Subgroups — C₂×C₃×#5680 #11900578

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#938	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5680	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#883	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#67⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#879	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#877	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#529	—	3	1	no	maximal
14	C₂×#5680	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#67	C₂²	1	2	yes	—
18	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
19	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₃²×#124	C₂²	1	8	yes	complemented
23	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
26	C₂×C₃×#217	C₂²	1	2	yes	—
27	C₂×C₃×#217	C₂²	1	2	yes	—
28	C₃×#946	C₂²	1	8	yes	complemented
29	C₃×Q₈×Dic₃	C₂²	1	8	yes	complemented
30	C₃×#938	C₂²	1	8	yes	—
31	C₃×D₄×Dic₃	C₂²	1	8	yes	complemented
32	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
41	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
43	C₃×#883	C₂²	1	16	yes	complemented
44	C₃×#67⋊C₄	C₂²	1	16	yes	complemented
45	C₃×#879	C₂²	1	16	yes	complemented
46	C₃×#877	C₂²	1	16	yes	complemented
47	C₃×C₄²×D₃	C₂²	1	8	yes	complemented
48	C₃×#870	C₂²	1	8	yes	complemented
49	C₃×#529	—	3	16	no	—
50	C₂×C₃×#126	—	3	2	no	—
51	C₂×C₃×#125	—	3	1	no	—
52	C₂×C₃×#124	—	2	1	no	—
53	C₂×C₃×#124	D₃	1	1	yes	characteristic, complemented
54	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×#123	—	3	2	no	—
56	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
57	C₂×C₃×#121	—	3	1	no	—
58	C₂×C₃×C₄×Q₈	—	3	1	no	—
59	C₂×C₃×C₄×D₄	—	3	1	no	—
60	C₂×C₃×C₄×D₄	—	3	2	no	—
61	C₂×C₃×#117	—	3	2	no	—
62	C₂²×C₃×C₄²	—	3	1	no	—
63	C₂×#946	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×#938	C₂×C₃	1	1	yes	characteristic
66	C₂×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
67	#5680	C₂×C₃	1	16	yes	direct product factor
68	C₂×#883	C₂×C₃	1	2	yes	complemented
69	C₂×#67⋊C₄	C₂×C₃	1	2	yes	complemented
70	C₂×#879	C₂×C₃	1	2	yes	complemented
71	C₂×#877	C₂×C₃	1	2	yes	complemented
72	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#870	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂⁴×C₃²	C₂³	1	2	yes	—
75	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	C₂³	1	4	yes	—
78	C₂×C₃²×D₄	—	2	4	no	—
79	C₂×C₃²×D₄	C₂³	1	4	yes	—
80	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂³	1	2	yes	—
83	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
84	C₂×C₃×#67	—	2	8	no	—
85	C₂×C₃×#67	C₂³	1	8	yes	—
86	C₂²×C₃×Dic₃	—	2	8	no	—
87	C₂²×C₃×Dic₃	C₂³	1	8	yes	—
88	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
91	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
92	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	—	2	4	no	—
94	C₂×C₃×C₄×D₃	—	2	4	no	—
95	C₂×C₃×C₄×D₃	—	2	4	no	—
96	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
97	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
98	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
99	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₃²×C₄²	C₂³	1	4	yes	—
