Subgroups — C₃×#79606 #11885809

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#912	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5554	C₂	1	2	yes	maximal, complemented
4	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5016	C₂	1	2	yes	maximal, complemented
6	C₃×#4887	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4781	C₂	1	2	yes	maximal, complemented
9	C₃×#4776	C₂	1	2	yes	maximal, complemented
10	C₃×#4696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3280	—	3	1	no	maximal
13	#79606	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#237	C₂²	1	2	yes	complemented
15	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
16	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
17	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
18	C₂×C₃×#214	C₂²	1	2	yes	complemented
19	C₂×C₃×#213	C₂²	1	2	yes	—
20	C₃×#930	—	2	2	no	—
21	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
22	C₃×#912	—	2	4	no	—
23	C₃×D₃×D₈	—	2	4	no	—
24	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×#204	C₂²	1	2	yes	complemented
27	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#897	C₂²	1	2	yes	—
30	C₃×#895	C₂²	1	2	yes	complemented
31	C₃×#886	—	2	2	no	—
32	C₃×#882	—	2	2	no	—
33	C₃×#875	C₂²	1	2	yes	complemented
34	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
35	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#102	C₂²	1	2	yes	complemented
37	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×#810	C₂²	1	2	yes	complemented
41	C₃×#809	C₂²	1	2	yes	complemented
42	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×#135	—	3	1	no	—
44	C₂²×C₃×D₈	—	3	1	no	—
45	C₃×#546	—	3	2	no	—
46	C₂×#912	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×D₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
48	#5554	C₂×C₃	1	2	yes	complemented
49	C₃×#495	—	3	1	no	—
50	C₃×#467	—	3	1	no	—
51	C₃×#466	—	3	1	no	—
52	C₃×#463	—	3	2	no	—
53	C₃×#450	—	3	2	no	—
54	C₃×#449	—	3	2	no	—
55	C₃×C₄×D₈	—	2	1	no	—
56	C₃×C₄×D₈	D₃	1	1	yes	characteristic, complemented
57	C₃×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×C₈×D₄	—	3	1	no	—
59	#5016	C₂×C₃	1	2	yes	complemented
60	#4887	C₂×C₃	1	1	yes	characteristic, complemented
61	#4883	C₂×C₃	1	1	yes	characteristic, complemented
62	#4781	C₂×C₃	1	2	yes	complemented
63	#4776	C₂×C₃	1	2	yes	complemented
64	#4696	C₂×C₃	1	1	yes	characteristic, complemented
65	C₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂³×C₃×D₃	—	2	2	no	—
67	C₂×C₃²×D₄	C₂³	1	2	yes	—
68	C₂²×C₃²×C₄	—	2	2	no	—
69	C₂×C₃×#67	—	2	2	no	—
70	C₂×C₃×#67	—	2	2	no	—
71	C₂²×C₃×Dic₃	—	2	2	no	—
72	C₃×#237	—	2	4	no	—
73	C₃×#237	—	4	2	no	—
74	C₃×D₃×D₄	—	2	4	no	—
75	C₃×D₃×D₄	—	4	2	no	—
76	C₂×C₃×D₁₂	—	2	2	no	—
77	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
78	C₂×C₃×D₁₂	C₂³	1	2	yes	—
