Subgroups — C₂²×#89026 #13181600

Order 1728.

9116 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#6290	C₂	1	2	yes	maximal, complemented
6	C₂×#89026	C₂	1	24	yes	maximal, direct product factor
7	C₂²×D₄×C₃⋊D₃	—	3	1	no	maximal
8	C₂²×#3802	—	3	4	no	maximal
9	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
12	C₂²×D₃×C₃⋊D₃	—	2	16	no	—
13	C₂²×D₃×C₃⋊D₃	C₂²	1	24	yes	complemented
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
18	C₂×C₃²×D₁₂	C₂²	1	12	yes	complemented
19	C₂×#6290	C₂²	1	24	yes	complemented
20	#89026	C₂²	1	64	yes	direct product factor
21	C₂⁴×C₃⋊D₃	—	3	2	no	—
22	C₂³×D₃²	—	3	8	no	—
23	C₂²×C₃²×D₄	—	3	1	no	—
24	C₂²×#638	—	3	2	no	—
25	C₂×D₄×C₃⋊D₃	—	3	24	no	—
26	C₂²×C₄⋊(C₃⋊D₃)	D₃	1	1	yes	characteristic, complemented
27	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
28	C₂²×C₄×C₃⋊D₃	—	3	4	no	—
29	C₂²×C₄×C₃⋊D₃	—	6	4	no	—
30	C₂²×C₃×D₁₂	—	3	4	no	—
31	C₂²×C₃×D₁₂	D₃	1	4	yes	complemented
32	C₂²×#625	—	3	8	no	—
33	C₂×#3802	—	3	96	no	—
34	C₂³×C₃³	C₂³	1	1	yes	characteristic
35	C₂²×C₃⋊(C₃⋊D₃)	D₄	1	8	yes	complemented
36	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	6	yes	—
37	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
38	C₂²×C₃×C₃⋊D₃	C₂³	1	12	yes	complemented
39	C₂²×C₃²×D₃	—	2	8	no	—
40	C₂²×C₃²×D₃	C₂³	1	12	yes	complemented
41	C₂×D₃×C₃⋊D₃	—	2	96	no	—
42	C₂×D₃×C₃⋊D₃	C₂³	1	32	yes	complemented
43	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
44	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	complemented
45	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
46	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
47	C₃²×D₁₂	C₂³	1	16	yes	complemented
48	#6290	C₂³	1	32	yes	complemented
49	C₂²×D₃×D₄	—	9	4	no	—
50	C₂²×D₃×D₄	—	9	1	no	—
51	C₂⁴×C₃²	—	3	2	no	—
52	C₂³×C₃⋊D₃	—	3	1	no	—
53	C₂³×C₃⋊D₃	—	3	4	no	—
54	C₂³×C₃⋊D₃	—	3	24	no	—
55	C₂³×C₃⋊D₃	—	6	16	no	—
56	C₂³×C₃⋊D₃	—	6	4	no	—
57	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
58	C₂³×C₃×D₃	—	3	8	no	—
59	C₂³×C₃×D₃	C₂×D₃	1	8	yes	complemented
60	C₂²×D₃²	—	3	96	no	—
61	C₂²×D₃²	—	6	64	no	—
62	C₂×C₃²×D₄	—	3	12	no	—
63	C₂²×C₃²×C₄	—	2	4	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
65	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
66	C₂×#638	—	3	24	no	—
67	C₂²×C₃⋊Dic₃	—	3	1	no	—
68	C₂²×C₃⋊Dic₃	—	3	4	no	—
