Subgroups — C₃⋊D₃×#1004 #13181613

Order 1728.

6052 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11724679	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#1004	C₂	1	1	yes	maximal, characteristic, complemented
4	#11724611	C₂	1	4	yes	maximal, complemented
5	C₂×C₃⋊D₃×#67	C₂	1	4	yes	maximal, complemented
6	#11724589	C₂	1	4	yes	maximal, complemented
7	#11724587	C₂	1	4	yes	maximal, complemented
8	C₃⋊D₃×#237	C₂	1	4	yes	maximal, complemented
9	D₃×D₄×C₃⋊D₃	C₂	1	4	yes	maximal, complemented
10	#11724580	C₂	1	2	yes	maximal, complemented
11	C₃⋊D₃×#235	C₂	1	2	yes	maximal, complemented
12	C₃⋊D₃×H(5,𝔽₂)	—	3	1	no	maximal
13	D₃×#1004	—	3	4	no	maximal
14	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
15	C₂²×D₃×C₃⋊D₃	C₂²	1	4	yes	complemented
16	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×#6312	C₂²	1	4	yes	complemented
18	#89078	C₂²	1	4	yes	complemented
19	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
20	#89076	C₂²	1	2	yes	complemented
21	C₂×C₃×#638	C₂²	1	2	yes	complemented
22	C₃×D₄×C₃⋊D₃	C₂²	1	4	yes	complemented
23	C₃×D₄×C₃⋊D₃	C₂²	1	4	yes	complemented
24	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃²×#67	C₂²	1	4	yes	complemented
27	C₃²×#237	C₂²	1	4	yes	complemented
28	C₃²×D₃×D₄	C₂²	1	4	yes	complemented
29	C₃²×#235	C₂²	1	2	yes	complemented
30	#89039	C₂²	1	8	yes	complemented
31	C₃⋊D₃×#67	C₂²	1	4	yes	complemented
32	C₃⋊D₃×#67	C₂²	1	8	yes	complemented
33	C₃⋊D₃×#67	C₂²	1	8	yes	complemented
34	C₃⋊D₃×#67	C₂²	1	8	yes	complemented
35	D₃×#638	C₂²	1	8	yes	complemented
36	C₂×#6292	C₂²	1	4	yes	complemented
37	C₂×#6290	C₂²	1	4	yes	complemented
38	#89031	C₂²	1	8	yes	complemented
39	C₂×Dic₃×C₃⋊D₃	C₂²	1	4	yes	complemented
40	#89029	C₂²	1	8	yes	complemented
41	#89028	C₂²	1	4	yes	complemented
42	#89026	C₂²	1	4	yes	complemented
43	C₃⋊D₃×D₁₂	C₂²	1	2	yes	complemented
44	D₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
45	C₄×D₃×C₃⋊D₃	C₂²	1	4	yes	complemented
46	#89021	C₂²	1	4	yes	complemented
47	#89020	C₂²	1	4	yes	complemented
48	#89018	C₂²	1	2	yes	complemented
49	#89017	C₂²	1	4	yes	complemented
50	C₃⋊D₃×Dic₆	C₂²	1	2	yes	complemented
51	#89014	C₂²	1	2	yes	complemented
52	C₃²×H(5,𝔽₂)	—	3	1	no	—
53	#64366	—	3	4	no	—
54	#64366	—	3	2	no	—
55	#41×C₃⋊D₃	—	3	4	no	—
56	#41×C₃⋊D₃	—	3	2	no	—
57	#64361	—	3	1	no	—
58	#64361	—	3	4	no	—
59	#64361	—	3	4	no	—
60	#64361	—	3	4	no	—
61	#64361	—	6	4	no	—
62	C₂×D₄×C₃⋊D₃	—	3	4	no	—
63	C₂×D₄×C₃⋊D₃	—	3	4	no	—
64	C₂×D₄×C₃⋊D₃	D₃	1	1	yes	characteristic, complemented
65	C₃×#1004	D₃	1	4	yes	complemented
66	C₂×C₃×D₃×D₄	—	3	4	no	—
67	#64330	—	3	16	no	—
68	C₂×D₃×#67	—	3	16	no	—
69	#64314	—	3	16	no	—
70	#64313	—	3	16	no	—
71	D₃×#237	—	3	16	no	—
72	D₃²×D₄	—	3	16	no	—
73	#64307	—	3	8	no	—
74	D₃×#235	—	3	8	no	—
75	C₂³×C₃³	C₂³	1	2	yes	complemented
76	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
77	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
78	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
79	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	complemented
81	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	complemented
82	C₂²×C₃²×D₃	C₂³	1	4	yes	complemented
83	C₂×D₃×C₃⋊D₃	—	4	8	no	—
84	C₂×D₃×C₃⋊D₃	C₂³	1	4	yes	—
85	C₂×D₃×C₃⋊D₃	C₂³	1	8	yes	complemented
86	C₃³×D₄	C₂³	1	4	yes	complemented
87	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic, complemented
88	#6312	C₂³	1	4	yes	complemented
89	#6312	C₂³	1	8	yes	complemented
