Subgroups — C₃×#80941 #11886899

Order 1152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5774	C₂	1	2	yes	maximal, complemented
2	C₃×#5757	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5752	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5198	C₂	1	2	yes	maximal, complemented
6	C₃×#5151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5144	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4749	C₂	1	2	yes	maximal, complemented
11	C₃×#4747	C₂	1	2	yes	maximal, complemented
12	C₃×#3292	—	3	1	no	maximal
13	#80941	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×#1009	C₂²	1	2	yes	complemented
15	C₃×#1004	C₂²	1	2	yes	complemented
16	C₃²×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
17	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
18	C₃²×#131	C₂²	1	1	yes	characteristic, complemented
19	C₃×#950	C₂²	1	1	yes	characteristic
20	C₃×#940	C₂²	1	2	yes	complemented
21	C₃×#932	C₂²	1	2	yes	complemented
22	C₂×C₃×#213	C₂²	1	2	yes	complemented
23	C₃×#916	—	2	2	no	—
24	C₃×#914	—	2	2	no	—
25	C₃×#912	—	2	1	no	—
26	C₃×#911	—	2	2	no	—
27	C₃×#911	—	2	2	no	—
28	C₃×D₃×D₈	—	2	2	no	—
29	C₃×D₃×D₈	—	2	1	no	—
30	C₃×#908	—	2	2	no	—
31	C₃×#908	C₂²	1	2	yes	complemented
32	C₃×#908	C₂²	1	2	yes	complemented
33	C₃×#907	C₂²	1	2	yes	complemented
34	C₃×#904	—	2	1	no	—
35	C₃×#904	C₂²	1	1	yes	characteristic
36	C₂×C₃×D₂₄	—	2	1	no	—
37	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×#901	C₂²	1	1	yes	characteristic, complemented
39	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
40	C₃²×#100	C₂²	1	2	yes	complemented
41	C₃×#837	C₂²	1	1	yes	characteristic, complemented
42	C₃×#825	C₂²	1	2	yes	complemented
43	C₃×#825	C₂²	1	1	yes	characteristic, complemented
44	C₃×#823	C₂²	1	2	yes	complemented
45	C₃×#822	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₃×#576	—	3	2	no	—
48	C₃×#576	—	3	1	no	—
49	C₃×#576	—	3	1	no	—
50	#5774	C₂×C₃	1	2	yes	complemented
51	#5757	C₂×C₃	1	1	yes	characteristic, complemented
52	#5752	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#493	—	3	1	no	—
54	C₃×#472	—	2	1	no	—
55	C₃×#472	—	3	1	no	—
56	C₃×#472	—	3	2	no	—
57	C₃×#472	D₃	1	1	yes	characteristic, complemented
58	C₃×#472	C₂×C₃	1	1	yes	characteristic, complemented
59	C₃×#453	—	3	2	no	—
60	C₃×#453	—	3	2	no	—
61	C₃×#443	—	3	1	no	—
62	C₃×#443	—	3	1	no	—
63	#5198	C₂×C₃	1	2	yes	complemented
64	#5151	C₂×C₃	1	1	yes	characteristic, complemented
65	#5144	C₂×C₃	1	1	yes	characteristic, complemented
66	#4897	C₂×C₃	1	1	yes	characteristic, complemented
67	#4895	C₂×C₃	1	1	yes	characteristic, complemented
68	#4749	C₂×C₃	1	2	yes	complemented
69	#4747	C₂×C₃	1	2	yes	complemented
70	C₃²×#41	C₂³	1	1	yes	characteristic
71	C₂×C₃²×D₄	C₂³	1	2	yes	—
72	C₂×C₃×#67	—	4	2	no	—
73	C₂×C₃×#67	—	4	2	no	—
