Subgroups — C₃×#79433 #11885812

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5550	C₂	1	2	yes	maximal, complemented
4	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5116	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4844	C₂	1	2	yes	maximal, complemented
8	C₃×#4734	C₂	1	2	yes	maximal, complemented
9	C₃×#4731	C₂	1	2	yes	maximal, complemented
10	C₃×#4696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3280	—	3	1	no	maximal
13	#79433	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	2	yes	complemented
15	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
19	C₃×#937	—	2	2	no	—
20	C₃×#930	C₂²	1	2	yes	complemented
21	C₃×#924	C₂²	1	2	yes	—
22	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₃×#904	—	2	4	no	—
24	C₂×C₃×D₂₄	—	2	4	no	—
25	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₂₄	C₂²	1	2	yes	—
27	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×#204	C₂²	1	2	yes	complemented
29	C₂×C₃×#204	C₂²	1	2	yes	complemented
30	C₃×#894	—	2	2	no	—
31	C₃×#884	—	2	2	no	—
32	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
33	C₃×#875	C₂²	1	2	yes	complemented
34	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
35	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×#821	C₂²	1	2	yes	complemented
40	C₃×#821	C₂²	1	2	yes	complemented
41	C₃×#818	C₂²	1	1	yes	characteristic, complemented
42	C₃×#816	C₂²	1	2	yes	complemented
43	C₂×C₃×#135	—	3	1	no	—
44	C₂²×C₃×D₈	—	3	1	no	—
45	C₃×#546	—	3	2	no	—
46	C₂×#904	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
48	#5550	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	—	3	1	no	—
56	C₃×C₈×D₄	—	2	1	no	—
57	C₃×C₈×D₄	D₃	1	1	yes	characteristic, complemented
58	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
59	#5116	C₂×C₃	1	1	yes	characteristic, complemented
60	#5115	C₂×C₃	1	1	yes	characteristic, complemented
61	#4844	C₂×C₃	1	2	yes	complemented
62	#4734	C₂×C₃	1	2	yes	complemented
63	#4731	C₂×C₃	1	2	yes	complemented
64	#4696	C₂×C₃	1	1	yes	characteristic, complemented
65	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂³×C₃×D₃	—	2	2	no	—
67	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
70	C₂×C₃×#67	—	2	2	no	—
71	C₂×C₃×#67	—	2	2	no	—
72	C₃×#235	—	2	4	no	—
73	C₃×#235	—	4	2	no	—
74	C₂×C₃×D₁₂	—	2	4	no	—
75	C₂×C₃×D₁₂	—	2	2	no	—
76	C₂×C₃×D₁₂	—	4	2	no	—
77	C₂×C₃×D₁₂	C₂³	1	2	yes	—
78	C₂×C₃×D₁₂	C₂³	1	2	yes	—
79	C₂×C₃×C₄×D₃	—	2	2	no	—
80	C₂×C₃×C₄×D₃	—	2	2	no	—
81	C₂×C₃×Dic₆	C₂³	1	2	yes	—
82	C₂×C₃²×C₈	—	2	2	no	—
83	C₂×C₃²×C₈	—	2	2	no	—
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₃²×C₄²	C₂³	1	1	yes	characteristic
92	C₃×#217	—	2	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
94	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
95	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
96	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
97	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
98	C₃×Dic₃⋊C₄	—	2	2	no	—
99	C₃×Dic₁₂	—	2	2	no	—
100	C₃×D₂₄	—	2	4	no	—
101	C₃×D₂₄	—	2	2	no	—
102	C₃×D₂₄	D₄	1	4	yes	complemented
