Subgroups — C₃×#86219 #11900875

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5828	C₂	1	2	yes	maximal, complemented
3	C₃×Dic₃×#41	C₂	1	2	yes	maximal, complemented
4	C₃×#5728	C₂	1	2	yes	maximal, complemented
5	C₃×#5716	C₂	1	2	yes	maximal, complemented
6	C₃×#5680	C₂	1	4	yes	maximal, complemented
7	C₃×#5606	C₂	1	4	yes	maximal, complemented
8	C₃×#5600	C₂	1	4	yes	maximal, complemented
9	C₃×#5557	C₂	1	4	yes	maximal, complemented
10	C₃×C₄×#237	C₂	1	4	yes	maximal, complemented
11	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3444	—	3	1	no	maximal
14	#86219	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂×C₃²×#41	C₂²	1	2	yes	—
16	C₂×C₃×#237	C₂²	1	4	yes	—
17	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
19	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃²×#127	C₂²	1	1	yes	characteristic, complemented
21	C₃²×#124	C₂²	1	2	yes	complemented
22	C₃²×#121	C₂²	1	4	yes	—
23	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
24	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
25	C₃×#946	C₂²	1	4	yes	—
26	C₃×Q₈×Dic₃	C₂²	1	4	yes	complemented
27	C₃×#938	C₂²	1	4	yes	—
28	C₃×#938	C₂²	1	4	yes	—
29	C₃×#937	C₂²	1	4	yes	—
30	C₃×#936	C₂²	1	4	yes	complemented
31	C₃×#935	C₂²	1	4	yes	—
32	C₃×D₄×Dic₃	C₂²	1	8	yes	—
33	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
34	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
35	C₃×C₄×#67	C₂²	1	8	yes	—
36	C₃×#926	C₂²	1	2	yes	—
37	C₃×#926	C₂²	1	4	yes	complemented
38	C₃×#924	C₂²	1	4	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	4	yes	complemented
42	C₃×#897	C₂²	1	4	yes	—
43	C₃×#892	C₂²	1	4	yes	—
44	C₃×#890	C₂²	1	4	yes	complemented
45	C₃×#887	C₂²	1	4	yes	complemented
46	C₃×#883	C₂²	1	8	yes	—
47	C₃×#67⋊C₄	C₂²	1	8	yes	—
48	C₃×#879	C₂²	1	8	yes	complemented
49	C₃×#877	C₂²	1	8	yes	complemented
50	C₃×C₄²×D₃	C₂²	1	2	yes	—
51	C₃×C₄²×D₃	C₂²	1	2	yes	—
52	C₃×C₄²×D₃	C₂²	1	2	yes	—
53	C₃×C₄²×D₃	C₂²	1	2	yes	—
54	C₃×#870	C₂²	1	2	yes	complemented
55	C₃×#869	C₂²	1	2	yes	complemented
56	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
57	C₃×#533	—	3	2	no	—
58	C₃×#533	—	3	1	no	—
59	C₃×#532	—	2	1	no	—
60	C₃×#532	—	3	2	no	—
61	C₃×#532	D₃	1	1	yes	characteristic, complemented
62	C₃×#532	C₂×C₃	1	1	yes	characteristic, complemented
63	C₃×#529	—	3	4	no	—
64	C₃×#529	—	3	4	no	—
65	C₃×#529	—	3	4	no	—
66	C₃×#525	—	3	2	no	—
67	C₃×#525	—	3	4	no	—
68	C₃×C₄×#41	—	3	2	no	—
69	C₃×C₄×#41	—	3	4	no	—
70	C₂²×C₃×C₄²	—	3	1	no	—
71	#5828	C₂×C₃	1	2	yes	complemented
72	Dic₃×#41	C₂×C₃	1	2	yes	complemented
73	#5728	C₂×C₃	1	2	yes	complemented
74	#5716	C₂×C₃	1	2	yes	complemented
75	#5680	C₂×C₃	1	4	yes	complemented
76	#5606	C₂×C₃	1	4	yes	complemented
77	#5600	C₂×C₃	1	4	yes	complemented
78	#5557	C₂×C₃	1	4	yes	complemented
79	C₄×#237	C₂×C₃	1	4	yes	complemented
80	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic, complemented
81	#5470	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
83	C₃²×#41	—	2	8	no	—
84	C₂×C₃²×Q₈	C₂³	1	2	yes	—
85	C₂×C₃²×D₄	C₂³	1	4	yes	—
86	C₂×C₃²×D₄	C₂³	1	2	yes	—
