Subgroups — C₃²×#3507 #11770556

Order 1152.

3036 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#559	C₂	1	2	yes	maximal, complemented
2	C₃²×#557	C₂	1	2	yes	maximal, complemented
3	C₃²×#556	C₂	1	2	yes	maximal, complemented
4	C₃²×#556	C₂	1	4	yes	maximal, complemented
5	C₃²×#554	C₂	1	2	yes	maximal, complemented
6	C₃²×#552	C₂	1	4	yes	maximal, complemented
7	C₃²×#539	C₂	1	4	yes	maximal, complemented
8	C₃²×#536	C₂	1	2	yes	maximal, complemented
9	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#532	C₂	1	1	yes	maximal, characteristic
11	C₃²×#529	C₂	1	4	yes	maximal, complemented
12	C₃²×#520	C₂	1	2	yes	maximal, complemented
13	C₂×C₃²×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3507	C₃	1	4	yes	maximal, direct product factor
15	C₂×C₃²×#41	C₂²	1	2	yes	—
16	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
17	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃²×C₄⋊Q₈	C₂²	1	4	yes	—
20	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃²×#127	C₂²	1	1	yes	characteristic
22	C₃²×#126	C₂²	1	8	yes	—
23	C₃²×#126	C₂²	1	8	yes	—
24	C₃²×#125	C₂²	1	2	yes	—
25	C₃²×#125	C₂²	1	8	yes	—
26	C₃²×#125	C₂²	1	4	yes	—
27	C₃²×#124	C₂²	1	2	yes	—
28	C₃²×#124	C₂²	1	4	yes	—
29	C₃²×#124	C₂²	1	4	yes	—
30	C₃²×#123	C₂²	1	8	yes	—
31	C₃²×#123	C₂²	1	8	yes	—
32	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₃²×C₂²⋊Q₈	C₂²	1	8	yes	—
35	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃²×#121	C₂²	1	2	yes	—
38	C₃²×#121	C₂²	1	2	yes	—
39	C₃²×C₄×Q₈	C₂²	1	2	yes	—
40	C₃²×C₄×Q₈	C₂²	1	2	yes	—
41	C₃²×C₄×Q₈	C₂²	1	2	yes	—
42	C₃²×C₄×Q₈	C₂²	1	2	yes	—
43	C₃²×C₄×Q₈	C₂²	1	4	yes	—
44	C₃²×C₄×Q₈	C₂²	1	4	yes	—
45	C₃²×C₄×Q₈	C₂²	1	2	yes	—
46	C₃²×C₄×Q₈	C₂²	1	2	yes	—
47	C₃²×C₄×D₄	C₂²	1	2	yes	—
48	C₃²×C₄×D₄	C₂²	1	2	yes	—
49	C₃²×C₄×D₄	C₂²	1	4	yes	—
50	C₃²×C₄×D₄	C₂²	1	4	yes	—
51	C₃²×C₄×D₄	C₂²	1	8	yes	—
52	C₃²×#117	C₂²	1	4	yes	—
53	C₃²×#117	C₂²	1	8	yes	—
54	C₃²×#117	C₂²	1	2	yes	—
55	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
56	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
58	C₂×C₃²×C₄²	C₂²	1	2	yes	—
59	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
60	C₃×#559	C₂×C₃	1	8	yes	complemented
61	C₃×#557	C₂×C₃	1	8	yes	complemented
62	C₃×#556	C₂×C₃	1	8	yes	complemented
63	C₃×#556	C₂×C₃	1	16	yes	complemented
64	C₃×#554	C₂×C₃	1	8	yes	complemented
65	C₃×#552	C₂×C₃	1	16	yes	complemented
66	C₃×#539	C₂×C₃	1	16	yes	complemented
67	C₃×#536	C₂×C₃	1	8	yes	complemented
68	C₃×#533	C₂×C₃	1	4	yes	complemented
69	C₃×#532	C₂×C₃	1	4	yes	—
70	C₃×#529	C₂×C₃	1	16	yes	complemented
71	C₃×#520	C₂×C₃	1	8	yes	complemented
72	C₂×C₃×C₄×Q₈	C₂×C₃	1	4	yes	complemented
73	C₃²×#41	—	2	8	no	—
74	C₂×C₃²×Q₈	—	2	4	no	—
75	C₂×C₃²×Q₈	C₂³	1	2	yes	—
76	C₂×C₃²×Q₈	C₂³	1	2	yes	—
77	C₂×C₃²×Q₈	C₂³	1	2	yes	—
78	C₂×C₃²×Q₈	C₂³	1	2	yes	—
79	C₂×C₃²×Q₈	C₂³	1	2	yes	—
80	C₂×C₃²×D₄	C₂³	1	4	yes	—
81	C₂×C₃²×D₄	C₂³	1	2	yes	—
82	C₂×C₃²×D₄	C₂³	1	2	yes	—
83	C₂×C₃²×D₄	C₂³	1	2	yes	—
84	C₂²×C₃²×C₄	C₂³	1	2	yes	—
85	C₂²×C₃²×C₄	C₂³	1	4	yes	—
86	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃²×C₄	C₂³	1	2	yes	—
88	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
89	C₂²×C₃²×C₄	C₂³	1	8	yes	—
90	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
91	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
92	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
93	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
94	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
95	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
96	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
97	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
98	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
99	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
100	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
101	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
102	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