90	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	4	yes	complemented
91	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	2	yes	complemented
92	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
93	#6308	C₂³	1	2	yes	complemented
94	C₃×#638	C₂³	1	8	yes	complemented
95	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
96	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
97	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
98	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	complemented
99	C₃²×#67	C₂³	1	4	yes	complemented
100	C₃²×#67	C₂³	1	8	yes	complemented
101	C₂×C₃²×Dic₃	C₂³	1	4	yes	complemented
102	C₃²×D₁₂	C₂³	1	2	yes	complemented
103	C₃²×C₄×D₃	C₂³	1	4	yes	complemented
104	C₃²×Dic₆	C₂³	1	2	yes	complemented
105	#6293	C₂³	1	4	yes	complemented
106	#6292	C₂³	1	8	yes	complemented
107	#6292	C₂³	1	4	yes	complemented
108	#6291	C₂³	1	4	yes	complemented
109	#6290	C₂³	1	4	yes	complemented
110	#6290	C₂³	1	8	yes	complemented
111	#6289	C₂³	1	4	yes	complemented
112	Dic₃×C₃⋊D₃	C₂³	1	4	yes	—
113	Dic₃×C₃⋊D₃	C₂³	1	8	yes	complemented
114	D₃×C₃⋊Dic₃	C₂³	1	4	yes	complemented
115	D₃×H(5,𝔽₂)	—	9	4	no	—
116	C₂×#1004	—	9	1	no	—
117	C₂³×C₃⋊D₃	—	3	4	no	—
118	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
119	C₂³×C₃×D₃	—	3	8	no	—
120	C₂²×D₃²	—	3	16	no	—
121	C₃²×#41	—	3	4	no	—
122	C₃²×#41	—	3	2	no	—
123	C₂×C₃²×D₄	—	2	4	no	—
124	C₂×C₃²×D₄	—	3	4	no	—
125	C₂×C₃²×D₄	—	3	4	no	—
126	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
127	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂×#638	—	3	4	no	—
129	C₂×#638	—	3	16	no	—
130	C₂×#638	—	3	4	no	—
131	C₂×#638	—	3	8	no	—
132	C₂×#638	—	6	16	no	—
133	C₂×#638	C₂×D₃	1	2	yes	complemented
134	#3832	—	3	4	no	—
135	#3832	—	3	2	no	—
136	Q₈×C₃⋊D₃	—	3	2	no	—
137	#3830	—	3	4	no	—
138	#3830	—	3	16	no	—
139	#3830	—	3	8	no	—
140	#3830	—	3	4	no	—
141	#3830	—	3	2	no	—
142	#3830	—	6	16	no	—
143	D₄×C₃⋊D₃	—	3	8	no	—
144	D₄×C₃⋊D₃	—	3	4	no	—
145	D₄×C₃⋊D₃	—	3	8	no	—
146	D₄×C₃⋊D₃	—	3	8	no	—
147	D₄×C₃⋊D₃	—	3	4	no	—
148	D₄×C₃⋊D₃	—	3	16	no	—
149	D₄×C₃⋊D₃	—	3	8	no	—
150	D₄×C₃⋊D₃	—	3	4	no	—
151	D₄×C₃⋊D₃	—	3	2	no	—
152	D₄×C₃⋊D₃	—	6	16	no	—
153	D₄×C₃⋊D₃	C₂×D₃	1	4	yes	complemented
154	D₄×C₃⋊D₃	C₂×D₃	1	4	yes	complemented
155	#3828	—	3	2	no	—
156	#3828	—	3	8	no	—
157	#3828	—	3	8	no	—
158	#3828	—	3	4	no	—
159	#3828	—	3	4	no	—
160	#3828	—	6	8	no	—
161	C₂×C₄⋊(C₃⋊D₃)	—	3	4	no	—
162	C₂×C₄⋊(C₃⋊D₃)	—	3	4	no	—
163	C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂×C₄×C₃⋊D₃	—	3	4	no	—
165	C₂×C₄×C₃⋊D₃	—	3	4	no	—
166	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic, complemented
167	C₂×C₃×#67	—	3	8	no	—
168	C₂×C₃×#67	C₂×D₃	1	16	yes	complemented
169	C₃×#237	C₂×D₃	1	16	yes	complemented
170	C₃×D₃×D₄	—	3	16	no	—
171	C₃×D₃×D₄	—	3	16	no	—
172	C₃×D₃×D₄	C₂×D₃	1	16	yes	complemented
173	C₃×#235	C₂×D₃	1	8	yes	complemented
174	C₂×C₃×D₁₂	—	3	4	no	—
175	C₂×C₃×C₄×D₃	—	3	4	no	—
176	#3811	—	3	32	no	—
177	D₃×#67	—	3	32	no	—
178	D₃×#67	—	3	16	no	—
179	D₃×#67	—	3	32	no	—
180	D₃×#67	—	3	32	no	—
181	D₃×#67	—	3	32	no	—
182	C₂×#626	—	3	16	no	—
183	C₂×#625	—	3	16	no	—
184	#3805	—	3	32	no	—
185	#3804	—	3	16	no	—
186	#3804	—	3	32	no	—
187	C₂×D₃×Dic₃	—	3	16	no	—
188	#3802	—	3	16	no	—
189	D₃×D₁₂	—	3	8	no	—
190	D₃×D₁₂	—	3	16	no	—
191	C₄×D₃²	—	3	16	no	—
192	#3799	—	3	8	no	—
193	#3798	—	3	16	no	—
194	#3796	—	3	16	no	—
195	#3795	—	3	8	no	—
196	#3795	—	3	16	no	—
197	D₃×Dic₆	—	3	8	no	—
