Subgroups — C₃×D₃×#576 #11918781

Order 1152.

3158 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₃²×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5835	C₂	1	2	yes	maximal, complemented
4	C₃×#5774	C₂	1	6	yes	maximal, complemented
5	C₃×D₃×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
6	C₃×#5769	C₂	1	3	yes	maximal, complemented
7	C₃×D₃×#135	C₂	1	3	yes	maximal, complemented
8	C₃×#5757	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×D₃×D₈	C₂	1	3	yes	maximal, complemented
10	C₃×#5752	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#576	—	3	1	no	maximal
13	D₃×#576	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×H(5,𝔽₂)	C₂²	1	2	yes	complemented
15	C₃×#1009	—	2	2	no	—
16	C₃×#1009	C₂²	1	6	yes	complemented
17	C₃×#1009	C₂²	1	2	yes	complemented
18	C₃×D₃×#41	—	2	2	no	—
19	C₃×D₃×#41	C₂²	1	1	yes	characteristic
20	C₃×D₃×#41	C₂²	1	6	yes	complemented
21	C₃×#1004	—	2	6	no	—
22	C₃×#1004	C₂²	1	6	yes	complemented
23	C₂×C₃×D₃×D₄	—	2	6	no	—
24	C₂×C₃×D₃×D₄	C₂²	1	6	yes	complemented
25	C₃²×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₃²×#135	C₂²	1	3	yes	complemented
27	C₂×C₃²×D₈	C₂²	1	3	yes	complemented
28	C₃²×#131	C₂²	1	1	yes	characteristic, complemented
29	C₃×#950	C₂²	1	6	yes	complemented
30	C₃×#949	C₂²	1	6	yes	complemented
31	C₃×#948	C₂²	1	1	yes	characteristic, complemented
32	C₃×#932	C₂²	1	6	yes	complemented
33	C₂×C₃×#213	C₂²	1	6	yes	complemented
34	C₃×#919	C₂²	1	3	yes	complemented
35	C₃×D₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₃×#916	C₂²	1	6	yes	complemented
37	C₃×#914	C₂²	1	12	yes	complemented
38	C₃×D₃×SD₁₆	C₂²	1	6	yes	complemented
39	C₃×#912	C₂²	1	3	yes	complemented
40	C₃×#911	C₂²	1	12	yes	complemented
41	C₃×D₃×D₈	C₂²	1	3	yes	complemented
42	C₃×D₃×D₈	C₂²	1	6	yes	complemented
43	C₃×D₃×D₈	C₂²	1	6	yes	complemented
44	C₃×D₃×D₈	C₂²	1	6	yes	complemented
45	C₃×#908	C₂²	1	6	yes	complemented
46	C₃×#907	C₂²	1	3	yes	complemented
47	C₃×D₃×M₁₆	C₂²	1	3	yes	complemented
48	C₃×#904	C₂²	1	3	yes	complemented
49	C₂×C₃×D₂₄	C₂²	1	3	yes	complemented
50	C₃×#901	C₂²	1	3	yes	complemented
51	C₂×C₃×D₃×C₈	C₂²	1	3	yes	complemented
52	C₂×C₃×H(5,𝔽₂)	—	3	2	no	—
53	D₃×H(5,𝔽₂)	C₂×C₃	1	2	yes	complemented
54	C₃×#576	—	2	1	no	—
55	C₃×#576	—	3	2	no	—
56	C₃×#576	—	3	6	no	—
57	C₃×#576	—	3	3	no	—
58	C₃×#576	—	3	3	no	—
59	C₃×#576	—	3	1	no	—
60	C₃×#576	D₃	1	1	yes	characteristic, direct product factor
61	C₃×#576	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×C₃×AGL(1,ℤ/8)	—	3	6	no	—
63	C₂×C₃×#135	—	3	3	no	—
64	C₂²×C₃×D₈	—	3	3	no	—
65	C₂×C₃×#131	—	3	1	no	—
66	#5835	C₂×C₃	1	2	yes	complemented
67	#5774	C₂×C₃	1	6	yes	complemented
68	D₃×AGL(1,ℤ/8)	C₂×C₃	1	6	yes	complemented
69	#5769	C₂×C₃	1	3	yes	complemented
70	D₃×#135	C₂×C₃	1	3	yes	complemented
71	#5757	C₂×C₃	1	3	yes	complemented
72	C₂×D₃×D₈	C₂×C₃	1	3	yes	complemented
73	#5752	C₂×C₃	1	1	yes	characteristic, complemented
74	D₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂³×C₃×D₃	—	2	6	no	—
76	C₃²×#41	—	2	2	no	—
77	C₃²×#41	C₂³	1	1	yes	characteristic
78	C₃²×#41	C₂³	1	6	yes	complemented
79	C₂×C₃²×D₄	—	2	6	no	—
80	C₂×C₃²×D₄	C₂³	1	6	yes	complemented
81	C₂×C₃×#67	—	2	12	no	—
82	C₂×C₃×#67	—	2	6	no	—
83	C₃×#239	—	2	2	no	—
84	C₃×#239	D₄	1	1	yes	characteristic
85	C₃×#239	C₂³	1	6	yes	complemented
86	C₃×D₃×Q₈	D₄	1	1	yes	characteristic
87	C₃×D₃×Q₈	C₂³	1	2	yes	—
88	C₃×#237	—	2	6	no	—
