Subgroups — C₃×#79000 #11859084

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5110	C₂	1	2	yes	maximal
4	C₃×#5101	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4840	C₂	1	4	yes	maximal, complemented
7	C₃×#4835	C₂	1	2	yes	maximal, complemented
8	C₃×#4833	C₂	1	2	yes	maximal, complemented
9	C₃×#2925	—	3	1	no	maximal
10	#79000	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×C₄×#67	C₄	1	2	yes	—
15	C₃×C₄×#67	C₄	1	2	yes	—
16	C₃×#926	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	2	yes	—
18	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
19	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
20	C₃×#872	C₂²	1	2	yes	—
21	C₃×C₄²×D₃	C₂²	1	2	yes	—
22	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
23	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
24	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
27	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
28	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
29	C₃×#815	C₂²	1	4	yes	—
30	C₃×C₈×Dic₃	C₂²	1	4	yes	—
31	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
33	C₃×C₄×#41	—	3	1	no	—
34	C₄×#235	C₂×C₃	1	1	yes	characteristic
35	C₃×#433	—	3	4	no	—
36	C₃×#432	—	3	2	no	—
37	C₃×#431	—	3	2	no	—
38	C₃×#423	—	3	1	no	—
39	C₂×C₃×C₄⋊C₈	—	2	1	no	—
40	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
41	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₃×#408	—	3	2	no	—
43	C₃×#405	—	3	2	no	—
44	#5110	C₂×C₃	1	2	yes	—
45	#5101	C₂×C₃	1	2	yes	complemented
46	#4924	C₂×C₃	1	1	yes	characteristic, complemented
47	#4840	C₂×C₃	1	4	yes	complemented
48	#4835	C₂×C₃	1	2	yes	complemented
49	#4833	C₂×C₃	1	2	yes	complemented
50	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃×#67	C₂×C₄	1	2	yes	—
54	C₃×#235	—	2	2	no	—
55	C₃×#235	—	2	2	no	—
56	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
60	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	—	2	4	no	—
62	C₂×C₃²×C₈	C₂³	1	2	yes	—
63	C₂×C₃²×C₈	C₂³	1	2	yes	—
64	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
66	C₃²×C₄²	C₂³	1	1	yes	characteristic
67	C₃²×C₄²	C₂³	1	1	yes	characteristic
68	C₃×#217	C₂×C₄	1	2	yes	—
69	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₃	C₂³	1	2	yes	—
78	C₃×#208	—	2	4	no	—
79	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
80	#2925	—	3	1	no	Sylow
81	C₂×C₃×#41	—	3	1	no	—
82	C₂×#235	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×M₁₆	—	3	2	no	—
84	C₂²×C₃×C₈	—	2	2	no	—
85	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
86	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
87	C₃×C₄×Q₈	—	3	1	no	—
88	C₃×C₄×Q₈	—	3	1	no	—
89	C₃×C₄×D₄	—	3	2	no	—
90	C₃×C₄×D₄	—	3	2	no	—
91	C₃×C₄×D₄	—	3	1	no	—
92	C₃×C₄×D₄	—	3	1	no	—
93	C₃×#117	—	3	1	no	—
94	C₃×#117	—	3	2	no	—
95	C₂×C₃×C₄²	—	2	1	no	—
96	C₂×C₃×C₄²	—	3	2	no	—
97	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
99	C₄×#67	C₃×C₄	1	2	yes	—
100	C₄×#67	C₃×C₄	1	2	yes	—
101	#926	C₂²×C₃	1	1	yes	characteristic
102	C₂×#208	C₂²×C₃	1	2	yes	—
103	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
104	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
105	#872	C₂²×C₃	1	2	yes	—
106	C₄²×D₃	C₂²×C₃	1	2	yes	—
107	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
108	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
109	C₃×C₄⋊C₈	—	2	1	no	—
110	C₃×C₄⋊C₈	—	2	1	no	—
111	C₃×C₄⋊C₈	—	2	2	no	—
112	C₃×C₄⋊C₈	—	3	2	no	—
113	C₃×C₄⋊C₈	—	3	2	no	—
114	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
115	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
116	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
