Subgroups — C₃²×#2522 #11769571

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#399	C₂	1	1	yes	maximal, characteristic
2	C₃²×#398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#396	C₂	1	1	yes	maximal, characteristic
5	C₃²×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#388	C₂	1	1	yes	maximal, characteristic
8	C₃²×#388	C₂	1	1	yes	maximal, characteristic
9	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#385	C₂	1	1	yes	maximal, characteristic
13	C₃²×#380	C₂	1	1	yes	maximal, characteristic
14	C₃²×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃²×C₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₃×#2522	C₃	1	4	yes	maximal, direct product factor
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
37	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
38	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
39	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
40	C₃²×#95	C₂²	1	1	yes	characteristic
41	C₃²×#95	C₂²	1	1	yes	characteristic
42	C₃²×#95	C₂²	1	1	yes	characteristic
43	C₃²×#95	C₂²	1	1	yes	characteristic
44	C₃²×#95	C₂²	1	1	yes	characteristic
45	C₃²×#95	C₂²	1	1	yes	characteristic
46	C₃²×#95	C₂²	1	1	yes	characteristic
47	C₃²×#95	C₂²	1	1	yes	characteristic
48	C₃²×#95	C₂²	1	1	yes	characteristic
49	C₃²×#95	C₂²	1	1	yes	characteristic
50	C₃²×#95	C₂²	1	1	yes	characteristic
51	C₃²×#95	C₂²	1	1	yes	characteristic
52	C₃×#399	C₂×C₃	1	4	yes	—
53	C₃×#398	C₂×C₃	1	4	yes	complemented
54	C₃×#398	C₂×C₃	1	4	yes	complemented
55	C₃×#396	C₂×C₃	1	4	yes	—
56	C₃×#389	C₂×C₃	1	4	yes	complemented
57	C₃×#389	C₂×C₃	1	4	yes	complemented
58	C₃×#388	C₂×C₃	1	4	yes	—
59	C₃×#388	C₂×C₃	1	4	yes	—
60	C₃×#387	C₂×C₃	1	4	yes	complemented
61	C₃×#387	C₂×C₃	1	4	yes	complemented
62	C₃×#387	C₂×C₃	1	4	yes	complemented
63	C₃×#385	C₂×C₃	1	4	yes	—
64	C₃×#380	C₂×C₃	1	4	yes	—
65	C₃×C₄×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
66	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	4	yes	—
67	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
68	C₂²×C₃²×C₄	—	2	2	no	—
69	C₂²×C₃²×C₄	—	2	2	no	—
70	C₂²×C₃²×C₄	—	4	1	no	—
71	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
73	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
74	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	—	2	2	no	—
86	C₃²×C₄⋊C₄	—	2	2	no	—
87	C₃²×C₄⋊C₄	—	2	2	no	—
88	C₃²×C₄⋊C₄	—	2	2	no	—
89	C₃²×C₄⋊C₄	—	2	2	no	—
90	C₃²×C₄⋊C₄	—	2	2	no	—
91	C₃²×C₄⋊C₄	—	2	2	no	—
92	C₃²×C₄⋊C₄	—	4	1	no	—
93	C₃²×C₄⋊C₄	—	4	1	no	—
94	C₃²×C₄⋊C₄	—	4	1	no	—
95	C₃²×C₄⋊C₄	—	4	1	no	—
96	C₃²×C₄⋊C₄	—	4	1	no	—
97	C₃²×C₂²⋊C₄	—	2	2	no	—
98	C₃²×C₂²⋊C₄	—	2	2	no	—
99	C₃²×C₂²⋊C₄	—	4	1	no	—
100	C₃²×C₂²⋊C₄	—	4	1	no	—
101	C₃²×C₂²⋊C₄	—	4	1	no	—
102	C₃²×C₂²⋊C₄	Q₈	1	4	yes	—
103	C₃²×C₄²	—	2	2	no	—
104	C₃²×C₄²	—	4	1	no	—
105	C₃²×C₄²	—	4	1	no	—
106	C₃²×C₄²	—	4	1	no	—
107	#2522	C₃²	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