89	C₃×#237	—	2	6	no	—
90	C₃×#237	D₄	1	3	yes	—
91	C₃×#237	C₂³	1	6	yes	complemented
92	C₃×D₃×D₄	—	2	6	no	—
93	C₃×D₃×D₄	—	2	6	no	—
94	C₃×D₃×D₄	—	2	12	no	—
95	C₃×D₃×D₄	—	2	6	no	—
96	C₃×D₃×D₄	—	2	6	no	—
97	C₃×D₃×D₄	—	2	6	no	—
98	C₃×D₃×D₄	D₄	1	3	yes	—
99	C₃×D₃×D₄	C₂³	1	6	yes	—
100	C₃×D₃×D₄	C₂³	1	12	yes	complemented
101	C₃×#235	—	2	6	no	—
102	C₃×#235	—	2	6	no	—
103	C₃×#235	C₂³	1	3	yes	—
104	C₃×#235	C₂³	1	6	yes	complemented
105	C₂×C₃×D₁₂	—	2	6	no	—
106	C₂×C₃×D₁₂	C₂³	1	6	yes	complemented
107	C₂×C₃×C₄×D₃	—	2	6	no	—
108	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
109	C₃²×Q₁₆	C₂³	1	1	yes	characteristic, complemented
110	C₃²×SD₁₆	C₂³	1	6	yes	complemented
111	C₃²×D₈	C₂³	1	3	yes	complemented
112	C₃²×D₈	C₂³	1	6	yes	complemented
113	C₃²×M₁₆	C₂³	1	3	yes	complemented
114	C₂×C₃²×C₈	C₂³	1	3	yes	complemented
115	C₃×#216	C₂³	1	2	yes	complemented
116	C₃×#215	C₂³	1	6	yes	complemented
117	C₃×#214	C₂³	1	6	yes	complemented
118	C₃×#213	C₂³	1	6	yes	complemented
119	C₃×#213	C₂³	1	12	yes	complemented
120	C₃×#208	C₂³	1	3	yes	complemented
121	C₂×C₃×C₃⋊C₈	C₂³	1	3	yes	complemented
122	C₃×Dic₁₂	C₂³	1	1	yes	characteristic, complemented
123	C₃×D₂₄	C₂³	1	3	yes	complemented
124	C₃×D₂₄	C₂³	1	6	yes	complemented
125	C₃×#204	C₂³	1	6	yes	complemented
126	C₃×ΓL(1,𝔽₂₅)	C₂³	1	6	yes	complemented
127	C₃×D₃×C₈	C₂³	1	1	yes	characteristic
128	C₃×D₃×C₈	C₂³	1	3	yes	—
129	C₃×D₃×C₈	C₂³	1	3	yes	complemented
130	C₃×D₃×C₈	C₂³	1	3	yes	complemented
131	C₂×#576	—	3	1	no	Sylow
132	C₃×H(5,𝔽₂)	—	2	2	no	—
133	C₃×H(5,𝔽₂)	—	3	2	no	—
134	C₃×H(5,𝔽₂)	—	3	6	no	—
135	C₃×H(5,𝔽₂)	—	3	6	no	—
136	C₃×H(5,𝔽₂)	—	6	6	no	—
137	C₃×H(5,𝔽₂)	—	6	2	no	—
138	C₃×H(5,𝔽₂)	C₂×D₃	1	2	yes	complemented
139	C₃×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
140	C₂×C₃×#41	—	3	1	no	—
141	C₂×C₃×#41	—	3	6	no	—
142	C₂×C₃×#41	—	6	2	no	—
143	C₂²×C₃×D₄	—	3	6	no	—
144	C₂²×C₃×D₄	—	6	6	no	—
145	#1009	—	2	2	no	—
146	#1009	C₂²×C₃	1	6	yes	complemented
147	#1009	C₂²×C₃	1	2	yes	complemented
148	D₃×#41	—	2	2	no	—
149	D₃×#41	C₂²×C₃	1	1	yes	characteristic
150	D₃×#41	C₂²×C₃	1	6	yes	complemented
151	#1004	—	2	6	no	—
152	#1004	C₂²×C₃	1	6	yes	complemented
153	C₂×D₃×D₄	—	2	6	no	—
154	C₂×D₃×D₄	C₂²×C₃	1	6	yes	complemented
155	C₃×AGL(1,ℤ/8)	—	2	6	no	—
156	C₃×AGL(1,ℤ/8)	—	3	6	no	—
157	C₃×AGL(1,ℤ/8)	—	3	6	no	—
158	C₃×AGL(1,ℤ/8)	—	3	12	no	—
159	C₃×AGL(1,ℤ/8)	—	3	12	no	—
160	C₃×AGL(1,ℤ/8)	—	3	6	no	—
161	C₃×AGL(1,ℤ/8)	C₂×D₃	1	6	yes	complemented
162	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	6	yes	complemented
163	C₃×#135	—	2	3	no	—
164	C₃×#135	—	3	6	no	—
165	C₃×#135	—	3	3	no	—
166	C₃×#135	—	3	6	no	—
167	C₃×#135	—	3	3	no	—
168	C₃×#135	—	3	3	no	—
169	C₃×#135	C₂×D₃	1	3	yes	complemented
170	C₃×#135	C₂²×C₃	1	3	yes	complemented
171	C₂×C₃×Q₁₆	—	3	1	no	—
172	C₂×C₃×SD₁₆	—	3	6	no	—
173	C₂×C₃×D₈	—	2	3	no	—
174	C₂×C₃×D₈	—	3	6	no	—
175	C₂×C₃×D₈	—	3	3	no	—
176	C₂×C₃×D₈	—	3	6	no	—
177	C₂×C₃×D₈	—	3	6	no	—
178	C₂×C₃×D₈	—	3	6	no	—
179	C₂×C₃×D₈	—	3	3	no	—
180	C₂×C₃×D₈	C₂×D₃	1	3	yes	complemented
181	C₂×C₃×D₈	C₂²×C₃	1	3	yes	complemented
182	C₃×#131	—	2	1	no	—
183	C₃×#131	—	3	1	no	—
184	C₃×#131	—	3	3	no	—
185	C₃×#131	—	3	3	no	—
186	C₃×#131	C₂×D₃	1	1	yes	characteristic, complemented
187	C₃×#131	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×C₃×M₁₆	—	3	3	no	—
189	C₂²×C₃×C₈	—	3	3	no	—
190	#950	C₂²×C₃	1	6	yes	complemented
