Subgroups — C₃×D₄×#638 #13179554

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#638	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64162	C₂	1	2	yes	maximal, complemented
5	C₃×#64149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64148	C₂	1	2	yes	maximal, complemented
7	C₃×#64147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64146	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#638	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×D₄×#67	—	3	4	no	maximal
14	C₂⁴×C₃³	C₂²	1	2	yes	complemented
15	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
16	C₂×C₃³×D₄	—	2	4	no	—
17	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃³×D₄	C₂²	1	2	yes	complemented
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×#638	—	2	8	no	—
22	C₂×C₃×#638	C₂²	1	1	yes	characteristic
23	C₂×C₃×#638	C₂²	1	2	yes	complemented
24	C₂×C₃×#638	C₂²	1	2	yes	complemented
25	C₂×C₃×#638	C₂²	1	2	yes	complemented
26	C₂×C₃×#638	C₂²	1	2	yes	complemented
27	C₂×C₃×#638	C₂²	1	2	yes	complemented
28	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
29	C₃×D₄×C₃⋊D₃	—	2	4	no	—
30	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3757	C₂²	1	2	yes	complemented
34	C₃×#3757	C₂²	1	2	yes	complemented
35	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3752	C₂²	1	2	yes	complemented
37	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₃²×D₄	—	2	4	no	—
41	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
42	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂²×#638	C₂×C₃	1	2	yes	complemented
44	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×C₃×#67	—	3	8	no	—
46	C₂×C₃×D₃×D₄	—	3	4	no	—
47	#64162	C₂×C₃	1	2	yes	complemented
48	#64149	C₂×C₃	1	1	yes	characteristic, complemented
49	#64148	C₂×C₃	1	2	yes	complemented
50	#64147	C₂×C₃	1	1	yes	characteristic, complemented
51	#64146	C₂×C₃	1	2	yes	complemented
52	D₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
53	#64139	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#953	—	3	8	no	—
56	C₃×#940	—	3	4	no	—
57	C₃×#939	—	3	8	no	—
58	C₃×#938	—	3	4	no	—
59	C₃×#937	—	3	8	no	—
60	C₃×D₄×Dic₃	—	3	4	no	—
61	C₃×#930	—	3	4	no	—
62	C₃×C₄×#67	—	3	4	no	—
63	C₂³×C₃³	—	2	4	no	—
64	C₂³×C₃³	—	2	4	no	—
65	C₂³×C₃³	—	4	2	no	—
66	C₂³×C₃³	C₂³	1	2	yes	—
67	C₂³×C₃³	C₂³	1	2	yes	—
68	C₂³×C₃³	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
70	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
71	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
72	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
73	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
74	C₃³×D₄	—	2	4	no	—
75	C₃³×D₄	—	2	2	no	—
76	C₃³×D₄	D₄	1	4	yes	complemented
77	C₂×C₃³×C₄	—	2	2	no	—
78	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
79	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
80	C₃×#638	—	2	4	no	—
81	C₃×#638	—	2	4	no	—
82	C₃×#638	—	2	4	no	—
83	C₃×#638	—	2	4	no	—
84	C₃×#638	—	4	2	no	—
85	C₃×#638	D₄	1	4	yes	direct product factor
86	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
87	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
