Subgroups — C₃×D₄×C₄⋊(C₃⋊D₃) #13179303

Order 1728.

2944 conjugacy classes of subgroups.

The subgroup lattice has 472 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	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64139	C₂	1	2	yes	maximal, complemented
5	C₃×#64104	C₂	1	2	yes	maximal, complemented
6	C₃×#64091	C₂	1	4	yes	maximal, complemented
7	C₃×#64083	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×D₄×D₁₂	—	3	4	no	maximal
11	C₂³×C₃×C₃⋊D₃	C₂²	1	4	yes	complemented
12	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
14	C₂×C₃×#638	C₂²	1	4	yes	complemented
15	C₃×D₄×C₃⋊D₃	—	2	8	no	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
19	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
20	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
21	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
23	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃³×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3752	C₂²	1	2	yes	complemented
27	C₃×#3752	C₂²	1	4	yes	complemented
28	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
30	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	2	yes	complemented
31	C₂×C₃×D₃×D₄	—	3	8	no	—
32	C₂²×C₃×D₁₂	—	3	8	no	—
33	C₃²×C₄×D₄	—	2	4	no	—
34	C₃²×C₄×D₄	D₃	1	4	yes	complemented
35	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
36	#64139	C₂×C₃	1	2	yes	complemented
37	#64104	C₂×C₃	1	2	yes	complemented
38	#64091	C₂×C₃	1	4	yes	complemented
39	#64083	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#930	—	3	8	no	—
42	C₃×#895	—	3	8	no	—
43	C₃×#882	—	3	16	no	—
44	C₃×#874	—	3	4	no	—
45	C₃×C₄×D₁₂	—	3	4	no	—
46	C₂³×C₃³	C₂³	1	2	yes	—
47	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
48	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
49	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
50	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
51	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
52	C₃³×D₄	D₄	1	4	yes	complemented
53	C₂×C₃³×C₄	—	2	4	no	—
54	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
55	C₂×C₃³×C₄	C₂³	1	2	yes	—
56	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	C₃×#638	—	2	8	no	—
59	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
60	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
61	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
62	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
63	C₃×C₄⋊(C₃⋊D₃)	—	4	2	no	—
64	C₃×C₄⋊(C₃⋊D₃)	D₄	1	4	yes	direct product factor
65	C₃×C₄×C₃⋊D₃	—	2	4	no	—
66	C₃×D₄²	—	9	1	no	—
67	D₄×D₁₂	—	3	4	no	—
68	C₂³×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
69	C₂³×C₃×D₃	—	3	16	no	—
70	C₂×C₃²×D₄	—	2	4	no	—
71	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
72	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃²×C₄	—	2	8	no	—
74	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	complemented
75	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	complemented
76	C₂×#638	C₂²×C₃	1	4	yes	complemented
77	D₄×C₃⋊D₃	—	2	8	no	—
78	C₂×C₄⋊(C₃⋊D₃)	—	2	8	no	—
79	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	complemented
81	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	complemented
82	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	complemented
