Subgroups — C₂×C₃×#5766 #11918907

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1007	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#942	C₂	1	2	yes	maximal, complemented
4	C₃×#5766	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#919	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#918	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#578	—	3	1	no	maximal
11	C₂×#5766	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
13	C₃×#1007	—	2	8	no	—
14	C₃×#1007	C₂²	1	16	yes	complemented
15	C₂×C₃×#239	—	2	2	no	—
16	C₂×C₃×#239	C₂²	1	4	yes	—
17	C₂×C₃×D₃×Q₈	—	2	2	no	—
18	C₂×C₃×D₃×Q₈	C₂²	1	4	yes	—
19	C₂×C₃×#235	—	2	4	no	—
20	C₂×C₃×#235	C₂²	1	1	yes	characteristic
21	C₂×C₃×#235	C₂²	1	2	yes	—
22	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
23	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
24	C₂×C₃²×Q₁₆	C₂²	1	8	yes	complemented
25	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#216	C₂²	1	4	yes	—
27	C₃×#942	C₂²	1	16	yes	complemented
28	C₂×C₃×#215	C₂²	1	4	yes	—
29	C₂×C₃×#208	C₂²	1	1	yes	characteristic
30	C₃×#919	C₂²	1	16	yes	complemented
31	C₃×#918	C₂²	1	32	yes	complemented
32	C₃×D₃×Q₁₆	C₂²	1	16	yes	complemented
33	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
34	C₃×#904	C₂²	1	8	yes	complemented
35	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×#204	C₂²	1	2	yes	—
37	C₃×#901	C₂²	1	8	yes	complemented
38	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
39	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
40	C₂×C₃×2₋¹⁺⁴	—	3	2	no	—
41	C₂×#1007	C₂×C₃	1	2	yes	complemented
42	C₃×#578	—	3	16	no	—
43	C₂×C₃×#137	—	3	2	no	—
44	C₂×C₃×#137	—	3	4	no	—
45	C₂×C₃×#135	—	3	2	no	—
46	C₂×C₃×#135	—	3	1	no	—
47	C₂²×C₃×Q₁₆	—	2	1	no	—
48	C₂²×C₃×Q₁₆	—	3	2	no	—
49	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
50	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×C₃×#131	—	3	1	no	—
52	C₂×#942	C₂×C₃	1	2	yes	complemented
53	#5766	C₂×C₃	1	16	yes	direct product factor
54	C₂×#919	C₂×C₃	1	2	yes	complemented
55	C₂×#918	C₂×C₃	1	4	yes	complemented
56	C₂×D₃×Q₁₆	C₂×C₃	1	2	yes	complemented
57	C₂×#904	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃²×Q₈	—	2	2	no	—
60	C₂×C₃²×Q₈	—	2	4	no	—
61	C₂×C₃²×Q₈	C₂³	1	4	yes	—
62	C₂×C₃²×Q₈	C₂³	1	8	yes	—
63	C₂²×C₃²×C₄	—	2	2	no	—
64	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃×#67	—	2	2	no	—
66	C₂×C₃×#67	D₄	1	2	yes	—
67	C₃×#239	—	2	16	no	—
68	C₃×#239	—	2	8	no	—
69	C₃×#239	C₂³	1	16	yes	—
70	C₃×D₃×Q₈	—	2	8	no	—
71	C₃×D₃×Q₈	—	2	16	no	—
72	C₃×D₃×Q₈	C₂³	1	16	yes	—
73	C₃×#235	—	2	4	no	—
74	C₃×#235	—	2	32	no	—
75	C₃×#235	D₄	1	4	yes	—
76	C₃×#235	C₂³	1	4	yes	—
77	C₃×#235	C₂³	1	8	yes	—
78	C₂×C₃×D₁₂	—	2	4	no	—