90	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
92	C₃×C₄×C₃⋊D₃	—	2	2	no	—
93	C₃×D₄²	—	9	1	no	—
94	D₄×#67	—	3	4	no	—
95	C₂⁴×C₃²	—	2	8	no	—
96	C₂⁴×C₃²	C₂×D₃	1	8	yes	complemented
97	C₂⁴×C₃²	C₂²×C₃	1	2	yes	complemented
98	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
99	C₂³×C₃×D₃	—	3	8	no	—
100	C₂×C₃²×D₄	—	2	32	no	—
101	C₂×C₃²×D₄	—	2	4	no	—
102	C₂×C₃²×D₄	—	2	8	no	—
103	C₂×C₃²×D₄	—	2	4	no	—
104	C₂×C₃²×D₄	—	2	16	no	—
105	C₂×C₃²×D₄	—	2	4	no	—
106	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
107	C₂×C₃²×D₄	C₂×D₃	1	8	yes	complemented
108	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
109	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	complemented
111	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×C₃²×C₄	—	2	4	no	—
113	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
114	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂×#638	—	2	8	no	—
116	C₂×#638	C₂²×C₃	1	1	yes	characteristic
117	C₂×#638	C₂²×C₃	1	2	yes	complemented
118	C₂×#638	C₂²×C₃	1	2	yes	complemented
119	C₂×#638	C₂²×C₃	1	2	yes	complemented
120	C₂×#638	C₂²×C₃	1	2	yes	complemented
121	C₂×#638	C₂²×C₃	1	2	yes	complemented
122	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
123	D₄×C₃⋊D₃	—	2	4	no	—
124	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₃×#67	—	3	4	no	—
127	C₂×C₃×#67	—	3	8	no	—
128	C₂×C₃×#67	—	3	8	no	—
129	C₂×C₃×#67	—	3	8	no	—
130	C₂×C₃×#67	—	3	8	no	—
131	C₂×C₃×#67	—	3	8	no	—
132	C₂×C₃×#67	—	6	32	no	—
133	C₂²×C₃×Dic₃	—	3	8	no	—
134	C₃×D₃×D₄	—	6	16	no	—
135	C₂×C₃×D₁₂	—	3	4	no	—
136	C₂×C₃×C₄×D₃	—	3	4	no	—
137	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
138	#3757	C₂²×C₃	1	2	yes	complemented
139	#3757	C₂²×C₃	1	2	yes	complemented
140	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
141	#3752	C₂²×C₃	1	2	yes	complemented
142	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
143	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₃×#217	—	3	4	no	—
146	C₃×#217	—	3	8	no	—
147	C₃×#217	—	3	8	no	—
148	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
149	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
150	C₃×C₄⋊Dic₃	—	3	4	no	—
151	C₃×Dic₃⋊C₄	—	3	4	no	—
152	C₃×C₄×Dic₃	—	3	4	no	—
153	C₂²×C₃³	—	2	1	no	—
154	C₂²×C₃³	—	2	2	no	—
155	C₂²×C₃³	—	2	1	no	—
156	C₂²×C₃³	—	2	2	no	—
157	C₂²×C₃³	—	2	2	no	—
158	C₂²×C₃³	—	2	2	no	—
159	C₂²×C₃³	—	2	2	no	—
160	C₂²×C₃³	—	4	8	no	—
161	C₂²×C₃³	C₂×D₄	1	2	yes	complemented
162	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
163	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
164	C₂×C₃×C₃⋊D₃	—	2	1	no	—
165	C₂×C₃×C₃⋊D₃	—	2	1	no	—
166	C₂×C₃×C₃⋊D₃	—	2	2	no	—
167	C₂×C₃×C₃⋊D₃	—	2	2	no	—
168	C₂×C₃×C₃⋊D₃	—	2	2	no	—
169	C₂×C₃×C₃⋊D₃	—	4	8	no	—
170	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	complemented
171	C₃³×C₄	—	2	1	no	—
172	C₃³×C₄	C₂×D₄	1	2	yes	complemented
173	C₃×C₃⋊Dic₃	—	2	1	no	—
174	C₃×C₃⋊Dic₃	—	2	2	no	—
175	C₃×C₃⋊Dic₃	—	2	1	no	—
176	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	complemented
177	C₂²×C₃×D₄	—	2	4	no	—
178	C₂²×C₃×D₄	—	9	2	no	—
179	C₂²×C₃×D₄	—	9	1	no	—