83	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	complemented
84	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
85	C₂×C₃×#67	—	3	16	no	—
86	C₃×D₃×D₄	—	6	32	no	—
87	C₂×C₃×D₁₂	—	3	4	no	—
88	C₂×C₃×D₁₂	—	3	16	no	—
89	C₂×C₃×D₁₂	—	3	8	no	—
90	C₂×C₃×D₁₂	—	3	8	no	—
91	C₂×C₃×D₁₂	—	3	8	no	—
92	C₂×C₃×D₁₂	—	6	32	no	—
93	C₂×C₃×C₄×D₃	—	3	8	no	—
94	C₃²×C₄⋊C₄	—	2	4	no	—
95	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
96	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₃²×C₂²⋊C₄	—	2	8	no	—
98	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	complemented
99	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₃²×C₄²	—	2	4	no	—
101	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
102	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
103	#3752	C₂²×C₃	1	2	yes	complemented
104	#3752	C₂²×C₃	1	4	yes	complemented
105	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
107	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
108	C₃×C₄⋊Dic₃	—	3	4	no	—
109	C₂²×C₃³	—	2	2	no	—
110	C₂²×C₃³	—	2	2	no	—
111	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
112	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
113	C₂×C₃×C₃⋊D₃	—	2	2	no	—
114	C₂×C₃×C₃⋊D₃	—	2	2	no	—
115	C₂×C₃×C₃⋊D₃	—	2	4	no	—
116	C₂×C₃×C₃⋊D₃	—	2	4	no	—
117	C₂×C₃×C₃⋊D₃	—	2	4	no	—
118	C₂×C₃×C₃⋊D₃	—	4	16	no	—
119	C₂×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	complemented
120	C₃³×C₄	—	2	2	no	—
121	C₃³×C₄	—	2	1	no	—
122	C₃³×C₄	C₂×D₄	1	2	yes	complemented
123	C₃³×C₄	C₂×D₄	1	2	yes	complemented
124	C₃×C₃⋊Dic₃	—	2	2	no	—
125	C₂²×C₃×D₄	—	9	2	no	—
126	C₂²×C₃×D₄	—	9	2	no	—
127	C₂×D₃×D₄	—	3	8	no	—
128	C₂²×D₁₂	—	3	8	no	—
129	C₃×#127	—	9	1	no	—
130	C₃×#121	—	9	2	no	—
131	C₃×#121	—	9	2	no	—
132	C₃×#120	—	9	4	no	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₃×C₄×D₄	—	9	1	no	—
135	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
136	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
137	#930	—	3	8	no	—
138	#895	—	3	8	no	—
139	#882	—	3	16	no	—
140	#874	—	3	4	no	—
141	C₄×D₁₂	—	3	4	no	—
142	C₂³×C₃²	—	2	8	no	—
143	C₂³×C₃²	C₂²×D₃	1	8	yes	—
144	C₂³×C₃²	C₂³×C₃	1	2	yes	—
145	C₂²×C₃⋊D₃	—	2	8	no	—
146	C₂²×C₃⋊D₃	—	2	8	no	—
147	C₂²×C₃⋊D₃	—	4	4	no	—
148	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
149	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
150	C₂²×C₃×D₃	—	3	8	no	—
151	C₂²×C₃×D₃	—	3	16	no	—
152	C₂²×C₃×D₃	—	6	32	no	—
153	C₂²×C₃×D₃	—	6	32	no	—
154	C₂²×C₃×D₃	—	12	16	no	—
155	C₃²×D₄	—	2	16	no	—
156	C₃²×D₄	D₁₂	1	16	yes	complemented
157	C₃²×D₄	C₃×D₄	1	4	yes	complemented
158	C₂×C₃²×C₄	—	2	4	no	—
159	C₂×C₃²×C₄	—	2	4	no	—
160	C₂×C₃²×C₄	—	2	4	no	—
161	C₂×C₃²×C₄	—	2	4	no	—
162	C₂×C₃²×C₄	—	2	8	no	—
163	C₂×C₃²×C₄	—	2	16	no	—
164	C₂×C₃²×C₄	—	4	16	no	—
165	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
166	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
167	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
169	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	#638	—	2	8	no	—
174	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
175	C₄⋊(C₃⋊D₃)	—	2	8	no	—
176	C₄⋊(C₃⋊D₃)	—	2	4	no	—
177	C₄⋊(C₃⋊D₃)	—	2	4	no	—
178	C₄⋊(C₃⋊D₃)	—	4	2	no	—
179	C₄⋊(C₃⋊D₃)	C₃×D₄	1	4	yes	direct product factor
180	C₄×C₃⋊D₃	—	2	4	no	—
