Subgroups — C₃×#5527 #10595624

Order 576.

534 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#929	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#882	C₂	1	1	yes	maximal, characteristic
9	C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#876	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#551	—	3	1	no	maximal
17	#5527	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂³×C₃×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
34	C₃×#217	C₂²	1	1	yes	characteristic
35	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃×#126	—	3	1	no	—
54	C₃×#126	—	3	1	no	—
55	C₃×#124	—	3	1	no	—
56	C₃×#123	—	3	1	no	—
57	C₃×#123	—	3	1	no	—
58	C₃×#123	—	3	1	no	—
59	C₃×C₂²⋊Q₈	—	3	1	no	—
60	C₃×C₂²⋊Q₈	—	3	1	no	—
61	C₃×#120	—	3	1	no	—
62	C₃×C₄×D₄	—	3	1	no	—
63	C₃×C₄×D₄	—	3	1	no	—
64	C₃×#117	—	2	1	no	—
65	C₃×#117	—	3	1	no	—
66	C₃×#117	D₃	1	1	yes	characteristic, complemented
67	C₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
69	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
70	#929	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
72	#898	C₂×C₃	1	1	yes	characteristic, complemented
73	#896	C₂×C₃	1	1	yes	characteristic, complemented
74	#894	C₂×C₃	1	1	yes	characteristic, complemented
75	#894	C₂×C₃	1	1	yes	characteristic, complemented
76	#882	C₂×C₃	1	1	yes	characteristic
77	#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
78	D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
79	#878	C₂×C₃	1	1	yes	characteristic, complemented
80	#876	C₂×C₃	1	1	yes	characteristic, complemented
81	#875	C₂×C₃	1	1	yes	characteristic, complemented
82	C₄×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
83	#872	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×C₃²	C₂³	1	1	yes	characteristic
85	C₂²×C₃×D₃	—	2	2	no	—
86	C₂²×C₃×D₃	—	2	2	no	—
87	C₂²×C₃×D₃	—	4	1	no	—
88	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
89	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
98	C₃×#67	—	2	2	no	—
99	C₂×C₃×Dic₃	—	4	1	no	—
100	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
102	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
103	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
104	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
105	C₃×D₁₂	—	2	2	no	—
106	C₃×D₁₂	—	4	1	no	—
107	C₃×C₄×D₃	—	2	2	no	—
108	C₃×C₄×D₃	—	4	1	no	—
109	C₃×C₄×D₃	—	4	1	no	—
110	C₃×Dic₆	—	4	1	no	—
111	#551	—	3	1	no	Sylow
112	C₂⁴×C₃	—	3	1	no	—
113	C₂³×D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×Q₈	—	3	1	no	—
115	C₂×C₃×D₄	—	3	1	no	—
116	C₂×C₃×D₄	—	3	1	no	—
117	C₂×C₃×D₄	—	3	1	no	—
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	3	1	no	—
120	C₂²×C₃×C₄	—	3	1	no	—
121	C₂²×C₃×C₄	—	3	1	no	—
122	C₂²×C₃×C₄	—	3	1	no	—
123	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
124	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×#67	C₂²×C₃	1	1	yes	characteristic
126	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
127	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
128	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₃×C₄⋊C₄	—	2	1	no	—
134	C₃×C₄⋊C₄	—	2	1	no	—
135	C₃×C₄⋊C₄	—	3	1	no	—
136	C₃×C₄⋊C₄	—	3	1	no	—
137	C₃×C₄⋊C₄	—	3	1	no	—
138	C₃×C₄⋊C₄	—	3	1	no	—
139	C₃×C₄⋊C₄	—	3	1	no	—
140	C₃×C₄⋊C₄	—	3	1	no	—
141	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
142	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
143	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₃×C₂²⋊C₄	—	2	1	no	—
146	C₃×C₂²⋊C₄	—	2	1	no	—
