Subgroups — C₃×#85900 #11904615

Order 1152.

3463 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5577	C₂	1	2	yes	maximal, complemented
5	C₃×#5576	C₂	1	2	yes	maximal, complemented
6	C₃×#5554	C₂	1	6	yes	maximal, complemented
7	C₃×D₄×D₁₂	C₂	1	6	yes	maximal, complemented
8	C₃×#5525	C₂	1	3	yes	maximal, complemented
9	C₃×#5524	C₂	1	3	yes	maximal, complemented
10	C₃×#5510	C₂	1	3	yes	maximal, complemented
11	C₂×C₃×#895	C₂	1	3	yes	maximal, complemented
12	C₃×#3488	—	3	1	no	maximal
13	#85900	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₃×#1009	—	2	8	no	—
16	C₃×D₃×#41	—	2	8	no	—
17	C₂×C₃×#239	C₂²	1	2	yes	complemented
18	C₂×C₃×#239	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#237	C₂²	1	3	yes	complemented
21	C₂×C₃×D₃×D₄	C₂²	1	3	yes	complemented
22	C₂×C₃×D₃×D₄	C₂²	1	6	yes	complemented
23	C₂×C₃×#235	C₂²	1	3	yes	complemented
24	C₂×C₃×#235	C₂²	1	3	yes	complemented
25	C₂²×C₃×D₁₂	C₂²	1	3	yes	complemented
26	C₂²×C₃×D₁₂	C₂²	1	6	yes	complemented
27	C₂²×C₃×C₄×D₃	C₂²	1	3	yes	complemented
28	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
29	C₃²×C₄×D₄	C₂²	1	6	yes	complemented
30	C₃²×#117	C₂²	1	3	yes	complemented
31	C₂×C₃²×C₄⋊C₄	C₂²	1	3	yes	complemented
32	C₃×#930	C₂²	1	12	yes	complemented
33	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
34	C₃×#897	C₂²	1	3	yes	complemented
35	C₃×#897	C₂²	1	6	yes	complemented
36	C₃×#897	C₂²	1	1	yes	characteristic, complemented
37	C₃×#895	C₂²	1	3	yes	complemented
38	C₃×#895	C₂²	1	6	yes	complemented
39	C₃×#895	C₂²	1	6	yes	complemented
40	C₃×#895	C₂²	1	6	yes	complemented
41	C₃×#895	C₂²	1	6	yes	complemented
42	C₃×#895	C₂²	1	3	yes	complemented
43	C₃×#886	C₂²	1	6	yes	complemented
44	C₃×#882	C₂²	1	6	yes	complemented
45	C₃×#882	C₂²	1	12	yes	complemented
46	C₃×#875	C₂²	1	6	yes	complemented
47	C₃×#874	C₂²	1	6	yes	complemented
48	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
49	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
50	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
51	C₂²×C₃×#41	—	3	1	no	—
52	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×D₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×#550	—	3	2	no	—
55	C₃×#548	—	3	2	no	—
56	C₃×#546	—	3	6	no	—
57	C₃×D₄²	—	3	6	no	—
58	C₃×#537	—	3	3	no	—
59	C₃×#535	—	3	3	no	—
60	C₃×#525	—	3	3	no	—
61	C₂×C₃×#121	—	3	3	no	—
62	C₃×#520	—	2	1	no	—
63	C₃×#520	D₃	1	1	yes	characteristic, complemented
64	C₃×#520	C₂×C₃	1	1	yes	characteristic, complemented
65	#5577	C₂×C₃	1	2	yes	complemented
66	#5576	C₂×C₃	1	2	yes	complemented
67	#5554	C₂×C₃	1	6	yes	complemented
68	D₄×D₁₂	C₂×C₃	1	6	yes	complemented
69	#5525	C₂×C₃	1	3	yes	complemented
70	#5524	C₂×C₃	1	3	yes	complemented
71	#5510	C₂×C₃	1	3	yes	complemented
72	C₂×#895	C₂×C₃	1	3	yes	complemented
73	C₂³×C₃×D₃	C₂³	1	3	yes	—
74	C₂³×C₃×D₃	C₂³	1	6	yes	—
75	C₃²×#41	D₄	1	8	yes	complemented
76	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃²×D₄	C₂³	1	3	yes	—
78	C₂²×C₃²×C₄	C₂³	1	6	yes	—
79	C₂²×C₃²×C₄	C₂³	1	3	yes	—
80	C₂×C₃×#67	C₂³	1	6	yes	—
81	C₂×C₃×#67	C₂³	1	6	yes	—
82	C₂²×C₃×Dic₃	C₂³	1	3	yes	—
83	C₃×#239	—	2	4	no	—
84	C₃×#239	—	2	8	no	—
85	C₃×D₃×Q₈	—	2	4	no	—
86	C₃×#237	—	2	12	no	—
87	C₃×D₃×D₄	—	2	12	no	—
88	C₃×D₃×D₄	—	2	24	no	—
