Subgroups — C₃×#79059 #11868658

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5131	C₂	1	2	yes	maximal
5	C₃×#5121	C₂	1	2	yes	maximal, complemented
6	C₃×#4847	C₂	1	4	yes	maximal, complemented
7	C₃×#4846	C₂	1	2	yes	maximal, complemented
8	C₃×#4842	C₂	1	2	yes	maximal, complemented
9	C₃×#3077	—	3	1	no	maximal
10	#79059	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₃	—	2	1	no	—
13	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₃×#926	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₃×#924	—	2	1	no	—
19	C₃×#924	—	2	1	no	—
20	C₃×C₄×D₁₂	—	2	1	no	—
21	C₃×C₄×D₁₂	—	2	1	no	—
22	C₃×C₄×D₁₂	C₂²	1	2	yes	—
23	C₃×C₄×D₁₂	C₂²	1	2	yes	—
24	C₃×#870	C₂²	1	2	yes	complemented
25	C₃×#869	C₂²	1	1	yes	characteristic, complemented
26	C₃×#869	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₄×Dic₆	—	2	1	no	—
28	C₃×C₄×Dic₆	—	2	1	no	—
29	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₃×#821	C₂²	1	4	yes	—
32	C₃×#821	C₂²	1	4	yes	—
33	C₃×#818	C₂²	1	4	yes	complemented
34	C₃×#817	C₂²	1	4	yes	complemented
35	C₃×#533	—	3	1	no	—
36	C₂×C₃×C₄×D₄	—	3	1	no	—
37	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
38	#5470	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#478	—	3	4	no	—
40	C₃×#476	—	3	2	no	—
41	C₃×#474	—	3	2	no	—
42	C₃×#428	—	3	2	no	—
43	C₃×#423	—	2	1	no	—
44	C₃×#423	D₃	1	1	yes	characteristic, complemented
45	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#418	—	3	2	no	—
47	#5131	C₂×C₃	1	2	yes	—
48	#5121	C₂×C₃	1	2	yes	complemented
49	#4847	C₂×C₃	1	4	yes	complemented
50	#4846	C₂×C₃	1	2	yes	complemented
51	#4842	C₂×C₃	1	2	yes	complemented
52	C₂³×C₃×D₃	—	2	1	no	—
53	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
54	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	—	2	1	no	—
57	C₂×C₃×D₁₂	—	2	1	no	—
58	C₂×C₃×D₁₂	—	2	2	no	—
59	C₂×C₃×D₁₂	Q₈	1	4	yes	complemented
60	C₂×C₃×D₁₂	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₃	—	2	2	no	—
62	C₂×C₃×C₄×D₃	—	2	2	no	—
63	C₂×C₃×C₄×D₃	—	4	4	no	—
64	C₂×C₃×Dic₆	—	2	1	no	—
65	C₂×C₃×Dic₆	—	2	1	no	—
66	C₃²×M₁₆	—	2	4	no	—
67	C₂×C₃²×C₈	C₂³	1	4	yes	—
68	C₃²×C₄²	D₄	1	1	yes	characteristic
69	C₃²×C₄²	D₄	1	1	yes	characteristic
70	C₃²×C₄²	C₂³	1	1	yes	characteristic
71	C₃²×C₄²	C₂³	1	1	yes	characteristic
72	C₃×#217	—	2	2	no	—
73	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₃×C₄⋊Dic₃	—	2	1	no	—
76	C₃×C₄⋊Dic₃	—	2	1	no	—
77	C₃×C₄⋊Dic₃	—	2	1	no	—
78	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
79	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
80	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
81	C₃×Dic₃⋊C₄	—	2	2	no	—
82	C₃×Dic₃⋊C₄	—	2	2	no	—
83	C₃×C₄×Dic₃	—	2	2	no	—
84	#3077	—	3	1	no	Sylow
85	C₂²×C₃×D₄	—	3	1	no	—
86	C₂³×C₃×C₄	—	6	1	no	—
87	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₄×D₃	—	2	1	no	—
89	C₂×C₃×M₁₆	—	2	2	no	—
90	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
91	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
92	C₃×C₄⋊Q₈	—	3	1	no	—
93	C₃×C₄⋊Q₈	—	3	1	no	—
94	C₃×#125	—	3	2	no	—
95	C₃×C₂²⋊Q₈	—	6	1	no	—
96	C₃×C₂²⋊Q₈	—	6	1	no	—
97	C₃×C₄×Q₈	—	6	1	no	—
98	C₃×C₄×Q₈	—	6	1	no	—