74	C₃×#239	—	2	2	no	—
75	C₃×#237	—	2	2	no	—
76	C₃×#237	—	2	2	no	—
77	C₃×D₃×D₄	—	2	2	no	—
78	C₃×D₃×D₄	—	2	2	no	—
79	C₃×D₃×D₄	—	2	2	no	—
80	C₃×D₃×D₄	—	4	2	no	—
81	C₃×#235	—	2	2	no	—
82	C₃×#235	C₂³	1	1	yes	characteristic
83	C₃×#235	C₂³	1	2	yes	—
84	C₂×C₃×D₁₂	—	2	2	no	—
85	C₂×C₃×D₁₂	C₂³	1	2	yes	—
86	C₃²×SD₁₆	—	2	2	no	—
87	C₃²×D₈	—	2	2	no	—
88	C₃²×D₈	—	2	1	no	—
89	C₃²×D₈	—	2	1	no	—
90	C₃²×M₁₆	—	2	1	no	—
91	C₃²×M₁₆	C₂³	1	2	yes	—
92	C₃²×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₃²×C₈	—	2	1	no	—
94	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
95	C₃×#216	D₄	1	1	yes	characteristic, complemented
96	C₃×#215	D₄	1	1	yes	characteristic, complemented
97	C₃×#214	—	2	2	no	—
98	C₃×#214	D₄	1	1	yes	characteristic, complemented
99	C₃×#213	—	2	2	no	—
100	C₃×#213	—	2	2	no	—
101	C₃×#213	—	2	2	no	—
102	C₃×#213	D₄	1	1	yes	characteristic, complemented
103	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
104	C₃×#208	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
106	C₃×Dic₁₂	D₄	1	1	yes	characteristic, complemented
107	C₃×D₂₄	—	2	2	no	—
108	C₃×D₂₄	—	2	2	no	—
109	C₃×D₂₄	—	2	1	no	—
110	C₃×D₂₄	—	2	1	no	—
111	C₃×D₂₄	D₄	1	1	yes	characteristic, complemented
112	C₃×#204	—	2	2	no	—
113	C₃×#204	—	2	2	no	—
114	C₃×#204	D₄	1	2	yes	complemented
115	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
116	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
117	C₃×D₃×C₈	—	2	1	no	—
118	C₃×D₃×C₈	—	2	2	no	—
119	#3292	—	3	1	no	Sylow
120	C₃×H(5,𝔽₂)	—	3	2	no	—
121	C₃×H(5,𝔽₂)	—	3	2	no	—
122	#1009	C₂²×C₃	1	2	yes	complemented
123	#1004	C₂²×C₃	1	2	yes	complemented
124	C₃×AGL(1,ℤ/8)	—	2	2	no	—
125	C₃×AGL(1,ℤ/8)	—	3	2	no	—
126	C₃×AGL(1,ℤ/8)	—	3	2	no	—
127	C₃×AGL(1,ℤ/8)	—	3	2	no	—
128	C₃×AGL(1,ℤ/8)	—	6	2	no	—
129	C₃×AGL(1,ℤ/8)	—	6	2	no	—
130	C₃×AGL(1,ℤ/8)	—	6	2	no	—
131	C₃×AGL(1,ℤ/8)	—	6	2	no	—
132	C₃×AGL(1,ℤ/8)	C₂×D₃	1	2	yes	complemented
133	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
134	C₃×#135	—	3	1	no	—
135	C₃×#135	—	3	1	no	—
136	C₃×#135	—	6	1	no	—
137	C₃×#135	—	6	1	no	—
138	C₃×#135	—	6	2	no	—
139	C₂×C₃×D₈	—	2	1	no	—
140	C₂×C₃×D₈	—	3	2	no	—
141	C₂×C₃×D₈	—	3	1	no	—
142	C₂×C₃×D₈	—	6	1	no	—
143	C₂×C₃×D₈	—	6	2	no	—
144	C₂×C₃×D₈	—	6	1	no	—
145	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic, complemented
146	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₃×#131	—	2	1	no	—
148	C₃×#131	—	3	2	no	—
149	C₃×#131	—	3	1	no	—
150	C₃×#131	C₂×D₃	1	1	yes	characteristic, complemented
151	C₃×#131	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₃×#127	—	3	2	no	—
153	#950	C₂²×C₃	1	1	yes	characteristic
154	#940	C₂²×C₃	1	2	yes	complemented
155	#932	C₂²×C₃	1	2	yes	complemented
156	C₂×#213	C₂²×C₃	1	2	yes	complemented
157	#916	—	2	2	no	—
158	#914	—	2	2	no	—
159	#912	—	2	1	no	—