89	C₃×#235	—	2	12	no	—
90	C₃×#235	—	2	12	no	—
91	C₂×C₃×D₁₂	—	2	12	no	—
92	C₂×C₃×D₁₂	—	4	12	no	—
93	C₂×C₃×D₁₂	C₂³	1	6	yes	—
94	C₂×C₃×D₁₂	C₂³	1	3	yes	—
95	C₂×C₃×D₁₂	C₂³	1	6	yes	—
96	C₂×C₃×D₁₂	C₂³	1	3	yes	—
97	C₂×C₃×D₁₂	C₂³	1	6	yes	—
98	C₂×C₃×D₁₂	C₂³	1	12	yes	—
99	C₂×C₃×C₄×D₃	—	2	12	no	—
100	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
102	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
103	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
104	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
105	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₆	C₂³	1	3	yes	—
107	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
108	C₃²×C₄⋊C₄	C₂³	1	6	yes	—
109	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
111	C₃²×C₄²	C₂³	1	6	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
114	C₃×(C₂×D₃)⋊C₄	C₂³	1	12	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
116	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
117	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
118	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
119	#3488	—	3	1	no	Sylow
120	C₃×H(5,𝔽₂)	—	6	8	no	—
121	C₂×C₃×#41	—	2	1	no	—
122	C₂×C₃×#41	—	3	1	no	—
123	C₂×C₃×#41	—	3	2	no	—
124	C₂×C₃×#41	—	3	3	no	—
125	C₂×C₃×#41	—	3	3	no	—
126	C₂×C₃×#41	—	3	3	no	—
127	C₂×C₃×#41	—	6	8	no	—
128	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×Q₈	—	3	1	no	—
131	C₂²×C₃×D₄	—	3	3	no	—
132	C₂²×C₃×D₄	—	3	6	no	—
133	C₂²×C₃×D₄	—	3	3	no	—
134	C₂²×C₃×D₄	—	3	6	no	—
135	C₂³×C₃×C₄	—	3	3	no	—
136	#1009	—	2	8	no	—
137	D₃×#41	—	2	8	no	—
138	C₂×#239	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₂×#239	C₂²×C₃	1	2	yes	complemented
140	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×#237	C₂²×C₃	1	3	yes	complemented
142	C₂×D₃×D₄	C₂²×C₃	1	3	yes	complemented
143	C₂×D₃×D₄	C₂²×C₃	1	6	yes	complemented
144	C₂×#235	C₂²×C₃	1	3	yes	complemented
145	C₂×#235	C₂²×C₃	1	3	yes	complemented
146	C₂²×D₁₂	C₂²×C₃	1	3	yes	complemented
147	C₂²×D₁₂	C₂²×C₃	1	6	yes	complemented
148	C₂²×C₄×D₃	C₂²×C₃	1	3	yes	complemented
149	C₃×#127	—	3	6	no	—
150	C₃×#124	—	3	6	no	—
151	C₃×#123	—	3	6	no	—
152	C₃×C₂²⋊Q₈	—	3	1	no	—
153	C₃×C₂²⋊Q₈	—	3	3	no	—
154	C₃×C₂²⋊Q₈	—	3	6	no	—
155	C₃×#121	—	3	12	no	—
156	C₃×#121	—	3	3	no	—
157	C₃×#121	—	3	6	no	—
158	C₃×#121	—	3	6	no	—
159	C₃×#121	—	3	6	no	—
160	C₃×#121	—	3	3	no	—
161	C₃×#121	—	3	6	no	—
162	C₃×#120	—	3	6	no	—
163	C₃×#120	—	3	12	no	—
164	C₃×C₄×Q₈	—	2	2	no	—
165	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
166	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
167	C₃×C₄×D₄	—	2	6	no	—
168	C₃×C₄×D₄	—	3	6	no	—
169	C₃×C₄×D₄	—	3	6	no	—
170	C₃×C₄×D₄	C₂×D₃	1	6	yes	complemented
171	C₃×C₄×D₄	C₂²×C₃	1	6	yes	complemented
172	C₃×#117	—	2	3	no	—
173	C₃×#117	C₂×D₃	1	3	yes	complemented
174	C₃×#117	C₂²×C₃	1	3	yes	complemented
175	C₂×C₃×C₄⋊C₄	—	2	3	no	—
176	C₂×C₃×C₄⋊C₄	C₂×D₃	1	3	yes	complemented
177	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
178	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
179	#930	C₂²×C₃	1	12	yes	complemented
180	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	complemented
181	#897	C₂²×C₃	1	3	yes	complemented
182	#897	C₂²×C₃	1	6	yes	complemented
