Subgroups — C₃×#79893 #11886851

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5770	C₂	1	2	yes	maximal, complemented
2	C₃×#5751	C₂	1	2	yes	maximal, complemented
3	C₃²×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5141	C₂	1	2	yes	maximal, complemented
5	C₃×#4898	C₂	1	2	yes	maximal, complemented
6	C₃×#4826	C₂	1	2	yes	maximal, complemented
7	C₃×#4822	C₂	1	2	yes	maximal, complemented
8	C₃×#4700	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4693	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3291	—	3	1	no	maximal
11	#79893	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₃×#1010	C₂²	1	2	yes	—
13	C₃×#1009	C₂²	1	2	yes	complemented
14	C₃²×#135	C₂²	1	1	yes	characteristic
15	C₃²×#131	C₂²	1	2	yes	complemented
16	C₃×#951	C₂²	1	2	yes	complemented
17	C₃×#949	C₂²	1	2	yes	—
18	C₃×#918	—	2	2	no	—
19	C₃×#916	—	2	2	no	—
20	C₃×D₃×SD₁₆	—	2	2	no	—
21	C₃×#911	—	2	2	no	—
22	C₃×#909	—	2	2	no	—
23	C₃×#909	C₂²	1	2	yes	complemented
24	C₃×#908	—	2	2	no	—
25	C₃×#908	C₂²	1	2	yes	—
26	C₃×#904	—	2	2	no	—
27	C₃×#904	C₂²	1	1	yes	characteristic
28	C₂×C₃×#204	—	2	2	no	—
29	C₂×C₃×#204	C₂²	1	2	yes	complemented
30	C₂×C₃×#204	C₂²	1	2	yes	complemented
31	C₃×#901	C₂²	1	2	yes	complemented
32	C₃×#874	C₂²	1	1	yes	characteristic
33	C₃×#869	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#104	C₂²	1	2	yes	complemented
36	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#824	C₂²	1	2	yes	complemented
38	C₃×#823	C₂²	1	2	yes	complemented
39	C₃×#819	C₂²	1	1	yes	characteristic, complemented
40	C₃×#805	C₂²	1	2	yes	complemented
41	C₃×#577	—	3	2	no	—
42	C₃×#577	—	3	2	no	—
43	#5770	C₂×C₃	1	2	yes	complemented
44	#5751	C₂×C₃	1	2	yes	complemented
45	C₃×#492	—	3	1	no	—
46	C₃×#471	—	3	2	no	—
47	C₃×#471	—	3	2	no	—
48	C₃×#456	—	3	2	no	—
49	C₃×#453	—	3	2	no	—
50	C₃×#443	—	2	1	no	—
51	C₃×#443	—	3	1	no	—
52	C₃×#443	D₃	1	1	yes	characteristic, complemented
53	C₃×#443	C₂×C₃	1	1	yes	characteristic, complemented
54	#5141	C₂×C₃	1	2	yes	complemented
55	#4898	C₂×C₃	1	2	yes	complemented
56	#4826	C₂×C₃	1	2	yes	complemented
57	#4822	C₂×C₃	1	2	yes	complemented
58	#4700	C₂×C₃	1	1	yes	characteristic, complemented
59	#4693	C₂×C₃	1	1	yes	characteristic, complemented
60	C₃²×#41	C₂³	1	2	yes	—
61	C₃×#239	—	2	2	no	—
62	C₃×D₃×Q₈	—	2	2	no	—
63	C₃×#237	—	2	2	no	—
64	C₃×#237	—	4	2	no	—
65	C₃×D₃×D₄	—	2	2	no	—
66	C₃×D₃×D₄	—	4	2	no	—
67	C₃×#235	—	2	2	no	—
68	C₃×#235	—	2	2	no	—
69	C₃×#235	C₂³	1	2	yes	—
70	C₂×C₃×D₁₂	—	2	2	no	—
71	C₂×C₃×D₁₂	—	4	1	no	—
72	C₂×C₃×D₁₂	C₂³	1	2	yes	—
73	C₂×C₃×Dic₆	—	2	2	no	—
74	C₂×C₃×Dic₆	C₂³	1	2	yes	—
75	C₃²×Q₁₆	D₄	1	1	yes	characteristic, complemented
76	C₃²×SD₁₆	D₄	1	2	yes	complemented