147	C₃×C₂²⋊C₄	—	3	1	no	—
148	C₃×C₂²⋊C₄	—	3	1	no	—
149	C₃×C₂²⋊C₄	—	3	1	no	—
150	C₃×C₂²⋊C₄	—	3	1	no	—
151	C₃×C₂²⋊C₄	—	3	1	no	—
152	C₃×C₂²⋊C₄	—	3	1	no	—
153	C₃×C₂²⋊C₄	—	3	1	no	—
154	C₃×C₂²⋊C₄	—	3	1	no	—
155	C₃×C₂²⋊C₄	—	3	1	no	—
156	C₃×C₂²⋊C₄	—	3	1	no	—
157	C₃×C₂²⋊C₄	—	3	1	no	—
158	C₃×C₂²⋊C₄	—	3	1	no	—
159	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
160	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
161	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₃×C₄²	—	2	1	no	—
164	C₃×C₄²	—	2	1	no	—
165	C₃×C₄²	—	3	1	no	—
166	C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
167	C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
168	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
170	#217	C₂²×C₃	1	1	yes	characteristic
171	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
180	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
181	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
183	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
184	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
185	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
186	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	#41	1	2	yes	—
192	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	1	no	—
194	C₂×C₃×D₃	—	2	1	no	—
195	C₂×C₃×D₃	—	2	1	no	—
196	C₂×C₃×D₃	—	2	1	no	—
197	C₂×C₃×D₃	—	2	1	no	—
198	C₂×C₃×D₃	—	2	1	no	—
199	C₂×C₃×D₃	—	2	1	no	—
200	C₂×C₃×D₃	—	2	1	no	—
201	C₂×C₃×D₃	—	4	4	no	—
202	C₂×C₃×D₃	#41	1	2	yes	—
203	C₃²×C₄	—	2	1	no	—
204	C₃²×C₄	—	2	1	no	—
205	C₃²×C₄	—	2	1	no	—
206	C₃²×C₄	—	2	1	no	—
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃×Dic₃	—	2	1	no	—
210	C₃×Dic₃	—	2	1	no	—
211	C₃×Dic₃	—	2	1	no	—
212	C₃×Dic₃	—	2	1	no	—
213	C₃×Dic₃	—	2	1	no	—
214	#126	—	3	1	no	—
215	#126	—	3	1	no	—
216	#124	—	3	1	no	—
217	#123	—	3	1	no	—
218	#123	—	3	1	no	—
219	#123	—	3	1	no	—
220	C₂²⋊Q₈	—	3	1	no	—
221	C₂²⋊Q₈	—	3	1	no	—
222	#120	—	3	1	no	—
223	C₄×D₄	—	3	1	no	—
224	C₄×D₄	—	3	1	no	—
225	#117	—	3	1	no	—
226	#117	C₃×D₃	1	1	yes	characteristic, complemented
227	C₂×C₂²⋊C₄	—	3	1	no	—
228	C₂×C₂²⋊C₄	—	3	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	3	1	no	—
231	C₂³×C₃	—	3	1	no	—
232	C₂³×C₃	—	3	1	no	—
233	C₂³×C₃	—	6	2	no	—
234	C₂³×C₃	—	6	2	no	—
235	C₂³×C₃	—	12	1	no	—
236	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
237	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
238	C₂²×D₃	—	2	2	no	—
239	C₂²×D₃	—	2	2	no	—
240	C₂²×D₃	—	4	1	no	—
241	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
242	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
243	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
244	C₃×Q₈	—	12	1	no	—
245	C₃×D₄	—	6	2	no	—
246	C₃×D₄	—	6	2	no	—
247	C₃×D₄	—	12	1	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	3	1	no	—
258	C₂×C₃×C₄	—	3	1	no	—
259	C₂×C₃×C₄	—	3	1	no	—
260	C₂×C₃×C₄	—	3	1	no	—
261	C₂×C₃×C₄	—	3	1	no	—
262	C₂×C₃×C₄	—	6	2	no	—
263	C₂×C₃×C₄	—	12	1	no	—
264	C₂×C₃×C₄	—	12	1	no	—
265	C₂×C₃×C₄	—	12	1	no	—
266	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
278	#67	—	2	2	no	—
279	C₂×Dic₃	—	4	1	no	—
280	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
281	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
282	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
283	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
284	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
285	D₁₂	—	2	2	no	—
286	D₁₂	—	4	1	no	—
287	C₄×D₃	—	2	2	no	—
288	C₄×D₃	—	4	1	no	—