103	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
104	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
105	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₃²×C₄²	C₂³	1	4	yes	—
113	C₃²×C₄²	C₂³	1	1	yes	characteristic
114	C₃²×C₄²	C₂³	1	1	yes	characteristic
115	C₃²×C₄²	C₂³	1	4	yes	—
116	C₃²×C₄²	C₂³	1	1	yes	characteristic
117	C₃²×C₄²	C₂³	1	1	yes	characteristic
118	C₃²×C₄²	C₂³	1	8	yes	—
119	C₃²×C₄²	C₂³	1	4	yes	—
120	#3507	C₃²	1	1	yes	characteristic, direct product factor, Sylow
121	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
122	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
123	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
124	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
125	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
126	C₃×C₄⋊Q₈	C₂²×C₃	1	16	yes	—
127	C₃×#127	C₂²×C₃	1	4	yes	—
128	C₃×#126	C₂²×C₃	1	32	yes	—
129	C₃×#126	C₂²×C₃	1	32	yes	—
130	C₃×#125	C₂²×C₃	1	16	yes	—
131	C₃×#125	C₂²×C₃	1	8	yes	—
132	C₃×#125	C₂²×C₃	1	32	yes	—
133	C₃×#124	C₂²×C₃	1	16	yes	—
134	C₃×#124	C₂²×C₃	1	16	yes	—
135	C₃×#124	C₂²×C₃	1	8	yes	—
136	C₃×#123	C₂²×C₃	1	32	yes	—
137	C₃×#123	C₂²×C₃	1	32	yes	—
138	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
139	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
140	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
141	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
142	C₃×C₂²⋊Q₈	C₂²×C₃	1	32	yes	—
143	C₃×#121	C₂²×C₃	1	8	yes	—
144	C₃×#121	C₂²×C₃	1	8	yes	—
145	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
146	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
147	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
148	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
149	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
150	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	—
151	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	—
152	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
153	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
154	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
155	C₃×C₄×D₄	C₂²×C₃	1	32	yes	—
156	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
157	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
158	C₃×#117	C₂²×C₃	1	8	yes	—
159	C₃×#117	C₂²×C₃	1	16	yes	—
160	C₃×#117	C₂²×C₃	1	32	yes	—
161	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
162	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
163	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
164	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	—
165	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
166	C₂³×C₃²	C₂⁴	1	4	yes	—
167	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
168	C₃²×Q₈	—	2	4	no	—
169	C₃²×Q₈	—	2	4	no	—
170	C₃²×Q₈	—	2	4	no	—
171	C₃²×Q₈	—	2	4	no	—
172	C₃²×Q₈	—	4	2	no	—
173	C₃²×D₄	—	2	8	no	—
174	C₃²×D₄	—	2	4	no	—
175	C₃²×D₄	—	2	4	no	—
176	C₃²×D₄	—	4	2	no	—
177	C₂×C₃²×C₄	—	2	4	no	—
178	C₂×C₃²×C₄	—	2	8	no	—
179	C₂×C₃²×C₄	—	2	2	no	—
180	C₂×C₃²×C₄	—	4	2	no	—
181	C₂×C₃²×C₄	—	4	8	no	—
182	C₂×C₃²×C₄	—	4	1	no	—
183	C₂×C₃²×C₄	#41	1	4	yes	—
184	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
186	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
187	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
188	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
190	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
191	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
192	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
193	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
195	#559	C₂×C₃²	1	2	yes	complemented
196	#557	C₂×C₃²	1	2	yes	complemented
197	#556	C₂×C₃²	1	2	yes	complemented
198	#556	C₂×C₃²	1	4	yes	complemented
199	#554	C₂×C₃²	1	2	yes	complemented
200	#552	C₂×C₃²	1	4	yes	complemented
201	#539	C₂×C₃²	1	4	yes	complemented
202	#536	C₂×C₃²	1	2	yes	complemented
203	#533	C₂×C₃²	1	1	yes	characteristic, complemented
