Subgroups — C₃×#83903 #11874276

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5832	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#950	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5191	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5183	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5175	C₂	1	2	yes	maximal, complemented
8	C₃×#5168	C₂	1	2	yes	maximal, complemented
9	C₃×#5155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3147	—	3	1	no	maximal
13	#83903	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	2	yes	—
15	C₂×C₃×#235	C₂²	1	2	yes	—
16	C₃²×#135	—	2	4	no	—
17	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
21	C₃×#950	—	2	8	no	—
22	C₃×#947	C₂²	1	2	yes	—
23	C₃×#944	C₂²	1	2	yes	—
24	C₂×C₃×#216	C₂²	1	2	yes	—
25	C₂×C₃×#215	C₂²	1	2	yes	—
26	C₃×#940	C₂²	1	2	yes	—
27	C₃×#939	—	2	4	no	—
28	C₃×#936	C₂²	1	2	yes	—
29	C₂×C₃×#214	C₂²	1	2	yes	—
30	C₂×C₃×#213	C₂²	1	2	yes	—
31	C₃×C₄×#67	—	2	4	no	—
32	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
35	C₃×#904	—	2	4	no	—
36	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×#204	C₂²	1	2	yes	—
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
40	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
41	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₃×#135	—	2	1	no	—
43	C₂×C₃×#135	—	3	2	no	—
44	C₂×C₃×#135	—	3	1	no	—
45	C₂×C₃×#135	D₃	1	1	yes	characteristic, complemented
46	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#532	—	3	2	no	—
48	#5832	C₂×C₃	1	2	yes	complemented
49	C₂×#950	C₂×C₃	1	2	yes	complemented
50	C₂×#904	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×#495	—	3	1	no	—
52	C₃×#495	—	3	2	no	—
53	C₃×#495	—	3	1	no	—
54	C₃×#494	—	3	1	no	—
55	C₃×#493	—	3	1	no	—
56	C₃×#492	—	3	2	no	—
57	C₂×C₃×C₄×C₈	—	3	1	no	—
58	#5191	C₂×C₃	1	1	yes	characteristic, complemented
59	#5183	C₂×C₃	1	1	yes	characteristic, complemented
60	#5175	C₂×C₃	1	2	yes	complemented
61	#5168	C₂×C₃	1	2	yes	complemented
62	#5155	C₂×C₃	1	1	yes	characteristic, complemented
63	#5151	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
65	C₃²×#41	—	2	4	no	—
66	C₃²×#41	—	2	4	no	—
67	C₂×C₃²×Q₈	C₂³	1	2	yes	—
68	C₂×C₃²×D₄	—	2	2	no	—
69	C₂×C₃²×D₄	C₂³	1	2	yes	—
70	C₂²×C₃²×C₄	—	2	2	no	—
71	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
72	C₂×C₃×#67	—	2	2	no	—
73	C₂×C₃×#67	—	2	4	no	—
74	C₂²×C₃×Dic₃	D₄	1	2	yes	—
75	C₃×#235	—	2	4	no	—
76	C₃×#235	—	2	4	no	—
77	C₂×C₃×D₁₂	C₂³	1	2	yes	—
78	C₂×C₃×C₄×D₃	—	2	2	no	—
79	C₂×C₃×Dic₆	C₂³	1	2	yes	—
80	C₃²×Q₁₆	—	2	2	no	—
81	C₃²×SD₁₆	—	2	4	no	—
82	C₃²×D₈	—	2	2	no	—
83	C₂×C₃²×C₈	D₄	1	4	yes	complemented
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₃×#217	—	2	4	no	—
87	C₃×#216	—	2	4	no	—
88	C₃×#215	—	2	4	no	—
89	C₃×#214	—	2	4	no	—
90	C₃×#213	—	2	4	no	—
91	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
92	C₃×Dic₃⋊C₄	—	2	4	no	—