191	#949	C₂²×C₃	1	6	yes	complemented
192	#948	C₂²×C₃	1	1	yes	characteristic, complemented
193	#932	C₂²×C₃	1	6	yes	complemented
194	C₂×#213	C₂²×C₃	1	6	yes	complemented
195	#919	C₂²×C₃	1	3	yes	complemented
196	D₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
197	#916	C₂²×C₃	1	6	yes	complemented
198	#914	C₂²×C₃	1	12	yes	complemented
199	D₃×SD₁₆	C₂²×C₃	1	6	yes	complemented
200	#912	C₂²×C₃	1	3	yes	complemented
201	#911	C₂²×C₃	1	12	yes	complemented
202	D₃×D₈	C₂²×C₃	1	3	yes	complemented
203	D₃×D₈	C₂²×C₃	1	6	yes	complemented
204	D₃×D₈	C₂²×C₃	1	6	yes	complemented
205	D₃×D₈	C₂²×C₃	1	6	yes	complemented
206	#908	C₂²×C₃	1	6	yes	complemented
207	#907	C₂²×C₃	1	3	yes	complemented
208	D₃×M₁₆	C₂²×C₃	1	3	yes	complemented
209	#904	C₂²×C₃	1	3	yes	complemented
210	C₂×D₂₄	C₂²×C₃	1	3	yes	complemented
211	#901	C₂²×C₃	1	3	yes	complemented
212	C₂×D₃×C₈	C₂²×C₃	1	3	yes	complemented
213	C₂³×C₃²	—	2	6	no	—
214	C₂²×C₃×D₃	—	2	6	no	—
215	C₂²×C₃×D₃	—	2	6	no	—
216	C₂²×C₃×D₃	—	2	12	no	—
217	C₂²×C₃×D₃	—	8	12	no	—
218	C₂²×C₃×D₃	C₂×D₄	1	3	yes	—
219	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
220	C₃²×Q₈	C₂⁴	1	2	yes	—
221	C₃²×D₄	—	2	6	no	—
222	C₃²×D₄	—	2	6	no	—
223	C₃²×D₄	C₂×D₄	1	3	yes	—
224	C₃²×D₄	C₂⁴	1	6	yes	—
225	C₂×C₃²×C₄	—	2	6	no	—
226	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
227	C₃×#67	—	2	6	no	—
228	C₃×#67	—	2	6	no	—
229	C₃×#67	—	2	6	no	—
230	C₃×#67	—	2	12	no	—
231	C₃×#67	C₂×D₄	1	6	yes	—
232	C₂×C₃×Dic₃	—	2	6	no	—
233	C₂×C₃×Dic₃	C₂×D₄	1	3	yes	—
234	C₃×D₁₂	—	2	6	no	—
235	C₃×D₁₂	—	2	6	no	—
236	C₃×D₁₂	C₂×D₄	1	3	yes	—
237	C₃×D₁₂	C₂⁴	1	6	yes	—
238	C₃×C₄×D₃	—	2	2	no	—
239	C₃×C₄×D₃	—	2	6	no	—
240	C₃×C₄×D₃	—	2	6	no	—
241	C₃×C₄×D₃	C₂×D₄	1	3	yes	—
242	C₃×C₄×D₃	C₂×D₄	1	3	yes	—
243	C₃×C₄×D₃	C₂⁴	1	1	yes	characteristic
244	C₃×C₄×D₃	C₂⁴	1	3	yes	—
245	C₃×Dic₆	—	2	2	no	—
246	C₃×Dic₆	C₂×D₄	1	3	yes	—
247	C₃×Dic₆	C₂⁴	1	2	yes	—
248	C₃²×C₈	C₂⁴	1	1	yes	characteristic
249	C₃²×C₈	C₂⁴	1	3	yes	—
250	C₃×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
251	C₃×C₃⋊C₈	C₂⁴	1	3	yes	—
252	C₂×H(5,𝔽₂)	—	3	2	no	—
253	#576	—	3	2	no	—
254	#576	—	3	6	no	—
255	#576	—	3	3	no	—
256	#576	—	3	3	no	—
257	#576	—	3	1	no	—
258	#576	C₃×D₃	1	1	yes	characteristic, direct product factor
259	C₂×AGL(1,ℤ/8)	—	3	6	no	—
260	C₂×#135	—	3	3	no	—
261	C₂²×D₈	—	3	3	no	—
262	C₂×#131	—	3	1	no	—
263	C₂⁴×C₃	—	6	6	no	—
264	C₂³×D₃	—	2	6	no	—
265	C₃×#41	—	2	2	no	—
266	C₃×#41	—	2	2	no	—
267	C₃×#41	—	2	1	no	—
268	C₃×#41	—	2	6	no	—
269	C₃×#41	—	3	1	no	—
270	C₃×#41	—	3	3	no	—
271	C₃×#41	—	3	3	no	—
272	C₃×#41	—	3	6	no	—
273	C₃×#41	—	3	6	no	—
274	C₃×#41	—	3	6	no	—
275	C₃×#41	—	4	2	no	—
276	C₃×#41	—	6	6	no	—
277	C₃×#41	—	6	6	no	—
278	C₃×#41	—	6	6	no	—
279	C₃×#41	—	6	6	no	—
280	C₃×#41	—	6	2	no	—
281	C₃×#41	C₂²×D₃	1	1	yes	characteristic
282	C₃×#41	C₂²×D₃	1	6	yes	complemented
283	C₃×#41	C₂³×C₃	1	1	yes	characteristic
284	C₃×#41	C₂³×C₃	1	6	yes	complemented
285	C₂×C₃×Q₈	—	3	1	no	—
286	C₂×C₃×Q₈	—	3	2	no	—
287	C₂×C₃×D₄	—	2	6	no	—
288	C₂×C₃×D₄	—	2	6	no	—
289	C₂×C₃×D₄	—	2	6	no	—
290	C₂×C₃×D₄	—	3	3	no	—
291	C₂×C₃×D₄	—	3	6	no	—
292	C₂×C₃×D₄	—	3	12	no	—
293	C₂×C₃×D₄	—	3	6	no	—
294	C₂×C₃×D₄	—	4	6	no	—
295	C₂×C₃×D₄	—	6	6	no	—
296	C₂×C₃×D₄	—	6	6	no	—
297	C₂×C₃×D₄	—	6	6	no	—
298	C₂×C₃×D₄	—	6	6	no	—
299	C₂×C₃×D₄	—	6	12	no	—
300	C₂×C₃×D₄	—	6	6	no	—
301	C₂×C₃×D₄	—	6	6	no	—
302	C₂×C₃×D₄	—	6	12	no	—
303	C₂×C₃×D₄	—	6	6	no	—
