Subgroups — C₂×C₃×D₈×C₃⋊D₃ #13179505

Order 1728.

2332 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₃³×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3753	C₂	1	2	yes	maximal, complemented
4	C₃×D₈×C₃⋊D₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3745	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₈×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×D₃×D₈	—	3	4	no	maximal
9	C₂³×C₃×C₃⋊D₃	—	2	2	no	—
10	C₂×C₃³×D₄	C₂²	1	2	yes	complemented
11	C₂×C₃×#638	—	2	2	no	—
12	C₃×D₄×C₃⋊D₃	—	2	4	no	—
13	C₃×D₄×C₃⋊D₃	C₂²	1	8	yes	complemented
14	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
15	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	C₃³×D₈	C₂²	1	4	yes	complemented
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×#3753	C₂²	1	8	yes	complemented
19	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
20	C₃×#3745	C₂²	1	4	yes	complemented
21	C₃×C₈×C₃⋊D₃	C₂²	1	4	yes	complemented
22	C₂×D₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
23	C₂×C₃×D₃×D₄	—	3	8	no	—
24	C₂×C₃²×D₈	—	2	4	no	—
25	C₂×C₃²×D₈	D₃	1	4	yes	complemented
26	C₂×C₃²×D₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3753	C₂×C₃	1	2	yes	complemented
28	D₈×C₃⋊D₃	C₂×C₃	1	8	yes	direct product factor
29	C₂×#3745	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#213	—	3	8	no	—
32	C₃×D₃×D₈	—	3	32	no	—
33	C₂×C₃×D₂₄	—	3	4	no	—
34	C₂×C₃×D₃×C₈	—	3	4	no	—
35	C₂³×C₃³	—	2	2	no	—
36	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
37	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
38	C₂²×C₃×C₃⋊D₃	—	4	8	no	—
39	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
40	C₃³×D₄	—	2	2	no	—
41	C₃³×D₄	C₂³	1	4	yes	complemented
42	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
43	C₃×#638	—	2	8	no	—
44	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
45	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
46	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
47	C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
48	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
49	C₃³×C₈	C₂³	1	2	yes	complemented
50	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	complemented
51	C₂²×C₃×D₈	—	9	1	no	—
52	C₂×D₃×D₈	—	3	4	no	—
53	C₂³×C₃⋊D₃	—	2	2	no	—
54	C₂³×C₃×D₃	—	6	8	no	—
55	C₂×C₃²×D₄	—	2	8	no	—
56	C₂×C₃²×D₄	C₂×D₃	1	8	yes	complemented
57	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	complemented
58	C₂×#638	—	2	2	no	—
59	D₄×C₃⋊D₃	—	2	4	no	—
60	D₄×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
61	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	complemented
62	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×#67	—	6	8	no	—
64	C₃×D₃×D₄	—	3	32	no	—
65	C₃×D₃×D₄	—	6	16	no	—
66	C₂×C₃×D₁₂	—	3	8	no	—
67	C₂×C₃×C₄×D₃	—	3	4	no	—
68	C₃²×D₈	—	2	16	no	—
69	C₃²×D₈	C₂×D₃	1	16	yes	complemented
70	C₃²×D₈	C₂²×C₃	1	4	yes	complemented
71	C₂×C₃²×C₈	—	2	4	no	—
72	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
73	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
74	#3753	C₂²×C₃	1	8	yes	complemented
