Subgroups — C₃×#85735 #11901193

Order 1152.

3277 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5526	C₂	1	4	yes	maximal, complemented
4	C₃×#5525	C₂	1	4	yes	maximal, complemented
5	C₃×#5524	C₂	1	8	yes	maximal, complemented
6	C₃×#5510	C₂	1	4	yes	maximal, complemented
7	C₃×#5493	C₂	1	4	yes	maximal, complemented
8	C₃×#5477	C₂	1	4	yes	maximal, complemented
9	C₃×#3449	—	3	1	no	maximal
10	#85735	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×#67	C₂²	1	4	yes	—
13	C₂×C₃×#235	—	2	16	no	—
14	C₂×C₃×#235	C₂²	1	4	yes	—
15	C₂×C₃×#235	C₂²	1	4	yes	—
16	C₂×C₃×#235	C₂²	1	4	yes	complemented
17	C₂×C₃×#235	C₂²	1	4	yes	complemented
18	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	complemented
20	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
21	C₃²×#117	C₂²	1	4	yes	complemented
22	C₃²×#117	C₂²	1	4	yes	complemented
23	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
26	C₃×#930	C₂²	1	16	yes	complemented
27	C₃×#897	C₂²	1	16	yes	complemented
28	C₃×#895	C₂²	1	16	yes	complemented
29	C₃×#886	C₂²	1	16	yes	complemented
30	C₃×#882	C₂²	1	16	yes	complemented
31	C₃×#875	C₂²	1	8	yes	complemented
32	C₃×#874	C₂²	1	4	yes	complemented
33	C₃×C₄×D₁₂	C₂²	1	16	yes	complemented
34	C₃×#869	C₂²	1	4	yes	complemented
35	C₂²×C₃×#41	—	3	2	no	—
36	C₂²×#235	C₂×C₃	1	2	yes	complemented
37	C₃×#537	—	3	4	no	—
38	C₃×#536	—	3	4	no	—
39	C₃×#535	—	3	4	no	—
40	C₃×#534	—	3	4	no	—
41	C₃×#532	—	3	4	no	—
42	C₃×#525	—	3	8	no	—
43	C₂×C₃×#117	—	2	1	no	—
44	C₂×C₃×#117	D₃	1	1	yes	characteristic, complemented
45	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
46	#5526	C₂×C₃	1	4	yes	complemented
47	#5525	C₂×C₃	1	4	yes	complemented
48	#5524	C₂×C₃	1	8	yes	complemented
49	#5510	C₂×C₃	1	4	yes	complemented
50	#5493	C₂×C₃	1	4	yes	complemented
51	#5477	C₂×C₃	1	4	yes	complemented
52	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
53	C₂³×C₃×D₃	C₂³	1	4	yes	—
54	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
55	C₂²×C₃²×C₄	C₂³	1	4	yes	—
56	C₂²×C₃²×C₄	C₂³	1	2	yes	—
57	C₂²×C₃²×C₄	C₂³	1	2	yes	—
58	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
59	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃×#67	—	2	16	no	—
61	C₂×C₃×#67	C₂³	1	8	yes	—
62	C₂×C₃×#67	C₂³	1	8	yes	—
63	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
64	C₃×#235	—	2	16	no	—
65	C₃×#235	—	2	16	no	—
66	C₃×#235	—	2	16	no	—
67	C₃×#235	—	2	16	no	—
68	C₂×C₃×D₁₂	—	2	8	no	—
69	C₂×C₃×D₁₂	C₂³	1	4	yes	—
70	C₂×C₃×D₁₂	C₂³	1	4	yes	—
71	C₂×C₃×D₁₂	C₂³	1	16	yes	—
72	C₂×C₃×C₄×D₃	—	2	16	no	—
73	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
74	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
75	C₂×C₃×Dic₆	—	2	8	no	—
76	C₂×C₃×Dic₆	C₂³	1	4	yes	—
77	C₂×C₃×Dic₆	C₂³	1	4	yes	—
78	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
79	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₃²×C₄²	C₂³	1	4	yes	—
81	C₃²×C₄²	C₂³	1	4	yes	—
82	C₃×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
83	C₃×C₄⋊Dic₃	C₂³	1	16	yes	—