183	#897	C₂²×C₃	1	1	yes	characteristic, complemented
184	#895	C₂²×C₃	1	3	yes	complemented
185	#895	C₂²×C₃	1	6	yes	complemented
186	#895	C₂²×C₃	1	6	yes	complemented
187	#895	C₂²×C₃	1	6	yes	complemented
188	#895	C₂²×C₃	1	6	yes	complemented
189	#895	C₂²×C₃	1	3	yes	complemented
190	#886	C₂²×C₃	1	6	yes	complemented
191	#882	C₂²×C₃	1	6	yes	complemented
192	#882	C₂²×C₃	1	12	yes	complemented
193	#875	C₂²×C₃	1	6	yes	complemented
194	#874	C₂²×C₃	1	6	yes	complemented
195	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
196	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
197	C₂³×C₃²	C₂⁴	1	3	yes	—
198	C₂²×C₃×D₃	—	2	6	no	—
199	C₂²×C₃×D₃	—	2	12	no	—
200	C₂²×C₃×D₃	—	2	6	no	—
201	C₂²×C₃×D₃	—	4	3	no	—
202	C₂²×C₃×D₃	—	4	6	no	—
203	C₂²×C₃×D₃	—	4	6	no	—
204	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
205	C₂²×C₃×D₃	C₂⁴	1	3	yes	—
206	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
207	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
208	C₃²×D₄	C₂×D₄	1	12	yes	complemented
209	C₂×C₃²×C₄	—	4	6	no	—
210	C₂×C₃²×C₄	C₂×D₄	1	12	yes	complemented
211	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
212	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
213	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
214	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
215	C₃×#67	—	2	12	no	—
216	C₃×#67	—	2	12	no	—
217	C₂×C₃×Dic₃	—	2	6	no	—
218	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
219	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
220	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
221	C₃×D₁₂	—	2	12	no	—
222	C₃×D₁₂	—	2	6	no	—
223	C₃×D₁₂	—	2	12	no	—
224	C₃×D₁₂	—	2	6	no	—
225	C₃×D₁₂	—	4	12	no	—
226	C₃×D₁₂	—	4	6	no	—
227	C₃×C₄×D₃	—	2	2	no	—
228	C₃×C₄×D₃	—	2	6	no	—
229	C₃×C₄×D₃	—	2	6	no	—
230	C₃×C₄×D₃	—	2	6	no	—
231	C₃×C₄×D₃	—	2	12	no	—
232	C₃×Dic₆	—	2	2	no	—
233	C₃×Dic₆	—	2	6	no	—
234	C₂×H(5,𝔽₂)	—	3	1	no	—
235	C₂²×#41	—	3	1	no	—
236	#550	—	3	2	no	—
237	#548	—	3	2	no	—
238	#546	—	3	6	no	—
239	D₄²	—	3	6	no	—
240	#537	—	3	3	no	—
241	#535	—	3	3	no	—
242	#525	—	3	3	no	—
243	C₂×#121	—	3	3	no	—
244	#520	C₃×D₃	1	1	yes	characteristic, complemented
245	C₂⁴×C₃	—	3	3	no	—
246	C₂⁴×C₃	—	3	6	no	—
247	C₂³×D₃	C₂³×C₃	1	3	yes	—
248	C₂³×D₃	C₂³×C₃	1	6	yes	—
249	C₃×#41	—	2	8	no	—
250	C₃×#41	—	6	4	no	—
251	C₃×#41	—	6	8	no	—
252	C₃×#41	—	6	12	no	—
253	C₃×#41	—	6	12	no	—
254	C₃×#41	—	6	12	no	—
255	C₃×#41	D₁₂	1	8	yes	complemented
256	C₃×#41	C₃×D₄	1	8	yes	complemented
257	C₂×C₃×Q₈	—	2	1	no	—
258	C₂×C₃×Q₈	—	3	1	no	—
259	C₂×C₃×Q₈	—	3	3	no	—
260	C₂×C₃×Q₈	—	6	4	no	—
261	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×D₄	—	2	3	no	—
264	C₂×C₃×D₄	—	3	6	no	—
265	C₂×C₃×D₄	—	3	6	no	—
266	C₂×C₃×D₄	—	3	6	no	—
267	C₂×C₃×D₄	—	3	3	no	—
268	C₂×C₃×D₄	—	3	6	no	—
269	C₂×C₃×D₄	—	3	3	no	—
270	C₂×C₃×D₄	—	3	6	no	—
271	C₂×C₃×D₄	—	3	12	no	—
272	C₂×C₃×D₄	—	6	12	no	—
273	C₂×C₃×D₄	—	6	24	no	—
274	C₂×C₃×D₄	—	6	12	no	—
275	C₂×C₃×D₄	—	12	12	no	—
276	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
277	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
278	C₂²×C₃×C₄	—	2	3	no	—
279	C₂²×C₃×C₄	—	2	6	no	—
280	C₂²×C₃×C₄	—	3	3	no	—
281	C₂²×C₃×C₄	—	3	3	no	—
282	C₂²×C₃×C₄	—	3	3	no	—
283	C₂²×C₃×C₄	—	3	6	no	—