204	#532	C₂×C₃²	1	1	yes	characteristic
205	#529	C₂×C₃²	1	4	yes	complemented
206	#520	C₂×C₃²	1	2	yes	complemented
207	C₂×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
208	C₃×#41	—	2	32	no	—
209	C₂×C₃×Q₈	—	2	16	no	—
210	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
211	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
212	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
213	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
214	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
215	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
216	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
217	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
218	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
219	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
220	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
221	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
222	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
223	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
224	C₂²×C₃×C₄	C₂³×C₃	1	32	yes	—
225	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
226	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
227	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
228	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
229	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
230	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
231	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
232	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
233	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
234	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
235	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
236	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
237	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
238	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
239	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
240	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
241	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
242	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
243	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
244	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
245	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
246	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
247	C₃×C₄²	C₂³×C₃	1	16	yes	—
248	C₃×C₄²	C₂³×C₃	1	4	yes	—
249	C₃×C₄²	C₂³×C₃	1	4	yes	—
250	C₃×C₄²	C₂³×C₃	1	16	yes	—
251	C₃×C₄²	C₂³×C₃	1	4	yes	—
252	C₃×C₄²	C₂³×C₃	1	4	yes	—
253	C₃×C₄²	C₂³×C₃	1	32	yes	—
254	C₃×C₄²	C₂³×C₃	1	16	yes	—
255	C₂²×C₃²	—	2	1	no	—
256	C₂²×C₃²	—	2	1	no	—
257	C₂²×C₃²	—	2	4	no	—
258	C₂²×C₃²	—	2	4	no	—
259	C₂²×C₃²	—	2	4	no	—
260	C₂²×C₃²	C₂×#41	1	2	yes	—
261	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
262	C₃²×C₄	—	2	4	no	—
263	C₃²×C₄	—	2	4	no	—
264	C₃²×C₄	—	2	1	no	—
265	C₃²×C₄	—	2	4	no	—
266	C₃²×C₄	—	2	4	no	—
267	C₃²×C₄	—	2	4	no	—
268	C₃²×C₄	—	2	1	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	C₂×#41	1	2	yes	—
271	C₃²×C₄	C₂×#41	1	2	yes	—
272	C₃²×C₄	2₋¹⁺⁴	1	2	yes	—
273	C₂×#41	C₂²×C₃²	1	2	yes	—
274	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
275	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
276	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
277	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×C₃²	1	4	yes	—
279	#127	C₂²×C₃²	1	1	yes	characteristic
280	#126	C₂²×C₃²	1	8	yes	—
281	#126	C₂²×C₃²	1	8	yes	—
282	#125	C₂²×C₃²	1	4	yes	—
283	#125	C₂²×C₃²	1	2	yes	—
284	#125	C₂²×C₃²	1	8	yes	—
285	#124	C₂²×C₃²	1	4	yes	—
286	#124	C₂²×C₃²	1	2	yes	—
287	#124	C₂²×C₃²	1	4	yes	—
288	#123	C₂²×C₃²	1	8	yes	—
289	#123	C₂²×C₃²	1	8	yes	—
290	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
291	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
292	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