79	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
80	C₂×C₃×D₁₂	C₂³	1	2	yes	—
81	C₂×C₃×C₄×D₃	—	2	4	no	—
82	C₂×C₃×C₄×D₃	—	2	2	no	—
83	C₂×C₃×C₄×D₃	—	2	4	no	—
84	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
85	C₂×C₃×Dic₆	—	2	4	no	—
86	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
87	C₂×C₃×Dic₆	C₂³	1	2	yes	—
88	C₃²×Q₁₆	C₂³	1	8	yes	—
89	C₃²×Q₁₆	C₂³	1	8	yes	—
90	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₃²×C₈	C₂³	1	4	yes	—
93	C₃×#216	C₂³	1	16	yes	—
94	C₃×#215	C₂³	1	16	yes	—
95	C₃×#208	C₂³	1	4	yes	—
96	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
97	C₃×Dic₁₂	C₂³	1	4	yes	—
98	C₃×D₂₄	C₂³	1	4	yes	—
99	C₃×#204	C₂³	1	8	yes	—
100	C₃×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	—
101	C₃×D₃×C₈	C₂³	1	8	yes	—
102	C₂×#578	—	3	1	no	Sylow
103	C₃×2₋¹⁺⁴	—	3	16	no	—
104	C₃×2₋¹⁺⁴	—	6	8	no	—
105	C₂×C₃×#41	—	3	1	no	—
106	C₂×C₃×#41	—	3	4	no	—
107	C₂×C₃×#41	—	3	2	no	—
108	C₂×C₃×#41	—	6	4	no	—
109	C₂×C₃×#41	—	6	2	no	—
110	C₂²×C₃×Q₈	—	2	2	no	—
111	C₂²×C₃×Q₈	—	3	4	no	—
112	C₂²×C₃×Q₈	—	6	2	no	—
113	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
114	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
115	#1007	—	2	8	no	—
116	#1007	C₂²×C₃	1	16	yes	complemented
117	C₂×#239	—	2	2	no	—
118	C₂×#239	C₂²×C₃	1	4	yes	—
119	C₂×D₃×Q₈	—	2	2	no	—
120	C₂×D₃×Q₈	C₂²×C₃	1	4	yes	—
121	C₂×#235	—	2	4	no	—
122	C₂×#235	C₂²×C₃	1	1	yes	characteristic
123	C₂×#235	C₂²×C₃	1	2	yes	—
124	C₃×#137	—	3	16	no	—
125	C₃×#137	—	3	32	no	—
126	C₃×#135	—	3	16	no	—
127	C₃×#135	—	3	8	no	—
128	C₂×C₃×Q₁₆	—	2	2	no	—
129	C₂×C₃×Q₁₆	—	2	2	no	—
130	C₂×C₃×Q₁₆	—	2	8	no	—
131	C₂×C₃×Q₁₆	—	3	4	no	—
132	C₂×C₃×Q₁₆	—	3	16	no	—
133	C₂×C₃×Q₁₆	—	3	1	no	—
134	C₂×C₃×Q₁₆	C₂×D₃	1	2	yes	—
135	C₂×C₃×Q₁₆	C₂×D₃	1	2	yes	—
136	C₂×C₃×Q₁₆	C₂×D₃	1	8	yes	complemented
137	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
138	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
139	C₂×C₃×Q₁₆	C₂²×C₃	1	8	yes	complemented
140	C₂×C₃×SD₁₆	—	3	4	no	—
141	C₂×C₃×SD₁₆	—	3	2	no	—
142	C₂×C₃×D₈	—	3	1	no	—
143	C₃×#131	—	3	8	no	—
144	C₂×C₃×M₁₆	—	3	1	no	—
145	C₂×C₃×M₁₆	—	3	2	no	—
146	C₂²×C₃×C₈	—	2	1	no	—
147	C₂²×C₃×C₈	—	3	2	no	—
148	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
149	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₂×#216	C₂²×C₃	1	4	yes	—
151	#942	C₂²×C₃	1	16	yes	complemented
152	C₂×#215	C₂²×C₃	1	4	yes	—
153	C₂×#208	C₂²×C₃	1	1	yes	characteristic
154	#919	C₂²×C₃	1	16	yes	complemented
155	#918	C₂²×C₃	1	32	yes	complemented
156	D₃×Q₁₆	C₂²×C₃	1	16	yes	complemented
157	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
158	#904	C₂²×C₃	1	8	yes	complemented
159	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×#204	C₂²×C₃	1	2	yes	—