284	C₂²×C₃×C₄	—	3	1	no	—
285	C₂²×C₃×C₄	—	3	3	no	—
286	C₂²×C₃×C₄	—	6	12	no	—
287	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
288	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
289	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
290	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
291	C₂×#67	C₂³×C₃	1	6	yes	—
292	C₂×#67	C₂³×C₃	1	6	yes	—
293	C₂²×Dic₃	C₂³×C₃	1	3	yes	—
294	#239	—	2	4	no	—
295	#239	—	2	8	no	—
296	D₃×Q₈	—	2	4	no	—
297	#237	—	2	12	no	—
298	D₃×D₄	—	2	12	no	—
299	D₃×D₄	—	2	24	no	—
300	#235	—	2	12	no	—
301	#235	—	2	12	no	—
302	C₂×D₁₂	—	2	12	no	—
303	C₂×D₁₂	—	4	12	no	—
304	C₂×D₁₂	C₂³×C₃	1	6	yes	—
305	C₂×D₁₂	C₂³×C₃	1	3	yes	—
306	C₂×D₁₂	C₂³×C₃	1	6	yes	—
307	C₂×D₁₂	C₂³×C₃	1	3	yes	—
308	C₂×D₁₂	C₂³×C₃	1	6	yes	—
309	C₂×D₁₂	C₂³×C₃	1	12	yes	—
310	C₂×C₄×D₃	—	2	12	no	—
311	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
312	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
313	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
314	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
315	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
316	C₂×Dic₆	C₂³×C₃	1	3	yes	—
317	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
318	C₃×C₄⋊C₄	—	2	3	no	—
319	C₃×C₄⋊C₄	—	2	6	no	—
320	C₃×C₄⋊C₄	—	2	1	no	—
321	C₃×C₄⋊C₄	—	3	2	no	—
322	C₃×C₄⋊C₄	—	3	6	no	—
323	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
324	C₃×C₄⋊C₄	C₂²×D₃	1	6	yes	—
325	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
326	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
328	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
329	C₃×C₂²⋊C₄	—	2	6	no	—
330	C₃×C₂²⋊C₄	—	3	6	no	—
331	C₃×C₂²⋊C₄	—	3	12	no	—
332	C₃×C₂²⋊C₄	—	3	2	no	—
333	C₃×C₂²⋊C₄	—	3	6	no	—
334	C₃×C₂²⋊C₄	—	3	6	no	—
335	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
336	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
337	C₃×C₄²	—	2	6	no	—
338	C₃×C₄²	C₂²×D₃	1	6	yes	—
339	C₃×C₄²	C₂³×C₃	1	6	yes	—
340	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
341	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
342	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
343	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
344	(C₂×D₃)⋊C₄	C₂³×C₃	1	12	yes	—
345	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
346	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
347	C₂²×C₃²	—	2	3	no	—
348	C₂²×C₃²	—	2	3	no	—
349	C₂²×C₃²	C₂²×D₄	1	6	yes	—
350	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
351	C₂×C₃×D₃	—	2	1	no	—
352	C₂×C₃×D₃	—	2	1	no	—
353	C₂×C₃×D₃	—	2	3	no	—
354	C₂×C₃×D₃	—	2	6	no	—
355	C₂×C₃×D₃	—	2	6	no	—
356	C₂×C₃×D₃	—	2	3	no	—
357	C₂×C₃×D₃	—	2	3	no	—
358	C₂×C₃×D₃	—	2	6	no	—
359	C₂×C₃×D₃	—	4	12	no	—
360	C₂×C₃×D₃	—	8	12	no	—
361	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	complemented
362	C₃²×C₄	—	2	6	no	—
363	C₃²×C₄	—	2	2	no	—
364	C₃²×C₄	C₂²×D₄	1	2	yes	—
365	C₃²×C₄	C₂²×D₄	1	6	yes	—
366	C₃×Dic₃	—	2	3	no	—
367	C₃×Dic₃	—	2	2	no	—
368	C₃×Dic₃	—	2	1	no	—
369	H(5,𝔽₂)	—	6	8	no	—
370	C₂×#41	—	3	2	no	—
371	C₂×#41	—	3	1	no	—
372	C₂×#41	—	3	3	no	—
373	C₂×#41	—	3	3	no	—
374	C₂×#41	—	3	3	no	—
375	C₂×#41	—	6	8	no	—
376	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
377	C₂²×Q₈	—	3	1	no	—