99	C₃×C₄×D₄	—	3	2	no	—
100	C₃×C₄×D₄	—	3	2	no	—
101	C₃×C₄×D₄	—	6	1	no	—
102	C₃×C₄×D₄	—	6	1	no	—
103	C₃×#117	—	3	2	no	—
104	C₂×C₃×C₄⋊C₄	—	3	1	no	—
105	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
106	C₂×C₃×C₄²	—	2	1	no	—
107	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
109	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
110	#926	C₂²×C₃	1	2	yes	—
111	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
112	#924	—	2	1	no	—
113	#924	—	2	1	no	—
114	C₄×D₁₂	—	2	1	no	—
115	C₄×D₁₂	—	2	1	no	—
116	C₄×D₁₂	C₂²×C₃	1	2	yes	—
117	C₄×D₁₂	C₂²×C₃	1	2	yes	—
118	#870	C₂²×C₃	1	2	yes	complemented
119	#869	C₂²×C₃	1	1	yes	characteristic, complemented
120	#869	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₄×Dic₆	—	2	1	no	—
122	C₄×Dic₆	—	2	1	no	—
123	C₃×#107	—	3	4	no	—
124	C₃×#106	—	3	4	no	—
125	C₃×C₄⋊C₈	—	2	2	no	—
126	C₃×C₄⋊C₈	—	2	2	no	—
127	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
128	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
129	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
130	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
131	C₃×#102	—	3	4	no	—
132	C₃×#102	—	3	4	no	—
133	#821	C₂²×C₃	1	4	yes	—
134	#821	C₂²×C₃	1	4	yes	—
135	#818	C₂²×C₃	1	4	yes	complemented
136	#817	C₂²×C₃	1	4	yes	complemented
137	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×D₃	—	2	4	no	—
139	C₂²×C₃×D₃	—	2	2	no	—
140	C₂²×C₃×D₃	—	4	2	no	—
141	C₂²×C₃×D₃	—	4	2	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	4	1	no	—
144	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
150	C₂×C₃²×C₄	#41	1	2	yes	—
151	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
152	C₂×C₃×Dic₃	—	2	2	no	—
153	C₂×C₃×Dic₃	—	2	2	no	—
154	C₂×C₃×Dic₃	—	2	2	no	—
155	C₂×C₃×Dic₃	—	4	2	no	—
156	C₃×D₁₂	—	2	4	no	—
157	C₃×D₁₂	—	2	2	no	—
158	C₃×D₁₂	C₂×Q₈	1	4	yes	—
159	C₃×C₄×D₃	—	4	4	no	—
160	C₃×C₄×D₃	—	4	4	no	—
161	C₃×Dic₆	—	4	2	no	—
162	C₃×Dic₆	—	4	2	no	—
163	C₃²×C₈	—	2	4	no	—
164	#533	—	3	1	no	—
165	C₂×C₄×D₄	—	3	1	no	—
166	#478	—	3	4	no	—
167	#476	—	3	2	no	—
168	#474	—	3	2	no	—
169	#428	—	3	2	no	—
170	#423	C₃×D₃	1	1	yes	characteristic, complemented
171	#418	—	3	2	no	—
172	C₂⁴×C₃	—	6	1	no	—
173	C₂³×D₃	—	2	1	no	—
174	C₂×C₃×Q₈	—	6	1	no	—
175	C₂×C₃×Q₈	—	6	1	no	—
176	C₂×C₃×D₄	—	3	4	no	—
177	C₂×C₃×D₄	—	3	2	no	—
178	C₂×C₃×D₄	—	6	1	no	—
179	C₂×C₃×D₄	—	6	2	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	6	1	no	—
184	C₂²×C₃×C₄	—	6	2	no	—
185	C₂²×C₃×C₄	—	6	2	no	—
186	C₂²×C₃×C₄	—	12	4	no	—
187	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
188	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×Dic₃	—	2	1	no	—
194	C₂×D₁₂	—	2	1	no	—
195	C₂×D₁₂	—	2	2	no	—
196	C₂×D₁₂	C₃×Q₈	1	4	yes	complemented
197	C₂×D₁₂	C₂³×C₃	1	2	yes	—
198	C₂×C₄×D₃	—	2	2	no	—
199	C₂×C₄×D₃	—	2	2	no	—
200	C₂×C₄×D₃	—	4	4	no	—
201	C₂×Dic₆	—	2	1	no	—
202	C₂×Dic₆	—	2	1	no	—
203	C₃×M₁₆	—	2	4	no	—
204	C₃×M₁₆	—	2	4	no	—
205	C₃×M₁₆	—	4	4	no	—
206	C₂×C₃×C₈	—	2	4	no	—
207	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
208	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
209	C₃×C₄⋊C₄	—	3	2	no	—
210	C₃×C₄⋊C₄	—	3	2	no	—
