Subgroups — C₃×#79654 #11870862

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5580	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5169	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5165	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4863	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4819	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4811	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4773	C₂	1	1	yes	maximal, characteristic
13	C₃×#4766	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4685	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3105	—	3	1	no	maximal
17	#79654	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	—	2	1	no	—
20	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
21	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₃×#947	C₂²	1	1	yes	characteristic, complemented
24	C₃×#946	C₂²	1	1	yes	characteristic
25	C₂×C₃×#215	C₂²	1	1	yes	characteristic
26	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₃×#213	C₂²	1	1	yes	characteristic
28	C₃×C₄×#67	—	2	1	no	—
29	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
30	C₃×#898	—	2	1	no	—
31	C₃×#895	C₂²	1	1	yes	characteristic
32	C₃×#894	—	2	1	no	—
33	C₃×#893	C₂²	1	1	yes	characteristic
34	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×#890	C₂²	1	1	yes	characteristic, complemented
36	C₃×#67⋊C₄	—	2	1	no	—
37	C₃×D₃×C₂²⋊C₄	—	2	1	no	—
38	C₃×C₄×D₁₂	—	2	1	no	—
39	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
40	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
41	C₃×#872	—	2	1	no	—
42	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
43	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
44	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
45	C₃²×#102	C₂²	1	1	yes	characteristic
46	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×#835	C₂²	1	1	yes	characteristic, complemented
48	C₃×#832	C₂²	1	1	yes	characteristic
49	C₃×#821	C₂²	1	1	yes	characteristic
50	C₃×#821	C₂²	1	1	yes	characteristic, complemented
51	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
52	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
53	C₃×#818	C₂²	1	1	yes	characteristic, complemented
54	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×#809	C₂²	1	1	yes	characteristic
57	C₃×#809	C₂²	1	1	yes	characteristic, complemented
58	C₃×#808	C₂²	1	1	yes	characteristic, complemented
59	C₃×#807	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×#529	—	3	1	no	—
62	C₂×C₃×C₄×D₄	—	3	1	no	—
63	#5580	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
65	C₃×#484	—	3	1	no	—
66	C₃×#481	—	3	1	no	—
67	C₃×#478	—	3	1	no	—
68	C₃×#478	—	3	1	no	—
69	C₃×#463	—	3	1	no	—
70	C₃×#463	—	3	1	no	—
71	C₃×#450	—	3	1	no	—
72	C₃×#447	—	3	1	no	—
73	C₃×C₄×SD₁₆	—	2	1	no	—
74	C₃×C₄×SD₁₆	—	3	1	no	—
75	C₃×C₄×SD₁₆	D₃	1	1	yes	characteristic, complemented
76	C₃×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
77	C₃×C₄×D₈	—	3	1	no	—
78	C₃×C₄×D₈	—	3	1	no	—
79	C₃×#431	—	3	1	no	—
80	#5169	C₂×C₃	1	1	yes	characteristic, complemented
81	#5165	C₂×C₃	1	1	yes	characteristic, complemented
82	C₄×#215	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×#213	C₂×C₃	1	1	yes	characteristic, complemented