161	#901	C₂²×C₃	1	8	yes	complemented
162	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
163	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
164	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₃×D₃	—	2	2	no	—
166	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
167	C₃²×Q₈	—	2	4	no	—
168	C₃²×Q₈	—	2	8	no	—
169	C₃²×Q₈	C₂⁴	1	8	yes	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	2	8	no	—
172	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
174	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
175	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
176	C₃×#67	—	2	8	no	—
177	C₃×#67	C₂×D₄	1	8	yes	—
178	C₂×C₃×Dic₃	—	2	2	no	—
179	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
180	C₃×D₁₂	—	2	16	no	—
181	C₃×D₁₂	—	2	2	no	—
182	C₃×D₁₂	C₂×D₄	1	4	yes	—
183	C₃×D₁₂	C₂⁴	1	4	yes	—
184	C₃×C₄×D₃	—	2	16	no	—
185	C₃×C₄×D₃	—	2	8	no	—
186	C₃×C₄×D₃	—	2	16	no	—
187	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
188	C₃×C₄×D₃	C₂⁴	1	4	yes	—
189	C₃×Dic₆	—	2	2	no	—
190	C₃×Dic₆	—	2	16	no	—
191	C₃×Dic₆	C₂×D₄	1	4	yes	—
192	C₃×Dic₆	C₂⁴	1	4	yes	—
193	C₃²×C₈	C₂⁴	1	2	yes	—
194	C₃²×C₈	C₂⁴	1	2	yes	—
195	C₃×C₃⋊C₈	C₂⁴	1	4	yes	—
196	C₂×2₋¹⁺⁴	—	3	2	no	—
197	#578	—	3	16	no	—
198	C₂×#137	—	3	2	no	—
199	C₂×#137	—	3	4	no	—
200	C₂×#135	—	3	2	no	—
201	C₂×#135	—	3	1	no	—
202	C₂²×Q₁₆	—	3	2	no	—
203	C₂²×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
204	C₂×#131	—	3	1	no	—
205	C₃×#41	—	3	4	no	—
206	C₃×#41	—	3	4	no	—
207	C₃×#41	—	3	16	no	—
208	C₃×#41	—	3	8	no	—
209	C₃×#41	—	6	32	no	—
210	C₃×#41	—	6	8	no	—
211	C₃×#41	—	6	16	no	—
212	C₃×#41	—	6	4	no	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	2	4	no	—
215	C₂×C₃×Q₈	—	2	2	no	—
216	C₂×C₃×Q₈	—	2	4	no	—
217	C₂×C₃×Q₈	—	2	4	no	—
218	C₂×C₃×Q₈	—	2	8	no	—
219	C₂×C₃×Q₈	—	3	1	no	—
220	C₂×C₃×Q₈	—	3	16	no	—
221	C₂×C₃×Q₈	—	3	2	no	—
222	C₂×C₃×Q₈	—	4	2	no	—
223	C₂×C₃×Q₈	—	4	4	no	—
224	C₂×C₃×Q₈	—	6	4	no	—
225	C₂×C₃×Q₈	—	6	8	no	—
226	C₂×C₃×Q₈	—	6	16	no	—
227	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
228	C₂×C₃×Q₈	C₂²×D₃	1	8	yes	—
229	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
230	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
231	C₂×C₃×D₄	—	3	2	no	—
232	C₂×C₃×D₄	—	3	1	no	—
233	C₂×C₃×D₄	—	3	2	no	—
234	C₂×C₃×D₄	—	6	4	no	—
235	C₂×C₃×D₄	—	6	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	—	2	1	no	—
239	C₂²×C₃×C₄	—	3	2	no	—
240	C₂²×C₃×C₄	—	4	2	no	—
241	C₂²×C₃×C₄	—	6	4	no	—
242	C₂²×C₃×C₄	—	6	4	no	—
243	C₂²×C₃×C₄	—	6	2	no	—
244	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂×#67	—	2	2	no	—
247	C₂×#67	C₃×D₄	1	2	yes	—
248	#239	—	2	16	no	—
249	#239	—	2	8	no	—
250	#239	C₂³×C₃	1	16	yes	—