293	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
294	C₂²⋊Q₈	C₂²×C₃²	1	8	yes	—
295	#121	C₂²×C₃²	1	2	yes	—
296	#121	C₂²×C₃²	1	2	yes	—
297	C₄×Q₈	C₂²×C₃²	1	2	yes	—
298	C₄×Q₈	C₂²×C₃²	1	2	yes	—
299	C₄×Q₈	C₂²×C₃²	1	2	yes	—
300	C₄×Q₈	C₂²×C₃²	1	2	yes	—
301	C₄×Q₈	C₂²×C₃²	1	4	yes	—
302	C₄×Q₈	C₂²×C₃²	1	4	yes	—
303	C₄×Q₈	C₂²×C₃²	1	2	yes	—
304	C₄×Q₈	C₂²×C₃²	1	2	yes	—
305	C₄×D₄	C₂²×C₃²	1	8	yes	—
306	C₄×D₄	C₂²×C₃²	1	4	yes	—
307	C₄×D₄	C₂²×C₃²	1	4	yes	—
308	C₄×D₄	C₂²×C₃²	1	2	yes	—
309	C₄×D₄	C₂²×C₃²	1	2	yes	—
310	#117	C₂²×C₃²	1	2	yes	—
311	#117	C₂²×C₃²	1	4	yes	—
312	#117	C₂²×C₃²	1	8	yes	—
313	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
315	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
316	C₂×C₄²	C₂²×C₃²	1	2	yes	—
317	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
318	C₂³×C₃	C₂⁴×C₃	1	16	yes	—
319	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
320	C₃×Q₈	—	2	16	no	—
321	C₃×Q₈	—	2	16	no	—
322	C₃×Q₈	—	2	16	no	—
323	C₃×Q₈	—	2	16	no	—
324	C₃×Q₈	—	4	8	no	—
325	C₃×D₄	—	2	32	no	—
326	C₃×D₄	—	2	16	no	—
327	C₃×D₄	—	2	16	no	—
328	C₃×D₄	—	4	8	no	—
329	C₂×C₃×C₄	—	2	16	no	—
330	C₂×C₃×C₄	—	2	32	no	—
331	C₂×C₃×C₄	—	2	8	no	—
332	C₂×C₃×C₄	—	4	8	no	—
333	C₂×C₃×C₄	—	4	32	no	—
334	C₂×C₃×C₄	—	4	4	no	—
335	C₂×C₃×C₄	C₃×#41	1	16	yes	—
336	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
337	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
338	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
339	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
340	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
341	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
342	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
343	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
344	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
345	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
346	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
347	C₂×C₃²	—	2	2	no	—
348	C₂×C₃²	—	4	4	no	—
349	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
350	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
351	C₂×C₃²	#585	1	1	yes	characteristic
352	#41	—	2	8	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	C₂³×C₃²	1	2	yes	—
355	C₂×Q₈	C₂³×C₃²	1	2	yes	—
356	C₂×Q₈	C₂³×C₃²	1	2	yes	—
357	C₂×Q₈	C₂³×C₃²	1	2	yes	—
358	C₂×Q₈	C₂³×C₃²	1	2	yes	—
359	C₂×D₄	C₂³×C₃²	1	2	yes	—
360	C₂×D₄	C₂³×C₃²	1	4	yes	—
361	C₂×D₄	C₂³×C₃²	1	2	yes	—
362	C₂×D₄	C₂³×C₃²	1	2	yes	—
363	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₃²	1	2	yes	—
365	C₂²×C₄	C₂³×C₃²	1	4	yes	—
366	C₂²×C₄	C₂³×C₃²	1	2	yes	—
367	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
368	C₂²×C₄	C₂³×C₃²	1	8	yes	—
369	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
370	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
371	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
372	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
373	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
374	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
375	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
376	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
377	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
378	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
379	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
380	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
381	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
382	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
383	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
384	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
385	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
386	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
387	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
388	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
389	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