77	C₃²×D₈	D₄	1	1	yes	characteristic, complemented
78	C₃²×M₁₆	—	2	2	no	—
79	C₃²×M₁₆	C₂³	1	2	yes	—
80	C₂×C₃²×C₈	—	2	2	no	—
81	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
83	C₃²×C₄²	C₂³	1	1	yes	characteristic
84	C₃×#216	—	2	2	no	—
85	C₃×#215	—	2	2	no	—
86	C₃×#214	—	2	2	no	—
87	C₃×#213	—	2	2	no	—
88	C₃×C₄⋊Dic₃	—	4	1	no	—
89	C₃×#208	C₂³	1	2	yes	—
90	C₃×Dic₁₂	—	2	2	no	—
91	C₃×Dic₁₂	D₄	1	1	yes	characteristic, complemented
92	C₃×D₂₄	—	2	2	no	—
93	C₃×D₂₄	D₄	1	1	yes	characteristic, complemented
94	C₃×#204	—	2	2	no	—
95	C₃×#204	—	2	2	no	—
96	C₃×#204	—	2	2	no	—
97	C₃×#204	—	2	2	no	—
98	C₃×#204	—	2	2	no	—
99	C₃×#204	—	2	2	no	—
100	C₃×#204	D₄	1	2	yes	complemented
101	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
102	C₃×D₃×C₈	—	2	2	no	—
103	#3291	—	3	1	no	Sylow
104	C₃×2₋¹⁺⁴	—	3	2	no	—
105	C₃×H(5,𝔽₂)	—	3	2	no	—
106	#1010	C₂²×C₃	1	2	yes	—
107	#1009	C₂²×C₃	1	2	yes	complemented
108	C₃×#137	—	3	2	no	—
109	C₃×#137	—	3	2	no	—
110	C₃×#137	—	6	2	no	—
111	C₃×#137	—	6	2	no	—
112	C₃×AGL(1,ℤ/8)	—	3	2	no	—
113	C₃×AGL(1,ℤ/8)	—	3	2	no	—
114	C₃×AGL(1,ℤ/8)	—	6	2	no	—
115	C₃×AGL(1,ℤ/8)	—	6	2	no	—
116	C₃×#135	—	2	1	no	—
117	C₃×#135	—	3	1	no	—
118	C₃×#135	—	6	2	no	—
119	C₃×#135	—	6	2	no	—
120	C₃×#135	C₂×D₃	1	1	yes	characteristic
121	C₃×#135	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×SD₁₆	—	3	2	no	—
123	C₂×C₃×SD₁₆	—	3	2	no	—
124	C₂×C₃×SD₁₆	—	6	2	no	—
125	C₂×C₃×SD₁₆	—	6	2	no	—
126	C₃×#131	—	2	2	no	—
127	C₃×#131	—	3	2	no	—
128	C₃×#131	C₂×D₃	1	2	yes	complemented
129	C₃×#131	C₂²×C₃	1	2	yes	complemented
130	C₃×C₄⋊Q₈	—	3	1	no	—
131	C₃×#127	—	3	1	no	—
132	#951	C₂²×C₃	1	2	yes	complemented
133	#949	C₂²×C₃	1	2	yes	—
134	#918	—	2	2	no	—
135	#916	—	2	2	no	—
136	D₃×SD₁₆	—	2	2	no	—
137	#911	—	2	2	no	—
138	#909	—	2	2	no	—
139	#909	C₂²×C₃	1	2	yes	complemented
140	#908	—	2	2	no	—
141	#908	C₂²×C₃	1	2	yes	—
142	#904	—	2	2	no	—
143	#904	C₂²×C₃	1	1	yes	characteristic
144	C₂×#204	—	2	2	no	—
145	C₂×#204	C₂²×C₃	1	2	yes	complemented
146	C₂×#204	C₂²×C₃	1	2	yes	complemented
147	#901	C₂²×C₃	1	2	yes	complemented
148	#874	C₂²×C₃	1	1	yes	characteristic
149	#869	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₃×#108	—	2	1	no	—
151	C₃×#108	—	3	1	no	—
152	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
153	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₃×#104	—	2	2	no	—
155	C₃×#104	—	3	2	no	—
156	C₃×#104	C₂×D₃	1	2	yes	complemented
157	C₃×#104	C₂²×C₃	1	2	yes	complemented
158	C₃×#101	—	3	2	no	—
159	C₃×#100	—	3	2	no	—
160	C₃×C₄×C₈	—	2	1	no	—
161	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
162	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