84	#3449	—	3	1	no	Sylow
85	C₂×C₃×#41	—	3	4	no	—
86	C₂×C₃×#41	—	3	4	no	—
87	C₂×C₃×#41	—	3	4	no	—
88	C₂×C₃×#41	—	3	4	no	—
89	C₂×C₃×#41	—	6	16	no	—
90	C₂²×C₃×Q₈	—	3	2	no	—
91	C₂²×C₃×D₄	—	3	4	no	—
92	C₂²×C₃×D₄	—	3	2	no	—
93	C₂³×C₃×C₄	—	2	1	no	—
94	C₂³×C₃×C₄	—	3	4	no	—
95	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂²×#67	C₂²×C₃	1	4	yes	—
98	C₂×#235	—	2	16	no	—
99	C₂×#235	C₂²×C₃	1	4	yes	—
100	C₂×#235	C₂²×C₃	1	4	yes	—
101	C₂×#235	C₂²×C₃	1	4	yes	complemented
102	C₂×#235	C₂²×C₃	1	4	yes	complemented
103	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
104	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	complemented
105	C₂²×Dic₆	C₂²×C₃	1	2	yes	complemented
106	C₃×C₄⋊Q₈	—	3	4	no	—
107	C₃×#127	—	3	4	no	—
108	C₃×#124	—	3	8	no	—
109	C₃×#123	—	3	16	no	—
110	C₃×C₂²⋊Q₈	—	3	16	no	—
111	C₃×#121	—	3	16	no	—
112	C₃×#121	—	3	16	no	—
113	C₃×#120	—	3	16	no	—
114	C₃×C₄×D₄	—	3	16	no	—
115	C₃×#117	—	2	4	no	—
116	C₃×#117	—	2	4	no	—
117	C₃×#117	C₂×D₃	1	4	yes	complemented
118	C₃×#117	C₂×D₃	1	4	yes	complemented
119	C₃×#117	C₂²×C₃	1	4	yes	complemented
120	C₃×#117	C₂²×C₃	1	4	yes	complemented
121	C₂×C₃×C₄⋊C₄	—	2	2	no	—
122	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
124	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
127	C₂×C₃×C₄²	—	2	2	no	—
128	C₂×C₃×C₄²	C₂×D₃	1	2	yes	complemented
129	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	complemented
130	#930	C₂²×C₃	1	16	yes	complemented
131	#897	C₂²×C₃	1	16	yes	complemented
132	#895	C₂²×C₃	1	16	yes	complemented
133	#886	C₂²×C₃	1	16	yes	complemented
134	#882	C₂²×C₃	1	16	yes	complemented
135	#875	C₂²×C₃	1	8	yes	complemented
136	#874	C₂²×C₃	1	4	yes	complemented
137	C₄×D₁₂	C₂²×C₃	1	16	yes	complemented
138	#869	C₂²×C₃	1	4	yes	complemented
139	C₂³×C₃²	—	4	2	no	—
140	C₂³×C₃²	C₂×D₄	1	4	yes	—
141	C₂³×C₃²	C₂⁴	1	2	yes	—
142	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
143	C₂²×C₃×D₃	—	2	8	no	—
144	C₂²×C₃×D₃	—	4	8	no	—
145	C₂²×C₃×D₃	C₂⁴	1	8	yes	—
146	C₂×C₃²×C₄	—	4	4	no	—
147	C₂×C₃²×C₄	C₂×D₄	1	8	yes	—
148	C₂×C₃²×C₄	C₂×D₄	1	8	yes	—
149	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
150	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
151	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
152	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
154	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
155	C₃×#67	—	2	16	no	—
156	C₃×#67	—	2	16	no	—
157	C₂×C₃×Dic₃	—	2	8	no	—
158	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
159	C₃×D₁₂	—	2	8	no	—
160	C₃×D₁₂	—	2	8	no	—
161	C₃×D₁₂	—	4	16	no	—
162	C₃×C₄×D₃	—	2	16	no	—
163	C₃×C₄×D₃	—	2	16	no	—
164	C₃×Dic₆	—	2	8	no	—
165	C₃×Dic₆	—	2	8	no	—
166	C₂²×#41	—	3	2	no	—
167	#537	—	3	4	no	—
168	#536	—	3	4	no	—
169	#535	—	3	4	no	—
170	#534	—	3	4	no	—
171	#532	—	3	4	no	—
172	#525	—	3	8	no	—
173	C₂×#117	C₃×D₃	1	1	yes	characteristic, complemented
174	C₂⁴×C₃	—	2	1	no	—
175	C₂⁴×C₃	—	3	4	no	—
176	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
