Subgroups — C₃×#79894 #11886905

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5769	C₂	1	2	yes	maximal, complemented
2	C₃×#5752	C₂	1	2	yes	maximal, complemented
3	C₃²×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5142	C₂	1	2	yes	maximal, complemented
5	C₃×#4897	C₂	1	2	yes	maximal, complemented
6	C₃×#4822	C₂	1	4	yes	maximal, complemented
7	C₃×#4700	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4695	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3292	—	3	1	no	maximal
10	#79894	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#1009	C₂²	1	4	yes	complemented
12	C₃²×#135	C₂²	1	1	yes	characteristic
13	C₃²×#131	C₂²	1	2	yes	complemented
14	C₃×#949	C₂²	1	4	yes	complemented
15	C₃×#919	—	2	2	no	—
16	C₃×#914	—	2	4	no	—
17	C₃×D₃×D₈	—	2	2	no	—
18	C₃×#908	—	2	4	no	—
19	C₃×#908	C₂²	1	4	yes	complemented
20	C₃×#904	—	2	2	no	—
21	C₃×#904	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₂₄	—	2	2	no	—
23	C₂×C₃×D₂₄	C₂²	1	2	yes	complemented
24	C₂×C₃×D₂₄	C₂²	1	2	yes	complemented
25	C₃×#901	C₂²	1	2	yes	complemented
26	C₃×#874	C₂²	1	2	yes	complemented
27	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
28	C₃²×#104	C₂²	1	2	yes	complemented
29	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×#823	C₂²	1	4	yes	complemented
31	C₃×#819	C₂²	1	1	yes	characteristic, complemented
32	C₃×#805	C₂²	1	2	yes	complemented
33	C₃×#576	—	3	2	no	—
34	C₃×#576	—	3	2	no	—
35	#5769	C₂×C₃	1	2	yes	complemented
36	#5752	C₂×C₃	1	2	yes	complemented
37	C₃×#493	—	3	1	no	—
38	C₃×#472	—	3	2	no	—
39	C₃×#472	—	3	2	no	—
40	C₃×#453	—	3	4	no	—
41	C₃×#443	—	2	1	no	—
42	C₃×#443	—	3	1	no	—
43	C₃×#443	D₃	1	1	yes	characteristic, complemented
44	C₃×#443	C₂×C₃	1	1	yes	characteristic, complemented
45	#5142	C₂×C₃	1	2	yes	complemented
46	#4897	C₂×C₃	1	2	yes	complemented
47	#4822	C₂×C₃	1	4	yes	complemented
48	#4700	C₂×C₃	1	1	yes	characteristic, complemented
49	#4695	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃²×#41	C₂³	1	2	yes	—
51	C₃×#239	—	2	4	no	—
52	C₃×D₃×D₄	—	2	4	no	—
53	C₃×D₃×D₄	—	4	4	no	—
54	C₃×#235	—	2	4	no	—
55	C₃×#235	C₂³	1	2	yes	—
56	C₂×C₃×D₁₂	—	2	4	no	—
57	C₂×C₃×D₁₂	—	4	2	no	—
58	C₂×C₃×D₁₂	C₂³	1	4	yes	—
59	C₃²×Q₁₆	D₄	1	1	yes	characteristic, complemented
60	C₃²×SD₁₆	D₄	1	2	yes	complemented
61	C₃²×D₈	D₄	1	1	yes	characteristic, complemented
62	C₃²×M₁₆	—	2	2	no	—
63	C₃²×M₁₆	C₂³	1	2	yes	—
64	C₂×C₃²×C₈	—	2	2	no	—
65	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
67	C₃²×C₄²	C₂³	1	1	yes	characteristic
68	C₃×#215	—	2	4	no	—
69	C₃×#213	—	2	4	no	—
70	C₃×#208	C₂³	1	2	yes	—