289	C₄×D₃	—	4	1	no	—
290	Dic₆	—	4	1	no	—
291	C₂×C₃²	—	2	2	no	—
292	C₂×C₃²	C₂×#41	1	1	yes	characteristic
293	C₂×C₃²	C₂×#41	1	1	yes	characteristic
294	C₂×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
295	C₃×D₃	—	2	2	no	—
296	C₃×D₃	—	4	1	no	—
297	C₃×D₃	—	4	1	no	—
298	C₂⁴	—	3	1	no	—
299	C₂×Q₈	—	3	1	no	—
300	C₂×D₄	—	3	1	no	—
301	C₂×D₄	—	3	1	no	—
302	C₂×D₄	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	—	3	1	no	—
307	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
308	C₄⋊C₄	—	3	1	no	—
309	C₄⋊C₄	—	3	1	no	—
310	C₄⋊C₄	—	3	1	no	—
311	C₄⋊C₄	—	3	1	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	—	3	1	no	—
314	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
315	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
316	C₂²⋊C₄	—	3	1	no	—
317	C₂²⋊C₄	—	3	1	no	—
318	C₂²⋊C₄	—	3	1	no	—
319	C₂²⋊C₄	—	3	1	no	—
320	C₂²⋊C₄	—	3	1	no	—
321	C₂²⋊C₄	—	3	1	no	—
322	C₂²⋊C₄	—	3	1	no	—
323	C₂²⋊C₄	—	3	1	no	—
324	C₂²⋊C₄	—	3	1	no	—
325	C₂²⋊C₄	—	3	1	no	—
326	C₂²⋊C₄	—	3	1	no	—
327	C₂²⋊C₄	—	3	1	no	—
328	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
330	C₄²	—	3	1	no	—
331	C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
332	C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	3	2	no	—
340	C₂²×C₃	—	4	1	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	—	6	1	no	—
343	C₂²×C₃	—	6	1	no	—
344	C₂²×C₃	—	6	1	no	—
345	C₂²×C₃	—	6	1	no	—
346	C₂²×C₃	—	6	1	no	—
347	C₂²×C₃	—	6	1	no	—
348	C₂²×C₃	—	6	1	no	—
349	C₂²×C₃	—	6	1	no	—
350	C₂²×C₃	—	12	4	no	—
351	C₂²×C₃	#235	1	2	yes	—
352	C₂²×C₃	C₃×#41	1	2	yes	—
353	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
354	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
355	C₂×D₃	—	2	1	no	—
356	C₂×D₃	—	2	1	no	—
357	C₂×D₃	—	2	1	no	—
358	C₂×D₃	—	2	1	no	—
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	2	1	no	—
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	—	4	4	no	—
364	C₂×D₃	C₃×#41	1	2	yes	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	4	1	no	—
380	C₃×C₄	—	4	1	no	—
381	C₃×C₄	—	4	1	no	—
382	C₃×C₄	—	4	1	no	—
383	C₃×C₄	—	6	1	no	—
384	C₃×C₄	—	6	1	no	—
385	C₃×C₄	—	6	1	no	—
386	C₃×C₄	—	6	1	no	—
387	C₃×C₄	—	6	1	no	—
388	Dic₃	—	2	1	no	—
389	Dic₃	—	2	1	no	—
390	Dic₃	—	2	1	no	—
391	Dic₃	—	2	1	no	—
392	Dic₃	—	2	1	no	—
393	C₃²	#551	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	3	1	no	—
395	C₂³	—	3	1	no	—
396	C₂³	—	3	1	no	—
397	C₂³	—	6	2	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	12	1	no	—
400	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
401	Q₈	—	12	1	no	—
402	D₄	—	6	2	no	—
403	D₄	—	6	2	no	—
404	D₄	—	12	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	3	1	no	—
407	C₂×C₄	—	3	1	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	3	1	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	12	1	no	—
413	C₂×C₄	—	12	1	no	—
414	C₂×C₄	—	12	1	no	—
415	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	2	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	2	1	no	—
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	—	6	2	no	—
428	C₂×C₃	—	12	1	no	—
429	C₂×C₃	—	12	1	no	—
430	C₂×C₃	C₂×#235	1	1	yes	characteristic
431	C₂×C₃	D₃×#41	1	1	yes	characteristic
432	C₂×C₃	#1009	1	1	yes	characteristic
433	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
434	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
435	C₂×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
436	D₃	—	2	2	no	—
437	D₃	—	4	1	no	—
438	D₃	—	4	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	3	2	no	—
