C₃	—	9	6	no	—
210	C₂³×C₃	—	9	8	no	—
211	C₂³×C₃	—	9	12	no	—
212	C₂³×C₃	—	9	32	no	—
213	C₂³×C₃	—	18	96	no	—
214	C₂³×C₃	—	18	8	no	—
215	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
216	C₂³×C₃	C₂²×C₃×D₃	1	48	yes	complemented
217	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
218	C₂³×C₃	C₂²×C₃⋊D₃	1	12	yes	complemented
219	C₂²×D₃	—	3	24	no	—
220	C₂²×D₃	—	3	32	no	—
221	C₂²×D₃	—	3	48	no	—
222	C₂²×D₃	—	3	128	no	—
223	C₂²×D₃	—	6	384	no	—
224	C₂²×D₃	—	6	32	no	—
225	C₃×D₄	—	2	64	no	—
226	C₃×D₄	—	9	32	no	—
227	C₃×D₄	—	9	16	no	—
228	C₃×D₄	C₂²×C₃×D₃	1	64	yes	complemented
229	C₃×D₄	C₂²×C₃⋊D₃	1	16	yes	direct product factor
230	C₂×C₃×C₄	—	2	24	no	—
231	C₂×C₃×C₄	—	9	6	no	—
232	C₂×C₃×C₄	—	9	16	no	—
233	C₂×C₃×C₄	C₂²×C₃×D₃	1	24	yes	complemented
234	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	6	yes	complemented
235	#67	—	3	128	no	—
236	C₂×Dic₃	—	3	24	no	—
237	D₁₂	—	3	64	no	—
238	C₄×D₃	—	3	64	no	—
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	—	4	32	no	—
244	C₂×C₃²	C₂×D₃×D₄	1	24	yes	complemented
245	C₂×C₃²	C₂²×C₃×D₄	1	6	yes	complemented
246	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
247	C₂×C₃²	C₂⁵×C₃	1	1	yes	characteristic
248	C₃⋊D₃	—	2	8	no	—
249	C₃⋊D₃	C₂²×C₃×D₄	1	8	yes	direct product factor
250	C₃×D₃	—	3	32	no	—
251	C₃×D₃	—	6	32	no	—
252	C₂⁴	—	9	1	no	—
253	C₂⁴	—	9	2	no	—
254	C₂⁴	—	9	24	no	—
255	C₂⁴	—	18	16	no	—
256	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
257	C₂×D₄	—	9	24	no	—
258	C₂×D₄	—	9	64	no	—
259	C₂×D₄	—	9	12	no	—
260	C₂×D₄	C₂×C₃×C₃⋊D₃	1	12	yes	direct product factor
261	C₂²×C₄	—	9	1	no	—
262	C₂²×C₄	—	9	12	no	—
263	C₂²×C₄	C₂×C₃×C₃⋊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	—	4	96	no	—
270	C₂²×C₃	—	9	24	no	—
271	C₂²×C₃	—	9	4	no	—
272	C₂²×C₃	—	9	8	no	—
273	C₂²×C₃	—	18	64	no	—
274	C₂²×C₃	—	18	24	no	—
275	C₂²×C₃	C₃×D₃×D₄	1	16	yes	complemented
276	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	direct product factor
277	C₂²×C₃	C₂³×C₃×D₃	1	12	yes	—
278	C₂²×C₃	C₂³×C₃×D₃	1	32	yes	complemented
279	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
280	C₂²×C₃	C₂³×C₃⋊D₃	1	8	yes	complemented
281	C₂×D₃	—	3	96	no	—
282	C₂×D₃	—	3	16	no	—
283	C₂×D₃	—	3	32	no	—
284	C₂×D₃	—	6	256	no	—
285	C₂×D₃	—	6	96	no	—
286	C₃×C₄	—	2	16	no	—
287	C₃×C₄	—	9	4	no	—
288	C₃×C₄	C₂³×C₃×D₃	1	16	yes	complemented
289	C₃×C₄	C₂³×C₃⋊D₃	1	4	yes	complemented
290	Dic₃	—	3	16	no	—
291	C₃²	—	2	4	no	—
292	C₃²	C₂²×D₃×D₄	1	4	yes	complemented
293	C₃²	C₂³×C₃×D₄	1	1	yes	characteristic, complemented
294	C₂³	—	2	8	no	—
295	C₂³	—	9	6	no	—
296	C₂³	—	9	8	no	—
297	C₂³	—	9	12	no	—
298	C₂³	—	9	32	no	—
299	C₂³	—	18	96	no	—
300	C₂³	—	18	8	no	—
301	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
302	C₂³	C₂²×C₃×C₃⋊D₃	1	12	yes	complemented
303	D₄	—	9	32	no	—
304	D₄	—	9	16	no	—
305	D₄	C₂²×C₃×C₃⋊D₃	1	16	yes	direct product factor
306	C₂×C₄	—	9	6	no	—