198	C₂²×C₃³	—	4	2	no	—
199	C₂²×C₃³	C₂⁴	1	4	yes	—
200	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
201	C₂×C₃⋊(C₃⋊D₃)	—	4	4	no	—
202	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
203	C₂×C₃×C₃⋊D₃	—	2	8	no	—
204	C₂×C₃×C₃⋊D₃	—	2	2	no	—
205	C₂×C₃×C₃⋊D₃	—	4	2	no	—
206	C₂×C₃×C₃⋊D₃	—	4	4	no	—
207	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
208	C₂×C₃×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₃×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
210	C₂×C₃²×D₃	—	4	4	no	—
211	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
212	D₃×C₃⋊D₃	—	2	8	no	—
213	D₃×C₃⋊D₃	—	4	8	no	—
214	C₃³×C₄	C₂⁴	1	2	yes	—
215	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	—
216	C₃×C₃⋊Dic₃	C₂⁴	1	2	yes	—
217	C₃²×Dic₃	C₂⁴	1	4	yes	—
218	C₃×H(5,𝔽₂)	—	3	4	no	—
219	C₂²×C₃×D₄	—	9	1	no	—
220	C₂²×#67	—	9	4	no	—
221	#1009	—	9	8	no	—
222	#1009	—	9	16	no	—
223	D₃×#41	—	9	8	no	—
224	D₃×#41	—	9	16	no	—
225	#1004	—	9	16	no	—
226	#1004	—	9	16	no	—
227	#1004	—	9	4	no	—
228	#1004	—	9	1	no	—
229	#1004	—	9	4	no	—
230	#1004	—	9	4	no	—
231	#1004	—	9	4	no	—
232	#1004	—	9	2	no	—
233	#1004	—	18	4	no	—
234	#1004	C₃⋊D₃	1	1	yes	characteristic, direct product factor
235	C₂×#237	—	9	4	no	—
236	C₂×D₃×D₄	—	3	4	no	—
237	C₂×D₃×D₄	—	9	16	no	—
238	C₂×D₃×D₄	—	9	16	no	—
239	C₂×D₃×D₄	—	9	4	no	—
240	C₂×#235	—	9	2	no	—
241	C₂³×C₃²	—	2	8	no	—
242	C₂³×C₃²	—	3	4	no	—
243	C₂³×C₃²	C₂²×D₃	1	8	yes	complemented
244	C₂³×C₃²	C₂²×D₃	1	2	yes	complemented
245	C₂²×C₃⋊D₃	—	3	4	no	—
246	C₂²×C₃⋊D₃	—	3	4	no	—
247	C₂²×C₃⋊D₃	—	3	8	no	—
248	C₂²×C₃⋊D₃	—	3	16	no	—
249	C₂²×C₃⋊D₃	—	4	4	no	—
250	C₂²×C₃⋊D₃	—	6	16	no	—
251	C₂²×C₃⋊D₃	—	12	8	no	—
252	C₂²×C₃⋊D₃	C₂²×D₃	1	4	yes	—
253	C₂²×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
254	C₂²×C₃⋊D₃	C₂²×D₃	1	4	yes	complemented
255	C₂²×C₃⋊D₃	C₂²×D₃	1	2	yes	complemented
256	C₂²×C₃×D₃	—	3	16	no	—
257	C₂²×C₃×D₃	—	3	4	no	—
258	C₂²×C₃×D₃	—	3	16	no	—
259	C₂²×C₃×D₃	—	3	8	no	—
260	C₂²×C₃×D₃	—	12	16	no	—
261	C₂²×C₃×D₃	C₂²×D₃	1	16	yes	complemented
262	C₂×D₃²	—	3	16	no	—
263	C₂×D₃²	—	3	32	no	—
264	C₂×D₃²	—	12	32	no	—
265	C₃²×Q₈	—	3	2	no	—
266	C₃²×D₄	—	2	16	no	—
267	C₃²×D₄	—	3	8	no	—
268	C₃²×D₄	—	3	4	no	—
269	C₃²×D₄	—	3	2	no	—
270	C₃²×D₄	C₂²×D₃	1	16	yes	complemented
271	C₃²×D₄	C₂²×D₃	1	4	yes	complemented
272	C₂×C₃²×C₄	—	2	4	no	—
273	C₂×C₃²×C₄	—	3	4	no	—
274	C₂×C₃²×C₄	—	3	4	no	—
275	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	complemented
276	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic, complemented
277	#638	—	3	8	no	—
278	#638	—	3	4	no	—
279	#638	—	3	8	no	—
280	#638	—	3	4	no	—
281	#638	—	3	4	no	—
282	#638	—	3	16	no	—
283	#638	—	3	32	no	—
284	#638	—	6	16	no	—
285	#638	—	6	32	no	—
286	#638	C₂²×D₃	1	8	yes	complemented
287	C₂×C₃⋊Dic₃	—	3	4	no	—
288	C₂×C₃⋊Dic₃	—	3	4	no	—
289	C₂×C₃⋊Dic₃	—	3	16	no	—
290	C₂×C₃⋊Dic₃	—	6	16	no	—
291	C₂×C₃⋊Dic₃	C₂²×D₃	1	1	yes	characteristic, complemented
292	C₄⋊(C₃⋊D₃)	—	3	8	no	—
293	C₄⋊(C₃⋊D₃)	—	3	4	no	—
294	C₄⋊(C₃⋊D₃)	—	3	2	no	—
295	C₄⋊(C₃⋊D₃)	—	3	8	no	—
296	C₄⋊(C₃⋊D₃)	—	6	8	no	—
297	C₄⋊(C₃⋊D₃)	C₂²×D₃	1	4	yes	complemented
298	C₄×C₃⋊D₃	—	3	4	no	—
299	C₄×C₃⋊D₃	—	3	8	no	—
300	C₄×C₃⋊D₃	—	3	4	no	—
301	C₄×C₃⋊D₃	—	3	4	no	—
302	C₄×C₃⋊D₃	—	3	16	no	—
303	C₄×C₃⋊D₃	—	6	16	no	—
304	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	—
305	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	complemented
306	#634	—	3	2	no	—
307	#634	—	3	4	no	—
308	#634	—	3	8	no	—