180	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
181	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
182	C₂²×#67	—	3	8	no	—
183	C₂×D₃×D₄	—	3	4	no	—
184	C₃×#127	—	9	1	no	—
185	C₃×#121	—	9	1	no	—
186	C₃×#121	—	9	2	no	—
187	C₃×#121	—	9	1	no	—
188	C₃×#120	—	9	2	no	—
189	C₃×#120	—	9	2	no	—
190	C₃×C₄×D₄	—	9	1	no	—
191	C₃×C₄×D₄	—	9	1	no	—
192	#953	—	3	8	no	—
193	#940	—	3	4	no	—
194	#939	—	3	8	no	—
195	#938	—	3	4	no	—
196	#937	—	3	8	no	—
197	D₄×Dic₃	—	3	4	no	—
198	#930	—	3	4	no	—
199	C₄×#67	—	3	4	no	—
200	C₂³×C₃²	—	2	32	no	—
201	C₂³×C₃²	—	2	16	no	—
202	C₂³×C₃²	—	2	4	no	—
203	C₂³×C₃²	—	2	4	no	—
204	C₂³×C₃²	—	2	4	no	—
205	C₂³×C₃²	—	2	8	no	—
206	C₂³×C₃²	—	2	8	no	—
207	C₂³×C₃²	—	2	16	no	—
208	C₂³×C₃²	—	4	16	no	—
209	C₂³×C₃²	—	4	8	no	—
210	C₂³×C₃²	—	4	2	no	—
211	C₂³×C₃²	—	4	16	no	—
212	C₂³×C₃²	C₂²×D₃	1	8	yes	—
213	C₂³×C₃²	C₂²×D₃	1	4	yes	—
214	C₂³×C₃²	C₂²×D₃	1	8	yes	—
215	C₂³×C₃²	C₂³×C₃	1	2	yes	—
216	C₂³×C₃²	C₂³×C₃	1	2	yes	—
217	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃⋊D₃	—	2	4	no	—
219	C₂²×C₃⋊D₃	—	2	4	no	—
220	C₂²×C₃⋊D₃	—	4	2	no	—
221	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
222	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₃×D₃	—	3	4	no	—
224	C₂²×C₃×D₃	—	3	8	no	—
225	C₂²×C₃×D₃	—	6	16	no	—
226	C₂²×C₃×D₃	—	6	16	no	—
227	C₂²×C₃×D₃	—	12	8	no	—
228	C₃²×D₄	—	2	32	no	—
229	C₃²×D₄	—	2	16	no	—
230	C₃²×D₄	—	2	16	no	—
231	C₃²×D₄	—	2	4	no	—
232	C₃²×D₄	—	2	8	no	—
233	C₃²×D₄	—	2	2	no	—
234	C₃²×D₄	—	2	16	no	—
235	C₃²×D₄	#67	1	16	yes	complemented
236	C₃²×D₄	C₃×D₄	1	4	yes	complemented
237	C₂×C₃²×C₄	—	2	16	no	—
238	C₂×C₃²×C₄	—	2	8	no	—
239	C₂×C₃²×C₄	—	2	2	no	—
240	C₂×C₃²×C₄	—	2	4	no	—
241	C₂×C₃²×C₄	—	2	4	no	—
242	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
243	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
244	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
246	#638	—	2	4	no	—
247	#638	—	2	4	no	—
248	#638	—	2	4	no	—
249	#638	—	2	4	no	—
250	#638	—	4	2	no	—
251	#638	C₃×D₄	1	4	yes	direct product factor
252	C₂×C₃⋊Dic₃	—	2	4	no	—
253	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
254	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
256	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
257	C₄⋊(C₃⋊D₃)	—	2	2	no	—
258	C₄×C₃⋊D₃	—	2	2	no	—
259	C₃×#67	—	3	16	no	—
260	C₃×#67	—	6	16	no	—
261	C₃×#67	—	6	16	no	—
262	C₃×#67	—	6	16	no	—
263	C₃×#67	—	6	16	no	—
264	C₃×#67	—	12	8	no	—
265	C₂×C₃×Dic₃	—	3	4	no	—
266	C₂×C₃×Dic₃	—	3	4	no	—
267	C₂×C₃×Dic₃	—	3	4	no	—
268	C₂×C₃×Dic₃	—	3	8	no	—
269	C₂×C₃×Dic₃	—	6	16	no	—
270	C₃×D₁₂	—	6	8	no	—
271	C₃×C₄×D₃	—	6	8	no	—
272	D₄²	—	9	1	no	Sylow
273	C₂×C₃³	—	2	2	no	—
274	C₂×C₃³	—	2	4	no	—
275	C₂×C₃³	—	4	2	no	—
276	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
279	C₃×C₃⋊D₃	—	2	2	no	—
280	C₃×C₃⋊D₃	—	4	2	no	—
281	C₂⁴×C₃	—	2	8	no	—
282	C₂⁴×C₃	—	9	2	no	—
283	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	complemented
284	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	complemented
285	C₂³×D₃	—	3	8	no	—
286	C₂×C₃×D₄	—	2	32	no	—
287	C₂×C₃×D₄	—	2	16	no	—
288	C₂×C₃×D₄	—	2	4	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	8	no	—