307	C₂×C₄	—	9	16	no	—
308	C₂×C₄	C₂²×C₃×C₃⋊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	—	4	32	no	—
314	C₂×C₃	—	9	8	no	—
315	C₂×C₃	—	18	8	no	—
316	C₂×C₃	C₂×C₃×D₃×D₄	1	24	yes	complemented
317	C₂×C₃	C₂×D₄×C₃⋊D₃	1	6	yes	direct product factor
318	C₂×C₃	C₂⁴×C₃×D₃	1	4	yes	—
319	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
320	D₃	—	3	32	no	—
321	D₃	—	6	32	no	—
322	C₂²	—	2	24	no	—
323	C₂²	—	9	24	no	—
324	C₂²	—	9	4	no	—
325	C₂²	—	9	8	no	—
326	C₂²	—	18	64	no	—
327	C₂²	—	18	24	no	—
328	C₂²	C₃×D₄×C₃⋊D₃	1	4	yes	direct product factor
329	C₂²	C₂³×C₃×C₃⋊D₃	1	3	yes	—
330	C₂²	C₂³×C₃×C₃⋊D₃	1	8	yes	complemented
331	C₄	—	9	4	no	—
332	C₄	C₂³×C₃×C₃⋊D₃	1	4	yes	complemented
333	C₃	—	2	4	no	—
334	C₃	C₂²×C₃×D₃×D₄	1	4	yes	complemented
335	C₃	C₂²×D₄×C₃⋊D₃	1	1	yes	characteristic, direct product factor
336	C₂	—	2	8	no	—
337	C₂	—	9	8	no	—
338	C₂	—	18	8	no	—
339	C₂	C₂×C₃×D₄×C₃⋊D₃	1	6	yes	direct product factor
340	C₂	C₂⁴×C₃×C₃⋊D₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃³×D₄	C₂	semidirect
3. C₂²×C₃×#638	C₂	semidirect
4. C₂×C₃×D₄×C₃⋊D₃	C₂	direct (N × H)
5. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
6. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
7. C₂²×D₄×C₃⋊D₃	C₃	direct (N × H)
9. C₂⁴×C₃³	C₂²	semidirect
12. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
13. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
15. C₂²×C₃³×C₄	C₂²	semidirect
16. C₂×C₃×#638	C₂²	semidirect
17. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
18. C₃×D₄×C₃⋊D₃	C₂²	direct (N × H)
19. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
21. C₂⁴×C₃⋊D₃	C₂×C₃	semidirect
24. C₂²×C₃²×D₄	D₃	semidirect
25. C₂²×C₃²×D₄	C₂×C₃	semidirect
26. C₂²×#638	C₂×C₃	semidirect
27. C₂×D₄×C₃⋊D₃	C₂×C₃	direct (N × H)
28. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
29. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
36. C₂³×C₃³	C₂³	semidirect
39. C₂²×C₃×C₃⋊D₃	D₄	direct (N × H)
41. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
42. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
43. C₃³×D₄	C₂³	semidirect
44. C₂×C₃³×C₄	C₂³	semidirect
45. C₃×#638	C₂³	semidirect
46. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
47. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
48. C₃×C₄×C₃⋊D₃	C₂³	semidirect
52. C₂⁴×C₃²	C₂×D₃	semidirect
53. C₂⁴×C₃²	C₂²×C₃	semidirect
56. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
57. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
63. C₂×C₃²×D₄	C₂×D₃	semidirect
64. C₂×C₃²×D₄	C₂²×C₃	semidirect
66. C₂²×C₃²×C₄	C₂×D₃	semidirect
67. C₂²×C₃²×C₄	C₂²×C₃	semidirect
68. C₂×#638	C₂²×C₃	semidirect
69. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
70. D₄×C₃⋊D₃	C₂²×C₃	direct (N × H)
71. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
72. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
79. C₂²×C₃³	C₂×D₄	semidirect
