Subgroups — C₃²×#3102 #11770151

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#479	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#449	C₂	1	1	yes	maximal, characteristic
11	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3102	C₃	1	4	yes	maximal, direct product factor
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
22	C₃²×#126	—	2	1	no	—
23	C₃²×#125	C₂²	1	1	yes	characteristic
24	C₃²×#124	C₂²	1	1	yes	characteristic
25	C₃²×#123	—	2	1	no	—
26	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₃²×#121	C₂²	1	1	yes	characteristic
28	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
30	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₃²×C₄×D₄	—	2	1	no	—
32	C₃²×C₄×D₄	—	2	1	no	—
33	C₃²×C₄×D₄	—	2	1	no	—
34	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃²×#117	—	2	1	no	—
38	C₃²×#117	—	2	1	no	—
39	C₃²×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃²×C₄²	—	2	1	no	—
41	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
42	C₃²×#107	C₂²	1	1	yes	characteristic
43	C₃²×#107	C₂²	1	1	yes	characteristic
44	C₃²×#106	C₂²	1	1	yes	characteristic
45	C₃²×#106	C₂²	1	1	yes	characteristic
46	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₃²×#103	C₂²	1	1	yes	characteristic
49	C₃²×#103	C₂²	1	1	yes	characteristic
50	C₃²×#103	C₂²	1	1	yes	characteristic
51	C₃²×#103	C₂²	1	1	yes	characteristic
52	C₃²×#102	C₂²	1	1	yes	characteristic
53	C₃²×#102	C₂²	1	1	yes	characteristic
54	C₃²×#102	C₂²	1	1	yes	characteristic
55	C₃²×#102	C₂²	1	1	yes	characteristic
56	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
59	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
60	C₃×#529	C₂×C₃	1	4	yes	complemented
61	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
62	C₃×#485	C₂×C₃	1	4	yes	complemented
63	C₃×#482	C₂×C₃	1	4	yes	complemented
64	C₃×#479	C₂×C₃	1	4	yes	complemented
65	C₃×#478	C₂×C₃	1	4	yes	complemented
66	C₃×#464	C₂×C₃	1	4	yes	complemented
67	C₃×#463	C₂×C₃	1	4	yes	complemented
68	C₃×#452	C₂×C₃	1	4	yes	complemented
69	C₃×#449	C₂×C₃	1	4	yes	—
70	C₃×C₄×Q₁₆	C₂×C₃	1	4	yes	complemented
71	C₃×C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
72	C₃×C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
73	C₃×C₄×D₈	C₂×C₃	1	4	yes	complemented
74	C₃×#431	C₂×C₃	1	4	yes	complemented
75	C₃²×#41	—	2	2	no	—
76	C₃²×#41	—	2	2	no	—
77	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃²×D₄	—	2	1	no	—
80	C₂×C₃²×D₄	—	2	1	no	—
81	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃²×C₄	—	2	1	no	—
84	C₂²×C₃²×C₄	—	2	1	no	—
85	C₂²×C₃²×C₄	—	2	1	no	—
86	C₂²×C₃²×C₄	—	2	1	no	—
87	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
88	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
89	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
90	C₃²×Q₁₆	—	2	2	no	—
91	C₃²×SD₁₆	—	2	2	no	—
92	C₃²×SD₁₆	—	2	2	no	—
93	C₃²×D₈	—	2	2	no	—
94	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
96	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
98	C₃²×C₄⋊C₄	—	2	1	no	—
99	C₃²×C₄⋊C₄	—	2	1	no	—
100	C₃²×C₄⋊C₄	—	2	1	no	—
101	C₃²×C₄⋊C₄	—	2	1	no	—
102	C₃²×C₄⋊C₄	—	2	1	no	—
103	C₃²×C₄⋊C₄	—	2	1	no	—
104	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃²×C₂²⋊C₄	—	2	1	no	—
109	C₃²×C₂²⋊C₄	—	2	1	no	—
110	C₃²×C₂²⋊C₄	—	2	1	no	—
111	C₃²×C₂²⋊C₄	—	2	1	no	—
112	C₃²×C₂²⋊C₄	—	2	1	no	—
113	C₃²×C₂²⋊C₄	—	2	1	no	—
114	C₃²×C₂²⋊C₄	—	2	1	no	—
115	C₃²×C₂²⋊C₄	—	2	1	no	—