160	#911	—	2	2	no	—
161	#911	—	2	2	no	—
162	D₃×D₈	—	2	2	no	—
163	D₃×D₈	—	2	1	no	—
164	#908	—	2	2	no	—
165	#908	C₂²×C₃	1	2	yes	complemented
166	#908	C₂²×C₃	1	2	yes	complemented
167	#907	C₂²×C₃	1	2	yes	complemented
168	#904	—	2	1	no	—
169	#904	C₂²×C₃	1	1	yes	characteristic
170	C₂×D₂₄	—	2	1	no	—
171	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic, complemented
172	#901	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₃×#108	—	2	1	no	—
174	C₃×#108	—	3	1	no	—
175	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
176	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₃×#104	—	3	1	no	—
178	C₃×#104	—	3	2	no	—
179	C₃×#104	—	3	1	no	—
180	C₃×#100	—	2	2	no	—
181	C₃×#100	—	3	2	no	—
182	C₃×#100	C₂×D₃	1	2	yes	complemented
183	C₃×#100	C₂²×C₃	1	2	yes	complemented
184	C₃×C₄×C₈	—	3	1	no	—
185	#837	C₂²×C₃	1	1	yes	characteristic, complemented
186	#825	C₂²×C₃	1	1	yes	characteristic, complemented
187	#825	C₂²×C₃	1	2	yes	complemented
188	#823	C₂²×C₃	1	2	yes	complemented
189	#822	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂³×C₃²	—	2	2	no	—
192	C₂²×C₃×D₃	—	2	2	no	—
193	C₂²×C₃×D₃	—	4	2	no	—
194	C₂²×C₃×D₃	—	4	2	no	—
195	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
196	C₃²×D₄	—	2	1	no	—
197	C₃²×D₄	—	2	2	no	—
198	C₃²×D₄	—	2	2	no	—
199	C₃²×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃²×C₄	—	2	1	no	—
201	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
202	C₃×#67	—	2	2	no	—
203	C₃×#67	—	2	1	no	—
204	C₃×#67	—	4	2	no	—
205	C₃×#67	—	4	2	no	—
206	C₃×#67	—	4	2	no	—
207	C₃×#67	—	8	4	no	—
208	C₂×C₃×Dic₃	—	2	1	no	—
209	C₂×C₃×Dic₃	—	4	2	no	—
210	C₃×D₁₂	—	2	2	no	—
211	C₃×D₁₂	—	2	2	no	—
212	C₃×D₁₂	—	4	2	no	—
213	C₃×D₁₂	C₂×D₄	1	2	yes	—
214	C₃×D₁₂	C₂×D₄	1	1	yes	characteristic
215	C₃×C₄×D₃	—	2	1	no	—
216	C₃×C₄×D₃	—	2	2	no	—
217	C₃×C₄×D₃	—	4	2	no	—
218	C₃×Dic₆	C₂×D₄	1	1	yes	characteristic
219	C₃×Dic₆	C₂×D₄	1	2	yes	—
220	C₃²×C₈	—	2	2	no	—
221	C₃²×C₈	—	2	1	no	—
222	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
223	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
224	C₃×C₃⋊C₈	—	2	1	no	—
225	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
226	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
227	#576	—	3	2	no	—
228	#576	—	3	1	no	—
229	#576	—	3	1	no	—
230	#493	—	3	1	no	—
231	#472	—	3	1	no	—
232	#472	—	3	2	no	—
233	#472	C₃×D₃	1	1	yes	characteristic, complemented
234	#453	—	3	2	no	—
235	#453	—	3	2	no	—
236	#443	—	3	1	no	—
237	#443	—	3	1	no	—
238	C₃×#41	—	2	1	no	—
239	C₃×#41	—	3	2	no	—
240	C₃×#41	—	3	1	no	—
241	C₃×#41	—	6	2	no	—
242	C₃×#41	—	6	2	no	—
243	C₃×#41	—	6	2	no	—
244	C₃×#41	—	6	2	no	—
245	C₃×#41	C₂²×D₃	1	1	yes	characteristic
246	C₃×#41	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃×D₄	—	2	2	no	—
248	C₂×C₃×D₄	—	3	2	no	—