69	C₂²×C₃⋊Dic₃	—	6	4	no	—
70	D₄×C₃⋊D₃	—	3	64	no	—
71	C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	1	12	yes	complemented
72	C₂×C₄×C₃⋊D₃	—	3	12	no	—
73	C₂×C₄×C₃⋊D₃	—	3	48	no	—
74	C₂×C₄×C₃⋊D₃	—	6	48	no	—
75	C₂×C₃×D₁₂	—	3	48	no	—
76	C₂×C₃×D₁₂	C₂×D₃	1	48	yes	complemented
77	C₂×#625	—	3	96	no	—
78	#3802	—	3	256	no	—
79	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
80	C₂²×C₃³	C₂⁴	1	3	yes	—
81	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	24	yes	complemented
82	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
83	C₂×C₃×C₃⋊D₃	—	2	24	no	—
84	C₂×C₃×C₃⋊D₃	C₂⁴	1	8	yes	complemented
85	C₂×C₃²×D₃	—	2	24	no	—
86	C₂×C₃²×D₃	C₂⁴	1	8	yes	complemented
87	D₃×C₃⋊D₃	—	2	64	no	—
88	C₃³×C₄	C₂⁴	1	4	yes	complemented
89	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	complemented
90	C₂⁴×D₃	—	9	8	no	—
91	C₂⁴×D₃	—	9	2	no	—
92	C₂²×C₃×D₄	—	3	4	no	—
93	C₂²×C₃×D₄	—	9	1	no	—
94	C₂²×#67	—	9	8	no	—
95	C₂²×#67	—	9	2	no	—
96	C₂×D₃×D₄	—	9	96	no	—
97	C₂×D₃×D₄	—	9	24	no	—
98	C₂²×D₁₂	—	3	4	no	—
99	C₂²×D₁₂	C₃⋊D₃	1	1	yes	characteristic, complemented
100	C₂²×C₄×D₃	—	9	4	no	—
101	C₂²×C₄×D₃	—	9	1	no	—
102	C₂²×C₄×D₃	—	18	4	no	—
103	C₂³×C₃²	—	2	4	no	—
104	C₂³×C₃²	—	3	12	no	—
105	C₂³×C₃²	—	6	8	no	—
106	C₂³×C₃²	C₂²×D₃	1	4	yes	—
107	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
108	C₂²×C₃⋊D₃	—	2	8	no	—
109	C₂²×C₃⋊D₃	—	3	8	no	—
110	C₂²×C₃⋊D₃	—	3	6	no	—
111	C₂²×C₃⋊D₃	—	3	32	no	—
112	C₂²×C₃⋊D₃	—	3	32	no	—
113	C₂²×C₃⋊D₃	—	3	24	no	—
114	C₂²×C₃⋊D₃	—	6	32	no	—
115	C₂²×C₃⋊D₃	—	6	24	no	—
116	C₂²×C₃⋊D₃	—	6	96	no	—
117	C₂²×C₃⋊D₃	C₂²×D₃	1	12	yes	complemented
118	C₂²×C₃×D₃	—	2	32	no	—
119	C₂²×C₃×D₃	—	3	48	no	—
120	C₂²×C₃×D₃	—	6	32	no	—
121	C₂²×C₃×D₃	C₂²×D₃	1	48	yes	complemented
122	C₂×D₃²	—	3	128	no	—
123	C₂×D₃²	—	6	384	no	—
124	C₃²×D₄	—	3	16	no	—
125	C₂×C₃²×C₄	—	2	24	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	24	yes	complemented
127	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	complemented
128	#638	—	3	32	no	—
129	C₂×C₃⋊Dic₃	—	3	6	no	—
130	C₂×C₃⋊Dic₃	—	3	24	no	—
131	C₂×C₃⋊Dic₃	—	6	24	no	—
132	C₄⋊(C₃⋊D₃)	C₂²×D₃	1	16	yes	complemented
133	C₄×C₃⋊D₃	—	3	16	no	—
134	C₄×C₃⋊D₃	—	3	64	no	—
135	C₄×C₃⋊D₃	—	6	64	no	—
136	C₃×D₁₂	—	3	64	no	—
137	C₃×D₁₂	C₂²×D₃	1	64	yes	complemented
138	#625	—	3	128	no	—
139	C₂³×D₄	—	27	1	no	Sylow