304	C₂×C₃×D₄	C₂²×D₃	1	6	yes	complemented
305	C₂×C₃×D₄	C₂³×C₃	1	6	yes	complemented
306	C₂²×C₃×C₄	—	3	3	no	—
307	C₂²×C₃×C₄	—	6	6	no	—
308	C₂×#67	—	2	12	no	—
309	C₂×#67	—	2	6	no	—
310	#239	—	2	2	no	—
311	#239	C₃×D₄	1	1	yes	characteristic
312	#239	C₂³×C₃	1	6	yes	complemented
313	D₃×Q₈	C₃×D₄	1	1	yes	characteristic
314	D₃×Q₈	C₂³×C₃	1	2	yes	—
315	#237	—	2	6	no	—
316	#237	—	2	6	no	—
317	#237	C₃×D₄	1	3	yes	—
318	#237	C₂³×C₃	1	6	yes	complemented
319	D₃×D₄	—	2	6	no	—
320	D₃×D₄	—	2	6	no	—
321	D₃×D₄	—	2	12	no	—
322	D₃×D₄	—	2	6	no	—
323	D₃×D₄	—	2	6	no	—
324	D₃×D₄	—	2	6	no	—
325	D₃×D₄	C₃×D₄	1	3	yes	—
326	D₃×D₄	C₂³×C₃	1	6	yes	—
327	D₃×D₄	C₂³×C₃	1	12	yes	complemented
328	#235	—	2	6	no	—
329	#235	—	2	6	no	—
330	#235	C₂³×C₃	1	3	yes	—
331	#235	C₂³×C₃	1	6	yes	complemented
332	C₂×D₁₂	—	2	6	no	—
333	C₂×D₁₂	C₂³×C₃	1	6	yes	complemented
334	C₂×C₄×D₃	—	2	6	no	—
335	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
336	C₃×Q₁₆	—	2	1	no	—
337	C₃×Q₁₆	—	3	2	no	—
338	C₃×Q₁₆	—	3	1	no	—
339	C₃×Q₁₆	C₂²×D₃	1	1	yes	characteristic, complemented
340	C₃×Q₁₆	C₂³×C₃	1	1	yes	characteristic, complemented
341	C₃×SD₁₆	—	2	6	no	—
342	C₃×SD₁₆	—	3	6	no	—
343	C₃×SD₁₆	—	3	6	no	—
344	C₃×SD₁₆	—	3	6	no	—
345	C₃×SD₁₆	C₂²×D₃	1	6	yes	complemented
346	C₃×SD₁₆	C₂³×C₃	1	6	yes	complemented
347	C₃×D₈	—	2	3	no	—
348	C₃×D₈	—	2	6	no	—
349	C₃×D₈	—	3	6	no	—
350	C₃×D₈	—	3	12	no	—
351	C₃×D₈	—	3	3	no	—
352	C₃×D₈	—	3	6	no	—
353	C₃×D₈	C₂²×D₃	1	3	yes	complemented
354	C₃×D₈	C₂²×D₃	1	6	yes	complemented
355	C₃×D₈	C₂³×C₃	1	3	yes	complemented
356	C₃×D₈	C₂³×C₃	1	6	yes	complemented
357	C₃×M₁₆	—	2	3	no	—
358	C₃×M₁₆	—	3	3	no	—
359	C₃×M₁₆	—	3	6	no	—
360	C₃×M₁₆	C₂²×D₃	1	3	yes	complemented
361	C₃×M₁₆	C₂³×C₃	1	3	yes	complemented
362	C₂×C₃×C₈	—	2	3	no	—
363	C₂×C₃×C₈	—	3	3	no	—
364	C₂×C₃×C₈	—	3	1	no	—
365	C₂×C₃×C₈	—	3	3	no	—
366	C₂×C₃×C₈	—	3	3	no	—
367	C₂×C₃×C₈	—	3	3	no	—
368	C₂×C₃×C₈	C₂²×D₃	1	3	yes	complemented
369	C₂×C₃×C₈	C₂³×C₃	1	3	yes	complemented
370	#216	C₂³×C₃	1	2	yes	complemented
371	#215	C₂³×C₃	1	6	yes	complemented
372	#214	C₂³×C₃	1	6	yes	complemented
373	#213	C₂³×C₃	1	6	yes	complemented
374	#213	C₂³×C₃	1	12	yes	complemented
375	#208	C₂³×C₃	1	3	yes	complemented
376	C₂×C₃⋊C₈	C₂³×C₃	1	3	yes	complemented
377	Dic₁₂	C₂³×C₃	1	1	yes	characteristic, complemented
378	D₂₄	C₂³×C₃	1	3	yes	complemented
379	D₂₄	C₂³×C₃	1	6	yes	complemented
380	#204	C₂³×C₃	1	6	yes	complemented
381	ΓL(1,𝔽₂₅)	C₂³×C₃	1	6	yes	complemented
382	D₃×C₈	C₂³×C₃	1	1	yes	characteristic
383	D₃×C₈	C₂³×C₃	1	3	yes	—
384	D₃×C₈	C₂³×C₃	1	3	yes	complemented
385	D₃×C₈	C₂³×C₃	1	3	yes	complemented
386	C₂²×C₃²	—	2	6	no	—
387	C₂²×C₃²	—	8	6	no	—
388	C₂²×C₃²	C₂²×D₄	1	3	yes	—
389	C₂×C₃×D₃	—	2	6	no	—
390	C₂×C₃×D₃	—	2	6	no	—
391	C₂×C₃×D₃	—	4	12	no	—
392	C₂×C₃×D₃	—	8	12	no	—
393	C₂×C₃×D₃	—	8	6	no	—
394	C₂×C₃×D₃	C₂²×D₄	1	3	yes	—
395	C₂×C₃×D₃	C₂²×D₄	1	1	yes	characteristic
396	C₃²×C₄	—	2	2	no	—
397	C₃²×C₄	C₂²×D₄	1	3	yes	—
398	C₃²×C₄	C₂⁵	1	1	yes	characteristic
399	C₃×Dic₃	—	2	2	no	—
400	C₃×Dic₃	C₂²×D₄	1	1	yes	characteristic
401	C₃×Dic₃	C₂²×D₄	1	3	yes	—
402	H(5,𝔽₂)	—	3	2	no	—
403	H(5,𝔽₂)	—	3	6	no	—
404	H(5,𝔽₂)	—	3	6	no	—
405	H(5,𝔽₂)	—	6	6	no	—
406	H(5,𝔽₂)	—	6	2	no	—
407	H(5,𝔽₂)	C₂×C₃×D₃	1	2	yes	complemented
408	C₂×#41	—	3	1	no	—
409	C₂×#41	—	3	6	no	—
410	C₂×#41	—	6	2	no	—
411	C₂²×D₄	—	3	6	no	—
412	C₂²×D₄	—	6	6	no	—
413	AGL(1,ℤ/8)	—	3	6	no	—
414	AGL(1,ℤ/8)	—	3	6	no	—