102	C₃×#217	C₂³	1	8	yes	—
103	C₃×#217	C₂³	1	8	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
105	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
106	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
107	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
108	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
109	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
110	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
111	C₃×C₄×Dic₃	C₂³	1	4	yes	—
112	C₃×C₄×Dic₃	C₂³	1	8	yes	—
113	C₃×C₄×Dic₃	C₂³	1	4	yes	—
114	C₃×C₄×Dic₃	C₂³	1	4	yes	—
115	C₂×#529	—	3	1	no	Sylow
116	C₂²×C₃×Q₈	—	2	1	no	—
117	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
118	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₃×D₄	—	2	1	no	—
120	C₂²×C₃×D₄	—	3	2	no	—
121	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₂³×C₃×C₄	—	3	2	no	—
124	C₂³×C₃×C₄	—	3	1	no	—
125	C₂³×C₃×C₄	—	3	1	no	—
126	C₂³×C₃×C₄	—	3	1	no	—
127	C₂²×#67	C₂²×C₃	1	2	yes	—
128	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
129	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
131	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
132	C₃×#126	—	3	16	no	—
133	C₃×#125	—	3	8	no	—
134	C₃×#124	—	2	8	no	—
135	C₃×#124	C₂×D₃	1	8	yes	complemented
136	C₃×#124	C₂²×C₃	1	8	yes	complemented
137	C₃×#123	—	3	16	no	—
138	C₃×C₂²⋊Q₈	—	3	8	no	—
139	C₃×#121	—	3	8	no	—
140	C₃×C₄×Q₈	—	3	8	no	—
141	C₃×C₄×D₄	—	3	8	no	—
142	C₃×C₄×D₄	—	3	16	no	—
143	C₃×#117	—	3	16	no	—
144	C₂×C₃×C₄⋊C₄	—	3	2	no	—
145	C₂×C₃×C₄⋊C₄	—	3	2	no	—
146	C₂×C₃×C₄⋊C₄	—	3	2	no	—
147	C₂×C₃×C₄⋊C₄	—	3	1	no	—
148	C₂×C₃×C₄⋊C₄	—	3	1	no	—
149	C₂×C₃×C₄⋊C₄	—	3	2	no	—
150	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
151	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
152	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
153	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
155	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
159	C₂×C₃×C₄²	—	2	1	no	—
160	C₂×C₃×C₄²	—	3	1	no	—
161	C₂×C₃×C₄²	—	3	1	no	—
162	C₂×C₃×C₄²	—	3	1	no	—
163	C₂×C₃×C₄²	—	3	2	no	—
164	C₂×C₃×C₄²	—	3	8	no	—
165	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
167	C₂×#217	C₂²×C₃	1	2	yes	—
168	C₂×#217	C₂²×C₃	1	2	yes	—
169	#946	C₂²×C₃	1	8	yes	complemented
170	Q₈×Dic₃	C₂²×C₃	1	8	yes	complemented
171	#938	C₂²×C₃	1	8	yes	—
172	D₄×Dic₃	C₂²×C₃	1	8	yes	complemented
173	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
174	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
177	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
178	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
179	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
180	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
184	#883	C₂²×C₃	1	16	yes	complemented
185	#67⋊C₄	C₂²×C₃	1	16	yes	complemented
186	#879	C₂²×C₃	1	16	yes	complemented
187	#877	C₂²×C₃	1	16	yes	complemented
188	C₄²×D₃	C₂²×C₃	1	8	yes	complemented
189	#870	C₂²×C₃	1	8	yes	complemented
190	C₂³×C₃²	—	2	4	no	—
191	C₂³×C₃²	—	2	4	no	—
192	C₂³×C₃²	—	2	4	no	—
193	C₂³×C₃²	C₂⁴	1	4	yes	—
194	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
195	C₂²×C₃×D₃	—	2	2	no	—
