Subgroups — C₃×#87297 #11918964

Order 1152.

3253 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5964	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5838	C₂	1	4	yes	maximal, complemented
4	C₃×#5837	C₂	1	4	yes	maximal, complemented
5	C₃×#5836	C₂	1	4	yes	maximal, complemented
6	C₃×#5835	C₂	1	4	yes	maximal, complemented
7	C₃×#5822	C₂	1	6	yes	maximal, complemented
8	C₂×C₃×#950	C₂	1	6	yes	maximal, complemented
9	C₂×C₃×#948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3584	—	3	1	no	maximal
11	#87297	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₃²×2₋¹⁺⁴	—	2	1	no	—
13	C₃²×2₋¹⁺⁴	C₂²	1	4	yes	complemented
14	C₃²×H(5,𝔽₂)	—	2	3	no	—
15	C₃²×H(5,𝔽₂)	C₂²	1	4	yes	complemented
16	C₂×C₃²×#41	—	2	4	no	—
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃²×#41	C₂²	1	6	yes	complemented
19	C₃×#1010	C₂²	1	4	yes	complemented
20	C₃×#1009	C₂²	1	4	yes	complemented
21	C₃×D₃×#41	—	2	4	no	—
22	C₃×#1007	—	2	1	no	—
23	C₃×#1004	—	2	3	no	—
24	C₂×C₃×#235	C₂²	1	6	yes	complemented
25	C₃×#951	C₂²	1	12	yes	complemented
26	C₃×#950	C₂²	1	4	yes	complemented
27	C₃×#950	C₂²	1	12	yes	complemented
28	C₃×#950	C₂²	1	12	yes	complemented
29	C₃×#950	C₂²	1	12	yes	complemented
30	C₃×#949	C₂²	1	12	yes	complemented
31	C₃×#948	C₂²	1	4	yes	complemented
32	C₃×#948	C₂²	1	4	yes	complemented
33	C₂×C₃×#216	C₂²	1	6	yes	complemented
34	C₃×#942	C₂²	1	12	yes	complemented
35	C₂×C₃×#215	C₂²	1	6	yes	complemented
36	C₂×C₃×#214	C₂²	1	6	yes	complemented
37	C₃×#932	C₂²	1	12	yes	complemented
38	C₂×C₃×#213	C₂²	1	6	yes	complemented
39	C₂×C₃×#208	C₂²	1	3	yes	complemented
40	C₂²×C₃×C₃⋊C₈	C₂²	1	3	yes	complemented
41	C₃×#585	—	2	1	no	—
42	C₃×#585	—	3	1	no	—
43	C₃×#585	D₃	1	1	yes	characteristic, complemented
44	C₃×#585	C₂×C₃	1	1	yes	characteristic, complemented
45	#5964	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#578	—	3	4	no	—
47	C₃×#577	—	3	4	no	—
48	C₃×#577	—	3	4	no	—
49	C₃×#576	—	3	4	no	—
50	C₃×#575	—	3	6	no	—
51	C₂×C₃×#135	—	3	6	no	—
52	C₂×C₃×#131	—	3	1	no	—
53	#5838	C₂×C₃	1	4	yes	complemented
54	#5837	C₂×C₃	1	4	yes	complemented
55	#5836	C₂×C₃	1	4	yes	complemented
56	#5835	C₂×C₃	1	4	yes	complemented
57	#5822	C₂×C₃	1	6	yes	complemented
58	C₂×#950	C₂×C₃	1	6	yes	complemented
59	C₂×#948	C₂×C₃	1	1	yes	characteristic, complemented
60	C₃²×#41	—	2	4	no	—
61	C₃²×#41	—	2	12	no	—
62	C₃²×#41	—	2	6	no	—
63	C₃²×#41	—	2	6	no	—
64	C₃²×#41	D₄	1	4	yes	—
65	C₃²×#41	C₂³	1	12	yes	—
66	C₃²×#41	C₂³	1	4	yes	—