75	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
76	#3745	C₂²×C₃	1	4	yes	complemented
77	C₈×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
78	C₃×#213	—	3	32	no	—
79	C₂×C₃×C₃⋊C₈	—	3	4	no	—
80	C₃×D₂₄	—	3	16	no	—
81	C₃×D₃×C₈	—	3	16	no	—
82	C₂²×C₃³	—	2	4	no	—
83	C₂²×C₃³	—	4	4	no	—
84	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₃⋊D₃	—	2	4	no	—
86	C₂×C₃×C₃⋊D₃	—	4	4	no	—
87	C₂×C₃×C₃⋊D₃	—	4	16	no	—
88	C₂×C₃×C₃⋊D₃	D₈	1	4	yes	direct product factor
89	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
90	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
91	C₃³×C₄	C₂⁴	1	1	yes	characteristic
92	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
93	C₂²×C₃×D₄	—	9	2	no	—
94	C₂×D₃×D₄	—	3	8	no	—
95	C₂×C₃×D₈	—	2	4	no	—
96	C₂×C₃×D₈	—	9	2	no	—
97	C₂×C₃×D₈	—	9	8	no	—
98	C₂×C₃×D₈	—	9	1	no	—
99	C₂×C₃×D₈	C₃×D₃	1	4	yes	complemented
100	C₂×C₃×D₈	C₃⋊D₃	1	1	yes	characteristic, direct product factor
101	C₂²×C₃×C₈	—	9	1	no	—
102	C₂×#213	—	3	8	no	—
103	D₃×D₈	—	3	32	no	—
104	C₂×D₂₄	—	3	4	no	—
105	C₂×D₃×C₈	—	3	4	no	—
106	C₂³×C₃²	—	2	2	no	—
107	C₂³×C₃²	—	2	8	no	—
108	C₂³×C₃²	—	4	8	no	—
109	C₂²×C₃⋊D₃	—	2	2	no	—
110	C₂²×C₃⋊D₃	—	2	8	no	—
111	C₂²×C₃⋊D₃	—	4	8	no	—
112	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
113	C₂²×C₃×D₃	—	3	4	no	—
114	C₂²×C₃×D₃	—	6	32	no	—
115	C₂²×C₃×D₃	—	6	8	no	—
116	C₂²×C₃×D₃	—	12	32	no	—
117	C₃²×D₄	—	2	2	no	—
118	C₃²×D₄	—	2	16	no	—
119	C₃²×D₄	—	2	8	no	—
120	C₃²×D₄	—	4	8	no	—
121	C₃²×D₄	C₂²×D₃	1	16	yes	complemented
122	C₃²×D₄	C₂³×C₃	1	4	yes	complemented
123	C₂×C₃²×C₄	—	2	4	no	—
124	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
125	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
126	#638	—	2	8	no	—
127	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
128	C₄⋊(C₃⋊D₃)	—	2	2	no	—
129	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	complemented
130	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
131	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
132	C₃×#67	—	6	32	no	—
133	C₂×C₃×Dic₃	—	3	4	no	—
134	C₃×D₁₂	—	3	16	no	—
135	C₃×D₁₂	—	6	8	no	—
136	C₃×C₄×D₃	—	3	8	no	—
137	C₃×C₄×D₃	—	3	8	no	—
138	C₃²×C₈	—	2	8	no	—
139	C₃²×C₈	C₂²×D₃	1	8	yes	complemented
140	C₃²×C₈	C₂³×C₃	1	2	yes	complemented
141	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	complemented
142	C₃×C₃⋊C₈	—	3	8	no	—
143	C₂²×D₈	—	9	1	no	Sylow
144	C₂×C₃³	—	4	4	no	—
145	C₂×C₃³	C₂×D₈	1	2	yes	complemented
146	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
147	C₃×C₃⋊D₃	—	4	4	no	—
148	C₃×C₃⋊D₃	C₂×D₈	1	4	yes	direct product factor
149	C₂⁴×C₃	—	18	2	no	—
150	C₂³×D₃	—	6	8	no	—
151	C₂×C₃×D₄	—	2	8	no	—
152	C₂×C₃×D₄	—	9	8	no	—
153	C₂×C₃×D₄	—	9	2	no	—
154	C₂×C₃×D₄	—	18	4	no	—
155	C₂×C₃×D₄	—	18	2	no	—
156	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	complemented
157	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	complemented
158	C₂²×C₃×C₄	—	9	1	no	—
159	C₂×#67	—	6	8	no	—
160	D₃×D₄	—	3	32	no	—
161	D₃×D₄	—	6	16	no	—
162	C₂×D₁₂	—	3	8	no	—
163	C₂×C₄×D₃	—	3	4	no	—
