Subgroups — C₃²×#3510 #11770559

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 456 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	4	yes	maximal, complemented
2	C₃²×#556	C₂	1	4	yes	maximal, complemented
3	C₃²×#551	C₂	1	8	yes	maximal, complemented
4	C₃²×#542	C₂	1	4	yes	maximal, complemented
5	C₃²×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#535	C₂	1	1	yes	maximal, characteristic
7	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#529	C₂	1	4	yes	maximal, complemented
9	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#519	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#518	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3510	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
17	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₃²×#127	C₂²	1	2	yes	—
20	C₃²×#126	C₂²	1	8	yes	complemented
21	C₃²×#126	C₂²	1	8	yes	complemented
22	C₃²×#125	C₂²	1	2	yes	complemented
23	C₃²×#124	C₂²	1	2	yes	—
24	C₃²×#124	C₂²	1	4	yes	—
25	C₃²×#124	C₂²	1	2	yes	—
26	C₃²×#124	C₂²	1	2	yes	—
27	C₃²×#124	C₂²	1	8	yes	complemented
28	C₃²×#124	C₂²	1	2	yes	complemented
29	C₃²×#123	C₂²	1	4	yes	—
30	C₃²×#123	C₂²	1	8	yes	complemented
31	C₃²×#123	C₂²	1	8	yes	complemented
32	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃²×C₂²⋊Q₈	C₂²	1	8	yes	complemented
34	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
35	C₃²×#121	C₂²	1	4	yes	—
36	C₃²×#120	C₂²	1	4	yes	—
37	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
38	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
39	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
40	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
41	C₃²×C₄×D₄	C₂²	1	4	yes	—
42	C₃²×C₄×D₄	C₂²	1	4	yes	—
43	C₃²×C₄×D₄	C₂²	1	4	yes	—
44	C₃²×C₄×D₄	C₂²	1	8	yes	complemented
45	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
46	C₃²×#117	C₂²	1	4	yes	—
47	C₃²×#117	C₂²	1	1	yes	characteristic
48	C₃²×#117	C₂²	1	1	yes	characteristic
49	C₃²×#117	C₂²	1	1	yes	characteristic
50	C₃²×#117	C₂²	1	8	yes	complemented
51	C₃²×#117	C₂²	1	2	yes	complemented
52	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	—
54	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
55	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
56	C₃×#559	C₂×C₃	1	16	yes	complemented
57	C₃×#556	C₂×C₃	1	16	yes	complemented
58	C₃×#551	C₂×C₃	1	32	yes	complemented
59	C₃×#542	C₂×C₃	1	16	yes	complemented
60	C₃×#536	C₂×C₃	1	4	yes	complemented
61	C₃×#535	C₂×C₃	1	4	yes	—
62	C₃×#533	C₂×C₃	1	4	yes	complemented
63	C₃×#529	C₂×C₃	1	16	yes	complemented
64	C₂×C₃×#124	C₂×C₃	1	4	yes	complemented
65	C₃×#519	C₂×C₃	1	4	yes	complemented
66	C₃×#518	C₂×C₃	1	4	yes	complemented
67	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
68	C₂⁴×C₃²	C₂³	1	2	yes	—
69	C₃²×#41	—	2	4	no	—
70	C₂×C₃²×Q₈	—	2	4	no	—
71	C₂×C₃²×Q₈	C₂³	1	2	yes	—
72	C₂×C₃²×Q₈	C₂³	1	2	yes	—
73	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
74	C₂×C₃²×Q₈	C₂³	1	4	yes	—
75	C₂×C₃²×D₄	—	2	4	no	—
76	C₂×C₃²×D₄	C₂³	1	2	yes	—
77	C₂×C₃²×D₄	C₂³	1	2	yes	—
78	C₂×C₃²×D₄	C₂³	1	2	yes	—
79	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
80	C₂×C₃²×D₄	C₂³	1	8	yes	—
81	C₂²×C₃²×C₄	C₂³	1	2	yes	—
82	C₂²×C₃²×C₄	C₂³	1	2	yes	—
83	C₂²×C₃²×C₄	C₂³	1	2	yes	—
84	C₂²×C₃²×C₄	C₂³	1	4	yes	—
85	C₂²×C₃²×C₄	C₂³	1	8	yes	—
86	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
88	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
89	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
90	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
91	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
92	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
93	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
94	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
95	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
96	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
97	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
98	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₃²×C₄²	C₂³	1	1	yes	characteristic
106	C₃²×C₄²	C₂³	1	1	yes	characteristic
107	C₃²×C₄²	C₂³	1	2	yes	—
108	C₃²×C₄²	C₂³	1	2	yes	—
109	C₃²×C₄²	C₂³	1	4	yes	—
110	C₃²×C₄²	C₂³	1	8	yes	—
111	C₃²×C₄²	C₂³	1	2	yes	—
112	C₃²×C₄²	C₂³	1	2	yes	—
113	#3510	C₃²	1	1	yes	characteristic, direct product factor, Sylow
114	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
115	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
116	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
117	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
118	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
119	C₃×#127	C₂²×C₃	1	8	yes	—
120	C₃×#126	C₂²×C₃	1	32	yes	complemented
121	C₃×#126	C₂²×C₃	1	32	yes	complemented
122	C₃×#125	C₂²×C₃	1	8	yes	complemented
123	C₃×#124	C₂²×C₃	1	16	yes	—
124	C₃×#124	C₂²×C₃	1	8	yes	—
125	C₃×#124	C₂²×C₃	1	8	yes	—
126	C₃×#124	C₂²×C₃	1	8	yes	—
127	C₃×#124	C₂²×C₃	1	8	yes	complemented
128	C₃×#124	C₂²×C₃	1	32	yes	complemented
129	C₃×#123	C₂²×C₃	1	16	yes	—
130	C₃×#123	C₂²×C₃	1	32	yes	complemented
131	C₃×#123	C₂²×C₃	1	32	yes	complemented
132	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
133	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
134	C₃×C₂²⋊Q₈	C₂²×C₃	1	32	yes	complemented
135	C₃×#121	C₂²×C₃	1	16	yes	—
136	C₃×#120	C₂²×C₃	1	16	yes	—
137	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	complemented