79	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₃×Dic₆	C₂³	1	2	yes	—
82	C₃²×D₈	D₄	1	4	yes	complemented
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
86	C₃²×C₂²⋊C₄	—	2	2	no	—
87	C₃²×C₄²	C₂³	1	1	yes	characteristic
88	C₃×#214	—	2	4	no	—
89	C₃×#213	—	2	4	no	—
90	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
91	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
94	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
95	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
96	C₃×C₄⋊Dic₃	—	2	2	no	—
97	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
98	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₃×Dic₁₂	—	2	2	no	—
101	C₃×D₂₄	—	2	2	no	—
102	C₃×#204	—	4	2	no	—
103	C₃×D₃×C₈	—	2	2	no	—
104	C₃×D₃×C₈	—	2	2	no	—
105	#3280	—	3	1	no	Sylow
106	C₂×C₃×#41	—	3	2	no	—
107	C₂²×C₃×D₄	—	3	2	no	—
108	C₂×#237	C₂²×C₃	1	2	yes	complemented
109	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
110	C₃×#135	—	6	4	no	—
111	C₂×C₃×Q₁₆	—	3	1	no	—
112	C₂×C₃×SD₁₆	—	3	2	no	—
113	C₂×C₃×SD₁₆	—	3	2	no	—
114	C₂×C₃×D₈	—	2	1	no	—
115	C₂×C₃×D₈	—	3	2	no	—
116	C₂×C₃×D₈	—	3	1	no	—
117	C₂×C₃×D₈	—	6	4	no	—
118	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
119	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₃×C₈	—	3	1	no	—
121	C₂²×C₃×C₈	—	3	1	no	—
122	C₃×#124	—	3	2	no	—
123	C₃×#123	—	6	2	no	—
124	C₃×C₂²⋊Q₈	—	3	2	no	—
125	C₃×#121	—	3	2	no	—
126	C₃×#121	—	6	2	no	—
127	C₃×#120	—	6	2	no	—
128	C₃×C₄×D₄	—	2	2	no	—
129	C₃×C₄×D₄	—	3	1	no	—
130	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
131	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
132	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
133	C₂×#214	C₂²×C₃	1	2	yes	complemented
134	C₂×#213	C₂²×C₃	1	2	yes	—
135	#930	—	2	2	no	—
136	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
137	#912	—	2	4	no	—
138	D₃×D₈	—	2	4	no	—
139	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×#204	C₂²×C₃	1	2	yes	complemented
142	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
143	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
144	#897	C₂²×C₃	1	2	yes	—
145	#895	C₂²×C₃	1	2	yes	complemented
146	#886	—	2	2	no	—
147	#882	—	2	2	no	—
148	#875	C₂²×C₃	1	2	yes	complemented
149	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
150	C₃×#107	—	2	1	no	—
151	C₃×#107	C₂×D₃	1	1	yes	characteristic, complemented
152	C₃×#107	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₃×C₄⋊C₈	—	3	1	no	—
154	C₃×#103	—	3	2	no	—
155	C₃×#102	—	2	2	no	—
156	C₃×#102	—	3	2	no	—
157	C₃×#102	C₂×D₃	1	2	yes	complemented
158	C₃×#102	C₂²×C₃	1	2	yes	complemented
159	C₃×C₂²⋊C₈	—	3	1	no	—
160	C₃×C₂²⋊C₈	—	3	1	no	—
161	C₃×C₄×C₈	—	2	1	no	—
162	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
163	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
165	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