291	C₂×C₃×D₄	—	2	4	no	—
292	C₂×C₃×D₄	—	9	1	no	—
293	C₂×C₃×D₄	—	9	2	no	—
294	C₂×C₃×D₄	—	9	2	no	—
295	C₂×C₃×D₄	—	9	2	no	—
296	C₂×C₃×D₄	—	9	2	no	—
297	C₂×C₃×D₄	—	9	2	no	—
298	C₂×C₃×D₄	—	9	1	no	—
299	C₂×C₃×D₄	—	18	8	no	—
300	C₂×C₃×D₄	—	18	4	no	—
301	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
302	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	complemented
303	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
304	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
305	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	complemented
306	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	9	2	no	—
309	C₂²×C₃×C₄	—	9	1	no	—
310	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
311	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
312	C₂×#67	—	3	4	no	—
313	C₂×#67	—	3	8	no	—
314	C₂×#67	—	3	8	no	—
315	C₂×#67	—	3	8	no	—
316	C₂×#67	—	3	8	no	—
317	C₂×#67	—	3	8	no	—
318	C₂×#67	—	6	32	no	—
319	C₂²×Dic₃	—	3	8	no	—
320	D₃×D₄	—	6	16	no	—
321	C₂×D₁₂	—	3	4	no	—
322	C₂×C₄×D₃	—	3	4	no	—
323	C₃×C₄⋊C₄	—	9	1	no	—
324	C₃×C₄⋊C₄	—	9	1	no	—
325	C₃×C₂²⋊C₄	—	9	1	no	—
326	C₃×C₂²⋊C₄	—	9	2	no	—
327	C₃×C₂²⋊C₄	—	9	2	no	—
328	C₃×C₂²⋊C₄	—	9	1	no	—
329	C₃×C₂²⋊C₄	—	9	2	no	—
330	C₃×C₄²	—	9	1	no	—
331	#217	—	3	4	no	—
332	#217	—	3	8	no	—
333	#217	—	3	8	no	—
334	(C₂×D₃)⋊C₄	—	3	4	no	—
335	(C₂×D₃)⋊C₄	—	3	8	no	—
336	C₄⋊Dic₃	—	3	4	no	—
337	Dic₃⋊C₄	—	3	4	no	—
338	C₄×Dic₃	—	3	4	no	—
339	C₂²×C₃²	—	2	8	no	—
340	C₂²×C₃²	—	2	8	no	—
341	C₂²×C₃²	—	2	4	no	—
342	C₂²×C₃²	—	2	4	no	—
343	C₂²×C₃²	—	2	2	no	—
344	C₂²×C₃²	—	2	1	no	—
345	C₂²×C₃²	—	2	2	no	—
346	C₂²×C₃²	—	2	1	no	—
347	C₂²×C₃²	—	2	16	no	—
348	C₂²×C₃²	—	2	8	no	—
349	C₂²×C₃²	—	2	2	no	—
350	C₂²×C₃²	—	2	2	no	—
351	C₂²×C₃²	—	2	2	no	—
352	C₂²×C₃²	—	2	4	no	—
353	C₂²×C₃²	—	2	8	no	—
354	C₂²×C₃²	—	2	16	no	—
355	C₂²×C₃²	—	2	8	no	—
356	C₂²×C₃²	—	2	8	no	—
357	C₂²×C₃²	—	2	8	no	—
358	C₂²×C₃²	—	2	8	no	—
359	C₂²×C₃²	—	4	8	no	—
360	C₂²×C₃²	—	4	8	no	—
361	C₂²×C₃²	—	4	8	no	—
362	C₂²×C₃²	—	4	8	no	—
363	C₂²×C₃²	—	4	8	no	—
364	C₂²×C₃²	—	4	32	no	—
365	C₂²×C₃²	—	4	64	no	—
366	C₂²×C₃²	D₃×D₄	1	8	yes	complemented
367	C₂²×C₃²	C₂×#67	1	16	yes	complemented
368	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	complemented
369	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
370	C₂²×C₃²	C₂³×D₃	1	4	yes	—
371	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
372	C₂×C₃⋊D₃	—	2	1	no	—
373	C₂×C₃⋊D₃	—	2	1	no	—
374	C₂×C₃⋊D₃	—	2	2	no	—
375	C₂×C₃⋊D₃	—	2	2	no	—
376	C₂×C₃⋊D₃	—	2	2	no	—
377	C₂×C₃⋊D₃	—	4	8	no	—
378	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	complemented
379	C₂×C₃×D₃	—	3	8	no	—
380	C₂×C₃×D₃	—	6	4	no	—
381	C₂×C₃×D₃	—	6	4	no	—
382	C₂×C₃×D₃	—	6	8	no	—
383	C₂×C₃×D₃	—	6	8	no	—
384	C₂×C₃×D₃	—	6	8	no	—
385	C₂×C₃×D₃	—	12	32	no	—
386	C₃²×C₄	—	2	8	no	—
387	C₃²×C₄	—	2	4	no	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	2	8	no	—
390	C₃²×C₄	C₂×#67	1	8	yes	complemented
391	C₃²×C₄	C₂×C₃×D₄	1	2	yes	complemented
392	C₃⋊Dic₃	—	2	1	no	—
393	C₃⋊Dic₃	—	2	2	no	—
394	C₃⋊Dic₃	—	2	1	no	—
395	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	complemented