103	C₃×#204	—	2	4	no	—
104	C₃×#204	—	4	2	no	—
105	#3280	—	3	1	no	Sylow
106	C₂×C₃×#41	—	3	2	no	—
107	C₂²×C₃×D₄	—	3	2	no	—
108	C₂×#235	C₂²×C₃	1	2	yes	complemented
109	C₂²×D₁₂	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	—	3	1	no	—
115	C₂×C₃×D₈	—	3	2	no	—
116	C₂×C₃×D₈	—	3	1	no	—
117	C₂×C₃×D₈	—	6	4	no	—
118	C₂²×C₃×C₈	—	2	1	no	—
119	C₂²×C₃×C₈	—	2	1	no	—
120	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₃×#124	—	3	2	no	—
125	C₃×#123	—	6	2	no	—
126	C₃×C₂²⋊Q₈	—	3	2	no	—
127	C₃×#121	—	3	2	no	—
128	C₃×#121	—	6	2	no	—
129	C₃×#120	—	6	2	no	—
130	C₃×C₄×D₄	—	2	1	no	—
131	C₃×C₄×D₄	—	3	2	no	—
132	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
133	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
135	#937	—	2	2	no	—
136	#930	C₂²×C₃	1	2	yes	complemented
137	#924	C₂²×C₃	1	2	yes	—
138	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
139	#904	—	2	4	no	—
140	C₂×D₂₄	—	2	4	no	—
141	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×D₂₄	C₂²×C₃	1	2	yes	—
143	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×#204	C₂²×C₃	1	2	yes	complemented
145	C₂×#204	C₂²×C₃	1	2	yes	complemented
146	#894	—	2	2	no	—
147	#884	—	2	2	no	—
148	D₃×C₂²⋊C₄	—	2	2	no	—
149	#875	C₂²×C₃	1	2	yes	complemented
150	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
151	C₃×#107	—	3	1	no	—
152	C₃×C₄⋊C₈	—	2	1	no	—
153	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
154	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₃×#103	—	3	2	no	—
156	C₃×#102	—	3	2	no	—
157	C₃×#102	—	3	2	no	—
158	C₃×C₂²⋊C₈	—	2	1	no	—
159	C₃×C₂²⋊C₈	—	2	1	no	—
160	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
161	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
162	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
163	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₃×C₄×C₈	—	2	1	no	—
165	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
166	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
167	#821	C₂²×C₃	1	2	yes	complemented
168	#821	C₂²×C₃	1	2	yes	complemented
169	#818	C₂²×C₃	1	1	yes	characteristic, complemented
170	#816	C₂²×C₃	1	2	yes	complemented
171	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₃×D₃	—	2	2	no	—
174	C₂²×C₃×D₃	—	2	2	no	—
175	C₂²×C₃×D₃	—	4	4	no	—
176	C₂²×C₃×D₃	—	4	4	no	—
177	C₂²×C₃×D₃	—	8	2	no	—
178	C₃²×D₄	—	2	2	no	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	—	2	1	no	—
181	C₂×C₃²×C₄	—	2	1	no	—
182	C₂×C₃²×C₄	—	2	1	no	—
183	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
188	C₃×#67	—	4	4	no	—
189	C₃×#67	—	8	2	no	—
190	C₂×C₃×Dic₃	—	2	2	no	—
191	C₂×C₃×Dic₃	—	2	2	no	—
192	C₃×D₁₂	—	2	2	no	—
193	C₃×D₁₂	—	2	2	no	—
194	C₃×D₁₂	—	2	2	no	—
195	C₃×D₁₂	—	4	4	no	—
196	C₃×D₁₂	C₂×D₄	1	4	yes	—
197	C₃×C₄×D₃	—	4	4	no	—
198	C₃×C₄×D₃	—	8	2	no	—
199	C₃×Dic₆	—	2	2	no	—
200	C₃×Dic₆	—	2	2	no	—
201	C₃²×C₈	—	2	1	no	—
202	C₃²×C₈	—	2	1	no	—
203	C₃²×C₈	—	2	1	no	—
204	C₃²×C₈	C₂×D₄	1	2	yes	—
205	C₂×#135	—	3	1	no	—
206	C₂²×D₈	—	3	1	no	—
207	#546	—	3	2	no	—
208	#495	—	3	1	no	—
209	#467	—	3	1	no	—
210	#466	—	3	1	no	—
