Subgroups — C₃×#79305 #11878837

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#874	C₂	1	1	yes	maximal, characteristic
2	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4848	C₂	1	4	yes	maximal, complemented
5	C₃×#4731	C₂	1	4	yes	maximal, complemented
6	C₃×#4694	C₂	1	2	yes	maximal, complemented
7	C₃×#4693	C₂	1	2	yes	maximal, complemented
8	C₃×#3208	—	3	1	no	maximal
9	#79305	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×D₁₂	—	2	1	no	—
11	C₂²×C₃×D₁₂	—	2	1	no	—
12	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×#926	—	2	1	no	—
15	C₃×#924	—	2	1	no	—
16	C₃×#924	C₂²	1	2	yes	—
17	C₂×C₃×#204	C₂²	1	8	yes	complemented
18	C₃×#874	—	2	1	no	—
19	C₃×#874	—	2	1	no	—
20	C₃×#874	C₂²	1	2	yes	—
21	C₃×#874	C₂²	1	2	yes	—
22	C₃×#870	—	2	1	no	—
23	C₃×#869	C₂²	1	1	yes	characteristic, complemented
24	C₃×#869	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×Dic₆	—	2	1	no	—
26	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
27	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
30	C₃×#821	C₂²	1	8	yes	complemented
31	C₃×#533	—	3	1	no	—
32	C₂×C₃×#127	—	3	1	no	—
33	C₂×#874	C₂×C₃	1	1	yes	characteristic
34	#5470	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#492	—	3	2	no	—
36	C₃×#486	—	3	2	no	—
37	C₃×#460	—	3	4	no	—
38	C₃×#450	—	3	4	no	—
39	C₃×#431	—	2	1	no	—
40	C₃×#431	D₃	1	1	yes	characteristic, complemented
41	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
42	#4848	C₂×C₃	1	4	yes	complemented
43	#4731	C₂×C₃	1	4	yes	complemented
44	#4694	C₂×C₃	1	2	yes	complemented
45	#4693	C₂×C₃	1	2	yes	complemented
46	C₂³×C₃×D₃	—	2	2	no	—
47	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
49	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃×D₁₂	—	2	2	no	—
51	C₂×C₃×D₁₂	—	2	2	no	—
52	C₂×C₃×D₁₂	—	2	2	no	—
53	C₂×C₃×D₁₂	—	2	2	no	—
54	C₂×C₃×D₁₂	—	2	2	no	—
55	C₂×C₃×D₁₂	—	4	4	no	—
56	C₂×C₃×D₁₂	—	4	4	no	—
57	C₂×C₃×D₁₂	—	4	4	no	—
58	C₂×C₃×D₁₂	C₂³	1	4	yes	—
59	C₂×C₃×Dic₆	—	2	1	no	—
60	C₂×C₃×Dic₆	C₂³	1	2	yes	—
61	C₂×C₃²×C₈	C₂³	1	4	yes	—
62	C₃²×C₄²	D₄	1	1	yes	characteristic
63	C₃²×C₄²	D₄	1	1	yes	characteristic
64	C₃²×C₄²	C₂³	1	1	yes	characteristic
65	C₃²×C₄²	C₂³	1	1	yes	characteristic
66	C₃×#217	—	2	2	no	—
67	C₃×C₄⋊Dic₃	—	2	1	no	—
68	C₃×C₄⋊Dic₃	—	2	1	no	—
69	C₃×C₄⋊Dic₃	—	2	1	no	—
70	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
71	C₃×Dic₃⋊C₄	—	2	2	no	—
72	C₃×Dic₃⋊C₄	—	2	2	no	—
73	C₃×C₄×Dic₃	—	2	2	no	—
74	C₃×#204	—	4	8	no	—
75	#3208	—	3	1	no	Sylow
76	C₂²×C₃×D₄	—	3	2	no	—
77	C₂²×C₃×D₄	—	6	1	no	—
78	C₂²×C₃×D₄	—	6	1	no	—
79	C₂²×D₁₂	—	2	1	no	—
80	C₂²×D₁₂	—	2	1	no	—
81	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×SD₁₆	—	3	8	no	—
83	C₃×C₄⋊Q₈	—	3	1	no	—
84	C₃×C₄⋊Q₈	—	3	1	no	—
85	C₃×#127	—	3	2	no	—
86	C₃×#127	—	3	2	no	—
87	C₃×#127	—	6	1	no	—
88	C₃×#127	—	6	1	no	—