84	#4871	C₂×C₃	1	1	yes	characteristic, complemented
85	#4863	C₂×C₃	1	1	yes	characteristic, complemented
86	#4819	C₂×C₃	1	1	yes	characteristic, complemented
87	#4811	C₂×C₃	1	1	yes	characteristic, complemented
88	#4773	C₂×C₃	1	1	yes	characteristic
89	#4766	C₂×C₃	1	1	yes	characteristic, complemented
90	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
91	#4685	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂³×C₃×D₃	—	2	1	no	—
93	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃²×C₄	—	2	1	no	—
96	C₂×C₃×#67	—	2	1	no	—
97	C₂²×C₃×Dic₃	—	2	1	no	—
98	C₃×D₃×D₄	—	2	2	no	—
99	C₃×D₃×D₄	—	2	2	no	—
100	C₂×C₃×D₁₂	—	2	1	no	—
101	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
102	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄×D₃	—	2	1	no	—
104	C₂×C₃×C₄×D₃	—	2	1	no	—
105	C₂×C₃×C₄×D₃	—	2	1	no	—
106	C₂×C₃×C₄×D₃	—	2	1	no	—
107	C₂×C₃×C₄×D₃	—	4	4	no	—
108	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
111	C₃²×SD₁₆	—	2	2	no	—
112	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	—	2	1	no	—
115	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃²×C₂²⋊C₄	—	2	1	no	—
118	C₃²×C₄²	—	2	1	no	—
119	C₃²×C₄²	C₂³	1	1	yes	characteristic
120	C₃×#217	—	2	1	no	—
121	C₃×#215	—	2	2	no	—
122	C₃×#213	—	2	2	no	—
123	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
125	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
126	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
129	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
130	C₃×C₄⋊Dic₃	—	2	1	no	—
131	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
133	C₃×Dic₃⋊C₄	—	2	1	no	—
134	C₃×Dic₃⋊C₄	—	2	1	no	—
135	C₃×Dic₃⋊C₄	—	2	1	no	—
136	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
137	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
138	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
141	C₃×D₂₄	—	2	2	no	—
142	#3105	—	3	1	no	Sylow
143	C₂²×C₃×D₄	—	3	1	no	—
144	C₂³×C₃×C₄	—	6	1	no	—
145	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₄×D₃	—	2	1	no	—
147	C₂×C₃×SD₁₆	—	2	1	no	—
148	C₂×C₃×SD₁₆	—	3	1	no	—
149	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
150	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×D₈	—	3	1	no	—
152	C₂×C₃×D₈	—	3	1	no	—
153	C₃×#126	—	6	1	no	—
154	C₃×#125	—	3	1	no	—
155	C₃×#124	—	3	1	no	—
156	C₃×#123	—	6	1	no	—
157	C₃×C₂²⋊Q₈	—	3	1	no	—
158	C₃×#121	—	3	1	no	—
159	C₃×C₄×Q₈	—	2	1	no	—
160	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
161	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₃×C₄×D₄	—	2	1	no	—
163	C₃×C₄×D₄	—	3	1	no	—
164	C₃×C₄×D₄	—	3	1	no	—
165	C₃×C₄×D₄	—	3	1	no	—
166	C₃×C₄×D₄	—	3	1	no	—
167	C₃×C₄×D₄	—	6	1	no	—
168	C₃×C₄×D₄	—	6	1	no	—
169	C₃×C₄×D₄	—	6	1	no	—
170	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
171	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₃×#117	—	6	1	no	—
173	C₂×C₃×C₄⋊C₄	—	3	1	no	—
174	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
175	C₂×C₃×C₄²	—	3	1	no	—
176	#947	C₂²×C₃	1	1	yes	characteristic, complemented
177	#946	C₂²×C₃	1	1	yes	characteristic
178	C₂×#215	C₂²×C₃	1	1	yes	characteristic
179	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
180	C₂×#213	C₂²×C₃	1	1	yes	characteristic
181	C₄×#67	—	2	1	no	—