309	#634	—	6	8	no	—
310	C₃×#67	—	3	32	no	—
311	C₃×#67	C₂²×D₃	1	16	yes	complemented
312	C₃×#67	C₂²×D₃	1	32	yes	complemented
313	C₂×C₃×Dic₃	—	3	4	no	—
314	C₂×C₃×Dic₃	C₂²×D₃	1	16	yes	complemented
315	C₃×D₁₂	—	3	16	no	—
316	C₃×D₁₂	C₂²×D₃	1	8	yes	complemented
317	C₃×C₄×D₃	—	3	8	no	—
318	C₃×C₄×D₃	—	3	8	no	—
319	C₃×C₄×D₃	C₂²×D₃	1	16	yes	complemented
320	C₃×Dic₆	C₂²×D₃	1	8	yes	complemented
321	#627	—	3	16	no	—
322	#626	—	3	16	no	—
323	#626	—	3	32	no	—
324	#626	—	3	16	no	—
325	#625	—	3	16	no	—
326	#625	—	3	32	no	—
327	#624	—	3	16	no	—
328	D₃×Dic₃	—	3	16	no	—
329	D₃×Dic₃	—	3	16	no	—
330	D₃×Dic₃	—	3	32	no	—
331	C₂×H(5,𝔽₂)	—	27	1	no	Sylow
332	C₂×C₃³	—	2	4	no	—
333	C₂×C₃³	—	2	1	no	—
334	C₂×C₃³	C₂⁵	1	1	yes	characteristic
335	C₃⋊(C₃⋊D₃)	—	2	4	no	—
336	C₃×C₃⋊D₃	—	2	4	no	—
337	C₃×C₃⋊D₃	—	2	1	no	—
338	C₃×C₃⋊D₃	H(5,𝔽₂)	1	2	yes	complemented
339	C₃²×D₃	—	2	4	no	—
340	C₂⁴×C₃	—	9	2	no	—
341	C₂³×D₃	—	3	8	no	—
342	C₂³×D₃	—	9	16	no	—
343	C₂³×D₃	—	9	4	no	—
344	C₃×#41	—	3	16	no	—
345	C₃×#41	—	3	8	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	3	16	no	—
348	C₂×C₃×D₄	—	3	16	no	—
349	C₂×C₃×D₄	—	9	2	no	—
350	C₂×C₃×D₄	—	9	4	no	—
351	C₂×C₃×D₄	—	9	4	no	—
352	C₂×C₃×D₄	—	9	1	no	—
353	C₂×C₃×D₄	D₃²	1	4	yes	complemented
354	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
355	C₂²×C₃×C₄	—	9	1	no	—
356	C₂×#67	—	3	8	no	—
357	C₂×#67	—	9	32	no	—
358	C₂×#67	—	9	16	no	—
359	C₂×#67	—	9	16	no	—
360	C₂×#67	—	9	4	no	—
361	C₂×#67	—	9	4	no	—
362	C₂×#67	—	9	4	no	—
363	C₂×#67	—	9	8	no	—
364	C₂×#67	—	9	8	no	—
365	C₂×#67	—	9	8	no	—
366	C₂×#67	—	9	4	no	—
367	C₂×#67	—	18	16	no	—
368	C₂×#67	C₂×C₃⋊D₃	1	4	yes	complemented
369	C₂²×Dic₃	—	9	4	no	—
370	#239	—	9	8	no	—
371	#239	—	9	16	no	—
372	D₃×Q₈	—	9	8	no	—
373	#237	—	9	8	no	—
374	#237	—	9	16	no	—
375	#237	—	9	32	no	—
376	#237	—	9	16	no	—
377	#237	—	9	4	no	—
378	#237	—	9	8	no	—
379	#237	—	9	8	no	—
380	#237	—	9	4	no	—
381	#237	—	9	4	no	—
382	#237	—	18	16	no	—
383	#237	C₂×C₃⋊D₃	1	4	yes	complemented
384	D₃×D₄	—	3	16	no	—
385	D₃×D₄	—	3	16	no	—
386	D₃×D₄	—	9	8	no	—
387	D₃×D₄	—	9	16	no	—
388	D₃×D₄	—	9	32	no	—
389	D₃×D₄	—	9	16	no	—
390	D₃×D₄	—	9	32	no	—
391	D₃×D₄	—	9	32	no	—
392	D₃×D₄	—	9	32	no	—
393	D₃×D₄	—	9	8	no	—
394	D₃×D₄	—	9	16	no	—
395	D₃×D₄	—	9	4	no	—
396	D₃×D₄	—	9	8	no	—
397	D₃×D₄	—	9	4	no	—
398	D₃×D₄	—	9	4	no	—
399	D₃×D₄	—	18	16	no	—
400	D₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
401	#235	—	9	16	no	—
402	#235	—	9	16	no	—
403	#235	—	9	32	no	—
404	#235	—	9	8	no	—
405	#235	—	9	2	no	—
406	#235	—	9	4	no	—
407	#235	—	9	2	no	—
408	#235	—	9	4	no	—
409	#235	—	9	2	no	—
410	#235	—	18	8	no	—
411	#235	C₂×C₃⋊D₃	1	2	yes	complemented
412	C₂×D₁₂	—	3	4	no	—
413	C₂×D₁₂	—	9	16	no	—
414	C₂×D₁₂	—	9	16	no	—
415	C₂×D₁₂	—	9	2	no	—
416	C₂×C₄×D₃	—	3	4	no	—
417	C₂×C₄×D₃	—	9	16	no	—
418	C₂×C₄×D₃	—	9	16	no	—
419	C₂×C₄×D₃	—	9	4	no	—
420	C₂×Dic₆	—	9	2	no	—
421	C₂²×C₃²	—	2	16	no	—
422	C₂²×C₃²	—	2	4	no	—
423	C₂²×C₃²	—	3	4	no	—
424	C₂²×C₃²	—	4	2	no	—
425	C₂²×C₃²	—	4	8	no	—
426	C₂²×C₃²	—	8	8	no	—
427	C₂²×C₃²	—	12	4	no	—
428	C₂²×C₃²	C₂³×D₃	1	4	yes	—
429	C₂²×C₃²	C₂³×D₃	1	16	yes	—
430	C₂²×C₃²	C₂³×D₃	1	4	yes	—
431	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
432	C₂×C₃⋊D₃	—	2	2	no	—
433	C₂×C₃⋊D₃	—	2	8	no	—
434	C₂×C₃⋊D₃	—	3	4	no	—
435	C₂×C₃⋊D₃	—	3	16	no	—
436	C₂×C₃⋊D₃	—	4	4	no	—
437	C₂×C₃⋊D₃	—	4	2	no	—
438	C₂×C₃⋊D₃	—	6	16	no	—
439	C₂×C₃⋊D₃	—	6	8	no	—
440	C₂×C₃⋊D₃	—	12	8	no	—
441	C₂×C₃⋊D₃	—	12	4	no	—