196	C₂²×C₃×D₃	—	2	2	no	—
197	C₂²×C₃×D₃	#41	1	4	yes	—
198	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
199	C₃²×Q₈	—	2	8	no	—
200	C₃²×D₄	—	2	8	no	—
201	C₂×C₃²×C₄	—	2	2	no	—
202	C₂×C₃²×C₄	—	2	2	no	—
203	C₂×C₃²×C₄	—	2	4	no	—
204	C₂×C₃²×C₄	#41	1	4	yes	—
205	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
206	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
207	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
208	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
209	C₃×#67	—	2	16	no	—
210	C₂×C₃×Dic₃	—	2	2	no	—
211	C₂×C₃×Dic₃	—	2	2	no	—
212	C₂×C₃×Dic₃	—	2	4	no	—
213	C₂×C₃×Dic₃	—	2	4	no	—
214	C₂×C₃×Dic₃	—	2	16	no	—
215	C₂×C₃×Dic₃	#41	1	4	yes	—
216	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
217	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
218	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
219	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
220	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
221	C₃×C₄×D₃	—	2	8	no	—
222	C₃×C₄×D₃	—	2	8	no	—
223	C₃×C₄×D₃	—	2	8	no	—
224	#529	—	3	16	no	—
225	C₂×#126	—	3	2	no	—
226	C₂×#125	—	3	1	no	—
227	C₂×#124	C₃×D₃	1	1	yes	characteristic, complemented
228	C₂×#123	—	3	2	no	—
229	C₂×C₂²⋊Q₈	—	3	1	no	—
230	C₂×#121	—	3	1	no	—
231	C₂×C₄×Q₈	—	3	1	no	—
232	C₂×C₄×D₄	—	3	1	no	—
233	C₂×C₄×D₄	—	3	2	no	—
234	C₂×#117	—	3	2	no	—
235	C₂²×C₄²	—	3	1	no	—
236	C₂⁴×C₃	—	2	2	no	—
237	C₂⁴×C₃	—	3	1	no	—
238	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
239	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
240	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃×Q₈	—	2	4	no	—
242	C₂×C₃×Q₈	—	2	4	no	—
243	C₂×C₃×Q₈	—	2	4	no	—
244	C₂×C₃×Q₈	—	4	4	no	—
245	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
246	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
247	C₂×C₃×D₄	—	2	4	no	—
248	C₂×C₃×D₄	—	2	4	no	—
249	C₂×C₃×D₄	—	2	4	no	—
250	C₂×C₃×D₄	—	3	8	no	—
251	C₂×C₃×D₄	—	4	4	no	—
252	C₂×C₃×D₄	—	6	8	no	—
253	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
254	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
255	C₂²×C₃×C₄	—	2	1	no	—
256	C₂²×C₃×C₄	—	2	1	no	—
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	2	2	no	—
259	C₂²×C₃×C₄	—	3	1	no	—
260	C₂²×C₃×C₄	—	3	8	no	—
261	C₂²×C₃×C₄	—	3	1	no	—
262	C₂²×C₃×C₄	—	3	1	no	—
263	C₂²×C₃×C₄	—	3	2	no	—
264	C₂²×C₃×C₄	—	3	2	no	—
265	C₂²×C₃×C₄	—	3	4	no	—
266	C₂²×C₃×C₄	—	3	4	no	—
267	C₂²×C₃×C₄	—	3	4	no	—
268	C₂²×C₃×C₄	—	6	4	no	—
269	C₂²×C₃×C₄	—	6	4	no	—
270	C₂²×C₃×C₄	—	6	8	no	—
271	C₂²×C₃×C₄	—	6	4	no	—
272	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
275	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂×#67	—	2	8	no	—
281	C₂×#67	C₂³×C₃	1	8	yes	—
282	C₂²×Dic₃	—	2	8	no	—
283	C₂²×Dic₃	C₂³×C₃	1	8	yes	—
284	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
285	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
287	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
288	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₄×D₃	—	2	4	no	—
290	C₂×C₄×D₃	—	2	4	no	—
291	C₂×C₄×D₃	—	2	4	no	—
292	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