182	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
183	#898	—	2	1	no	—
184	#895	C₂²×C₃	1	1	yes	characteristic
185	#894	—	2	1	no	—
186	#893	C₂²×C₃	1	1	yes	characteristic
187	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	#890	C₂²×C₃	1	1	yes	characteristic, complemented
189	#67⋊C₄	—	2	1	no	—
190	D₃×C₂²⋊C₄	—	2	1	no	—
191	C₄×D₁₂	—	2	1	no	—
192	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
193	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
194	#872	—	2	1	no	—
195	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
196	C₃×#107	—	3	1	no	—
197	C₃×#107	—	3	1	no	—
198	C₃×#106	—	2	1	no	—
199	C₃×#106	—	3	1	no	—
200	C₃×#106	C₂×D₃	1	1	yes	characteristic, complemented
201	C₃×#106	C₂²×C₃	1	1	yes	characteristic, complemented
202	C₃×C₄⋊C₈	—	3	1	no	—
203	C₃×C₄⋊C₈	—	3	1	no	—
204	C₃×#103	—	2	1	no	—
205	C₃×#103	—	3	1	no	—
206	C₃×#103	C₂×D₃	1	1	yes	characteristic, complemented
207	C₃×#103	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₃×#102	—	2	1	no	—
209	C₃×#102	—	3	1	no	—
210	C₃×#102	—	3	1	no	—
211	C₃×#102	—	3	1	no	—
212	C₃×#102	—	3	1	no	—
213	C₃×#102	—	3	1	no	—
214	C₃×#102	C₂×D₃	1	1	yes	characteristic
215	C₃×#102	C₂²×C₃	1	1	yes	characteristic
216	C₃×C₂²⋊C₈	—	3	1	no	—
217	C₃×C₂²⋊C₈	—	3	1	no	—
218	C₃×C₄×C₈	—	2	1	no	—
219	C₃×C₄×C₈	—	3	1	no	—
220	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
221	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
222	#835	C₂²×C₃	1	1	yes	characteristic, complemented
223	#832	C₂²×C₃	1	1	yes	characteristic
224	#821	C₂²×C₃	1	1	yes	characteristic
225	#821	C₂²×C₃	1	1	yes	characteristic, complemented
226	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
227	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
228	#818	C₂²×C₃	1	1	yes	characteristic, complemented
229	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
230	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
231	#809	C₂²×C₃	1	1	yes	characteristic
232	#809	C₂²×C₃	1	1	yes	characteristic, complemented
233	#808	C₂²×C₃	1	1	yes	characteristic, complemented
234	#807	C₂²×C₃	1	1	yes	characteristic, complemented
235	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₂³×C₃²	—	2	1	no	—
237	C₂²×C₃×D₃	—	2	4	no	—
238	C₂²×C₃×D₃	—	2	1	no	—
239	C₂²×C₃×D₃	—	2	1	no	—
240	C₂²×C₃×D₃	—	4	2	no	—
241	C₂²×C₃×D₃	—	4	2	no	—
242	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
243	C₃²×Q₈	—	2	1	no	—
244	C₃²×Q₈	—	2	1	no	—
245	C₃²×D₄	—	2	1	no	—
246	C₃²×D₄	#41	1	2	yes	—
247	C₂×C₃²×C₄	—	2	1	no	—
248	C₂×C₃²×C₄	—	2	1	no	—
249	C₂×C₃²×C₄	—	2	1	no	—
250	C₂×C₃²×C₄	—	4	2	no	—
251	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
253	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
254	C₃×#67	—	2	4	no	—
255	C₂×C₃×Dic₃	—	2	1	no	—
256	C₂×C₃×Dic₃	—	2	1	no	—
257	C₂×C₃×Dic₃	—	4	2	no	—
258	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
259	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
260	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
261	C₃×D₁₂	—	2	1	no	—
262	C₃×D₁₂	—	2	1	no	—
263	C₃×D₁₂	—	2	1	no	—
264	C₃×D₁₂	—	4	2	no	—
265	C₃×D₁₂	#41	1	2	yes	—
266	C₃×C₄×D₃	—	2	2	no	—
267	C₃×C₄×D₃	—	2	2	no	—
268	C₃×C₄×D₃	—	2	1	no	—
269	C₃×C₄×D₃	—	2	1	no	—
270	C₃×C₄×D₃	—	4	2	no	—
271	C₃×C₄×D₃	—	4	2	no	—