71	C₃×Dic₁₂	D₄	1	1	yes	characteristic, complemented
72	C₃×D₂₄	—	2	4	no	—
73	C₃×D₂₄	—	2	2	no	—
74	C₃×D₂₄	—	2	2	no	—
75	C₃×D₂₄	—	2	2	no	—
76	C₃×D₂₄	—	2	2	no	—
77	C₃×D₂₄	D₄	1	1	yes	characteristic, complemented
78	C₃×#204	—	2	4	no	—
79	C₃×#204	D₄	1	2	yes	complemented
80	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
81	C₃×D₃×C₈	—	2	2	no	—
82	#3292	—	3	1	no	Sylow
83	C₃×H(5,𝔽₂)	—	3	4	no	—
84	#1009	C₂²×C₃	1	4	yes	complemented
85	C₃×AGL(1,ℤ/8)	—	3	4	no	—
86	C₃×AGL(1,ℤ/8)	—	3	4	no	—
87	C₃×AGL(1,ℤ/8)	—	6	4	no	—
88	C₃×AGL(1,ℤ/8)	—	6	4	no	—
89	C₃×#135	—	2	1	no	—
90	C₃×#135	—	3	1	no	—
91	C₃×#135	—	6	2	no	—
92	C₃×#135	—	6	2	no	—
93	C₃×#135	C₂×D₃	1	1	yes	characteristic
94	C₃×#135	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×D₈	—	3	2	no	—
96	C₂×C₃×D₈	—	3	2	no	—
97	C₂×C₃×D₈	—	6	2	no	—
98	C₂×C₃×D₈	—	6	2	no	—
99	C₃×#131	—	2	2	no	—
100	C₃×#131	—	3	2	no	—
101	C₃×#131	C₂×D₃	1	2	yes	complemented
102	C₃×#131	C₂²×C₃	1	2	yes	complemented
103	C₃×#127	—	3	2	no	—
104	#949	C₂²×C₃	1	4	yes	complemented
105	#919	—	2	2	no	—
106	#914	—	2	4	no	—
107	D₃×D₈	—	2	2	no	—
108	#908	—	2	4	no	—
109	#908	C₂²×C₃	1	4	yes	complemented
110	#904	—	2	2	no	—
111	#904	C₂²×C₃	1	1	yes	characteristic
112	C₂×D₂₄	—	2	2	no	—
113	C₂×D₂₄	C₂²×C₃	1	2	yes	complemented
114	C₂×D₂₄	C₂²×C₃	1	2	yes	complemented
115	#901	C₂²×C₃	1	2	yes	complemented
116	#874	C₂²×C₃	1	2	yes	complemented
117	C₃×#108	—	2	1	no	—
118	C₃×#108	—	3	1	no	—
119	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
120	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₃×#104	—	2	2	no	—
122	C₃×#104	—	3	2	no	—
123	C₃×#104	C₂×D₃	1	2	yes	complemented
124	C₃×#104	C₂²×C₃	1	2	yes	complemented
125	C₃×#100	—	3	4	no	—
126	C₃×C₄×C₈	—	2	1	no	—
127	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
128	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
129	#823	C₂²×C₃	1	4	yes	complemented
130	#819	C₂²×C₃	1	1	yes	characteristic, complemented
131	#805	C₂²×C₃	1	2	yes	complemented
132	C₂²×C₃×D₃	—	2	4	no	—
133	C₂²×C₃×D₃	—	4	4	no	—
134	C₃²×Q₈	C₂×D₄	1	2	yes	—
135	C₃²×D₄	—	2	2	no	—
136	C₃²×D₄	C₂×D₄	1	2	yes	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
140	C₃×#67	—	2	2	no	—
141	C₃×#67	—	4	4	no	—
142	C₃×D₁₂	—	2	4	no	—
143	C₃×D₁₂	—	2	4	no	—
144	C₃×D₁₂	—	4	4	no	—
145	C₃×D₁₂	—	8	4	no	—
146	C₃×D₁₂	C₂×D₄	1	2	yes	—
147	C₃×C₄×D₃	—	2	2	no	—
148	C₃×C₄×D₃	—	4	4	no	—
149	C₃×Dic₆	C₂×D₄	1	2	yes	—
150	C₃²×C₈	—	2	2	no	—
151	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
152	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
153	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