89	C₃×#125	—	6	1	no	—
90	C₃×C₂²⋊Q₈	—	3	2	no	—
91	C₃×C₂²⋊Q₈	—	6	1	no	—
92	C₃×C₄×Q₈	—	3	2	no	—
93	C₃×C₄×Q₈	—	6	1	no	—
94	C₃×#117	—	6	1	no	—
95	C₂×C₃×C₄²	—	2	1	no	—
96	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
98	#926	—	2	1	no	—
99	#924	—	2	1	no	—
100	#924	C₂²×C₃	1	2	yes	—
101	C₂×#204	C₂²×C₃	1	8	yes	complemented
102	#874	—	2	1	no	—
103	#874	—	2	1	no	—
104	#874	C₂²×C₃	1	2	yes	—
105	#874	C₂²×C₃	1	2	yes	—
106	#870	—	2	1	no	—
107	#869	C₂²×C₃	1	1	yes	characteristic, complemented
108	#869	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₄×Dic₆	—	2	1	no	—
110	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
111	C₃×C₄⋊C₈	—	2	2	no	—
112	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
113	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
114	C₃×#102	—	3	8	no	—
115	C₃×C₂²⋊C₈	—	2	2	no	—
116	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
117	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
118	C₃×C₄×C₈	—	2	2	no	—
119	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
120	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
121	#821	C₂²×C₃	1	8	yes	complemented
122	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₃×D₃	—	2	4	no	—
124	C₂²×C₃×D₃	—	4	4	no	—
125	C₂²×C₃×D₃	—	4	4	no	—
126	C₂²×C₃×D₃	—	4	4	no	—
127	C₂×C₃²×C₄	—	2	2	no	—
128	C₂×C₃²×C₄	—	2	2	no	—
129	C₂×C₃²×C₄	SD₁₆	1	4	yes	complemented
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×Dic₃	—	2	2	no	—
137	C₂×C₃×Dic₃	—	2	2	no	—
138	C₃×D₁₂	—	2	8	no	—
139	C₃×D₁₂	—	4	4	no	—
140	C₃×D₁₂	—	4	4	no	—
141	C₃×D₁₂	—	4	4	no	—
142	C₃×D₁₂	—	4	4	no	—
143	C₃×D₁₂	—	4	4	no	—
144	C₃×Dic₆	—	2	4	no	—
145	C₃×Dic₆	—	4	2	no	—
146	C₃²×C₈	—	2	4	no	—
147	#533	—	3	1	no	—
148	C₂×#127	—	3	1	no	—
149	#492	—	3	2	no	—
150	#486	—	3	2	no	—
151	#460	—	3	4	no	—
152	#450	—	3	4	no	—
153	#431	C₃×D₃	1	1	yes	characteristic, complemented
154	C₂⁴×C₃	—	6	2	no	—
155	C₂³×D₃	—	2	2	no	—
156	C₂×C₃×Q₈	—	3	2	no	—
157	C₂×C₃×Q₈	—	6	1	no	—
158	C₂×C₃×D₄	—	3	4	no	—
159	C₂×C₃×D₄	—	6	2	no	—
160	C₂×C₃×D₄	—	6	2	no	—
161	C₂×C₃×D₄	—	6	2	no	—
162	C₂×C₃×D₄	—	6	2	no	—
163	C₂×C₃×D₄	—	6	2	no	—
164	C₂×C₃×D₄	—	12	4	no	—
165	C₂×C₃×D₄	—	12	4	no	—
166	C₂×C₃×D₄	—	12	4	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
171	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×D₁₂	—	2	2	no	—
177	C₂×D₁₂	—	2	2	no	—
178	C₂×D₁₂	—	2	2	no	—
179	C₂×D₁₂	—	2	2	no	—
180	C₂×D₁₂	—	2	2	no	—
181	C₂×D₁₂	—	4	4	no	—
182	C₂×D₁₂	—	4	4	no	—
183	C₂×D₁₂	—	4	4	no	—
184	C₂×D₁₂	C₂³×C₃	1	4	yes	—
185	C₂×Dic₆	—	2	1	no	—
186	C₂×Dic₆	C₂³×C₃	1	2	yes	—
187	C₃×SD₁₆	—	12	8	no	—
188	C₂×C₃×C₈	—	2	4	no	—
189	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
190	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
191	C₃×C₄⋊C₄	—	3	2	no	—
192	C₃×C₄⋊C₄	—	6	2	no	—
193	C₃×C₄⋊C₄	—	6	2	no	—