87	C₂×C₃²×D₄	C₂³	1	4	yes	—
88	C₂²×C₃²×C₄	C₂³	1	2	yes	—
89	C₂²×C₃²×C₄	C₂³	1	4	yes	—
90	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
91	C₂×C₃×#67	C₂³	1	8	yes	—
92	C₂²×C₃×Dic₃	C₂³	1	8	yes	—
93	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
94	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
95	C₃×#237	—	2	16	no	—
96	C₂×C₃×C₄×D₃	—	2	4	no	—
97	C₂×C₃×C₄×D₃	—	2	8	no	—
98	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
99	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
100	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
102	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
103	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
104	C₂×C₃×Dic₆	C₂³	1	4	yes	—
105	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₃²×C₄²	C₂³	1	2	yes	—
108	C₃²×C₄²	C₂³	1	1	yes	characteristic
109	C₃²×C₄²	C₂³	1	1	yes	characteristic
110	C₃×#217	C₂³	1	8	yes	—
111	C₃×#217	C₂³	1	8	yes	—
112	C₃×#217	C₂³	1	4	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
114	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
115	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
116	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
117	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
118	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
119	C₃×C₄×Dic₃	C₂³	1	2	yes	—
120	C₃×C₄×Dic₃	C₂³	1	8	yes	—
121	C₃×C₄×Dic₃	C₂³	1	2	yes	—
122	C₃×C₄×Dic₃	C₂³	1	2	yes	—
123	C₃×C₄×Dic₃	C₂³	1	2	yes	—
124	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
125	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
126	C₃×C₄×Dic₃	C₂³	1	2	yes	—
127	C₃×C₄×Dic₃	C₂³	1	4	yes	—
128	#3444	—	3	1	no	Sylow
129	C₂×C₃×#41	—	2	2	no	—
130	C₂×C₃×#41	—	3	4	no	—
131	C₂×C₃×#41	C₂×D₃	1	2	yes	—
132	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
133	C₂³×C₃×C₄	—	3	2	no	—
134	C₂³×C₃×C₄	—	3	1	no	—
135	C₂×#237	C₂²×C₃	1	4	yes	—
136	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
137	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
138	C₃×C₄⋊Q₈	—	2	1	no	—
139	C₃×C₄⋊Q₈	—	3	2	no	—
140	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
141	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₃×#127	—	2	1	no	—
143	C₃×#127	C₂×D₃	1	1	yes	characteristic, complemented
144	C₃×#127	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₃×#126	—	3	8	no	—
146	C₃×#125	—	3	4	no	—
147	C₃×#125	—	3	2	no	—
148	C₃×#124	—	2	2	no	—
149	C₃×#124	—	3	4	no	—
150	C₃×#124	C₂×D₃	1	2	yes	complemented
151	C₃×#124	C₂²×C₃	1	2	yes	complemented
152	C₃×#123	—	3	4	no	—
153	C₃×#123	—	3	8	no	—
154	C₃×C₂²⋊Q₈	—	3	4	no	—
155	C₃×C₂²⋊Q₈	—	3	4	no	—
156	C₃×C₂²⋊Q₈	—	3	4	no	—
157	C₃×#121	—	2	4	no	—
158	C₃×#121	—	3	4	no	—
159	C₃×#121	—	3	4	no	—
160	C₃×#121	C₂×D₃	1	4	yes	—
161	C₃×#121	C₂²×C₃	1	4	yes	—
162	C₃×#120	—	3	4	no	—
163	C₃×C₄×Q₈	—	3	4	no	—
164	C₃×C₄×Q₈	—	3	4	no	—
165	C₃×C₄×Q₈	—	3	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	3	8	no	—
168	C₃×C₄×D₄	—	3	4	no	—
169	C₃×C₄×D₄	—	3	4	no	—
170	C₃×C₄×D₄	—	3	8	no	—
171	C₃×C₄×D₄	—	3	8	no	—
172	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