415	AGL(1,ℤ/8)	—	3	12	no	—
416	AGL(1,ℤ/8)	—	3	12	no	—
417	AGL(1,ℤ/8)	—	3	6	no	—
418	AGL(1,ℤ/8)	C₂×C₃×D₃	1	6	yes	complemented
419	#135	—	3	6	no	—
420	#135	—	3	3	no	—
421	#135	—	3	6	no	—
422	#135	—	3	3	no	—
423	#135	—	3	3	no	—
424	#135	C₂×C₃×D₃	1	3	yes	complemented
425	C₂×Q₁₆	—	3	1	no	—
426	C₂×SD₁₆	—	3	6	no	—
427	C₂×D₈	—	3	6	no	—
428	C₂×D₈	—	3	3	no	—
429	C₂×D₈	—	3	6	no	—
430	C₂×D₈	—	3	6	no	—
431	C₂×D₈	—	3	6	no	—
432	C₂×D₈	—	3	3	no	—
433	C₂×D₈	C₂×C₃×D₃	1	3	yes	complemented
434	#131	—	3	1	no	—
435	#131	—	3	3	no	—
436	#131	—	3	3	no	—
437	#131	C₂×C₃×D₃	1	1	yes	characteristic, complemented
438	C₂×M₁₆	—	3	3	no	—
439	C₂²×C₈	—	3	3	no	—
440	C₂³×C₃	—	2	6	no	—
441	C₂³×C₃	—	2	6	no	—
442	C₂³×C₃	—	3	3	no	—
443	C₂³×C₃	—	4	6	no	—
444	C₂³×C₃	—	6	6	no	—
445	C₂³×C₃	—	6	12	no	—
446	C₂³×C₃	—	6	6	no	—
447	C₂³×C₃	—	24	12	no	—
448	C₂²×D₃	—	2	6	no	—
449	C₂²×D₃	—	2	6	no	—
450	C₂²×D₃	—	2	12	no	—
451	C₂²×D₃	—	8	12	no	—
452	C₂²×D₃	C₂×C₃×D₄	1	3	yes	—
453	C₃×Q₈	—	2	2	no	—
454	C₃×Q₈	—	2	1	no	—
455	C₃×Q₈	—	3	3	no	—
456	C₃×Q₈	—	3	2	no	—
457	C₃×Q₈	—	6	2	no	—
458	C₃×Q₈	D₃×D₄	1	1	yes	characteristic
459	C₃×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
460	C₃×Q₈	C₂³×D₃	1	2	yes	—
461	C₃×Q₈	C₂⁴×C₃	1	2	yes	—
462	C₃×D₄	—	2	6	no	—
463	C₃×D₄	—	2	6	no	—
464	C₃×D₄	—	2	6	no	—
465	C₃×D₄	—	2	6	no	—
466	C₃×D₄	—	2	6	no	—
467	C₃×D₄	—	2	3	no	—
468	C₃×D₄	—	3	6	no	—
469	C₃×D₄	—	3	3	no	—
470	C₃×D₄	—	3	6	no	—
471	C₃×D₄	—	4	6	no	—
472	C₃×D₄	—	4	6	no	—
473	C₃×D₄	—	6	6	no	—
474	C₃×D₄	—	6	6	no	—
475	C₃×D₄	—	6	12	no	—
476	C₃×D₄	—	6	6	no	—
477	C₃×D₄	—	6	6	no	—
478	C₃×D₄	—	6	6	no	—
479	C₃×D₄	D₃×D₄	1	3	yes	—
480	C₃×D₄	C₂×C₃×D₄	1	3	yes	—
481	C₃×D₄	C₂³×D₃	1	6	yes	—
482	C₃×D₄	C₂⁴×C₃	1	6	yes	—
483	C₂×C₃×C₄	—	2	6	no	—
484	C₂×C₃×C₄	—	2	6	no	—
485	C₂×C₃×C₄	—	2	3	no	—
486	C₂×C₃×C₄	—	3	3	no	—
487	C₂×C₃×C₄	—	3	3	no	—
488	C₂×C₃×C₄	—	3	3	no	—
489	C₂×C₃×C₄	—	3	1	no	—
490	C₂×C₃×C₄	—	3	3	no	—
491	C₂×C₃×C₄	—	4	6	no	—
492	C₂×C₃×C₄	—	6	6	no	—
493	C₂×C₃×C₄	—	6	2	no	—
494	C₂×C₃×C₄	—	6	6	no	—
495	C₂×C₃×C₄	—	6	6	no	—
496	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
497	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
498	#67	—	2	6	no	—
499	#67	—	2	6	no	—
500	#67	—	2	6	no	—
501	#67	—	2	12	no	—
502	#67	C₂×C₃×D₄	1	6	yes	—
503	C₂×Dic₃	—	2	6	no	—
504	C₂×Dic₃	C₂×C₃×D₄	1	3	yes	—
505	D₁₂	—	2	6	no	—
506	D₁₂	—	2	6	no	—
507	D₁₂	C₂×C₃×D₄	1	3	yes	—
508	D₁₂	C₂⁴×C₃	1	6	yes	—
509	C₄×D₃	—	2	2	no	—
510	C₄×D₃	—	2	6	no	—
511	C₄×D₃	—	2	6	no	—
512	C₄×D₃	C₂×C₃×D₄	1	3	yes	—
513	C₄×D₃	C₂×C₃×D₄	1	3	yes	—
514	C₄×D₃	C₂⁴×C₃	1	1	yes	characteristic
515	C₄×D₃	C₂⁴×C₃	1	3	yes	—
516	Dic₆	—	2	2	no	—
517	Dic₆	C₂×C₃×D₄	1	3	yes	—
518	Dic₆	C₂⁴×C₃	1	2	yes	—
519	C₃×C₈	—	2	1	no	—
520	C₃×C₈	—	2	3	no	—
521	C₃×C₈	—	3	1	no	—
522	C₃×C₈	—	3	3	no	—
523	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
524	C₃×C₈	C₂³×D₃	1	3	yes	—
525	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
526	C₃×C₈	C₂⁴×C₃	1	3	yes	—
527	C₃⋊C₈	C₂⁴×C₃	1	1	yes	characteristic
528	C₃⋊C₈	C₂⁴×C₃	1	3	yes	—
529	C₂×C₃²	—	2	3	no	—
530	C₂×C₃²	—	4	6	no	—
531	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
532	C₃×D₃	—	2	3	no	—
533	C₃×D₃	—	4	6	no	—
534	C₃×D₃	#576	1	2	yes	direct product factor
535	C₂⁴	—	6	6	no	—
536	#41	—	2	2	no	—
537	#41	—	3	1	no	—
538	#41	—	3	3	no	—
539	#41	—	3	3	no	—
540	#41	—	3	6	no	—
541	#41	—	3	6	no	—
542	#41	—	3	6	no	—
543	#41	—	6	6	no	—
544	#41	—	6	6	no	—