177	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
178	C₂³×D₃	C₂³×C₃	1	4	yes	—
179	C₃×#41	—	6	16	no	—
180	C₃×#41	—	6	16	no	—
181	C₃×#41	—	6	16	no	—
182	C₃×#41	—	6	16	no	—
183	C₂×C₃×Q₈	—	3	4	no	—
184	C₂×C₃×Q₈	—	3	4	no	—
185	C₂×C₃×Q₈	—	6	8	no	—
186	C₂×C₃×D₄	—	3	8	no	—
187	C₂×C₃×D₄	—	3	8	no	—
188	C₂×C₃×D₄	—	3	4	no	—
189	C₂×C₃×D₄	—	3	4	no	—
190	C₂×C₃×D₄	—	3	16	no	—
191	C₂×C₃×D₄	—	6	16	no	—
192	C₂×C₃×D₄	—	6	8	no	—
193	C₂²×C₃×C₄	—	2	8	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	3	4	no	—
200	C₂²×C₃×C₄	—	3	8	no	—
201	C₂²×C₃×C₄	—	3	8	no	—
202	C₂²×C₃×C₄	—	6	16	no	—
203	C₂²×C₃×C₄	D₁₂	1	8	yes	complemented
204	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
205	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
206	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
208	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
211	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
215	C₂×#67	—	2	16	no	—
216	C₂×#67	C₂³×C₃	1	8	yes	—
217	C₂×#67	C₂³×C₃	1	8	yes	—
218	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
219	#235	—	2	16	no	—
220	#235	—	2	16	no	—
221	#235	—	2	16	no	—
222	#235	—	2	16	no	—
223	C₂×D₁₂	—	2	8	no	—
224	C₂×D₁₂	C₂³×C₃	1	4	yes	—
225	C₂×D₁₂	C₂³×C₃	1	4	yes	—
226	C₂×D₁₂	C₂³×C₃	1	16	yes	—
227	C₂×C₄×D₃	—	2	16	no	—
228	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
229	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
230	C₂×Dic₆	—	2	8	no	—
231	C₂×Dic₆	C₂³×C₃	1	4	yes	—
232	C₂×Dic₆	C₂³×C₃	1	4	yes	—
233	C₃×C₄⋊C₄	—	2	8	no	—
234	C₃×C₄⋊C₄	—	3	16	no	—
235	C₃×C₄⋊C₄	C₂²×D₃	1	8	yes	—
236	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
237	C₃×C₂²⋊C₄	—	2	8	no	—
238	C₃×C₂²⋊C₄	—	3	32	no	—
239	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
240	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
241	C₃×C₄²	—	2	4	no	—
242	C₃×C₄²	—	2	4	no	—
243	C₃×C₄²	C₂²×D₃	1	4	yes	—
244	C₃×C₄²	C₂²×D₃	1	4	yes	—
245	C₃×C₄²	C₂³×C₃	1	4	yes	—
246	C₃×C₄²	C₂³×C₃	1	4	yes	—
247	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	—
248	C₄⋊Dic₃	C₂³×C₃	1	16	yes	—
249	C₂²×C₃²	—	2	2	no	—
250	C₂²×C₃²	—	2	4	no	—
251	C₂²×C₃²	—	4	4	no	—
252	C₂²×C₃²	C₂²×D₄	1	4	yes	—
253	C₂²×C₃²	C₂²×D₄	1	2	yes	—
254	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
255	C₂×C₃×D₃	—	2	8	no	—
256	C₂×C₃×D₃	—	2	16	no	—
257	C₂×C₃×D₃	—	4	16	no	—
258	C₃²×C₄	—	2	8	no	—
259	C₃²×C₄	C₂²×D₄	1	2	yes	—
260	C₃²×C₄	C₂²×D₄	1	4	yes	—
261	C₃²×C₄	C₂²×D₄	1	2	yes	—
262	C₃×Dic₃	—	2	8	no	—
263	C₂×#41	—	3	4	no	—
264	C₂×#41	—	3	4	no	—
265	C₂×#41	—	3	4	no	—
266	C₂×#41	—	3	4	no	—
267	C₂×#41	—	6	16	no	—
268	C₂²×Q₈	—	3	2	no	—
269	C₂²×D₄	—	3	4	no	—
270	C₂²×D₄	—	3	2	no	—
271	C₂³×C₄	—	3	4	no	—
272	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
273	C₄⋊Q₈	—	3	4	no	—
274	#127	—	3	4	no	—
275	#124	—	3	8	no	—
276	#123	—	3	16	no	—
277	C₂²⋊Q₈	—	3	16	no	—
278	#121	—	3	16	no	—
279	#121	—	3	16	no	—
280	#120	—	3	16	no	—
281	C₄×D₄	—	3	16	no	—
282	#117	C₂×C₃×D₃	1	4	yes	complemented
283	#117	C₂×C₃×D₃	1	4	yes	complemented