249	C₂×C₃×D₄	—	6	2	no	—
250	C₂×C₃×D₄	—	6	2	no	—
251	C₂×C₃×D₄	—	6	2	no	—
252	C₂×C₃×D₄	—	6	2	no	—
253	C₂×C₃×D₄	—	12	2	no	—
254	C₂×C₃×D₄	—	12	2	no	—
255	C₂×C₃×D₄	—	12	2	no	—
256	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
257	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
258	C₂×#67	—	4	2	no	—
259	C₂×#67	—	4	2	no	—
260	#239	—	2	2	no	—
261	#237	—	2	2	no	—
262	#237	—	2	2	no	—
263	D₃×D₄	—	2	2	no	—
264	D₃×D₄	—	2	2	no	—
265	D₃×D₄	—	2	2	no	—
266	D₃×D₄	—	4	2	no	—
267	#235	—	2	2	no	—
268	#235	C₂³×C₃	1	1	yes	characteristic
269	#235	C₂³×C₃	1	2	yes	—
270	C₂×D₁₂	—	2	2	no	—
271	C₂×D₁₂	C₂³×C₃	1	2	yes	—
272	C₃×Q₁₆	—	3	1	no	—
273	C₃×Q₁₆	—	3	1	no	—
274	C₃×SD₁₆	—	2	2	no	—
275	C₃×SD₁₆	—	2	2	no	—
276	C₃×SD₁₆	—	3	1	no	—
277	C₃×SD₁₆	—	3	1	no	—
278	C₃×SD₁₆	—	3	2	no	—
279	C₃×SD₁₆	—	4	2	no	—
280	C₃×SD₁₆	—	6	2	no	—
281	C₃×SD₁₆	—	6	2	no	—
282	C₃×SD₁₆	—	6	2	no	—
283	C₃×D₈	—	2	2	no	—
284	C₃×D₈	—	2	2	no	—
285	C₃×D₈	—	2	1	no	—
286	C₃×D₈	—	2	1	no	—
287	C₃×D₈	—	2	1	no	—
288	C₃×D₈	—	2	1	no	—
289	C₃×D₈	—	3	1	no	—
290	C₃×D₈	—	3	1	no	—
291	C₃×D₈	—	4	1	no	—
292	C₃×D₈	—	4	1	no	—
293	C₃×D₈	—	4	2	no	—
294	C₃×D₈	—	6	2	no	—
295	C₃×D₈	—	6	2	no	—
296	C₃×D₈	—	6	2	no	—
297	C₃×D₈	—	6	2	no	—
298	C₃×D₈	—	6	2	no	—
299	C₃×D₈	—	6	1	no	—
300	C₃×D₈	—	6	1	no	—
301	C₃×M₁₆	—	2	1	no	—
302	C₃×M₁₆	—	2	1	no	—
303	C₃×M₁₆	—	2	1	no	—
304	C₃×M₁₆	—	2	2	no	—
305	C₃×M₁₆	—	3	1	no	—
306	C₃×M₁₆	—	4	1	no	—
307	C₃×M₁₆	—	6	2	no	—
308	C₃×M₁₆	—	6	1	no	—
309	C₃×M₁₆	C₂²×D₃	1	2	yes	—
310	C₃×M₁₆	C₂²×D₃	1	1	yes	characteristic
311	C₃×M₁₆	C₂³×C₃	1	1	yes	characteristic
312	C₃×M₁₆	C₂³×C₃	1	2	yes	—
313	C₂×C₃×C₈	—	2	1	no	—
314	C₂×C₃×C₈	—	2	1	no	—
315	C₂×C₃×C₈	—	2	1	no	—
316	C₂×C₃×C₈	—	3	1	no	—
317	C₂×C₃×C₈	—	4	1	no	—
318	C₂×C₃×C₈	—	6	2	no	—
319	C₂×C₃×C₈	—	6	1	no	—
320	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
321	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
322	C₃×C₄²	—	3	1	no	—
323	#216	C₃×D₄	1	1	yes	characteristic, complemented
324	#215	C₃×D₄	1	1	yes	characteristic, complemented
325	#214	—	2	2	no	—
326	#214	C₃×D₄	1	1	yes	characteristic, complemented
327	#213	—	2	2	no	—
328	#213	—	2	2	no	—
329	#213	—	2	2	no	—
330	#213	C₃×D₄	1	1	yes	characteristic, complemented
331	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
332	#208	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
334	Dic₁₂	C₃×D₄	1	1	yes	characteristic, complemented
335	D₂₄	—	2	2	no	—
336	D₂₄	—	2	2	no	—
337	D₂₄	—	2	1	no	—
338	D₂₄	—	2	1	no	—
339	D₂₄	C₃×D₄	1	1	yes	characteristic, complemented
340	#204	—	2	2	no	—
341	#204	—	2	2	no	—
342	#204	C₃×D₄	1	2	yes	complemented
343	ΓL(1,𝔽₂₅)	—	2	1	no	—
344	ΓL(1,𝔽₂₅)	—	2	2	no	—
345	D₃×C₈	—	2	1	no	—
346	D₃×C₈	—	2	2	no	—
347	C₂²×C₃²	—	2	1	no	—
348	C₂²×C₃²	—	4	2	no	—
349	C₂²×C₃²	—	8	2	no	—
