Subgroups — C₃×#85738 #11901754

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5791	C₂	1	2	yes	maximal, complemented
3	C₃×#5535	C₂	1	2	yes	maximal, complemented
4	C₃×#5534	C₂	1	4	yes	maximal, complemented
5	C₃×#5528	C₂	1	8	yes	maximal, complemented
6	C₃×#5518	C₂	1	2	yes	maximal, complemented
7	C₃×#5515	C₂	1	4	yes	maximal, complemented
8	C₃×#5494	C₂	1	4	yes	maximal, complemented
9	C₃×#5477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×#235	C₂	1	2	yes	maximal, complemented
11	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3455	—	3	1	no	maximal
13	#85738	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#235	C₂²	1	2	yes	—
16	C₃²×#117	C₂²	1	2	yes	—
17	C₃²×#117	C₂²	1	4	yes	—
18	C₃²×#117	C₂²	1	2	yes	—
19	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
23	C₃×#953	C₂²	1	4	yes	—
24	C₃×#930	C₂²	1	4	yes	—
25	C₃×#930	C₂²	1	4	yes	—
26	C₃×#929	C₂²	1	4	yes	—
27	C₃×C₄×#67	C₂²	1	8	yes	—
28	C₃×C₄×#67	C₂²	1	8	yes	—
29	C₃×#926	C₂²	1	2	yes	—
30	C₃×#924	C₂²	1	4	yes	—
31	C₃×#924	C₂²	1	4	yes	—
32	C₃×#898	C₂²	1	8	yes	complemented
33	C₃×#896	C₂²	1	8	yes	complemented
34	C₃×#894	C₂²	1	8	yes	complemented
35	C₃×#889	C₂²	1	8	yes	complemented
36	C₃×#885	C₂²	1	8	yes	—
37	C₃×#884	C₂²	1	8	yes	—
38	C₃×#883	C₂²	1	8	yes	—
39	C₃×#879	C₂²	1	8	yes	—
40	C₃×#875	C₂²	1	2	yes	complemented
41	C₃×#874	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
43	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
44	C₃×#872	C₂²	1	4	yes	complemented
45	C₃×C₄²×D₃	C₂²	1	4	yes	complemented
46	C₃×#870	C₂²	1	2	yes	complemented
47	C₃×#869	C₂²	1	1	yes	characteristic, complemented
48	C₃×#869	C₂²	1	2	yes	complemented
49	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
50	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
51	C₃×#542	—	3	4	no	—
52	C₃×#541	—	3	2	no	—
53	C₃×#540	—	3	2	no	—
54	C₃×#539	—	3	4	no	—
55	C₃×#538	—	3	4	no	—
56	C₃×#533	—	3	1	no	—
57	C₃×#532	—	3	1	no	—
58	C₃×#529	—	3	8	no	—
59	C₃×#525	—	3	2	no	—
60	C₃×C₄×#41	—	3	2	no	—
61	C₂×C₃×#117	—	2	1	no	—
62	C₂×C₃×#117	D₃	1	1	yes	characteristic, complemented
63	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
64	#5791	C₂×C₃	1	2	yes	complemented
65	#5535	C₂×C₃	1	2	yes	complemented
66	#5534	C₂×C₃	1	4	yes	complemented
67	#5528	C₂×C₃	1	8	yes	complemented
68	#5518	C₂×C₃	1	2	yes	complemented
69	#5515	C₂×C₃	1	4	yes	complemented
70	#5494	C₂×C₃	1	4	yes	complemented
71	#5477	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×#235	C₂×C₃	1	2	yes	complemented
73	#5470	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
75	C₂²×C₃²×C₄	—	2	4	no	—
76	C₂²×C₃²×C₄	C₂³	1	2	yes	—
77	C₂²×C₃²×C₄	C₂³	1	2	yes	—
78	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂³	1	2	yes	—
80	C₂²×C₃²×C₄	C₂³	1	2	yes	—
81	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×#67	C₂³	1	4	yes	—
83	C₂×C₃×#67	C₂³	1	8	yes	—
84	C₃×#235	—	2	8	no	—