173	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
174	C₃×#117	—	3	2	no	—
175	C₃×#117	—	3	4	no	—
176	C₃×#117	—	3	4	no	—
177	C₃×#117	—	3	8	no	—
178	C₂×C₃×C₄²	—	2	1	no	—
179	C₂×C₃×C₄²	—	3	1	no	—
180	C₂×C₃×C₄²	—	3	2	no	—
181	C₂×C₃×C₄²	—	3	4	no	—
182	C₂×C₃×C₄²	—	3	2	no	—
183	C₂×C₃×C₄²	—	3	2	no	—
184	C₂×C₃×C₄²	—	3	2	no	—
185	C₂×C₃×C₄²	—	3	2	no	—
186	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
187	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
188	#946	C₂²×C₃	1	4	yes	—
189	Q₈×Dic₃	C₂²×C₃	1	4	yes	complemented
190	#938	C₂²×C₃	1	4	yes	—
191	#938	C₂²×C₃	1	4	yes	—
192	#937	C₂²×C₃	1	4	yes	—
193	#936	C₂²×C₃	1	4	yes	complemented
194	#935	C₂²×C₃	1	4	yes	—
195	D₄×Dic₃	C₂²×C₃	1	8	yes	—
196	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
197	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
198	C₄×#67	C₂²×C₃	1	8	yes	—
199	#926	C₂²×C₃	1	2	yes	—
200	#926	C₂²×C₃	1	4	yes	complemented
201	#924	C₂²×C₃	1	4	yes	—
202	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
203	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
204	C₂×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
205	#897	C₂²×C₃	1	4	yes	—
206	#892	C₂²×C₃	1	4	yes	—
207	#890	C₂²×C₃	1	4	yes	complemented
208	#887	C₂²×C₃	1	4	yes	complemented
209	#883	C₂²×C₃	1	8	yes	—
210	#67⋊C₄	C₂²×C₃	1	8	yes	—
211	#879	C₂²×C₃	1	8	yes	complemented
212	#877	C₂²×C₃	1	8	yes	complemented
213	C₄²×D₃	C₂²×C₃	1	2	yes	—
214	C₄²×D₃	C₂²×C₃	1	2	yes	—
215	C₄²×D₃	C₂²×C₃	1	2	yes	—
216	C₄²×D₃	C₂²×C₃	1	2	yes	—
217	#870	C₂²×C₃	1	2	yes	complemented
218	#869	C₂²×C₃	1	2	yes	complemented
219	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
220	C₂³×C₃²	C₂⁴	1	4	yes	—
221	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
222	C₂²×C₃×D₃	—	2	2	no	—
223	C₂²×C₃×D₃	—	2	4	no	—
224	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
225	C₃²×Q₈	—	2	4	no	—
226	C₃²×D₄	—	2	8	no	—
227	C₃²×D₄	—	2	8	no	—
228	C₃²×D₄	—	2	4	no	—
229	C₂×C₃²×C₄	—	2	4	no	—
230	C₂×C₃²×C₄	—	2	8	no	—
231	C₂×C₃²×C₄	#41	1	4	yes	complemented
232	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
233	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
234	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
236	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
237	C₃×#67	—	2	16	no	—
238	C₂×C₃×Dic₃	—	2	2	no	—
239	C₂×C₃×Dic₃	—	2	4	no	—
240	C₂×C₃×Dic₃	—	2	16	no	—
241	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
242	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
243	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
244	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
245	C₃×C₄×D₃	—	2	4	no	—
246	C₃×C₄×D₃	—	2	4	no	—
247	C₃×C₄×D₃	—	2	4	no	—
248	C₃×C₄×D₃	—	2	4	no	—
249	C₃×C₄×D₃	—	2	4	no	—
250	C₃×C₄×D₃	#41	1	8	yes	complemented
251	C₃×Dic₆	—	2	8	no	—
252	#533	—	3	2	no	—
253	#533	—	3	1	no	—
254	#532	—	3	2	no	—
255	#532	C₃×D₃	1	1	yes	characteristic, complemented
256	#529	—	3	4	no	—
257	#529	—	3	4	no	—
258	#529	—	3	4	no	—
259	#525	—	3	2	no	—
260	#525	—	3	4	no	—
261	C₄×#41	—	3	2	no	—