154	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
155	C₃×C₃⋊C₈	—	2	2	no	—
156	#576	—	3	2	no	—
157	#576	—	3	2	no	—
158	#493	—	3	1	no	—
159	#472	—	3	2	no	—
160	#472	—	3	2	no	—
161	#453	—	3	4	no	—
162	#443	—	3	1	no	—
163	#443	C₃×D₃	1	1	yes	characteristic, complemented
164	C₃×#41	—	2	2	no	—
165	C₃×#41	—	3	2	no	—
166	C₃×#41	—	6	4	no	—
167	C₃×#41	—	6	4	no	—
168	C₃×#41	C₂²×D₃	1	2	yes	—
169	C₃×#41	C₂³×C₃	1	2	yes	—
170	C₂×C₃×D₄	—	3	4	no	—
171	C₂×C₃×D₄	—	6	4	no	—
172	C₂×C₃×D₄	—	6	4	no	—
173	C₂×C₃×D₄	—	12	2	no	—
174	C₂×C₃×D₄	—	12	4	no	—
175	#239	—	2	4	no	—
176	D₃×D₄	—	2	4	no	—
177	D₃×D₄	—	4	4	no	—
178	#235	—	2	4	no	—
179	#235	C₂³×C₃	1	2	yes	—
180	C₂×D₁₂	—	2	4	no	—
181	C₂×D₁₂	—	4	2	no	—
182	C₂×D₁₂	C₂³×C₃	1	4	yes	—
183	C₃×Q₁₆	—	2	1	no	—
184	C₃×Q₁₆	—	3	1	no	—
185	C₃×Q₁₆	D₁₂	1	1	yes	characteristic, complemented
186	C₃×Q₁₆	C₃×D₄	1	1	yes	characteristic, complemented
187	C₃×SD₁₆	—	2	2	no	—
188	C₃×SD₁₆	—	3	2	no	—
189	C₃×SD₁₆	—	6	4	no	—
190	C₃×SD₁₆	—	6	4	no	—
191	C₃×SD₁₆	D₁₂	1	2	yes	complemented
192	C₃×SD₁₆	C₃×D₄	1	2	yes	complemented
193	C₃×D₈	—	2	1	no	—
194	C₃×D₈	—	3	1	no	—
195	C₃×D₈	—	6	4	no	—
196	C₃×D₈	—	6	4	no	—
197	C₃×D₈	—	6	2	no	—
198	C₃×D₈	—	6	2	no	—
199	C₃×D₈	—	6	2	no	—
200	C₃×D₈	—	6	2	no	—
201	C₃×D₈	D₁₂	1	1	yes	characteristic, complemented
202	C₃×D₈	C₃×D₄	1	1	yes	characteristic, complemented
203	C₃×M₁₆	—	2	2	no	—
204	C₃×M₁₆	—	2	2	no	—
205	C₃×M₁₆	—	2	2	no	—
206	C₃×M₁₆	—	3	2	no	—
207	C₃×M₁₆	—	4	2	no	—
208	C₃×M₁₆	—	6	2	no	—
209	C₃×M₁₆	C₂²×D₃	1	2	yes	—
210	C₃×M₁₆	C₂³×C₃	1	2	yes	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	4	2	no	—
216	C₂×C₃×C₈	—	6	2	no	—
217	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
223	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
224	#215	—	2	4	no	—
225	#213	—	2	4	no	—
226	#208	C₂³×C₃	1	2	yes	—
227	Dic₁₂	C₃×D₄	1	1	yes	characteristic, complemented
228	D₂₄	—	2	4	no	—
229	D₂₄	—	2	2	no	—
230	D₂₄	—	2	2	no	—
231	D₂₄	—	2	2	no	—
232	D₂₄	—	2	2	no	—
233	D₂₄	C₃×D₄	1	1	yes	characteristic, complemented
234	#204	—	2	4	no	—
235	#204	C₃×D₄	1	2	yes	complemented
236	ΓL(1,𝔽₂₅)	—	2	2	no	—
237	D₃×C₈	—	2	2	no	—
238	C₂²×C₃²	—	2	2	no	—
239	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₃×D₃	—	2	2	no	—
241	C₂×C₃×D₃	—	4	4	no	—
242	C₂×C₃×D₃	—	8	4	no	—
243	C₂×C₃×D₃	—	16	4	no	—
244	C₃²×C₄	—	2	2	no	—
245	C₃²×C₄	—	2	2	no	—
246	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
247	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
248	C₃×Dic₃	—	2	2	no	—
249	H(5,𝔽₂)	—	3	4	no	—
250	AGL(1,ℤ/8)	—	3	4	no	—
251	AGL(1,ℤ/8)	—	3	4	no	—