251	D₃×Q₈	—	2	8	no	—
252	D₃×Q₈	—	2	16	no	—
253	D₃×Q₈	C₂³×C₃	1	16	yes	—
254	#235	—	2	4	no	—
255	#235	—	2	32	no	—
256	#235	C₃×D₄	1	4	yes	—
257	#235	C₂³×C₃	1	4	yes	—
258	#235	C₂³×C₃	1	8	yes	—
259	C₂×D₁₂	—	2	4	no	—
260	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
261	C₂×D₁₂	C₂³×C₃	1	2	yes	—
262	C₂×C₄×D₃	—	2	4	no	—
263	C₂×C₄×D₃	—	2	2	no	—
264	C₂×C₄×D₃	—	2	4	no	—
265	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
266	C₂×Dic₆	—	2	4	no	—
267	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
268	C₂×Dic₆	C₂³×C₃	1	2	yes	—
269	C₃×Q₁₆	—	2	8	no	—
270	C₃×Q₁₆	—	2	8	no	—
271	C₃×Q₁₆	—	3	16	no	—
272	C₃×Q₁₆	—	3	4	no	—
273	C₃×Q₁₆	C₂²×D₃	1	8	yes	—
274	C₃×Q₁₆	C₂²×D₃	1	8	yes	—
275	C₃×Q₁₆	C₂³×C₃	1	8	yes	—
276	C₃×Q₁₆	C₂³×C₃	1	8	yes	—
277	C₃×SD₁₆	—	3	16	no	—
278	C₃×SD₁₆	—	3	8	no	—
279	C₃×D₈	—	3	4	no	—
280	C₃×M₁₆	—	3	4	no	—
281	C₃×M₁₆	—	3	8	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	2	4	no	—
285	C₂×C₃×C₈	—	3	2	no	—
286	C₂×C₃×C₈	—	3	8	no	—
287	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
290	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
293	#216	C₂³×C₃	1	16	yes	—
294	#215	C₂³×C₃	1	16	yes	—
295	#208	C₂³×C₃	1	4	yes	—
296	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
297	Dic₁₂	C₂³×C₃	1	4	yes	—
298	D₂₄	C₂³×C₃	1	4	yes	—
299	#204	C₂³×C₃	1	8	yes	—
300	ΓL(1,𝔽₂₅)	C₂³×C₃	1	8	yes	—
301	D₃×C₈	C₂³×C₃	1	8	yes	—
302	C₂²×C₃²	—	2	2	no	—
303	C₂²×C₃²	C₂²×D₄	1	2	yes	—
304	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₃×D₃	—	2	4	no	—
306	C₂×C₃×D₃	—	2	4	no	—
307	C₂×C₃×D₃	—	4	4	no	—
308	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
309	C₃²×C₄	—	2	8	no	—
310	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₃²×C₄	C₂²×D₄	1	2	yes	—
312	C₃²×C₄	C₂⁵	1	1	yes	characteristic
313	C₃×Dic₃	—	2	4	no	—
314	C₃×Dic₃	C₂²×D₄	1	4	yes	—
315	2₋¹⁺⁴	—	3	16	no	—
316	2₋¹⁺⁴	—	6	8	no	—
317	C₂×#41	—	3	1	no	—
318	C₂×#41	—	3	4	no	—
319	C₂×#41	—	3	2	no	—
320	C₂×#41	—	6	4	no	—
321	C₂×#41	—	6	2	no	—
322	C₂²×Q₈	—	3	4	no	—
323	C₂²×Q₈	—	6	2	no	—
324	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
325	#137	—	3	16	no	—
326	#137	—	3	32	no	—
327	#135	—	3	16	no	—
328	#135	—	3	8	no	—
329	C₂×Q₁₆	—	3	4	no	—
330	C₂×Q₁₆	—	3	16	no	—
331	C₂×Q₁₆	—	3	1	no	—
332	C₂×Q₁₆	C₂×C₃×D₃	1	2	yes	—
333	C₂×Q₁₆	C₂×C₃×D₃	1	2	yes	—
334	C₂×Q₁₆	C₂×C₃×D₃	1	8	yes	complemented
335	C₂×SD₁₆	—	3	4	no	—
336	C₂×SD₁₆	—	3	2	no	—
337	C₂×D₈	—	3	1	no	—
338	#131	—	3	8	no	—
339	C₂×M₁₆	—	3	1	no	—
340	C₂×M₁₆	—	3	2	no	—
341	C₂²×C₈	—	3	2	no	—
342	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	3	2	no	—
345	C₂³×C₃	—	6	2	no	—
346	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
347	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