396	C₃×Dic₃	—	3	8	no	—
397	C₃×Dic₃	—	6	8	no	—
398	C₃×Dic₃	—	6	4	no	—
399	C₃×Dic₃	—	6	4	no	—
400	C₂²×D₄	—	9	2	no	—
401	C₂²×D₄	—	9	1	no	—
402	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
403	#127	—	9	1	no	—
404	#121	—	9	1	no	—
405	#121	—	9	2	no	—
406	#121	—	9	1	no	—
407	#120	—	9	2	no	—
408	#120	—	9	2	no	—
409	C₄×D₄	—	9	1	no	—
410	C₄×D₄	—	9	1	no	—
411	C₃³	D₄²	1	1	yes	characteristic, complemented, Sylow
412	C₂³×C₃	—	2	32	no	—
413	C₂³×C₃	—	2	16	no	—
414	C₂³×C₃	—	2	16	no	—
415	C₂³×C₃	—	2	4	no	—
416	C₂³×C₃	—	2	4	no	—
417	C₂³×C₃	—	2	4	no	—
418	C₂³×C₃	—	2	8	no	—
419	C₂³×C₃	—	2	8	no	—
420	C₂³×C₃	—	4	16	no	—
421	C₂³×C₃	—	4	8	no	—
422	C₂³×C₃	—	4	2	no	—
423	C₂³×C₃	—	4	16	no	—
424	C₂³×C₃	—	9	1	no	—
425	C₂³×C₃	—	9	2	no	—
426	C₂³×C₃	—	18	4	no	—
427	C₂³×C₃	—	18	4	no	—
428	C₂³×C₃	—	36	2	no	—
429	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
430	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
431	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
432	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
433	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
434	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
435	C₂²×D₃	—	3	4	no	—
436	C₂²×D₃	—	3	8	no	—
437	C₂²×D₃	—	6	16	no	—
438	C₂²×D₃	—	6	16	no	—
439	C₂²×D₃	—	12	8	no	—
440	C₃×D₄	—	2	32	no	—
441	C₃×D₄	—	2	16	no	—
442	C₃×D₄	—	2	16	no	—
443	C₃×D₄	—	2	4	no	—
444	C₃×D₄	—	2	8	no	—
445	C₃×D₄	—	2	2	no	—
446	C₃×D₄	—	2	16	no	—
447	C₃×D₄	—	9	4	no	—
448	C₃×D₄	—	18	4	no	—
449	C₃×D₄	—	18	4	no	—
450	C₃×D₄	—	18	4	no	—
451	C₃×D₄	—	18	4	no	—
452	C₃×D₄	—	18	2	no	—
453	C₃×D₄	—	36	2	no	—
454	C₃×D₄	C₃×#67	1	16	yes	complemented
455	C₃×D₄	#638	1	4	yes	direct product factor
456	C₂×C₃×C₄	—	2	16	no	—
457	C₂×C₃×C₄	—	2	8	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	4	no	—
460	C₂×C₃×C₄	—	2	4	no	—
461	C₂×C₃×C₄	—	9	1	no	—
462	C₂×C₃×C₄	—	9	1	no	—
463	C₂×C₃×C₄	—	9	2	no	—
464	C₂×C₃×C₄	—	9	1	no	—
465	C₂×C₃×C₄	—	18	4	no	—
466	C₂×C₃×C₄	—	18	2	no	—
467	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
468	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
469	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
471	#67	—	3	16	no	—
472	#67	—	6	16	no	—
473	#67	—	6	16	no	—
474	#67	—	6	16	no	—
475	#67	—	6	16	no	—
476	#67	—	12	8	no	—
477	C₂×Dic₃	—	3	4	no	—
478	C₂×Dic₃	—	3	4	no	—
479	C₂×Dic₃	—	3	4	no	—
480	C₂×Dic₃	—	3	8	no	—
481	C₂×Dic₃	—	6	16	no	—
482	D₁₂	—	6	8	no	—
483	C₄×D₃	—	6	8	no	—
484	C₂×C₃²	—	2	16	no	—
485	C₂×C₃²	—	2	8	no	—
486	C₂×C₃²	—	2	4	no	—
487	C₂×C₃²	—	2	2	no	—
488	C₂×C₃²	—	2	4	no	—
489	C₂×C₃²	—	2	4	no	—
490	C₂×C₃²	—	2	4	no	—
491	C₂×C₃²	—	2	16	no	—
492	C₂×C₃²	—	4	16	no	—
493	C₂×C₃²	—	4	16	no	—
494	C₂×C₃²	—	4	8	no	—
495	C₂×C₃²	—	4	2	no	—
496	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
497	C₂×C₃²	#1004	1	4	yes	—
498	C₂×C₃²	C₂²×#67	1	4	yes	—
499	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
500	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
501	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
502	C₃⋊D₃	—	2	2	no	—
503	C₃⋊D₃	—	4	2	no	—
504	C₃×D₃	—	6	8	no	—