117	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
118	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
120	C₃×C₂²⋊C₈	—	3	4	no	—
121	C₃×C₂²⋊C₈	—	3	4	no	—
122	C₃×#97	—	3	4	no	—
123	C₃×C₄×C₈	—	3	4	no	—
124	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
125	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
126	#815	C₂²×C₃	1	4	yes	—
127	C₈×Dic₃	C₂²×C₃	1	4	yes	—
128	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
129	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
130	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	4	1	no	—
134	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	#41	1	2	yes	—
140	C₂×C₃²×C₄	#41	1	2	yes	—
141	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
142	C₃×#67	—	2	4	no	—
143	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
144	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
145	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
146	C₃×D₁₂	—	2	2	no	—
147	C₃×C₄×D₃	—	2	4	no	—
148	C₃×C₄×D₃	—	2	2	no	—
149	C₃×C₄×D₃	—	2	2	no	—
150	C₃×C₄×D₃	—	4	2	no	—
151	C₃×Dic₆	—	2	2	no	—
152	C₃²×C₈	—	2	2	no	—
153	C₃²×C₈	—	2	2	no	—
154	C₃×C₃⋊C₈	—	2	4	no	—
155	C₄×#41	—	3	1	no	—
156	#433	—	3	4	no	—
157	#432	—	3	2	no	—
158	#431	—	3	2	no	—
159	#423	—	3	1	no	—
160	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
161	#408	—	3	2	no	—
162	#405	—	3	2	no	—
163	C₃×#41	—	6	2	no	—
164	C₃×#41	—	6	2	no	—
165	C₂×C₃×Q₈	—	3	1	no	—
166	C₂×C₃×D₄	—	3	2	no	—
167	C₂×C₃×D₄	—	3	1	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	3	2	no	—
172	C₂²×C₃×C₄	—	3	2	no	—
173	C₂²×C₃×C₄	—	3	2	no	—
174	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂×#67	C₂×C₃×C₄	1	2	yes	—
181	#235	—	2	2	no	—
182	#235	—	2	2	no	—
183	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
185	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
186	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
187	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
188	C₃×M₁₆	—	6	4	no	—
189	C₂×C₃×C₈	—	2	4	no	—
190	C₂×C₃×C₈	—	2	4	no	—
191	C₂×C₃×C₈	—	2	2	no	—
192	C₂×C₃×C₈	—	2	2	no	—
193	C₂×C₃×C₈	—	3	4	no	—
194	C₂×C₃×C₈	—	4	4	no	—
195	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
196	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
197	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
198	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
199	C₃×C₄⋊C₄	—	3	2	no	—
200	C₃×C₄⋊C₄	—	3	2	no	—
201	C₃×C₄⋊C₄	—	3	1	no	—
202	C₃×C₄⋊C₄	—	3	1	no	—
203	C₃×C₂²⋊C₄	—	3	2	no	—
204	C₃×C₂²⋊C₄	—	3	2	no	—
205	C₃×C₂²⋊C₄	—	3	2	no	—
206	C₃×C₄²	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	—	3	2	no	—
211	C₃×C₄²	—	3	2	no	—
212	C₃×C₄²	—	3	2	no	—
213	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
214	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
215	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
216	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
217	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
218	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
219	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
220	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
221	#217	C₂×C₃×C₄	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
223	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
224	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
226	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
227	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
228	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
229	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