140	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
141	C₂×C₃³	C₂⁵	1	1	yes	characteristic
142	C₃⋊(C₃⋊D₃)	C₂²×D₄	1	8	yes	complemented
143	C₃×C₃⋊D₃	—	2	8	no	—
144	C₃²×D₃	—	2	8	no	—
145	C₂⁴×C₃	—	3	8	no	—
146	C₂⁴×C₃	—	9	2	no	—
147	C₂³×D₃	—	3	8	no	—
148	C₂³×D₃	—	9	96	no	—
149	C₂³×D₃	—	9	4	no	—
150	C₂³×D₃	—	9	1	no	—
151	C₂³×D₃	—	9	24	no	—
152	C₂³×D₃	—	18	4	no	—
153	C₂³×D₃	—	18	16	no	—
154	C₂³×D₃	—	18	64	no	—
155	C₂³×D₃	C₂×C₃⋊D₃	1	2	yes	complemented
156	C₂×C₃×D₄	—	3	48	no	—
157	C₂×C₃×D₄	—	9	12	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	D₃²	1	4	yes	complemented
160	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
161	C₂×#67	—	9	96	no	—
162	C₂×#67	—	9	24	no	—
163	C₂²×Dic₃	—	9	4	no	—
164	C₂²×Dic₃	—	9	1	no	—
165	C₂²×Dic₃	—	18	4	no	—
166	D₃×D₄	—	9	256	no	—
167	D₃×D₄	—	9	64	no	—
168	C₂×D₁₂	—	3	48	no	—
169	C₂×D₁₂	C₂×C₃⋊D₃	1	12	yes	complemented
170	C₂×C₄×D₃	—	9	48	no	—
171	C₂×C₄×D₃	—	9	12	no	—
172	C₂×C₄×D₃	—	18	48	no	—
173	C₂²×C₃²	—	2	12	no	—
174	C₂²×C₃²	—	2	16	no	—
175	C₂²×C₃²	—	3	8	no	—
176	C₂²×C₃²	—	6	24	no	—
177	C₂²×C₃²	D₃×D₄	1	16	yes	complemented
178	C₂²×C₃²	D₃×D₄	1	4	yes	complemented
179	C₂²×C₃²	C₂³×D₃	1	12	yes	—
180	C₂²×C₃²	C₂³×D₃	1	3	yes	—
181	C₂×C₃⋊D₃	—	2	24	no	—
182	C₂×C₃⋊D₃	—	3	24	no	—
183	C₂×C₃⋊D₃	—	3	4	no	—
184	C₂×C₃⋊D₃	—	3	96	no	—
185	C₂×C₃⋊D₃	—	3	16	no	—
186	C₂×C₃⋊D₃	—	6	96	no	—
187	C₂×C₃⋊D₃	—	6	16	no	—
188	C₂×C₃⋊D₃	—	6	64	no	—
189	C₂×C₃⋊D₃	C₂³×D₃	1	8	yes	complemented
190	C₂×C₃×D₃	—	2	96	no	—
191	C₂×C₃×D₃	—	3	32	no	—
192	C₂×C₃×D₃	—	6	96	no	—
193	C₂×C₃×D₃	C₂³×D₃	1	32	yes	complemented
194	D₃²	—	6	256	no	—
195	C₃²×C₄	—	2	16	no	—
196	C₃²×C₄	C₂³×D₃	1	16	yes	complemented
197	C₃²×C₄	C₂³×D₃	1	4	yes	complemented
198	C₃⋊Dic₃	—	3	4	no	—
199	C₃⋊Dic₃	—	3	16	no	—
200	C₃⋊Dic₃	—	6	16	no	—
201	C₂⁵	—	27	2	no	—
202	C₂²×D₄	—	3	1	no	—
203	C₂²×D₄	—	9	1	no	—
204	C₂²×D₄	—	27	24	no	—
205	C₂²×D₄	—	27	2	no	—
206	C₂³×C₄	—	27	1	no	—
207	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₃	—	2	4	no	—
209	C₂³×C₃	—	3	48	no	—
210	C₂³×C₃	—	6	32	no	—
211	C₂³×C₃	—	9	12	no	—
212	C₂³×C₃	—	18	8	no	—
213	C₂³×C₃	C₂×D₃²	1	4	yes	—
214	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
215	C₂²×D₃	—	2	8	no	—
216	C₂²×D₃	—	3	48	no	—
217	C₂²×D₃	—	6	32	no	—
218	C₂²×D₃	—	9	128	no	—
219	C₂²×D₃	—	9	24	no	—
220	C₂²×D₃	—	9	6	no	—
221	C₂²×D₃	—	9	32	no	—