127	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
128	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
129	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
130	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
131	C₃×#95	C₂²×C₃	1	4	yes	—
132	C₃×#95	C₂²×C₃	1	4	yes	—
133	C₃×#95	C₂²×C₃	1	4	yes	—
134	C₃×#95	C₂²×C₃	1	4	yes	—
135	C₃×#95	C₂²×C₃	1	4	yes	—
136	C₃×#95	C₂²×C₃	1	4	yes	—
137	C₃×#95	C₂²×C₃	1	4	yes	—
138	C₃×#95	C₂²×C₃	1	4	yes	—
139	C₃×#95	C₂²×C₃	1	4	yes	—
140	C₃×#95	C₂²×C₃	1	4	yes	—
141	C₃×#95	C₂²×C₃	1	4	yes	—
142	C₃×#95	C₂²×C₃	1	4	yes	—
143	C₂³×C₃²	—	2	1	no	—
144	C₂³×C₃²	—	2	1	no	—
145	C₂³×C₃²	—	2	1	no	—
146	C₂³×C₃²	—	2	1	no	—
147	C₂³×C₃²	—	2	1	no	—
148	C₂³×C₃²	—	2	1	no	—
149	C₂³×C₃²	C₂×Q₈	1	2	yes	—
150	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
151	C₂×C₃²×C₄	—	2	1	no	—
152	C₂×C₃²×C₄	—	2	1	no	—
153	C₂×C₃²×C₄	—	2	1	no	—
154	C₂×C₃²×C₄	—	2	1	no	—
155	C₂×C₃²×C₄	—	2	1	no	—
156	C₂×C₃²×C₄	—	2	1	no	—
157	C₂×C₃²×C₄	—	2	1	no	—
158	C₂×C₃²×C₄	—	2	1	no	—
159	C₂×C₃²×C₄	—	2	1	no	—
160	C₂×C₃²×C₄	—	2	1	no	—
161	C₂×C₃²×C₄	—	2	1	no	—
162	C₂×C₃²×C₄	—	2	1	no	—
163	C₂×C₃²×C₄	—	2	1	no	—
164	C₂×C₃²×C₄	—	2	1	no	—
165	C₂×C₃²×C₄	—	2	1	no	—
166	C₂×C₃²×C₄	—	2	1	no	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	1	no	—
170	C₂×C₃²×C₄	—	2	1	no	—
171	C₂×C₃²×C₄	—	2	1	no	—
172	C₂×C₃²×C₄	—	2	1	no	—
173	C₂×C₃²×C₄	—	2	1	no	—
174	C₂×C₃²×C₄	—	2	1	no	—
175	C₂×C₃²×C₄	—	2	1	no	—
176	C₂×C₃²×C₄	—	2	1	no	—
177	C₂×C₃²×C₄	—	2	1	no	—
178	C₂×C₃²×C₄	—	2	1	no	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	—	2	1	no	—
181	C₂×C₃²×C₄	—	2	1	no	—
182	C₂×C₃²×C₄	—	2	1	no	—
183	C₂×C₃²×C₄	—	2	1	no	—
184	C₂×C₃²×C₄	—	2	1	no	—
185	C₂×C₃²×C₄	—	2	1	no	—
186	C₂×C₃²×C₄	—	2	1	no	—
187	C₂×C₃²×C₄	—	4	4	no	—
188	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
189	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
190	C₂×C₃²×C₄	#41	1	2	yes	—
191	C₂×C₃²×C₄	#41	1	2	yes	—
192	C₂×C₃²×C₄	#41	1	2	yes	—
193	C₂×C₃²×C₄	#41	1	2	yes	—
194	#399	C₂×C₃²	1	1	yes	characteristic
195	#398	C₂×C₃²	1	1	yes	characteristic, complemented
196	#398	C₂×C₃²	1	1	yes	characteristic, complemented
197	#396	C₂×C₃²	1	1	yes	characteristic
198	#389	C₂×C₃²	1	1	yes	characteristic, complemented
199	#389	C₂×C₃²	1	1	yes	characteristic, complemented
200	#388	C₂×C₃²	1	1	yes	characteristic
201	#388	C₂×C₃²	1	1	yes	characteristic
202	#387	C₂×C₃²	1	1	yes	characteristic, complemented
203	#387	C₂×C₃²	1	1	yes	characteristic, complemented
204	#387	C₂×C₃²	1	1	yes	characteristic, complemented
205	#385	C₂×C₃²	1	1	yes	characteristic
206	#380	C₂×C₃²	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂×C₃²	1	1	yes	characteristic, complemented
208	C₄×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
209	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
210	C₂²×C₃×C₄	—	2	8	no	—
211	C₂²×C₃×C₄	—	2	8	no	—
212	C₂²×C₃×C₄	—	4	4	no	—