211	C₃×C₄⋊C₄	—	3	2	no	—
212	C₃×C₄⋊C₄	—	6	2	no	—
213	C₃×C₄⋊C₄	—	6	2	no	—
214	C₃×C₄⋊C₄	—	6	1	no	—
215	C₃×C₄⋊C₄	—	6	1	no	—
216	C₃×C₄⋊C₄	—	6	1	no	—
217	C₃×C₂²⋊C₄	—	6	2	no	—
218	C₃×C₂²⋊C₄	—	6	2	no	—
219	C₃×C₂²⋊C₄	—	6	2	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	—	2	1	no	—
223	C₃×C₄²	—	2	1	no	—
224	C₃×C₄²	—	6	2	no	—
225	C₃×C₄²	D₁₂	1	1	yes	characteristic
226	C₃×C₄²	D₁₂	1	1	yes	characteristic
227	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
228	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
229	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
230	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
231	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
232	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
233	#217	—	2	2	no	—
234	(C₂×D₃)⋊C₄	—	2	2	no	—
235	(C₂×D₃)⋊C₄	—	2	2	no	—
236	C₄⋊Dic₃	—	2	1	no	—
237	C₄⋊Dic₃	—	2	1	no	—
238	C₄⋊Dic₃	—	2	1	no	—
239	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
240	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
241	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
242	Dic₃⋊C₄	—	2	2	no	—
243	Dic₃⋊C₄	—	2	2	no	—
244	C₄×Dic₃	—	2	2	no	—
245	C₂²×C₃²	—	2	1	no	—
246	C₂²×C₃²	—	2	1	no	—
247	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
248	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₃×D₃	—	2	4	no	—
250	C₂×C₃×D₃	—	4	8	no	—
251	C₂×C₃×D₃	—	4	2	no	—
252	C₂×C₃×D₃	—	4	2	no	—
253	C₃²×C₄	—	2	1	no	—
254	C₃²×C₄	—	2	1	no	—
255	C₃²×C₄	—	2	1	no	—
256	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
257	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
258	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
259	C₃²×C₄	C₂×#41	1	1	yes	characteristic
260	C₃×Dic₃	—	4	2	no	—
261	C₃×Dic₃	—	4	2	no	—
262	C₃×Dic₃	—	4	2	no	—
263	C₂²×D₄	—	3	1	no	—
264	C₂³×C₄	—	6	1	no	—
265	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
266	C₄⋊Q₈	—	3	1	no	—
267	C₄⋊Q₈	—	3	1	no	—
268	#125	—	3	2	no	—
269	C₂²⋊Q₈	—	6	1	no	—
270	C₂²⋊Q₈	—	6	1	no	—
271	C₄×Q₈	—	6	1	no	—
272	C₄×Q₈	—	6	1	no	—
273	C₄×D₄	—	3	2	no	—
274	C₄×D₄	—	3	2	no	—
275	C₄×D₄	—	6	1	no	—
276	C₄×D₄	—	6	1	no	—
277	#117	—	3	2	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₂²⋊C₄	—	6	1	no	—
280	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
281	#107	—	3	4	no	—
282	#106	—	3	4	no	—
283	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
284	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
285	#102	—	3	4	no	—
286	#102	—	3	4	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	6	4	no	—
289	C₂³×C₃	—	6	2	no	—
290	C₂³×C₃	—	12	2	no	—
291	C₂³×C₃	—	12	2	no	—
292	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
293	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂²×D₃	—	2	4	no	—
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	4	2	no	—
297	C₂²×D₃	—	4	2	no	—
298	C₃×Q₈	—	12	2	no	—
299	C₃×Q₈	—	12	2	no	—
300	C₃×D₄	—	3	4	no	—
301	C₃×D₄	—	6	4	no	—
302	C₃×D₄	—	6	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	4	2	no	—
314	C₂×C₃×C₄	—	4	1	no	—
315	C₂×C₃×C₄	—	4	1	no	—
316	C₂×C₃×C₄	—	4	2	no	—
317	C₂×C₃×C₄	—	6	2	no	—
318	C₂×C₃×C₄	—	6	2	no	—