116	C₃²×C₄²	—	2	1	no	—
117	C₃²×C₄²	—	2	1	no	—
118	C₃²×C₄²	—	2	1	no	—
119	C₃²×C₄²	—	2	1	no	—
120	C₃²×C₄²	D₄	1	1	yes	characteristic
121	C₃²×C₄²	D₄	1	1	yes	characteristic
122	C₃²×C₄²	C₂³	1	1	yes	characteristic
123	C₃²×C₄²	C₂³	1	1	yes	characteristic
124	#3102	C₃²	1	1	yes	characteristic, direct product factor, Sylow
125	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
126	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
127	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
128	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
129	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
130	C₃×#126	—	2	4	no	—
131	C₃×#125	C₂²×C₃	1	4	yes	—
132	C₃×#124	C₂²×C₃	1	4	yes	—
133	C₃×#123	—	2	4	no	—
134	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
135	C₃×#121	C₂²×C₃	1	4	yes	—
136	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
137	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
138	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
139	C₃×C₄×D₄	—	2	4	no	—
140	C₃×C₄×D₄	—	2	4	no	—
141	C₃×C₄×D₄	—	2	4	no	—
142	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
143	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
144	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
145	C₃×#117	—	2	4	no	—
146	C₃×#117	—	2	4	no	—
147	C₃×#117	C₂²×C₃	1	4	yes	—
148	C₂×C₃×C₄²	—	2	4	no	—
149	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
150	C₃×#107	C₂²×C₃	1	4	yes	—
151	C₃×#107	C₂²×C₃	1	4	yes	—
152	C₃×#106	C₂²×C₃	1	4	yes	—
153	C₃×#106	C₂²×C₃	1	4	yes	—
154	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
155	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
156	C₃×#103	C₂²×C₃	1	4	yes	—
157	C₃×#103	C₂²×C₃	1	4	yes	—
158	C₃×#103	C₂²×C₃	1	4	yes	—
159	C₃×#103	C₂²×C₃	1	4	yes	—
160	C₃×#102	C₂²×C₃	1	4	yes	—
161	C₃×#102	C₂²×C₃	1	4	yes	—
162	C₃×#102	C₂²×C₃	1	4	yes	—
163	C₃×#102	C₂²×C₃	1	4	yes	—
164	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
165	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
166	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
167	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
168	C₂³×C₃²	—	2	1	no	—
169	C₂³×C₃²	—	2	1	no	—
170	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
171	C₃²×Q₈	—	2	1	no	—
172	C₃²×Q₈	—	2	1	no	—
173	C₃²×Q₈	—	2	1	no	—
174	C₃²×Q₈	#41	1	2	yes	—
175	C₃²×D₄	—	2	4	no	—
176	C₃²×D₄	—	2	1	no	—
177	C₃²×D₄	—	2	1	no	—
178	C₃²×D₄	—	2	1	no	—
179	C₃²×D₄	—	4	2	no	—
180	C₃²×D₄	#41	1	2	yes	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	1	no	—
183	C₂×C₃²×C₄	—	2	2	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	—	2	1	no	—
188	C₂×C₃²×C₄	—	2	1	no	—
189	C₂×C₃²×C₄	—	2	1	no	—
190	C₂×C₃²×C₄	—	2	1	no	—
191	C₂×C₃²×C₄	—	4	1	no	—
192	C₂×C₃²×C₄	—	4	2	no	—
193	C₂×C₃²×C₄	—	4	2	no	—
194	C₂×C₃²×C₄	—	4	2	no	—
195	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
198	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
199	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
201	C₃²×C₈	—	2	1	no	—
202	C₃²×C₈	—	2	1	no	—
203	C₃²×C₈	—	2	1	no	—
204	C₃²×C₈	—	2	1	no	—
205	#529	C₂×C₃²	1	1	yes	characteristic, complemented
206	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
207	#485	C₂×C₃²	1	1	yes	characteristic, complemented
208	#482	C₂×C₃²	1	1	yes	characteristic, complemented
209	#479	C₂×C₃²	1	1	yes	characteristic, complemented
210	#478	C₂×C₃²	1	1	yes	characteristic, complemented