213	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
214	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
215	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
216	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
217	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
218	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
219	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
220	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
221	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
222	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
223	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
224	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
225	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
226	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
227	C₃×C₄⋊C₄	—	2	8	no	—
228	C₃×C₄⋊C₄	—	2	8	no	—
229	C₃×C₄⋊C₄	—	2	8	no	—
230	C₃×C₄⋊C₄	—	2	8	no	—
231	C₃×C₄⋊C₄	—	2	8	no	—
232	C₃×C₄⋊C₄	—	2	8	no	—
233	C₃×C₄⋊C₄	—	2	8	no	—
234	C₃×C₄⋊C₄	—	4	4	no	—
235	C₃×C₄⋊C₄	—	4	4	no	—
236	C₃×C₄⋊C₄	—	4	4	no	—
237	C₃×C₄⋊C₄	—	4	4	no	—
238	C₃×C₄⋊C₄	—	4	4	no	—
239	C₃×C₂²⋊C₄	—	2	8	no	—
240	C₃×C₂²⋊C₄	—	2	8	no	—
241	C₃×C₂²⋊C₄	—	4	4	no	—
242	C₃×C₂²⋊C₄	—	4	4	no	—
243	C₃×C₂²⋊C₄	—	4	4	no	—
244	C₃×C₂²⋊C₄	C₃×Q₈	1	16	yes	—
245	C₃×C₄²	—	2	8	no	—
246	C₃×C₄²	—	4	4	no	—
247	C₃×C₄²	—	4	4	no	—
248	C₃×C₄²	—	4	4	no	—
249	C₂²×C₃²	—	2	2	no	—
250	C₂²×C₃²	—	2	2	no	—
251	C₂²×C₃²	—	2	2	no	—
252	C₂²×C₃²	—	4	1	no	—
253	C₂²×C₃²	—	4	1	no	—
254	C₂²×C₃²	—	4	1	no	—
255	C₂²×C₃²	—	4	1	no	—
256	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
257	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
258	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
259	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
260	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
261	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
263	C₃²×C₄	—	2	2	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	2	no	—
266	C₃²×C₄	—	2	2	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	4	1	no	—
270	C₃²×C₄	—	4	1	no	—
271	C₃²×C₄	—	4	1	no	—
272	C₃²×C₄	—	4	1	no	—
273	C₃²×C₄	—	4	1	no	—
274	C₃²×C₄	—	4	1	no	—
275	C₃²×C₄	—	4	1	no	—
276	C₃²×C₄	—	4	1	no	—
277	C₂³×C₄	C₂²×C₃²	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
296	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
297	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
298	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
299	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
300	#95	C₂²×C₃²	1	1	yes	characteristic
301	#95	C₂²×C₃²	1	1	yes	characteristic
302	#95	C₂²×C₃²	1	1	yes	characteristic
303	#95	C₂²×C₃²	1	1	yes	characteristic
304	#95	C₂²×C₃²	1	1	yes	characteristic
305	#95	C₂²×C₃²	1	1	yes	characteristic
306	#95	C₂²×C₃²	1	1	yes	characteristic
307	#95	C₂²×C₃²	1	1	yes	characteristic