93	C₃×C₄×Dic₃	D₄	1	2	yes	—
94	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
95	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
97	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₃×Dic₁₂	—	2	2	no	—
100	C₃×D₂₄	—	2	2	no	—
101	C₃×#204	—	2	4	no	—
102	#3147	—	3	1	no	Sylow
103	C₂×C₃×#41	—	2	2	no	—
104	C₂×C₃×#41	—	3	2	no	—
105	C₂×C₃×#41	C₂×D₃	1	2	yes	—
106	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
107	C₂×#235	C₂²×C₃	1	2	yes	—
108	C₃×#135	—	2	8	no	—
109	C₃×#135	—	2	4	no	—
110	C₃×#135	—	2	4	no	—
111	C₃×#135	—	6	8	no	—
112	C₃×#135	—	6	4	no	—
113	C₂×C₃×Q₁₆	—	2	1	no	—
114	C₂×C₃×Q₁₆	—	3	2	no	—
115	C₂×C₃×Q₁₆	—	3	1	no	—
116	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
117	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×SD₁₆	—	2	2	no	—
119	C₂×C₃×SD₁₆	—	3	2	no	—
120	C₂×C₃×SD₁₆	—	3	2	no	—
121	C₂×C₃×SD₁₆	—	3	2	no	—
122	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
123	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
124	C₂×C₃×D₈	—	2	1	no	—
125	C₂×C₃×D₈	—	3	2	no	—
126	C₂×C₃×D₈	—	3	1	no	—
127	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
128	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
129	C₂²×C₃×C₈	—	2	1	no	—
130	C₂²×C₃×C₈	—	3	1	no	—
131	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
133	C₃×C₄⋊Q₈	—	3	2	no	—
134	C₃×#127	—	3	2	no	—
135	C₃×#124	—	3	2	no	—
136	C₃×#124	—	3	2	no	—
137	C₃×#121	—	6	4	no	—
138	C₃×C₄×D₄	—	6	4	no	—
139	C₂×C₃×C₄²	—	3	1	no	—
140	#950	—	2	8	no	—
141	#947	C₂²×C₃	1	2	yes	—
142	#944	C₂²×C₃	1	2	yes	—
143	C₂×#216	C₂²×C₃	1	2	yes	—
144	C₂×#215	C₂²×C₃	1	2	yes	—
145	#940	C₂²×C₃	1	2	yes	—
146	#939	—	2	4	no	—
147	#936	C₂²×C₃	1	2	yes	—
148	C₂×#214	C₂²×C₃	1	2	yes	—
149	C₂×#213	C₂²×C₃	1	2	yes	—
150	C₄×#67	—	2	4	no	—
151	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
152	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
153	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
154	#904	—	2	4	no	—
155	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×#204	C₂²×C₃	1	2	yes	—
157	C₃×C₄×C₈	—	3	1	no	—
158	C₃×C₄×C₈	—	3	1	no	—
159	C₃×C₄×C₈	—	3	1	no	—
160	C₃×C₄×C₈	—	3	1	no	—
161	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
162	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
163	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
164	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
165	C₂³×C₃²	—	2	2	no	—
166	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₃×D₃	—	2	2	no	—
168	C₃²×Q₈	—	2	2	no	—
169	C₃²×Q₈	—	2	2	no	—
170	C₃²×D₄	—	2	2	no	—
171	C₃²×D₄	—	2	2	no	—
172	C₃²×D₄	—	4	4	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	—	4	4	no	—
175	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
176	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
178	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
179	C₃×#67	—	4	4	no	—