378	C₂²×D₄	—	3	3	no	—
379	C₂²×D₄	—	3	6	no	—
380	C₂²×D₄	—	3	3	no	—
381	C₂²×D₄	—	3	6	no	—
382	C₂³×C₄	—	3	3	no	—
383	#127	—	3	6	no	—
384	#124	—	3	6	no	—
385	#123	—	3	6	no	—
386	C₂²⋊Q₈	—	3	1	no	—
387	C₂²⋊Q₈	—	3	3	no	—
388	C₂²⋊Q₈	—	3	6	no	—
389	#121	—	3	12	no	—
390	#121	—	3	3	no	—
391	#121	—	3	6	no	—
392	#121	—	3	6	no	—
393	#121	—	3	6	no	—
394	#121	—	3	3	no	—
395	#121	—	3	6	no	—
396	#120	—	3	6	no	—
397	#120	—	3	12	no	—
398	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
399	C₄×D₄	—	3	6	no	—
400	C₄×D₄	—	3	6	no	—
401	C₄×D₄	C₂×C₃×D₃	1	6	yes	complemented
402	#117	C₂×C₃×D₃	1	3	yes	complemented
403	C₂×C₄⋊C₄	C₂×C₃×D₃	1	3	yes	complemented
404	C₂×C₂²⋊C₄	—	3	6	no	—
405	C₂³×C₃	—	2	3	no	—
406	C₂³×C₃	—	3	1	no	—
407	C₂³×C₃	—	3	6	no	—
408	C₂³×C₃	—	3	3	no	—
409	C₂³×C₃	—	6	6	no	—
410	C₂³×C₃	—	6	6	no	—
411	C₂³×C₃	—	6	12	no	—
412	C₂³×C₃	—	12	3	no	—
413	C₂³×C₃	—	12	6	no	—
414	C₂³×C₃	—	12	6	no	—
415	C₂³×C₃	C₂³×D₃	1	3	yes	—
416	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
417	C₂²×D₃	—	2	6	no	—
418	C₂²×D₃	—	2	12	no	—
419	C₂²×D₃	—	2	6	no	—
420	C₂²×D₃	—	4	3	no	—
421	C₂²×D₃	—	4	6	no	—
422	C₂²×D₃	—	4	6	no	—
423	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
424	C₂²×D₃	C₂⁴×C₃	1	3	yes	—
425	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
426	C₃×Q₈	—	2	4	no	—
427	C₃×Q₈	—	6	6	no	—
428	C₃×Q₈	—	6	2	no	—
429	C₃×Q₈	C₂×D₁₂	1	4	yes	complemented
430	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
431	C₃×D₄	—	2	12	no	—
432	C₃×D₄	—	6	12	no	—
433	C₃×D₄	—	6	12	no	—
434	C₃×D₄	—	6	12	no	—
435	C₃×D₄	—	6	6	no	—
436	C₃×D₄	—	6	12	no	—
437	C₃×D₄	—	6	6	no	—
438	C₃×D₄	—	12	6	no	—
439	C₃×D₄	—	12	12	no	—
440	C₃×D₄	C₂×D₁₂	1	12	yes	complemented
441	C₃×D₄	C₂×C₃×D₄	1	12	yes	complemented
442	C₂×C₃×C₄	—	2	3	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	2	no	—
445	C₂×C₃×C₄	—	2	6	no	—
446	C₂×C₃×C₄	—	2	12	no	—
447	C₂×C₃×C₄	—	3	1	no	—
448	C₂×C₃×C₄	—	3	3	no	—
449	C₂×C₃×C₄	—	3	2	no	—
450	C₂×C₃×C₄	—	4	6	no	—
451	C₂×C₃×C₄	—	4	6	no	—
452	C₂×C₃×C₄	—	6	6	no	—
453	C₂×C₃×C₄	—	6	2	no	—
454	C₂×C₃×C₄	—	6	6	no	—
455	C₂×C₃×C₄	—	6	6	no	—
456	C₂×C₃×C₄	—	6	6	no	—
457	C₂×C₃×C₄	—	6	12	no	—
458	C₂×C₃×C₄	—	8	6	no	—
459	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	complemented
460	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	complemented
461	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
462	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
463	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
464	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
466	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
467	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
468	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
469	#67	—	2	12	no	—
470	#67	—	2	12	no	—
471	C₂×Dic₃	—	2	6	no	—
472	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
473	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
474	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
475	D₁₂	—	2	12	no	—
476	D₁₂	—	2	6	no	—
477	D₁₂	—	2	12	no	—
478	D₁₂	—	2	6	no	—
479	D₁₂	—	4	12	no	—
480	D₁₂	—	4	6	no	—
481	C₄×D₃	—	2	2	no	—
482	C₄×D₃	—	2	6	no	—
483	C₄×D₃	—	2	6	no	—
484	C₄×D₃	—	2	6	no	—
485	C₄×D₃	—	2	12	no	—
486	Dic₆	—	2	2	no	—