67	C₃²×#41	C₂³	1	4	yes	—
68	C₂×C₃²×Q₈	—	2	4	no	—
69	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
70	C₂×C₃²×Q₈	C₂³	1	6	yes	—
71	C₂×C₃²×D₄	—	2	6	no	—
72	C₂×C₃²×D₄	—	2	12	no	—
73	C₂×C₃²×D₄	D₄	1	3	yes	—
74	C₂×C₃²×D₄	C₂³	1	6	yes	—
75	C₂²×C₃²×C₄	—	2	6	no	—
76	C₂²×C₃²×C₄	C₂³	1	3	yes	—
77	C₂×C₃×#67	—	2	6	no	—
78	C₃×#239	—	2	4	no	—
79	C₃×D₃×Q₈	—	2	4	no	—
80	C₃×#237	—	2	12	no	—
81	C₃×D₃×D₄	—	2	12	no	—
82	C₃×#235	—	2	6	no	—
83	C₃×#235	—	2	6	no	—
84	C₃×#235	C₂³	1	12	yes	—
85	C₃×#235	C₂³	1	4	yes	—
86	C₂×C₃×D₁₂	C₂³	1	6	yes	—
87	C₂×C₃×C₄×D₃	—	2	6	no	—
88	C₂×C₃×Dic₆	C₂³	1	6	yes	—
89	C₃×#216	C₂³	1	12	yes	—
90	C₃×#216	C₂³	1	4	yes	—
91	C₃×#215	C₂³	1	4	yes	—
92	C₃×#215	C₂³	1	12	yes	—
93	C₃×#214	C₂³	1	12	yes	—
94	C₃×#214	C₂³	1	4	yes	—
95	C₃×#213	C₂³	1	4	yes	—
96	C₃×#213	C₂³	1	12	yes	—
97	C₃×#208	C₂³	1	12	yes	—
98	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂³	1	3	yes	—
100	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	—
101	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	—
102	#3584	—	3	1	no	Sylow
103	C₃×2₋¹⁺⁴	—	2	2	no	—
104	C₃×2₋¹⁺⁴	—	2	1	no	—
105	C₃×2₋¹⁺⁴	—	2	1	no	—
106	C₃×2₋¹⁺⁴	—	2	4	no	—
107	C₃×2₋¹⁺⁴	—	3	4	no	—
108	C₃×2₋¹⁺⁴	—	6	1	no	—
109	C₃×2₋¹⁺⁴	C₂×D₃	1	4	yes	complemented
110	C₃×2₋¹⁺⁴	C₂²×C₃	1	4	yes	complemented
111	C₃×H(5,𝔽₂)	—	2	6	no	—
112	C₃×H(5,𝔽₂)	—	2	3	no	—
113	C₃×H(5,𝔽₂)	—	2	3	no	—
114	C₃×H(5,𝔽₂)	—	2	4	no	—
115	C₃×H(5,𝔽₂)	—	3	4	no	—
116	C₃×H(5,𝔽₂)	—	6	3	no	—
117	C₃×H(5,𝔽₂)	C₂×D₃	1	4	yes	complemented
118	C₃×H(5,𝔽₂)	C₂²×C₃	1	4	yes	complemented
119	C₂×C₃×#41	—	2	8	no	—
120	C₂×C₃×#41	—	2	4	no	—
121	C₂×C₃×#41	—	2	4	no	—
122	C₂×C₃×#41	—	2	1	no	—
123	C₂×C₃×#41	—	2	6	no	—
124	C₂×C₃×#41	—	3	6	no	—
125	C₂×C₃×#41	—	6	4	no	—
126	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
127	C₂×C₃×#41	C₂×D₃	1	6	yes	complemented
128	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×#41	C₂²×C₃	1	6	yes	complemented
130	#1010	C₂²×C₃	1	4	yes	complemented
131	#1009	C₂²×C₃	1	4	yes	complemented
132	D₃×#41	—	2	4	no	—
133	#1007	—	2	1	no	—
134	#1004	—	2	3	no	—
135	C₂×#235	C₂²×C₃	1	6	yes	complemented
136	C₃×#137	—	3	12	no	—
137	C₃×#137	—	3	12	no	—
138	C₃×AGL(1,ℤ/8)	—	3	12	no	—
139	C₃×AGL(1,ℤ/8)	—	3	12	no	—
140	C₃×#135	—	3	4	no	—
141	C₃×#135	—	3	12	no	—
142	C₃×#135	—	3	12	no	—
143	C₃×#135	—	3	12	no	—
144	C₂×C₃×Q₁₆	—	3	6	no	—
145	C₂×C₃×SD₁₆	—	3	6	no	—
146	C₂×C₃×SD₁₆	—	3	6	no	—
147	C₂×C₃×D₈	—	3	6	no	—
148	C₃×#131	—	3	4	no	—
149	C₃×#131	—	3	4	no	—
150	C₂×C₃×M₁₆	—	3	3	no	—