166	#810	C₂²×C₃	1	2	yes	complemented
167	#809	C₂²×C₃	1	2	yes	complemented
168	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂³×C₃²	—	2	2	no	—
170	C₂²×C₃×D₃	—	2	2	no	—
171	C₂²×C₃×D₃	—	4	4	no	—
172	C₂²×C₃×D₃	—	4	4	no	—
173	C₂²×C₃×D₃	—	8	2	no	—
174	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
176	C₃²×D₄	—	2	2	no	—
177	C₃²×D₄	C₂×D₄	1	4	yes	—
178	C₂×C₃²×C₄	—	2	2	no	—
179	C₂×C₃²×C₄	—	8	2	no	—
180	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
183	C₃×#67	—	4	4	no	—
184	C₃×#67	—	4	4	no	—
185	C₂×C₃×Dic₃	—	2	2	no	—
186	C₂×C₃×Dic₃	—	4	4	no	—
187	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
189	C₃×D₁₂	—	2	2	no	—
190	C₃×D₁₂	—	2	2	no	—
191	C₃×D₁₂	—	2	2	no	—
192	C₃×D₁₂	—	8	2	no	—
193	C₃×C₄×D₃	—	2	1	no	—
194	C₃×C₄×D₃	—	2	1	no	—
195	C₃×C₄×D₃	—	2	1	no	—
196	C₃×C₄×D₃	—	2	1	no	—
197	C₃×Dic₆	—	2	2	no	—
198	C₃×Dic₆	—	2	2	no	—
199	C₃²×C₈	—	2	1	no	—
200	C₃²×C₈	C₂×D₄	1	2	yes	—
201	C₃×C₃⋊C₈	—	2	1	no	—
202	C₃×C₃⋊C₈	—	2	1	no	—
203	C₂×#135	—	3	1	no	—
204	C₂²×D₈	—	3	1	no	—
205	#546	—	3	2	no	—
206	#495	—	3	1	no	—
207	#467	—	3	1	no	—
208	#466	—	3	1	no	—
209	#463	—	3	2	no	—
210	#450	—	3	2	no	—
211	#449	—	3	2	no	—
212	C₄×D₈	C₃×D₃	1	1	yes	characteristic, complemented
213	C₈×D₄	—	3	1	no	—
214	C₂⁴×C₃	—	6	2	no	—
215	C₂³×D₃	—	2	2	no	—
216	C₃×#41	—	6	4	no	—
217	C₃×#41	—	12	2	no	—
218	C₂×C₃×Q₈	—	3	2	no	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	3	1	no	—
221	C₂×C₃×D₄	—	3	2	no	—
222	C₂×C₃×D₄	—	6	2	no	—
223	C₂×C₃×D₄	—	6	2	no	—
224	C₂×C₃×D₄	—	6	4	no	—
225	C₂×C₃×D₄	—	6	2	no	—
226	C₂×C₃×D₄	—	12	2	no	—
227	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
228	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
229	C₂²×C₃×C₄	—	2	2	no	—
230	C₂²×C₃×C₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	3	1	no	—
232	C₂²×C₃×C₄	—	3	1	no	—
233	C₂²×C₃×C₄	—	4	2	no	—
234	C₂²×C₃×C₄	—	6	2	no	—
235	C₂×#67	—	2	2	no	—
236	C₂×#67	—	2	2	no	—
237	C₂²×Dic₃	—	2	2	no	—
238	#237	—	2	4	no	—
239	#237	—	4	2	no	—
240	D₃×D₄	—	2	4	no	—
241	D₃×D₄	—	4	2	no	—
242	C₂×D₁₂	—	2	2	no	—
243	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
244	C₂×D₁₂	C₂³×C₃	1	2	yes	—
245	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
246	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
247	C₂×Dic₆	C₂³×C₃	1	2	yes	—
248	C₃×Q₁₆	—	6	2	no	—
249	C₃×SD₁₆	—	6	4	no	—
250	C₃×SD₁₆	—	12	2	no	—
251	C₃×D₈	—	2	4	no	—
252	C₃×D₈	—	6	4	no	—
253	C₃×D₈	—	6	2	no	—
254	C₃×D₈	D₁₂	1	4	yes	complemented
255	C₃×D₈	C₃×D₄	1	4	yes	complemented
256	C₂×C₃×C₈	—	2	1	no	—
257	C₂×C₃×C₈	—	2	1	no	—
258	C₂×C₃×C₈	—	3	1	no	—
259	C₂×C₃×C₈	—	3	1	no	—
260	C₂×C₃×C₈	—	6	2	no	—
261	C₂×C₃×C₈	—	6	2	no	—
262	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
264	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
266	C₃×C₄⋊C₄	—	2	2	no	—
267	C₃×C₄⋊C₄	—	3	1	no	—