293	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
294	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
295	C₃×C₄⋊C₄	—	3	8	no	—
296	C₃×C₄⋊C₄	—	3	8	no	—
297	C₃×C₄⋊C₄	—	3	8	no	—
298	C₃×C₄⋊C₄	—	3	4	no	—
299	C₃×C₄⋊C₄	—	3	4	no	—
300	C₃×C₄⋊C₄	—	3	8	no	—
301	C₃×C₂²⋊C₄	—	2	8	no	—
302	C₃×C₂²⋊C₄	—	2	8	no	—
303	C₃×C₂²⋊C₄	—	3	8	no	—
304	C₃×C₂²⋊C₄	—	3	8	no	—
305	C₃×C₂²⋊C₄	—	3	8	no	—
306	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
307	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
308	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
309	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
310	C₃×C₄²	—	2	4	no	—
311	C₃×C₄²	—	3	4	no	—
312	C₃×C₄²	—	3	4	no	—
313	C₃×C₄²	—	3	4	no	—
314	C₃×C₄²	—	3	8	no	—
315	C₃×C₄²	C₂²×D₃	1	4	yes	—
316	C₃×C₄²	C₂³×C₃	1	4	yes	—
317	#217	C₂³×C₃	1	8	yes	—
318	#217	C₂³×C₃	1	8	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
320	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
321	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
322	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
323	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
324	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
325	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
326	C₄×Dic₃	C₂³×C₃	1	4	yes	—
327	C₄×Dic₃	C₂³×C₃	1	4	yes	—
328	C₄×Dic₃	C₂³×C₃	1	4	yes	—
329	C₄×Dic₃	C₂³×C₃	1	8	yes	—
330	C₂²×C₃²	—	2	4	no	—
331	C₂²×C₃²	—	2	4	no	—
332	C₂²×C₃²	—	2	4	no	—
333	C₂²×C₃²	—	4	8	no	—
334	C₂²×C₃²	C₂×#41	1	2	yes	—
335	C₂²×C₃²	C₂×#41	1	2	yes	—
336	C₂²×C₃²	C₂×#41	1	2	yes	—
337	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
338	C₂×C₃×D₃	—	2	8	no	—
339	C₂×C₃×D₃	—	2	2	no	—
340	C₂×C₃×D₃	—	2	2	no	—
341	C₂×C₃×D₃	C₂×#41	1	4	yes	—
342	C₃²×C₄	—	2	2	no	—
343	C₃²×C₄	—	2	2	no	—
344	C₃²×C₄	—	2	4	no	—
345	C₃²×C₄	C₂×#41	1	4	yes	—
346	C₃×Dic₃	—	2	2	no	—
347	C₃×Dic₃	—	2	2	no	—
348	C₃×Dic₃	—	2	4	no	—
349	C₃×Dic₃	—	2	4	no	—
350	C₃×Dic₃	C₂×#41	1	4	yes	—
351	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
352	C₂²×D₄	—	3	2	no	—
353	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
354	C₂³×C₄	—	3	2	no	—
355	C₂³×C₄	—	3	1	no	—
356	C₂³×C₄	—	3	1	no	—
357	C₂³×C₄	—	3	1	no	—
358	#126	—	3	16	no	—
359	#125	—	3	8	no	—
360	#124	C₂×C₃×D₃	1	8	yes	complemented
361	#123	—	3	16	no	—
362	C₂²⋊Q₈	—	3	8	no	—
363	#121	—	3	8	no	—
364	C₄×Q₈	—	3	8	no	—
365	C₄×D₄	—	3	8	no	—
366	C₄×D₄	—	3	16	no	—
367	#117	—	3	16	no	—
368	C₂×C₄⋊C₄	—	3	2	no	—
369	C₂×C₄⋊C₄	—	3	2	no	—
370	C₂×C₄⋊C₄	—	3	1	no	—
371	C₂×C₄⋊C₄	—	3	2	no	—
372	C₂×C₄⋊C₄	—	3	1	no	—
373	C₂×C₄⋊C₄	—	3	2	no	—
374	C₂×C₂²⋊C₄	—	3	2	no	—
375	C₂×C₂²⋊C₄	—	3	2	no	—
376	C₂×C₂²⋊C₄	—	3	2	no	—
377	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
379	C₂×C₄²	—	3	1	no	—
380	C₂×C₄²	—	3	2	no	—
381	C₂×C₄²	—	3	1	no	—
382	C₂×C₄²	—	3	1	no	—
383	C₂×C₄²	—	3	8	no	—
384	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
385	C₂³×C₃	—	2	4	no	—
386	C₂³×C₃	—	2	4	no	—
387	C₂³×C₃	—	2	4	no	—
388	C₂³×C₃	—	2	4	no	—
389	C₂³×C₃	—	2	4	no	—
390	C₂³×C₃	—	2	4	no	—
391	C₂³×C₃	—	2	1	no	—
392	C₂³×C₃	—	2	4	no	—
393	C₂³×C₃	—	3	4	no	—
394	C₂³×C₃	—	3	2	no	—
395	C₂³×C₃	—	4	4	no	—
396	C₂³×C₃	—	4	4	no	—
397	C₂³×C₃	—	4	4	no	—