85	C₂×C₃×D₁₂	C₂³	1	2	yes	—
86	C₂×C₃×D₁₂	C₂³	1	4	yes	—
87	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
88	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
89	C₂×C₃×Dic₆	C₂³	1	2	yes	—
90	C₂×C₃×Dic₆	C₂³	1	4	yes	—
91	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
92	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
93	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₃²×C₄²	C₂³	1	2	yes	—
96	C₃²×C₄²	C₂³	1	2	yes	—
97	C₃²×C₄²	C₂³	1	1	yes	characteristic
98	C₃²×C₄²	C₂³	1	1	yes	characteristic
99	C₃²×C₄²	C₂³	1	2	yes	—
100	C₃×#217	C₂³	1	8	yes	—
101	C₃×#217	C₂³	1	4	yes	—
102	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
103	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
105	C₃×C₄⋊Dic₃	C₂³	1	4	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	8	yes	—
112	C₃×C₄×Dic₃	C₂³	1	4	yes	—
113	#3455	—	3	1	no	Sylow
114	C₂×C₃×#41	—	3	2	no	—
115	C₂³×C₃×C₄	—	2	1	no	—
116	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×#235	C₂²×C₃	1	2	yes	—
119	C₃×C₄⋊Q₈	—	3	1	no	—
120	C₃×C₄⋊Q₈	—	3	2	no	—
121	C₃×#127	—	3	1	no	—
122	C₃×#126	—	3	8	no	—
123	C₃×#126	—	3	8	no	—
124	C₃×#125	—	3	8	no	—
125	C₃×#125	—	3	2	no	—
126	C₃×#124	—	3	8	no	—
127	C₃×#124	—	3	2	no	—
128	C₃×#123	—	3	4	no	—
129	C₃×#123	—	3	8	no	—
130	C₃×#123	—	3	8	no	—
131	C₃×C₂²⋊Q₈	—	3	4	no	—
132	C₃×C₂²⋊Q₈	—	3	4	no	—
133	C₃×C₂²⋊Q₈	—	3	8	no	—
134	C₃×#121	—	3	4	no	—
135	C₃×#121	—	3	4	no	—
136	C₃×#121	—	3	8	no	—
137	C₃×#120	—	3	4	no	—
138	C₃×C₄×Q₈	—	3	4	no	—
139	C₃×C₄×Q₈	—	3	4	no	—
140	C₃×C₄×D₄	—	3	8	no	—
141	C₃×C₄×D₄	—	3	8	no	—
142	C₃×C₄×D₄	—	3	4	no	—
143	C₃×C₄×D₄	—	3	4	no	—
144	C₃×#117	—	2	4	no	—
145	C₃×#117	—	2	2	no	—
146	C₃×#117	—	2	2	no	—
147	C₃×#117	—	3	2	no	—
148	C₃×#117	—	3	4	no	—
149	C₃×#117	C₂×D₃	1	4	yes	—
150	C₃×#117	C₂×D₃	1	2	yes	—
151	C₃×#117	C₂×D₃	1	2	yes	—
152	C₃×#117	C₂²×C₃	1	2	yes	—
153	C₃×#117	C₂²×C₃	1	4	yes	—
154	C₃×#117	C₂²×C₃	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	—	2	2	no	—
156	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
161	C₂×C₃×C₄²	—	2	1	no	—
162	C₂×C₃×C₄²	—	2	1	no	—
163	C₂×C₃×C₄²	—	3	4	no	—
164	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
168	#953	C₂²×C₃	1	4	yes	—
169	#930	C₂²×C₃	1	4	yes	—
170	#930	C₂²×C₃	1	4	yes	—
171	#929	C₂²×C₃	1	4	yes	—
172	C₄×#67	C₂²×C₃	1	8	yes	—
173	C₄×#67	C₂²×C₃	1	8	yes	—
174	#926	C₂²×C₃	1	2	yes	—
175	#924	C₂²×C₃	1	4	yes	—
176	#924	C₂²×C₃	1	4	yes	—
177	#898	C₂²×C₃	1	8	yes	complemented
178	#896	C₂²×C₃	1	8	yes	complemented
179	#894	C₂²×C₃	1	8	yes	complemented
180	#889	C₂²×C₃	1	8	yes	complemented
181	#885	C₂²×C₃	1	8	yes	—
182	#884	C₂²×C₃	1	8	yes	—
183	#883	C₂²×C₃	1	8	yes	—
184	#879	C₂²×C₃	1	8	yes	—
185	#875	C₂²×C₃	1	2	yes	complemented
186	#874	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
188	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
189	#872	C₂²×C₃	1	4	yes	complemented