442	C₂×C₃⋊D₃	—	12	16	no	—
443	C₂×C₃⋊D₃	—	24	16	no	—
444	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
445	C₂×C₃⋊D₃	C₂³×D₃	1	1	yes	characteristic
446	C₂×C₃⋊D₃	C₂³×D₃	1	1	yes	characteristic
447	C₂×C₃×D₃	—	3	4	no	—
448	C₂×C₃×D₃	—	3	16	no	—
449	C₂×C₃×D₃	—	3	4	no	—
450	C₂×C₃×D₃	—	4	16	no	—
451	C₂×C₃×D₃	—	6	32	no	—
452	C₂×C₃×D₃	—	6	8	no	—
453	C₂×C₃×D₃	—	12	8	no	—
454	C₂×C₃×D₃	—	12	16	no	—
455	C₂×C₃×D₃	C₂³×D₃	1	16	yes	—
456	D₃²	—	6	32	no	—
457	D₃²	—	12	32	no	—
458	C₃²×C₄	—	2	8	no	—
459	C₃²×C₄	—	3	4	no	—
460	C₃²×C₄	C₂³×D₃	1	8	yes	—
461	C₃²×C₄	C₂³×D₃	1	2	yes	—
462	C₃⋊Dic₃	—	3	4	no	—
463	C₃⋊Dic₃	—	3	16	no	—
464	C₃⋊Dic₃	—	6	16	no	—
465	C₃⋊Dic₃	C₂³×D₃	1	2	yes	—
466	C₃×Dic₃	—	3	8	no	—
467	C₃×Dic₃	C₂³×D₃	1	16	yes	—
468	H(5,𝔽₂)	—	3	1	no	—
469	H(5,𝔽₂)	—	27	4	no	—
470	H(5,𝔽₂)	—	27	4	no	—
471	H(5,𝔽₂)	—	27	4	no	—
472	H(5,𝔽₂)	—	27	2	no	—
473	H(5,𝔽₂)	—	27	1	no	—
474	C₂×#41	—	27	2	no	—
475	C₂×#41	—	27	4	no	—
476	C₂²×D₄	—	9	1	no	—
477	C₂²×D₄	—	27	4	no	—
478	C₂²×D₄	—	27	4	no	—
479	C₃³	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
480	C₂³×C₃	—	2	8	no	—
481	C₂³×C₃	—	3	16	no	—
482	C₂³×C₃	—	9	4	no	—
483	C₂³×C₃	—	9	1	no	—
484	C₂³×C₃	—	9	2	no	—
485	C₂³×C₃	—	9	4	no	—
486	C₂³×C₃	—	36	4	no	—
487	C₂³×C₃	C₂×D₃²	1	8	yes	complemented
488	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	complemented
489	C₂²×D₃	—	3	4	no	—
490	C₂²×D₃	—	3	16	no	—
491	C₂²×D₃	—	3	8	no	—
492	C₂²×D₃	—	3	16	no	—
493	C₂²×D₃	—	9	16	no	—
494	C₂²×D₃	—	9	32	no	—
495	C₂²×D₃	—	9	16	no	—
496	C₂²×D₃	—	9	4	no	—
497	C₂²×D₃	—	9	4	no	—
498	C₂²×D₃	—	9	8	no	—
499	C₂²×D₃	—	12	16	no	—
500	C₂²×D₃	—	18	16	no	—
501	C₂²×D₃	—	36	8	no	—
502	C₂²×D₃	—	36	32	no	—
503	C₂²×D₃	C₂²×C₃⋊D₃	1	4	yes	complemented
504	C₃×Q₈	—	3	8	no	—
505	C₃×D₄	—	2	16	no	—
506	C₃×D₄	—	3	16	no	—
507	C₃×D₄	—	3	32	no	—
508	C₃×D₄	—	3	8	no	—
509	C₃×D₄	—	9	8	no	—
510	C₃×D₄	—	9	4	no	—
511	C₃×D₄	C₂×D₃²	1	16	yes	complemented
512	C₃×D₄	C₂²×C₃⋊D₃	1	4	yes	complemented
513	C₂×C₃×C₄	—	2	4	no	—
514	C₂×C₃×C₄	—	3	16	no	—
515	C₂×C₃×C₄	—	3	16	no	—
516	C₂×C₃×C₄	—	9	1	no	—
517	C₂×C₃×C₄	—	9	2	no	—
518	C₂×C₃×C₄	—	9	2	no	—
519	C₂×C₃×C₄	C₂×D₃²	1	4	yes	complemented
520	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
521	#67	—	3	32	no	—
522	#67	—	9	16	no	—
523	#67	—	9	16	no	—
524	#67	—	9	32	no	—
525	#67	—	9	16	no	—
526	#67	—	9	32	no	—
527	#67	—	9	4	no	—
528	#67	—	9	8	no	—
529	#67	—	9	4	no	—
530	#67	—	9	8	no	—
531	#67	—	9	4	no	—
532	#67	—	9	8	no	—
533	#67	—	18	16	no	—
534	#67	—	18	32	no	—
535	#67	C₂²×C₃⋊D₃	1	4	yes	complemented
536	#67	C₂²×C₃⋊D₃	1	8	yes	complemented
537	C₂×Dic₃	—	3	4	no	—
538	C₂×Dic₃	—	9	16	no	—
539	C₂×Dic₃	—	9	16	no	—
540	C₂×Dic₃	—	9	4	no	—
541	C₂×Dic₃	—	9	4	no	—
542	C₂×Dic₃	—	9	8	no	—
543	C₂×Dic₃	—	18	16	no	—
544	C₂×Dic₃	C₂²×C₃⋊D₃	1	4	yes	complemented
545	D₁₂	—	3	16	no	—
546	D₁₂	—	9	16	no	—
547	D₁₂	—	9	32	no	—
548	D₁₂	—	9	4	no	—
549	D₁₂	—	9	8	no	—
550	D₁₂	—	9	2	no	—
551	D₁₂	—	18	8	no	—
552	D₁₂	C₂²×C₃⋊D₃	1	2	yes	complemented
553	C₄×D₃	—	3	8	no	—
554	C₄×D₃	—	3	8	no	—
555	C₄×D₃	—	9	16	no	—
556	C₄×D₃	—	9	16	no	—
557	C₄×D₃	—	9	32	no	—
558	C₄×D₃	—	9	4	no	—
559	C₄×D₃	—	9	16	no	—
560	C₄×D₃	—	9	4	no	—
561	C₄×D₃	—	9	4	no	—
562	C₄×D₃	—	18	16	no	—
563	C₄×D₃	C₂²×C₃⋊D₃	1	4	yes	complemented
564	Dic₆	—	9	16	no	—
565	Dic₆	—	9	8	no	—
566	Dic₆	—	9	2	no	—
567	Dic₆	—	9	4	no	—
568	Dic₆	—	18	8	no	—
569	Dic₆	C₂²×C₃⋊D₃	1	2	yes	complemented
570	C₂×C₃²	—	2	1	no	—
571	C₂×C₃²	—	2	4	no	—
572	C₂×C₃²	—	2	4	no	—