272	C₃×C₄×D₃	—	4	2	no	—
273	C₃×C₄×D₃	—	4	2	no	—
274	C₃²×C₈	—	2	1	no	—
275	C₃²×C₈	—	2	1	no	—
276	C₃×C₃⋊C₈	—	2	1	no	—
277	C₃×C₃⋊C₈	—	2	1	no	—
278	#529	—	3	1	no	—
279	C₂×C₄×D₄	—	3	1	no	—
280	#484	—	3	1	no	—
281	#481	—	3	1	no	—
282	#478	—	3	1	no	—
283	#478	—	3	1	no	—
284	#463	—	3	1	no	—
285	#463	—	3	1	no	—
286	#450	—	3	1	no	—
287	#447	—	3	1	no	—
288	C₄×SD₁₆	—	3	1	no	—
289	C₄×SD₁₆	C₃×D₃	1	1	yes	characteristic, complemented
290	C₄×D₈	—	3	1	no	—
291	C₄×D₈	—	3	1	no	—
292	#431	—	3	1	no	—
293	C₂⁴×C₃	—	6	1	no	—
294	C₂³×D₃	—	2	1	no	—
295	C₂×C₃×Q₈	—	2	1	no	—
296	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	3	1	no	—
300	C₂×C₃×D₄	—	3	1	no	—
301	C₂×C₃×D₄	—	6	1	no	—
302	C₂×C₃×D₄	—	6	1	no	—
303	C₂×C₃×D₄	—	6	2	no	—
304	C₂×C₃×D₄	—	6	2	no	—
305	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
307	C₂²×C₃×C₄	—	2	1	no	—
308	C₂²×C₃×C₄	—	2	1	no	—
309	C₂²×C₃×C₄	—	3	1	no	—
310	C₂²×C₃×C₄	—	3	1	no	—
311	C₂²×C₃×C₄	—	3	1	no	—
312	C₂²×C₃×C₄	—	4	1	no	—
313	C₂²×C₃×C₄	—	6	1	no	—
314	C₂²×C₃×C₄	—	6	1	no	—
315	C₂²×C₃×C₄	—	6	1	no	—
316	C₂²×C₃×C₄	—	6	1	no	—
317	C₂²×C₃×C₄	—	6	1	no	—
318	C₂²×C₃×C₄	—	12	4	no	—
319	C₂×#67	—	2	1	no	—
320	C₂²×Dic₃	—	2	1	no	—
321	D₃×D₄	—	2	2	no	—
322	D₃×D₄	—	2	2	no	—
323	C₂×D₁₂	—	2	1	no	—
324	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
325	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
326	C₂×C₄×D₃	—	2	1	no	—
327	C₂×C₄×D₃	—	2	1	no	—
328	C₂×C₄×D₃	—	2	1	no	—
329	C₂×C₄×D₃	—	2	1	no	—
330	C₂×C₄×D₃	—	4	4	no	—
331	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
332	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
333	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
334	C₃×SD₁₆	—	2	4	no	—
335	C₃×SD₁₆	—	2	2	no	—
336	C₃×SD₁₆	—	2	2	no	—
337	C₃×SD₁₆	—	6	2	no	—
338	C₃×D₈	—	6	2	no	—
339	C₃×D₈	—	6	2	no	—
340	C₂×C₃×C₈	—	2	1	no	—
341	C₂×C₃×C₈	—	2	1	no	—
342	C₂×C₃×C₈	—	3	1	no	—
343	C₂×C₃×C₈	—	3	1	no	—
344	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
345	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
346	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
347	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
348	C₃×C₄⋊C₄	—	2	1	no	—
349	C₃×C₄⋊C₄	—	2	1	no	—
350	C₃×C₄⋊C₄	—	2	1	no	—
351	C₃×C₄⋊C₄	—	2	1	no	—
352	C₃×C₄⋊C₄	—	3	1	no	—
353	C₃×C₄⋊C₄	—	3	1	no	—
354	C₃×C₄⋊C₄	—	4	1	no	—
355	C₃×C₄⋊C₄	—	6	1	no	—
356	C₃×C₄⋊C₄	—	6	1	no	—
357	C₃×C₄⋊C₄	—	6	1	no	—
358	C₃×C₄⋊C₄	—	6	1	no	—
359	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
360	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
361	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
362	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
363	C₃×C₂²⋊C₄	—	2	1	no	—
364	C₃×C₂²⋊C₄	—	2	1	no	—
365	C₃×C₂²⋊C₄	—	4	1	no	—
366	C₃×C₂²⋊C₄	—	6	1	no	—
367	C₃×C₂²⋊C₄	—	6	1	no	—
368	C₃×C₂²⋊C₄	—	6	1	no	—
369	C₃×C₂²⋊C₄	—	6	1	no	—
370	C₃×C₂²⋊C₄	—	6	1	no	—
371	C₃×C₂²⋊C₄	—	6	1	no	—
372	C₃×C₂²⋊C₄	—	6	1	no	—
373	C₃×C₂²⋊C₄	—	6	1	no	—
374	C₃×C₄²	—	2	1	no	—
375	C₃×C₄²	—	2	1	no	—
376	C₃×C₄²	—	2	1	no	—
377	C₃×C₄²	—	3	1	no	—
378	C₃×C₄²	—	3	1	no	—
379	C₃×C₄²	—	3	1	no	—
380	C₃×C₄²	—	4	1	no	—
381	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
382	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
383	#217	—	2	1	no	—