398	C₂³×C₃	—	6	2	no	—
399	C₂³×C₃	—	6	2	no	—
400	C₂³×C₃	C₂³×D₃	1	4	yes	—
401	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
402	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
403	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
404	C₂²×D₃	—	2	2	no	—
405	C₂²×D₃	—	2	2	no	—
406	C₂²×D₃	C₃×#41	1	4	yes	—
407	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
408	C₃×Q₈	—	2	8	no	—
409	C₃×Q₈	—	2	8	no	—
410	C₃×Q₈	—	4	8	no	—
411	C₃×D₄	—	2	8	no	—
412	C₃×D₄	—	2	8	no	—
413	C₃×D₄	—	4	8	no	—
414	C₃×D₄	—	6	16	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	2	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	3	4	no	—
427	C₂×C₃×C₄	—	3	2	no	—
428	C₂×C₃×C₄	—	3	2	no	—
429	C₂×C₃×C₄	—	3	2	no	—
430	C₂×C₃×C₄	—	3	4	no	—
431	C₂×C₃×C₄	—	3	4	no	—
432	C₂×C₃×C₄	—	4	2	no	—
433	C₂×C₃×C₄	—	4	2	no	—
434	C₂×C₃×C₄	—	4	4	no	—
435	C₂×C₃×C₄	—	6	8	no	—
436	C₂×C₃×C₄	—	6	8	no	—
437	C₂×C₃×C₄	—	6	16	no	—
438	C₂×C₃×C₄	—	6	2	no	—
439	C₂×C₃×C₄	—	6	4	no	—
440	C₂×C₃×C₄	—	6	2	no	—
441	C₂×C₃×C₄	—	6	4	no	—
442	C₂×C₃×C₄	—	6	8	no	—
443	C₂×C₃×C₄	#237	1	4	yes	—
444	C₂×C₃×C₄	C₃×#41	1	4	yes	—
445	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
446	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
447	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
448	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
449	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
450	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
451	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
452	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
453	#67	—	2	16	no	—
454	C₂×Dic₃	—	2	2	no	—
455	C₂×Dic₃	—	2	2	no	—
456	C₂×Dic₃	—	2	4	no	—
457	C₂×Dic₃	—	2	4	no	—
458	C₂×Dic₃	—	2	16	no	—
459	C₂×Dic₃	C₃×#41	1	4	yes	—
460	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
461	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
462	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
463	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
464	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
465	C₄×D₃	—	2	8	no	—
466	C₄×D₃	—	2	8	no	—
467	C₄×D₃	—	2	8	no	—
468	C₂×C₃²	—	4	4	no	—
469	C₂×C₃²	#529	1	4	yes	complemented
470	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
471	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
472	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
473	C₃×D₃	—	2	4	no	—
474	C₂⁴	—	3	1	no	—
475	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
476	C₂×Q₈	—	2	4	no	—
477	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	3	8	no	—
480	C₂×D₄	—	6	8	no	—
481	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
482	C₂²×C₄	—	3	1	no	—
483	C₂²×C₄	—	3	1	no	—
484	C₂²×C₄	—	3	1	no	—
485	C₂²×C₄	—	3	2	no	—
486	C₂²×C₄	—	3	2	no	—
487	C₂²×C₄	—	3	8	no	—
488	C₂²×C₄	—	3	4	no	—
489	C₂²×C₄	—	3	4	no	—
490	C₂²×C₄	—	3	4	no	—
491	C₂²×C₄	—	6	4	no	—
492	C₂²×C₄	—	6	4	no	—
493	C₂²×C₄	—	6	8	no	—
494	C₂²×C₄	—	6	4	no	—
495	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
498	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
499	C₄⋊C₄	—	3	8	no	—
500	C₄⋊C₄	—	3	8	no	—
501	C₄⋊C₄	—	3	4	no	—
502	C₄⋊C₄	—	3	8	no	—