350	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₃×D₃	—	2	2	no	—
352	C₂×C₃×D₃	—	2	1	no	—
353	C₂×C₃×D₃	—	4	2	no	—
354	C₂×C₃×D₃	—	8	2	no	—
355	C₂×C₃×D₃	—	16	2	no	—
356	C₂×C₃×D₃	—	16	2	no	—
357	C₃²×C₄	—	2	1	no	—
358	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
359	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
360	C₃×Dic₃	—	2	2	no	—
361	C₃×Dic₃	—	2	2	no	—
362	C₃×Dic₃	—	2	1	no	—
363	H(5,𝔽₂)	—	3	2	no	—
364	H(5,𝔽₂)	—	3	2	no	—
365	AGL(1,ℤ/8)	—	3	2	no	—
366	AGL(1,ℤ/8)	—	3	2	no	—
367	AGL(1,ℤ/8)	—	3	2	no	—
368	AGL(1,ℤ/8)	—	6	2	no	—
369	AGL(1,ℤ/8)	—	6	2	no	—
370	AGL(1,ℤ/8)	—	6	2	no	—
371	AGL(1,ℤ/8)	—	6	2	no	—
372	AGL(1,ℤ/8)	C₂×C₃×D₃	1	2	yes	complemented
373	#135	—	3	1	no	—
374	#135	—	3	1	no	—
375	#135	—	6	1	no	—
376	#135	—	6	1	no	—
377	#135	—	6	2	no	—
378	C₂×D₈	—	3	2	no	—
379	C₂×D₈	—	3	1	no	—
380	C₂×D₈	—	6	1	no	—
381	C₂×D₈	—	6	2	no	—
382	C₂×D₈	—	6	1	no	—
383	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
384	#131	—	3	2	no	—
385	#131	—	3	1	no	—
386	#131	C₂×C₃×D₃	1	1	yes	characteristic, complemented
387	#127	—	3	2	no	—
388	#108	—	3	1	no	—
389	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
390	#104	—	3	1	no	—
391	#104	—	3	2	no	—
392	#104	—	3	1	no	—
393	#100	—	3	2	no	—
394	#100	C₂×C₃×D₃	1	2	yes	complemented
395	C₄×C₈	—	3	1	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	—	4	2	no	—
399	C₂³×C₃	—	6	2	no	—
400	C₂³×C₃	—	12	2	no	—
401	C₂³×C₃	—	12	2	no	—
402	C₂²×D₃	—	2	2	no	—
403	C₂²×D₃	—	4	2	no	—
404	C₂²×D₃	—	4	2	no	—
405	C₃×Q₈	—	2	1	no	—
406	C₃×Q₈	—	3	1	no	—
407	C₃×Q₈	—	3	2	no	—
408	C₃×Q₈	D₃×D₄	1	1	yes	characteristic
409	C₃×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	2	1	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	2	2	no	—
414	C₃×D₄	—	2	2	no	—
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	2	1	no	—
417	C₃×D₄	—	3	1	no	—
418	C₃×D₄	—	3	2	no	—
419	C₃×D₄	—	4	2	no	—
420	C₃×D₄	—	4	2	no	—
421	C₃×D₄	—	4	1	no	—
422	C₃×D₄	—	6	2	no	—
423	C₃×D₄	—	6	1	no	—
424	C₃×D₄	—	6	2	no	—
425	C₃×D₄	—	6	2	no	—
426	C₃×D₄	—	12	2	no	—
427	C₃×D₄	—	12	2	no	—
428	C₃×D₄	—	12	2	no	—
429	C₃×D₄	—	12	2	no	—
430	C₃×D₄	—	24	4	no	—
431	C₃×D₄	D₃×D₄	1	1	yes	characteristic
432	C₃×D₄	C₂×C₃×D₄	1	1	yes	characteristic
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	4	1	no	—
437	C₂×C₃×C₄	—	6	1	no	—
438	C₂×C₃×C₄	—	6	2	no	—
439	C₂×C₃×C₄	—	6	1	no	—
440	C₂×C₃×C₄	—	12	2	no	—
441	C₂×C₃×C₄	—	12	2	no	—
442	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
444	#67	—	2	2	no	—
445	#67	—	2	1	no	—
446	#67	—	4	2	no	—
447	#67	—	4	2	no	—
448	#67	—	4	2	no	—
449	#67	—	8	4	no	—
450	C₂×Dic₃	—	2	1	no	—
451	C₂×Dic₃	—	4	2	no	—
452	D₁₂	—	2	2	no	—
453	D₁₂	—	2	2	no	—
454	D₁₂	—	4	2	no	—
455	D₁₂	C₂×C₃×D₄	1	2	yes	—
456	D₁₂	C₂×C₃×D₄	1	1	yes	characteristic
457	C₄×D₃	—	2	1	no	—
458	C₄×D₃	—	2	2	no	—