211	#463	—	3	2	no	—
212	#450	—	3	2	no	—
213	#449	—	3	2	no	—
214	C₄×D₈	—	3	1	no	—
215	C₈×D₄	C₃×D₃	1	1	yes	characteristic, complemented
216	C₂⁴×C₃	—	6	2	no	—
217	C₂³×D₃	—	2	2	no	—
218	C₃×#41	—	6	4	no	—
219	C₃×#41	—	12	2	no	—
220	C₂×C₃×Q₈	—	3	2	no	—
221	C₂×C₃×D₄	—	2	1	no	—
222	C₂×C₃×D₄	—	3	2	no	—
223	C₂×C₃×D₄	—	3	2	no	—
224	C₂×C₃×D₄	—	6	4	no	—
225	C₂×C₃×D₄	—	6	2	no	—
226	C₂×C₃×D₄	—	6	2	no	—
227	C₂×C₃×D₄	—	6	2	no	—
228	C₂×C₃×D₄	—	12	2	no	—
229	C₂×C₃×D₄	D₁₂	1	1	yes	characteristic
230	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	—	6	2	no	—
234	C₂²×C₃×C₄	—	6	2	no	—
235	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂×#67	—	2	2	no	—
240	C₂×#67	—	2	2	no	—
241	#235	—	2	4	no	—
242	#235	—	4	2	no	—
243	C₂×D₁₂	—	2	4	no	—
244	C₂×D₁₂	—	2	2	no	—
245	C₂×D₁₂	—	4	2	no	—
246	C₂×D₁₂	C₂³×C₃	1	2	yes	—
247	C₂×D₁₂	C₂³×C₃	1	2	yes	—
248	C₂×C₄×D₃	—	2	2	no	—
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×Dic₆	C₂³×C₃	1	2	yes	—
251	C₃×Q₁₆	—	6	2	no	—
252	C₃×SD₁₆	—	6	4	no	—
253	C₃×SD₁₆	—	12	2	no	—
254	C₃×D₈	—	3	4	no	—
255	C₃×D₈	—	6	4	no	—
256	C₃×D₈	—	6	2	no	—
257	C₂×C₃×C₈	—	2	2	no	—
258	C₂×C₃×C₈	—	2	2	no	—
259	C₂×C₃×C₈	—	2	2	no	—
260	C₂×C₃×C₈	—	2	2	no	—
261	C₂×C₃×C₈	—	2	1	no	—
262	C₂×C₃×C₈	—	2	1	no	—
263	C₂×C₃×C₈	—	2	1	no	—
264	C₂×C₃×C₈	—	2	1	no	—
265	C₂×C₃×C₈	—	4	2	no	—
266	C₂×C₃×C₈	—	4	2	no	—
267	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	3	2	no	—
277	C₃×C₄⋊C₄	—	6	2	no	—
278	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	6	2	no	—
283	C₃×C₂²⋊C₄	—	6	2	no	—
284	C₃×C₂²⋊C₄	—	6	2	no	—
285	C₃×C₂²⋊C₄	—	6	2	no	—
286	C₃×C₂²⋊C₄	—	6	2	no	—
287	C₃×C₂²⋊C₄	D₁₂	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	D₁₂	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
291	C₃×C₄²	—	2	1	no	—
292	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
293	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
294	#217	—	2	2	no	—
295	(C₂×D₃)⋊C₄	—	2	2	no	—
296	(C₂×D₃)⋊C₄	—	2	2	no	—
297	(C₂×D₃)⋊C₄	—	2	2	no	—
298	(C₂×D₃)⋊C₄	—	2	2	no	—
299	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
300	Dic₃⋊C₄	—	2	2	no	—
301	Dic₁₂	—	2	2	no	—
302	D₂₄	—	2	4	no	—
303	D₂₄	—	2	2	no	—
304	D₂₄	C₃×D₄	1	4	yes	complemented
305	#204	—	2	4	no	—
306	#204	—	4	2	no	—
307	C₂²×C₃²	—	2	1	no	—
308	C₂²×C₃²	—	2	1	no	—
309	C₂²×C₃²	—	2	1	no	—
310	C₂²×C₃²	—	2	1	no	—
311	C₂²×C₃²	—	2	1	no	—
312	C₂²×C₃²	#135	1	2	yes	complemented
313	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₃×D₃	—	2	4	no	—
315	C₂×C₃×D₃	—	4	2	no	—
316	C₂×C₃×D₃	—	4	2	no	—
317	C₂×C₃×D₃	—	4	2	no	—
318	C₂×C₃×D₃	—	4	2	no	—
319	C₂×C₃×D₃	—	4	2	no	—
320	C₂×C₃×D₃	—	8	8	no	—
321	C₃²×C₄	—	2	1	no	—
322	C₃²×C₄	—	2	1	no	—
323	C₃²×C₄	—	2	1	no	—
324	C₃²×C₄	—	2	1	no	—
325	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
327	C₃×Dic₃	—	4	2	no	—
328	C₃×Dic₃	—	4	2	no	—
329	C₂×#41	—	3	2	no	—
330	C₂²×D₄	—	3	2	no	—
331	#135	—	6	4	no	—
332	C₂×Q₁₆	—	3	1	no	—
333	C₂×SD₁₆	—	3	2	no	—
334	C₂×SD₁₆	—	3	2	no	—
335	C₂×D₈	—	3	1	no	—
336	C₂×D₈	—	3	2	no	—
337	C₂×D₈	—	3	1	no	—
338	C₂×D₈	—	6	4	no	—