503	C₄⋊C₄	—	3	4	no	—
504	C₄⋊C₄	—	3	8	no	—
505	C₂²⋊C₄	—	3	8	no	—
506	C₂²⋊C₄	—	3	8	no	—
507	C₂²⋊C₄	—	3	8	no	—
508	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
509	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
510	C₄²	—	3	4	no	—
511	C₄²	—	3	4	no	—
512	C₄²	—	3	4	no	—
513	C₄²	—	3	8	no	—
514	C₄²	C₂²×C₃×D₃	1	4	yes	—
515	C₂²×C₃	—	2	4	no	—
516	C₂²×C₃	—	2	4	no	—
517	C₂²×C₃	—	2	4	no	—
518	C₂²×C₃	—	2	4	no	—
519	C₂²×C₃	—	2	4	no	—
520	C₂²×C₃	—	2	4	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	3	4	no	—
526	C₂²×C₃	—	4	4	no	—
527	C₂²×C₃	—	4	4	no	—
528	C₂²×C₃	—	4	4	no	—
529	C₂²×C₃	—	4	8	no	—
530	C₂²×C₃	—	4	8	no	—
531	C₂²×C₃	—	6	8	no	—
532	C₂²×C₃	—	6	2	no	—
533	C₂²×C₃	—	6	2	no	—
534	C₂²×C₃	—	8	8	no	—
535	C₂²×C₃	C₂×#237	1	2	yes	—
536	C₂²×C₃	D₃×#41	1	2	yes	—
537	C₂²×C₃	D₃×#41	1	2	yes	—
538	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
539	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
540	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
541	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
542	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
543	C₂×D₃	—	2	2	no	—
544	C₂×D₃	—	2	2	no	—
545	C₂×D₃	—	2	8	no	—
546	C₂×D₃	C₂×C₃×#41	1	4	yes	—
547	C₃×C₄	—	2	4	no	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	4	no	—
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	3	4	no	—
555	C₃×C₄	—	4	4	no	—
556	C₃×C₄	—	4	2	no	—
557	C₃×C₄	—	4	2	no	—
558	C₃×C₄	—	6	2	no	—
559	C₃×C₄	—	6	4	no	—
560	C₃×C₄	—	6	2	no	—
561	C₃×C₄	—	6	4	no	—
562	C₃×C₄	C₂×#237	1	4	yes	—
563	C₃×C₄	C₂×C₃×#41	1	4	yes	—
564	Dic₃	—	2	2	no	—
565	Dic₃	—	2	2	no	—
566	Dic₃	—	2	4	no	—
567	Dic₃	—	2	4	no	—
568	Dic₃	C₂×C₃×#41	1	4	yes	—
569	C₃²	C₂×#529	1	1	yes	characteristic, complemented, Sylow
570	C₂³	—	2	4	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	3	4	no	—
574	C₂³	—	3	2	no	—
575	C₂³	—	6	2	no	—
576	C₂³	—	6	2	no	—
577	C₂³	C₂³×C₃×D₃	1	4	yes	—
578	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
579	Q₈	—	2	8	no	—
580	D₄	—	2	8	no	—
581	D₄	—	6	16	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	3	4	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	3	2	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	4	no	—
590	C₂×C₄	—	3	4	no	—
591	C₂×C₄	—	6	8	no	—
592	C₂×C₄	—	6	8	no	—
593	C₂×C₄	—	6	16	no	—
594	C₂×C₄	—	6	2	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	4	no	—
598	C₂×C₄	—	6	8	no	—
599	C₂×C₄	C₃×#237	1	4	yes	—
600	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
601	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
602	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
603	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
604	C₂×C₃	—	2	1	no	—
605	C₂×C₃	—	2	1	no	—
606	C₂×C₃	—	2	1	no	—
607	C₂×C₃	—	2	4	no	—
608	C₂×C₃	—	4	4	no	—
609	C₂×C₃	—	4	4	no	—
610	C₂×C₃	—	6	4	no	—
611	C₂×C₃	—	8	4	no	—
612	C₂×C₃	#5680	1	4	yes	direct product factor
613	C₂×C₃	C₃×#529	1	4	yes	complemented
614	C₂×C₃	C₂²×#237	1	1	yes	characteristic
615	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
616	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
617	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