505	C₃×D₃	—	12	8	no	—
506	C₂⁴	—	9	2	no	—
507	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	9	1	no	—
510	C₂×D₄	—	9	2	no	—
511	C₂×D₄	—	9	2	no	—
512	C₂×D₄	—	9	2	no	—
513	C₂×D₄	—	9	2	no	—
514	C₂×D₄	—	9	2	no	—
515	C₂×D₄	—	9	1	no	—
516	C₂×D₄	—	18	8	no	—
517	C₂×D₄	—	18	4	no	—
518	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
519	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
520	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
521	C₂²×C₄	—	9	2	no	—
522	C₂²×C₄	—	9	1	no	—
523	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
524	C₄⋊C₄	—	9	1	no	—
525	C₄⋊C₄	—	9	1	no	—
526	C₂²⋊C₄	—	9	1	no	—
527	C₂²⋊C₄	—	9	2	no	—
528	C₂²⋊C₄	—	9	2	no	—
529	C₂²⋊C₄	—	9	1	no	—
530	C₂²⋊C₄	—	9	2	no	—
531	C₄²	—	9	1	no	—
532	C₂²×C₃	—	2	8	no	—
533	C₂²×C₃	—	2	8	no	—
534	C₂²×C₃	—	2	8	no	—
535	C₂²×C₃	—	2	8	no	—
536	C₂²×C₃	—	2	4	no	—
537	C₂²×C₃	—	2	4	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	2	1	no	—
540	C₂²×C₃	—	2	2	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	16	no	—
543	C₂²×C₃	—	2	8	no	—
544	C₂²×C₃	—	2	8	no	—
545	C₂²×C₃	—	2	8	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	2	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	2	8	no	—
551	C₂²×C₃	—	2	16	no	—
552	C₂²×C₃	—	4	8	no	—
553	C₂²×C₃	—	4	8	no	—
554	C₂²×C₃	—	4	8	no	—
555	C₂²×C₃	—	4	8	no	—
556	C₂²×C₃	—	4	32	no	—
557	C₂²×C₃	—	4	8	no	—
558	C₂²×C₃	—	4	64	no	—
559	C₂²×C₃	—	9	2	no	—
560	C₂²×C₃	—	18	1	no	—
561	C₂²×C₃	—	18	1	no	—
562	C₂²×C₃	—	18	2	no	—
563	C₂²×C₃	—	18	2	no	—
564	C₂²×C₃	—	18	2	no	—
565	C₂²×C₃	—	36	8	no	—
566	C₂²×C₃	C₃×D₃×D₄	1	8	yes	complemented
567	C₂²×C₃	C₂×C₃×#67	1	16	yes	complemented
568	C₂²×C₃	D₄×C₃⋊D₃	1	2	yes	complemented
569	C₂²×C₃	C₂×#638	1	4	yes	complemented
570	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
571	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
572	C₂×D₃	—	3	8	no	—
573	C₂×D₃	—	6	4	no	—
574	C₂×D₃	—	6	4	no	—
575	C₂×D₃	—	6	8	no	—
576	C₂×D₃	—	6	8	no	—
577	C₂×D₃	—	6	8	no	—
578	C₂×D₃	—	12	32	no	—
579	C₃×C₄	—	2	8	no	—
580	C₃×C₄	—	2	4	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	8	no	—
583	C₃×C₄	—	9	2	no	—
584	C₃×C₄	—	18	2	no	—
585	C₃×C₄	—	18	1	no	—
586	C₃×C₄	—	18	1	no	—
587	C₃×C₄	C₂×C₃×#67	1	8	yes	complemented
588	C₃×C₄	C₂×#638	1	2	yes	complemented
589	Dic₃	—	3	8	no	—
590	Dic₃	—	6	8	no	—
591	Dic₃	—	6	4	no	—
592	Dic₃	—	6	4	no	—
593	C₃²	—	2	4	no	—
594	C₃²	D₄×#67	1	4	yes	complemented
595	C₃²	C₃×D₄²	1	1	yes	characteristic, complemented
596	C₂³	—	2	4	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	9	1	no	—
600	C₂³	—	9	2	no	—
601	C₂³	—	18	4	no	—
602	C₂³	—	18	4	no	—
603	C₂³	—	36	2	no	—
604	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
605	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
606	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	9	4	no	—
610	D₄	—	18	4	no	—
611	D₄	—	18	4	no	—
612	D₄	—	18	4	no	—
613	D₄	—	18	4	no	—
614	D₄	—	18	2	no	—
615	D₄	—	36	2	no	—
616	D₄	C₃×#638	1	4	yes	direct product factor
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	9	1	no	—
619	C₂×C₄	—	9	1	no	—
620	C₂×C₄	—	9	2	no	—
621	C₂×C₄	—	9	1	no	—