573	C₂×C₃²	—	2	16	no	—
574	C₂×C₃²	—	2	4	no	—
575	C₂×C₃²	—	4	16	no	—
576	C₂×C₃²	—	4	4	no	—
577	C₂×C₃²	—	6	4	no	—
578	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
579	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
580	C₃⋊D₃	—	2	1	no	—
581	C₃⋊D₃	—	2	4	no	—
582	C₃⋊D₃	—	6	4	no	—
583	C₃⋊D₃	—	6	16	no	—
584	C₃⋊D₃	—	12	16	no	—
585	C₃⋊D₃	#1004	1	2	yes	direct product factor
586	C₃×D₃	—	2	16	no	—
587	C₃×D₃	—	3	8	no	—
588	C₃×D₃	—	6	16	no	—
589	C₃×D₃	—	6	4	no	—
590	C₂⁴	—	9	2	no	—
591	C₂⁴	—	27	4	no	—
592	#41	—	3	4	no	—
593	#41	—	3	2	no	—
594	#41	—	27	4	no	—
595	#41	—	27	8	no	—
596	#41	—	27	4	no	—
597	#41	—	27	4	no	—
598	#41	—	27	2	no	—
599	#41	—	27	2	no	—
600	#41	—	27	8	no	—
601	#41	—	27	4	no	—
602	#41	—	27	4	no	—
603	#41	—	27	2	no	—
604	C₂×Q₈	—	27	2	no	—
605	C₂×D₄	—	3	4	no	—
606	C₂×D₄	—	3	4	no	—
607	C₂×D₄	—	9	2	no	—
608	C₂×D₄	—	9	4	no	—
609	C₂×D₄	—	9	4	no	—
610	C₂×D₄	—	9	1	no	—
611	C₂×D₄	—	27	4	no	—
612	C₂×D₄	—	27	4	no	—
613	C₂×D₄	—	27	2	no	—
614	C₂×D₄	—	27	8	no	—
615	C₂×D₄	—	27	4	no	—
616	C₂×D₄	—	27	4	no	—
617	C₂×D₄	—	27	8	no	—
618	C₂×D₄	—	27	8	no	—
619	C₂×D₄	—	27	8	no	—
620	C₂×D₄	—	27	8	no	—
621	C₂×D₄	—	27	4	no	—
622	C₂×D₄	—	27	4	no	—
623	C₂×D₄	—	27	4	no	—
624	C₂×D₄	D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
625	C₂²×C₄	—	9	1	no	—
626	C₂²×C₄	—	27	4	no	—
627	C₂²×C₄	—	27	4	no	—
628	C₂²×C₃	—	2	16	no	—
629	C₂²×C₃	—	2	4	no	—
630	C₂²×C₃	—	3	16	no	—
631	C₂²×C₃	—	4	8	no	—
632	C₂²×C₃	—	4	2	no	—
633	C₂²×C₃	—	8	8	no	—
634	C₂²×C₃	—	9	1	no	—
635	C₂²×C₃	—	9	4	no	—
636	C₂²×C₃	—	9	1	no	—
637	C₂²×C₃	—	12	16	no	—
638	C₂²×C₃	—	18	8	no	—
639	C₂²×C₃	—	18	2	no	—
640	C₂²×C₃	—	36	4	no	—
641	C₂²×C₃	—	36	2	no	—
642	C₂²×C₃	C₂²×D₃²	1	4	yes	—
643	C₂²×C₃	C₂²×D₃²	1	16	yes	—
644	C₂²×C₃	C₂³×C₃⋊D₃	1	4	yes	—
645	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
646	C₂×D₃	—	3	4	no	—
647	C₂×D₃	—	3	4	no	—
648	C₂×D₃	—	3	16	no	—
649	C₂×D₃	—	4	4	no	—
650	C₂×D₃	—	6	8	no	—
651	C₂×D₃	—	6	32	no	—
652	C₂×D₃	—	9	16	no	—
653	C₂×D₃	—	9	4	no	—
654	C₂×D₃	—	12	16	no	—
655	C₂×D₃	—	12	8	no	—
656	C₂×D₃	—	18	16	no	—
657	C₂×D₃	—	18	8	no	—
658	C₂×D₃	—	18	32	no	—
659	C₂×D₃	—	36	8	no	—
660	C₂×D₃	—	36	32	no	—
661	C₂×D₃	—	36	4	no	—
662	C₂×D₃	—	36	16	no	—
663	C₂×D₃	—	72	16	no	—
664	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	—
665	C₃×C₄	—	2	8	no	—
666	C₃×C₄	—	3	16	no	—
667	C₃×C₄	—	9	2	no	—
668	C₃×C₄	C₂²×D₃²	1	8	yes	—
669	C₃×C₄	C₂³×C₃⋊D₃	1	2	yes	—
670	Dic₃	—	3	8	no	—
671	Dic₃	—	9	16	no	—
672	Dic₃	—	9	4	no	—
673	Dic₃	—	18	16	no	—
674	Dic₃	C₂³×C₃⋊D₃	1	4	yes	—
675	C₃²	—	2	4	no	—
676	C₃²	C₂×#1004	1	1	yes	characteristic, complemented
677	C₃²	D₃×H(5,𝔽₂)	1	4	yes	complemented
678	C₂³	—	3	4	no	—
679	C₂³	—	9	1	no	—
680	C₂³	—	9	4	no	—
681	C₂³	—	9	4	no	—
682	C₂³	—	9	2	no	—
683	C₂³	—	27	4	no	—
684	C₂³	—	27	8	no	—
685	C₂³	—	27	4	no	—
686	C₂³	—	36	4	no	—
687	C₂³	—	108	8	no	—
688	C₂³	C₂×D₃×C₃⋊D₃	1	2	yes	complemented
689	Q₈	—	3	2	no	—
690	Q₈	—	27	4	no	—
691	Q₈	—	27	2	no	—
692	D₄	—	3	8	no	—
693	D₄	—	3	4	no	—
694	D₄	—	3	2	no	—
695	D₄	—	9	8	no	—
696	D₄	—	9	4	no	—
697	D₄	—	27	4	no	—
698	D₄	—	27	8	no	—
699	D₄	—	27	4	no	—
700	D₄	—	27	4	no	—
701	D₄	—	27	8	no	—
702	D₄	—	27	8	no	—
703	D₄	—	27	4	no	—
704	D₄	—	27	2	no	—
705	D₄	C₂×D₃×C₃⋊D₃	1	4	yes	complemented
706	C₂×C₄	—	3	4	no	—
707	C₂×C₄	—	3	4	no	—
708	C₂×C₄	—	9	1	no	—
709	C₂×C₄	—	9	2	no	—
710	C₂×C₄	—	9	2	no	—
711	C₂×C₄	—	27	4	no	—
712	C₂×C₄	—	27	4	no	—
713	C₂×C₄	—	27	8	no	—
714	C₂×C₄	—	27	4	no	—