190	C₄²×D₃	C₂²×C₃	1	4	yes	complemented
191	#870	C₂²×C₃	1	2	yes	complemented
192	#869	C₂²×C₃	1	2	yes	complemented
193	#869	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
195	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
196	C₂³×C₃²	—	2	2	no	—
197	C₂³×C₃²	—	4	2	no	—
198	C₂³×C₃²	C₂⁴	1	2	yes	—
199	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
200	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
201	C₂×C₃²×C₄	—	2	2	no	—
202	C₂×C₃²×C₄	—	2	4	no	—
203	C₂×C₃²×C₄	—	2	4	no	—
204	C₂×C₃²×C₄	—	4	2	no	—
205	C₂×C₃²×C₄	—	4	2	no	—
206	C₂×C₃²×C₄	#41	1	4	yes	—
207	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
208	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
209	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
210	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
211	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
212	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
213	C₃×#67	—	2	8	no	—
214	C₃×#67	—	4	8	no	—
215	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
216	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
217	C₃×D₁₂	—	2	4	no	—
218	C₃×D₁₂	—	4	4	no	—
219	C₃×C₄×D₃	—	2	8	no	—
220	C₃×C₄×D₃	—	4	8	no	—
221	C₃×Dic₆	—	2	4	no	—
222	C₃×Dic₆	—	4	4	no	—
223	#542	—	3	4	no	—
224	#541	—	3	2	no	—
225	#540	—	3	2	no	—
226	#539	—	3	4	no	—
227	#538	—	3	4	no	—
228	#533	—	3	1	no	—
229	#532	—	3	1	no	—
230	#529	—	3	8	no	—
231	#525	—	3	2	no	—
232	C₄×#41	—	3	2	no	—
233	C₂×#117	C₃×D₃	1	1	yes	characteristic, complemented
234	C₂⁴×C₃	—	2	1	no	—
235	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
236	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
237	C₃×#41	—	6	8	no	—
238	C₂×C₃×Q₈	—	3	2	no	—
239	C₂×C₃×Q₈	—	3	4	no	—
240	C₂×C₃×D₄	—	3	4	no	—
241	C₂×C₃×D₄	—	3	8	no	—
242	C₂×C₃×D₄	—	3	2	no	—
243	C₂×C₃×D₄	—	3	4	no	—
244	C₂²×C₃×C₄	—	2	8	no	—
245	C₂²×C₃×C₄	—	2	4	no	—
246	C₂²×C₃×C₄	—	2	4	no	—
247	C₂²×C₃×C₄	—	2	1	no	—
248	C₂²×C₃×C₄	—	2	1	no	—
249	C₂²×C₃×C₄	—	2	2	no	—
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	3	4	no	—
254	C₂²×C₃×C₄	—	3	8	no	—
255	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
257	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
258	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
259	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
260	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
262	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
263	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
266	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
267	C₂×#67	C₂³×C₃	1	4	yes	—
268	C₂×#67	C₂³×C₃	1	8	yes	—
269	#235	—	2	8	no	—
270	C₂×D₁₂	C₂³×C₃	1	2	yes	—
271	C₂×D₁₂	C₂³×C₃	1	4	yes	—
272	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
273	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
274	C₂×Dic₆	C₂³×C₃	1	2	yes	—
275	C₂×Dic₆	C₂³×C₃	1	4	yes	—