622	C₂×C₄	—	18	4	no	—
623	C₂×C₄	—	18	2	no	—
624	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
626	C₂×C₃	—	2	16	no	—
627	C₂×C₃	—	2	16	no	—
628	C₂×C₃	—	2	8	no	—
629	C₂×C₃	—	2	2	no	—
630	C₂×C₃	—	2	4	no	—
631	C₂×C₃	—	2	4	no	—
632	C₂×C₃	—	2	4	no	—
633	C₂×C₃	—	2	4	no	—
634	C₂×C₃	—	4	16	no	—
635	C₂×C₃	—	4	16	no	—
636	C₂×C₃	—	4	8	no	—
637	C₂×C₃	—	4	2	no	—
638	C₂×C₃	—	18	2	no	—
639	C₂×C₃	—	36	2	no	—
640	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
641	C₂×C₃	C₃×#1004	1	4	yes	—
642	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
643	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
644	C₂×C₃	#64361	1	1	yes	characteristic
645	C₂×C₃	C₂²×#638	1	1	yes	characteristic
646	D₃	—	6	8	no	—
647	D₃	—	12	8	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	8	no	—
656	C₂²	—	9	2	no	—
657	C₂²	—	18	1	no	—
658	C₂²	—	18	1	no	—
659	C₂²	—	18	2	no	—
660	C₂²	—	18	2	no	—
661	C₂²	—	18	2	no	—
662	C₂²	—	36	8	no	—
663	C₂²	C₃×D₄×C₃⋊D₃	1	2	yes	complemented
664	C₂²	C₂×C₃×#638	1	4	yes	complemented
665	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	9	2	no	—
668	C₄	—	18	2	no	—
669	C₄	—	18	1	no	—
670	C₄	—	18	1	no	—
671	C₄	C₂×C₃×#638	1	2	yes	complemented
672	C₃	—	2	4	no	—
673	C₃	C₃×D₄×#67	1	4	yes	complemented
674	C₃	D₄×#638	1	1	yes	characteristic, direct product factor
675	C₂	—	2	2	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	18	2	no	—
679	C₂	—	36	2	no	—
680	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
681	C₂	C₃×#64361	1	1	yes	characteristic
682	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×D₄²
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
4. C₃×#64162	C₂	semidirect
5. C₃×#64149	C₂	semidirect
6. C₃×#64148	C₂	semidirect
7. C₃×#64147	C₂	semidirect
8. C₃×#64146	C₂	semidirect
9. C₃×D₄×C₃⋊Dic₃	C₂	semidirect
10. C₃×#64139	C₂	semidirect
11. C₃×C₄×#638	C₂	semidirect
12. D₄×#638	C₃	direct (N × H)
14. C₂⁴×C₃³	C₂²	semidirect
15. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
18. C₂×C₃³×D₄	C₂²	semidirect
19. C₂×C₃³×D₄	C₂²	semidirect
20. C₂²×C₃³×C₄	C₂²	semidirect
23. C₂×C₃×#638	C₂²	semidirect
24. C₂×C₃×#638	C₂²	semidirect
25. C₂×C₃×#638	C₂²	semidirect
26. C₂×C₃×#638	C₂²	semidirect
27. C₂×C₃×#638	C₂²	semidirect
28. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
30. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
31. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
32. C₃×#3757	C₂²	semidirect
33. C₃×#3757	C₂²	semidirect
34. C₃×#3757	C₂²	semidirect
35. C₃×#3752	C₂²	semidirect
36. C₃×#3752	C₂²	semidirect
37. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
38. C₃×#3750	C₂²	semidirect
39. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
41. C₂²×C₃²×D₄	D₃	semidirect
42. C₂²×C₃²×D₄	C₂×C₃	semidirect
43. C₂²×#638	C₂×C₃	semidirect
44. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
47. #64162	C₂×C₃	semidirect
48. #64149	C₂×C₃	semidirect
49. #64148	C₂×C₃	semidirect
50. #64147	C₂×C₃	semidirect
51. #64146	C₂×C₃	semidirect
52. D₄×C₃⋊Dic₃	C₂×C₃	semidirect
53. #64139	C₂×C₃	semidirect
54. C₄×#638	C₂×C₃	semidirect
76. C₃³×D₄	D₄	semidirect