164	C₃×D₈	—	2	16	no	—
165	C₃×D₈	—	9	8	no	—
166	C₃×D₈	—	9	4	no	—
167	C₃×D₈	C₂×C₃×D₃	1	16	yes	complemented
168	C₃×D₈	C₂×C₃⋊D₃	1	4	yes	direct product factor
169	C₂×C₃×C₈	—	2	4	no	—
170	C₂×C₃×C₈	—	9	1	no	—
171	C₂×C₃×C₈	—	9	4	no	—
172	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
173	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
174	#213	—	3	32	no	—
175	C₂×C₃⋊C₈	—	3	4	no	—
176	D₂₄	—	3	16	no	—
177	D₃×C₈	—	3	16	no	—
178	C₂²×C₃²	—	2	4	no	—
179	C₂²×C₃²	—	2	4	no	—
180	C₂²×C₃²	—	2	16	no	—
181	C₂²×C₃²	—	4	16	no	—
182	C₂²×C₃²	—	4	4	no	—
183	C₂²×C₃²	—	4	16	no	—
184	C₂²×C₃²	—	8	16	no	—
185	C₂²×C₃²	D₃×D₄	1	4	yes	—
186	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
187	C₂×C₃⋊D₃	—	2	4	no	—
188	C₂×C₃⋊D₃	—	4	4	no	—
189	C₂×C₃⋊D₃	—	4	16	no	—
190	C₂×C₃⋊D₃	C₃×D₈	1	4	yes	direct product factor
191	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
192	C₂×C₃×D₃	—	3	16	no	—
193	C₂×C₃×D₃	—	3	8	no	—
194	C₂×C₃×D₃	—	6	16	no	—
195	C₂×C₃×D₃	—	12	64	no	—
196	C₂×C₃×D₃	—	12	16	no	—
197	C₃²×C₄	—	2	4	no	—
198	C₃²×C₄	—	2	4	no	—
199	C₃²×C₄	D₃×D₄	1	4	yes	—
200	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
201	C₃²×C₄	C₂³×D₃	1	4	yes	—
202	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
203	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
204	C₃×Dic₃	—	3	8	no	—
205	C₂²×D₄	—	9	2	no	—
206	C₂×D₈	—	9	2	no	—
207	C₂×D₈	—	9	8	no	—
208	C₂×D₈	—	9	1	no	—
209	C₂×D₈	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
210	C₂²×C₈	—	9	1	no	—
211	C₃³	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₃	—	2	8	no	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	4	8	no	—
215	C₂³×C₃	—	9	1	no	—
216	C₂³×C₃	—	18	8	no	—
217	C₂³×C₃	—	18	2	no	—
218	C₂³×C₃	—	36	8	no	—
219	C₂²×D₃	—	3	4	no	—
220	C₂²×D₃	—	6	32	no	—
221	C₂²×D₃	—	6	8	no	—
222	C₂²×D₃	—	12	32	no	—
223	C₃×D₄	—	2	8	no	—
224	C₃×D₄	—	2	2	no	—
225	C₃×D₄	—	2	16	no	—
226	C₃×D₄	—	4	8	no	—
227	C₃×D₄	—	9	4	no	—
228	C₃×D₄	—	18	8	no	—
229	C₃×D₄	—	18	2	no	—
230	C₃×D₄	C₂²×C₃×D₃	1	16	yes	complemented
231	C₃×D₄	C₂²×C₃⋊D₃	1	4	yes	complemented
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	9	1	no	—
234	C₂×C₃×C₄	—	9	2	no	—
235	C₂×C₃×C₄	—	9	2	no	—
236	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
237	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
238	#67	—	6	32	no	—
239	C₂×Dic₃	—	3	4	no	—
240	D₁₂	—	3	16	no	—
241	D₁₂	—	6	8	no	—
242	C₄×D₃	—	3	8	no	—
243	C₄×D₃	—	3	8	no	—
244	C₃×C₈	—	2	8	no	—
245	C₃×C₈	—	9	2	no	—
246	C₃×C₈	C₂²×C₃×D₃	1	8	yes	complemented
247	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
248	C₃⋊C₈	—	3	8	no	—
249	C₂×C₃²	—	2	8	no	—
250	C₂×C₃²	—	2	4	no	—
251	C₂×C₃²	—	4	4	no	—
252	C₂×C₃²	—	4	16	no	—
253	C₂×C₃²	—	8	16	no	—
254	C₂×C₃²	D₃×D₈	1	8	yes	complemented
255	C₂×C₃²	C₂×C₃×D₈	1	2	yes	complemented
256	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
257	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
258	C₃⋊D₃	—	4	4	no	—
259	C₃⋊D₃	C₂×C₃×D₈	1	4	yes	direct product factor
260	C₃×D₃	—	3	16	no	—
261	C₃×D₃	—	12	16	no	—
262	C₂⁴	—	18	2	no	—