268	C₃×C₄⋊C₄	—	6	2	no	—
269	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
270	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	3	1	no	—
274	C₃×C₂²⋊C₄	—	3	1	no	—
275	C₃×C₂²⋊C₄	—	4	2	no	—
276	C₃×C₂²⋊C₄	—	6	2	no	—
277	C₃×C₂²⋊C₄	—	6	2	no	—
278	C₃×C₂²⋊C₄	—	6	2	no	—
279	C₃×C₂²⋊C₄	—	6	2	no	—
280	C₃×C₄²	—	2	1	no	—
281	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
282	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
283	#214	—	2	4	no	—
284	#213	—	2	4	no	—
285	(C₂×D₃)⋊C₄	—	2	2	no	—
286	(C₂×D₃)⋊C₄	—	2	2	no	—
287	(C₂×D₃)⋊C₄	—	2	2	no	—
288	(C₂×D₃)⋊C₄	—	2	2	no	—
289	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
290	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
291	C₄⋊Dic₃	—	2	2	no	—
292	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
293	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
295	Dic₁₂	—	2	2	no	—
296	D₂₄	—	2	2	no	—
297	#204	—	4	2	no	—
298	D₃×C₈	—	2	2	no	—
299	D₃×C₈	—	2	2	no	—
300	C₂²×C₃²	—	2	4	no	—
301	C₂²×C₃²	—	4	2	no	—
302	C₂²×C₃²	—	4	2	no	—
303	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₃×D₃	—	2	1	no	—
305	C₂×C₃×D₃	—	2	1	no	—
306	C₂×C₃×D₃	—	2	1	no	—
307	C₂×C₃×D₃	—	2	1	no	—
308	C₂×C₃×D₃	—	2	1	no	—
309	C₂×C₃×D₃	—	4	2	no	—
310	C₂×C₃×D₃	—	4	2	no	—
311	C₂×C₃×D₃	—	4	2	no	—
312	C₂×C₃×D₃	—	8	8	no	—
313	C₂×C₃×D₃	#135	1	2	yes	complemented
314	C₃²×C₄	—	2	1	no	—
315	C₃²×C₄	—	2	1	no	—
316	C₃²×C₄	—	4	2	no	—
317	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
318	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
319	C₃×Dic₃	—	2	1	no	—
320	C₃×Dic₃	—	2	1	no	—
321	C₃×Dic₃	—	4	2	no	—
322	C₂×#41	—	3	2	no	—
323	C₂²×D₄	—	3	2	no	—
324	#135	—	6	4	no	—
325	C₂×Q₁₆	—	3	1	no	—
326	C₂×SD₁₆	—	3	2	no	—
327	C₂×SD₁₆	—	3	2	no	—
328	C₂×D₈	—	3	2	no	—
329	C₂×D₈	—	3	1	no	—
330	C₂×D₈	—	6	4	no	—
331	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
332	C₂²×C₈	—	3	1	no	—
333	C₂²×C₈	—	3	1	no	—
334	#124	—	3	2	no	—
335	#123	—	6	2	no	—
336	C₂²⋊Q₈	—	3	2	no	—
337	#121	—	3	2	no	—
338	#121	—	6	2	no	—
339	#120	—	6	2	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
342	C₂×C₂²⋊C₄	—	6	2	no	—
343	#107	C₂×C₃×D₃	1	1	yes	characteristic, complemented
344	C₄⋊C₈	—	3	1	no	—
345	#103	—	3	2	no	—
346	#102	—	3	2	no	—
347	#102	C₂×C₃×D₃	1	2	yes	complemented
348	C₂²⋊C₈	—	3	1	no	—
349	C₂²⋊C₈	—	3	1	no	—
350	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	3	1	no	—
354	C₂³×C₃	—	3	1	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	6	2	no	—
357	C₂³×C₃	—	12	4	no	—
358	C₂³×C₃	—	12	4	no	—
359	C₂³×C₃	—	24	2	no	—
360	C₂²×D₃	—	2	2	no	—
361	C₂²×D₃	—	4	4	no	—
362	C₂²×D₃	—	4	4	no	—
363	C₂²×D₃	—	8	2	no	—
364	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
365	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
366	C₃×Q₈	—	6	2	no	—
367	C₃×Q₈	—	6	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	—	6	2	no	—