163	#824	C₂²×C₃	1	2	yes	complemented
164	#823	C₂²×C₃	1	2	yes	complemented
165	#819	C₂²×C₃	1	1	yes	characteristic, complemented
166	#805	C₂²×C₃	1	2	yes	complemented
167	C₂²×C₃×D₃	—	2	2	no	—
168	C₂²×C₃×D₃	—	4	2	no	—
169	C₃²×Q₈	C₂×D₄	1	2	yes	—
170	C₃²×D₄	—	2	2	no	—
171	C₃²×D₄	C₂×D₄	1	2	yes	—
172	C₂×C₃²×C₄	—	2	1	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
175	C₃×#67	—	2	2	no	—
176	C₃×#67	—	4	2	no	—
177	C₃×#67	—	4	2	no	—
178	C₂×C₃×Dic₃	—	2	2	no	—
179	C₂×C₃×Dic₃	—	4	2	no	—
180	C₃×D₁₂	—	2	2	no	—
181	C₃×D₁₂	—	2	2	no	—
182	C₃×D₁₂	—	4	2	no	—
183	C₃×D₁₂	—	8	2	no	—
184	C₃×D₁₂	C₂×D₄	1	2	yes	—
185	C₃×C₄×D₃	—	2	2	no	—
186	C₃×C₄×D₃	—	4	2	no	—
187	C₃×C₄×D₃	—	4	2	no	—
188	C₃×Dic₆	—	2	2	no	—
189	C₃×Dic₆	—	2	2	no	—
190	C₃×Dic₆	—	4	2	no	—
191	C₃×Dic₆	C₂×D₄	1	2	yes	—
192	C₃²×C₈	—	2	2	no	—
193	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
194	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
195	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
196	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
197	C₃×C₃⋊C₈	—	2	2	no	—
198	#577	—	3	2	no	—
199	#577	—	3	2	no	—
200	#492	—	3	1	no	—
201	#471	—	3	2	no	—
202	#471	—	3	2	no	—
203	#456	—	3	2	no	—
204	#453	—	3	2	no	—
205	#443	—	3	1	no	—
206	#443	C₃×D₃	1	1	yes	characteristic, complemented
207	C₃×#41	—	2	2	no	—
208	C₃×#41	—	3	2	no	—
209	C₃×#41	—	6	2	no	—
210	C₃×#41	—	6	2	no	—
211	C₃×#41	—	6	2	no	—
212	C₃×#41	—	6	2	no	—
213	C₃×#41	—	12	2	no	—
214	C₃×#41	C₂²×D₃	1	2	yes	—
215	C₃×#41	C₂³×C₃	1	2	yes	—
216	C₂×C₃×Q₈	—	3	2	no	—
217	C₂×C₃×Q₈	—	6	2	no	—
218	C₂×C₃×Q₈	—	6	2	no	—
219	C₂×C₃×D₄	—	3	2	no	—
220	C₂×C₃×D₄	—	6	2	no	—
221	C₂×C₃×D₄	—	6	2	no	—
222	C₂×C₃×D₄	—	12	1	no	—
223	C₂×C₃×D₄	—	12	2	no	—
224	#239	—	2	2	no	—
225	D₃×Q₈	—	2	2	no	—
226	#237	—	2	2	no	—
227	#237	—	4	2	no	—
228	D₃×D₄	—	2	2	no	—
229	D₃×D₄	—	4	2	no	—
230	#235	—	2	2	no	—
231	#235	—	2	2	no	—
232	#235	C₂³×C₃	1	2	yes	—
233	C₂×D₁₂	—	2	2	no	—
234	C₂×D₁₂	—	4	1	no	—
235	C₂×D₁₂	C₂³×C₃	1	2	yes	—
236	C₂×Dic₆	—	2	2	no	—
237	C₂×Dic₆	C₂³×C₃	1	2	yes	—
238	C₃×Q₁₆	—	2	1	no	—
239	C₃×Q₁₆	—	3	1	no	—
240	C₃×Q₁₆	—	6	2	no	—
241	C₃×Q₁₆	—	6	2	no	—
242	C₃×Q₁₆	D₁₂	1	1	yes	characteristic, complemented
243	C₃×Q₁₆	C₃×D₄	1	1	yes	characteristic, complemented
244	C₃×SD₁₆	—	2	2	no	—
245	C₃×SD₁₆	—	3	2	no	—
246	C₃×SD₁₆	—	6	2	no	—
247	C₃×SD₁₆	—	6	2	no	—
248	C₃×SD₁₆	—	6	2	no	—
249	C₃×SD₁₆	—	6	2	no	—
250	C₃×SD₁₆	—	6	2	no	—
251	C₃×SD₁₆	—	6	2	no	—
252	C₃×SD₁₆	—	6	2	no	—
253	C₃×SD₁₆	—	6	2	no	—
254	C₃×SD₁₆	D₁₂	1	2	yes	complemented
255	C₃×SD₁₆	C₃×D₄	1	2	yes	complemented
256	C₃×D₈	—	2	1	no	—
257	C₃×D₈	—	3	1	no	—
258	C₃×D₈	—	6	2	no	—
259	C₃×D₈	—	6	2	no	—
260	C₃×D₈	D₁₂	1	1	yes	characteristic, complemented