487	Dic₆	—	2	6	no	—
488	C₂×C₃²	—	2	6	no	—
489	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
490	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂×C₃²	#585	1	1	yes	characteristic
492	C₃×D₃	—	2	2	no	—
493	C₃×D₃	—	4	3	no	—
494	C₃×D₃	—	4	6	no	—
495	C₂⁴	—	3	3	no	—
496	C₂⁴	—	3	6	no	—
497	#41	—	6	4	no	—
498	#41	—	6	8	no	—
499	#41	—	6	12	no	—
500	#41	—	6	12	no	—
501	#41	—	6	12	no	—
502	#41	C₃×D₁₂	1	8	yes	complemented
503	C₂×Q₈	—	3	1	no	—
504	C₂×Q₈	—	3	3	no	—
505	C₂×Q₈	—	6	4	no	—
506	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
507	C₂×D₄	—	3	6	no	—
508	C₂×D₄	—	3	6	no	—
509	C₂×D₄	—	3	6	no	—
510	C₂×D₄	—	3	3	no	—
511	C₂×D₄	—	3	6	no	—
512	C₂×D₄	—	3	3	no	—
513	C₂×D₄	—	3	6	no	—
514	C₂×D₄	—	3	12	no	—
515	C₂×D₄	—	6	12	no	—
516	C₂×D₄	—	6	24	no	—
517	C₂×D₄	—	6	12	no	—
518	C₂×D₄	—	12	12	no	—
519	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
520	C₂²×C₄	—	3	3	no	—
521	C₂²×C₄	—	3	3	no	—
522	C₂²×C₄	—	3	3	no	—
523	C₂²×C₄	—	3	6	no	—
524	C₂²×C₄	—	3	1	no	—
525	C₂²×C₄	—	3	3	no	—
526	C₂²×C₄	—	6	12	no	—
527	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
528	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
529	C₄⋊C₄	—	3	2	no	—
530	C₄⋊C₄	—	3	6	no	—
531	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
532	C₄⋊C₄	C₂²×C₃×D₃	1	6	yes	—
533	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
534	C₂²⋊C₄	—	3	6	no	—
535	C₂²⋊C₄	—	3	12	no	—
536	C₂²⋊C₄	—	3	2	no	—
537	C₂²⋊C₄	—	3	6	no	—
538	C₂²⋊C₄	—	3	6	no	—
539	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
540	C₄²	C₂²×C₃×D₃	1	6	yes	—
541	C₂²×C₃	—	2	3	no	—
542	C₂²×C₃	—	2	3	no	—
543	C₂²×C₃	—	2	3	no	—
544	C₂²×C₃	—	2	3	no	—
545	C₂²×C₃	—	2	6	no	—
546	C₂²×C₃	—	2	1	no	—
547	C₂²×C₃	—	3	2	no	—
548	C₂²×C₃	—	4	3	no	—
549	C₂²×C₃	—	4	3	no	—
550	C₂²×C₃	—	6	1	no	—
551	C₂²×C₃	—	6	1	no	—
552	C₂²×C₃	—	6	3	no	—
553	C₂²×C₃	—	6	6	no	—
554	C₂²×C₃	—	6	6	no	—
555	C₂²×C₃	—	6	3	no	—
556	C₂²×C₃	—	6	3	no	—
557	C₂²×C₃	—	6	6	no	—
558	C₂²×C₃	—	12	12	no	—
559	C₂²×C₃	—	24	12	no	—
560	C₂²×C₃	C₂²×D₁₂	1	6	yes	—
561	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
562	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
563	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
564	C₂×D₃	—	2	1	no	—
565	C₂×D₃	—	2	1	no	—
566	C₂×D₃	—	2	3	no	—
567	C₂×D₃	—	2	6	no	—
568	C₂×D₃	—	2	6	no	—
569	C₂×D₃	—	2	3	no	—
570	C₂×D₃	—	2	3	no	—
571	C₂×D₃	—	2	6	no	—
572	C₂×D₃	—	4	12	no	—
573	C₂×D₃	—	8	12	no	—
574	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	complemented
575	C₃×C₄	—	2	6	no	—
576	C₃×C₄	—	2	2	no	—
577	C₃×C₄	—	2	6	no	—
578	C₃×C₄	—	2	2	no	—
579	C₃×C₄	—	2	2	no	—
580	C₃×C₄	—	2	6	no	—
581	C₃×C₄	—	4	6	no	—
582	C₃×C₄	—	4	2	no	—
583	C₃×C₄	—	6	1	no	—
584	C₃×C₄	—	6	2	no	—
585	C₃×C₄	—	6	3	no	—
586	C₃×C₄	C₂²×D₁₂	1	2	yes	—
587	C₃×C₄	C₂²×D₁₂	1	6	yes	—
588	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
589	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
590	Dic₃	—	2	3	no	—
591	Dic₃	—	2	2	no	—
592	Dic₃	—	2	1	no	—
593	C₃²	#3488	1	1	yes	characteristic, complemented, Sylow
594	C₂³	—	3	1	no	—
595	C₂³	—	3	6	no	—
596	C₂³	—	3	3	no	—
597	C₂³	—	6	6	no	—
598	C₂³	—	6	6	no	—
599	C₂³	—	6	12	no	—
600	C₂³	—	12	3	no	—
601	C₂³	—	12	6	no	—
602	C₂³	—	12	6	no	—
603	C₂³	C₂³×C₃×D₃	1	3	yes	—