262	C₄×#41	—	3	4	no	—
263	C₂²×C₄²	—	3	1	no	—
264	C₂⁴×C₃	—	3	1	no	—
265	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
266	C₃×#41	—	2	8	no	—
267	C₃×#41	—	2	8	no	—
268	C₃×#41	—	4	8	no	—
269	C₃×#41	—	6	16	no	—
270	C₂×C₃×Q₈	—	2	2	no	—
271	C₂×C₃×Q₈	—	3	4	no	—
272	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
273	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	2	no	—
277	C₂×C₃×D₄	—	3	8	no	—
278	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
279	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
280	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
281	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
282	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
283	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
284	C₂²×C₃×C₄	—	2	1	no	—
285	C₂²×C₃×C₄	—	2	2	no	—
286	C₂²×C₃×C₄	—	2	4	no	—
287	C₂²×C₃×C₄	—	3	2	no	—
288	C₂²×C₃×C₄	—	3	2	no	—
289	C₂²×C₃×C₄	—	3	1	no	—
290	C₂²×C₃×C₄	—	3	8	no	—
291	C₂²×C₃×C₄	—	3	2	no	—
292	C₂²×C₃×C₄	—	3	2	no	—
293	C₂²×C₃×C₄	—	3	2	no	—
294	C₂²×C₃×C₄	—	3	2	no	—
295	C₂²×C₃×C₄	—	3	2	no	—
296	C₂²×C₃×C₄	—	6	8	no	—
297	C₂²×C₃×C₄	—	6	4	no	—
298	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
299	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
300	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
302	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
303	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
304	C₂×#67	C₂³×C₃	1	8	yes	—
305	C₂²×Dic₃	C₂³×C₃	1	8	yes	—
306	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
307	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
308	#237	—	2	16	no	—
309	C₂×C₄×D₃	—	2	4	no	—
310	C₂×C₄×D₃	—	2	8	no	—
311	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
312	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
313	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
314	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
315	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
316	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
317	C₂×Dic₆	C₂³×C₃	1	4	yes	—
318	C₃×C₄⋊C₄	—	2	4	no	—
319	C₃×C₄⋊C₄	—	3	8	no	—
320	C₃×C₄⋊C₄	—	3	8	no	—
321	C₃×C₄⋊C₄	—	3	4	no	—
322	C₃×C₄⋊C₄	—	3	4	no	—
323	C₃×C₄⋊C₄	—	3	8	no	—
324	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
325	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
326	C₃×C₂²⋊C₄	—	2	8	no	—
327	C₃×C₂²⋊C₄	—	3	4	no	—
328	C₃×C₂²⋊C₄	—	3	8	no	—
329	C₃×C₂²⋊C₄	—	3	8	no	—
330	C₃×C₂²⋊C₄	—	3	8	no	—
331	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
333	C₃×C₄²	—	2	2	no	—
334	C₃×C₄²	—	2	1	no	—
335	C₃×C₄²	—	2	1	no	—
336	C₃×C₄²	—	3	2	no	—
337	C₃×C₄²	—	3	2	no	—
338	C₃×C₄²	—	3	2	no	—
339	C₃×C₄²	—	3	2	no	—
340	C₃×C₄²	—	3	2	no	—
341	C₃×C₄²	—	3	8	no	—
342	C₃×C₄²	—	3	1	no	—
343	C₃×C₄²	—	3	1	no	—
344	C₃×C₄²	—	3	4	no	—
345	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
346	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
347	C₃×C₄²	C₂²×D₃	1	2	yes	—
348	C₃×C₄²	C₂³×C₃	1	2	yes	—
349	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