459	C₄×D₃	—	4	2	no	—
460	Dic₆	C₂×C₃×D₄	1	1	yes	characteristic
461	Dic₆	C₂×C₃×D₄	1	2	yes	—
462	C₃×C₈	—	2	1	no	—
463	C₃×C₈	—	2	2	no	—
464	C₃×C₈	—	2	2	no	—
465	C₃×C₈	—	2	1	no	—
466	C₃×C₈	—	2	1	no	—
467	C₃×C₈	—	2	1	no	—
468	C₃×C₈	—	3	1	no	—
469	C₃×C₈	—	3	1	no	—
470	C₃×C₈	—	4	1	no	—
471	C₃×C₈	—	4	2	no	—
472	C₃×C₈	—	6	1	no	—
473	C₃×C₈	D₃×D₄	1	1	yes	characteristic
474	C₃×C₈	D₃×D₄	1	1	yes	characteristic
475	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
476	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
477	C₃⋊C₈	—	2	1	no	—
478	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
479	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
480	C₂×C₃²	—	2	1	no	—
481	C₂×C₃²	—	4	1	no	—
482	C₂×C₃²	—	8	2	no	—
483	C₂×C₃²	D₄²	1	1	yes	characteristic
484	C₃×D₃	—	4	2	no	—
485	C₃×D₃	—	4	1	no	—
486	C₃×D₃	—	8	2	no	—
487	#41	—	3	2	no	—
488	#41	—	3	1	no	—
489	#41	—	6	2	no	—
490	#41	—	6	2	no	—
491	#41	—	6	2	no	—
492	#41	—	6	2	no	—
493	#41	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂×D₄	—	3	2	no	—
495	C₂×D₄	—	6	2	no	—
496	C₂×D₄	—	6	2	no	—
497	C₂×D₄	—	6	2	no	—
498	C₂×D₄	—	6	2	no	—
499	C₂×D₄	—	12	2	no	—
500	C₂×D₄	—	12	2	no	—
501	C₂×D₄	—	12	2	no	—
502	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
503	Q₁₆	—	3	1	no	—
504	Q₁₆	—	3	1	no	—
505	SD₁₆	—	2	2	no	—
506	SD₁₆	—	3	1	no	—
507	SD₁₆	—	3	1	no	—
508	SD₁₆	—	3	2	no	—
509	SD₁₆	—	6	2	no	—
510	SD₁₆	—	6	2	no	—
511	SD₁₆	—	6	2	no	—
512	D₈	—	2	2	no	—
513	D₈	—	2	1	no	—
514	D₈	—	2	1	no	—
515	D₈	—	3	1	no	—
516	D₈	—	3	1	no	—
517	D₈	—	6	2	no	—
518	D₈	—	6	2	no	—
519	D₈	—	6	2	no	—
520	D₈	—	6	2	no	—
521	D₈	—	6	2	no	—
522	D₈	—	6	1	no	—
523	D₈	—	6	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	3	1	no	—
526	M₁₆	—	6	2	no	—
527	M₁₆	—	6	1	no	—
528	M₁₆	C₂²×C₃×D₃	1	2	yes	—
529	M₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	3	1	no	—
532	C₂×C₈	—	6	2	no	—
533	C₂×C₈	—	6	1	no	—
534	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
535	C₄²	—	3	1	no	—
536	C₂²×C₃	—	2	1	no	—
537	C₂²×C₃	—	2	1	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	2	no	—
541	C₂²×C₃	—	4	2	no	—
542	C₂²×C₃	—	6	2	no	—
543	C₂²×C₃	—	6	1	no	—
544	C₂²×C₃	—	8	2	no	—
545	C₂²×C₃	—	8	2	no	—
546	C₂²×C₃	—	8	2	no	—
547	C₂²×C₃	—	12	2	no	—
548	C₂²×C₃	—	16	2	no	—
549	C₂²×C₃	—	24	2	no	—
550	C₂²×C₃	—	48	2	no	—
551	C₂²×C₃	—	48	2	no	—
552	C₂²×C₃	#1009	1	1	yes	characteristic
553	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	1	no	—
556	C₂×D₃	—	4	2	no	—
557	C₂×D₃	—	8	2	no	—
558	C₂×D₃	—	16	2	no	—
559	C₂×D₃	—	16	2	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	—	6	2	no	—
566	C₃×C₄	—	6	2	no	—
567	C₃×C₄	—	6	1	no	—
568	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
569	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