222	C₂²×D₃	—	9	8	no	—
223	C₂²×D₃	—	9	32	no	—
224	C₂²×D₃	—	18	24	no	—
225	C₂²×D₃	—	18	32	no	—
226	C₂²×D₃	—	18	96	no	—
227	C₂²×D₃	—	18	384	no	—
228	C₂²×D₃	C₂²×C₃⋊D₃	1	12	yes	complemented
229	C₃×D₄	—	3	64	no	—
230	C₃×D₄	—	9	16	no	—
231	C₂×C₃×C₄	—	2	24	no	—
232	C₂×C₃×C₄	C₂×D₃²	1	24	yes	complemented
233	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	6	yes	complemented
234	#67	—	9	128	no	—
235	#67	—	9	32	no	—
236	C₂×Dic₃	—	9	24	no	—
237	C₂×Dic₃	—	9	6	no	—
238	C₂×Dic₃	—	18	24	no	—
239	D₁₂	—	3	64	no	—
240	D₁₂	C₂²×C₃⋊D₃	1	16	yes	complemented
241	C₄×D₃	—	9	64	no	—
242	C₄×D₃	—	9	16	no	—
243	C₄×D₃	—	18	64	no	—
244	C₂×C₃²	—	2	24	no	—
245	C₂×C₃²	—	2	4	no	—
246	C₂×C₃²	—	6	8	no	—
247	C₂×C₃²	C₂×D₃×D₄	1	24	yes	complemented
248	C₂×C₃²	C₂×D₃×D₄	1	6	yes	complemented
249	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
250	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
251	C₃⋊D₃	—	2	8	no	—
252	C₃⋊D₃	—	3	8	no	—
253	C₃⋊D₃	—	3	32	no	—
254	C₃⋊D₃	—	6	32	no	—
255	C₃×D₃	—	2	32	no	—
256	C₃×D₃	—	6	32	no	—
257	C₂⁴	—	3	2	no	—
258	C₂⁴	—	9	2	no	—
259	C₂⁴	—	27	24	no	—
260	C₂⁴	—	27	1	no	—
261	C₂⁴	—	54	16	no	—
262	C₂×D₄	—	3	12	no	—
263	C₂×D₄	—	9	12	no	—
264	C₂×D₄	—	27	64	no	—
265	C₂×D₄	—	27	24	no	—
266	C₂²×C₄	—	27	1	no	—
267	C₂²×C₄	—	27	12	no	—
268	C₂²×C₄	D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
269	C₂²×C₃	—	2	12	no	—
270	C₂²×C₃	—	2	16	no	—
271	C₂²×C₃	—	3	32	no	—
272	C₂²×C₃	—	6	96	no	—
273	C₂²×C₃	—	9	8	no	—
274	C₂²×C₃	—	18	24	no	—
275	C₂²×C₃	#3802	1	16	yes	complemented
276	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	complemented
277	C₂²×C₃	C₂²×D₃²	1	12	yes	—
278	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
279	C₂×D₃	—	2	24	no	—
280	C₂×D₃	—	3	32	no	—
281	C₂×D₃	—	6	96	no	—
282	C₂×D₃	—	9	96	no	—
283	C₂×D₃	—	9	24	no	—
284	C₂×D₃	—	9	16	no	—
285	C₂×D₃	—	9	4	no	—
286	C₂×D₃	—	18	16	no	—
287	C₂×D₃	—	18	96	no	—
288	C₂×D₃	—	18	64	no	—
289	C₂×D₃	—	18	256	no	—
290	C₂×D₃	C₂³×C₃⋊D₃	1	8	yes	complemented
291	C₃×C₄	—	2	16	no	—
292	C₃×C₄	C₂²×D₃²	1	16	yes	complemented
293	C₃×C₄	C₂³×C₃⋊D₃	1	4	yes	complemented
294	Dic₃	—	9	16	no	—
295	Dic₃	—	9	4	no	—
296	Dic₃	—	18	16	no	—
297	C₃²	—	2	4	no	—
298	C₃²	C₂²×D₃×D₄	1	4	yes	complemented
299	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic, complemented
300	C₂³	—	3	12	no	—