308	#95	C₂²×C₃²	1	1	yes	characteristic
309	#95	C₂²×C₃²	1	1	yes	characteristic
310	#95	C₂²×C₃²	1	1	yes	characteristic
311	#95	C₂²×C₃²	1	1	yes	characteristic
312	C₂³×C₃	—	2	4	no	—
313	C₂³×C₃	—	2	4	no	—
314	C₂³×C₃	—	2	4	no	—
315	C₂³×C₃	—	2	4	no	—
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	—	2	4	no	—
318	C₂³×C₃	C₂×C₃×Q₈	1	8	yes	—
319	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
320	C₂×C₃×C₄	—	2	4	no	—
321	C₂×C₃×C₄	—	2	4	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	2	4	no	—
325	C₂×C₃×C₄	—	2	4	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	2	4	no	—
332	C₂×C₃×C₄	—	2	4	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	4	no	—
338	C₂×C₃×C₄	—	2	4	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	4	no	—
341	C₂×C₃×C₄	—	2	4	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	4	no	—
344	C₂×C₃×C₄	—	2	4	no	—
345	C₂×C₃×C₄	—	2	4	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	2	4	no	—
348	C₂×C₃×C₄	—	2	4	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	4	no	—
351	C₂×C₃×C₄	—	2	4	no	—
352	C₂×C₃×C₄	—	2	4	no	—
353	C₂×C₃×C₄	—	2	4	no	—
354	C₂×C₃×C₄	—	2	4	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	4	16	no	—
357	C₂×C₃×C₄	C₂×C₃×Q₈	1	8	yes	—
358	C₂×C₃×C₄	C₂×C₃×Q₈	1	8	yes	—
359	C₂×C₃×C₄	C₃×#41	1	8	yes	—
360	C₂×C₃×C₄	C₃×#41	1	8	yes	—
361	C₂×C₃×C₄	C₃×#41	1	8	yes	—
362	C₂×C₃×C₄	C₃×#41	1	8	yes	—
363	C₂×C₃²	—	4	2	no	—
364	C₂×C₃²	#529	1	1	yes	characteristic
365	C₂×C₃²	#533	1	1	yes	characteristic
366	C₂×C₃²	#540	1	1	yes	characteristic
367	C₂×C₃²	#551	1	1	yes	characteristic
368	C₂×C₃²	#553	1	1	yes	characteristic
369	C₂×C₃²	#554	1	1	yes	characteristic
370	C₂×C₃²	#554	1	1	yes	characteristic
371	C₂⁴	C₂³×C₃²	1	1	yes	characteristic
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
376	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
378	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
380	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
381	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
382	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
383	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
385	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
386	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₂²⋊C₄	C₃²×Q₈	1	4	yes	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₂²×C₃	—	2	8	no	—
412	C₂²×C₃	—	2	8	no	—
413	C₂²×C₃	—	2	8	no	—
414	C₂²×C₃	—	4	4	no	—
415	C₂²×C₃	—	4	4	no	—
416	C₂²×C₃	—	4	4	no	—
417	C₂²×C₃	—	4	4	no	—
418	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	—
419	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
420	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
421	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
422	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
423	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
424	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