570	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
571	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
572	Dic₃	—	2	2	no	—
573	Dic₃	—	2	2	no	—
574	Dic₃	—	2	1	no	—
575	C₃²	#3292	1	1	yes	characteristic, complemented, Sylow
576	C₂³	—	2	2	no	—
577	C₂³	—	6	2	no	—
578	C₂³	—	12	2	no	—
579	C₂³	—	12	2	no	—
580	Q₈	—	3	1	no	—
581	Q₈	—	3	2	no	—
582	Q₈	C₃×D₃×D₄	1	1	yes	characteristic
583	D₄	—	2	1	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	3	1	no	—
587	D₄	—	3	2	no	—
588	D₄	—	6	2	no	—
589	D₄	—	6	1	no	—
590	D₄	—	6	2	no	—
591	D₄	—	6	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	2	no	—
595	D₄	—	12	2	no	—
596	D₄	—	24	4	no	—
597	D₄	C₃×D₃×D₄	1	1	yes	characteristic
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	6	1	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	6	1	no	—
602	C₂×C₄	—	12	2	no	—
603	C₂×C₄	—	12	2	no	—
604	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
605	C₈	—	2	1	no	—
606	C₈	—	2	2	no	—
607	C₈	—	3	1	no	—
608	C₈	—	3	1	no	—
609	C₈	—	6	1	no	—
610	C₈	C₃×D₃×D₄	1	1	yes	characteristic
611	C₈	C₃×D₃×D₄	1	1	yes	characteristic
612	C₂×C₃	—	2	1	no	—
613	C₂×C₃	—	2	1	no	—
614	C₂×C₃	—	2	1	no	—
615	C₂×C₃	—	4	1	no	—
616	C₂×C₃	—	4	1	no	—
617	C₂×C₃	—	4	1	no	—
618	C₂×C₃	—	8	1	no	—
619	C₂×C₃	—	8	2	no	—
620	C₂×C₃	—	8	2	no	—
621	C₂×C₃	—	12	2	no	—
622	C₂×C₃	—	12	1	no	—
623	C₂×C₃	—	16	2	no	—
624	C₂×C₃	—	24	2	no	—
625	C₂×C₃	#5609	1	1	yes	characteristic
626	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
627	D₃	—	4	2	no	—
628	D₃	—	4	1	no	—
629	D₃	—	8	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	6	2	no	—
633	C₂²	—	6	1	no	—
634	C₂²	—	8	2	no	—
635	C₂²	—	12	2	no	—
636	C₂²	—	24	2	no	—
637	C₂²	—	48	2	no	—
638	C₂²	—	48	2	no	—
639	C₂²	C₃×#1009	1	1	yes	characteristic
640	C₄	—	2	1	no	—
641	C₄	—	6	2	no	—
642	C₄	—	6	2	no	—
643	C₄	—	6	1	no	—
644	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
645	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
646	C₃	—	2	1	no	—
647	C₃	#80941	1	1	yes	characteristic, direct product factor
648	C₃	C₃×#3292	1	1	yes	characteristic, complemented
649	C₂	—	2	1	no	—
650	C₂	—	4	1	no	—
651	C₂	—	8	2	no	—
652	C₂	—	12	2	no	—
653	C₂	—	12	1	no	—
654	C₂	—	24	2	no	—
655	C₂	C₃×#5609	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#5609
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#472	C₂
socle	C₂×C₃²	D₄²
hypercenter	C₃×#472	D₃
hypocenter	C₃	C₃×#3292
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#472

Complements

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

N	H ≅ G/N	type
1. C₃×#5774	C₂	semidirect
2. C₃×#5757	C₂	semidirect
3. C₃×#5752	C₂	semidirect
4. C₃²×#472	C₂	semidirect
5. C₃×#5198	C₂	semidirect
6. C₃×#5151	C₂	semidirect
7. C₃×#5144	C₂	semidirect
8. C₃×#4897	C₂	semidirect
9. C₃×#4895	C₂	semidirect