181	C₃×#67	—	6	32	no	—
182	C₂×C₃×Dic₃	—	3	8	no	—
183	C₃×D₁₂	—	3	16	no	—
184	C₃×D₁₂	—	6	32	no	—
185	C₃×D₁₂	—	6	16	no	—
186	C₃×D₁₂	—	6	16	no	—
187	C₃×D₁₂	—	12	8	no	—
188	C₃×C₄×D₃	—	6	16	no	—
189	D₄²	—	9	1	no	Sylow
190	C₂×C₃³	—	2	4	no	—
191	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
194	C₃×C₃⋊D₃	—	2	4	no	—
195	C₃×C₃⋊D₃	—	4	4	no	—
196	C₂⁴×C₃	—	9	4	no	—
197	C₂³×D₃	—	3	16	no	—
198	C₂×C₃×D₄	—	2	4	no	—
199	C₂×C₃×D₄	—	9	4	no	—
200	C₂×C₃×D₄	—	9	1	no	—
201	C₂×C₃×D₄	—	9	4	no	—
202	C₂×C₃×D₄	—	9	2	no	—
203	C₂×C₃×D₄	—	9	2	no	—
204	C₂×C₃×D₄	—	9	2	no	—
205	C₂×C₃×D₄	—	18	8	no	—
206	C₂×C₃×D₄	—	18	8	no	—
207	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
208	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
209	C₂²×C₃×C₄	—	2	8	no	—
210	C₂²×C₃×C₄	—	9	2	no	—
211	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	complemented
212	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	complemented
213	C₂×#67	—	3	16	no	—
214	D₃×D₄	—	6	32	no	—
215	C₂×D₁₂	—	3	4	no	—
216	C₂×D₁₂	—	3	8	no	—
217	C₂×D₁₂	—	3	8	no	—
218	C₂×D₁₂	—	3	16	no	—
219	C₂×D₁₂	—	3	8	no	—
220	C₂×D₁₂	—	6	32	no	—
221	C₂×C₄×D₃	—	3	8	no	—
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₄⋊C₄	—	9	1	no	—
224	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
225	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
226	C₃×C₂²⋊C₄	—	2	8	no	—
227	C₃×C₂²⋊C₄	—	9	2	no	—
228	C₃×C₂²⋊C₄	—	9	4	no	—
229	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
230	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	complemented
231	C₃×C₄²	—	2	4	no	—
232	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
233	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
234	(C₂×D₃)⋊C₄	—	3	8	no	—
235	(C₂×D₃)⋊C₄	—	3	16	no	—
236	C₄⋊Dic₃	—	3	4	no	—
237	C₂²×C₃²	—	2	2	no	—
238	C₂²×C₃²	—	2	2	no	—
239	C₂²×C₃²	—	2	4	no	—
240	C₂²×C₃²	—	2	16	no	—
241	C₂²×C₃²	—	2	8	no	—
242	C₂²×C₃²	—	2	8	no	—
243	C₂²×C₃²	—	4	8	no	—
244	C₂²×C₃²	—	4	8	no	—
245	C₂²×C₃²	C₂×D₁₂	1	16	yes	complemented
246	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
247	C₂²×C₃²	C₂³×D₃	1	4	yes	—
248	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
249	C₂×C₃⋊D₃	—	2	2	no	—
250	C₂×C₃⋊D₃	—	2	2	no	—
251	C₂×C₃⋊D₃	—	2	4	no	—
252	C₂×C₃⋊D₃	—	2	4	no	—
253	C₂×C₃⋊D₃	—	2	4	no	—
254	C₂×C₃⋊D₃	—	4	16	no	—
255	C₂×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	complemented
256	C₂×C₃×D₃	—	3	16	no	—
257	C₂×C₃×D₃	—	6	8	no	—
258	C₂×C₃×D₃	—	6	8	no	—
259	C₂×C₃×D₃	—	6	16	no	—
260	C₂×C₃×D₃	—	6	16	no	—
261	C₂×C₃×D₃	—	6	16	no	—
262	C₂×C₃×D₃	—	12	64	no	—
263	C₃²×C₄	—	2	2	no	—
264	C₃²×C₄	—	2	1	no	—
265	C₃²×C₄	—	2	8	no	—
266	C₃²×C₄	—	2	8	no	—
267	C₃²×C₄	—	2	8	no	—
268	C₃²×C₄	—	2	4	no	—
269	C₃²×C₄	—	4	4	no	—
270	C₃²×C₄	—	4	8	no	—
271	C₃²×C₄	C₂×D₁₂	1	8	yes	complemented
272	C₃²×C₄	D₃×D₄	1	8	yes	complemented
273	C₃²×C₄	C₂×C₃×D₄	1	2	yes	complemented
274	C₃²×C₄	C₂×C₃×D₄	1	2	yes	complemented
275	C₃⋊Dic₃	—	2	2	no	—
276	C₃×Dic₃	—	6	8	no	—
277	C₂²×D₄	—	9	2	no	—
278	C₂²×D₄	—	9	2	no	—
279	#127	—	9	1	no	—
280	#121	—	9	2	no	—
281	#121	—	9	2	no	—
282	#120	—	9	4	no	—
283	C₄×D₄	—	9	1	no	—
284	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
285	C₃³	D₄²	1	1	yes	characteristic, complemented, Sylow
286	C₂³×C₃	—	2	8	no	—
287	C₂³×C₃	—	9	2	no	—