350	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
351	#217	C₂³×C₃	1	8	yes	—
352	#217	C₂³×C₃	1	8	yes	—
353	#217	C₂³×C₃	1	4	yes	—
354	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
355	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
356	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
357	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
358	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
359	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
360	C₄×Dic₃	C₂³×C₃	1	4	yes	—
361	C₄×Dic₃	C₂³×C₃	1	2	yes	—
362	C₄×Dic₃	C₂³×C₃	1	2	yes	—
363	C₄×Dic₃	C₂³×C₃	1	2	yes	—
364	C₄×Dic₃	C₂³×C₃	1	2	yes	—
365	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
366	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
367	C₄×Dic₃	C₂³×C₃	1	2	yes	—
368	C₄×Dic₃	C₂³×C₃	1	8	yes	—
369	C₂²×C₃²	—	2	2	no	—
370	C₂²×C₃²	—	2	8	no	—
371	C₂²×C₃²	—	2	4	no	—
372	C₂²×C₃²	C₂×#41	1	2	yes	—
373	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
374	C₂×C₃×D₃	—	2	8	no	—
375	C₂×C₃×D₃	—	2	2	no	—
376	C₂×C₃×D₃	—	2	2	no	—
377	C₂×C₃×D₃	C₂×#41	1	4	yes	—
378	C₃²×C₄	—	2	2	no	—
379	C₃²×C₄	—	2	4	no	—
380	C₃²×C₄	C₂×#41	1	2	yes	—
381	C₃²×C₄	C₂×#41	1	2	yes	—
382	C₃²×C₄	C₂×#41	1	4	yes	—
383	C₃×Dic₃	—	2	8	no	—
384	C₃×Dic₃	—	2	2	no	—
385	C₃×Dic₃	—	2	2	no	—
386	C₃×Dic₃	C₂×#41	1	4	yes	—
387	C₂×#41	—	3	4	no	—
388	C₂×#41	C₂×C₃×D₃	1	2	yes	—
389	C₂³×C₄	—	3	2	no	—
390	C₂³×C₄	—	3	1	no	—
391	C₄⋊Q₈	—	3	2	no	—
392	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
393	#127	C₂×C₃×D₃	1	1	yes	characteristic, complemented
394	#126	—	3	8	no	—
395	#125	—	3	4	no	—
396	#125	—	3	2	no	—
397	#124	—	3	4	no	—
398	#124	C₂×C₃×D₃	1	2	yes	complemented
399	#123	—	3	4	no	—
400	#123	—	3	8	no	—
401	C₂²⋊Q₈	—	3	4	no	—
402	C₂²⋊Q₈	—	3	4	no	—
403	C₂²⋊Q₈	—	3	4	no	—
404	#121	—	3	4	no	—
405	#121	—	3	4	no	—
406	#121	C₂×C₃×D₃	1	4	yes	—
407	#120	—	3	4	no	—
408	C₄×Q₈	—	3	4	no	—
409	C₄×Q₈	—	3	4	no	—
410	C₄×Q₈	—	3	4	no	—
411	C₄×D₄	—	3	8	no	—
412	C₄×D₄	—	3	4	no	—
413	C₄×D₄	—	3	4	no	—
414	C₄×D₄	—	3	8	no	—
415	C₄×D₄	—	3	8	no	—
416	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
417	#117	—	3	2	no	—
418	#117	—	3	4	no	—
419	#117	—	3	4	no	—
420	#117	—	3	8	no	—
421	C₂×C₄²	—	3	4	no	—
422	C₂×C₄²	—	3	1	no	—
423	C₂×C₄²	—	3	2	no	—
424	C₂×C₄²	—	3	2	no	—
425	C₂×C₄²	—	3	2	no	—
426	C₂×C₄²	—	3	2	no	—
427	C₂×C₄²	—	3	2	no	—
428	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
429	C₂³×C₃	—	2	1	no	—
430	C₂³×C₃	—	2	4	no	—
431	C₂³×C₃	—	3	2	no	—
432	C₂³×C₃	—	6	4	no	—
433	C₂³×C₃	—	6	2	no	—
434	C₂³×C₃	C₂³×D₃	1	4	yes	—
435	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
436	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
437	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
438	C₂²×D₃	—	2	2	no	—
439	C₂²×D₃	—	2	4	no	—
440	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
441	C₃×Q₈	—	2	4	no	—
442	C₃×Q₈	—	2	4	no	—
443	C₃×Q₈	—	4	4	no	—
444	C₃×Q₈	—	6	8	no	—
445	C₃×D₄	—	2	8	no	—
446	C₃×D₄	—	2	8	no	—
447	C₃×D₄	—	2	4	no	—
448	C₃×D₄	—	2	8	no	—
449	C₃×D₄	—	2	8	no	—
450	C₃×D₄	—	2	4	no	—
451	C₃×D₄	—	4	8	no	—