230	C₄×Dic₃	C₂³×C₃	1	2	yes	—
231	#208	—	2	4	no	—
232	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
233	C₂²×C₃²	—	2	1	no	—
234	C₂²×C₃²	—	2	1	no	—
235	C₂²×C₃²	#117	1	2	yes	—
236	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₃×D₃	—	2	2	no	—
238	C₂×C₃×D₃	—	2	2	no	—
239	C₂×C₃×D₃	—	2	2	no	—
240	C₃²×C₄	—	2	1	no	—
241	C₃²×C₄	—	2	1	no	—
242	C₃²×C₄	—	2	1	no	—
243	C₃²×C₄	#117	1	2	yes	—
244	C₃²×C₄	#131	1	2	yes	—
245	C₃²×C₄	C₂×#41	1	1	yes	characteristic
246	C₃²×C₄	C₂×#41	1	1	yes	characteristic
247	C₃×Dic₃	—	2	2	no	—
248	C₃×Dic₃	—	2	2	no	—
249	C₃×Dic₃	—	2	2	no	—
250	C₂×#41	—	3	1	no	—
251	C₂×M₁₆	—	3	2	no	—
252	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
253	C₄×Q₈	—	3	1	no	—
254	C₄×Q₈	—	3	1	no	—
255	C₄×D₄	—	3	2	no	—
256	C₄×D₄	—	3	2	no	—
257	C₄×D₄	—	3	1	no	—
258	C₄×D₄	—	3	1	no	—
259	#117	—	3	1	no	—
260	#117	—	3	2	no	—
261	C₂×C₄²	—	3	2	no	—
262	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
263	C₄⋊C₈	—	3	2	no	—
264	C₄⋊C₈	—	3	2	no	—
265	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
266	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
267	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
268	C₂²⋊C₈	—	3	4	no	—
269	C₂²⋊C₈	—	3	4	no	—
270	#97	—	3	4	no	—
271	C₄×C₈	—	3	4	no	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	3	2	no	—
274	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
275	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
276	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
277	C₃×Q₈	—	6	2	no	—
278	C₃×D₄	—	6	4	no	—
279	C₃×D₄	—	6	2	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	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	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	3	2	no	—
292	C₂×C₃×C₄	—	3	2	no	—
293	C₂×C₃×C₄	—	3	2	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	1	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	—	6	4	no	—
298	C₂×C₃×C₄	—	6	2	no	—
299	C₂×C₃×C₄	—	6	2	no	—
300	C₂×C₃×C₄	—	12	2	no	—
301	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
306	C₂×C₃×C₄	#237	1	2	yes	—
307	C₂×C₃×C₄	#239	1	2	yes	—
308	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₃×#41	1	2	yes	—
314	C₂×C₃×C₄	C₃×#41	1	2	yes	—
315	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
317	#67	—	2	4	no	—
318	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
319	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
320	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
321	D₁₂	—	2	2	no	—
322	C₄×D₃	—	2	4	no	—
323	C₄×D₃	—	2	2	no	—
324	C₄×D₃	—	2	2	no	—
325	C₄×D₃	—	4	2	no	—
326	Dic₆	—	2	2	no	—
327	C₃×C₈	—	2	2	no	—
328	C₃×C₈	—	2	2	no	—
329	C₃×C₈	—	2	2	no	—
330	C₃×C₈	—	2	2	no	—
331	C₃×C₈	—	4	2	no	—
332	C₃×C₈	—	4	2	no	—
333	C₃×C₈	—	6	4	no	—
334	C₃⋊C₈	—	2	4	no	—
335	C₂×C₃²	—	2	2	no	—
336	C₂×C₃²	C₂×#117	1	1	yes	characteristic
337	C₂×C₃²	C₂×#131	1	1	yes	characteristic
338	C₂×C₃²	#568	1	1	yes	characteristic
339	C₃×D₃	—	4	2	no	—
340	#41	—	6	2	no	—
341	#41	—	6	2	no	—
342	C₂×Q₈	—	3	1	no	—
343	C₂×D₄	—	3	2	no	—
344	C₂×D₄	—	3	1	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	—	3	2	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
349	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
351	M₁₆	—	6	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	3	4	no	—
354	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
355	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	3	1	no	—
359	C₄⋊C₄	—	3	1	no	—
360	C₂²⋊C₄	—	3	2	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	3	2	no	—
365	C₄²	—	3	2	no	—
366	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