373	C₃×D₄	—	6	2	no	—
374	C₃×D₄	—	6	2	no	—
375	C₃×D₄	—	12	4	no	—
376	C₃×D₄	—	12	4	no	—
377	C₃×D₄	—	24	2	no	—
378	C₃×D₄	C₂×D₁₂	1	4	yes	—
379	C₃×D₄	C₂×C₃×D₄	1	4	yes	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	3	1	no	—
386	C₂×C₃×C₄	—	3	1	no	—
387	C₂×C₃×C₄	—	4	2	no	—
388	C₂×C₃×C₄	—	6	1	no	—
389	C₂×C₃×C₄	—	6	1	no	—
390	C₂×C₃×C₄	—	6	1	no	—
391	C₂×C₃×C₄	—	6	1	no	—
392	C₂×C₃×C₄	—	6	2	no	—
393	C₂×C₃×C₄	—	8	2	no	—
394	C₂×C₃×C₄	—	8	2	no	—
395	C₂×C₃×C₄	—	8	4	no	—
396	C₂×C₃×C₄	—	12	4	no	—
397	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
403	#67	—	4	4	no	—
404	#67	—	4	4	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	—	4	4	no	—
407	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
408	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
409	D₁₂	—	2	2	no	—
410	D₁₂	—	2	2	no	—
411	D₁₂	—	2	2	no	—
412	D₁₂	—	8	2	no	—
413	C₄×D₃	—	2	1	no	—
414	C₄×D₃	—	2	1	no	—
415	C₄×D₃	—	2	1	no	—
416	C₄×D₃	—	2	1	no	—
417	Dic₆	—	2	2	no	—
418	Dic₆	—	2	2	no	—
419	C₃×C₈	—	2	1	no	—
420	C₃×C₈	—	2	1	no	—
421	C₃×C₈	—	2	2	no	—
422	C₃×C₈	—	4	1	no	—
423	C₃×C₈	—	6	1	no	—
424	C₃×C₈	—	6	1	no	—
425	C₃×C₈	C₂×D₁₂	1	2	yes	—
426	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
427	C₃⋊C₈	—	2	1	no	—
428	C₃⋊C₈	—	2	1	no	—
429	C₂×C₃²	—	4	4	no	—
430	C₂×C₃²	D₄²	1	1	yes	characteristic
431	C₂×C₃²	C₂×#135	1	1	yes	characteristic
432	C₂×C₃²	#576	1	1	yes	characteristic
433	C₃×D₃	—	2	2	no	—
434	C₃×D₃	—	4	1	no	—
435	C₃×D₃	—	8	2	no	—
436	C₂⁴	—	6	2	no	—
437	#41	—	6	4	no	—
438	#41	—	12	2	no	—
439	C₂×Q₈	—	3	2	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	6	2	no	—
443	C₂×D₄	—	6	2	no	—
444	C₂×D₄	—	6	4	no	—
445	C₂×D₄	—	6	2	no	—
446	C₂×D₄	—	12	2	no	—
447	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	6	2	no	—
452	Q₁₆	—	6	2	no	—
453	SD₁₆	—	6	4	no	—
454	SD₁₆	—	12	2	no	—
455	D₈	—	6	4	no	—
456	D₈	—	6	2	no	—
457	D₈	C₃×D₁₂	1	4	yes	complemented
458	C₂×C₈	—	3	1	no	—
459	C₂×C₈	—	3	1	no	—
460	C₂×C₈	—	6	2	no	—
461	C₂×C₈	—	6	2	no	—
462	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
463	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	6	2	no	—
466	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	3	1	no	—
469	C₂²⋊C₄	—	3	1	no	—
470	C₂²⋊C₄	—	6	2	no	—
471	C₂²⋊C₄	—	6	2	no	—
472	C₂²⋊C₄	—	6	2	no	—
473	C₂²⋊C₄	—	6	2	no	—
474	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	2	4	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	3	2	no	—
479	C₂²×C₃	—	4	4	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	6	1	no	—
485	C₂²×C₃	—	6	1	no	—
486	C₂²×C₃	—	6	1	no	—
487	C₂²×C₃	—	6	1	no	—
488	C₂²×C₃	—	6	1	no	—
489	C₂²×C₃	—	8	2	no	—
490	C₂²×C₃	—	8	2	no	—
491	C₂²×C₃	—	12	2	no	—
492	C₂²×C₃	—	12	2	no	—
493	C₂²×C₃	—	12	2	no	—
494	C₂²×C₃	—	24	8	no	—
495	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