384	#215	—	2	2	no	—
385	#213	—	2	2	no	—
386	(C₂×D₃)⋊C₄	—	2	1	no	—
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	(C₂×D₃)⋊C₄	—	2	1	no	—
389	(C₂×D₃)⋊C₄	—	2	1	no	—
390	(C₂×D₃)⋊C₄	—	2	1	no	—
391	(C₂×D₃)⋊C₄	—	2	1	no	—
392	(C₂×D₃)⋊C₄	—	2	1	no	—
393	C₄⋊Dic₃	—	2	1	no	—
394	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
395	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	—	2	1	no	—
399	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
400	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
401	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
404	D₂₄	—	2	2	no	—
405	C₂²×C₃²	—	2	2	no	—
406	C₂²×C₃²	—	4	1	no	—
407	C₂²×C₃²	—	4	1	no	—
408	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₃×D₃	—	2	1	no	—
410	C₂×C₃×D₃	—	2	1	no	—
411	C₂×C₃×D₃	—	2	2	no	—
412	C₂×C₃×D₃	—	4	8	no	—
413	C₂×C₃×D₃	—	4	1	no	—
414	C₂×C₃×D₃	—	4	1	no	—
415	C₂×C₃×D₃	—	4	1	no	—
416	C₂×C₃×D₃	—	4	1	no	—
417	C₂×C₃×D₃	—	4	1	no	—
418	C₂×C₃×D₃	#135	1	2	yes	—
419	C₃²×C₄	—	2	1	no	—
420	C₃²×C₄	—	4	1	no	—
421	C₃²×C₄	—	4	1	no	—
422	C₃²×C₄	—	4	1	no	—
423	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
424	C₃²×C₄	C₂×#41	1	1	yes	characteristic
425	C₃²×C₄	C₂×#41	1	1	yes	characteristic
426	C₃×Dic₃	—	2	1	no	—
427	C₃×Dic₃	—	2	1	no	—
428	C₃×Dic₃	—	2	1	no	—
429	C₃×Dic₃	—	4	1	no	—
430	C₃×Dic₃	—	4	1	no	—
431	C₂²×D₄	—	3	1	no	—
432	C₂³×C₄	—	6	1	no	—
433	C₂×SD₁₆	—	3	1	no	—
434	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
435	C₂×D₈	—	3	1	no	—
436	C₂×D₈	—	3	1	no	—
437	#126	—	6	1	no	—
438	#125	—	3	1	no	—
439	#124	—	3	1	no	—
440	#123	—	6	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	#121	—	3	1	no	—
443	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
444	C₄×D₄	—	3	1	no	—
445	C₄×D₄	—	3	1	no	—
446	C₄×D₄	—	3	1	no	—
447	C₄×D₄	—	3	1	no	—
448	C₄×D₄	—	6	1	no	—
449	C₄×D₄	—	6	1	no	—
450	C₄×D₄	—	6	1	no	—
451	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
452	#117	—	6	1	no	—
453	C₂×C₄⋊C₄	—	3	1	no	—
454	C₂×C₂²⋊C₄	—	6	1	no	—
455	C₂×C₄²	—	3	1	no	—
456	#107	—	3	1	no	—
457	#107	—	3	1	no	—
458	#106	—	3	1	no	—
459	#106	C₂×C₃×D₃	1	1	yes	characteristic, complemented
460	C₄⋊C₈	—	3	1	no	—
461	C₄⋊C₈	—	3	1	no	—
462	#103	—	3	1	no	—
463	#103	C₂×C₃×D₃	1	1	yes	characteristic, complemented
464	#102	—	3	1	no	—
465	#102	—	3	1	no	—
466	#102	—	3	1	no	—
467	#102	—	3	1	no	—
468	#102	—	3	1	no	—
469	#102	C₂×C₃×D₃	1	1	yes	characteristic
470	C₂²⋊C₈	—	3	1	no	—
471	C₂²⋊C₈	—	3	1	no	—
472	C₄×C₈	—	3	1	no	—
473	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	3	1	no	—
477	C₂³×C₃	—	4	1	no	—
478	C₂³×C₃	—	6	4	no	—
479	C₂³×C₃	—	6	1	no	—
480	C₂³×C₃	—	6	1	no	—
481	C₂³×C₃	—	12	2	no	—
482	C₂³×C₃	—	12	2	no	—
483	C₂²×D₃	—	2	4	no	—
484	C₂²×D₃	—	2	1	no	—
485	C₂²×D₃	—	2	1	no	—
486	C₂²×D₃	—	4	2	no	—
487	C₂²×D₃	—	4	2	no	—
488	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
489	C₃×Q₈	—	2	2	no	—
490	C₃×Q₈	—	2	1	no	—
491	C₃×Q₈	—	2	1	no	—
492	C₃×Q₈	—	2	1	no	—
493	C₃×Q₈	—	2	1	no	—
494	C₃×Q₈	—	4	1	no	—
495	C₃×D₄	—	2	1	no	—
496	C₃×D₄	—	2	1	no	—
497	C₃×D₄	—	2	2	no	—
498	C₃×D₄	—	3	2	no	—
499	C₃×D₄	—	4	1	no	—
500	C₃×D₄	—	6	4	no	—
501	C₃×D₄	—	6	1	no	—
502	C₃×D₄	—	6	1	no	—
503	C₃×D₄	—	6	1	no	—
504	C₃×D₄	—	12	2	no	—
505	C₃×D₄	#235	1	2	yes	—