618	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
619	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
620	D₃	—	2	4	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	3	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	6	2	no	—
627	C₂²	—	6	2	no	—
628	C₂²	—	6	8	no	—
629	C₂²	C₂×C₃×#237	1	2	yes	—
630	C₂²	C₃×D₃×#41	1	2	yes	—
631	C₂²	C₃×D₃×#41	1	2	yes	—
632	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
633	C₄	—	2	4	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	3	4	no	—
637	C₄	—	6	2	no	—
638	C₄	—	6	4	no	—
639	C₄	—	6	2	no	—
640	C₄	—	6	4	no	—
641	C₄	C₂×C₃×#237	1	4	yes	—
642	C₃	—	2	1	no	—
643	C₃	C₂×#5680	1	1	yes	characteristic, direct product factor
644	C₃	C₂×C₃×#529	1	1	yes	characteristic, complemented
645	C₂	—	4	4	no	—
646	C₂	—	6	4	no	—
647	C₂	C₃×#5680	1	4	yes	direct product factor
648	C₂	C₂²×C₃×#237	1	1	yes	characteristic
649	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
650	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#124	C₂
socle	C₂³×C₃²	C₂⁴
prime radical	C₂×C₃×#938	C₂
hypercenter	C₂×C₃×#124	D₃
hypocenter	C₃	C₂×C₃×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#124	C₂	semidirect
2. C₂×C₃×#946	C₂	semidirect
3. C₂×C₃×Q₈×Dic₃	C₂	semidirect
5. C₂×C₃×D₄×Dic₃	C₂	semidirect
6. C₃×#5680	C₂	direct (N × H)
7. C₂×C₃×#883	C₂	semidirect
8. C₂×C₃×#67⋊C₄	C₂	semidirect
9. C₂×C₃×#879	C₂	semidirect
10. C₂×C₃×#877	C₂	semidirect
11. C₂×C₃×C₄²×D₃	C₂	semidirect
12. C₂×C₃×#870	C₂	semidirect
14. C₂×#5680	C₃	direct (N × H)
22. C₃²×#124	C₂²	semidirect
28. C₃×#946	C₂²	semidirect
29. C₃×Q₈×Dic₃	C₂²	semidirect
31. C₃×D₄×Dic₃	C₂²	semidirect
43. C₃×#883	C₂²	semidirect
44. C₃×#67⋊C₄	C₂²	semidirect
45. C₃×#879	C₂²	semidirect
46. C₃×#877	C₂²	semidirect
47. C₃×C₄²×D₃	C₂²	semidirect
48. C₃×#870	C₂²	semidirect
53. C₂×C₃×#124	D₃	semidirect
54. C₂×C₃×#124	C₂×C₃	semidirect
63. C₂×#946	C₂×C₃	semidirect
64. C₂×Q₈×Dic₃	C₂×C₃	semidirect
66. C₂×D₄×Dic₃	C₂×C₃	semidirect
67. #5680	C₂×C₃	direct (N × H)
68. C₂×#883	C₂×C₃	semidirect
69. C₂×#67⋊C₄	C₂×C₃	semidirect
70. C₂×#879	C₂×C₃	semidirect
71. C₂×#877	C₂×C₃	semidirect
72. C₂×C₄²×D₃	C₂×C₃	semidirect
73. C₂×#870	C₂×C₃	semidirect
135. C₃×#124	C₂×D₃	semidirect
136. C₃×#124	C₂²×C₃	semidirect
169. #946	C₂²×C₃	semidirect
170. Q₈×Dic₃	C₂²×C₃	semidirect
172. D₄×Dic₃	C₂²×C₃	semidirect
184. #883	C₂²×C₃	semidirect
185. #67⋊C₄	C₂²×C₃	semidirect
186. #879	C₂²×C₃	semidirect
187. #877	C₂²×C₃	semidirect
188. C₄²×D₃	C₂²×C₃	semidirect
189. #870	C₂²×C₃	semidirect
227. C₂×#124	C₃×D₃	semidirect
360. #124	C₂×C₃×D₃	semidirect
469. C₂×C₃²	#529	semidirect
569. C₃²	C₂×#529	semidirect
612. C₂×C₃	#5680	direct (N × H)
613. C₂×C₃	C₃×#529	semidirect
643. C₃	C₂×#5680	direct (N × H)
644. C₃	C₂×C₃×#529	semidirect
647. C₂	C₃×#5680	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×C₃²×#124	2
C₂×C₃×#946	2
C₂×C₃×Q₈×Dic₃	2
C₂×C₃×#938	2
C₂×C₃×D₄×Dic₃	2
C₃×#5680	2
C₂×C₃×#883	2
C₂×C₃×#67⋊C₄	2
C₂×C₃×#879	2
C₂×C₃×#877	2
C₂×C₃×C₄²×D₃	2
C₂×C₃×#870	2
C₂×C₃×#529	3
C₂×#5680	3

Subgroups — C2×C3×#5680 #11900578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5680 #11900578