276	C₃×C₄⋊C₄	—	2	4	no	—
277	C₃×C₄⋊C₄	—	2	4	no	—
278	C₃×C₄⋊C₄	—	3	8	no	—
279	C₃×C₄⋊C₄	—	3	8	no	—
280	C₃×C₄⋊C₄	—	3	8	no	—
281	C₃×C₄⋊C₄	—	3	4	no	—
282	C₃×C₄⋊C₄	—	3	4	no	—
283	C₃×C₄⋊C₄	—	3	4	no	—
284	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
285	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
286	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
287	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
288	C₃×C₂²⋊C₄	—	2	4	no	—
289	C₃×C₂²⋊C₄	—	2	4	no	—
290	C₃×C₂²⋊C₄	—	3	4	no	—
291	C₃×C₂²⋊C₄	—	3	8	no	—
292	C₃×C₂²⋊C₄	—	3	8	no	—
293	C₃×C₂²⋊C₄	—	3	8	no	—
294	C₃×C₂²⋊C₄	—	3	8	no	—
295	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
296	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
297	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
298	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
299	C₃×C₄²	—	2	2	no	—
300	C₃×C₄²	—	2	2	no	—
301	C₃×C₄²	—	2	2	no	—
302	C₃×C₄²	—	2	1	no	—
303	C₃×C₄²	—	2	1	no	—
304	C₃×C₄²	—	3	8	no	—
305	C₃×C₄²	—	3	4	no	—
306	C₃×C₄²	C₂²×D₃	1	2	yes	—
307	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
308	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
309	C₃×C₄²	C₂²×D₃	1	2	yes	—
310	C₃×C₄²	C₂²×D₃	1	2	yes	—
311	C₃×C₄²	C₂³×C₃	1	2	yes	—
312	C₃×C₄²	C₂³×C₃	1	2	yes	—
313	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
314	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
315	C₃×C₄²	C₂³×C₃	1	2	yes	—
316	#217	C₂³×C₃	1	8	yes	—
317	#217	C₂³×C₃	1	4	yes	—
318	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
320	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
321	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
322	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
323	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
324	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
325	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
326	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
327	C₄×Dic₃	C₂³×C₃	1	4	yes	—
328	C₄×Dic₃	C₂³×C₃	1	8	yes	—
329	C₂²×C₃²	—	2	2	no	—
330	C₂²×C₃²	—	2	2	no	—
331	C₂²×C₃²	—	2	4	no	—
332	C₂²×C₃²	—	4	4	no	—
333	C₂²×C₃²	C₂×#41	1	2	yes	—
334	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
335	C₂×C₃×D₃	—	2	4	no	—
336	C₂×C₃×D₃	—	2	8	no	—
337	C₃²×C₄	—	2	2	no	—
338	C₃²×C₄	—	2	2	no	—
339	C₃²×C₄	—	2	4	no	—
340	C₃²×C₄	—	2	2	no	—
341	C₃²×C₄	C₂×#41	1	2	yes	—
342	C₃²×C₄	C₂×#41	1	2	yes	—
343	C₃×Dic₃	—	2	4	no	—
344	C₃×Dic₃	—	2	8	no	—
345	C₂×#41	—	3	2	no	—
346	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	3	1	no	—
348	C₄⋊Q₈	—	3	2	no	—
349	#127	—	3	1	no	—
350	#126	—	3	8	no	—
351	#126	—	3	8	no	—
352	#125	—	3	8	no	—
353	#125	—	3	2	no	—
354	#124	—	3	8	no	—
355	#124	—	3	2	no	—
356	#123	—	3	4	no	—
357	#123	—	3	8	no	—
358	#123	—	3	8	no	—
359	C₂²⋊Q₈	—	3	4	no	—
360	C₂²⋊Q₈	—	3	4	no	—
361	C₂²⋊Q₈	—	3	8	no	—
362	#121	—	3	4	no	—
363	#121	—	3	4	no	—
364	#121	—	3	8	no	—