151	C₂²×C₃×C₈	—	3	3	no	—
152	#951	C₂²×C₃	1	12	yes	complemented
153	#950	C₂²×C₃	1	4	yes	complemented
154	#950	C₂²×C₃	1	12	yes	complemented
155	#950	C₂²×C₃	1	12	yes	complemented
156	#950	C₂²×C₃	1	12	yes	complemented
157	#949	C₂²×C₃	1	12	yes	complemented
158	#948	C₂²×C₃	1	4	yes	complemented
159	#948	C₂²×C₃	1	4	yes	complemented
160	C₂×#216	C₂²×C₃	1	6	yes	complemented
161	#942	C₂²×C₃	1	12	yes	complemented
162	C₂×#215	C₂²×C₃	1	6	yes	complemented
163	C₂×#214	C₂²×C₃	1	6	yes	complemented
164	#932	C₂²×C₃	1	12	yes	complemented
165	C₂×#213	C₂²×C₃	1	6	yes	complemented
166	C₂×#208	C₂²×C₃	1	3	yes	complemented
167	C₂²×C₃⋊C₈	C₂²×C₃	1	3	yes	complemented
168	C₂³×C₃²	—	2	6	no	—
169	C₂³×C₃²	C₂×D₄	1	3	yes	—
170	C₂²×C₃×D₃	—	2	6	no	—
171	C₃²×Q₈	—	2	6	no	—
172	C₃²×Q₈	C₂×D₄	1	4	yes	—
173	C₃²×Q₈	C₂⁴	1	4	yes	—
174	C₃²×D₄	—	2	12	no	—
175	C₃²×D₄	—	2	4	no	—
176	C₃²×D₄	—	2	6	no	—
177	C₃²×D₄	C₂×D₄	1	12	yes	—
178	C₃²×D₄	C₂⁴	1	4	yes	—
179	C₂×C₃²×C₄	—	2	6	no	—
180	C₂×C₃²×C₄	—	2	4	no	—
181	C₂×C₃²×C₄	—	2	12	no	—
182	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
183	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
184	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
186	C₃×#67	—	2	4	no	—
187	C₃×#67	—	2	12	no	—
188	C₂×C₃×Dic₃	—	2	6	no	—
189	C₃×D₁₂	—	2	6	no	—
190	C₃×D₁₂	C₂⁴	1	4	yes	—
191	C₃×C₄×D₃	—	2	4	no	—
192	C₃×C₄×D₃	—	2	12	no	—
193	C₃×Dic₆	—	2	6	no	—
194	C₃×Dic₆	C₂⁴	1	4	yes	—
195	C₃×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
196	C₃×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
197	C₃×C₃⋊C₈	C₂⁴	1	6	yes	—
198	#585	—	3	1	no	—
199	#585	C₃×D₃	1	1	yes	characteristic, complemented
200	#578	—	3	4	no	—
201	#577	—	3	4	no	—
202	#577	—	3	4	no	—
203	#576	—	3	4	no	—
204	#575	—	3	6	no	—
205	C₂×#135	—	3	6	no	—
206	C₂×#131	—	3	1	no	—
207	C₃×#41	—	2	12	no	—
208	C₃×#41	—	2	8	no	—
209	C₃×#41	—	2	24	no	—
210	C₃×#41	—	2	12	no	—
211	C₃×#41	—	2	4	no	—
212	C₃×#41	—	2	4	no	—
213	C₃×#41	—	2	12	no	—
214	C₃×#41	—	2	12	no	—
215	C₃×#41	—	2	6	no	—
216	C₃×#41	—	2	6	no	—
217	C₃×#41	—	2	6	no	—
218	C₃×#41	—	2	6	no	—
219	C₃×#41	—	2	4	no	—
220	C₃×#41	—	2	4	no	—
221	C₃×#41	—	2	12	no	—
222	C₃×#41	—	2	4	no	—
223	C₃×#41	—	3	4	no	—
224	C₃×#41	—	3	12	no	—
225	C₃×#41	—	6	4	no	—
226	C₃×#41	—	6	12	no	—
227	C₃×#41	—	6	6	no	—
228	C₃×#41	—	6	6	no	—
229	C₃×#41	#67	1	4	yes	—
230	C₃×#41	C₃×D₄	1	4	yes	—
231	C₃×#41	C₂²×D₃	1	4	yes	—
232	C₃×#41	C₂²×D₃	1	12	yes	—
233	C₃×#41	C₂²×D₃	1	4	yes	—
234	C₃×#41	C₂³×C₃	1	12	yes	—