348	C₂²×D₃	—	2	2	no	—
349	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
350	C₃×Q₈	—	2	4	no	—
351	C₃×Q₈	—	2	8	no	—
352	C₃×Q₈	—	2	4	no	—
353	C₃×Q₈	—	2	8	no	—
354	C₃×Q₈	—	2	8	no	—
355	C₃×Q₈	—	3	4	no	—
356	C₃×Q₈	—	3	4	no	—
357	C₃×Q₈	—	4	4	no	—
358	C₃×Q₈	—	4	8	no	—
359	C₃×Q₈	—	6	16	no	—
360	C₃×Q₈	—	6	2	no	—
361	C₃×Q₈	C₂³×D₃	1	8	yes	—
362	C₃×Q₈	C₂⁴×C₃	1	8	yes	—
363	C₃×D₄	—	3	8	no	—
364	C₃×D₄	—	3	4	no	—
365	C₃×D₄	—	3	4	no	—
366	C₃×D₄	—	6	16	no	—
367	C₃×D₄	—	6	8	no	—
368	C₃×D₄	—	6	2	no	—
369	C₂×C₃×C₄	—	2	8	no	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	8	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	3	2	no	—
378	C₂×C₃×C₄	—	3	4	no	—
379	C₂×C₃×C₄	—	3	4	no	—
380	C₂×C₃×C₄	—	4	4	no	—
381	C₂×C₃×C₄	—	4	8	no	—
382	C₂×C₃×C₄	—	6	16	no	—
383	C₂×C₃×C₄	—	6	16	no	—
384	C₂×C₃×C₄	—	6	2	no	—
385	C₂×C₃×C₄	—	6	8	no	—
386	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
387	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
390	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
391	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
394	#67	—	2	8	no	—
395	#67	C₂×C₃×D₄	1	8	yes	—
396	C₂×Dic₃	—	2	2	no	—
397	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
398	D₁₂	—	2	16	no	—
399	D₁₂	—	2	2	no	—
400	D₁₂	C₂×C₃×D₄	1	4	yes	—
401	D₁₂	C₂⁴×C₃	1	4	yes	—
402	C₄×D₃	—	2	16	no	—
403	C₄×D₃	—	2	8	no	—
404	C₄×D₃	—	2	16	no	—
405	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
406	C₄×D₃	C₂⁴×C₃	1	4	yes	—
407	Dic₆	—	2	2	no	—
408	Dic₆	—	2	16	no	—
409	Dic₆	C₂×C₃×D₄	1	4	yes	—
410	Dic₆	C₂⁴×C₃	1	4	yes	—
411	C₃×C₈	—	2	2	no	—
412	C₃×C₈	—	2	2	no	—
413	C₃×C₈	—	3	4	no	—
414	C₃×C₈	C₂³×D₃	1	2	yes	—
415	C₃×C₈	C₂³×D₃	1	2	yes	—
416	C₃×C₈	C₂⁴×C₃	1	2	yes	—
417	C₃×C₈	C₂⁴×C₃	1	2	yes	—
418	C₃⋊C₈	C₂⁴×C₃	1	4	yes	—
419	C₂×C₃²	—	2	2	no	—
420	C₂×C₃²	#578	1	2	yes	complemented
421	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
422	C₃×D₃	—	2	4	no	—
423	C₃×D₃	—	4	4	no	—
424	#41	—	3	4	no	—
425	#41	—	3	4	no	—
426	#41	—	3	16	no	—
427	#41	—	3	8	no	—
428	#41	—	6	32	no	—
429	#41	—	6	8	no	—
430	#41	—	6	16	no	—
431	#41	—	6	4	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	3	1	no	—
435	C₂×Q₈	—	3	16	no	—
436	C₂×Q₈	—	3	2	no	—
437	C₂×Q₈	—	6	4	no	—
438	C₂×Q₈	—	6	8	no	—
439	C₂×Q₈	—	6	16	no	—
440	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
441	C₂×Q₈	C₂²×C₃×D₃	1	8	yes	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	1	no	—
445	C₂×D₄	—	6	4	no	—
446	C₂×D₄	—	6	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	6	4	no	—
450	C₂²×C₄	—	6	4	no	—
451	C₂²×C₄	—	6	2	no	—
452	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
453	Q₁₆	—	3	16	no	—
454	Q₁₆	—	3	4	no	—
455	Q₁₆	C₂²×C₃×D₃	1	8	yes	—