180	C₃×#67	—	4	8	no	—
181	C₂×C₃×Dic₃	—	2	4	no	—
182	C₂×C₃×Dic₃	—	2	2	no	—
183	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
184	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
185	C₃×D₁₂	—	2	2	no	—
186	C₃×D₁₂	—	2	2	no	—
187	C₃×C₄×D₃	—	4	4	no	—
188	C₃×Dic₆	—	2	2	no	—
189	C₃×Dic₆	—	2	2	no	—
190	C₃²×C₈	C₂×D₄	1	2	yes	—
191	C₃²×C₈	C₂×D₄	1	2	yes	—
192	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
193	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
194	C₂×#135	—	3	2	no	—
195	C₂×#135	—	3	1	no	—
196	C₂×#135	C₃×D₃	1	1	yes	characteristic, complemented
197	#532	—	3	2	no	—
198	#495	—	3	1	no	—
199	#495	—	3	2	no	—
200	#495	—	3	1	no	—
201	#494	—	3	1	no	—
202	#493	—	3	1	no	—
203	#492	—	3	2	no	—
204	C₂×C₄×C₈	—	3	1	no	—
205	C₃×#41	—	2	8	no	—
206	C₃×#41	—	2	4	no	—
207	C₃×#41	—	2	4	no	—
208	C₃×#41	—	2	4	no	—
209	C₃×#41	—	2	4	no	—
210	C₃×#41	—	4	4	no	—
211	C₃×#41	—	6	4	no	—
212	C₃×#41	—	6	4	no	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	3	2	no	—
215	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
216	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
217	C₂×C₃×D₄	—	2	2	no	—
218	C₂×C₃×D₄	—	2	2	no	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	3	2	no	—
221	C₂×C₃×D₄	—	4	2	no	—
222	C₂×C₃×D₄	—	6	4	no	—
223	C₂×C₃×D₄	—	6	2	no	—
224	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
225	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
226	C₂²×C₃×C₄	—	2	2	no	—
227	C₂²×C₃×C₄	—	2	2	no	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	—	3	2	no	—
230	C₂²×C₃×C₄	—	4	2	no	—
231	C₂²×C₃×C₄	—	6	2	no	—
232	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
234	C₂×#67	—	2	2	no	—
235	C₂×#67	—	2	4	no	—
236	C₂²×Dic₃	C₃×D₄	1	2	yes	—
237	#235	—	2	4	no	—
238	#235	—	2	4	no	—
239	C₂×D₁₂	C₂³×C₃	1	2	yes	—
240	C₂×C₄×D₃	—	2	2	no	—
241	C₂×Dic₆	C₂³×C₃	1	2	yes	—
242	C₃×Q₁₆	—	2	4	no	—
243	C₃×Q₁₆	—	2	2	no	—
244	C₃×Q₁₆	—	2	2	no	—
245	C₃×Q₁₆	—	6	4	no	—
246	C₃×Q₁₆	—	6	2	no	—
247	C₃×SD₁₆	—	2	8	no	—
248	C₃×SD₁₆	—	2	4	no	—
249	C₃×SD₁₆	—	2	4	no	—
250	C₃×SD₁₆	—	6	4	no	—
251	C₃×SD₁₆	—	6	4	no	—
252	C₃×SD₁₆	—	6	4	no	—
253	C₃×D₈	—	2	4	no	—
254	C₃×D₈	—	2	2	no	—
255	C₃×D₈	—	2	2	no	—
256	C₃×D₈	—	6	4	no	—
257	C₃×D₈	—	6	2	no	—
258	C₂×C₃×C₈	—	2	4	no	—
259	C₂×C₃×C₈	—	2	1	no	—
260	C₂×C₃×C₈	—	2	1	no	—
261	C₂×C₃×C₈	—	3	4	no	—
262	C₂×C₃×C₈	—	3	1	no	—
263	C₂×C₃×C₈	—	3	1	no	—
264	C₂×C₃×C₈	#67	1	4	yes	complemented
265	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
266	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	6	4	no	—
271	C₃×C₂²⋊C₄	—	6	4	no	—
272	C₃×C₂²⋊C₄	—	6	4	no	—
273	C₃×C₄²	—	3	2	no	—
274	C₃×C₄²	—	3	1	no	—
275	C₃×C₄²	—	3	1	no	—
276	#217	—	2	4	no	—
277	#216	—	2	4	no	—
278	#215	—	2	4	no	—
279	#214	—	2	4	no	—
280	#213	—	2	4	no	—
281	(C₂×D₃)⋊C₄	—	2	4	no	—
282	Dic₃⋊C₄	—	2	4	no	—
283	C₄×Dic₃	C₃×D₄	1	2	yes	—