496	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	1	no	—
500	C₂×D₃	—	2	1	no	—
501	C₂×D₃	—	2	1	no	—
502	C₂×D₃	—	4	2	no	—
503	C₂×D₃	—	4	2	no	—
504	C₂×D₃	—	4	2	no	—
505	C₂×D₃	—	8	8	no	—
506	C₂×D₃	C₃×#135	1	2	yes	complemented
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	—	4	1	no	—
515	C₃×C₄	—	4	2	no	—
516	C₃×C₄	—	4	2	no	—
517	C₃×C₄	—	6	1	no	—
518	C₃×C₄	—	6	1	no	—
519	C₃×C₄	—	8	2	no	—
520	C₃×C₄	—	12	2	no	—
521	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
522	C₃×C₄	#1009	1	1	yes	characteristic
523	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
524	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
525	Dic₃	—	2	1	no	—
526	Dic₃	—	2	1	no	—
527	Dic₃	—	4	2	no	—
528	C₃²	#3280	1	1	yes	characteristic, complemented, Sylow
529	C₂³	—	2	2	no	—
530	C₂³	—	3	1	no	—
531	C₂³	—	3	1	no	—
532	C₂³	—	6	2	no	—
533	C₂³	—	12	4	no	—
534	C₂³	—	12	4	no	—
535	C₂³	—	24	2	no	—
536	Q₈	—	6	2	no	—
537	Q₈	—	6	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	6	2	no	—
540	D₄	—	6	2	no	—
541	D₄	—	6	2	no	—
542	D₄	—	12	4	no	—
543	D₄	—	12	4	no	—
544	D₄	—	24	2	no	—
545	D₄	C₂×C₃×D₁₂	1	4	yes	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	3	1	no	—
548	C₂×C₄	—	3	1	no	—
549	C₂×C₄	—	6	1	no	—
550	C₂×C₄	—	6	1	no	—
551	C₂×C₄	—	6	1	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	6	2	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	12	4	no	—
556	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
557	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
558	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	6	1	no	—
561	C₈	—	6	1	no	—
562	C₈	C₂×C₃×D₁₂	1	2	yes	—
563	C₂×C₃	—	2	1	no	—
564	C₂×C₃	—	2	1	no	—
565	C₂×C₃	—	2	1	no	—
566	C₂×C₃	—	4	4	no	—
567	C₂×C₃	—	4	4	no	—
568	C₂×C₃	—	6	2	no	—
569	C₂×C₃	—	8	4	no	—
570	C₂×C₃	—	12	1	no	—
571	C₂×C₃	—	24	2	no	—
572	C₂×C₃	D₄×D₁₂	1	1	yes	characteristic
573	C₂×C₃	#5757	1	1	yes	characteristic
574	C₂×C₃	D₃×#135	1	1	yes	characteristic
575	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
576	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
577	C₂×C₃	C₃×#576	1	1	yes	characteristic
578	D₃	—	2	2	no	—
579	D₃	—	4	1	no	—
580	D₃	—	8	2	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	3	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	6	1	no	—
586	C₂²	—	6	1	no	—
587	C₂²	—	6	1	no	—
588	C₂²	—	6	1	no	—
589	C₂²	—	6	1	no	—
590	C₂²	—	12	2	no	—
591	C₂²	—	12	2	no	—
592	C₂²	—	12	2	no	—
593	C₂²	—	24	8	no	—
594	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	6	1	no	—
599	C₄	—	6	1	no	—
600	C₄	—	12	2	no	—
601	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
602	C₄	C₃×#1009	1	1	yes	characteristic
603	C₃	—	2	1	no	—
604	C₃	#79606	1	1	yes	characteristic, direct product factor
605	C₃	C₃×#3280	1	1	yes	characteristic, complemented
606	C₂	—	4	4	no	—
607	C₂	—	6	2	no	—
608	C₂	—	12	1	no	—