456	Q₁₆	C₂²×C₃×D₃	1	8	yes	—
457	SD₁₆	—	3	16	no	—
458	SD₁₆	—	3	8	no	—
459	D₈	—	3	4	no	—
460	M₁₆	—	3	4	no	—
461	M₁₆	—	3	8	no	—
462	C₂×C₈	—	3	2	no	—
463	C₂×C₈	—	3	8	no	—
464	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
465	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
466	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
467	C₂²×C₃	—	2	4	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	3	4	no	—
473	C₂²×C₃	—	6	4	no	—
474	C₂²×C₃	—	6	4	no	—
475	C₂²×C₃	—	12	4	no	—
476	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
477	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
478	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
479	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
480	C₂×D₃	—	2	4	no	—
481	C₂×D₃	—	2	4	no	—
482	C₂×D₃	—	4	4	no	—
483	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
484	C₃×C₄	—	2	8	no	—
485	C₃×C₄	—	2	8	no	—
486	C₃×C₄	—	2	1	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	—	2	1	no	—
489	C₃×C₄	—	3	4	no	—
490	C₃×C₄	—	4	8	no	—
491	C₃×C₄	—	6	4	no	—
492	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
493	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
494	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
495	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
496	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
497	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
498	Dic₃	—	2	4	no	—
499	Dic₃	C₂²×C₃×D₄	1	4	yes	—
500	C₃²	C₂×#578	1	1	yes	characteristic, complemented, Sylow
501	C₂³	—	3	2	no	—
502	C₂³	—	6	2	no	—
503	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
504	Q₈	—	2	4	no	—
505	Q₈	—	2	8	no	—
506	Q₈	—	3	4	no	—
507	Q₈	—	3	4	no	—
508	Q₈	—	6	16	no	—
509	Q₈	—	6	2	no	—
510	Q₈	C₂³×C₃×D₃	1	8	yes	—
511	D₄	—	3	8	no	—
512	D₄	—	3	4	no	—
513	D₄	—	3	4	no	—
514	D₄	—	6	16	no	—
515	D₄	—	6	8	no	—
516	D₄	—	6	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	3	2	no	—
520	C₂×C₄	—	3	4	no	—
521	C₂×C₄	—	3	4	no	—
522	C₂×C₄	—	6	16	no	—
523	C₂×C₄	—	6	16	no	—
524	C₂×C₄	—	6	2	no	—
525	C₂×C₄	—	6	8	no	—
526	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
527	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
528	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
529	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
530	C₈	—	3	4	no	—
531	C₈	C₂³×C₃×D₃	1	2	yes	—
532	C₈	C₂³×C₃×D₃	1	2	yes	—
533	C₂×C₃	—	2	4	no	—
534	C₂×C₃	—	2	2	no	—
535	C₂×C₃	—	2	2	no	—
536	C₂×C₃	—	2	2	no	—
537	C₂×C₃	—	2	1	no	—
538	C₂×C₃	—	6	4	no	—
539	C₂×C₃	—	12	4	no	—
540	C₂×C₃	#5766	1	2	yes	direct product factor
541	C₂×C₃	C₃×#578	1	2	yes	complemented
542	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