365	#120	—	3	4	no	—
366	C₄×Q₈	—	3	4	no	—
367	C₄×Q₈	—	3	4	no	—
368	C₄×D₄	—	3	8	no	—
369	C₄×D₄	—	3	8	no	—
370	C₄×D₄	—	3	4	no	—
371	C₄×D₄	—	3	4	no	—
372	#117	—	3	2	no	—
373	#117	—	3	4	no	—
374	#117	C₂×C₃×D₃	1	4	yes	—
375	#117	C₂×C₃×D₃	1	2	yes	—
376	#117	C₂×C₃×D₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
379	C₂×C₄²	—	3	4	no	—
380	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
381	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
382	C₂³×C₃	—	2	4	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	2	no	—
387	C₂³×C₃	—	3	4	no	—
388	C₂³×C₃	—	4	2	no	—
389	C₂³×C₃	—	4	2	no	—
390	C₂³×C₃	—	4	4	no	—
391	C₂³×C₃	C₂³×D₃	1	2	yes	—
392	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
393	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
394	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
395	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
396	C₃×Q₈	—	6	4	no	—
397	C₃×Q₈	—	12	4	no	—
398	C₃×D₄	—	6	8	no	—
399	C₃×D₄	—	6	4	no	—
400	C₃×D₄	—	12	4	no	—
401	C₃×D₄	—	12	8	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	8	no	—
404	C₂×C₃×C₄	—	2	8	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	4	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	4	no	—
418	C₂×C₃×C₄	—	3	4	no	—
419	C₂×C₃×C₄	—	3	8	no	—
420	C₂×C₃×C₄	—	4	2	no	—
421	C₂×C₃×C₄	—	4	2	no	—
422	C₂×C₃×C₄	—	4	2	no	—
423	C₂×C₃×C₄	—	4	2	no	—
424	C₂×C₃×C₄	—	4	4	no	—
425	C₂×C₃×C₄	—	4	4	no	—
426	C₂×C₃×C₄	—	6	8	no	—
427	C₂×C₃×C₄	—	12	8	no	—
428	C₂×C₃×C₄	#235	1	4	yes	—
429	C₂×C₃×C₄	C₃×#41	1	4	yes	—
430	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
431	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
432	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
433	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
434	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
437	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
438	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
439	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
440	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
442	#67	—	2	8	no	—
443	#67	—	4	8	no	—
444	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
445	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
446	D₁₂	—	2	4	no	—
447	D₁₂	—	4	4	no	—
448	C₄×D₃	—	2	8	no	—
449	C₄×D₃	—	4	8	no	—
450	Dic₆	—	2	4	no	—
451	Dic₆	—	4	4	no	—
452	C₂×C₃²	—	2	2	no	—
453	C₂×C₃²	—	4	2	no	—
454	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
455	C₂×C₃²	#585	1	2	yes	—
456	C₃×D₃	—	4	4	no	—
457	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
458	#41	—	6	8	no	—
459	C₂×Q₈	—	3	2	no	—
460	C₂×Q₈	—	3	4	no	—
461	C₂×D₄	—	3	4	no	—
462	C₂×D₄	—	3	8	no	—
463	C₂×D₄	—	3	2	no	—
464	C₂×D₄	—	3	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	3	4	no	—
467	C₂²×C₄	—	3	8	no	—
468	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