319	C₂×C₃×C₄	—	6	2	no	—
320	C₂×C₃×C₄	—	12	4	no	—
321	C₂×C₃×C₄	—	12	2	no	—
322	C₂×C₃×C₄	—	12	4	no	—
323	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
328	C₂×C₃×C₄	#237	1	2	yes	—
329	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
330	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
336	C₂×C₃×C₄	C₃×#41	1	2	yes	—
337	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
339	C₂×Dic₃	—	2	2	no	—
340	C₂×Dic₃	—	2	2	no	—
341	C₂×Dic₃	—	2	2	no	—
342	C₂×Dic₃	—	4	2	no	—
343	D₁₂	—	2	4	no	—
344	D₁₂	—	2	2	no	—
345	D₁₂	C₂×C₃×Q₈	1	4	yes	—
346	C₄×D₃	—	4	4	no	—
347	C₄×D₃	—	4	4	no	—
348	Dic₆	—	4	2	no	—
349	Dic₆	—	4	2	no	—
350	C₃×C₈	—	2	4	no	—
351	C₃×C₈	—	2	4	no	—
352	C₃×C₈	—	4	4	no	—
353	C₂×C₃²	—	2	2	no	—
354	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
355	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂×C₃²	#575	1	1	yes	characteristic
357	C₃×D₃	—	4	4	no	—
358	C₂⁴	—	6	1	no	—
359	C₂×Q₈	—	6	1	no	—
360	C₂×Q₈	—	6	1	no	—
361	C₂×D₄	—	3	2	no	—
362	C₂×D₄	—	3	4	no	—
363	C₂×D₄	—	6	1	no	—
364	C₂×D₄	—	6	2	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	2	no	—
367	C₂²×C₄	—	6	2	no	—
368	C₂²×C₄	—	12	4	no	—
369	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
370	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
372	M₁₆	—	2	4	no	—
373	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	6	1	no	—
378	C₄⋊C₄	—	6	2	no	—
379	C₄⋊C₄	—	6	2	no	—
380	C₄⋊C₄	—	6	1	no	—
381	C₄⋊C₄	—	6	1	no	—
382	C₂²⋊C₄	—	6	2	no	—
383	C₂²⋊C₄	—	6	2	no	—
384	C₂²⋊C₄	—	6	2	no	—
385	C₄²	—	6	2	no	—
386	C₄²	C₃×D₁₂	1	1	yes	characteristic
387	C₄²	C₃×D₁₂	1	1	yes	characteristic
388	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
389	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	6	4	no	—
399	C₂²×C₃	—	12	8	no	—
400	C₂²×C₃	—	12	2	no	—
401	C₂²×C₃	—	12	2	no	—
402	C₂²×C₃	#897	1	2	yes	—
403	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
404	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
405	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
406	C₂×D₃	—	2	4	no	—
407	C₂×D₃	—	4	8	no	—
408	C₂×D₃	—	4	2	no	—
409	C₂×D₃	—	4	2	no	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	2	1	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	—	4	1	no	—
423	C₃×C₄	—	12	2	no	—
424	C₃×C₄	—	12	2	no	—
425	C₃×C₄	—	12	2	no	—
426	C₃×C₄	#897	1	2	yes	—
427	C₃×C₄	#908	1	2	yes	—
428	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
429	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
430	C₃×C₄	C₂×#237	1	1	yes	characteristic
431	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
432	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
433	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
434	Dic₃	—	4	2	no	—
435	Dic₃	—	4	2	no	—
436	Dic₃	—	4	2	no	—
437	C₃²	#3077	1	1	yes	characteristic, complemented, Sylow
438	C₂³	—	6	4	no	—
439	C₂³	—	6	2	no	—
440	C₂³	—	12	2	no	—
441	C₂³	—	12	2	no	—
442	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
443	Q₈	—	12	2	no	—
444	Q₈	—	12	2	no	—
445	D₄	—	3	4	no	—
446	D₄	—	6	4	no	—
447	D₄	—	6	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	6	2	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	12	4	no	—