715	C₂×C₄	—	27	4	no	—
716	C₂×C₄	—	27	4	no	—
717	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
718	C₂×C₃	—	2	4	no	—
719	C₂×C₃	—	2	16	no	—
720	C₂×C₃	—	2	4	no	—
721	C₂×C₃	—	2	1	no	—
722	C₂×C₃	—	2	4	no	—
723	C₂×C₃	—	4	16	no	—
724	C₂×C₃	—	4	4	no	—
725	C₂×C₃	—	6	16	no	—
726	C₂×C₃	—	9	2	no	—
727	C₂×C₃	—	18	4	no	—
728	C₂×C₃	—	18	1	no	—
729	C₂×C₃	C₂³×D₃²	1	4	yes	—
730	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
731	D₃	—	2	4	no	—
732	D₃	—	3	8	no	—
733	D₃	—	6	4	no	—
734	D₃	—	6	16	no	—
735	D₃	—	18	16	no	—
736	D₃	—	18	4	no	—
737	D₃	—	36	16	no	—
738	C₂²	—	3	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	9	1	no	—
741	C₂²	—	9	1	no	—
742	C₂²	—	9	4	no	—
743	C₂²	—	12	4	no	—
744	C₂²	—	18	2	no	—
745	C₂²	—	18	8	no	—
746	C₂²	—	27	4	no	—
747	C₂²	—	36	2	no	—
748	C₂²	—	36	4	no	—
749	C₂²	—	54	8	no	—
750	C₂²	—	108	4	no	—
751	C₂²	—	108	8	no	—
752	C₂²	C₂²×D₃×C₃⋊D₃	1	4	yes	—
753	C₂²	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
754	C₄	—	3	4	no	—
755	C₄	—	9	2	no	—
756	C₄	—	27	4	no	—
757	C₄	C₂²×D₃×C₃⋊D₃	1	2	yes	—
758	C₃	—	2	4	no	—
759	C₃	D₃×#1004	1	4	yes	complemented
760	C₃	C₃⋊D₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
761	C₂	—	2	1	no	—
762	C₂	—	2	4	no	—
763	C₂	—	6	4	no	—
764	C₂	—	9	2	no	—
765	C₂	—	18	1	no	—
766	C₂	—	18	4	no	—
767	C₂	—	54	4	no	—
768	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₃×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃³	C₂⁵
Fitting	C₂×C₃³×D₄	C₂²
hypercenter	C₂×D₄	D₃×C₃⋊D₃
hypocenter	C₃³	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #11724679	C₂	semidirect
2. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
3. C₃²×#1004	C₂	semidirect
4. #11724611	C₂	semidirect
5. C₂×C₃⋊D₃×#67	C₂	semidirect
6. #11724589	C₂	semidirect
7. #11724587	C₂	semidirect
8. C₃⋊D₃×#237	C₂	semidirect
9. D₃×D₄×C₃⋊D₃	C₂	semidirect
10. #11724580	C₂	semidirect
11. C₃⋊D₃×#235	C₂	semidirect
14. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
15. C₂²×D₃×C₃⋊D₃	C₂²	semidirect
16. C₂×C₃³×D₄	C₂²	semidirect
17. C₂×#6312	C₂²	semidirect
18. #89078	C₂²	semidirect
19. D₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
20. #89076	C₂²	semidirect
21. C₂×C₃×#638	C₂²	semidirect
22. C₃×D₄×C₃⋊D₃	C₂²	semidirect
23. C₃×D₄×C₃⋊D₃	C₂²	semidirect
24. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
25. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
26. C₂×C₃²×#67	C₂²	semidirect
27. C₃²×#237	C₂²	semidirect
28. C₃²×D₃×D₄	C₂²	semidirect
29. C₃²×#235	C₂²	semidirect
30. #89039	C₂²	semidirect
31. C₃⋊D₃×#67	C₂²	semidirect
32. C₃⋊D₃×#67	C₂²	semidirect
33. C₃⋊D₃×#67	C₂²	semidirect
34. C₃⋊D₃×#67	C₂²	semidirect
35. D₃×#638	C₂²	semidirect
36. C₂×#6292	C₂²	semidirect
37. C₂×#6290	C₂²	semidirect
38. #89031	C₂²	semidirect
39. C₂×Dic₃×C₃⋊D₃	C₂²	semidirect
40. #89029	C₂²	semidirect
41. #89028	C₂²	semidirect
42. #89026	C₂²	semidirect
43. C₃⋊D₃×D₁₂	C₂²	semidirect
44. D₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
45. C₄×D₃×C₃⋊D₃	C₂²	semidirect
46. #89021	C₂²	semidirect
47. #89020	C₂²	semidirect
48. #89018	C₂²	semidirect
49. #89017	C₂²	semidirect
50. C₃⋊D₃×Dic₆	C₂²	semidirect
51. #89014	C₂²	semidirect
64. C₂×D₄×C₃⋊D₃	D₃	semidirect
65. C₃×#1004	D₃	semidirect
75. C₂³×C₃³	C₂³	semidirect
76. C₂²×C₃⋊(C₃⋊D₃)	C₂³	semidirect
80. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
81. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
82. C₂²×C₃²×D₃	C₂³	semidirect