339	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
340	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
341	#124	—	3	2	no	—
342	#123	—	6	2	no	—
343	C₂²⋊Q₈	—	3	2	no	—
344	#121	—	3	2	no	—
345	#121	—	6	2	no	—
346	#120	—	6	2	no	—
347	C₄×D₄	—	3	2	no	—
348	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	—	6	2	no	—
350	#107	—	3	1	no	—
351	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
352	#103	—	3	2	no	—
353	#102	—	3	2	no	—
354	#102	—	3	2	no	—
355	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
356	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
357	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	6	2	no	—
361	C₂³×C₃	—	6	2	no	—
362	C₂³×C₃	—	12	4	no	—
363	C₂³×C₃	—	12	4	no	—
364	C₂³×C₃	—	24	2	no	—
365	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
366	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
367	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
369	C₂²×D₃	—	2	2	no	—
370	C₂²×D₃	—	2	2	no	—
371	C₂²×D₃	—	4	4	no	—
372	C₂²×D₃	—	4	4	no	—
373	C₂²×D₃	—	8	2	no	—
374	C₃×Q₈	—	6	2	no	—
375	C₃×Q₈	—	6	2	no	—
376	C₃×D₄	—	2	4	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	3	4	no	—
380	C₃×D₄	—	6	2	no	—
381	C₃×D₄	—	6	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	12	4	no	—
384	C₃×D₄	—	12	4	no	—
385	C₃×D₄	—	24	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	4	1	no	—
400	C₂×C₃×C₄	—	4	1	no	—
401	C₂×C₃×C₄	—	4	1	no	—
402	C₂×C₃×C₄	—	4	1	no	—
403	C₂×C₃×C₄	—	6	2	no	—
404	C₂×C₃×C₄	—	6	2	no	—
405	C₂×C₃×C₄	—	12	4	no	—
406	C₂×C₃×C₄	—	24	2	no	—
407	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
417	#67	—	4	4	no	—
418	#67	—	8	2	no	—
419	C₂×Dic₃	—	2	2	no	—
420	C₂×Dic₃	—	2	2	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	—	2	2	no	—
423	D₁₂	—	2	2	no	—
424	D₁₂	—	4	4	no	—
425	D₁₂	C₂×C₃×D₄	1	4	yes	—
426	C₄×D₃	—	4	4	no	—
427	C₄×D₃	—	8	2	no	—
428	Dic₆	—	2	2	no	—
429	Dic₆	—	2	2	no	—
430	C₃×C₈	—	2	1	no	—
431	C₃×C₈	—	2	1	no	—
432	C₃×C₈	—	2	1	no	—
433	C₃×C₈	—	2	1	no	—
434	C₃×C₈	—	2	1	no	—
435	C₃×C₈	—	2	1	no	—
436	C₃×C₈	—	2	2	no	—
437	C₃×C₈	—	4	1	no	—
438	C₃×C₈	—	4	1	no	—
439	C₃×C₈	—	4	1	no	—
440	C₃×C₈	D₃×D₄	1	2	yes	—
441	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
442	C₂×C₃²	—	2	2	no	—
443	C₂×C₃²	—	4	1	no	—
444	C₂×C₃²	D₄²	1	1	yes	characteristic
445	C₂×C₃²	C₂×#135	1	1	yes	characteristic
446	C₂×C₃²	#576	1	1	yes	characteristic
447	C₃×D₃	—	4	4	no	—
448	C₃×D₃	—	8	2	no	—
449	C₂⁴	—	6	2	no	—
450	#41	—	6	4	no	—
451	#41	—	12	2	no	—
452	C₂×Q₈	—	3	2	no	—
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	6	4	no	—
456	C₂×D₄	—	6	2	no	—
457	C₂×D₄	—	6	2	no	—
458	C₂×D₄	—	6	2	no	—
459	C₂×D₄	—	12	2	no	—
460	C₂×D₄	C₃×D₁₂	1	1	yes	characteristic
461	C₂²×C₄	—	6	2	no	—
462	C₂²×C₄	—	6	2	no	—
463	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
465	Q₁₆	—	6	2	no	—
466	SD₁₆	—	6	4	no	—
467	SD₁₆	—	12	2	no	—
468	D₈	—	3	4	no	—
469	D₈	—	6	4	no	—
470	D₈	—	6	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
475	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
476	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	6	2	no	—