506	C₃×D₄	C₃×#41	1	2	yes	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	3	1	no	—
517	C₂×C₃×C₄	—	3	1	no	—
518	C₂×C₃×C₄	—	3	1	no	—
519	C₂×C₃×C₄	—	4	1	no	—
520	C₂×C₃×C₄	—	4	1	no	—
521	C₂×C₃×C₄	—	4	1	no	—
522	C₂×C₃×C₄	—	4	2	no	—
523	C₂×C₃×C₄	—	4	2	no	—
524	C₂×C₃×C₄	—	6	2	no	—
525	C₂×C₃×C₄	—	6	2	no	—
526	C₂×C₃×C₄	—	6	1	no	—
527	C₂×C₃×C₄	—	6	1	no	—
528	C₂×C₃×C₄	—	6	1	no	—
529	C₂×C₃×C₄	—	6	1	no	—
530	C₂×C₃×C₄	—	8	2	no	—
531	C₂×C₃×C₄	—	12	2	no	—
532	C₂×C₃×C₄	—	12	2	no	—
533	C₂×C₃×C₄	—	12	2	no	—
534	C₂×C₃×C₄	—	12	2	no	—
535	C₂×C₃×C₄	—	12	2	no	—
536	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
537	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
538	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
542	#67	—	2	4	no	—
543	C₂×Dic₃	—	2	1	no	—
544	C₂×Dic₃	—	2	1	no	—
545	C₂×Dic₃	—	4	2	no	—
546	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
547	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
548	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
549	D₁₂	—	2	1	no	—
550	D₁₂	—	2	1	no	—
551	D₁₂	—	2	1	no	—
552	D₁₂	—	4	2	no	—
553	D₁₂	C₃×#41	1	2	yes	—
554	C₄×D₃	—	2	2	no	—
555	C₄×D₃	—	2	2	no	—
556	C₄×D₃	—	2	1	no	—
557	C₄×D₃	—	2	1	no	—
558	C₄×D₃	—	4	2	no	—
559	C₄×D₃	—	4	2	no	—
560	C₄×D₃	—	4	2	no	—
561	C₄×D₃	—	4	2	no	—
562	C₃×C₈	—	2	2	no	—
563	C₃×C₈	—	2	1	no	—
564	C₃×C₈	—	2	1	no	—
565	C₃×C₈	—	2	1	no	—
566	C₃×C₈	—	2	1	no	—
567	C₃×C₈	—	4	1	no	—
568	C₃×C₈	—	6	1	no	—
569	C₃×C₈	—	6	1	no	—
570	C₃⋊C₈	—	2	1	no	—
571	C₃⋊C₈	—	2	1	no	—
572	C₂×C₃²	—	4	2	no	—
573	C₂×C₃²	#525	1	1	yes	characteristic
574	C₂×C₃²	C₂×#135	1	1	yes	characteristic
575	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
576	C₃×D₃	—	2	2	no	—
577	C₃×D₃	—	4	2	no	—
578	C₃×D₃	—	8	1	no	—
579	C₂⁴	—	6	1	no	—
580	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
581	C₂×D₄	—	3	1	no	—
582	C₂×D₄	—	3	1	no	—
583	C₂×D₄	—	6	1	no	—
584	C₂×D₄	—	6	1	no	—
585	C₂×D₄	—	6	2	no	—
586	C₂×D₄	—	6	2	no	—
587	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	3	1	no	—
590	C₂²×C₄	—	3	1	no	—
591	C₂²×C₄	—	3	1	no	—
592	C₂²×C₄	—	6	1	no	—
593	C₂²×C₄	—	6	1	no	—
594	C₂²×C₄	—	6	1	no	—
595	C₂²×C₄	—	6	1	no	—
596	C₂²×C₄	—	6	1	no	—
597	C₂²×C₄	—	12	4	no	—
598	SD₁₆	—	2	2	no	—
599	SD₁₆	—	6	2	no	—
600	D₈	—	6	2	no	—
601	D₈	—	6	2	no	—
602	C₂×C₈	—	3	1	no	—
603	C₂×C₈	—	3	1	no	—
604	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
605	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	3	1	no	—
608	C₄⋊C₄	—	3	1	no	—
609	C₄⋊C₄	—	6	1	no	—
610	C₄⋊C₄	—	6	1	no	—
611	C₄⋊C₄	—	6	1	no	—
612	C₄⋊C₄	—	6	1	no	—
613	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
614	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	6	1	no	—
617	C₂²⋊C₄	—	6	1	no	—
618	C₂²⋊C₄	—	6	1	no	—
619	C₂²⋊C₄	—	6	1	no	—
620	C₂²⋊C₄	—	6	1	no	—
621	C₂²⋊C₄	—	6	1	no	—
622	C₂²⋊C₄	—	6	1	no	—
623	C₂²⋊C₄	—	6	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	3	1	no	—
626	C₄²	—	3	1	no	—
627	C₄²	—	3	1	no	—
628	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	2	2	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	—	3	2	no	—
633	C₂²×C₃	—	4	2	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	4	1	no	—
636	C₂²×C₃	—	4	1	no	—
637	C₂²×C₃	—	4	1	no	—
638	C₂²×C₃	—	6	1	no	—
639	C₂²×C₃	—	6	1	no	—
640	C₂²×C₃	—	6	2	no	—