194	C₃×C₄⋊C₄	—	6	1	no	—
195	C₃×C₄⋊C₄	—	6	1	no	—
196	C₃×C₄⋊C₄	—	6	1	no	—
197	C₃×C₂²⋊C₄	—	6	2	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	—	2	1	no	—
202	C₃×C₄²	—	6	2	no	—
203	C₃×C₄²	D₁₂	1	1	yes	characteristic
204	C₃×C₄²	D₁₂	1	1	yes	characteristic
205	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
206	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
207	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
208	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
209	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
210	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
211	#217	—	2	2	no	—
212	C₄⋊Dic₃	—	2	1	no	—
213	C₄⋊Dic₃	—	2	1	no	—
214	C₄⋊Dic₃	—	2	1	no	—
215	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
216	Dic₃⋊C₄	—	2	2	no	—
217	Dic₃⋊C₄	—	2	2	no	—
218	C₄×Dic₃	—	2	2	no	—
219	#204	—	4	8	no	—
220	C₂²×C₃²	—	2	1	no	—
221	C₂²×C₃²	—	2	1	no	—
222	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
223	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₃×D₃	—	4	4	no	—
225	C₂×C₃×D₃	—	4	4	no	—
226	C₂×C₃×D₃	—	4	4	no	—
227	C₂×C₃×D₃	—	8	8	no	—
228	C₃²×C₄	—	2	1	no	—
229	C₃²×C₄	—	2	1	no	—
230	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
231	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
232	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
233	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
234	C₃×Dic₃	—	4	2	no	—
235	C₃×Dic₃	—	4	2	no	—
236	C₂²×D₄	—	3	2	no	—
237	C₂²×D₄	—	6	1	no	—
238	C₂²×D₄	—	6	1	no	—
239	C₂×SD₁₆	—	3	8	no	—
240	C₄⋊Q₈	—	3	1	no	—
241	C₄⋊Q₈	—	3	1	no	—
242	#127	—	3	2	no	—
243	#127	—	3	2	no	—
244	#127	—	6	1	no	—
245	#127	—	6	1	no	—
246	#125	—	6	1	no	—
247	C₂²⋊Q₈	—	3	2	no	—
248	C₂²⋊Q₈	—	6	1	no	—
249	C₄×Q₈	—	3	2	no	—
250	C₄×Q₈	—	6	1	no	—
251	#117	—	6	1	no	—
252	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
253	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
254	#102	—	3	8	no	—
255	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
256	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	—	6	4	no	—
259	C₂³×C₃	—	12	4	no	—
260	C₂³×C₃	—	12	4	no	—
261	C₂³×C₃	—	12	4	no	—
262	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
263	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂²×D₃	—	2	4	no	—
265	C₂²×D₃	—	4	4	no	—
266	C₂²×D₃	—	4	4	no	—
267	C₂²×D₃	—	4	4	no	—
268	C₃×Q₈	—	6	4	no	—
269	C₃×Q₈	—	12	2	no	—
270	C₃×D₄	—	6	8	no	—
271	C₃×D₄	—	12	4	no	—
272	C₃×D₄	—	12	4	no	—
273	C₃×D₄	—	12	4	no	—
274	C₃×D₄	—	12	4	no	—
275	C₃×D₄	—	12	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	6	2	no	—
290	C₂×C₃×C₄	—	6	2	no	—
291	C₂×C₃×C₄	#204	1	4	yes	complemented
292	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	complemented
293	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	—	2	2	no	—