235	C₃×#41	C₂³×C₃	1	4	yes	—
236	C₃×#41	C₂³×C₃	1	4	yes	—
237	C₂×C₃×Q₈	—	2	8	no	—
238	C₂×C₃×Q₈	—	2	4	no	—
239	C₂×C₃×Q₈	—	2	4	no	—
240	C₂×C₃×Q₈	—	2	1	no	—
241	C₂×C₃×Q₈	—	2	6	no	—
242	C₂×C₃×Q₈	—	3	6	no	—
243	C₂×C₃×Q₈	—	6	4	no	—
244	C₂×C₃×Q₈	#67	1	1	yes	characteristic
245	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
246	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
247	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
248	C₂×C₃×D₄	—	2	12	no	—
249	C₂×C₃×D₄	—	2	24	no	—
250	C₂×C₃×D₄	—	2	6	no	—
251	C₂×C₃×D₄	—	2	6	no	—
252	C₂×C₃×D₄	—	2	12	no	—
253	C₂×C₃×D₄	—	2	12	no	—
254	C₂×C₃×D₄	—	2	3	no	—
255	C₂×C₃×D₄	—	2	6	no	—
256	C₂×C₃×D₄	—	3	6	no	—
257	C₂×C₃×D₄	—	6	6	no	—
258	C₂×C₃×D₄	—	6	12	no	—
259	C₂×C₃×D₄	#67	1	3	yes	—
260	C₂×C₃×D₄	C₃×D₄	1	3	yes	—
261	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
262	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
263	C₂²×C₃×C₄	—	2	12	no	—
264	C₂²×C₃×C₄	—	2	6	no	—
265	C₂²×C₃×C₄	—	2	6	no	—
266	C₂²×C₃×C₄	—	2	3	no	—
267	C₂²×C₃×C₄	—	6	6	no	—
268	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
269	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
270	C₂×#67	—	2	6	no	—
271	#239	—	2	4	no	—
272	D₃×Q₈	—	2	4	no	—
273	#237	—	2	12	no	—
274	D₃×D₄	—	2	12	no	—
275	#235	—	2	6	no	—
276	#235	—	2	6	no	—
277	#235	C₂³×C₃	1	12	yes	—
278	#235	C₂³×C₃	1	4	yes	—
279	C₂×D₁₂	C₂³×C₃	1	6	yes	—
280	C₂×C₄×D₃	—	2	6	no	—
281	C₂×Dic₆	C₂³×C₃	1	6	yes	—
282	C₃×Q₁₆	—	3	4	no	—
283	C₃×Q₁₆	—	3	12	no	—
284	C₃×SD₁₆	—	3	4	no	—
285	C₃×SD₁₆	—	3	12	no	—
286	C₃×SD₁₆	—	3	4	no	—
287	C₃×SD₁₆	—	3	12	no	—
288	C₃×D₈	—	3	4	no	—
289	C₃×D₈	—	3	12	no	—
290	C₃×M₁₆	—	3	12	no	—
291	C₂×C₃×C₈	—	3	1	no	—
292	C₂×C₃×C₈	—	3	3	no	—
293	C₂×C₃×C₈	—	3	6	no	—
294	C₂×C₃×C₈	—	3	6	no	—
295	#216	C₂³×C₃	1	12	yes	—
296	#216	C₂³×C₃	1	4	yes	—
297	#215	C₂³×C₃	1	4	yes	—
298	#215	C₂³×C₃	1	12	yes	—
299	#214	C₂³×C₃	1	12	yes	—
300	#214	C₂³×C₃	1	4	yes	—
301	#213	C₂³×C₃	1	4	yes	—
302	#213	C₂³×C₃	1	12	yes	—
303	#208	C₂³×C₃	1	12	yes	—
304	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₃⋊C₈	C₂³×C₃	1	3	yes	—
306	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	—
307	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	—
308	C₂²×C₃²	—	2	4	no	—
309	C₂²×C₃²	—	4	3	no	—
310	C₂²×C₃²	—	8	6	no	—
311	C₂²×C₃²	C₂²×D₄	1	6	yes	—
312	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₃×D₃	—	2	4	no	—
314	C₂×C₃×D₃	—	8	6	no	—
315	C₃²×C₄	—	2	4	no	—
316	C₃²×C₄	C₂²×D₄	1	6	yes	—