390	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
391	C₄²	C₂³×C₃²	1	4	yes	—
392	C₄²	C₂³×C₃²	1	1	yes	characteristic
393	C₄²	C₂³×C₃²	1	1	yes	characteristic
394	C₄²	C₂³×C₃²	1	4	yes	—
395	C₄²	C₂³×C₃²	1	1	yes	characteristic
396	C₄²	C₂³×C₃²	1	1	yes	characteristic
397	C₄²	C₂³×C₃²	1	8	yes	—
398	C₄²	C₂³×C₃²	1	4	yes	—
399	C₂²×C₃	—	2	4	no	—
400	C₂²×C₃	—	2	4	no	—
401	C₂²×C₃	—	2	16	no	—
402	C₂²×C₃	—	2	16	no	—
403	C₂²×C₃	—	2	16	no	—
404	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
405	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
406	C₃×C₄	—	2	16	no	—
407	C₃×C₄	—	2	16	no	—
408	C₃×C₄	—	2	4	no	—
409	C₃×C₄	—	2	16	no	—
410	C₃×C₄	—	2	16	no	—
411	C₃×C₄	—	2	16	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	C₂×C₃×#41	1	8	yes	—
415	C₃×C₄	C₂×C₃×#41	1	8	yes	—
416	C₃×C₄	C₃×2₋¹⁺⁴	1	8	yes	—
417	C₃²	#3507	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	C₂⁴×C₃²	1	4	yes	—
419	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	2	4	no	—
423	Q₈	—	2	4	no	—
424	Q₈	—	4	2	no	—
425	D₄	—	2	8	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	C₃²×#41	1	4	yes	—
436	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
437	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
438	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
439	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
440	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
441	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
442	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
443	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
444	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
445	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
446	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
447	C₂×C₃	—	2	8	no	—
448	C₂×C₃	—	4	16	no	—
449	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
450	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
451	C₂×C₃	C₃×#585	1	4	yes	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	C₂×C₃²×#41	1	2	yes	—
458	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	C₂×C₃²×#41	1	2	yes	—
468	C₄	C₂×C₃²×#41	1	2	yes	—
469	C₄	C₃²×2₋¹⁺⁴	1	2	yes	—
470	C₃	C₃×#3507	1	4	yes	direct product factor
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
474	C₂	C₂×C₃²×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂	C₃²×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
prime radical	C₃²×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#559	C₂	semidirect
2. C₃²×#557	C₂	semidirect
3. C₃²×#556	C₂	semidirect
4. C₃²×#556	C₂	semidirect
5. C₃²×#554	C₂	semidirect
6. C₃²×#552	C₂	semidirect
7. C₃²×#539	C₂	semidirect
8. C₃²×#536	C₂	semidirect
9. C₃²×#533	C₂	semidirect
11. C₃²×#529	C₂	semidirect
12. C₃²×#520	C₂	semidirect
13. C₂×C₃²×C₄×Q₈	C₂	semidirect
14. C₃×#3507	C₃	direct (N × H)
60. C₃×#559	C₂×C₃	semidirect
61. C₃×#557	C₂×C₃	semidirect
62. C₃×#556	C₂×C₃	semidirect
63. C₃×#556	C₂×C₃	semidirect
64. C₃×#554	C₂×C₃	semidirect
65. C₃×#552	C₂×C₃	semidirect
66. C₃×#539	C₂×C₃	semidirect
67. C₃×#536	C₂×C₃	semidirect
68. C₃×#533	C₂×C₃	semidirect
70. C₃×#529	C₂×C₃	semidirect
71. C₃×#520	C₂×C₃	semidirect
72. C₂×C₃×C₄×Q₈	C₂×C₃	semidirect
120. #3507	C₃²	direct (N × H)
195. #559	C₂×C₃²	semidirect
196. #557	C₂×C₃²	semidirect
197. #556	C₂×C₃²	semidirect
198. #556	C₂×C₃²	semidirect
199. #554	C₂×C₃²	semidirect
200. #552	C₂×C₃²	semidirect
201. #539	C₂×C₃²	semidirect
202. #536	C₂×C₃²	semidirect
203. #533	C₂×C₃²	semidirect
205. #529	C₂×C₃²	semidirect
206. #520	C₂×C₃²	semidirect
207. C₂×C₄×Q₈	C₂×C₃²	semidirect
417. C₃²	#3507	direct (N × H)
470. C₃	C₃×#3507	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#559	2
C₃²×#557	2
C₃²×#556	2
C₃²×#554	2
C₃²×#552	2
C₃²×#539	2
C₃²×#536	2
C₃²×#533	2
C₃²×#532	2
C₃²×#529	2
C₃²×#520	2
C₂×C₃²×C₄×Q₈	2
C₃×#3507	3

Subgroups — C32×#3507 #11770556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3507 #11770556