252	AGL(1,ℤ/8)	—	6	4	no	—
253	AGL(1,ℤ/8)	—	6	4	no	—
254	#135	—	3	1	no	—
255	#135	—	6	2	no	—
256	#135	—	6	2	no	—
257	#135	C₂×C₃×D₃	1	1	yes	characteristic
258	C₂×D₈	—	3	2	no	—
259	C₂×D₈	—	3	2	no	—
260	C₂×D₈	—	6	2	no	—
261	C₂×D₈	—	6	2	no	—
262	#131	—	3	2	no	—
263	#131	C₂×C₃×D₃	1	2	yes	complemented
264	#127	—	3	2	no	—
265	#108	—	3	1	no	—
266	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
267	#104	—	3	2	no	—
268	#104	C₂×C₃×D₃	1	2	yes	complemented
269	#100	—	3	4	no	—
270	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
271	C₂³×C₃	—	6	4	no	—
272	C₂³×C₃	—	12	4	no	—
273	C₂²×D₃	—	2	4	no	—
274	C₂²×D₃	—	4	4	no	—
275	C₃×Q₈	—	2	2	no	—
276	C₃×Q₈	—	3	2	no	—
277	C₃×Q₈	C₂×D₁₂	1	2	yes	—
278	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
279	C₃×D₄	—	2	2	no	—
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	3	2	no	—
283	C₃×D₄	—	4	2	no	—
284	C₃×D₄	—	6	2	no	—
285	C₃×D₄	—	6	4	no	—
286	C₃×D₄	—	6	4	no	—
287	C₃×D₄	—	12	4	no	—
288	C₃×D₄	—	12	4	no	—
289	C₃×D₄	—	24	4	no	—
290	C₃×D₄	C₂×D₁₂	1	2	yes	—
291	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	6	2	no	—
300	C₂×C₃×C₄	—	12	4	no	—
301	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
303	#67	—	2	2	no	—
304	#67	—	4	4	no	—
305	D₁₂	—	2	4	no	—
306	D₁₂	—	2	4	no	—
307	D₁₂	—	4	4	no	—
308	D₁₂	—	8	4	no	—
309	D₁₂	C₂×C₃×D₄	1	2	yes	—
310	C₄×D₃	—	2	2	no	—
311	C₄×D₃	—	4	4	no	—
312	Dic₆	C₂×C₃×D₄	1	2	yes	—
313	C₃×C₈	—	2	2	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃×C₈	—	2	1	no	—
316	C₃×C₈	—	2	1	no	—
317	C₃×C₈	—	2	1	no	—
318	C₃×C₈	—	2	1	no	—
319	C₃×C₈	—	4	2	no	—
320	C₃×C₈	—	6	2	no	—
321	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
322	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
323	C₃×C₈	D₃×D₄	1	1	yes	characteristic
324	C₃×C₈	D₃×D₄	1	1	yes	characteristic
325	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
326	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
327	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
328	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
329	C₃⋊C₈	—	2	2	no	—
330	C₂×C₃²	—	2	1	no	—
331	C₂×C₃²	—	4	2	no	—
332	C₂×C₃²	D₄²	1	1	yes	characteristic
333	C₃×D₃	—	4	2	no	—
334	C₃×D₃	—	8	4	no	—
335	#41	—	3	2	no	—
336	#41	—	6	4	no	—
337	#41	—	6	4	no	—
338	#41	C₂²×C₃×D₃	1	2	yes	—
339	C₂×D₄	—	3	4	no	—
340	C₂×D₄	—	6	4	no	—
341	C₂×D₄	—	6	4	no	—
342	C₂×D₄	—	12	2	no	—
343	C₂×D₄	—	12	4	no	—
344	Q₁₆	—	3	1	no	—
345	Q₁₆	C₃×D₁₂	1	1	yes	characteristic, complemented
346	SD₁₆	—	3	2	no	—
347	SD₁₆	—	6	4	no	—
348	SD₁₆	—	6	4	no	—
349	SD₁₆	C₃×D₁₂	1	2	yes	complemented
350	D₈	—	3	1	no	—
351	D₈	—	6	4	no	—