604	Q₈	—	6	6	no	—
605	Q₈	—	6	2	no	—
606	Q₈	C₂×C₃×D₁₂	1	4	yes	complemented
607	D₄	—	6	12	no	—
608	D₄	—	6	12	no	—
609	D₄	—	6	12	no	—
610	D₄	—	6	6	no	—
611	D₄	—	6	12	no	—
612	D₄	—	6	6	no	—
613	D₄	—	12	12	no	—
614	D₄	—	12	6	no	—
615	D₄	C₂×C₃×D₁₂	1	12	yes	complemented
616	C₂×C₄	—	3	1	no	—
617	C₂×C₄	—	3	3	no	—
618	C₂×C₄	—	3	2	no	—
619	C₂×C₄	—	4	6	no	—
620	C₂×C₄	—	6	6	no	—
621	C₂×C₄	—	6	2	no	—
622	C₂×C₄	—	6	6	no	—
623	C₂×C₄	—	6	6	no	—
624	C₂×C₄	—	6	6	no	—
625	C₂×C₄	—	6	12	no	—
626	C₂×C₄	C₂×C₃×D₁₂	1	12	yes	complemented
627	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
628	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
629	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
630	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
631	C₂×C₃	—	2	6	no	—
632	C₂×C₃	—	2	6	no	—
633	C₂×C₃	—	2	1	no	—
634	C₂×C₃	—	2	1	no	—
635	C₂×C₃	—	2	1	no	—
636	C₂×C₃	—	4	6	no	—
637	C₂×C₃	—	6	2	no	—
638	C₂×C₃	—	12	3	no	—
639	C₂×C₃	—	12	6	no	—
640	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
641	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂×C₃	#5968	1	1	yes	characteristic
643	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
644	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₃	C₃×#585	1	1	yes	characteristic
646	D₃	—	2	2	no	—
647	D₃	—	4	3	no	—
648	D₃	—	4	6	no	—
649	C₂²	—	2	3	no	—
650	C₂²	—	2	3	no	—
651	C₂²	—	3	2	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	3	no	—
655	C₂²	—	6	6	no	—
656	C₂²	—	6	6	no	—
657	C₂²	—	6	3	no	—
658	C₂²	—	6	3	no	—
659	C₂²	—	6	6	no	—
660	C₂²	—	12	12	no	—
661	C₂²	—	24	12	no	—
662	C₂²	C₂²×C₃×D₁₂	1	6	yes	—
663	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
664	C₄	—	2	6	no	—
665	C₄	—	2	2	no	—
666	C₄	—	6	1	no	—
667	C₄	—	6	2	no	—
668	C₄	—	6	3	no	—
669	C₄	C₂²×C₃×D₁₂	1	2	yes	—
670	C₄	C₂²×C₃×D₁₂	1	6	yes	—
671	C₃	—	2	1	no	—
672	C₃	#85900	1	1	yes	characteristic, direct product factor
673	C₃	C₃×#3488	1	1	yes	characteristic, complemented
674	C₂	—	2	6	no	—
675	C₂	—	6	2	no	—
676	C₂	—	12	3	no	—
677	C₂	—	12	6	no	—
678	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
679	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#520	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#520	D₃
hypocenter	C₃	C₃×#3488
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#520

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1009	C₂	semidirect
2. C₂×C₃×D₃×#41	C₂	semidirect
3. C₃²×#520	C₂	semidirect
4. C₃×#5577	C₂	semidirect
5. C₃×#5576	C₂	semidirect
6. C₃×#5554	C₂	semidirect
7. C₃×D₄×D₁₂	C₂	semidirect
8. C₃×#5525	C₂	semidirect
9. C₃×#5524	C₂	semidirect
10. C₃×#5510	C₂	semidirect
11. C₂×C₃×#895	C₂	semidirect
13. #85900	C₃	direct (N × H)
17. C₂×C₃×#239	C₂²	semidirect
18. C₂×C₃×#239	C₂²	semidirect
19. C₂×C₃×D₃×Q₈	C₂²	semidirect
20. C₂×C₃×#237	C₂²	semidirect
21. C₂×C₃×D₃×D₄	C₂²	semidirect
22. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂×C₃×#235	C₂²	semidirect
24. C₂×C₃×#235	C₂²	semidirect
25. C₂²×C₃×D₁₂	C₂²	semidirect
26. C₂²×C₃×D₁₂	C₂²	semidirect
27. C₂²×C₃×C₄×D₃	C₂²	semidirect
28. C₃²×C₄×Q₈	C₂²	semidirect
29. C₃²×C₄×D₄	C₂²	semidirect
30. C₃²×#117	C₂²	semidirect
31. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