367	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
368	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
369	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	6	2	no	—
379	C₂²×C₃	—	6	2	no	—
380	C₂²×C₃	—	6	2	no	—
381	C₂²×C₃	#892	1	2	yes	—
382	C₂²×C₃	C₃×#117	1	2	yes	—
383	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
384	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
385	C₂×D₃	—	2	2	no	—
386	C₂×D₃	—	2	2	no	—
387	C₂×D₃	—	2	2	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	4	1	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	6	2	no	—
402	C₃×C₄	—	6	2	no	—
403	C₃×C₄	—	6	2	no	—
404	C₃×C₄	#892	1	2	yes	—
405	C₃×C₄	#901	1	2	yes	—
406	C₃×C₄	C₃×#117	1	2	yes	—
407	C₃×C₄	C₃×#131	1	2	yes	—
408	C₃×C₄	C₂×#237	1	1	yes	characteristic
409	C₃×C₄	C₂×#239	1	1	yes	characteristic
410	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
411	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
412	Dic₃	—	2	2	no	—
413	Dic₃	—	2	2	no	—
414	Dic₃	—	2	2	no	—
415	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
416	C₂³	—	3	2	no	—
417	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
418	Q₈	—	6	2	no	—
419	D₄	—	6	4	no	—
420	D₄	—	6	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	6	4	no	—
427	C₂×C₄	—	6	2	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	12	2	no	—
430	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
434	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
435	C₂×C₄	C₃×#237	1	2	yes	—
436	C₂×C₄	C₃×#239	1	2	yes	—
437	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	6	4	no	—
441	C₂×C₃	—	2	4	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	2	2	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	12	2	no	—
448	C₂×C₃	C₂×#892	1	1	yes	characteristic
449	C₂×C₃	C₂×#901	1	1	yes	characteristic
450	C₂×C₃	#5745	1	1	yes	characteristic
451	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
452	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
453	C₂×C₃	C₃×#568	1	1	yes	characteristic
454	D₃	—	4	2	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	6	2	no	—
460	C₂²	C₃×#892	1	2	yes	—
461	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	6	2	no	—
466	C₄	—	6	2	no	—
467	C₄	—	6	2	no	—
468	C₄	C₃×#892	1	2	yes	—
469	C₄	C₃×#901	1	2	yes	—
470	C₄	C₂×C₃×#237	1	1	yes	characteristic
471	C₄	C₂×C₃×#239	1	1	yes	characteristic
472	C₃	—	2	1	no	—
473	C₃	#79000	1	1	yes	characteristic, direct product factor
474	C₃	C₃×#2925	1	1	yes	characteristic, complemented
475	C₂	—	2	2	no	—
476	C₂	—	12	2	no	—
477	C₂	C₂×C₃×#892	1	1	yes	characteristic
478	C₂	C₂×C₃×#901	1	1	yes	characteristic
479	C₂	C₃×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄⋊C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₃×#2925
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄⋊C₈	C₂	semidirect
4. C₃×#5101	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4840	C₂	semidirect
7. C₃×#4835	C₂	semidirect
8. C₃×#4833	C₂	semidirect
10. #79000	C₃	direct (N × H)
40. C₂×C₃×C₄⋊C₈	D₃	semidirect
41. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
45. #5101	C₂×C₃	semidirect
46. #4924	C₂×C₃	semidirect
47. #4840	C₂×C₃	semidirect
48. #4835	C₂×C₃	semidirect
49. #4833	C₂×C₃	semidirect
160. C₂×C₄⋊C₈	C₃×D₃	semidirect
415. C₃²	#2925	semidirect
473. C₃	#79000	direct (N × H)
474. C₃	C₃×#2925	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
C₂×C₃²×C₄⋊C₈	2
C₃×#5110	2
C₃×#5101	2
C₃×#4924	2
C₃×#4840	2
C₃×#4835	2
C₃×#4833	2
C₃×#2925	3
#79000	3

Subgroups — C3×#79000 #11859084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79000 #11859084