545	#41	—	6	6	no	—
546	#41	—	6	6	no	—
547	#41	—	6	2	no	—
548	#41	C₂²×C₃×D₃	1	1	yes	characteristic
549	#41	C₂²×C₃×D₃	1	6	yes	complemented
550	C₂×Q₈	—	3	1	no	—
551	C₂×Q₈	—	3	2	no	—
552	C₂×D₄	—	2	6	no	—
553	C₂×D₄	—	3	3	no	—
554	C₂×D₄	—	3	6	no	—
555	C₂×D₄	—	3	12	no	—
556	C₂×D₄	—	3	6	no	—
557	C₂×D₄	—	6	6	no	—
558	C₂×D₄	—	6	6	no	—
559	C₂×D₄	—	6	6	no	—
560	C₂×D₄	—	6	6	no	—
561	C₂×D₄	—	6	12	no	—
562	C₂×D₄	—	6	6	no	—
563	C₂×D₄	—	6	6	no	—
564	C₂×D₄	—	6	12	no	—
565	C₂×D₄	—	6	6	no	—
566	C₂×D₄	C₂²×C₃×D₃	1	6	yes	complemented
567	C₂²×C₄	—	3	3	no	—
568	C₂²×C₄	—	6	6	no	—
569	Q₁₆	—	3	2	no	—
570	Q₁₆	—	3	1	no	—
571	Q₁₆	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
572	SD₁₆	—	3	6	no	—
573	SD₁₆	—	3	6	no	—
574	SD₁₆	—	3	6	no	—
575	SD₁₆	C₂²×C₃×D₃	1	6	yes	complemented
576	D₈	—	3	6	no	—
577	D₈	—	3	12	no	—
578	D₈	—	3	3	no	—
579	D₈	—	3	6	no	—
580	D₈	C₂²×C₃×D₃	1	3	yes	complemented
581	D₈	C₂²×C₃×D₃	1	6	yes	complemented
582	M₁₆	—	3	3	no	—
583	M₁₆	—	3	6	no	—
584	M₁₆	C₂²×C₃×D₃	1	3	yes	complemented
585	C₂×C₈	—	3	3	no	—
586	C₂×C₈	—	3	1	no	—
587	C₂×C₈	—	3	3	no	—
588	C₂×C₈	—	3	3	no	—
589	C₂×C₈	—	3	3	no	—
590	C₂×C₈	C₂²×C₃×D₃	1	3	yes	complemented
591	C₂²×C₃	—	2	6	no	—
592	C₂²×C₃	—	2	6	no	—
593	C₂²×C₃	—	2	3	no	—
594	C₂²×C₃	—	3	1	no	—
595	C₂²×C₃	—	3	3	no	—
596	C₂²×C₃	—	4	6	no	—
597	C₂²×C₃	—	6	6	no	—
598	C₂²×C₃	—	6	6	no	—
599	C₂²×C₃	—	8	6	no	—
600	C₂²×C₃	—	8	6	no	—
601	C₂²×C₃	—	12	12	no	—
602	C₂²×C₃	—	16	6	no	—
603	C₂²×C₃	—	24	6	no	—
604	C₂²×C₃	—	24	12	no	—
605	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
606	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
607	C₂×D₃	—	2	6	no	—
608	C₂×D₃	—	2	6	no	—
609	C₂×D₃	—	4	12	no	—
610	C₂×D₃	—	8	12	no	—
611	C₂×D₃	—	8	6	no	—
612	C₂×D₃	C₂²×C₃×D₄	1	3	yes	—
613	C₂×D₃	C₂²×C₃×D₄	1	1	yes	characteristic
614	C₃×C₄	—	2	2	no	—
615	C₃×C₄	—	2	2	no	—
616	C₃×C₄	—	2	3	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	3	1	no	—
619	C₃×C₄	—	3	3	no	—
620	C₃×C₄	—	4	2	no	—
621	C₃×C₄	—	6	2	no	—
622	C₃×C₄	C₂×D₃×D₄	1	3	yes	—
623	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
624	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
625	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
626	Dic₃	—	2	2	no	—
627	Dic₃	C₂²×C₃×D₄	1	1	yes	characteristic
628	Dic₃	C₂²×C₃×D₄	1	3	yes	—
629	C₃²	C₂×#576	1	1	yes	characteristic, complemented, Sylow
630	C₂³	—	2	6	no	—
631	C₂³	—	3	3	no	—
632	C₂³	—	6	6	no	—
633	C₂³	—	6	12	no	—
634	C₂³	—	6	6	no	—
635	C₂³	—	24	12	no	—
636	Q₈	—	3	3	no	—
637	Q₈	—	3	2	no	—
638	Q₈	—	6	2	no	—
639	Q₈	C₃×D₃×D₄	1	1	yes	characteristic
640	Q₈	C₂³×C₃×D₃	1	2	yes	—
641	D₄	—	2	6	no	—
642	D₄	—	2	6	no	—
643	D₄	—	3	6	no	—
644	D₄	—	3	3	no	—
645	D₄	—	3	6	no	—
646	D₄	—	6	6	no	—
647	D₄	—	6	6	no	—
648	D₄	—	6	12	no	—
649	D₄	—	6	6	no	—
650	D₄	—	6	6	no	—
651	D₄	—	6	6	no	—
652	D₄	C₃×D₃×D₄	1	3	yes	—
653	D₄	C₂³×C₃×D₃	1	6	yes	—
654	C₂×C₄	—	2	6	no	—
655	C₂×C₄	—	3	3	no	—
656	C₂×C₄	—	3	3	no	—
657	C₂×C₄	—	3	3	no	—
658	C₂×C₄	—	3	1	no	—
659	C₂×C₄	—	3	3	no	—
660	C₂×C₄	—	6	6	no	—
661	C₂×C₄	—	6	2	no	—
662	C₂×C₄	—	6	6	no	—
663	C₂×C₄	—	6	6	no	—
664	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
665	C₈	—	3	1	no	—
666	C₈	—	3	3	no	—
667	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
668	C₈	C₂³×C₃×D₃	1	3	yes	—
669	C₂×C₃	—	2	3	no	—
670	C₂×C₃	—	2	3	no	—
671	C₂×C₃	—	2	1	no	—
672	C₂×C₃	—	3	2	no	—
673	C₂×C₃	—	4	3	no	—
674	C₂×C₃	—	4	6	no	—