288	C₂³×C₃	—	9	4	no	—
289	C₂³×C₃	—	18	8	no	—
290	C₂³×C₃	—	18	8	no	—
291	C₂³×C₃	—	36	4	no	—
292	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
293	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
294	C₂²×D₃	—	3	8	no	—
295	C₂²×D₃	—	3	16	no	—
296	C₂²×D₃	—	6	32	no	—
297	C₂²×D₃	—	6	32	no	—
298	C₂²×D₃	—	12	16	no	—
299	C₃×D₄	—	2	16	no	—
300	C₃×D₄	—	9	4	no	—
301	C₃×D₄	—	18	8	no	—
302	C₃×D₄	—	18	8	no	—
303	C₃×D₄	—	18	4	no	—
304	C₃×D₄	—	18	4	no	—
305	C₃×D₄	—	36	2	no	—
306	C₃×D₄	C₃×D₁₂	1	16	yes	complemented
307	C₃×D₄	C₄⋊(C₃⋊D₃)	1	4	yes	direct product factor
308	C₂×C₃×C₄	—	2	16	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	4	16	no	—
315	C₂×C₃×C₄	—	9	2	no	—
316	C₂×C₃×C₄	—	18	4	no	—
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
321	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
323	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
325	#67	—	6	32	no	—
326	C₂×Dic₃	—	3	8	no	—
327	D₁₂	—	3	16	no	—
328	D₁₂	—	6	32	no	—
329	D₁₂	—	6	16	no	—
330	D₁₂	—	6	16	no	—
331	D₁₂	—	12	8	no	—
332	C₄×D₃	—	6	16	no	—
333	C₂×C₃²	—	2	4	no	—
334	C₂×C₃²	—	2	4	no	—
335	C₂×C₃²	—	2	4	no	—
336	C₂×C₃²	—	2	4	no	—
337	C₂×C₃²	—	2	16	no	—
338	C₂×C₃²	—	4	16	no	—
339	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
340	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
341	C₂×C₃²	#1009	1	4	yes	—
342	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₃⋊D₃	—	2	4	no	—
346	C₃⋊D₃	—	4	4	no	—
347	C₃×D₃	—	6	16	no	—
348	C₃×D₃	—	12	16	no	—
349	C₂⁴	—	9	4	no	—
350	C₂×D₄	—	9	4	no	—
351	C₂×D₄	—	9	1	no	—
352	C₂×D₄	—	9	4	no	—
353	C₂×D₄	—	9	2	no	—
354	C₂×D₄	—	9	2	no	—
355	C₂×D₄	—	9	2	no	—
356	C₂×D₄	—	18	8	no	—
357	C₂×D₄	—	18	8	no	—
358	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
359	C₂²×C₄	—	9	2	no	—
360	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
361	C₄⋊C₄	—	9	1	no	—
362	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
363	C₂²⋊C₄	—	9	2	no	—
364	C₂²⋊C₄	—	9	4	no	—
365	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
366	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
367	C₂²×C₃	—	2	8	no	—
368	C₂²×C₃	—	2	8	no	—
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	2	4	no	—
372	C₂²×C₃	—	2	16	no	—
373	C₂²×C₃	—	4	8	no	—
374	C₂²×C₃	—	4	8	no	—
375	C₂²×C₃	—	9	4	no	—
376	C₂²×C₃	—	18	2	no	—
377	C₂²×C₃	—	18	2	no	—
378	C₂²×C₃	—	18	4	no	—
379	C₂²×C₃	—	18	4	no	—
380	C₂²×C₃	—	18	4	no	—
381	C₂²×C₃	—	36	16	no	—
382	C₂²×C₃	C₂×C₃×D₁₂	1	16	yes	complemented
383	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
384	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
385	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
386	C₂×D₃	—	3	16	no	—
387	C₂×D₃	—	6	8	no	—
388	C₂×D₃	—	6	8	no	—
389	C₂×D₃	—	6	16	no	—
390	C₂×D₃	—	6	16	no	—
391	C₂×D₃	—	6	16	no	—
392	C₂×D₃	—	12	64	no	—
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	—	2	4	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	8	no	—
398	C₃×C₄	—	2	8	no	—
399	C₃×C₄	—	4	8	no	—
400	C₃×C₄	—	4	4	no	—
401	C₃×C₄	—	18	2	no	—
402	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	complemented
403	C₃×C₄	C₃×D₃×D₄	1	8	yes	complemented
404	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	complemented
405	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	complemented