317	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
318	C₃²×C₄	C₂⁵	1	1	yes	characteristic
319	C₃×Dic₃	—	2	4	no	—
320	2₋¹⁺⁴	—	2	1	no	—
321	2₋¹⁺⁴	—	3	4	no	—
322	2₋¹⁺⁴	—	6	1	no	—
323	2₋¹⁺⁴	C₂×C₃×D₃	1	4	yes	complemented
324	H(5,𝔽₂)	—	2	3	no	—
325	H(5,𝔽₂)	—	3	4	no	—
326	H(5,𝔽₂)	—	6	3	no	—
327	H(5,𝔽₂)	C₂×C₃×D₃	1	4	yes	complemented
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	3	6	no	—
330	C₂×#41	—	6	4	no	—
331	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
332	C₂×#41	C₂×C₃×D₃	1	6	yes	complemented
333	#137	—	3	12	no	—
334	#137	—	3	12	no	—
335	AGL(1,ℤ/8)	—	3	12	no	—
336	AGL(1,ℤ/8)	—	3	12	no	—
337	#135	—	3	4	no	—
338	#135	—	3	12	no	—
339	#135	—	3	12	no	—
340	#135	—	3	12	no	—
341	C₂×Q₁₆	—	3	6	no	—
342	C₂×SD₁₆	—	3	6	no	—
343	C₂×SD₁₆	—	3	6	no	—
344	C₂×D₈	—	3	6	no	—
345	#131	—	3	4	no	—
346	#131	—	3	4	no	—
347	C₂×M₁₆	—	3	3	no	—
348	C₂²×C₈	—	3	3	no	—
349	C₂³×C₃	—	2	12	no	—
350	C₂³×C₃	—	2	6	no	—
351	C₂³×C₃	—	2	6	no	—
352	C₂³×C₃	—	2	3	no	—
353	C₂³×C₃	—	6	6	no	—
354	C₂³×C₃	C₂×#67	1	3	yes	—
355	C₂³×C₃	C₂×C₃×D₄	1	3	yes	—
356	C₂²×D₃	—	2	6	no	—
357	C₃×Q₈	—	2	12	no	—
358	C₃×Q₈	—	2	6	no	—
359	C₃×Q₈	—	2	6	no	—
360	C₃×Q₈	—	2	4	no	—
361	C₃×Q₈	—	2	4	no	—
362	C₃×Q₈	—	3	4	no	—
363	C₃×Q₈	—	6	6	no	—
364	C₃×Q₈	C₂×#67	1	4	yes	—
365	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
366	C₃×Q₈	C₂³×D₃	1	4	yes	—
367	C₃×Q₈	C₂⁴×C₃	1	4	yes	—
368	C₃×D₄	—	2	24	no	—
369	C₃×D₄	—	2	8	no	—
370	C₃×D₄	—	2	12	no	—
371	C₃×D₄	—	2	12	no	—
372	C₃×D₄	—	2	4	no	—
373	C₃×D₄	—	2	12	no	—
374	C₃×D₄	—	2	4	no	—
375	C₃×D₄	—	2	6	no	—
376	C₃×D₄	—	2	6	no	—
377	C₃×D₄	—	2	4	no	—
378	C₃×D₄	—	2	12	no	—
379	C₃×D₄	—	3	4	no	—
380	C₃×D₄	—	6	12	no	—
381	C₃×D₄	—	6	4	no	—
382	C₃×D₄	—	6	6	no	—
383	C₃×D₄	C₂×#67	1	12	yes	—
384	C₃×D₄	C₂×C₃×D₄	1	12	yes	—
385	C₃×D₄	C₂³×D₃	1	4	yes	—
386	C₃×D₄	C₂⁴×C₃	1	4	yes	—
387	C₂×C₃×C₄	—	2	8	no	—
388	C₂×C₃×C₄	—	2	12	no	—
389	C₂×C₃×C₄	—	2	24	no	—
390	C₂×C₃×C₄	—	2	6	no	—
391	C₂×C₃×C₄	—	2	6	no	—
392	C₂×C₃×C₄	—	2	12	no	—
393	C₂×C₃×C₄	—	2	4	no	—
394	C₂×C₃×C₄	—	2	4	no	—
395	C₂×C₃×C₄	—	2	12	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	6	no	—
398	C₂×C₃×C₄	—	2	6	no	—
399	C₂×C₃×C₄	—	2	3	no	—
400	C₂×C₃×C₄	—	6	6	no	—
401	C₂×C₃×C₄	—	6	12	no	—
402	C₂×C₃×C₄	—	6	4	no	—
403	C₂×C₃×C₄	C₂×#67	1	3	yes	—
404	C₂×C₃×C₄	C₂×#67	1	6	yes	—
405	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
406	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
407	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