32. C₃×#930	C₂²	semidirect
33. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₃×#897	C₂²	semidirect
35. C₃×#897	C₂²	semidirect
36. C₃×#897	C₂²	semidirect
37. C₃×#895	C₂²	semidirect
38. C₃×#895	C₂²	semidirect
39. C₃×#895	C₂²	semidirect
40. C₃×#895	C₂²	semidirect
41. C₃×#895	C₂²	semidirect
42. C₃×#895	C₂²	semidirect
43. C₃×#886	C₂²	semidirect
44. C₃×#882	C₂²	semidirect
45. C₃×#882	C₂²	semidirect
46. C₃×#875	C₂²	semidirect
47. C₃×#874	C₂²	semidirect
48. C₃×C₄×D₁₂	C₂²	semidirect
49. C₃×C₄×D₁₂	C₂²	semidirect
52. C₂×#1009	C₂×C₃	semidirect
53. C₂×D₃×#41	C₂×C₃	semidirect
63. C₃×#520	D₃	semidirect
64. C₃×#520	C₂×C₃	semidirect
65. #5577	C₂×C₃	semidirect
66. #5576	C₂×C₃	semidirect
67. #5554	C₂×C₃	semidirect
68. D₄×D₁₂	C₂×C₃	semidirect
69. #5525	C₂×C₃	semidirect
70. #5524	C₂×C₃	semidirect
71. #5510	C₂×C₃	semidirect
72. C₂×#895	C₂×C₃	semidirect
75. C₃²×#41	D₄	semidirect
138. C₂×#239	C₂²×C₃	semidirect
139. C₂×#239	C₂²×C₃	semidirect
140. C₂×D₃×Q₈	C₂²×C₃	semidirect
141. C₂×#237	C₂²×C₃	semidirect
142. C₂×D₃×D₄	C₂²×C₃	semidirect
143. C₂×D₃×D₄	C₂²×C₃	semidirect
144. C₂×#235	C₂²×C₃	semidirect
145. C₂×#235	C₂²×C₃	semidirect
146. C₂²×D₁₂	C₂²×C₃	semidirect
147. C₂²×D₁₂	C₂²×C₃	semidirect
148. C₂²×C₄×D₃	C₂²×C₃	semidirect
165. C₃×C₄×Q₈	C₂×D₃	semidirect
166. C₃×C₄×Q₈	C₂²×C₃	semidirect
170. C₃×C₄×D₄	C₂×D₃	semidirect
171. C₃×C₄×D₄	C₂²×C₃	semidirect
173. C₃×#117	C₂×D₃	semidirect
174. C₃×#117	C₂²×C₃	semidirect
176. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
177. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
179. #930	C₂²×C₃	semidirect
180. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
181. #897	C₂²×C₃	semidirect
182. #897	C₂²×C₃	semidirect
183. #897	C₂²×C₃	semidirect
184. #895	C₂²×C₃	semidirect
185. #895	C₂²×C₃	semidirect
186. #895	C₂²×C₃	semidirect
187. #895	C₂²×C₃	semidirect
188. #895	C₂²×C₃	semidirect
189. #895	C₂²×C₃	semidirect
190. #886	C₂²×C₃	semidirect
191. #882	C₂²×C₃	semidirect
192. #882	C₂²×C₃	semidirect
193. #875	C₂²×C₃	semidirect
194. #874	C₂²×C₃	semidirect
195. C₄×D₁₂	C₂²×C₃	semidirect
196. C₄×D₁₂	C₂²×C₃	semidirect
207. C₃²×Q₈	C₂×D₄	semidirect
208. C₃²×D₄	C₂×D₄	semidirect
210. C₂×C₃²×C₄	C₂×D₄	semidirect
244. #520	C₃×D₃	semidirect
255. C₃×#41	D₁₂	semidirect
256. C₃×#41	C₃×D₄	semidirect
361. C₂×C₃×D₃	H(5,𝔽₂)	semidirect
398. C₄×Q₈	C₂×C₃×D₃	semidirect
401. C₄×D₄	C₂×C₃×D₃	semidirect
402. #117	C₂×C₃×D₃	semidirect
403. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
429. C₃×Q₈	C₂×D₁₂	semidirect
430. C₃×Q₈	C₂×C₃×D₄	semidirect
440. C₃×D₄	C₂×D₁₂	semidirect
441. C₃×D₄	C₂×C₃×D₄	semidirect
459. C₂×C₃×C₄	C₂×D₁₂	semidirect
460. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
502. #41	C₃×D₁₂	semidirect
574. C₂×D₃	C₃×H(5,𝔽₂)	semidirect
593. C₃²	#3488	semidirect
606. Q₈	C₂×C₃×D₁₂	semidirect
615. D₄	C₂×C₃×D₁₂	semidirect
626. C₂×C₄	C₂×C₃×D₁₂	semidirect
672. C₃	#85900	direct (N × H)
673. C₃	C₃×#3488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1009	2
C₂×C₃×D₃×#41	2
C₃²×#520	2
C₃×#5577	2
C₃×#5576	2
C₃×#5554	2
C₃×D₄×D₁₂	2
C₃×#5525	2
C₃×#5524	2
C₃×#5510	2
C₂×C₃×#895	2
C₃×#3488	3
#85900	3

Subgroups — C3×#85900 #11904615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85900 #11904615