261	C₃×D₈	C₃×D₄	1	1	yes	characteristic, complemented
262	C₃×M₁₆	—	2	2	no	—
263	C₃×M₁₆	—	2	2	no	—
264	C₃×M₁₆	—	2	2	no	—
265	C₃×M₁₆	—	3	2	no	—
266	C₃×M₁₆	—	4	2	no	—
267	C₃×M₁₆	—	6	2	no	—
268	C₃×M₁₆	C₂²×D₃	1	2	yes	—
269	C₃×M₁₆	C₂³×C₃	1	2	yes	—
270	C₂×C₃×C₈	—	2	2	no	—
271	C₂×C₃×C₈	—	2	2	no	—
272	C₂×C₃×C₈	—	2	1	no	—
273	C₂×C₃×C₈	—	2	1	no	—
274	C₂×C₃×C₈	—	4	2	no	—
275	C₂×C₃×C₈	—	6	2	no	—
276	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
277	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
280	C₃×C₄⋊C₄	—	12	1	no	—
281	C₃×C₄²	—	2	1	no	—
282	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
283	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
284	#216	—	2	2	no	—
285	#215	—	2	2	no	—
286	#214	—	2	2	no	—
287	#213	—	2	2	no	—
288	C₄⋊Dic₃	—	4	1	no	—
289	#208	C₂³×C₃	1	2	yes	—
290	Dic₁₂	—	2	2	no	—
291	Dic₁₂	C₃×D₄	1	1	yes	characteristic, complemented
292	D₂₄	—	2	2	no	—
293	D₂₄	C₃×D₄	1	1	yes	characteristic, complemented
294	#204	—	2	2	no	—
295	#204	—	2	2	no	—
296	#204	—	2	2	no	—
297	#204	—	2	2	no	—
298	#204	—	2	2	no	—
299	#204	—	2	2	no	—
300	#204	C₃×D₄	1	2	yes	complemented
301	ΓL(1,𝔽₂₅)	—	2	2	no	—
302	D₃×C₈	—	2	2	no	—
303	C₂²×C₃²	—	2	2	no	—
304	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₃×D₃	—	2	2	no	—
306	C₂×C₃×D₃	—	4	2	no	—
307	C₂×C₃×D₃	—	8	2	no	—
308	C₂×C₃×D₃	—	16	2	no	—
309	C₃²×C₄	—	2	2	no	—
310	C₃²×C₄	—	2	2	no	—
311	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
312	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₃×Dic₃	—	2	2	no	—
314	C₃×Dic₃	—	4	2	no	—
315	2₋¹⁺⁴	—	3	2	no	—
316	H(5,𝔽₂)	—	3	2	no	—
317	#137	—	3	2	no	—
318	#137	—	3	2	no	—
319	#137	—	6	2	no	—
320	#137	—	6	2	no	—
321	AGL(1,ℤ/8)	—	3	2	no	—
322	AGL(1,ℤ/8)	—	3	2	no	—
323	AGL(1,ℤ/8)	—	6	2	no	—
324	AGL(1,ℤ/8)	—	6	2	no	—
325	#135	—	3	1	no	—
326	#135	—	6	2	no	—
327	#135	—	6	2	no	—
328	#135	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂×SD₁₆	—	3	2	no	—
330	C₂×SD₁₆	—	3	2	no	—
331	C₂×SD₁₆	—	6	2	no	—
332	C₂×SD₁₆	—	6	2	no	—
333	#131	—	3	2	no	—
334	#131	C₂×C₃×D₃	1	2	yes	complemented
335	C₄⋊Q₈	—	3	1	no	—
336	#127	—	3	1	no	—
337	#108	—	3	1	no	—
338	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
339	#104	—	3	2	no	—
340	#104	C₂×C₃×D₃	1	2	yes	complemented
341	#101	—	3	2	no	—
342	#100	—	3	2	no	—
343	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
344	C₂³×C₃	—	6	2	no	—
345	C₂³×C₃	—	12	2	no	—
346	C₂²×D₃	—	2	2	no	—
347	C₂²×D₃	—	4	2	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	—	3	2	no	—
350	C₃×Q₈	—	6	2	no	—
351	C₃×Q₈	—	6	2	no	—
352	C₃×Q₈	—	12	2	no	—
353	C₃×Q₈	C₂×D₁₂	1	2	yes	—
354	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	3	2	no	—