452	C₃×D₄	—	4	4	no	—
453	C₃×D₄	—	4	8	no	—
454	C₃×D₄	—	6	16	no	—
455	C₂×C₃×C₄	—	2	8	no	—
456	C₂×C₃×C₄	—	2	4	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	—	2	8	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	4	no	—
464	C₂×C₃×C₄	—	2	4	no	—
465	C₂×C₃×C₄	—	3	2	no	—
466	C₂×C₃×C₄	—	3	8	no	—
467	C₂×C₃×C₄	—	3	2	no	—
468	C₂×C₃×C₄	—	3	2	no	—
469	C₂×C₃×C₄	—	3	8	no	—
470	C₂×C₃×C₄	—	4	4	no	—
471	C₂×C₃×C₄	—	4	8	no	—
472	C₂×C₃×C₄	—	6	4	no	—
473	C₂×C₃×C₄	—	6	4	no	—
474	C₂×C₃×C₄	—	6	4	no	—
475	C₂×C₃×C₄	—	6	16	no	—
476	C₂×C₃×C₄	—	6	2	no	—
477	C₂×C₃×C₄	—	6	4	no	—
478	C₂×C₃×C₄	—	6	4	no	—
479	C₂×C₃×C₄	—	6	4	no	—
480	C₂×C₃×C₄	#237	1	4	yes	complemented
481	C₂×C₃×C₄	C₃×#41	1	4	yes	complemented
482	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
483	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
484	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
486	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
488	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
489	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
492	#67	—	2	16	no	—
493	C₂×Dic₃	—	2	2	no	—
494	C₂×Dic₃	—	2	4	no	—
495	C₂×Dic₃	—	2	16	no	—
496	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
497	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
498	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
499	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
500	C₄×D₃	—	2	4	no	—
501	C₄×D₃	—	2	4	no	—
502	C₄×D₃	—	2	4	no	—
503	C₄×D₃	—	2	4	no	—
504	C₄×D₃	—	2	4	no	—
505	C₄×D₃	C₃×#41	1	8	yes	complemented
506	Dic₆	—	2	8	no	—
507	C₂×C₃²	—	2	2	no	—
508	C₂×C₃²	—	4	4	no	—
509	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
510	C₂×C₃²	C₂²×#41	1	2	yes	—
511	C₃×D₃	—	2	4	no	—
512	C₂⁴	—	3	1	no	—
513	#41	—	2	8	no	—
514	#41	—	6	16	no	—
515	C₂×Q₈	—	3	4	no	—
516	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
517	C₂×D₄	—	3	8	no	—
518	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
519	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
520	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
521	C₂²×C₄	—	3	2	no	—
522	C₂²×C₄	—	3	2	no	—
523	C₂²×C₄	—	3	1	no	—
524	C₂²×C₄	—	3	8	no	—
525	C₂²×C₄	—	3	2	no	—
526	C₂²×C₄	—	3	2	no	—
527	C₂²×C₄	—	3	2	no	—
528	C₂²×C₄	—	3	2	no	—
529	C₂²×C₄	—	3	2	no	—
530	C₂²×C₄	—	6	8	no	—
531	C₂²×C₄	—	6	4	no	—
532	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
533	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
534	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
535	C₄⋊C₄	—	3	4	no	—
536	C₄⋊C₄	—	3	4	no	—
537	C₄⋊C₄	—	3	8	no	—
538	C₄⋊C₄	—	3	8	no	—
539	C₄⋊C₄	—	3	8	no	—
540	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
541	C₂²⋊C₄	—	3	4	no	—
542	C₂²⋊C₄	—	3	8	no	—
543	C₂²⋊C₄	—	3	8	no	—
544	C₂²⋊C₄	—	3	8	no	—
545	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
546	C₄²	—	3	1	no	—
547	C₄²	—	3	2	no	—
548	C₄²	—	3	1	no	—
549	C₄²	—	3	2	no	—
550	C₄²	—	3	2	no	—
551	C₄²	—	3	2	no	—
552	C₄²	—	3	2	no	—
553	C₄²	—	3	8	no	—
554	C₄²	—	3	4	no	—
555	C₄²	C₂²×C₃×D₃	1	2	yes	—
556	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