284	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
285	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
287	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
289	Dic₁₂	—	2	2	no	—
290	D₂₄	—	2	2	no	—
291	#204	—	2	4	no	—
292	C₂²×C₃²	—	2	2	no	—
293	C₂²×C₃²	—	4	2	no	—
294	C₂²×C₃²	—	4	4	no	—
295	C₂²×C₃²	#127	1	2	yes	—
296	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₃×D₃	—	4	2	no	—
298	C₂×C₃×D₃	—	4	4	no	—
299	C₃²×C₄	—	4	2	no	—
300	C₃²×C₄	#127	1	2	yes	—
301	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
302	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
303	C₃×Dic₃	—	2	2	no	—
304	C₃×Dic₃	—	4	2	no	—
305	C₃×Dic₃	#135	1	4	yes	complemented
306	C₂×#41	—	3	2	no	—
307	C₂×#41	C₂×C₃×D₃	1	2	yes	—
308	#135	—	2	4	no	—
309	#135	—	6	8	no	—
310	#135	—	6	4	no	—
311	C₂×Q₁₆	—	3	2	no	—
312	C₂×Q₁₆	—	3	1	no	—
313	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂×SD₁₆	—	3	2	no	—
315	C₂×SD₁₆	—	3	2	no	—
316	C₂×SD₁₆	—	3	2	no	—
317	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
318	C₂×D₈	—	3	2	no	—
319	C₂×D₈	—	3	1	no	—
320	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
321	C₂²×C₈	—	3	1	no	—
322	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
323	C₄⋊Q₈	—	3	2	no	—
324	#127	—	3	2	no	—
325	#124	—	3	2	no	—
326	#124	—	3	2	no	—
327	#121	—	6	4	no	—
328	C₄×D₄	—	6	4	no	—
329	C₂×C₄²	—	3	1	no	—
330	C₄×C₈	—	3	1	no	—
331	C₄×C₈	—	3	1	no	—
332	C₄×C₈	—	3	1	no	—
333	C₄×C₈	—	3	1	no	—
334	C₂³×C₃	—	2	2	no	—
335	C₂³×C₃	—	2	2	no	—
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	—	4	2	no	—
338	C₂³×C₃	—	6	2	no	—
339	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
340	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂²×D₃	—	2	2	no	—
342	C₃×Q₈	—	2	4	no	—
343	C₃×Q₈	—	2	2	no	—
344	C₃×Q₈	—	2	2	no	—
345	C₃×Q₈	—	2	2	no	—
346	C₃×Q₈	—	2	2	no	—
347	C₃×Q₈	—	4	2	no	—
348	C₃×Q₈	—	6	2	no	—
349	C₃×Q₈	—	6	2	no	—
350	C₃×D₄	—	2	4	no	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	2	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	4	2	no	—
356	C₃×D₄	—	4	8	no	—
357	C₃×D₄	—	4	4	no	—
358	C₃×D₄	—	4	4	no	—
359	C₃×D₄	—	6	2	no	—
360	C₃×D₄	—	6	2	no	—
361	C₃×D₄	—	12	8	no	—
362	C₃×D₄	—	12	4	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	3	2	no	—
370	C₂×C₃×C₄	—	3	2	no	—
371	C₂×C₃×C₄	—	4	2	no	—
372	C₂×C₃×C₄	—	4	8	no	—
373	C₂×C₃×C₄	—	4	4	no	—
374	C₂×C₃×C₄	—	4	4	no	—
375	C₂×C₃×C₄	—	6	4	no	—
376	C₂×C₃×C₄	—	6	2	no	—
377	C₂×C₃×C₄	—	12	4	no	—
378	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
379	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×#67	1	2	yes	—
381	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
383	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
386	#67	—	4	4	no	—
387	#67	—	4	8	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
391	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
392	D₁₂	—	2	2	no	—