10. C₃×#4749	C₂	semidirect
11. C₃×#4747	C₂	semidirect
13. #80941	C₃	direct (N × H)
14. C₃×#1009	C₂²	semidirect
15. C₃×#1004	C₂²	semidirect
16. C₃²×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₃²×D₈	C₂²	semidirect
18. C₃²×#131	C₂²	semidirect
20. C₃×#940	C₂²	semidirect
21. C₃×#932	C₂²	semidirect
22. C₂×C₃×#213	C₂²	semidirect
31. C₃×#908	C₂²	semidirect
32. C₃×#908	C₂²	semidirect
33. C₃×#907	C₂²	semidirect
37. C₂×C₃×D₂₄	C₂²	semidirect
38. C₃×#901	C₂²	semidirect
39. C₃²×#108	C₂²	semidirect
40. C₃²×#100	C₂²	semidirect
41. C₃×#837	C₂²	semidirect
42. C₃×#825	C₂²	semidirect
43. C₃×#825	C₂²	semidirect
44. C₃×#823	C₂²	semidirect
45. C₃×#822	C₂²	semidirect
46. C₃×C₈×Dic₃	C₂²	semidirect
50. #5774	C₂×C₃	semidirect
51. #5757	C₂×C₃	semidirect
52. #5752	C₂×C₃	semidirect
57. C₃×#472	D₃	semidirect
58. C₃×#472	C₂×C₃	semidirect
63. #5198	C₂×C₃	semidirect
64. #5151	C₂×C₃	semidirect
65. #5144	C₂×C₃	semidirect
66. #4897	C₂×C₃	semidirect
67. #4895	C₂×C₃	semidirect
68. #4749	C₂×C₃	semidirect
69. #4747	C₂×C₃	semidirect
95. C₃×#216	D₄	semidirect
96. C₃×#215	D₄	semidirect
98. C₃×#214	D₄	semidirect
102. C₃×#213	D₄	semidirect
106. C₃×Dic₁₂	D₄	semidirect
111. C₃×D₂₄	D₄	semidirect
114. C₃×#204	D₄	semidirect
122. #1009	C₂²×C₃	semidirect
123. #1004	C₂²×C₃	semidirect
132. C₃×AGL(1,ℤ/8)	C₂×D₃	semidirect
133. C₃×AGL(1,ℤ/8)	C₂²×C₃	semidirect
145. C₂×C₃×D₈	C₂×D₃	semidirect
146. C₂×C₃×D₈	C₂²×C₃	semidirect
150. C₃×#131	C₂×D₃	semidirect
151. C₃×#131	C₂²×C₃	semidirect
154. #940	C₂²×C₃	semidirect
155. #932	C₂²×C₃	semidirect
156. C₂×#213	C₂²×C₃	semidirect
165. #908	C₂²×C₃	semidirect
166. #908	C₂²×C₃	semidirect
167. #907	C₂²×C₃	semidirect
171. C₂×D₂₄	C₂²×C₃	semidirect
172. #901	C₂²×C₃	semidirect
175. C₃×#108	C₂×D₃	semidirect
176. C₃×#108	C₂²×C₃	semidirect
182. C₃×#100	C₂×D₃	semidirect
183. C₃×#100	C₂²×C₃	semidirect
185. #837	C₂²×C₃	semidirect
186. #825	C₂²×C₃	semidirect
187. #825	C₂²×C₃	semidirect
188. #823	C₂²×C₃	semidirect
189. #822	C₂²×C₃	semidirect
190. C₈×Dic₃	C₂²×C₃	semidirect
233. #472	C₃×D₃	semidirect
323. #216	C₃×D₄	semidirect
324. #215	C₃×D₄	semidirect
326. #214	C₃×D₄	semidirect
330. #213	C₃×D₄	semidirect
334. Dic₁₂	C₃×D₄	semidirect
339. D₂₄	C₃×D₄	semidirect
342. #204	C₃×D₄	semidirect
372. AGL(1,ℤ/8)	C₂×C₃×D₃	semidirect
383. C₂×D₈	C₂×C₃×D₃	semidirect
386. #131	C₂×C₃×D₃	semidirect
389. #108	C₂×C₃×D₃	semidirect
394. #100	C₂×C₃×D₃	semidirect
575. C₃²	#3292	semidirect
647. C₃	#80941	direct (N × H)
648. C₃	C₃×#3292	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5774	2
C₃×#5757	2
C₃×#5752	2
C₃²×#472	2
C₃×#5198	2
C₃×#5151	2
C₃×#5144	2
C₃×#4897	2
C₃×#4895	2
C₃×#4749	2
C₃×#4747	2
C₃×#3292	3
#80941	3

Subgroups — C3×#80941 #11886899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#80941 #11886899