408	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
411	#67	—	2	4	no	—
412	#67	—	2	12	no	—
413	C₂×Dic₃	—	2	6	no	—
414	D₁₂	—	2	6	no	—
415	D₁₂	C₂⁴×C₃	1	4	yes	—
416	C₄×D₃	—	2	4	no	—
417	C₄×D₃	—	2	12	no	—
418	Dic₆	—	2	6	no	—
419	Dic₆	C₂⁴×C₃	1	4	yes	—
420	C₃×C₈	—	3	1	no	—
421	C₃×C₈	—	3	1	no	—
422	C₃×C₈	—	3	6	no	—
423	C₃⋊C₈	C₂⁴×C₃	1	1	yes	characteristic
424	C₃⋊C₈	C₂⁴×C₃	1	1	yes	characteristic
425	C₃⋊C₈	C₂⁴×C₃	1	6	yes	—
426	C₂×C₃²	—	2	6	no	—
427	C₂×C₃²	—	2	1	no	—
428	C₂×C₃²	—	4	4	no	—
429	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
430	C₃×D₃	—	4	4	no	—
431	#41	—	2	4	no	—
432	#41	—	2	12	no	—
433	#41	—	2	6	no	—
434	#41	—	2	6	no	—
435	#41	—	3	4	no	—
436	#41	—	3	12	no	—
437	#41	—	6	4	no	—
438	#41	—	6	12	no	—
439	#41	—	6	6	no	—
440	#41	—	6	6	no	—
441	#41	C₃×#67	1	4	yes	—
442	#41	C₂²×C₃×D₃	1	4	yes	—
443	#41	C₂²×C₃×D₃	1	12	yes	—
444	#41	C₂²×C₃×D₃	1	4	yes	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	3	6	no	—
447	C₂×Q₈	—	6	4	no	—
448	C₂×Q₈	C₃×#67	1	1	yes	characteristic
449	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
450	C₂×D₄	—	2	6	no	—
451	C₂×D₄	—	2	12	no	—
452	C₂×D₄	—	3	6	no	—
453	C₂×D₄	—	6	6	no	—
454	C₂×D₄	—	6	12	no	—
455	C₂×D₄	C₃×#67	1	3	yes	—
456	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
457	C₂²×C₄	—	2	6	no	—
458	C₂²×C₄	—	6	6	no	—
459	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
460	Q₁₆	—	3	4	no	—
461	Q₁₆	—	3	12	no	—
462	SD₁₆	—	3	4	no	—
463	SD₁₆	—	3	12	no	—
464	SD₁₆	—	3	4	no	—
465	SD₁₆	—	3	12	no	—
466	D₈	—	3	4	no	—
467	D₈	—	3	12	no	—
468	M₁₆	—	3	12	no	—
469	C₂×C₈	—	3	1	no	—
470	C₂×C₈	—	3	3	no	—
471	C₂×C₈	—	3	6	no	—
472	C₂×C₈	—	3	6	no	—
473	C₂²×C₃	—	2	8	no	—
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	2	6	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	4	3	no	—
479	C₂²×C₃	—	4	3	no	—
480	C₂²×C₃	—	6	4	no	—
481	C₂²×C₃	—	8	3	no	—
482	C₂²×C₃	—	8	6	no	—
483	C₂²×C₃	—	8	6	no	—
484	C₂²×C₃	—	8	12	no	—
485	C₂²×C₃	—	24	6	no	—
486	C₂²×C₃	C₂²×#67	1	6	yes	—
487	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
488	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
489	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
490	C₂×D₃	—	2	4	no	—
491	C₂×D₃	—	8	6	no	—
492	C₃×C₄	—	2	8	no	—
493	C₃×C₄	—	2	4	no	—
494	C₃×C₄	—	2	4	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	6	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	6	4	no	—
499	C₃×C₄	C₂²×#67	1	6	yes	—
500	C₃×C₄	C₂²×#67	1	1	yes	characteristic