359	C₃×D₄	—	4	2	no	—
360	C₃×D₄	—	6	2	no	—
361	C₃×D₄	—	6	2	no	—
362	C₃×D₄	—	6	2	no	—
363	C₃×D₄	—	12	2	no	—
364	C₃×D₄	—	12	2	no	—
365	C₃×D₄	—	12	2	no	—
366	C₃×D₄	—	24	2	no	—
367	C₃×D₄	C₂×D₁₂	1	2	yes	—
368	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	4	2	no	—
375	C₂×C₃×C₄	—	4	1	no	—
376	C₂×C₃×C₄	—	6	2	no	—
377	C₂×C₃×C₄	—	6	2	no	—
378	C₂×C₃×C₄	—	12	2	no	—
379	C₂×C₃×C₄	—	12	2	no	—
380	C₂×C₃×C₄	—	12	2	no	—
381	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
383	#67	—	2	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	4	2	no	—
388	D₁₂	—	2	2	no	—
389	D₁₂	—	2	2	no	—
390	D₁₂	—	4	2	no	—
391	D₁₂	—	8	2	no	—
392	D₁₂	C₂×C₃×D₄	1	2	yes	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	—	4	2	no	—
396	Dic₆	—	2	2	no	—
397	Dic₆	—	2	2	no	—
398	Dic₆	—	4	2	no	—
399	Dic₆	C₂×C₃×D₄	1	2	yes	—
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	—	2	2	no	—
402	C₃×C₈	—	2	1	no	—
403	C₃×C₈	—	2	1	no	—
404	C₃×C₈	—	2	1	no	—
405	C₃×C₈	—	2	1	no	—
406	C₃×C₈	—	4	2	no	—
407	C₃×C₈	—	6	2	no	—
408	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
409	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
410	C₃×C₈	D₃×D₄	1	1	yes	characteristic
411	C₃×C₈	D₃×D₄	1	1	yes	characteristic
412	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
413	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
414	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
415	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
416	C₃⋊C₈	—	2	2	no	—
417	C₂×C₃²	—	2	1	no	—
418	C₂×C₃²	—	4	2	no	—
419	C₂×C₃²	D₄²	1	1	yes	characteristic
420	C₃×D₃	—	4	2	no	—
421	C₃×D₃	—	8	2	no	—
422	#41	—	3	2	no	—
423	#41	—	6	2	no	—
424	#41	—	6	2	no	—
425	#41	—	6	2	no	—
426	#41	—	6	2	no	—
427	#41	—	12	2	no	—
428	#41	C₂²×C₃×D₃	1	2	yes	—
429	C₂×Q₈	—	3	2	no	—
430	C₂×Q₈	—	6	2	no	—
431	C₂×Q₈	—	6	2	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	6	2	no	—
434	C₂×D₄	—	6	2	no	—
435	C₂×D₄	—	12	1	no	—
436	C₂×D₄	—	12	2	no	—
437	Q₁₆	—	3	1	no	—
438	Q₁₆	—	6	2	no	—
439	Q₁₆	—	6	2	no	—
440	Q₁₆	C₃×D₁₂	1	1	yes	characteristic, complemented
441	SD₁₆	—	3	2	no	—
442	SD₁₆	—	6	2	no	—
443	SD₁₆	—	6	2	no	—
444	SD₁₆	—	6	2	no	—
445	SD₁₆	—	6	2	no	—
446	SD₁₆	—	6	2	no	—
447	SD₁₆	—	6	2	no	—
448	SD₁₆	—	6	2	no	—
449	SD₁₆	—	6	2	no	—
450	SD₁₆	C₃×D₁₂	1	2	yes	complemented
451	D₈	—	3	1	no	—
452	D₈	—	6	2	no	—
453	D₈	—	6	2	no	—
454	D₈	C₃×D₁₂	1	1	yes	characteristic, complemented
455	M₁₆	—	2	2	no	—
456	M₁₆	—	3	2	no	—
457	M₁₆	—	6	2	no	—
458	M₁₆	C₂²×C₃×D₃	1	2	yes	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	6	2	no	—
461	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
462	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