284	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
285	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
286	C₂×C₄²	C₂×C₃×D₃	1	2	yes	complemented
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	—	3	8	no	—
291	C₂³×C₃	—	4	2	no	—
292	C₂³×C₃	—	4	2	no	—
293	C₂³×C₃	—	4	4	no	—
294	C₂³×C₃	—	6	8	no	—
295	C₂³×C₃	—	12	8	no	—
296	C₂³×C₃	C₂×D₁₂	1	4	yes	—
297	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
298	C₂³×C₃	C₂³×D₃	1	2	yes	—
299	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
300	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
301	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
302	C₂²×D₃	—	2	8	no	—
303	C₂²×D₃	—	4	8	no	—
304	C₂²×D₃	C₂⁴×C₃	1	8	yes	—
305	C₃×Q₈	—	6	8	no	—
306	C₃×Q₈	—	6	8	no	—
307	C₃×D₄	—	6	16	no	—
308	C₃×D₄	—	6	16	no	—
309	C₃×D₄	—	6	8	no	—
310	C₃×D₄	—	6	8	no	—
311	C₃×D₄	—	12	16	no	—
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	8	no	—
316	C₂×C₃×C₄	—	2	8	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	3	8	no	—
321	C₂×C₃×C₄	—	4	4	no	—
322	C₂×C₃×C₄	—	4	4	no	—
323	C₂×C₃×C₄	—	4	8	no	—
324	C₂×C₃×C₄	—	6	8	no	—
325	C₂×C₃×C₄	—	6	16	no	—
326	C₂×C₃×C₄	—	6	16	no	—
327	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
328	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
329	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
330	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
331	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
332	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
333	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
334	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
335	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
336	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
338	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
340	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
343	#67	—	2	16	no	—
344	#67	—	2	16	no	—
345	C₂×Dic₃	—	2	8	no	—
346	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
347	D₁₂	—	2	8	no	—
348	D₁₂	—	2	8	no	—
349	D₁₂	—	4	16	no	—
350	C₄×D₃	—	2	16	no	—
351	C₄×D₃	—	2	16	no	—
352	Dic₆	—	2	8	no	—
353	Dic₆	—	2	8	no	—
354	C₂×C₃²	—	2	2	no	—
355	C₂×C₃²	—	2	4	no	—
356	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
357	C₂×C₃²	#585	1	2	yes	—
358	C₃×D₃	—	4	8	no	—
359	C₂⁴	—	3	4	no	—
360	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
361	#41	—	6	16	no	—
362	#41	—	6	16	no	—
363	#41	—	6	16	no	—
364	#41	—	6	16	no	—
365	C₂×Q₈	—	3	4	no	—
366	C₂×Q₈	—	3	4	no	—
367	C₂×Q₈	—	6	8	no	—
368	C₂×D₄	—	3	8	no	—
369	C₂×D₄	—	3	8	no	—
370	C₂×D₄	—	3	4	no	—
371	C₂×D₄	—	3	4	no	—
372	C₂×D₄	—	3	16	no	—
373	C₂×D₄	—	6	16	no	—
374	C₂×D₄	—	6	8	no	—
375	C₂²×C₄	—	3	4	no	—
376	C₂²×C₄	—	3	8	no	—
377	C₂²×C₄	—	3	8	no	—
378	C₂²×C₄	—	6	16	no	—
379	C₂²×C₄	C₃×D₁₂	1	8	yes	complemented
380	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
381	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
384	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