307	D₁₂	—	2	8	no	—
308	D₁₂	—	4	4	no	—
309	D₁₂	—	4	4	no	—
310	D₁₂	—	4	4	no	—
311	D₁₂	—	4	4	no	—
312	D₁₂	—	4	4	no	—
313	Dic₆	—	2	4	no	—
314	Dic₆	—	4	2	no	—
315	C₃×C₈	—	2	4	no	—
316	C₃×C₈	—	2	4	no	—
317	C₃×C₈	—	4	4	no	—
318	C₂×C₃²	—	2	2	no	—
319	C₂×C₃²	#535	1	1	yes	characteristic
320	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
321	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₃×D₃	—	8	4	no	—
323	C₂⁴	—	6	2	no	—
324	C₂×Q₈	—	3	2	no	—
325	C₂×Q₈	—	6	1	no	—
326	C₂×D₄	—	3	4	no	—
327	C₂×D₄	—	6	2	no	—
328	C₂×D₄	—	6	2	no	—
329	C₂×D₄	—	6	2	no	—
330	C₂×D₄	—	6	2	no	—
331	C₂×D₄	—	6	2	no	—
332	C₂×D₄	—	12	4	no	—
333	C₂×D₄	—	12	4	no	—
334	C₂×D₄	—	12	4	no	—
335	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
336	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	SD₁₆	—	12	8	no	—
339	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
340	C₄⋊C₄	—	3	2	no	—
341	C₄⋊C₄	—	6	1	no	—
342	C₄⋊C₄	—	6	1	no	—
343	C₄⋊C₄	—	6	2	no	—
344	C₄⋊C₄	—	6	2	no	—
345	C₄⋊C₄	—	6	1	no	—
346	C₂²⋊C₄	—	6	2	no	—
347	C₄²	—	6	2	no	—
348	C₄²	C₃×D₁₂	1	1	yes	characteristic
349	C₄²	C₃×D₁₂	1	1	yes	characteristic
350	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
351	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	—	4	1	no	—
360	C₂²×C₃	—	12	4	no	—
361	C₂²×C₃	—	12	4	no	—
362	C₂²×C₃	—	12	4	no	—
363	C₂²×C₃	—	24	8	no	—
364	C₂²×C₃	C₂×#204	1	2	yes	—
365	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
366	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
367	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₂×D₃	—	4	4	no	—
369	C₂×D₃	—	4	4	no	—
370	C₂×D₃	—	4	4	no	—
371	C₂×D₃	—	8	8	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	4	1	no	—
381	C₃×C₄	—	4	1	no	—
382	C₃×C₄	—	12	2	no	—
383	C₃×C₄	—	12	2	no	—
384	C₃×C₄	C₂×#204	1	2	yes	—
385	C₃×C₄	C₂×#204	1	2	yes	—
386	C₃×C₄	#908	1	2	yes	—
387	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
388	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
389	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
390	C₃×C₄	#1009	1	2	yes	—
391	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
392	Dic₃	—	4	2	no	—
393	Dic₃	—	4	2	no	—
394	C₃²	#3208	1	1	yes	characteristic, complemented, Sylow
395	C₂³	—	6	4	no	—
396	C₂³	—	12	4	no	—
397	C₂³	—	12	4	no	—
398	C₂³	—	12	4	no	—
399	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
400	Q₈	—	6	4	no	—
401	Q₈	—	12	2	no	—
402	D₄	—	6	8	no	—
403	D₄	—	12	4	no	—
404	D₄	—	12	4	no	—
405	D₄	—	12	4	no	—
406	D₄	—	12	4	no	—
407	D₄	—	12	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	6	2	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	C₃×#204	1	4	yes	complemented
413	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
414	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