641	C₂²×C₃	—	8	1	no	—
642	C₂²×C₃	—	8	1	no	—
643	C₂²×C₃	—	12	8	no	—
644	C₂²×C₃	—	12	1	no	—
645	C₂²×C₃	—	12	1	no	—
646	C₂²×C₃	—	12	1	no	—
647	C₂²×C₃	—	12	1	no	—
648	C₂²×C₃	—	12	1	no	—
649	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
650	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
651	C₂×D₃	—	2	1	no	—
652	C₂×D₃	—	2	1	no	—
653	C₂×D₃	—	2	2	no	—
654	C₂×D₃	—	4	8	no	—
655	C₂×D₃	—	4	1	no	—
656	C₂×D₃	—	4	1	no	—
657	C₂×D₃	—	4	1	no	—
658	C₂×D₃	—	4	1	no	—
659	C₂×D₃	—	4	1	no	—
660	C₂×D₃	C₃×#135	1	2	yes	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	2	1	no	—
663	C₃×C₄	—	2	2	no	—
664	C₃×C₄	—	2	1	no	—
665	C₃×C₄	—	2	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	2	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	—	4	1	no	—
670	C₃×C₄	—	4	1	no	—
671	C₃×C₄	—	4	1	no	—
672	C₃×C₄	—	4	1	no	—
673	C₃×C₄	—	4	1	no	—
674	C₃×C₄	—	6	1	no	—
675	C₃×C₄	—	6	1	no	—
676	C₃×C₄	—	6	1	no	—
677	C₃×C₄	—	8	1	no	—
678	C₃×C₄	—	8	1	no	—
679	C₃×C₄	—	12	1	no	—
680	C₃×C₄	—	12	1	no	—
681	C₃×C₄	#914	1	2	yes	—
682	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
683	C₃×C₄	C₂×#235	1	1	yes	characteristic
684	C₃×C₄	D₃×#41	1	1	yes	characteristic
685	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
686	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
687	Dic₃	—	2	1	no	—
688	Dic₃	—	2	1	no	—
689	Dic₃	—	2	1	no	—
690	Dic₃	—	4	1	no	—
691	Dic₃	—	4	1	no	—
692	C₃²	#3105	1	1	yes	characteristic, complemented, Sylow
693	C₂³	—	2	1	no	—
694	C₂³	—	3	1	no	—
695	C₂³	—	6	4	no	—
696	C₂³	—	6	1	no	—
697	C₂³	—	6	1	no	—
698	C₂³	—	12	2	no	—
699	C₂³	—	12	2	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	1	no	—
702	D₄	—	2	1	no	—
703	D₄	—	3	2	no	—
704	D₄	—	6	4	no	—
705	D₄	—	6	1	no	—
706	D₄	—	6	1	no	—
707	D₄	—	6	1	no	—
708	D₄	—	12	2	no	—
709	D₄	C₃×#235	1	2	yes	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	3	1	no	—
714	C₂×C₄	—	3	1	no	—
715	C₂×C₄	—	3	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	6	2	no	—
718	C₂×C₄	—	6	2	no	—
719	C₂×C₄	—	6	1	no	—
720	C₂×C₄	—	6	1	no	—
721	C₂×C₄	—	6	1	no	—
722	C₂×C₄	—	6	1	no	—
723	C₂×C₄	—	12	2	no	—
724	C₂×C₄	—	12	2	no	—
725	C₂×C₄	—	12	2	no	—
726	C₂×C₄	—	12	2	no	—
727	C₂×C₄	—	12	2	no	—
728	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
729	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	6	1	no	—
734	C₈	—	6	1	no	—
735	C₂×C₃	—	2	1	no	—
736	C₂×C₃	—	2	1	no	—
737	C₂×C₃	—	2	1	no	—
738	C₂×C₃	—	4	2	no	—
739	C₂×C₃	—	4	2	no	—
740	C₂×C₃	—	6	2	no	—
741	C₂×C₃	—	8	2	no	—
742	C₂×C₃	—	12	2	no	—
743	C₂×C₃	—	24	1	no	—
744	C₂×C₃	#5547	1	1	yes	characteristic
745	C₂×C₃	C₂×#914	1	1	yes	characteristic
746	C₂×C₃	D₃×#135	1	1	yes	characteristic
747	C₂×C₃	C₃×#525	1	1	yes	characteristic
748	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
749	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
750	D₃	—	2	2	no	—
751	D₃	—	4	2	no	—
752	D₃	—	8	1	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	3	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	6	1	no	—
758	C₂²	—	6	1	no	—
759	C₂²	—	6	2	no	—
760	C₂²	—	12	8	no	—
761	C₂²	—	12	1	no	—
762	C₂²	—	12	1	no	—
763	C₂²	—	12	1	no	—
764	C₂²	—	12	1	no	—
765	C₂²	—	12	1	no	—
766	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	6	1	no	—