211	#464	C₂×C₃²	1	1	yes	characteristic, complemented
212	#463	C₂×C₃²	1	1	yes	characteristic, complemented
213	#452	C₂×C₃²	1	1	yes	characteristic, complemented
214	#449	C₂×C₃²	1	1	yes	characteristic
215	C₄×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
216	C₄×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
217	C₄×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
218	C₄×D₈	C₂×C₃²	1	1	yes	characteristic, complemented
219	#431	C₂×C₃²	1	1	yes	characteristic, complemented
220	C₃×#41	—	2	8	no	—
221	C₃×#41	—	2	8	no	—
222	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
223	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
224	C₂×C₃×D₄	—	2	4	no	—
225	C₂×C₃×D₄	—	2	4	no	—
226	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
227	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
228	C₂²×C₃×C₄	—	2	4	no	—
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	2	4	no	—
231	C₂²×C₃×C₄	—	2	4	no	—
232	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
233	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
234	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
235	C₃×Q₁₆	—	2	8	no	—
236	C₃×SD₁₆	—	2	8	no	—
237	C₃×SD₁₆	—	2	8	no	—
238	C₃×D₈	—	2	8	no	—
239	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
240	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
241	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
242	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
243	C₃×C₄⋊C₄	—	2	4	no	—
244	C₃×C₄⋊C₄	—	2	4	no	—
245	C₃×C₄⋊C₄	—	2	4	no	—
246	C₃×C₄⋊C₄	—	2	4	no	—
247	C₃×C₄⋊C₄	—	2	4	no	—
248	C₃×C₄⋊C₄	—	2	4	no	—
249	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
250	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
251	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
252	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
253	C₃×C₂²⋊C₄	—	2	4	no	—
254	C₃×C₂²⋊C₄	—	2	4	no	—
255	C₃×C₂²⋊C₄	—	2	4	no	—
256	C₃×C₂²⋊C₄	—	2	4	no	—
257	C₃×C₂²⋊C₄	—	2	4	no	—
258	C₃×C₂²⋊C₄	—	2	4	no	—
259	C₃×C₂²⋊C₄	—	2	4	no	—
260	C₃×C₂²⋊C₄	—	2	4	no	—
261	C₃×C₄²	—	2	4	no	—
262	C₃×C₄²	—	2	4	no	—
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	2	4	no	—
265	C₃×C₄²	C₃×D₄	1	4	yes	—
266	C₃×C₄²	C₃×D₄	1	4	yes	—
267	C₃×C₄²	C₂³×C₃	1	4	yes	—
268	C₃×C₄²	C₂³×C₃	1	4	yes	—
269	C₂²×C₃²	—	2	1	no	—
270	C₂²×C₃²	—	2	2	no	—
271	C₂²×C₃²	—	2	1	no	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	4	1	no	—
274	C₂²×C₃²	—	4	1	no	—
275	C₂²×C₃²	—	4	1	no	—
276	C₂²×C₃²	—	4	1	no	—
277	C₂²×C₃²	—	4	1	no	—
278	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	2	2	no	—
281	C₃²×C₄	—	2	1	no	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	—	2	1	no	—
284	C₃²×C₄	—	4	1	no	—
285	C₃²×C₄	—	4	1	no	—
286	C₃²×C₄	—	4	1	no	—
287	C₃²×C₄	—	4	1	no	—
288	C₃²×C₄	—	4	1	no	—
289	C₃²×C₄	#135	1	2	yes	—
290	C₃²×C₄	C₂×#41	1	1	yes	characteristic
291	C₃²×C₄	C₂×#41	1	1	yes	characteristic
292	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
293	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
294	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
295	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
296	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
297	#126	—	2	1	no	—
298	#125	C₂²×C₃²	1	1	yes	characteristic
299	#124	C₂²×C₃²	1	1	yes	characteristic
300	#123	—	2	1	no	—
301	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
302	#121	C₂²×C₃²	1	1	yes	characteristic