463	C₄⋊C₄	—	12	1	no	—
464	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	2	1	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	6	2	no	—
470	C₂²×C₃	—	12	2	no	—
471	C₂²×C₃	—	24	2	no	—
472	C₂²×C₃	—	48	2	no	—
473	C₂²×C₃	#1009	1	1	yes	characteristic
474	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	4	2	no	—
477	C₂×D₃	—	8	2	no	—
478	C₂×D₃	—	16	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	4	2	no	—
486	C₃×C₄	—	4	2	no	—
487	C₃×C₄	—	6	2	no	—
488	C₃×C₄	—	12	2	no	—
489	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
490	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
491	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
492	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
493	Dic₃	—	2	2	no	—
494	Dic₃	—	4	2	no	—
495	C₃²	#3291	1	1	yes	characteristic, complemented, Sylow
496	C₂³	—	6	2	no	—
497	C₂³	—	12	2	no	—
498	Q₈	—	3	2	no	—
499	Q₈	—	6	2	no	—
500	Q₈	—	6	2	no	—
501	Q₈	—	12	2	no	—
502	Q₈	C₂×C₃×D₁₂	1	2	yes	—
503	D₄	—	2	2	no	—
504	D₄	—	3	2	no	—
505	D₄	—	6	2	no	—
506	D₄	—	6	2	no	—
507	D₄	—	6	2	no	—
508	D₄	—	12	2	no	—
509	D₄	—	12	2	no	—
510	D₄	—	12	2	no	—
511	D₄	—	24	2	no	—
512	D₄	C₂×C₃×D₁₂	1	2	yes	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	6	2	no	—
517	C₂×C₄	—	12	2	no	—
518	C₂×C₄	—	12	2	no	—
519	C₂×C₄	—	12	2	no	—
520	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	6	2	no	—
523	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
524	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
525	C₈	C₃×D₃×D₄	1	1	yes	characteristic
526	C₈	C₃×D₃×D₄	1	1	yes	characteristic
527	C₂×C₃	—	2	1	no	—
528	C₂×C₃	—	2	1	no	—
529	C₂×C₃	—	2	1	no	—
530	C₂×C₃	—	4	1	no	—
531	C₂×C₃	—	4	2	no	—
532	C₂×C₃	—	4	2	no	—
533	C₂×C₃	—	8	2	no	—
534	C₂×C₃	—	12	2	no	—
535	C₂×C₃	—	24	2	no	—
536	C₂×C₃	D₄×D₁₂	1	1	yes	characteristic
537	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
538	D₃	—	4	2	no	—
539	D₃	—	8	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	6	2	no	—
542	C₂²	—	12	2	no	—
543	C₂²	—	24	2	no	—
544	C₂²	—	48	2	no	—
545	C₂²	C₃×#1009	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	6	2	no	—
549	C₄	—	12	2	no	—
550	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
551	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
552	C₃	—	2	1	no	—
553	C₃	#79893	1	1	yes	characteristic, direct product factor
554	C₃	C₃×#3291	1	1	yes	characteristic, complemented
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	12	2	no	—
558	C₂	—	24	2	no	—
559	C₂	C₃×D₄×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#443	C₂
socle	C₂×C₃²	D₄²
hypercenter	C₃×#443	D₃
hypocenter	C₃	C₃×#3291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#443