772	C₄	—	6	1	no	—
773	C₄	—	6	1	no	—
774	C₄	—	12	1	no	—
775	C₄	—	12	1	no	—
776	C₄	C₃×#914	1	2	yes	—
777	C₄	C₂×C₃×#235	1	1	yes	characteristic
778	C₄	C₃×D₃×#41	1	1	yes	characteristic
779	C₃	—	2	1	no	—
780	C₃	#79654	1	1	yes	characteristic, direct product factor
781	C₃	C₃×#3105	1	1	yes	characteristic, complemented
782	C₂	—	4	2	no	—
783	C₂	—	6	2	no	—
784	C₂	—	12	2	no	—
785	C₂	—	24	1	no	—
786	C₂	C₃×#5547	1	1	yes	characteristic
787	C₂	C₂×C₃×#914	1	1	yes	characteristic
788	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×SD₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃×#4773	C₂
hypercenter	C₃×C₄×SD₁₆	D₃
hypocenter	C₃	C₃×#3105
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#5580	C₂	semidirect
2. C₃×C₄×D₃×D₄	C₂	semidirect
3. C₃²×C₄×SD₁₆	C₂	semidirect
4. C₃×#5169	C₂	semidirect
5. C₃×#5165	C₂	semidirect
6. C₃×C₄×#215	C₂	semidirect
7. C₃×C₄×#213	C₂	semidirect
8. C₃×#4871	C₂	semidirect
9. C₃×#4863	C₂	semidirect
10. C₃×#4819	C₂	semidirect
11. C₃×#4811	C₂	semidirect
13. C₃×#4766	C₂	semidirect
14. C₃×C₄×D₂₄	C₂	semidirect
15. C₃×#4685	C₂	semidirect
17. #79654	C₃	direct (N × H)
21. C₃²×C₄×Q₈	C₂²	semidirect
23. C₃×#947	C₂²	semidirect
35. C₃×#890	C₂²	semidirect
40. C₃×C₄×D₁₂	C₂²	semidirect
43. C₃²×#106	C₂²	semidirect
44. C₃²×#103	C₂²	semidirect
46. C₃²×C₄×C₈	C₂²	semidirect
47. C₃×#835	C₂²	semidirect
50. C₃×#821	C₂²	semidirect
53. C₃×#818	C₂²	semidirect
54. C₃×Dic₃⋊C₈	C₂²	semidirect
55. C₃×Dic₃⋊C₈	C₂²	semidirect
57. C₃×#809	C₂²	semidirect
58. C₃×#808	C₂²	semidirect
59. C₃×#807	C₂²	semidirect
60. C₃×C₄×C₃⋊C₈	C₂²	semidirect
63. #5580	C₂×C₃	semidirect
64. C₄×D₃×D₄	C₂×C₃	semidirect
75. C₃×C₄×SD₁₆	D₃	semidirect
76. C₃×C₄×SD₁₆	C₂×C₃	semidirect
80. #5169	C₂×C₃	semidirect
81. #5165	C₂×C₃	semidirect
82. C₄×#215	C₂×C₃	semidirect
83. C₄×#213	C₂×C₃	semidirect
84. #4871	C₂×C₃	semidirect
85. #4863	C₂×C₃	semidirect
86. #4819	C₂×C₃	semidirect
87. #4811	C₂×C₃	semidirect
89. #4766	C₂×C₃	semidirect
90. C₄×D₂₄	C₂×C₃	semidirect
91. #4685	C₂×C₃	semidirect
160. C₃×C₄×Q₈	C₂×D₃	semidirect
161. C₃×C₄×Q₈	C₂²×C₃	semidirect
176. #947	C₂²×C₃	semidirect
188. #890	C₂²×C₃	semidirect
193. C₄×D₁₂	C₂²×C₃	semidirect
200. C₃×#106	C₂×D₃	semidirect
201. C₃×#106	C₂²×C₃	semidirect
206. C₃×#103	C₂×D₃	semidirect
207. C₃×#103	C₂²×C₃	semidirect
220. C₃×C₄×C₈	C₂×D₃	semidirect
221. C₃×C₄×C₈	C₂²×C₃	semidirect
222. #835	C₂²×C₃	semidirect
225. #821	C₂²×C₃	semidirect
228. #818	C₂²×C₃	semidirect
229. Dic₃⋊C₈	C₂²×C₃	semidirect
230. Dic₃⋊C₈	C₂²×C₃	semidirect
232. #809	C₂²×C₃	semidirect
233. #808	C₂²×C₃	semidirect
234. #807	C₂²×C₃	semidirect
235. C₄×C₃⋊C₈	C₂²×C₃	semidirect
289. C₄×SD₁₆	C₃×D₃	semidirect
443. C₄×Q₈	C₂×C₃×D₃	semidirect
459. #106	C₂×C₃×D₃	semidirect
463. #103	C₂×C₃×D₃	semidirect
473. C₄×C₈	C₂×C₃×D₃	semidirect
692. C₃²	#3105	semidirect
780. C₃	#79654	direct (N × H)
781. C₃	C₃×#3105	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5580	2
C₃×C₄×D₃×D₄	2
C₃²×C₄×SD₁₆	2
C₃×#5169	2
C₃×#5165	2
C₃×C₄×#215	2
C₃×C₄×#213	2
C₃×#4871	2
C₃×#4863	2
C₃×#4819	2
C₃×#4811	2
C₃×#4773	2
C₃×#4766	2
C₃×C₄×D₂₄	2
C₃×#4685	2
C₃×#3105	3
#79654	3

Subgroups — C3×#79654 #11870862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79654 #11870862