263	C₂×D₄	—	9	8	no	—
264	C₂×D₄	—	9	2	no	—
265	C₂×D₄	—	18	4	no	—
266	C₂×D₄	—	18	2	no	—
267	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
268	C₂²×C₄	—	9	1	no	—
269	D₈	—	9	8	no	—
270	D₈	—	9	4	no	—
271	D₈	C₂×C₃×C₃⋊D₃	1	4	yes	direct product factor
272	C₂×C₈	—	9	1	no	—
273	C₂×C₈	—	9	4	no	—
274	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
275	C₂²×C₃	—	2	16	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	4	16	no	—
279	C₂²×C₃	—	4	16	no	—
280	C₂²×C₃	—	4	4	no	—
281	C₂²×C₃	—	8	16	no	—
282	C₂²×C₃	—	9	2	no	—
283	C₂²×C₃	—	9	4	no	—
284	C₂²×C₃	—	18	4	no	—
285	C₂²×C₃	—	36	16	no	—
286	C₂²×C₃	—	36	4	no	—
287	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
288	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
289	C₂×D₃	—	3	16	no	—
290	C₂×D₃	—	3	8	no	—
291	C₂×D₃	—	6	16	no	—
292	C₂×D₃	—	12	64	no	—
293	C₂×D₃	—	12	16	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	9	2	no	—
297	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
298	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
299	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
300	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
301	Dic₃	—	3	8	no	—
302	C₃²	—	2	4	no	—
303	C₃²	C₂×D₃×D₈	1	4	yes	complemented
304	C₃²	C₂²×C₃×D₈	1	1	yes	characteristic, complemented
305	C₂³	—	2	2	no	—
306	C₂³	—	9	1	no	—
307	C₂³	—	18	8	no	—
308	C₂³	—	18	2	no	—
309	C₂³	—	36	8	no	—
310	D₄	—	2	2	no	—
311	D₄	—	9	4	no	—
312	D₄	—	18	8	no	—
313	D₄	—	18	2	no	—
314	D₄	C₂²×C₃×C₃⋊D₃	1	4	yes	complemented
315	C₂×C₄	—	9	1	no	—
316	C₂×C₄	—	9	2	no	—
317	C₂×C₄	—	9	2	no	—
318	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
319	C₈	—	9	2	no	—
320	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	complemented
321	C₂×C₃	—	2	8	no	—
322	C₂×C₃	—	2	4	no	—
323	C₂×C₃	—	4	16	no	—
324	C₂×C₃	—	4	4	no	—
325	C₂×C₃	—	8	16	no	—
326	C₂×C₃	—	9	4	no	—
327	C₂×C₃	—	36	4	no	—
328	C₂×C₃	C₃×D₃×D₈	1	8	yes	complemented
329	C₂×C₃	D₈×C₃⋊D₃	1	2	yes	direct product factor
330	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
331	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
332	D₃	—	3	16	no	—
333	D₃	—	12	16	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	9	4	no	—
337	C₂²	—	9	2	no	—
338	C₂²	—	18	4	no	—
339	C₂²	—	36	16	no	—
340	C₂²	—	36	4	no	—
341	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
342	C₄	—	9	2	no	—
343	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
344	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
345	C₃	—	2	4	no	—
346	C₃	C₂×C₃×D₃×D₈	1	4	yes	complemented
347	C₃	C₂×D₈×C₃⋊D₃	1	1	yes	characteristic, direct product factor
348	C₂	—	4	4	no	—
349	C₂	—	9	4	no	—
350	C₂	—	36	4	no	—
351	C₂	C₃×D₈×C₃⋊D₃	1	2	yes	direct product factor
352	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×D₈	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃×D₈	C₃⋊D₃
hypocenter	C₃²	C₂²×C₃×D₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
2. C₂×C₃³×D₈	C₂	semidirect
3. C₂×C₃×#3753	C₂	semidirect
4. C₃×D₈×C₃⋊D₃	C₂	direct (N × H)
5. C₂×C₃×#3745	C₂	semidirect
6. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
7. C₂×D₈×C₃⋊D₃	C₃	direct (N × H)
10. C₂×C₃³×D₄	C₂²	semidirect
13. C₃×D₄×C₃⋊D₃	C₂²	semidirect
14. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
16. C₃³×D₈	C₂²	semidirect
17. C₂×C₃³×C₈	C₂²	semidirect
18. C₃×#3753	C₂²	semidirect
19. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
20. C₃×#3745	C₂²	semidirect
21. C₃×C₈×C₃⋊D₃	C₂²	semidirect
22. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
25. C₂×C₃²×D₈	D₃	semidirect
26. C₂×C₃²×D₈	C₂×C₃	semidirect
27. C₂×#3753	C₂×C₃	semidirect
28. D₈×C₃⋊D₃	C₂×C₃	direct (N × H)
29. C₂×#3745	C₂×C₃	semidirect
30. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
41. C₃³×D₄	C₂³	semidirect
46. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
49. C₃³×C₈	C₂³	semidirect
50. C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
56. C₂×C₃²×D₄	C₂×D₃	semidirect
57. C₂×C₃²×D₄	C₂²×C₃	semidirect
60. D₄×C₃⋊D₃	C₂²×C₃	semidirect
61. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
69. C₃²×D₈	C₂×D₃	semidirect
70. C₃²×D₈	C₂²×C₃	semidirect
72. C₂×C₃²×C₈	C₂×D₃	semidirect
73. C₂×C₃²×C₈	C₂²×C₃	semidirect
74. #3753	C₂²×C₃	semidirect
75. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
76. #3745	C₂²×C₃	semidirect
77. C₈×C₃⋊D₃	C₂²×C₃	semidirect
88. C₂×C₃×C₃⋊D₃	D₈	direct (N × H)
99. C₂×C₃×D₈	C₃×D₃	semidirect
100. C₂×C₃×D₈	C₃⋊D₃	direct (N × H)
121. C₃²×D₄	C₂²×D₃	semidirect
122. C₃²×D₄	C₂³×C₃	semidirect
129. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
139. C₃²×C₈	C₂²×D₃	semidirect
140. C₃²×C₈	C₂³×C₃	semidirect
141. C₃⋊(C₃⋊C₈)	C₂³×C₃	semidirect
145. C₂×C₃³	C₂×D₈	semidirect
148. C₃×C₃⋊D₃	C₂×D₈	direct (N × H)
156. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
157. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
167. C₃×D₈	C₂×C₃×D₃	semidirect
168. C₃×D₈	C₂×C₃⋊D₃	direct (N × H)
172. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
173. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
190. C₂×C₃⋊D₃	C₃×D₈	direct (N × H)
209. C₂×D₈	C₃×C₃⋊D₃	direct (N × H)
211. C₃³	C₂²×D₈	semidirect
230. C₃×D₄	C₂²×C₃×D₃	semidirect
231. C₃×D₄	C₂²×C₃⋊D₃	semidirect
246. C₃×C₈	C₂²×C₃×D₃	semidirect
247. C₃×C₈	C₂²×C₃⋊D₃	semidirect
254. C₂×C₃²	D₃×D₈	semidirect
255. C₂×C₃²	C₂×C₃×D₈	semidirect
259. C₃⋊D₃	C₂×C₃×D₈	direct (N × H)
267. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
271. D₈	C₂×C₃×C₃⋊D₃	direct (N × H)
274. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
303. C₃²	C₂×D₃×D₈	semidirect
304. C₃²	C₂²×C₃×D₈	semidirect
314. D₄	C₂²×C₃×C₃⋊D₃	semidirect
320. C₈	C₂²×C₃×C₃⋊D₃	semidirect
328. C₂×C₃	C₃×D₃×D₈	semidirect
329. C₂×C₃	D₈×C₃⋊D₃	direct (N × H)
346. C₃	C₂×C₃×D₃×D₈	semidirect
347. C₃	C₂×D₈×C₃⋊D₃	direct (N × H)
351. C₂	C₃×D₈×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
C₂×C₃×D₄×C₃⋊D₃	2
C₂×C₃³×D₈	2
C₂×C₃×#3753	2
C₃×D₈×C₃⋊D₃	2
C₂×C₃×#3745	2
C₂×C₃×C₈×C₃⋊D₃	2
C₂×D₈×C₃⋊D₃	3
C₂×C₃×D₃×D₈	3

Subgroups — C2×C3×D8×C3⋊D3 #13179505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₈×C₃⋊D₃ #13179505