303	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
304	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
305	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
310	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
311	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
312	#117	—	2	1	no	—
313	#117	—	2	1	no	—
314	#117	C₂²×C₃²	1	1	yes	characteristic
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
317	#107	C₂²×C₃²	1	1	yes	characteristic
318	#107	C₂²×C₃²	1	1	yes	characteristic
319	#106	C₂²×C₃²	1	1	yes	characteristic
320	#106	C₂²×C₃²	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
322	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
323	#103	C₂²×C₃²	1	1	yes	characteristic
324	#103	C₂²×C₃²	1	1	yes	characteristic
325	#103	C₂²×C₃²	1	1	yes	characteristic
326	#103	C₂²×C₃²	1	1	yes	characteristic
327	#102	C₂²×C₃²	1	1	yes	characteristic
328	#102	C₂²×C₃²	1	1	yes	characteristic
329	#102	C₂²×C₃²	1	1	yes	characteristic
330	#102	C₂²×C₃²	1	1	yes	characteristic
331	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
332	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
333	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
334	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
335	C₂³×C₃	—	2	4	no	—
336	C₂³×C₃	—	2	4	no	—
337	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
338	C₃×Q₈	—	2	4	no	—
339	C₃×Q₈	—	2	4	no	—
340	C₃×Q₈	—	2	4	no	—
341	C₃×Q₈	C₃×#41	1	8	yes	—
342	C₃×D₄	—	2	16	no	—
343	C₃×D₄	—	2	4	no	—
344	C₃×D₄	—	2	4	no	—
345	C₃×D₄	—	2	4	no	—
346	C₃×D₄	—	4	8	no	—
347	C₃×D₄	C₃×#41	1	8	yes	—
348	C₂×C₃×C₄	—	2	16	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	8	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	—	2	4	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	4	4	no	—
359	C₂×C₃×C₄	—	4	8	no	—
360	C₂×C₃×C₄	—	4	8	no	—
361	C₂×C₃×C₄	—	4	8	no	—
362	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
363	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
364	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
365	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
366	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
367	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
368	C₃×C₈	—	2	4	no	—
369	C₃×C₈	—	2	4	no	—
370	C₃×C₈	—	2	4	no	—
371	C₃×C₈	—	2	4	no	—
372	C₂×C₃²	—	4	1	no	—
373	C₂×C₃²	—	4	2	no	—
374	C₂×C₃²	—	8	1	no	—
375	C₂×C₃²	#525	1	1	yes	characteristic
376	C₂×C₃²	C₂×#135	1	1	yes	characteristic
377	C₂×C₃²	#575	1	1	yes	characteristic
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
381	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
385	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
393	Q₁₆	—	2	2	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	2	no	—
396	D₈	—	2	2	no	—
397	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
398	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
399	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
400	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
408	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
409	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
410	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	C₃²×D₄	1	1	yes	characteristic
424	C₄²	C₃²×D₄	1	1	yes	characteristic
425	C₄²	C₂³×C₃²	1	1	yes	characteristic
426	C₄²	C₂³×C₃²	1	1	yes	characteristic
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	4	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	—	2	8	no	—