675	C₂×C₃	—	4	6	no	—
676	C₂×C₃	—	6	3	no	—
677	C₂×C₃	—	8	6	no	—
678	C₂×C₃	—	12	6	no	—
679	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
680	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
681	D₃	—	2	3	no	—
682	D₃	—	4	6	no	—
683	D₃	C₃×#576	1	2	yes	direct product factor
684	C₂²	—	2	6	no	—
685	C₂²	—	3	1	no	—
686	C₂²	—	3	3	no	—
687	C₂²	—	6	6	no	—
688	C₂²	—	6	6	no	—
689	C₂²	—	8	6	no	—
690	C₂²	—	12	12	no	—
691	C₂²	—	24	6	no	—
692	C₂²	—	24	12	no	—
693	C₂²	C₂×C₃×D₃×D₄	1	3	yes	—
694	C₄	—	2	2	no	—
695	C₄	—	3	1	no	—
696	C₄	—	3	3	no	—
697	C₄	—	6	2	no	—
698	C₄	C₂×C₃×D₃×D₄	1	3	yes	—
699	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
700	C₃	—	2	1	no	—
701	C₃	D₃×#576	1	1	yes	characteristic, direct product factor
702	C₃	C₂×C₃×#576	1	1	yes	characteristic, complemented
703	C₂	—	2	3	no	—
704	C₂	—	3	2	no	—
705	C₂	—	4	6	no	—
706	C₂	—	6	3	no	—
707	C₂	—	12	6	no	—
708	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₃²×#576	C₂
socle	C₂×C₃²	C₂³×D₄
hypercenter	C₃×#576	D₃
hypocenter	C₃	C₂×C₃×#576
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ C₃×#576

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×H(5,𝔽₂)	C₂	semidirect
2. C₃²×#576	C₂	semidirect
3. C₃×#5835	C₂	semidirect
4. C₃×#5774	C₂	semidirect
5. C₃×D₃×AGL(1,ℤ/8)	C₂	semidirect
6. C₃×#5769	C₂	semidirect
7. C₃×D₃×#135	C₂	semidirect
8. C₃×#5757	C₂	semidirect
9. C₂×C₃×D₃×D₈	C₂	semidirect
10. C₃×#5752	C₂	semidirect
11. C₃×D₃×#131	C₂	semidirect
13. D₃×#576	C₃	direct (N × H)
14. C₃²×H(5,𝔽₂)	C₂²	semidirect
16. C₃×#1009	C₂²	semidirect
17. C₃×#1009	C₂²	semidirect
20. C₃×D₃×#41	C₂²	semidirect
22. C₃×#1004	C₂²	semidirect
24. C₂×C₃×D₃×D₄	C₂²	semidirect
25. C₃²×AGL(1,ℤ/8)	C₂²	semidirect
26. C₃²×#135	C₂²	semidirect
27. C₂×C₃²×D₈	C₂²	semidirect
28. C₃²×#131	C₂²	semidirect
29. C₃×#950	C₂²	semidirect
30. C₃×#949	C₂²	semidirect
31. C₃×#948	C₂²	semidirect
32. C₃×#932	C₂²	semidirect
33. C₂×C₃×#213	C₂²	semidirect
34. C₃×#919	C₂²	semidirect
35. C₃×D₃×Q₁₆	C₂²	semidirect
36. C₃×#916	C₂²	semidirect
37. C₃×#914	C₂²	semidirect
38. C₃×D₃×SD₁₆	C₂²	semidirect
39. C₃×#912	C₂²	semidirect
40. C₃×#911	C₂²	semidirect
41. C₃×D₃×D₈	C₂²	semidirect
42. C₃×D₃×D₈	C₂²	semidirect
43. C₃×D₃×D₈	C₂²	semidirect
44. C₃×D₃×D₈	C₂²	semidirect
45. C₃×#908	C₂²	semidirect
46. C₃×#907	C₂²	semidirect
47. C₃×D₃×M₁₆	C₂²	semidirect
48. C₃×#904	C₂²	semidirect
49. C₂×C₃×D₂₄	C₂²	semidirect
50. C₃×#901	C₂²	semidirect
51. C₂×C₃×D₃×C₈	C₂²	semidirect
53. D₃×H(5,𝔽₂)	C₂×C₃	semidirect
60. C₃×#576	D₃	direct (N × H)
61. C₃×#576	C₂×C₃	semidirect
66. #5835	C₂×C₃	semidirect
67. #5774	C₂×C₃	semidirect
68. D₃×AGL(1,ℤ/8)	C₂×C₃	semidirect
69. #5769	C₂×C₃	semidirect
70. D₃×#135	C₂×C₃	semidirect
71. #5757	C₂×C₃	semidirect
72. C₂×D₃×D₈	C₂×C₃	semidirect
73. #5752	C₂×C₃	semidirect
74. D₃×#131	C₂×C₃	semidirect
78. C₃²×#41	C₂³	semidirect
80. C₂×C₃²×D₄	C₂³	semidirect
85. C₃×#239	C₂³	semidirect
91. C₃×#237	C₂³	semidirect
100. C₃×D₃×D₄	C₂³	semidirect
104. C₃×#235	C₂³	semidirect
106. C₂×C₃×D₁₂	C₂³	semidirect
109. C₃²×Q₁₆	C₂³	semidirect
110. C₃²×SD₁₆	C₂³	semidirect
111. C₃²×D₈	C₂³	semidirect
112. C₃²×D₈	C₂³	semidirect
113. C₃²×M₁₆	C₂³	semidirect
114. C₂×C₃²×C₈	C₂³	semidirect
115. C₃×#216	C₂³	semidirect
116. C₃×#215	C₂³	semidirect
117. C₃×#214	C₂³	semidirect
118. C₃×#213	C₂³	semidirect
119. C₃×#213	C₂³	semidirect
120. C₃×#208	C₂³	semidirect