543	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
544	D₃	—	2	4	no	—
545	D₃	—	4	4	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	3	4	no	—
548	C₂²	—	6	4	no	—
549	C₂²	—	6	4	no	—
550	C₂²	—	12	4	no	—
551	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
552	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
553	C₄	—	2	8	no	—
554	C₄	—	3	4	no	—
555	C₄	—	6	4	no	—
556	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
557	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
558	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
559	C₃	—	2	1	no	—
560	C₃	C₂×#5766	1	1	yes	characteristic, direct product factor
561	C₃	C₂×C₃×#578	1	1	yes	characteristic, complemented
562	C₂	—	2	2	no	—
563	C₂	—	6	4	no	—
564	C₂	—	12	4	no	—
565	C₂	C₃×#5766	1	2	yes	direct product factor
566	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×Q₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₂²×C₃×Q₁₆	D₃
hypocenter	C₃	C₂×C₃×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1007	C₂	semidirect
2. C₂²×C₃²×Q₁₆	C₂	semidirect
3. C₂×C₃×#942	C₂	semidirect
4. C₃×#5766	C₂	direct (N × H)
5. C₂×C₃×#919	C₂	semidirect
6. C₂×C₃×#918	C₂	semidirect
7. C₂×C₃×D₃×Q₁₆	C₂	semidirect
8. C₂×C₃×#904	C₂	semidirect
9. C₂×C₃×#901	C₂	semidirect
11. C₂×#5766	C₃	direct (N × H)
14. C₃×#1007	C₂²	semidirect
24. C₂×C₃²×Q₁₆	C₂²	semidirect
27. C₃×#942	C₂²	semidirect
30. C₃×#919	C₂²	semidirect
31. C₃×#918	C₂²	semidirect
32. C₃×D₃×Q₁₆	C₂²	semidirect
34. C₃×#904	C₂²	semidirect
37. C₃×#901	C₂²	semidirect
41. C₂×#1007	C₂×C₃	semidirect
49. C₂²×C₃×Q₁₆	D₃	semidirect
50. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
52. C₂×#942	C₂×C₃	semidirect
53. #5766	C₂×C₃	direct (N × H)
54. C₂×#919	C₂×C₃	semidirect
55. C₂×#918	C₂×C₃	semidirect
56. C₂×D₃×Q₁₆	C₂×C₃	semidirect
57. C₂×#904	C₂×C₃	semidirect
58. C₂×#901	C₂×C₃	semidirect
116. #1007	C₂²×C₃	semidirect
136. C₂×C₃×Q₁₆	C₂×D₃	semidirect
139. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
151. #942	C₂²×C₃	semidirect
154. #919	C₂²×C₃	semidirect
155. #918	C₂²×C₃	semidirect
156. D₃×Q₁₆	C₂²×C₃	semidirect
158. #904	C₂²×C₃	semidirect
161. #901	C₂²×C₃	semidirect
203. C₂²×Q₁₆	C₃×D₃	semidirect
334. C₂×Q₁₆	C₂×C₃×D₃	semidirect
420. C₂×C₃²	#578	semidirect
500. C₃²	C₂×#578	semidirect
540. C₂×C₃	#5766	direct (N × H)
541. C₂×C₃	C₃×#578	semidirect
560. C₃	C₂×#5766	direct (N × H)
561. C₃	C₂×C₃×#578	semidirect
565. C₂	C₃×#5766	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#1007	2
C₂²×C₃²×Q₁₆	2
C₂×C₃×#942	2
C₃×#5766	2
C₂×C₃×#919	2
C₂×C₃×#918	2
C₂×C₃×D₃×Q₁₆	2
C₂×C₃×#904	2
C₂×C₃×#901	2
C₂×C₃×#578	3
C₂×#5766	3

Subgroups — C2×C3×#5766 #11918907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5766 #11918907