85. C₂×D₃×C₃⋊D₃	C₂³	semidirect
86. C₃³×D₄	C₂³	semidirect
87. C₂×C₃³×C₄	C₂³	semidirect
88. #6312	C₂³	semidirect
89. #6312	C₂³	semidirect
90. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
91. C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	semidirect
92. C₄×C₃⋊(C₃⋊D₃)	C₂³	semidirect
93. #6308	C₂³	semidirect
94. C₃×#638	C₂³	semidirect
95. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
96. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
98. C₃×C₄×C₃⋊D₃	C₂³	semidirect
99. C₃²×#67	C₂³	semidirect
100. C₃²×#67	C₂³	semidirect
101. C₂×C₃²×Dic₃	C₂³	semidirect
102. C₃²×D₁₂	C₂³	semidirect
103. C₃²×C₄×D₃	C₂³	semidirect
104. C₃²×Dic₆	C₂³	semidirect
105. #6293	C₂³	semidirect
106. #6292	C₂³	semidirect
107. #6292	C₂³	semidirect
108. #6291	C₂³	semidirect
109. #6290	C₂³	semidirect
110. #6290	C₂³	semidirect
111. #6289	C₂³	semidirect
113. Dic₃×C₃⋊D₃	C₂³	semidirect
114. D₃×C₃⋊Dic₃	C₂³	semidirect
118. C₂³×C₃⋊D₃	C₂×D₃	semidirect
126. C₂×C₃²×D₄	C₂×D₃	semidirect
127. C₂×C₃²×D₄	C₂×D₃	semidirect
133. C₂×#638	C₂×D₃	semidirect
153. D₄×C₃⋊D₃	C₂×D₃	semidirect
154. D₄×C₃⋊D₃	C₂×D₃	semidirect
163. C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	semidirect
166. C₂×C₄×C₃⋊D₃	C₂×D₃	semidirect
168. C₂×C₃×#67	C₂×D₃	semidirect
169. C₃×#237	C₂×D₃	semidirect
172. C₃×D₃×D₄	C₂×D₃	semidirect
173. C₃×#235	C₂×D₃	semidirect
234. #1004	C₃⋊D₃	direct (N × H)
243. C₂³×C₃²	C₂²×D₃	semidirect
244. C₂³×C₃²	C₂²×D₃	semidirect
254. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
255. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
261. C₂²×C₃×D₃	C₂²×D₃	semidirect
270. C₃²×D₄	C₂²×D₃	semidirect
271. C₃²×D₄	C₂²×D₃	semidirect
275. C₂×C₃²×C₄	C₂²×D₃	semidirect
276. C₂×C₃²×C₄	C₂²×D₃	semidirect
286. #638	C₂²×D₃	semidirect
291. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
297. C₄⋊(C₃⋊D₃)	C₂²×D₃	semidirect
305. C₄×C₃⋊D₃	C₂²×D₃	semidirect
311. C₃×#67	C₂²×D₃	semidirect
312. C₃×#67	C₂²×D₃	semidirect
314. C₂×C₃×Dic₃	C₂²×D₃	semidirect
316. C₃×D₁₂	C₂²×D₃	semidirect
319. C₃×C₄×D₃	C₂²×D₃	semidirect
320. C₃×Dic₆	C₂²×D₃	semidirect
338. C₃×C₃⋊D₃	H(5,𝔽₂)	semidirect
353. C₂×C₃×D₄	D₃²	semidirect
354. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
368. C₂×#67	C₂×C₃⋊D₃	semidirect
383. #237	C₂×C₃⋊D₃	semidirect
400. D₃×D₄	C₂×C₃⋊D₃	semidirect
411. #235	C₂×C₃⋊D₃	semidirect
479. C₃³	C₂×H(5,𝔽₂)	semidirect
487. C₂³×C₃	C₂×D₃²	semidirect
488. C₂³×C₃	C₂²×C₃⋊D₃	semidirect
503. C₂²×D₃	C₂²×C₃⋊D₃	semidirect
511. C₃×D₄	C₂×D₃²	semidirect
512. C₃×D₄	C₂²×C₃⋊D₃	semidirect
519. C₂×C₃×C₄	C₂×D₃²	semidirect
520. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
535. #67	C₂²×C₃⋊D₃	semidirect
536. #67	C₂²×C₃⋊D₃	semidirect
544. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
552. D₁₂	C₂²×C₃⋊D₃	semidirect
563. C₄×D₃	C₂²×C₃⋊D₃	semidirect
569. Dic₆	C₂²×C₃⋊D₃	semidirect
585. C₃⋊D₃	#1004	direct (N × H)
624. C₂×D₄	D₃×C₃⋊D₃	semidirect
676. C₃²	C₂×#1004	semidirect
677. C₃²	D₃×H(5,𝔽₂)	semidirect
688. C₂³	C₂×D₃×C₃⋊D₃	semidirect
705. D₄	C₂×D₃×C₃⋊D₃	semidirect
717. C₂×C₄	C₂×D₃×C₃⋊D₃	semidirect
759. C₃	D₃×#1004	semidirect
760. C₃	C₃⋊D₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#11724679	2
C₂×C₃×D₄×C₃⋊D₃	2
C₃²×#1004	2
#11724611	2
C₂×C₃⋊D₃×#67	2
#11724589	2
#11724587	2
C₃⋊D₃×#237	2
D₃×D₄×C₃⋊D₃	2
#11724580	2
C₃⋊D₃×#235	2
C₃⋊D₃×H(5,𝔽₂)	3
D₃×#1004	3

Subgroups — C3⋊D3×#1004 #13181613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#1004 #13181613