425	C₃×C₄	—	2	8	no	—
426	C₃×C₄	—	2	8	no	—
427	C₃×C₄	—	2	8	no	—
428	C₃×C₄	—	2	8	no	—
429	C₃×C₄	—	2	8	no	—
430	C₃×C₄	—	2	8	no	—
431	C₃×C₄	—	4	4	no	—
432	C₃×C₄	—	4	4	no	—
433	C₃×C₄	—	4	4	no	—
434	C₃×C₄	—	4	4	no	—
435	C₃×C₄	—	4	4	no	—
436	C₃×C₄	—	4	4	no	—
437	C₃×C₄	—	4	4	no	—
438	C₃×C₄	—	4	4	no	—
439	C₃²	#2522	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	C₂×C₃²×Q₈	1	2	yes	—
447	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	C₂×C₃²×Q₈	1	2	yes	—
486	C₂×C₄	C₂×C₃²×Q₈	1	2	yes	—
487	C₂×C₄	C₃²×#41	1	2	yes	—
488	C₂×C₄	C₃²×#41	1	2	yes	—
489	C₂×C₄	C₃²×#41	1	2	yes	—
490	C₂×C₄	C₃²×#41	1	2	yes	—
491	C₂×C₃	—	4	8	no	—
492	C₂×C₃	C₃×#529	1	4	yes	—
493	C₂×C₃	C₃×#533	1	4	yes	—
494	C₂×C₃	C₃×#540	1	4	yes	—
495	C₂×C₃	C₃×#551	1	4	yes	—
496	C₂×C₃	C₃×#553	1	4	yes	—
497	C₂×C₃	C₃×#554	1	4	yes	—
498	C₂×C₃	C₃×#554	1	4	yes	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	C₂²×C₃²×Q₈	1	1	yes	characteristic
507	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
508	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
509	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
510	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
511	C₂²	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂²	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₃	C₃×#2522	1	4	yes	direct product factor
528	C₂	—	4	2	no	—
529	C₂	C₃²×#529	1	1	yes	characteristic
530	C₂	C₃²×#533	1	1	yes	characteristic
531	C₂	C₃²×#540	1	1	yes	characteristic
532	C₂	C₃²×#551	1	1	yes	characteristic
533	C₂	C₃²×#553	1	1	yes	characteristic
534	C₂	C₃²×#554	1	1	yes	characteristic
535	C₂	C₃²×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃²	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
prime radical	C₂⁴×C₃²	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×#398	C₂	semidirect
3. C₃²×#398	C₂	semidirect
5. C₃²×#389	C₂	semidirect
6. C₃²×#389	C₂	semidirect
9. C₃²×#387	C₂	semidirect
10. C₃²×#387	C₂	semidirect
11. C₃²×#387	C₂	semidirect
14. C₃²×C₄×C₄⋊C₄	C₂	semidirect
16. C₃×#2522	C₃	direct (N × H)
53. C₃×#398	C₂×C₃	semidirect
54. C₃×#398	C₂×C₃	semidirect
56. C₃×#389	C₂×C₃	semidirect
57. C₃×#389	C₂×C₃	semidirect
60. C₃×#387	C₂×C₃	semidirect
61. C₃×#387	C₂×C₃	semidirect
62. C₃×#387	C₂×C₃	semidirect
65. C₃×C₄×C₄⋊C₄	C₂×C₃	semidirect
107. #2522	C₃²	direct (N × H)
195. #398	C₂×C₃²	semidirect
196. #398	C₂×C₃²	semidirect
198. #389	C₂×C₃²	semidirect
199. #389	C₂×C₃²	semidirect
202. #387	C₂×C₃²	semidirect
203. #387	C₂×C₃²	semidirect
204. #387	C₂×C₃²	semidirect
207. C₄×C₄⋊C₄	C₂×C₃²	semidirect
439. C₃²	#2522	direct (N × H)
527. C₃	C₃×#2522	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×#399	2
C₃²×#398	2
C₃²×#396	2
C₃²×#389	2
C₃²×#388	2
C₃²×#387	2
C₃²×#385	2
C₃²×#380	2
C₃²×C₄×C₄⋊C₄	2
C₃²×C₄×C₂²⋊C₄	2
C₃×#2522	3

Subgroups — C32×#2522 #11769571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2522 #11769571