470	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
471	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
472	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
473	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₄⋊C₄	—	3	4	no	—
475	C₄⋊C₄	—	3	8	no	—
476	C₄⋊C₄	—	3	4	no	—
477	C₄⋊C₄	—	3	8	no	—
478	C₄⋊C₄	—	3	8	no	—
479	C₄⋊C₄	—	3	4	no	—
480	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
481	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
482	C₂²⋊C₄	—	3	4	no	—
483	C₂²⋊C₄	—	3	8	no	—
484	C₂²⋊C₄	—	3	8	no	—
485	C₂²⋊C₄	—	3	8	no	—
486	C₂²⋊C₄	—	3	8	no	—
487	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
488	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
489	C₄²	—	3	4	no	—
490	C₄²	—	3	8	no	—
491	C₄²	C₂²×C₃×D₃	1	2	yes	—
492	C₄²	C₂²×C₃×D₃	1	2	yes	—
493	C₄²	C₂²×C₃×D₃	1	2	yes	—
494	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
495	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
496	C₂²×C₃	—	2	4	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	4	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	4	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	4	4	no	—
507	C₂²×C₃	—	4	8	no	—
508	C₂²×C₃	—	4	4	no	—
509	C₂²×C₃	—	4	4	no	—
510	C₂²×C₃	—	6	4	no	—
511	C₂²×C₃	—	6	8	no	—
512	C₂²×C₃	C₂×#235	1	2	yes	—
513	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
514	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
515	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
516	C₂×D₃	—	2	4	no	—
517	C₂×D₃	—	2	8	no	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	4	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	4	no	—
526	C₃×C₄	—	2	2	no	—
527	C₃×C₄	—	2	2	no	—
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	4	4	no	—
530	C₃×C₄	—	4	2	no	—
531	C₃×C₄	—	4	2	no	—
532	C₃×C₄	—	6	4	no	—
533	C₃×C₄	—	6	8	no	—
534	C₃×C₄	C₂×#235	1	2	yes	—
535	C₃×C₄	C₂×#235	1	2	yes	—
536	C₃×C₄	C₂×C₃×#41	1	2	yes	—
537	C₃×C₄	C₂×C₃×#41	1	2	yes	—
538	Dic₃	—	2	4	no	—
539	Dic₃	—	2	8	no	—
540	C₃²	#3455	1	1	yes	characteristic, complemented, Sylow
541	C₂³	—	2	2	no	—
542	C₂³	—	3	4	no	—
543	C₂³	—	4	2	no	—
544	C₂³	C₂³×C₃×D₃	1	2	yes	—
545	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
546	Q₈	—	6	4	no	—
547	Q₈	—	12	4	no	—
548	D₄	—	6	8	no	—
549	D₄	—	6	4	no	—
550	D₄	—	12	4	no	—
551	D₄	—	12	8	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	3	4	no	—
556	C₂×C₄	—	3	8	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	6	8	no	—
560	C₂×C₄	—	12	8	no	—
561	C₂×C₄	C₃×#235	1	4	yes	—
562	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
563	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
564	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
565	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
566	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
568	C₂×C₃	—	2	4	no	—
569	C₂×C₃	—	2	2	no	—
570	C₂×C₃	—	2	2	no	—