352	D₈	—	6	4	no	—
353	D₈	—	6	2	no	—
354	D₈	—	6	2	no	—
355	D₈	—	6	2	no	—
356	D₈	—	6	2	no	—
357	D₈	C₃×D₁₂	1	1	yes	characteristic, complemented
358	M₁₆	—	2	2	no	—
359	M₁₆	—	3	2	no	—
360	M₁₆	—	6	2	no	—
361	M₁₆	C₂²×C₃×D₃	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	6	2	no	—
364	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
365	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
366	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	2	1	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	—	6	2	no	—
372	C₂²×C₃	—	12	4	no	—
373	C₂²×C₃	—	24	4	no	—
374	C₂²×C₃	—	48	4	no	—
375	C₂²×C₃	#1009	1	1	yes	characteristic
376	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	4	4	no	—
379	C₂×D₃	—	8	4	no	—
380	C₂×D₃	—	16	4	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	6	2	no	—
390	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
391	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
392	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
393	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
394	Dic₃	—	2	2	no	—
395	C₃²	#3292	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	6	4	no	—
397	C₂³	—	12	4	no	—
398	Q₈	—	3	2	no	—
399	Q₈	C₂×C₃×D₁₂	1	2	yes	—
400	D₄	—	2	2	no	—
401	D₄	—	3	2	no	—
402	D₄	—	6	2	no	—
403	D₄	—	6	4	no	—
404	D₄	—	6	4	no	—
405	D₄	—	12	4	no	—
406	D₄	—	12	4	no	—
407	D₄	—	24	4	no	—
408	D₄	C₂×C₃×D₁₂	1	2	yes	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	12	4	no	—
413	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	6	2	no	—
416	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
417	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
418	C₈	C₃×D₃×D₄	1	1	yes	characteristic
419	C₈	C₃×D₃×D₄	1	1	yes	characteristic
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	4	1	no	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	—	4	2	no	—
426	C₂×C₃	—	8	2	no	—
427	C₂×C₃	—	12	2	no	—
428	C₂×C₃	—	24	4	no	—
429	C₂×C₃	D₄×D₁₂	1	1	yes	characteristic
430	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
431	D₃	—	4	2	no	—
432	D₃	—	8	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	6	2	no	—
435	C₂²	—	12	4	no	—
436	C₂²	—	24	4	no	—
437	C₂²	—	48	4	no	—
438	C₂²	C₃×#1009	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	6	2	no	—
442	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
443	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
444	C₃	—	2	1	no	—
445	C₃	#79894	1	1	yes	characteristic, direct product factor
446	C₃	C₃×#3292	1	1	yes	characteristic, complemented
447	C₂	—	2	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	12	2	no	—