454	C₂×C₄	—	12	2	no	—
455	C₂×C₄	—	12	4	no	—
456	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
457	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
458	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
459	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
460	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
461	C₂×C₄	C₃×#237	1	2	yes	—
462	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
463	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₂×C₃	—	2	2	no	—
466	C₂×C₃	—	2	2	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	2	no	—
471	C₂×C₃	—	12	4	no	—
472	C₂×C₃	C₂×#897	1	1	yes	characteristic
473	C₂×C₃	C₂×#908	1	1	yes	characteristic
474	C₂×C₃	#5748	1	1	yes	characteristic
475	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂×C₃	C₃×#575	1	1	yes	characteristic
478	D₃	—	4	4	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	6	4	no	—
482	C₂²	—	12	8	no	—
483	C₂²	—	12	2	no	—
484	C₂²	—	12	2	no	—
485	C₂²	C₃×#897	1	2	yes	—
486	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	12	2	no	—
491	C₄	—	12	2	no	—
492	C₄	—	12	2	no	—
493	C₄	C₃×#897	1	2	yes	—
494	C₄	C₃×#908	1	2	yes	—
495	C₄	C₂×C₃×#237	1	1	yes	characteristic
496	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
497	C₃	—	2	1	no	—
498	C₃	#79059	1	1	yes	characteristic, direct product factor
499	C₃	C₃×#3077	1	1	yes	characteristic, complemented
500	C₂	—	2	2	no	—
501	C₂	—	12	4	no	—
502	C₂	C₂×C₃×#897	1	1	yes	characteristic
503	C₂	C₂×C₃×#908	1	1	yes	characteristic
504	C₂	C₃×#5748	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×#423	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#3077
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
2. C₃×#5470	C₂	semidirect
3. C₃²×#423	C₂	semidirect
5. C₃×#5121	C₂	semidirect
6. C₃×#4847	C₂	semidirect
7. C₃×#4846	C₂	semidirect
8. C₃×#4842	C₂	semidirect
10. #79059	C₃	direct (N × H)
24. C₃×#870	C₂²	semidirect
25. C₃×#869	C₂²	semidirect
26. C₃×#869	C₂²	semidirect
29. C₃²×C₄⋊C₈	C₂²	semidirect
30. C₃²×C₄⋊C₈	C₂²	semidirect
33. C₃×#818	C₂²	semidirect
34. C₃×#817	C₂²	semidirect
38. #5470	C₂×C₃	semidirect
44. C₃×#423	D₃	semidirect
45. C₃×#423	C₂×C₃	semidirect
48. #5121	C₂×C₃	semidirect
49. #4847	C₂×C₃	semidirect
50. #4846	C₂×C₃	semidirect
51. #4842	C₂×C₃	semidirect
59. C₂×C₃×D₁₂	Q₈	semidirect
118. #870	C₂²×C₃	semidirect
119. #869	C₂²×C₃	semidirect
120. #869	C₂²×C₃	semidirect
127. C₃×C₄⋊C₈	C₂×D₃	semidirect
128. C₃×C₄⋊C₈	C₂×D₃	semidirect
129. C₃×C₄⋊C₈	C₂²×C₃	semidirect
130. C₃×C₄⋊C₈	C₂²×C₃	semidirect
135. #818	C₂²×C₃	semidirect
136. #817	C₂²×C₃	semidirect
170. #423	C₃×D₃	semidirect
196. C₂×D₁₂	C₃×Q₈	semidirect
283. C₄⋊C₈	C₂×C₃×D₃	semidirect
284. C₄⋊C₈	C₂×C₃×D₃	semidirect
437. C₃²	#3077	semidirect
498. C₃	#79059	direct (N × H)
499. C₃	C₃×#3077	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₂	2
C₃×#5470	2
C₃²×#423	2
C₃×#5131	2
C₃×#5121	2
C₃×#4847	2
C₃×#4846	2
C₃×#4842	2
C₃×#3077	3
#79059	3

Subgroups — C3×#79059 #11868658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79059 #11868658