479	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
480	C₂²⋊C₄	—	6	2	no	—
481	C₂²⋊C₄	—	6	2	no	—
482	C₂²⋊C₄	—	6	2	no	—
483	C₂²⋊C₄	—	6	2	no	—
484	C₂²⋊C₄	—	6	2	no	—
485	C₂²⋊C₄	C₃×D₁₂	1	1	yes	characteristic
486	C₂²⋊C₄	C₃×D₁₂	1	1	yes	characteristic
487	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	4	1	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	—	4	1	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	—	6	4	no	—
506	C₂²×C₃	—	12	2	no	—
507	C₂²×C₃	—	12	2	no	—
508	C₂²×C₃	—	12	2	no	—
509	C₂²×C₃	—	12	2	no	—
510	C₂²×C₃	—	12	2	no	—
511	C₂²×C₃	—	24	8	no	—
512	C₂²×C₃	#904	1	2	yes	complemented
513	C₂²×C₃	C₃×#135	1	2	yes	complemented
514	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
515	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
516	C₂×D₃	—	2	4	no	—
517	C₂×D₃	—	4	2	no	—
518	C₂×D₃	—	4	2	no	—
519	C₂×D₃	—	4	2	no	—
520	C₂×D₃	—	4	2	no	—
521	C₂×D₃	—	4	2	no	—
522	C₂×D₃	—	8	8	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	—	12	2	no	—
538	C₃×C₄	—	12	2	no	—
539	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
540	C₃×C₄	#1009	1	1	yes	characteristic
541	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
542	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
543	Dic₃	—	4	2	no	—
544	Dic₃	—	4	2	no	—
545	C₃²	#3280	1	1	yes	characteristic, complemented, Sylow
546	C₂³	—	6	2	no	—
547	C₂³	—	6	2	no	—
548	C₂³	—	12	4	no	—
549	C₂³	—	12	4	no	—
550	C₂³	—	24	2	no	—
551	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
552	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
553	Q₈	—	6	2	no	—
554	Q₈	—	6	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	3	4	no	—
557	D₄	—	6	2	no	—
558	D₄	—	6	2	no	—
559	D₄	—	6	2	no	—
560	D₄	—	12	4	no	—
561	D₄	—	12	4	no	—
562	D₄	—	24	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	—	6	2	no	—
569	C₂×C₄	—	12	4	no	—
570	C₂×C₄	—	24	2	no	—
571	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
572	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
573	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
574	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	C₃×D₃×D₄	1	2	yes	—
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	2	2	no	—
582	C₂×C₃	—	2	1	no	—
583	C₂×C₃	—	2	1	no	—
584	C₂×C₃	—	2	1	no	—
585	C₂×C₃	—	4	2	no	—
586	C₂×C₃	—	4	2	no	—
587	C₂×C₃	—	4	1	no	—
588	C₂×C₃	—	4	1	no	—
589	C₂×C₃	—	12	4	no	—
590	C₂×C₃	—	24	2	no	—
591	C₂×C₃	D₄×D₁₂	1	1	yes	characteristic
592	C₂×C₃	C₂×#904	1	1	yes	characteristic
593	C₂×C₃	#5752	1	1	yes	characteristic
594	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
595	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
596	C₂×C₃	C₃×#576	1	1	yes	characteristic
597	D₃	—	4	4	no	—
598	D₃	—	8	2	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	6	4	no	—
605	C₂²	—	12	2	no	—
606	C₂²	—	12	2	no	—
607	C₂²	—	12	2	no	—
608	C₂²	—	12	2	no	—
609	C₂²	—	12	2	no	—
610	C₂²	—	24	8	no	—
611	C₂²	C₃×#904	1	2	yes	complemented
612	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	12	2	no	—