609	C₂	—	24	2	no	—
610	C₂	C₃×D₄×D₁₂	1	1	yes	characteristic
611	C₂	C₃×#5757	1	1	yes	characteristic
612	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×D₈	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×C₄×D₈	D₃
hypocenter	C₃	C₃×#3280
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#912	C₂	semidirect
2. C₂×C₃×D₃×D₈	C₂	semidirect
3. C₃×#5554	C₂	semidirect
4. C₃²×C₄×D₈	C₂	semidirect
5. C₃×#5016	C₂	semidirect
6. C₃×#4887	C₂	semidirect
7. C₃×#4883	C₂	semidirect
8. C₃×#4781	C₂	semidirect
9. C₃×#4776	C₂	semidirect
10. C₃×#4696	C₂	semidirect
11. C₃×C₈×D₁₂	C₂	semidirect
13. #79606	C₃	direct (N × H)
14. C₂×C₃×#237	C₂²	semidirect
17. C₃²×C₄×D₄	C₂²	semidirect
18. C₂×C₃×#214	C₂²	semidirect
24. C₂×C₃×Dic₁₂	C₂²	semidirect
26. C₂×C₃×#204	C₂²	semidirect
28. C₂×C₃×D₃×C₈	C₂²	semidirect
30. C₃×#895	C₂²	semidirect
33. C₃×#875	C₂²	semidirect
35. C₃²×#107	C₂²	semidirect
36. C₃²×#102	C₂²	semidirect
37. C₃²×C₄×C₈	C₂²	semidirect
39. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
40. C₃×#810	C₂²	semidirect
41. C₃×#809	C₂²	semidirect
42. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
46. C₂×#912	C₂×C₃	semidirect
47. C₂×D₃×D₈	C₂×C₃	semidirect
48. #5554	C₂×C₃	semidirect
56. C₃×C₄×D₈	D₃	semidirect
57. C₃×C₄×D₈	C₂×C₃	semidirect
59. #5016	C₂×C₃	semidirect
60. #4887	C₂×C₃	semidirect
61. #4883	C₂×C₃	semidirect
62. #4781	C₂×C₃	semidirect
63. #4776	C₂×C₃	semidirect
64. #4696	C₂×C₃	semidirect
65. C₈×D₁₂	C₂×C₃	semidirect
82. C₃²×D₈	D₄	semidirect
108. C₂×#237	C₂²×C₃	semidirect
130. C₃×C₄×D₄	C₂×D₃	semidirect
131. C₃×C₄×D₄	C₂²×C₃	semidirect
133. C₂×#214	C₂²×C₃	semidirect
139. C₂×Dic₁₂	C₂²×C₃	semidirect
141. C₂×#204	C₂²×C₃	semidirect
143. C₂×D₃×C₈	C₂²×C₃	semidirect
145. #895	C₂²×C₃	semidirect
148. #875	C₂²×C₃	semidirect
151. C₃×#107	C₂×D₃	semidirect
152. C₃×#107	C₂²×C₃	semidirect
157. C₃×#102	C₂×D₃	semidirect
158. C₃×#102	C₂²×C₃	semidirect
162. C₃×C₄×C₈	C₂×D₃	semidirect
163. C₃×C₄×C₈	C₂²×C₃	semidirect
165. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
166. #810	C₂²×C₃	semidirect
167. #809	C₂²×C₃	semidirect
168. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
212. C₄×D₈	C₃×D₃	semidirect
254. C₃×D₈	D₁₂	semidirect
255. C₃×D₈	C₃×D₄	semidirect
313. C₂×C₃×D₃	#135	semidirect
341. C₄×D₄	C₂×C₃×D₃	semidirect
343. #107	C₂×C₃×D₃	semidirect
347. #102	C₂×C₃×D₃	semidirect
350. C₄×C₈	C₂×C₃×D₃	semidirect
457. D₈	C₃×D₁₂	semidirect
506. C₂×D₃	C₃×#135	semidirect
528. C₃²	#3280	semidirect
604. C₃	#79606	direct (N × H)
605. C₃	C₃×#3280	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#912	2
C₂×C₃×D₃×D₈	2
C₃×#5554	2
C₃²×C₄×D₈	2
C₃×#5016	2
C₃×#4887	2
C₃×#4883	2
C₃×#4781	2
C₃×#4776	2
C₃×#4696	2
C₃×C₈×D₁₂	2
C₃×#3280	3
#79606	3

Subgroups — C3×#79606 #11885809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79606 #11885809