385	C₄⋊C₄	—	3	16	no	—
386	C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	—
387	C₂²⋊C₄	—	3	32	no	—
388	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
389	C₄²	C₂²×C₃×D₃	1	4	yes	—
390	C₄²	C₂²×C₃×D₃	1	4	yes	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	2	2	no	—
393	C₂²×C₃	—	2	4	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	2	1	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	—	4	4	no	—
401	C₂²×C₃	—	4	4	no	—
402	C₂²×C₃	—	4	8	no	—
403	C₂²×C₃	—	6	8	no	—
404	C₂²×C₃	—	6	16	no	—
405	C₂²×C₃	—	12	16	no	—
406	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
407	C₂²×C₃	C₂²×D₁₂	1	2	yes	—
408	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
409	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
410	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
411	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
412	C₂×D₃	—	2	8	no	—
413	C₂×D₃	—	2	16	no	—
414	C₂×D₃	—	4	16	no	—
415	C₃×C₄	—	2	8	no	—
416	C₃×C₄	—	2	8	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	4	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	4	8	no	—
421	C₃×C₄	—	6	8	no	—
422	C₃×C₄	C₂²×D₁₂	1	2	yes	—
423	C₃×C₄	C₂²×D₁₂	1	4	yes	—
424	C₃×C₄	C₂²×D₁₂	1	2	yes	—
425	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
426	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
427	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
428	Dic₃	—	2	8	no	—
429	C₃²	#3449	1	1	yes	characteristic, complemented, Sylow
430	C₂³	—	3	8	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	6	8	no	—
433	C₂³	—	12	8	no	—
434	C₂³	C₂×C₃×D₁₂	1	4	yes	—
435	C₂³	C₂³×C₃×D₃	1	2	yes	—
436	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
437	Q₈	—	6	8	no	—
438	Q₈	—	6	8	no	—
439	D₄	—	6	16	no	—
440	D₄	—	6	16	no	—
441	D₄	—	6	8	no	—
442	D₄	—	6	8	no	—
443	D₄	—	12	16	no	—
444	C₂×C₄	—	3	8	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	6	8	no	—
447	C₂×C₄	—	6	16	no	—
448	C₂×C₄	—	6	16	no	—
449	C₂×C₄	C₂×C₃×D₁₂	1	8	yes	—
450	C₂×C₄	C₂×C₃×D₁₂	1	8	yes	—
451	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
452	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
453	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
454	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
456	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
457	C₂×C₃	—	2	4	no	—
458	C₂×C₃	—	2	4	no	—
459	C₂×C₃	—	2	2	no	—
460	C₂×C₃	—	2	4	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	1	no	—
463	C₂×C₃	—	2	2	no	—
464	C₂×C₃	—	4	4	no	—
465	C₂×C₃	—	12	8	no	—
466	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
467	C₂×C₃	#5964	1	2	yes	—
468	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
469	C₂×C₃	C₃×#585	1	2	yes	—
470	D₃	—	4	8	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	6	8	no	—
475	C₂²	—	6	16	no	—
476	C₂²	—	12	16	no	—
477	C₂²	C₂²×C₃×D₁₂	1	4	yes	—
478	C₂²	C₂²×C₃×D₁₂	1	2	yes	—
479	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
480	C₄	—	2	8	no	—
481	C₄	—	6	8	no	—