415	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
418	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₂×C₃	—	2	2	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	2	1	no	—
425	C₂×C₃	—	4	2	no	—
426	C₂×C₃	—	24	4	no	—
427	C₂×C₃	#5525	1	1	yes	characteristic
428	C₂×C₃	C₂²×#204	1	1	yes	characteristic
429	C₂×C₃	C₂×#908	1	1	yes	characteristic
430	C₂×C₃	C₃×#535	1	1	yes	characteristic
431	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
432	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
433	D₃	—	8	4	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	12	4	no	—
437	C₂²	—	12	4	no	—
438	C₂²	—	12	4	no	—
439	C₂²	—	24	8	no	—
440	C₂²	C₂×C₃×#204	1	2	yes	—
441	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	12	2	no	—
445	C₄	—	12	2	no	—
446	C₄	C₂×C₃×#204	1	2	yes	—
447	C₄	C₂×C₃×#204	1	2	yes	—
448	C₄	C₃×#908	1	2	yes	—
449	C₄	C₃×#1009	1	2	yes	—
450	C₃	—	2	1	no	—
451	C₃	#79305	1	1	yes	characteristic, direct product factor
452	C₃	C₃×#3208	1	1	yes	characteristic, complemented
453	C₂	—	2	2	no	—
454	C₂	—	24	4	no	—
455	C₂	C₃×#5525	1	1	yes	characteristic
456	C₂	C₂²×C₃×#204	1	1	yes	characteristic
457	C₂	C₂×C₃×#908	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×#431	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#874	C₂
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#3208
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃×#5470	C₂	semidirect
3. C₃²×#431	C₂	semidirect
4. C₃×#4848	C₂	semidirect
5. C₃×#4731	C₂	semidirect
6. C₃×#4694	C₂	semidirect
7. C₃×#4693	C₂	semidirect
9. #79305	C₃	direct (N × H)
17. C₂×C₃×#204	C₂²	semidirect
23. C₃×#869	C₂²	semidirect
24. C₃×#869	C₂²	semidirect
26. C₃×C₄×Dic₆	C₂²	semidirect
27. C₃²×C₄⋊C₈	C₂²	semidirect
29. C₃²×C₄×C₈	C₂²	semidirect
30. C₃×#821	C₂²	semidirect
34. #5470	C₂×C₃	semidirect
40. C₃×#431	D₃	semidirect
41. C₃×#431	C₂×C₃	semidirect
42. #4848	C₂×C₃	semidirect
43. #4731	C₂×C₃	semidirect
44. #4694	C₂×C₃	semidirect
45. #4693	C₂×C₃	semidirect
101. C₂×#204	C₂²×C₃	semidirect
107. #869	C₂²×C₃	semidirect
108. #869	C₂²×C₃	semidirect
110. C₄×Dic₆	C₂²×C₃	semidirect
112. C₃×C₄⋊C₈	C₂×D₃	semidirect
113. C₃×C₄⋊C₈	C₂²×C₃	semidirect
119. C₃×C₄×C₈	C₂×D₃	semidirect
120. C₃×C₄×C₈	C₂²×C₃	semidirect
121. #821	C₂²×C₃	semidirect
129. C₂×C₃²×C₄	SD₁₆	semidirect
153. #431	C₃×D₃	semidirect
253. C₄⋊C₈	C₂×C₃×D₃	semidirect
256. C₄×C₈	C₂×C₃×D₃	semidirect
291. C₂×C₃×C₄	#204	semidirect
292. C₂×C₃×C₄	C₃×SD₁₆	semidirect
394. C₃²	#3208	semidirect
412. C₂×C₄	C₃×#204	semidirect
451. C₃	#79305	direct (N × H)
452. C₃	C₃×#3208	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#874	2
C₃×#5470	2
C₃²×#431	2
C₃×#4848	2
C₃×#4731	2
C₃×#4694	2
C₃×#4693	2
C₃×#3208	3
#79305	3

Subgroups — C3×#79305 #11878837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79305 #11878837