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	2	2	no	—
573	C₂×C₃	—	4	4	no	—
574	C₂×C₃	—	4	2	no	—
575	C₂×C₃	—	4	2	no	—
576	C₂×C₃	—	12	4	no	—
577	C₂×C₃	C₂²×#235	1	1	yes	characteristic
578	C₂×C₃	#5964	1	2	yes	—
579	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
580	C₂×C₃	C₃×#585	1	2	yes	—
581	D₃	—	4	4	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	6	4	no	—
587	C₂²	—	6	8	no	—
588	C₂²	C₂×C₃×#235	1	2	yes	—
589	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	6	4	no	—
595	C₄	—	6	8	no	—
596	C₄	C₂×C₃×#235	1	2	yes	—
597	C₄	C₂×C₃×#235	1	2	yes	—
598	C₃	—	2	1	no	—
599	C₃	#85738	1	1	yes	characteristic, direct product factor
600	C₃	C₃×#3455	1	1	yes	characteristic, complemented
601	C₂	—	2	2	no	—
602	C₂	—	4	2	no	—
603	C₂	—	12	4	no	—
604	C₂	C₂²×C₃×#235	1	1	yes	characteristic
605	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×#3455
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. C₂×C₃²×#117	C₂	semidirect
2. C₃×#5791	C₂	semidirect
3. C₃×#5535	C₂	semidirect
4. C₃×#5534	C₂	semidirect
5. C₃×#5528	C₂	semidirect
6. C₃×#5518	C₂	semidirect
7. C₃×#5515	C₂	semidirect
8. C₃×#5494	C₂	semidirect
9. C₃×#5477	C₂	semidirect
10. C₃×C₄×#235	C₂	semidirect
11. C₃×#5470	C₂	semidirect
13. #85738	C₃	direct (N × H)
32. C₃×#898	C₂²	semidirect
33. C₃×#896	C₂²	semidirect
34. C₃×#894	C₂²	semidirect
35. C₃×#889	C₂²	semidirect
40. C₃×#875	C₂²	semidirect
41. C₃×#874	C₂²	semidirect
42. C₃×C₄×D₁₂	C₂²	semidirect
43. C₃×C₄×D₁₂	C₂²	semidirect
44. C₃×#872	C₂²	semidirect
45. C₃×C₄²×D₃	C₂²	semidirect
46. C₃×#870	C₂²	semidirect
47. C₃×#869	C₂²	semidirect
48. C₃×#869	C₂²	semidirect
49. C₃×C₄×Dic₆	C₂²	semidirect
50. C₃×C₄×Dic₆	C₂²	semidirect
62. C₂×C₃×#117	D₃	semidirect
63. C₂×C₃×#117	C₂×C₃	semidirect
64. #5791	C₂×C₃	semidirect
65. #5535	C₂×C₃	semidirect
66. #5534	C₂×C₃	semidirect
67. #5528	C₂×C₃	semidirect
68. #5518	C₂×C₃	semidirect
69. #5515	C₂×C₃	semidirect
70. #5494	C₂×C₃	semidirect
71. #5477	C₂×C₃	semidirect
72. C₄×#235	C₂×C₃	semidirect
73. #5470	C₂×C₃	semidirect
177. #898	C₂²×C₃	semidirect
178. #896	C₂²×C₃	semidirect
179. #894	C₂²×C₃	semidirect
180. #889	C₂²×C₃	semidirect
185. #875	C₂²×C₃	semidirect
186. #874	C₂²×C₃	semidirect
187. C₄×D₁₂	C₂²×C₃	semidirect
188. C₄×D₁₂	C₂²×C₃	semidirect
189. #872	C₂²×C₃	semidirect
190. C₄²×D₃	C₂²×C₃	semidirect
191. #870	C₂²×C₃	semidirect
192. #869	C₂²×C₃	semidirect
193. #869	C₂²×C₃	semidirect
194. C₄×Dic₆	C₂²×C₃	semidirect
195. C₄×Dic₆	C₂²×C₃	semidirect
233. C₂×#117	C₃×D₃	semidirect
540. C₃²	#3455	semidirect
599. C₃	#85738	direct (N × H)
600. C₃	C₃×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#117	2
C₃×#5791	2
C₃×#5535	2
C₃×#5534	2
C₃×#5528	2
C₃×#5518	2
C₃×#5515	2
C₃×#5494	2
C₃×#5477	2
C₃×C₄×#235	2
C₃×#5470	2
C₃×#3455	3
#85738	3

Subgroups — C3×#85738 #11901754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85738 #11901754