301	C₂³	—	6	8	no	—
302	C₂³	—	9	12	no	—
303	C₂³	—	18	8	no	—
304	C₂³	—	27	32	no	—
305	C₂³	—	27	6	no	—
306	C₂³	—	27	8	no	—
307	C₂³	—	54	96	no	—
308	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
309	D₄	—	3	16	no	—
310	D₄	—	9	16	no	—
311	D₄	—	27	32	no	—
312	C₂×C₄	—	27	6	no	—
313	C₂×C₄	—	27	16	no	—
314	C₂×C₄	C₂×D₃×C₃⋊D₃	1	6	yes	complemented
315	C₂×C₃	—	2	24	no	—
316	C₂×C₃	—	2	4	no	—
317	C₂×C₃	—	6	32	no	—
318	C₂×C₃	—	18	8	no	—
319	C₂×C₃	C₂×#3802	1	24	yes	complemented
320	C₂×C₃	C₂×D₄×C₃⋊D₃	1	6	yes	complemented
321	C₂×C₃	C₂³×D₃²	1	4	yes	—
322	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
323	D₃	—	2	8	no	—
324	D₃	—	6	32	no	—
325	D₃	—	9	32	no	—
326	D₃	—	9	8	no	—
327	D₃	—	18	32	no	—
328	C₂²	—	3	8	no	—
329	C₂²	—	6	24	no	—
330	C₂²	—	9	8	no	—
331	C₂²	—	18	24	no	—
332	C₂²	—	27	24	no	—
333	C₂²	—	27	4	no	—
334	C₂²	—	54	64	no	—
335	C₂²	#89026	1	4	yes	direct product factor
336	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
337	C₄	—	27	4	no	—
338	C₄	C₂²×D₃×C₃⋊D₃	1	4	yes	complemented
339	C₃	—	2	4	no	—
340	C₃	C₂²×#3802	1	4	yes	complemented
341	C₃	C₂²×D₄×C₃⋊D₃	1	1	yes	characteristic, complemented
342	C₂	—	6	8	no	—
343	C₂	—	18	8	no	—
344	C₂	—	27	8	no	—
345	C₂	C₂×#89026	1	6	yes	direct product factor
346	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₄	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₄	D₃×C₃⋊D₃
hypocenter	C₃³	C₂³×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×D₃×C₃⋊D₃	C₂	semidirect
2. C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
4. C₂²×C₃²×D₁₂	C₂	semidirect
5. C₂²×#6290	C₂	semidirect
6. C₂×#89026	C₂	direct (N × H)
10. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
11. C₂³×C₃²×D₃	C₂²	semidirect
13. C₂²×D₃×C₃⋊D₃	C₂²	semidirect
14. C₂²×C₃³×C₄	C₂²	semidirect
15. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
16. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₂×C₃²×D₁₂	C₂²	semidirect
19. C₂×#6290	C₂²	semidirect
20. #89026	C₂²	direct (N × H)
26. C₂²×C₄⋊(C₃⋊D₃)	D₃	semidirect
31. C₂²×C₃×D₁₂	D₃	semidirect
35. C₂²×C₃⋊(C₃⋊D₃)	D₄	semidirect
38. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
40. C₂²×C₃²×D₃	C₂³	semidirect
42. C₂×D₃×C₃⋊D₃	C₂³	semidirect
43. C₂×C₃³×C₄	C₂³	semidirect
44. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
45. C₄×C₃⋊(C₃⋊D₃)	C₂³	semidirect
46. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
47. C₃²×D₁₂	C₂³	semidirect
48. #6290	C₂³	semidirect
57. C₂³×C₃⋊D₃	C₂×D₃	semidirect
59. C₂³×C₃×D₃	C₂×D₃	semidirect
64. C₂²×C₃²×C₄	C₂×D₃	semidirect
65. C₂²×C₃²×C₄	C₂×D₃	semidirect
71. C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	semidirect
76. C₂×C₃×D₁₂	C₂×D₃	semidirect
79. C₂²×C₃³	C₂×D₄	semidirect
81. C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	semidirect
84. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
86. C₂×C₃²×D₃	C₂⁴	semidirect
88. C₃³×C₄	C₂⁴	semidirect
89. C₃⋊(C₃⋊Dic₃)	C₂⁴	semidirect
99. C₂²×D₁₂	C₃⋊D₃	semidirect
117. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
121. C₂²×C₃×D₃	C₂²×D₃	semidirect
126. C₂×C₃²×C₄	C₂²×D₃	semidirect
127. C₂×C₃²×C₄	C₂²×D₃	semidirect
132. C₄⋊(C₃⋊D₃)	C₂²×D₃	semidirect
137. C₃×D₁₂	C₂²×D₃	semidirect
140. C₂×C₃³	C₂²×D₄	semidirect
142. C₃⋊(C₃⋊D₃)	C₂²×D₄	semidirect
155. C₂³×D₃	C₂×C₃⋊D₃	semidirect
159. C₂²×C₃×C₄	D₃²	semidirect
160. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
169. C₂×D₁₂	C₂×C₃⋊D₃	semidirect
177. C₂²×C₃²	D₃×D₄	semidirect
178. C₂²×C₃²	D₃×D₄	semidirect
189. C₂×C₃⋊D₃	C₂³×D₃	semidirect
193. C₂×C₃×D₃	C₂³×D₃	semidirect
196. C₃²×C₄	C₂³×D₃	semidirect
197. C₃²×C₄	C₂³×D₃	semidirect
207. C₃³	C₂³×D₄	semidirect
228. C₂²×D₃	C₂²×C₃⋊D₃	semidirect
232. C₂×C₃×C₄	C₂×D₃²	semidirect
233. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
240. D₁₂	C₂²×C₃⋊D₃	semidirect
247. C₂×C₃²	C₂×D₃×D₄	semidirect
248. C₂×C₃²	C₂×D₃×D₄	semidirect
268. C₂²×C₄	D₃×C₃⋊D₃	semidirect
275. C₂²×C₃	#3802	semidirect
276. C₂²×C₃	D₄×C₃⋊D₃	semidirect
290. C₂×D₃	C₂³×C₃⋊D₃	semidirect
292. C₃×C₄	C₂²×D₃²	semidirect
293. C₃×C₄	C₂³×C₃⋊D₃	semidirect
298. C₃²	C₂²×D₃×D₄	semidirect
299. C₃²	C₂²×D₃×D₄	semidirect
314. C₂×C₄	C₂×D₃×C₃⋊D₃	semidirect
319. C₂×C₃	C₂×#3802	semidirect
320. C₂×C₃	C₂×D₄×C₃⋊D₃	semidirect
335. C₂²	#89026	direct (N × H)
338. C₄	C₂²×D₃×C₃⋊D₃	semidirect
340. C₃	C₂²×#3802	semidirect
341. C₃	C₂²×D₄×C₃⋊D₃	semidirect
345. C₂	C₂×#89026	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×D₃×C₃⋊D₃	2
C₂²×C₄×C₃⋊(C₃⋊D₃)	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂²×C₃²×D₁₂	2
C₂²×#6290	2
C₂×#89026	2
C₂²×D₄×C₃⋊D₃	3
C₂²×#3802	3

Subgroups — C22×#89026 #13181600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#89026 #13181600