121. C₂×C₃×C₃⋊C₈	C₂³	semidirect
122. C₃×Dic₁₂	C₂³	semidirect
123. C₃×D₂₄	C₂³	semidirect
124. C₃×D₂₄	C₂³	semidirect
125. C₃×#204	C₂³	semidirect
126. C₃×ΓL(1,𝔽₂₅)	C₂³	semidirect
129. C₃×D₃×C₈	C₂³	semidirect
130. C₃×D₃×C₈	C₂³	semidirect
138. C₃×H(5,𝔽₂)	C₂×D₃	semidirect
139. C₃×H(5,𝔽₂)	C₂²×C₃	semidirect
146. #1009	C₂²×C₃	semidirect
147. #1009	C₂²×C₃	semidirect
150. D₃×#41	C₂²×C₃	semidirect
152. #1004	C₂²×C₃	semidirect
154. C₂×D₃×D₄	C₂²×C₃	semidirect
161. C₃×AGL(1,ℤ/8)	C₂×D₃	semidirect
162. C₃×AGL(1,ℤ/8)	C₂²×C₃	semidirect
169. C₃×#135	C₂×D₃	semidirect
170. C₃×#135	C₂²×C₃	semidirect
180. C₂×C₃×D₈	C₂×D₃	semidirect
181. C₂×C₃×D₈	C₂²×C₃	semidirect
186. C₃×#131	C₂×D₃	semidirect
187. C₃×#131	C₂²×C₃	semidirect
190. #950	C₂²×C₃	semidirect
191. #949	C₂²×C₃	semidirect
192. #948	C₂²×C₃	semidirect
193. #932	C₂²×C₃	semidirect
194. C₂×#213	C₂²×C₃	semidirect
195. #919	C₂²×C₃	semidirect
196. D₃×Q₁₆	C₂²×C₃	semidirect
197. #916	C₂²×C₃	semidirect
198. #914	C₂²×C₃	semidirect
199. D₃×SD₁₆	C₂²×C₃	semidirect
200. #912	C₂²×C₃	semidirect
201. #911	C₂²×C₃	semidirect
202. D₃×D₈	C₂²×C₃	semidirect
203. D₃×D₈	C₂²×C₃	semidirect
204. D₃×D₈	C₂²×C₃	semidirect
205. D₃×D₈	C₂²×C₃	semidirect
206. #908	C₂²×C₃	semidirect
207. #907	C₂²×C₃	semidirect
208. D₃×M₁₆	C₂²×C₃	semidirect
209. #904	C₂²×C₃	semidirect
210. C₂×D₂₄	C₂²×C₃	semidirect
211. #901	C₂²×C₃	semidirect
212. C₂×D₃×C₈	C₂²×C₃	semidirect
258. #576	C₃×D₃	direct (N × H)
282. C₃×#41	C₂²×D₃	semidirect
284. C₃×#41	C₂³×C₃	semidirect
304. C₂×C₃×D₄	C₂²×D₃	semidirect
305. C₂×C₃×D₄	C₂³×C₃	semidirect
312. #239	C₂³×C₃	semidirect
318. #237	C₂³×C₃	semidirect
327. D₃×D₄	C₂³×C₃	semidirect
331. #235	C₂³×C₃	semidirect
333. C₂×D₁₂	C₂³×C₃	semidirect
339. C₃×Q₁₆	C₂²×D₃	semidirect
340. C₃×Q₁₆	C₂³×C₃	semidirect
345. C₃×SD₁₆	C₂²×D₃	semidirect
346. C₃×SD₁₆	C₂³×C₃	semidirect
353. C₃×D₈	C₂²×D₃	semidirect
354. C₃×D₈	C₂²×D₃	semidirect
355. C₃×D₈	C₂³×C₃	semidirect
356. C₃×D₈	C₂³×C₃	semidirect
360. C₃×M₁₆	C₂²×D₃	semidirect
361. C₃×M₁₆	C₂³×C₃	semidirect
368. C₂×C₃×C₈	C₂²×D₃	semidirect
369. C₂×C₃×C₈	C₂³×C₃	semidirect
370. #216	C₂³×C₃	semidirect
371. #215	C₂³×C₃	semidirect
372. #214	C₂³×C₃	semidirect
373. #213	C₂³×C₃	semidirect
374. #213	C₂³×C₃	semidirect
375. #208	C₂³×C₃	semidirect
376. C₂×C₃⋊C₈	C₂³×C₃	semidirect
377. Dic₁₂	C₂³×C₃	semidirect
378. D₂₄	C₂³×C₃	semidirect
379. D₂₄	C₂³×C₃	semidirect
380. #204	C₂³×C₃	semidirect
381. ΓL(1,𝔽₂₅)	C₂³×C₃	semidirect
384. D₃×C₈	C₂³×C₃	semidirect
385. D₃×C₈	C₂³×C₃	semidirect
407. H(5,𝔽₂)	C₂×C₃×D₃	semidirect
418. AGL(1,ℤ/8)	C₂×C₃×D₃	semidirect
424. #135	C₂×C₃×D₃	semidirect
433. C₂×D₈	C₂×C₃×D₃	semidirect
437. #131	C₂×C₃×D₃	semidirect
534. C₃×D₃	#576	direct (N × H)
549. #41	C₂²×C₃×D₃	semidirect
566. C₂×D₄	C₂²×C₃×D₃	semidirect
571. Q₁₆	C₂²×C₃×D₃	semidirect
575. SD₁₆	C₂²×C₃×D₃	semidirect
580. D₈	C₂²×C₃×D₃	semidirect
581. D₈	C₂²×C₃×D₃	semidirect
584. M₁₆	C₂²×C₃×D₃	semidirect
590. C₂×C₈	C₂²×C₃×D₃	semidirect
629. C₃²	C₂×#576	semidirect
683. D₃	C₃×#576	direct (N × H)
701. C₃	D₃×#576	direct (N × H)
702. C₃	C₂×C₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×H(5,𝔽₂)	2
C₃²×#576	2
C₃×#5835	2
C₃×#5774	2
C₃×D₃×AGL(1,ℤ/8)	2
C₃×#5769	2
C₃×D₃×#135	2
C₃×#5757	2
C₂×C₃×D₃×D₈	2
C₃×#5752	2
C₃×D₃×#131	2
C₂×C₃×#576	3
D₃×#576	3

Subgroups — C3×D3×#576 #11918781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#576 #11918781