618	C₄	—	12	2	no	—
619	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
620	C₄	C₃×#1009	1	1	yes	characteristic
621	C₃	—	2	1	no	—
622	C₃	#79433	1	1	yes	characteristic, direct product factor
623	C₃	C₃×#3280	1	1	yes	characteristic, complemented
624	C₂	—	2	2	no	—
625	C₂	—	4	1	no	—
626	C₂	—	12	4	no	—
627	C₂	—	24	2	no	—
628	C₂	C₃×D₄×D₁₂	1	1	yes	characteristic
629	C₂	C₂×C₃×#904	1	1	yes	characteristic
630	C₂	C₃×#5752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₈×D₄	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×C₈×D₄	D₃
hypocenter	C₃	C₃×#3280
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#904	C₂	semidirect
2. C₂²×C₃×D₂₄	C₂	semidirect
3. C₃×#5550	C₂	semidirect
4. C₃²×C₈×D₄	C₂	semidirect
5. C₃×#5116	C₂	semidirect
6. C₃×#5115	C₂	semidirect
7. C₃×#4844	C₂	semidirect
8. C₃×#4734	C₂	semidirect
9. C₃×#4731	C₂	semidirect
10. C₃×#4696	C₂	semidirect
11. C₃×C₄×D₂₄	C₂	semidirect
13. #79433	C₃	direct (N × H)
14. C₂×C₃×#235	C₂²	semidirect
17. C₂²×C₃²×C₈	C₂²	semidirect
20. C₃×#930	C₂²	semidirect
22. C₂×C₃×Dic₁₂	C₂²	semidirect
28. C₂×C₃×#204	C₂²	semidirect
29. C₂×C₃×#204	C₂²	semidirect
33. C₃×#875	C₂²	semidirect
34. C₃×C₄×D₁₂	C₂²	semidirect
35. C₃²×C₄⋊C₈	C₂²	semidirect
37. C₃²×C₂²⋊C₈	C₂²	semidirect
38. C₃²×C₄×C₈	C₂²	semidirect
39. C₃×#821	C₂²	semidirect
40. C₃×#821	C₂²	semidirect
41. C₃×#818	C₂²	semidirect
42. C₃×#816	C₂²	semidirect
46. C₂×#904	C₂×C₃	semidirect
47. C₂²×D₂₄	C₂×C₃	semidirect
48. #5550	C₂×C₃	semidirect
57. C₃×C₈×D₄	D₃	semidirect
58. C₃×C₈×D₄	C₂×C₃	semidirect
59. #5116	C₂×C₃	semidirect
60. #5115	C₂×C₃	semidirect
61. #4844	C₂×C₃	semidirect
62. #4734	C₂×C₃	semidirect
63. #4731	C₂×C₃	semidirect
64. #4696	C₂×C₃	semidirect
65. C₄×D₂₄	C₂×C₃	semidirect
102. C₃×D₂₄	D₄	semidirect
108. C₂×#235	C₂²×C₃	semidirect
121. C₂²×C₃×C₈	C₂×D₃	semidirect
123. C₂²×C₃×C₈	C₂²×C₃	semidirect
136. #930	C₂²×C₃	semidirect
138. C₂×Dic₁₂	C₂²×C₃	semidirect
144. C₂×#204	C₂²×C₃	semidirect
145. C₂×#204	C₂²×C₃	semidirect
149. #875	C₂²×C₃	semidirect
150. C₄×D₁₂	C₂²×C₃	semidirect
153. C₃×C₄⋊C₈	C₂×D₃	semidirect
154. C₃×C₄⋊C₈	C₂²×C₃	semidirect
161. C₃×C₂²⋊C₈	C₂×D₃	semidirect
163. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
165. C₃×C₄×C₈	C₂×D₃	semidirect
166. C₃×C₄×C₈	C₂²×C₃	semidirect
167. #821	C₂²×C₃	semidirect
168. #821	C₂²×C₃	semidirect
169. #818	C₂²×C₃	semidirect
170. #816	C₂²×C₃	semidirect
215. C₈×D₄	C₃×D₃	semidirect
304. D₂₄	C₃×D₄	semidirect
312. C₂²×C₃²	#135	semidirect
340. C₂²×C₈	C₂×C₃×D₃	semidirect
351. C₄⋊C₈	C₂×C₃×D₃	semidirect
356. C₂²⋊C₈	C₂×C₃×D₃	semidirect
357. C₄×C₈	C₂×C₃×D₃	semidirect
512. C₂²×C₃	#904	semidirect
513. C₂²×C₃	C₃×#135	semidirect
545. C₃²	#3280	semidirect
611. C₂²	C₃×#904	semidirect
622. C₃	#79433	direct (N × H)
623. 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×#904	2
C₂²×C₃×D₂₄	2
C₃×#5550	2
C₃²×C₈×D₄	2
C₃×#5116	2
C₃×#5115	2
C₃×#4844	2
C₃×#4734	2
C₃×#4731	2
C₃×#4696	2
C₃×C₄×D₂₄	2
C₃×#3280	3
#79433	3

Subgroups — C3×#79433 #11885812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79433 #11885812