Complements

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

N	H ≅ G/N	type
1. C₃×#5770	C₂	semidirect
2. C₃×#5751	C₂	semidirect
3. C₃²×#443	C₂	semidirect
4. C₃×#5141	C₂	semidirect
5. C₃×#4898	C₂	semidirect
6. C₃×#4826	C₂	semidirect
7. C₃×#4822	C₂	semidirect
8. C₃×#4700	C₂	semidirect
9. C₃×#4693	C₂	semidirect
11. #79893	C₃	direct (N × H)
13. C₃×#1009	C₂²	semidirect
15. C₃²×#131	C₂²	semidirect
16. C₃×#951	C₂²	semidirect
23. C₃×#909	C₂²	semidirect
29. C₂×C₃×#204	C₂²	semidirect
30. C₂×C₃×#204	C₂²	semidirect
31. C₃×#901	C₂²	semidirect
33. C₃×#869	C₂²	semidirect
34. C₃²×#108	C₂²	semidirect
35. C₃²×#104	C₂²	semidirect
36. C₃²×C₄×C₈	C₂²	semidirect
37. C₃×#824	C₂²	semidirect
38. C₃×#823	C₂²	semidirect
39. C₃×#819	C₂²	semidirect
40. C₃×#805	C₂²	semidirect
43. #5770	C₂×C₃	semidirect
44. #5751	C₂×C₃	semidirect
52. C₃×#443	D₃	semidirect
53. C₃×#443	C₂×C₃	semidirect
54. #5141	C₂×C₃	semidirect
55. #4898	C₂×C₃	semidirect
56. #4826	C₂×C₃	semidirect
57. #4822	C₂×C₃	semidirect
58. #4700	C₂×C₃	semidirect
59. #4693	C₂×C₃	semidirect
75. C₃²×Q₁₆	D₄	semidirect
76. C₃²×SD₁₆	D₄	semidirect
77. C₃²×D₈	D₄	semidirect
91. C₃×Dic₁₂	D₄	semidirect
93. C₃×D₂₄	D₄	semidirect
100. C₃×#204	D₄	semidirect
107. #1009	C₂²×C₃	semidirect
128. C₃×#131	C₂×D₃	semidirect
129. C₃×#131	C₂²×C₃	semidirect
132. #951	C₂²×C₃	semidirect
139. #909	C₂²×C₃	semidirect
145. C₂×#204	C₂²×C₃	semidirect
146. C₂×#204	C₂²×C₃	semidirect
147. #901	C₂²×C₃	semidirect
149. #869	C₂²×C₃	semidirect
152. C₃×#108	C₂×D₃	semidirect
153. C₃×#108	C₂²×C₃	semidirect
156. C₃×#104	C₂×D₃	semidirect
157. C₃×#104	C₂²×C₃	semidirect
161. C₃×C₄×C₈	C₂×D₃	semidirect
162. C₃×C₄×C₈	C₂²×C₃	semidirect
163. #824	C₂²×C₃	semidirect
164. #823	C₂²×C₃	semidirect
165. #819	C₂²×C₃	semidirect
166. #805	C₂²×C₃	semidirect
206. #443	C₃×D₃	semidirect
242. C₃×Q₁₆	D₁₂	semidirect
243. C₃×Q₁₆	C₃×D₄	semidirect
254. C₃×SD₁₆	D₁₂	semidirect
255. C₃×SD₁₆	C₃×D₄	semidirect
260. C₃×D₈	D₁₂	semidirect
261. C₃×D₈	C₃×D₄	semidirect
291. Dic₁₂	C₃×D₄	semidirect
293. D₂₄	C₃×D₄	semidirect
300. #204	C₃×D₄	semidirect
334. #131	C₂×C₃×D₃	semidirect
338. #108	C₂×C₃×D₃	semidirect
340. #104	C₂×C₃×D₃	semidirect
343. C₄×C₈	C₂×C₃×D₃	semidirect
440. Q₁₆	C₃×D₁₂	semidirect
450. SD₁₆	C₃×D₁₂	semidirect
454. D₈	C₃×D₁₂	semidirect
495. C₃²	#3291	semidirect
553. C₃	#79893	direct (N × H)
554. C₃	C₃×#3291	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5770	2
C₃×#5751	2
C₃²×#443	2
C₃×#5141	2
C₃×#4898	2
C₃×#4826	2
C₃×#4822	2
C₃×#4700	2
C₃×#4693	2
C₃×#3291	3
#79893	3

Subgroups — C3×#79893 #11886851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79893 #11886851