431	C₂²×C₃	—	4	4	no	—
432	C₂²×C₃	—	4	4	no	—
433	C₂²×C₃	—	4	4	no	—
434	C₂²×C₃	—	4	4	no	—
435	C₂²×C₃	—	4	4	no	—
436	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
437	C₃×C₄	—	2	4	no	—
438	C₃×C₄	—	2	4	no	—
439	C₃×C₄	—	2	4	no	—
440	C₃×C₄	—	2	4	no	—
441	C₃×C₄	—	2	8	no	—
442	C₃×C₄	—	4	4	no	—
443	C₃×C₄	—	4	4	no	—
444	C₃×C₄	—	4	4	no	—
445	C₃×C₄	—	4	4	no	—
446	C₃×C₄	—	4	4	no	—
447	C₃×C₄	C₃×#135	1	8	yes	—
448	C₃×C₄	C₂×C₃×#41	1	4	yes	—
449	C₃×C₄	C₂×C₃×#41	1	4	yes	—
450	C₃²	#3102	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
454	Q₈	—	2	1	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	C₃²×#41	1	2	yes	—
458	D₄	—	2	4	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	1	no	—
462	D₄	—	4	2	no	—
463	D₄	C₃²×#41	1	2	yes	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	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	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
483	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
484	C₈	—	2	1	no	—
485	C₈	—	2	1	no	—
486	C₈	—	2	1	no	—
487	C₈	—	2	1	no	—
488	C₂×C₃	—	4	4	no	—
489	C₂×C₃	—	4	8	no	—
490	C₂×C₃	—	8	4	no	—
491	C₂×C₃	C₃×#525	1	4	yes	—
492	C₂×C₃	C₂×C₃×#135	1	4	yes	—
493	C₂×C₃	C₃×#575	1	4	yes	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	C₃²×#135	1	2	yes	—
515	C₄	C₂×C₃²×#41	1	1	yes	characteristic
516	C₄	C₂×C₃²×#41	1	1	yes	characteristic
517	C₃	C₃×#3102	1	4	yes	direct product factor
518	C₂	—	4	1	no	—
519	C₂	—	4	2	no	—
520	C₂	—	8	1	no	—
521	C₂	C₃²×#525	1	1	yes	characteristic
522	C₂	C₂×C₃²×#135	1	1	yes	characteristic
523	C₂	C₃²×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃²×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#529	C₂	semidirect
2. C₃²×C₄×#41	C₂	semidirect
3. C₃²×#485	C₂	semidirect
4. C₃²×#482	C₂	semidirect
5. C₃²×#479	C₂	semidirect
6. C₃²×#478	C₂	semidirect
7. C₃²×#464	C₂	semidirect
8. C₃²×#463	C₂	semidirect
9. C₃²×#452	C₂	semidirect
11. C₃²×C₄×Q₁₆	C₂	semidirect
12. C₃²×C₄×SD₁₆	C₂	semidirect
13. C₃²×C₄×SD₁₆	C₂	semidirect
14. C₃²×C₄×D₈	C₂	semidirect
15. C₃²×#431	C₂	semidirect
16. C₃×#3102	C₃	direct (N × H)
60. C₃×#529	C₂×C₃	semidirect
61. C₃×C₄×#41	C₂×C₃	semidirect
62. C₃×#485	C₂×C₃	semidirect
63. C₃×#482	C₂×C₃	semidirect
64. C₃×#479	C₂×C₃	semidirect
65. C₃×#478	C₂×C₃	semidirect
66. C₃×#464	C₂×C₃	semidirect
67. C₃×#463	C₂×C₃	semidirect
68. C₃×#452	C₂×C₃	semidirect
70. C₃×C₄×Q₁₆	C₂×C₃	semidirect
71. C₃×C₄×SD₁₆	C₂×C₃	semidirect
72. C₃×C₄×SD₁₆	C₂×C₃	semidirect
73. C₃×C₄×D₈	C₂×C₃	semidirect
74. C₃×#431	C₂×C₃	semidirect
124. #3102	C₃²	direct (N × H)
205. #529	C₂×C₃²	semidirect
206. C₄×#41	C₂×C₃²	semidirect
207. #485	C₂×C₃²	semidirect
208. #482	C₂×C₃²	semidirect
209. #479	C₂×C₃²	semidirect
210. #478	C₂×C₃²	semidirect
211. #464	C₂×C₃²	semidirect
212. #463	C₂×C₃²	semidirect
213. #452	C₂×C₃²	semidirect
215. C₄×Q₁₆	C₂×C₃²	semidirect
216. C₄×SD₁₆	C₂×C₃²	semidirect
217. C₄×SD₁₆	C₂×C₃²	semidirect
218. C₄×D₈	C₂×C₃²	semidirect
219. #431	C₂×C₃²	semidirect
450. C₃²	#3102	direct (N × H)
517. C₃	C₃×#3102	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×#529	2
C₃²×C₄×#41	2
C₃²×#485	2
C₃²×#482	2
C₃²×#479	2
C₃²×#478	2
C₃²×#464	2
C₃²×#463	2
C₃²×#452	2
C₃²×#449	2
C₃²×C₄×Q₁₆	2
C₃²×C₄×SD₁₆	2
C₃²×C₄×D₈	2
C₃²×#431	2
C₃×#3102	3

Subgroups — C32×#3102 #11770151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3102 #11770151