450	C₂	—	24	4	no	—
451	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×#3292
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×#5769	C₂	semidirect
2. C₃×#5752	C₂	semidirect
3. C₃²×#443	C₂	semidirect
4. C₃×#5142	C₂	semidirect
5. C₃×#4897	C₂	semidirect
6. C₃×#4822	C₂	semidirect
7. C₃×#4700	C₂	semidirect
8. C₃×#4695	C₂	semidirect
10. #79894	C₃	direct (N × H)
11. C₃×#1009	C₂²	semidirect
13. C₃²×#131	C₂²	semidirect
14. C₃×#949	C₂²	semidirect
19. C₃×#908	C₂²	semidirect
23. C₂×C₃×D₂₄	C₂²	semidirect
24. C₂×C₃×D₂₄	C₂²	semidirect
25. C₃×#901	C₂²	semidirect
26. C₃×#874	C₂²	semidirect
27. C₃²×#108	C₂²	semidirect
28. C₃²×#104	C₂²	semidirect
29. C₃²×C₄×C₈	C₂²	semidirect
30. C₃×#823	C₂²	semidirect
31. C₃×#819	C₂²	semidirect
32. C₃×#805	C₂²	semidirect
35. #5769	C₂×C₃	semidirect
36. #5752	C₂×C₃	semidirect
43. C₃×#443	D₃	semidirect
44. C₃×#443	C₂×C₃	semidirect
45. #5142	C₂×C₃	semidirect
46. #4897	C₂×C₃	semidirect
47. #4822	C₂×C₃	semidirect
48. #4700	C₂×C₃	semidirect
49. #4695	C₂×C₃	semidirect
59. C₃²×Q₁₆	D₄	semidirect
60. C₃²×SD₁₆	D₄	semidirect
61. C₃²×D₈	D₄	semidirect
71. C₃×Dic₁₂	D₄	semidirect
77. C₃×D₂₄	D₄	semidirect
79. C₃×#204	D₄	semidirect
84. #1009	C₂²×C₃	semidirect
101. C₃×#131	C₂×D₃	semidirect
102. C₃×#131	C₂²×C₃	semidirect
104. #949	C₂²×C₃	semidirect
109. #908	C₂²×C₃	semidirect
113. C₂×D₂₄	C₂²×C₃	semidirect
114. C₂×D₂₄	C₂²×C₃	semidirect
115. #901	C₂²×C₃	semidirect
116. #874	C₂²×C₃	semidirect
119. C₃×#108	C₂×D₃	semidirect
120. C₃×#108	C₂²×C₃	semidirect
123. C₃×#104	C₂×D₃	semidirect
124. C₃×#104	C₂²×C₃	semidirect
127. C₃×C₄×C₈	C₂×D₃	semidirect
128. C₃×C₄×C₈	C₂²×C₃	semidirect
129. #823	C₂²×C₃	semidirect
130. #819	C₂²×C₃	semidirect
131. #805	C₂²×C₃	semidirect
163. #443	C₃×D₃	semidirect
185. C₃×Q₁₆	D₁₂	semidirect
186. C₃×Q₁₆	C₃×D₄	semidirect
191. C₃×SD₁₆	D₁₂	semidirect
192. C₃×SD₁₆	C₃×D₄	semidirect
201. C₃×D₈	D₁₂	semidirect
202. C₃×D₈	C₃×D₄	semidirect
227. Dic₁₂	C₃×D₄	semidirect
233. D₂₄	C₃×D₄	semidirect
235. #204	C₃×D₄	semidirect
263. #131	C₂×C₃×D₃	semidirect
266. #108	C₂×C₃×D₃	semidirect
268. #104	C₂×C₃×D₃	semidirect
270. C₄×C₈	C₂×C₃×D₃	semidirect
345. Q₁₆	C₃×D₁₂	semidirect
349. SD₁₆	C₃×D₁₂	semidirect
357. D₈	C₃×D₁₂	semidirect
395. C₃²	#3292	semidirect
445. C₃	#79894	direct (N × H)
446. 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×#5769	2
C₃×#5752	2
C₃²×#443	2
C₃×#5142	2
C₃×#4897	2
C₃×#4822	2
C₃×#4700	2
C₃×#4695	2
C₃×#3292	3
#79894	3

Subgroups — C3×#79894 #11886905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79894 #11886905