81. C₂²×C₃³	C₂⁴	semidirect
84. C₂×C₃×C₃⋊D₃	C₂×D₄	direct (N × H)
86. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
87. C₃³×C₄	C₂⁴	semidirect
88. C₃×C₃⋊Dic₃	C₂⁴	semidirect
95. C₂²×C₃×D₄	C₃×D₃	semidirect
96. C₂²×C₃×D₄	C₃⋊D₃	direct (N × H)
108. C₂³×C₃²	C₂²×D₃	semidirect
110. C₂³×C₃²	C₂³×C₃	semidirect
113. C₂²×C₃⋊D₃	C₃×D₄	direct (N × H)
115. C₂²×C₃⋊D₃	C₂³×C₃	semidirect
116. C₂²×C₃⋊D₃	C₂³×C₃	semidirect
124. C₃²×D₄	C₂²×D₃	semidirect
125. C₃²×D₄	C₂³×C₃	semidirect
127. C₂×C₃²×C₄	C₂²×D₃	semidirect
128. C₂×C₃²×C₄	C₂³×C₃	semidirect
129. #638	C₂³×C₃	semidirect
130. C₂×C₃⋊Dic₃	C₂³×C₃	semidirect
131. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
132. C₄×C₃⋊D₃	C₂³×C₃	semidirect
139. C₂×C₃³	C₂²×D₄	semidirect
142. C₃×C₃⋊D₃	C₂²×D₄	direct (N × H)
148. C₂⁴×C₃	C₂×C₃×D₃	semidirect
149. C₂⁴×C₃	C₂×C₃⋊D₃	semidirect
158. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
159. C₂×C₃×D₄	C₂×C₃⋊D₃	direct (N × H)
163. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
164. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
176. C₂²×C₃²	D₃×D₄	semidirect
177. C₂²×C₃²	C₂×C₃×D₄	semidirect
179. C₂²×C₃²	C₂³×D₃	semidirect
181. C₂²×C₃²	C₂⁴×C₃	semidirect
184. C₂×C₃⋊D₃	C₂×C₃×D₄	direct (N × H)
186. C₂×C₃⋊D₃	C₂⁴×C₃	semidirect
193. C₃²×C₄	C₂³×D₃	semidirect
194. C₃²×C₄	C₂⁴×C₃	semidirect
195. C₃⋊Dic₃	C₂⁴×C₃	semidirect
201. C₂²×D₄	C₃×C₃⋊D₃	direct (N × H)
203. C₃³	C₂³×D₄	semidirect
216. C₂³×C₃	C₂²×C₃×D₃	semidirect
218. C₂³×C₃	C₂²×C₃⋊D₃	semidirect
228. C₃×D₄	C₂²×C₃×D₃	semidirect
229. C₃×D₄	C₂²×C₃⋊D₃	direct (N × H)
233. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
234. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
244. C₂×C₃²	C₂×D₃×D₄	semidirect
245. C₂×C₃²	C₂²×C₃×D₄	semidirect
249. C₃⋊D₃	C₂²×C₃×D₄	direct (N × H)
256. C₂⁴	C₂×C₃×C₃⋊D₃	semidirect
260. C₂×D₄	C₂×C₃×C₃⋊D₃	direct (N × H)
263. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
275. C₂²×C₃	C₃×D₃×D₄	semidirect
276. C₂²×C₃	D₄×C₃⋊D₃	direct (N × H)
278. C₂²×C₃	C₂³×C₃×D₃	semidirect
280. C₂²×C₃	C₂³×C₃⋊D₃	semidirect
288. C₃×C₄	C₂³×C₃×D₃	semidirect
289. C₃×C₄	C₂³×C₃⋊D₃	semidirect
292. C₃²	C₂²×D₃×D₄	semidirect
293. C₃²	C₂³×C₃×D₄	semidirect
302. C₂³	C₂²×C₃×C₃⋊D₃	semidirect
305. D₄	C₂²×C₃×C₃⋊D₃	direct (N × H)
308. C₂×C₄	C₂²×C₃×C₃⋊D₃	semidirect
316. C₂×C₃	C₂×C₃×D₃×D₄	semidirect
317. C₂×C₃	C₂×D₄×C₃⋊D₃	direct (N × H)
328. C₂²	C₃×D₄×C₃⋊D₃	direct (N × H)
330. C₂²	C₂³×C₃×C₃⋊D₃	semidirect
332. C₄	C₂³×C₃×C₃⋊D₃	semidirect
334. C₃	C₂²×C₃×D₃×D₄	semidirect
335. C₃	C₂²×D₄×C₃⋊D₃	direct (N × H)
339. C₂	C₂×C₃×D₄×C₃⋊D₃	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×C₃×C₃⋊D₃	2
C₂²×C₃³×D₄	2
C₂²×C₃×#638	2
C₂×C₃×D₄×C₃⋊D₃	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₂²×D₄×C₃⋊D₃	3
C₂²×C₃×D₃×D₄	3

Subgroups — C22×C3×D4×C3⋊D3 #13181734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₄×C₃⋊D₃ #13181734