393	D₁₂	—	2	2	no	—
394	C₄×D₃	—	4	4	no	—
395	Dic₆	—	2	2	no	—
396	Dic₆	—	2	2	no	—
397	C₃×C₈	—	2	2	no	—
398	C₃×C₈	—	2	2	no	—
399	C₃×C₈	—	3	2	no	—
400	C₃×C₈	—	3	2	no	—
401	C₃×C₈	C₂×#67	1	2	yes	—
402	C₃×C₈	C₂×#67	1	2	yes	—
403	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
404	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
405	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
406	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
407	C₂×C₃²	—	2	2	no	—
408	C₂×C₃²	—	8	2	no	—
409	C₂×C₃²	C₂×#127	1	1	yes	characteristic
410	C₂×C₃²	C₂×#135	1	2	yes	—
411	C₃×D₃	—	8	2	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	6	4	no	—
415	#41	—	6	4	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	3	2	no	—
420	C₂×D₄	—	6	4	no	—
421	C₂×D₄	—	6	2	no	—
422	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	6	2	no	—
426	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
427	Q₁₆	—	2	2	no	—
428	Q₁₆	—	6	4	no	—
429	Q₁₆	—	6	2	no	—
430	SD₁₆	—	2	4	no	—
431	SD₁₆	—	6	4	no	—
432	SD₁₆	—	6	4	no	—
433	SD₁₆	—	6	4	no	—
434	D₈	—	2	2	no	—
435	D₈	—	6	4	no	—
436	D₈	—	6	2	no	—
437	C₂×C₈	—	3	1	no	—
438	C₂×C₈	—	3	1	no	—
439	C₂×C₈	—	3	4	no	—
440	C₂×C₈	C₃×#67	1	4	yes	complemented
441	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
443	C₄⋊C₄	—	6	4	no	—
444	C₂²⋊C₄	—	6	4	no	—
445	C₂²⋊C₄	—	6	4	no	—
446	C₄²	—	3	1	no	—
447	C₄²	—	3	1	no	—
448	C₄²	—	3	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	4	4	no	—
455	C₂²×C₃	—	4	4	no	—
456	C₂²×C₃	—	4	4	no	—
457	C₂²×C₃	—	4	2	no	—
458	C₂²×C₃	—	4	2	no	—
459	C₂²×C₃	—	8	4	no	—
460	C₂²×C₃	—	12	4	no	—
461	C₂²×C₃	—	12	2	no	—
462	C₂²×C₃	#940	1	2	yes	—
463	C₂²×C₃	C₃×#127	1	2	yes	—
464	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
465	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
466	C₂×D₃	—	4	4	no	—
467	C₂×D₃	—	4	2	no	—
468	C₃×C₄	—	2	2	no	—
469	C₃×C₄	—	2	1	no	—
470	C₃×C₄	—	2	1	no	—
471	C₃×C₄	—	3	4	no	—
472	C₃×C₄	—	4	4	no	—
473	C₃×C₄	—	4	2	no	—
474	C₃×C₄	—	4	2	no	—
475	C₃×C₄	—	6	2	no	—
476	C₃×C₄	—	12	2	no	—
477	C₃×C₄	#940	1	2	yes	—
478	C₃×C₄	C₃×#127	1	2	yes	—
479	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
480	C₃×C₄	C₂²×#67	1	1	yes	characteristic
481	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
482	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
483	Dic₃	—	2	2	no	—
484	Dic₃	—	4	2	no	—
485	Dic₃	C₃×#135	1	4	yes	complemented
486	C₃²	#3147	1	1	yes	characteristic, complemented, Sylow
487	C₂³	—	2	2	no	—
488	C₂³	—	6	2	no	—
489	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
490	Q₈	—	2	2	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	6	2	no	—
493	Q₈	—	6	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	6	2	no	—
498	D₄	—	6	2	no	—
499	D₄	—	12	8	no	—
500	D₄	—	12	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	3	2	no	—
503	C₂×C₄	—	3	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	6	4	no	—