501	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
502	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
503	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
504	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
505	Dic₃	—	2	4	no	—
506	C₃²	#3584	1	1	yes	characteristic, complemented, Sylow
507	C₂³	—	2	6	no	—
508	C₂³	—	6	6	no	—
509	C₂³	C₂×C₃×#67	1	3	yes	—
510	Q₈	—	2	6	no	—
511	Q₈	—	3	4	no	—
512	Q₈	—	6	6	no	—
513	Q₈	C₂×C₃×#67	1	4	yes	—
514	Q₈	C₂³×C₃×D₃	1	4	yes	—
515	D₄	—	2	12	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	6	no	—
518	D₄	—	3	4	no	—
519	D₄	—	6	12	no	—
520	D₄	—	6	4	no	—
521	D₄	—	6	6	no	—
522	D₄	C₂×C₃×#67	1	12	yes	—
523	D₄	C₂³×C₃×D₃	1	4	yes	—
524	C₂×C₄	—	2	6	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	12	no	—
527	C₂×C₄	—	6	6	no	—
528	C₂×C₄	—	6	4	no	—
529	C₂×C₄	—	6	12	no	—
530	C₂×C₄	C₂×C₃×#67	1	6	yes	—
531	C₂×C₄	C₂×C₃×#67	1	3	yes	—
532	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
533	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
534	C₈	—	3	1	no	—
535	C₈	—	3	1	no	—
536	C₈	—	3	6	no	—
537	C₂×C₃	—	2	1	no	—
538	C₂×C₃	—	2	6	no	—
539	C₂×C₃	—	2	6	no	—
540	C₂×C₃	—	2	1	no	—
541	C₂×C₃	—	2	1	no	—
542	C₂×C₃	—	4	1	no	—
543	C₂×C₃	—	4	6	no	—
544	C₂×C₃	—	4	8	no	—
545	C₂×C₃	—	4	4	no	—
546	C₂×C₃	—	4	4	no	—
547	C₂×C₃	—	12	4	no	—
548	C₂×C₃	C₂³×#67	1	1	yes	characteristic
549	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
550	D₃	—	4	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	4	3	no	—
553	C₂²	—	6	4	no	—
554	C₂²	—	8	6	no	—
555	C₂²	—	24	6	no	—
556	C₂²	C₂²×C₃×#67	1	6	yes	—
557	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
558	C₄	—	2	4	no	—
559	C₄	—	6	4	no	—
560	C₄	C₂²×C₃×#67	1	1	yes	characteristic
561	C₄	C₂²×C₃×#67	1	6	yes	—
562	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
563	C₃	—	2	1	no	—
564	C₃	#87297	1	1	yes	characteristic, direct product factor
565	C₃	C₃×#3584	1	1	yes	characteristic, complemented
566	C₂	—	2	1	no	—
567	C₂	—	2	6	no	—
568	C₂	—	4	4	no	—
569	C₂	—	12	4	no	—
570	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×#67
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₃²×#585	C₂
socle	C₂×C₃²	C₂³×D₄
hypercenter	C₃×#585	D₃
hypocenter	C₃	C₃×#3584
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×#41 ◁ C₃×#585

Complements

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

N	H ≅ G/N	type
1. C₃²×#585	C₂	semidirect
2. C₃×#5964	C₂	semidirect