442	C₂²	—	6	1	no	—
443	C₂²	—	6	1	no	—
444	C₂²	—	6	1	no	—
445	C₂²	—	6	1	no	—
446	C₂²	—	6	1	no	—
447	C₂²	—	6	1	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	—	12	4	no	—
451	C₂²	C₃×#235	1	2	yes	—
452	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	6	1	no	—
460	C₄	—	6	1	no	—
461	C₄	—	6	1	no	—
462	C₄	—	6	1	no	—
463	C₄	—	6	1	no	—
464	C₃	—	2	1	no	—
465	C₃	#5527	1	1	yes	characteristic, direct product factor
466	C₃	C₃×#551	1	1	yes	characteristic, complemented
467	C₂	—	2	2	no	—
468	C₂	—	6	2	no	—
469	C₂	—	12	1	no	—
470	C₂	—	12	1	no	—
471	C₂	C₂×C₃×#235	1	1	yes	characteristic
472	C₂	C₃×D₃×#41	1	1	yes	characteristic
473	C₂	C₃×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#117	C₂
socle	C₂²×C₃²	C₂⁴
prime radical	C₃×#882	C₂
hypercenter	C₃×#117	D₃
hypocenter	C₃	C₃×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₃²×#117	C₂	semidirect
2. C₃×#929	C₂	semidirect
3. C₂×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
4. C₃×#898	C₂	semidirect
5. C₃×#896	C₂	semidirect
6. C₃×#894	C₂	semidirect
7. C₃×#894	C₂	semidirect
9. C₃×#67⋊C₄	C₂	semidirect
10. C₃×D₃×C₂²⋊C₄	C₂	semidirect
11. C₃×#878	C₂	semidirect
12. C₃×#876	C₂	semidirect
13. C₃×#875	C₂	semidirect
14. C₃×C₄×D₁₂	C₂	semidirect
15. C₃×#872	C₂	semidirect
17. #5527	C₃	direct (N × H)
26. C₂×C₃×C₄×D₃	C₂²	semidirect
27. C₂×C₃×Dic₆	C₂²	semidirect
28. C₃²×C₄⋊C₄	C₂²	semidirect
29. C₃²×C₄⋊C₄	C₂²	semidirect
32. C₃²×C₄²	C₂²	semidirect
33. C₃²×C₄²	C₂²	semidirect
43. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₃×C₄⋊Dic₃	C₂²	semidirect
47. C₃×Dic₃⋊C₄	C₂²	semidirect
48. C₃×Dic₃⋊C₄	C₂²	semidirect
49. C₃×Dic₃⋊C₄	C₂²	semidirect
50. C₃×Dic₃⋊C₄	C₂²	semidirect
51. C₃×Dic₃⋊C₄	C₂²	semidirect
52. C₃×C₄×Dic₃	C₂²	semidirect
66. C₃×#117	D₃	semidirect
67. C₃×#117	C₂×C₃	semidirect
70. #929	C₂×C₃	semidirect
71. C₂×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
72. #898	C₂×C₃	semidirect
73. #896	C₂×C₃	semidirect
74. #894	C₂×C₃	semidirect
75. #894	C₂×C₃	semidirect
77. #67⋊C₄	C₂×C₃	semidirect
78. D₃×C₂²⋊C₄	C₂×C₃	semidirect
79. #878	C₂×C₃	semidirect
80. #876	C₂×C₃	semidirect
81. #875	C₂×C₃	semidirect
82. C₄×D₁₂	C₂×C₃	semidirect
83. #872	C₂×C₃	semidirect
131. C₂×C₄×D₃	C₂²×C₃	semidirect
132. C₂×Dic₆	C₂²×C₃	semidirect
141. C₃×C₄⋊C₄	C₂×D₃	semidirect
142. C₃×C₄⋊C₄	C₂×D₃	semidirect
143. C₃×C₄⋊C₄	C₂²×C₃	semidirect
144. C₃×C₄⋊C₄	C₂²×C₃	semidirect
166. C₃×C₄²	C₂×D₃	semidirect
167. C₃×C₄²	C₂×D₃	semidirect
168. C₃×C₄²	C₂²×C₃	semidirect
169. C₃×C₄²	C₂²×C₃	semidirect
179. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
180. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
181. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
182. C₄⋊Dic₃	C₂²×C₃	semidirect
183. Dic₃⋊C₄	C₂²×C₃	semidirect
184. Dic₃⋊C₄	C₂²×C₃	semidirect
185. Dic₃⋊C₄	C₂²×C₃	semidirect
186. Dic₃⋊C₄	C₂²×C₃	semidirect
187. Dic₃⋊C₄	C₂²×C₃	semidirect
188. C₄×Dic₃	C₂²×C₃	semidirect
226. #117	C₃×D₃	semidirect
314. C₄⋊C₄	C₂×C₃×D₃	semidirect
315. C₄⋊C₄	C₂×C₃×D₃	semidirect
331. C₄²	C₂×C₃×D₃	semidirect
332. C₄²	C₂×C₃×D₃	semidirect
393. C₃²	#551	semidirect
465. C₃	#5527	direct (N × H)
466. C₃	C₃×#551	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#117	2
C₃×#929	2
C₂×C₃×(C₂×D₃)⋊C₄	2
C₃×#898	2
C₃×#896	2
C₃×#894	2
C₃×#882	2
C₃×#67⋊C₄	2
C₃×D₃×C₂²⋊C₄	2
C₃×#878	2
C₃×#876	2
C₃×#875	2
C₃×C₄×D₁₂	2
C₃×#872	2
C₃×#551	3
#5527	3

Subgroups — C3×#5527 #10595624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5527 #10595624