506	C₂×C₄	—	6	2	no	—
507	C₂×C₄	—	12	4	no	—
508	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
509	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
510	C₂×C₄	C₂×C₃×#67	1	2	yes	—
511	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
512	C₈	—	3	2	no	—
513	C₈	—	3	2	no	—
514	C₈	C₂×C₃×#67	1	2	yes	—
515	C₈	C₂×C₃×#67	1	2	yes	—
516	C₂×C₃	—	2	2	no	—
517	C₂×C₃	—	2	2	no	—
518	C₂×C₃	—	2	2	no	—
519	C₂×C₃	—	2	1	no	—
520	C₂×C₃	—	4	2	no	—
521	C₂×C₃	—	8	4	no	—
522	C₂×C₃	—	8	2	no	—
523	C₂×C₃	—	8	2	no	—
524	C₂×C₃	—	24	2	no	—
525	C₂×C₃	D₃×#135	1	2	yes	—
526	C₂×C₃	C₂×#940	1	1	yes	characteristic
527	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
528	C₂×C₃	C₂×C₃×#135	1	2	yes	—
529	D₃	—	8	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	12	4	no	—
534	C₂²	—	12	2	no	—
535	C₂²	C₃×#940	1	2	yes	—
536	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
537	C₄	—	3	4	no	—
538	C₄	—	4	2	no	—
539	C₄	—	6	2	no	—
540	C₄	—	12	2	no	—
541	C₄	C₃×#940	1	2	yes	—
542	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
543	C₄	C₂²×C₃×#67	1	1	yes	characteristic
544	C₃	—	2	1	no	—
545	C₃	#83903	1	1	yes	characteristic, direct product factor
546	C₃	C₃×#3147	1	1	yes	characteristic, complemented
547	C₂	—	2	2	no	—
548	C₂	—	8	2	no	—
549	C₂	—	24	2	no	—
550	C₂	C₃×D₃×#135	1	2	yes	—
551	C₂	C₂×C₃×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#135	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₃×#3147
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#135	C₂	semidirect
2. C₃×#5832	C₂	semidirect
3. C₂×C₃×#950	C₂	semidirect
4. C₂×C₃×#904	C₂	semidirect
5. C₃×#5191	C₂	semidirect
6. C₃×#5183	C₂	semidirect
7. C₃×#5175	C₂	semidirect
8. C₃×#5168	C₂	semidirect
9. C₃×#5155	C₂	semidirect
10. C₃×#5151	C₂	semidirect
11. C₂×C₃×C₈×Dic₃	C₂	semidirect
13. #83903	C₃	direct (N × H)
45. C₂×C₃×#135	D₃	semidirect
46. C₂×C₃×#135	C₂×C₃	semidirect
48. #5832	C₂×C₃	semidirect
49. C₂×#950	C₂×C₃	semidirect
50. C₂×#904	C₂×C₃	semidirect
58. #5191	C₂×C₃	semidirect
59. #5183	C₂×C₃	semidirect
60. #5175	C₂×C₃	semidirect
61. #5168	C₂×C₃	semidirect
62. #5155	C₂×C₃	semidirect
63. #5151	C₂×C₃	semidirect
64. C₂×C₈×Dic₃	C₂×C₃	semidirect
83. C₂×C₃²×C₈	D₄	semidirect
96. C₂×C₃×C₃⋊C₈	D₄	semidirect
196. C₂×#135	C₃×D₃	semidirect
264. C₂×C₃×C₈	#67	semidirect
265. C₂×C₃×C₈	C₃×D₄	semidirect
286. C₂×C₃⋊C₈	C₃×D₄	semidirect
305. C₃×Dic₃	#135	semidirect
440. C₂×C₈	C₃×#67	semidirect
485. Dic₃	C₃×#135	semidirect
486. C₃²	#3147	semidirect
545. C₃	#83903	direct (N × H)
546. C₃	C₃×#3147	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#135	2
C₃×#5832	2
C₂×C₃×#950	2
C₂×C₃×#904	2
C₃×#5191	2
C₃×#5183	2
C₃×#5175	2
C₃×#5168	2
C₃×#5155	2
C₃×#5151	2
C₂×C₃×C₈×Dic₃	2
C₃×#3147	3
#83903	3

Subgroups — C3×#83903 #11874276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83903 #11874276