85. C₃×#638	D₄	direct (N × H)
96. C₂⁴×C₃²	C₂×D₃	semidirect
97. C₂⁴×C₃²	C₂²×C₃	semidirect
98. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
107. C₂×C₃²×D₄	C₂×D₃	semidirect
108. C₂×C₃²×D₄	C₂×D₃	semidirect
110. C₂×C₃²×D₄	C₂²×C₃	semidirect
111. C₂×C₃²×D₄	C₂²×C₃	semidirect
113. C₂²×C₃²×C₄	C₂×D₃	semidirect
114. C₂²×C₃²×C₄	C₂²×C₃	semidirect
117. C₂×#638	C₂²×C₃	semidirect
118. C₂×#638	C₂²×C₃	semidirect
119. C₂×#638	C₂²×C₃	semidirect
120. C₂×#638	C₂²×C₃	semidirect
121. C₂×#638	C₂²×C₃	semidirect
122. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
124. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
125. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
137. #3757	C₂²×C₃	semidirect
138. #3757	C₂²×C₃	semidirect
139. #3757	C₂²×C₃	semidirect
140. #3752	C₂²×C₃	semidirect
141. #3752	C₂²×C₃	semidirect
142. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
143. #3750	C₂²×C₃	semidirect
144. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
161. C₂²×C₃³	C₂×D₄	semidirect
162. C₂²×C₃³	C₂×D₄	semidirect
170. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
172. C₃³×C₄	C₂×D₄	semidirect
176. C₃×C₃⋊Dic₃	C₂×D₄	semidirect
180. C₂²×C₃×D₄	C₃×D₃	semidirect
181. C₂²×C₃×D₄	C₃⋊D₃	semidirect
235. C₃²×D₄	#67	semidirect
236. C₃²×D₄	C₃×D₄	semidirect
251. #638	C₃×D₄	direct (N × H)
283. C₂⁴×C₃	C₂×C₃×D₃	semidirect
284. C₂⁴×C₃	C₂×C₃⋊D₃	semidirect
302. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
303. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
305. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
306. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
310. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
311. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
366. C₂²×C₃²	D₃×D₄	semidirect
367. C₂²×C₃²	C₂×#67	semidirect
368. C₂²×C₃²	C₂×C₃×D₄	semidirect
369. C₂²×C₃²	C₂×C₃×D₄	semidirect
378. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
390. C₃²×C₄	C₂×#67	semidirect
391. C₃²×C₄	C₂×C₃×D₄	semidirect
395. C₃⋊Dic₃	C₂×C₃×D₄	semidirect
402. C₂²×D₄	C₃×C₃⋊D₃	semidirect
411. C₃³	D₄²	semidirect
454. C₃×D₄	C₃×#67	semidirect
455. C₃×D₄	#638	direct (N × H)
507. C₂⁴	C₂×C₃×C₃⋊D₃	semidirect
519. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
520. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
523. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
566. C₂²×C₃	C₃×D₃×D₄	semidirect
567. C₂²×C₃	C₂×C₃×#67	semidirect
568. C₂²×C₃	D₄×C₃⋊D₃	semidirect
569. C₂²×C₃	C₂×#638	semidirect
587. C₃×C₄	C₂×C₃×#67	semidirect
588. C₃×C₄	C₂×#638	semidirect
594. C₃²	D₄×#67	semidirect
595. C₃²	C₃×D₄²	semidirect
616. D₄	C₃×#638	direct (N × H)
663. C₂²	C₃×D₄×C₃⋊D₃	semidirect
664. C₂²	C₂×C₃×#638	semidirect
671. C₄	C₂×C₃×#638	semidirect
673. C₃	C₃×D₄×#67	semidirect
674. C₃	D₄×#638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×D₄	2
C₂²×C₃×#638	2
C₂×C₃×D₄×C₃⋊D₃	2
C₃×#64162	2
C₃×#64149	2
C₃×#64148	2
C₃×#64147	2
C₃×#64146	2
C₃×D₄×C₃⋊Dic₃	2
C₃×#64139	2
C₃×C₄×#638	2
D₄×#638	3
C₃×D₄×#67	3

Subgroups — C3×D4×#638 #13179554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#638 #13179554