406	Dic₃	—	6	8	no	—
407	C₃²	—	2	4	no	—
408	C₃²	D₄×D₁₂	1	4	yes	complemented
409	C₃²	C₃×D₄²	1	1	yes	characteristic, complemented
410	C₂³	—	9	2	no	—
411	C₂³	—	9	4	no	—
412	C₂³	—	18	8	no	—
413	C₂³	—	18	8	no	—
414	C₂³	—	36	4	no	—
415	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
416	D₄	—	9	4	no	—
417	D₄	—	18	8	no	—
418	D₄	—	18	8	no	—
419	D₄	—	18	4	no	—
420	D₄	—	18	4	no	—
421	D₄	—	36	2	no	—
422	D₄	C₃×C₄⋊(C₃⋊D₃)	1	4	yes	direct product factor
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	9	2	no	—
425	C₂×C₄	—	18	4	no	—
426	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
428	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
430	C₂×C₃	—	2	16	no	—
431	C₂×C₃	—	2	4	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	2	4	no	—
434	C₂×C₃	—	2	4	no	—
435	C₂×C₃	—	4	16	no	—
436	C₂×C₃	—	18	4	no	—
437	C₂×C₃	—	36	4	no	—
438	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
439	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
440	C₂×C₃	C₃×#1009	1	4	yes	—
441	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
442	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
443	C₂×C₃	#64366	1	1	yes	characteristic
444	D₃	—	6	16	no	—
445	D₃	—	12	16	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	9	4	no	—
449	C₂²	—	18	2	no	—
450	C₂²	—	18	2	no	—
451	C₂²	—	18	4	no	—
452	C₂²	—	18	4	no	—
453	C₂²	—	18	4	no	—
454	C₂²	—	36	16	no	—
455	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
456	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	18	2	no	—
460	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	complemented
461	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	complemented
462	C₃	—	2	4	no	—
463	C₃	C₃×D₄×D₁₂	1	4	yes	complemented
464	C₃	D₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
465	C₂	—	2	4	no	—
466	C₂	—	18	4	no	—
467	C₂	—	36	4	no	—
468	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
469	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
470	C₂	C₃×#64366	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	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×D₄²
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

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. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. C₃×#64139	C₂	semidirect
5. C₃×#64104	C₂	semidirect
6. C₃×#64091	C₂	semidirect
7. C₃×#64083	C₂	semidirect
8. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
9. D₄×C₄⋊(C₃⋊D₃)	C₃	direct (N × H)
11. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
13. C₂²×C₃³×C₄	C₂²	semidirect
14. C₂×C₃×#638	C₂²	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
21. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
22. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
23. C₃³×C₄⋊C₄	C₂²	semidirect
24. C₃³×C₂²⋊C₄	C₂²	semidirect
25. C₃³×C₄²	C₂²	semidirect
26. C₃×#3752	C₂²	semidirect
27. C₃×#3752	C₂²	semidirect
28. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
29. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
30. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
34. C₃²×C₄×D₄	D₃	semidirect
35. C₃²×C₄×D₄	C₂×C₃	semidirect
36. #64139	C₂×C₃	semidirect
37. #64104	C₂×C₃	semidirect
38. #64091	C₂×C₃	semidirect
39. #64083	C₂×C₃	semidirect
40. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
52. C₃³×D₄	D₄	semidirect
64. C₃×C₄⋊(C₃⋊D₃)	D₄	direct (N × H)
68. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
74. C₂²×C₃²×C₄	C₂×D₃	semidirect
75. C₂²×C₃²×C₄	C₂²×C₃	semidirect
76. C₂×#638	C₂²×C₃	semidirect
80. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
81. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
82. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
83. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
84. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
95. C₃²×C₄⋊C₄	C₂×D₃	semidirect
96. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
98. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
99. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
101. C₃²×C₄²	C₂×D₃	semidirect
102. C₃²×C₄²	C₂²×C₃	semidirect
103. #3752	C₂²×C₃	semidirect
104. #3752	C₂²×C₃	semidirect
105. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
111. C₂²×C₃³	C₂×D₄	semidirect
119. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
122. C₃³×C₄	C₂×D₄	semidirect
123. C₃³×C₄	C₂×D₄	semidirect
135. C₃×C₄×D₄	C₃×D₃	semidirect
136. C₃×C₄×D₄	C₃⋊D₃	semidirect
156. C₃²×D₄	D₁₂	semidirect
157. C₃²×D₄	C₃×D₄	semidirect
179. C₄⋊(C₃⋊D₃)	C₃×D₄	direct (N × H)
211. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
212. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
224. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
225. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
229. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
230. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
232. C₃×C₄²	C₂×C₃×D₃	semidirect
233. C₃×C₄²	C₂×C₃⋊D₃	semidirect
245. C₂²×C₃²	C₂×D₁₂	semidirect
246. C₂²×C₃²	C₂×C₃×D₄	semidirect
255. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
271. C₃²×C₄	C₂×D₁₂	semidirect
272. C₃²×C₄	D₃×D₄	semidirect
273. C₃²×C₄	C₂×C₃×D₄	semidirect
274. C₃²×C₄	C₂×C₃×D₄	semidirect
284. C₄×D₄	C₃×C₃⋊D₃	semidirect
285. C₃³	D₄²	semidirect
306. C₃×D₄	C₃×D₁₂	semidirect
307. C₃×D₄	C₄⋊(C₃⋊D₃)	direct (N × H)
360. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
362. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
365. C₂²⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
366. C₄²	C₂×C₃×C₃⋊D₃	semidirect
382. C₂²×C₃	C₂×C₃×D₁₂	semidirect
383. C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	semidirect
402. C₃×C₄	C₂×C₃×D₁₂	semidirect
403. C₃×C₄	C₃×D₃×D₄	semidirect
404. C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	semidirect
405. C₃×C₄	D₄×C₃⋊D₃	semidirect
408. C₃²	D₄×D₁₂	semidirect
409. C₃²	C₃×D₄²	semidirect
422. D₄	C₃×C₄⋊(C₃⋊D₃)	direct (N × H)
455. C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	semidirect
460. C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	semidirect
461. C₄	C₃×D₄×C₃⋊D₃	semidirect
463. C₃	C₃×D₄×D₁₂	semidirect
464. C₃	D₄×C₄⋊(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
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₃³×C₄×D₄	2
C₃×#64139	2
C₃×#64104	2
C₃×#64091	2
C₃×#64083	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
D₄×C₄⋊(C₃⋊D₃)	3
C₃×D₄×D₁₂	3

Subgroups — C3×D4×C4⋊(C3⋊D3) #13179303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×C₄⋊(C₃⋊D₃) #13179303