482	C₄	C₂²×C₃×D₁₂	1	2	yes	—
483	C₄	C₂²×C₃×D₁₂	1	4	yes	—
484	C₄	C₂²×C₃×D₁₂	1	2	yes	—
485	C₃	—	2	1	no	—
486	C₃	#85735	1	1	yes	characteristic, direct product factor
487	C₃	C₃×#3449	1	1	yes	characteristic, complemented
488	C₂	—	2	4	no	—
489	C₂	—	2	2	no	—
490	C₂	—	12	8	no	—
491	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
492	C₂	C₃×#5964	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#117	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×#117	D₃
hypocenter	C₃	C₃×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#235	C₂	semidirect
2. C₂×C₃²×#117	C₂	semidirect
3. C₃×#5526	C₂	semidirect
4. C₃×#5525	C₂	semidirect
5. C₃×#5524	C₂	semidirect
6. C₃×#5510	C₂	semidirect
7. C₃×#5493	C₂	semidirect
8. C₃×#5477	C₂	semidirect
10. #85735	C₃	direct (N × H)
16. C₂×C₃×#235	C₂²	semidirect
17. C₂×C₃×#235	C₂²	semidirect
18. C₂²×C₃×D₁₂	C₂²	semidirect
19. C₂²×C₃×C₄×D₃	C₂²	semidirect
20. C₂²×C₃×Dic₆	C₂²	semidirect
21. C₃²×#117	C₂²	semidirect
22. C₃²×#117	C₂²	semidirect
23. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
25. C₂×C₃²×C₄²	C₂²	semidirect
26. C₃×#930	C₂²	semidirect
27. C₃×#897	C₂²	semidirect
28. C₃×#895	C₂²	semidirect
29. C₃×#886	C₂²	semidirect
30. C₃×#882	C₂²	semidirect
31. C₃×#875	C₂²	semidirect
32. C₃×#874	C₂²	semidirect
33. C₃×C₄×D₁₂	C₂²	semidirect
34. C₃×#869	C₂²	semidirect
36. C₂²×#235	C₂×C₃	semidirect
44. C₂×C₃×#117	D₃	semidirect
45. C₂×C₃×#117	C₂×C₃	semidirect
46. #5526	C₂×C₃	semidirect
47. #5525	C₂×C₃	semidirect
48. #5524	C₂×C₃	semidirect
49. #5510	C₂×C₃	semidirect
50. #5493	C₂×C₃	semidirect
51. #5477	C₂×C₃	semidirect
54. C₂²×C₃²×C₄	D₄	semidirect
101. C₂×#235	C₂²×C₃	semidirect
102. C₂×#235	C₂²×C₃	semidirect
103. C₂²×D₁₂	C₂²×C₃	semidirect
104. C₂²×C₄×D₃	C₂²×C₃	semidirect
105. C₂²×Dic₆	C₂²×C₃	semidirect
117. C₃×#117	C₂×D₃	semidirect
118. C₃×#117	C₂×D₃	semidirect
119. C₃×#117	C₂²×C₃	semidirect
120. C₃×#117	C₂²×C₃	semidirect
122. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
123. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
128. C₂×C₃×C₄²	C₂×D₃	semidirect
129. C₂×C₃×C₄²	C₂²×C₃	semidirect
130. #930	C₂²×C₃	semidirect
131. #897	C₂²×C₃	semidirect
132. #895	C₂²×C₃	semidirect
133. #886	C₂²×C₃	semidirect
134. #882	C₂²×C₃	semidirect
135. #875	C₂²×C₃	semidirect
136. #874	C₂²×C₃	semidirect
137. C₄×D₁₂	C₂²×C₃	semidirect
138. #869	C₂²×C₃	semidirect
173. C₂×#117	C₃×D₃	semidirect
203. C₂²×C₃×C₄	D₁₂	semidirect
204. C₂²×C₃×C₄	C₃×D₄	semidirect
282. #117	C₂×C₃×D₃	semidirect
283. #117	C₂×C₃×D₃	semidirect
284. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
286. C₂×C₄²	C₂×C₃×D₃	semidirect
379. C₂²×C₄	C₃×D₁₂	semidirect
429. C₃²	#3449	semidirect
486. C₃	#85735	direct (N × H)
487. C₃	C₃×#3449	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×#235	2
C₂×C₃²×#117	2
C₃×#5526	2
C₃×#5525	2
C₃×#5524	2
C₃×#5510	2
C₃×#5493	2
C₃×#5477	2
C₃×#3449	3
#85735	3

Subgroups — C3×#85735 #11901193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85735 #11901193