3. C₃×#5838	C₂	semidirect
4. C₃×#5837	C₂	semidirect
5. C₃×#5836	C₂	semidirect
6. C₃×#5835	C₂	semidirect
7. C₃×#5822	C₂	semidirect
8. C₂×C₃×#950	C₂	semidirect
9. C₂×C₃×#948	C₂	semidirect
11. #87297	C₃	direct (N × H)
13. C₃²×2₋¹⁺⁴	C₂²	semidirect
15. C₃²×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₃²×#41	C₂²	semidirect
19. C₃×#1010	C₂²	semidirect
20. C₃×#1009	C₂²	semidirect
24. C₂×C₃×#235	C₂²	semidirect
25. C₃×#951	C₂²	semidirect
26. C₃×#950	C₂²	semidirect
27. C₃×#950	C₂²	semidirect
28. C₃×#950	C₂²	semidirect
29. C₃×#950	C₂²	semidirect
30. C₃×#949	C₂²	semidirect
31. C₃×#948	C₂²	semidirect
32. C₃×#948	C₂²	semidirect
33. C₂×C₃×#216	C₂²	semidirect
34. C₃×#942	C₂²	semidirect
35. C₂×C₃×#215	C₂²	semidirect
36. C₂×C₃×#214	C₂²	semidirect
37. C₃×#932	C₂²	semidirect
38. C₂×C₃×#213	C₂²	semidirect
39. C₂×C₃×#208	C₂²	semidirect
40. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
43. C₃×#585	D₃	semidirect
44. C₃×#585	C₂×C₃	semidirect
45. #5964	C₂×C₃	semidirect
53. #5838	C₂×C₃	semidirect
54. #5837	C₂×C₃	semidirect
55. #5836	C₂×C₃	semidirect
56. #5835	C₂×C₃	semidirect
57. #5822	C₂×C₃	semidirect
58. C₂×#950	C₂×C₃	semidirect
59. C₂×#948	C₂×C₃	semidirect
109. C₃×2₋¹⁺⁴	C₂×D₃	semidirect
110. C₃×2₋¹⁺⁴	C₂²×C₃	semidirect
117. C₃×H(5,𝔽₂)	C₂×D₃	semidirect
118. C₃×H(5,𝔽₂)	C₂²×C₃	semidirect
127. C₂×C₃×#41	C₂×D₃	semidirect
129. C₂×C₃×#41	C₂²×C₃	semidirect
130. #1010	C₂²×C₃	semidirect
131. #1009	C₂²×C₃	semidirect
135. C₂×#235	C₂²×C₃	semidirect
152. #951	C₂²×C₃	semidirect
153. #950	C₂²×C₃	semidirect
154. #950	C₂²×C₃	semidirect
155. #950	C₂²×C₃	semidirect
156. #950	C₂²×C₃	semidirect
157. #949	C₂²×C₃	semidirect
158. #948	C₂²×C₃	semidirect
159. #948	C₂²×C₃	semidirect
160. C₂×#216	C₂²×C₃	semidirect
161. #942	C₂²×C₃	semidirect
162. C₂×#215	C₂²×C₃	semidirect
163. C₂×#214	C₂²×C₃	semidirect
164. #932	C₂²×C₃	semidirect
165. C₂×#213	C₂²×C₃	semidirect
166. C₂×#208	C₂²×C₃	semidirect
167. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
199. #585	C₃×D₃	semidirect
323. 2₋¹⁺⁴	C₂×C₃×D₃	semidirect
327. H(5,𝔽₂)	C₂×C₃×D₃	semidirect
332. C₂×#41	C₂×C₃×D₃	semidirect
506. C₃²	#3584	semidirect
564. C₃	#87297	direct (N × H)
565. C₃	C₃×#3584	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#585	2
C₃×#5964	2
C₃×#5838	2
C₃×#5837	2
C₃×#5836	2
C₃×#5835	2
C₃×#5822	2
C₂×C₃×#950	2
C₂×C₃×#948	2
C₃×#3584	3
#87297	3

Subgroups — C3×#87297 #11918964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87297 #11918964