557	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
558	C₂²×C₃	—	2	2	no	—
559	C₂²×C₃	—	2	2	no	—
560	C₂²×C₃	—	2	4	no	—
561	C₂²×C₃	—	2	8	no	—
562	C₂²×C₃	—	2	8	no	—
563	C₂²×C₃	—	2	4	no	—
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	1	no	—
566	C₂²×C₃	—	3	4	no	—
567	C₂²×C₃	—	4	2	no	—
568	C₂²×C₃	—	4	4	no	—
569	C₂²×C₃	—	4	8	no	—
570	C₂²×C₃	—	6	8	no	—
571	C₂²×C₃	—	6	2	no	—
572	C₂²×C₃	—	6	2	no	—
573	C₂²×C₃	C₂×#237	1	2	yes	—
574	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
575	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
576	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
577	C₂×D₃	—	2	8	no	—
578	C₂×D₃	—	2	2	no	—
579	C₂×D₃	—	2	2	no	—
580	C₂×D₃	C₂×C₃×#41	1	4	yes	—
581	C₃×C₄	—	2	4	no	—
582	C₃×C₄	—	2	2	no	—
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	2	4	no	—
588	C₃×C₄	—	3	4	no	—
589	C₃×C₄	—	4	4	no	—
590	C₃×C₄	—	4	2	no	—
591	C₃×C₄	—	6	2	no	—
592	C₃×C₄	—	6	2	no	—
593	C₃×C₄	—	6	8	no	—
594	C₃×C₄	C₂×#237	1	2	yes	—
595	C₃×C₄	C₂×#237	1	2	yes	—
596	C₃×C₄	D₃×#41	1	4	yes	—
597	C₃×C₄	C₂×C₃×#41	1	2	yes	—
598	C₃×C₄	C₂×C₃×#41	1	2	yes	—
599	C₃×C₄	C₂×C₃×#41	1	4	yes	—
600	Dic₃	—	2	8	no	—
601	Dic₃	—	2	2	no	—
602	Dic₃	—	2	2	no	—
603	Dic₃	C₂×C₃×#41	1	4	yes	—
604	C₃²	#3444	1	1	yes	characteristic, complemented, Sylow
605	C₂³	—	3	2	no	—
606	C₂³	—	6	4	no	—
607	C₂³	—	6	2	no	—
608	C₂³	C₂³×C₃×D₃	1	4	yes	—
609	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
610	Q₈	—	2	4	no	—
611	Q₈	—	6	8	no	—
612	D₄	—	2	8	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	8	no	—
615	D₄	—	6	16	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	3	2	no	—
619	C₂×C₄	—	3	8	no	—
620	C₂×C₄	—	3	2	no	—
621	C₂×C₄	—	3	2	no	—
622	C₂×C₄	—	3	8	no	—
623	C₂×C₄	—	6	4	no	—
624	C₂×C₄	—	6	4	no	—
625	C₂×C₄	—	6	4	no	—
626	C₂×C₄	—	6	16	no	—
627	C₂×C₄	—	6	2	no	—
628	C₂×C₄	—	6	4	no	—
629	C₂×C₄	—	6	4	no	—
630	C₂×C₄	—	6	4	no	—
631	C₂×C₄	C₃×#237	1	4	yes	complemented
632	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
633	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
634	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
635	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
637	C₂×C₃	—	2	2	no	—
638	C₂×C₃	—	2	2	no	—
639	C₂×C₃	—	2	1	no	—
640	C₂×C₃	—	2	2	no	—
641	C₂×C₃	—	4	2	no	—
642	C₂×C₃	—	4	4	no	—
643	C₂×C₃	—	4	4	no	—
644	C₂×C₃	—	6	4	no	—
645	C₂×C₃	—	8	4	no	—
646	C₂×C₃	C₂²×#237	1	1	yes	characteristic
647	C₂×C₃	C₂×D₃×#41	1	2	yes	—
648	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
649	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
650	D₃	—	2	4	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	3	4	no	—
655	C₂²	—	6	8	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	6	2	no	—
658	C₂²	C₂×C₃×#237	1	2	yes	—
659	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
660	C₄	—	2	4	no	—
661	C₄	—	2	2	no	—
662	C₄	—	3	4	no	—
663	C₄	—	6	2	no	—
664	C₄	—	6	2	no	—
665	C₄	—	6	8	no	—
666	C₄	C₂×C₃×#237	1	2	yes	—
667	C₄	C₂×C₃×#237	1	2	yes	—
668	C₄	C₃×D₃×#41	1	4	yes	—
669	C₃	—	2	1	no	—
670	C₃	#86219	1	1	yes	characteristic, direct product factor
671	C₃	C₃×#3444	1	1	yes	characteristic, complemented
672	C₂	—	2	2	no	—
673	C₂	—	4	4	no	—
674	C₂	—	6	4	no	—
675	C₂	C₂²×C₃×#237	1	1	yes	characteristic
676	C₂	C₂×C₃×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#532	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#532	D₃
hypocenter	C₃	C₃×#3444
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃²×#532	C₂	semidirect
2. C₃×#5828	C₂	semidirect
3. C₃×Dic₃×#41	C₂	semidirect
4. C₃×#5728	C₂	semidirect
5. C₃×#5716	C₂	semidirect
6. C₃×#5680	C₂	semidirect
7. C₃×#5606	C₂	semidirect
8. C₃×#5600	C₂	semidirect
9. C₃×#5557	C₂	semidirect
10. C₃×C₄×#237	C₂	semidirect
11. C₂×C₃×C₄²×D₃	C₂	semidirect
12. C₃×#5470	C₂	semidirect
14. #86219	C₃	direct (N × H)
19. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×#127	C₂²	semidirect
21. C₃²×#124	C₂²	semidirect
23. C₃²×C₄×D₄	C₂²	semidirect
26. C₃×Q₈×Dic₃	C₂²	semidirect
30. C₃×#936	C₂²	semidirect
33. C₃×D₄×Dic₃	C₂²	semidirect
34. C₃×D₄×Dic₃	C₂²	semidirect
37. C₃×#926	C₂²	semidirect
41. C₂×C₃×C₄×Dic₃	C₂²	semidirect
44. C₃×#890	C₂²	semidirect
45. C₃×#887	C₂²	semidirect
48. C₃×#879	C₂²	semidirect
49. C₃×#877	C₂²	semidirect
54. C₃×#870	C₂²	semidirect
55. C₃×#869	C₂²	semidirect
56. C₃×C₄×Dic₆	C₂²	semidirect
61. C₃×#532	D₃	semidirect
62. C₃×#532	C₂×C₃	semidirect
71. #5828	C₂×C₃	semidirect
72. Dic₃×#41	C₂×C₃	semidirect
73. #5728	C₂×C₃	semidirect
74. #5716	C₂×C₃	semidirect
75. #5680	C₂×C₃	semidirect
76. #5606	C₂×C₃	semidirect
77. #5600	C₂×C₃	semidirect
78. #5557	C₂×C₃	semidirect
79. C₄×#237	C₂×C₃	semidirect
80. C₂×C₄²×D₃	C₂×C₃	semidirect
81. #5470	C₂×C₃	semidirect
140. C₃×C₄⋊Q₈	C₂×D₃	semidirect
141. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
143. C₃×#127	C₂×D₃	semidirect
144. C₃×#127	C₂²×C₃	semidirect
150. C₃×#124	C₂×D₃	semidirect
151. C₃×#124	C₂²×C₃	semidirect
172. C₃×C₄×D₄	C₂×D₃	semidirect
173. C₃×C₄×D₄	C₂²×C₃	semidirect
189. Q₈×Dic₃	C₂²×C₃	semidirect
193. #936	C₂²×C₃	semidirect
196. D₄×Dic₃	C₂²×C₃	semidirect
197. D₄×Dic₃	C₂²×C₃	semidirect
200. #926	C₂²×C₃	semidirect
204. C₂×C₄×Dic₃	C₂²×C₃	semidirect
207. #890	C₂²×C₃	semidirect
208. #887	C₂²×C₃	semidirect
211. #879	C₂²×C₃	semidirect
212. #877	C₂²×C₃	semidirect
217. #870	C₂²×C₃	semidirect
218. #869	C₂²×C₃	semidirect
219. C₄×Dic₆	C₂²×C₃	semidirect
231. C₂×C₃²×C₄	#41	semidirect
250. C₃×C₄×D₃	#41	semidirect
255. #532	C₃×D₃	semidirect
392. C₄⋊Q₈	C₂×C₃×D₃	semidirect
393. #127	C₂×C₃×D₃	semidirect
398. #124	C₂×C₃×D₃	semidirect
416. C₄×D₄	C₂×C₃×D₃	semidirect
480. C₂×C₃×C₄	#237	semidirect
481. C₂×C₃×C₄	C₃×#41	semidirect
505. C₄×D₃	C₃×#41	semidirect
604. C₃²	#3444	semidirect
631. C₂×C₄	C₃×#237	semidirect
670. C₃	#86219	direct (N × H)
671. C₃	C₃×#3444	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#532	2
C₃×#5828	2
C₃×Dic₃×#41	2
C₃×#5728	2
C₃×#5716	2
C₃×#5680	2
C₃×#5606	2
C₃×#5600	2
C₃×#5557	2
C₃×C₄×#237	2
C₂×C₃×C₄²×D₃	2
C₃×#5470	2
C₃×#3444	3
#86219	3

Subgroups — C3×#86219 #11900875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86219 #11900875