138	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	complemented
139	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
140	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	complemented
141	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
142	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
143	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
144	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
145	C₃×C₄×D₄	C₂²×C₃	1	32	yes	complemented
146	C₃×#117	C₂²×C₃	1	4	yes	—
147	C₃×#117	C₂²×C₃	1	4	yes	—
148	C₃×#117	C₂²×C₃	1	4	yes	—
149	C₃×#117	C₂²×C₃	1	16	yes	—
150	C₃×#117	C₂²×C₃	1	8	yes	complemented
151	C₃×#117	C₂²×C₃	1	32	yes	complemented
152	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
154	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
155	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	complemented
156	C₂³×C₃²	—	2	4	no	—
157	C₂³×C₃²	—	4	4	no	—
158	C₂³×C₃²	C₂⁴	1	4	yes	—
159	C₂³×C₃²	C₂⁴	1	2	yes	—
160	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
161	C₃²×Q₈	—	2	4	no	—
162	C₃²×Q₈	—	2	4	no	—
163	C₃²×Q₈	—	2	2	no	—
164	C₃²×Q₈	—	4	4	no	—
165	C₃²×D₄	—	2	4	no	—
166	C₃²×D₄	—	2	4	no	—
167	C₃²×D₄	—	2	4	no	—
168	C₃²×D₄	—	2	2	no	—
169	C₃²×D₄	—	4	8	no	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	2	4	no	—
172	C₂×C₃²×C₄	—	4	4	no	—
173	C₂×C₃²×C₄	—	4	8	no	—
174	C₂×C₃²×C₄	—	4	2	no	—
175	C₂×C₃²×C₄	#41	1	4	yes	—
176	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
177	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
178	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
179	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
180	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
181	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
182	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
183	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
185	#559	C₂×C₃²	1	4	yes	complemented
186	#556	C₂×C₃²	1	4	yes	complemented
187	#551	C₂×C₃²	1	8	yes	complemented
188	#542	C₂×C₃²	1	4	yes	complemented
189	#536	C₂×C₃²	1	1	yes	characteristic, complemented
190	#535	C₂×C₃²	1	1	yes	characteristic
191	#533	C₂×C₃²	1	1	yes	characteristic, complemented
192	#529	C₂×C₃²	1	4	yes	complemented
193	C₂×#124	C₂×C₃²	1	1	yes	characteristic, complemented
194	#519	C₂×C₃²	1	1	yes	characteristic, complemented
195	#518	C₂×C₃²	1	1	yes	characteristic, complemented
196	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
197	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
198	C₃×#41	—	2	16	no	—
199	C₂×C₃×Q₈	—	2	16	no	—
200	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
201	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
202	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
203	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	—
204	C₂×C₃×D₄	—	2	16	no	—
205	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
206	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
207	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
208	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
209	C₂×C₃×D₄	C₂³×C₃	1	32	yes	—
210	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
211	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
212	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
213	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
214	C₂²×C₃×C₄	C₂³×C₃	1	32	yes	—
215	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
216	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
217	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
218	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
219	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
220	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
221	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
222	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
223	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
224	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
225	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
226	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
227	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
228	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
229	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
230	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
231	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
232	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
233	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
234	C₃×C₄²	C₂³×C₃	1	4	yes	—
235	C₃×C₄²	C₂³×C₃	1	4	yes	—
236	C₃×C₄²	C₂³×C₃	1	8	yes	—
237	C₃×C₄²	C₂³×C₃	1	8	yes	—
238	C₃×C₄²	C₂³×C₃	1	16	yes	—
239	C₃×C₄²	C₂³×C₃	1	32	yes	—
240	C₃×C₄²	C₂³×C₃	1	8	yes	—
241	C₃×C₄²	C₂³×C₃	1	8	yes	—
242	C₂²×C₃²	—	2	2	no	—
243	C₂²×C₃²	—	2	2	no	—
244	C₂²×C₃²	—	2	4	no	—
245	C₂²×C₃²	—	2	4	no	—
246	C₂²×C₃²	—	2	8	no	—
247	C₂²×C₃²	—	8	4	no	—
248	C₂²×C₃²	C₂×#41	1	2	yes	—
249	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
250	C₃²×C₄	—	2	2	no	—
251	C₃²×C₄	—	2	4	no	—
252	C₃²×C₄	—	2	2	no	—
253	C₃²×C₄	—	2	4	no	—
254	C₃²×C₄	—	2	4	no	—
255	C₃²×C₄	—	2	2	no	—
256	C₃²×C₄	—	2	4	no	—
257	C₃²×C₄	C₂×#41	1	2	yes	—
258	C₃²×C₄	C₂×#41	1	2	yes	—
259	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
260	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
261	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
262	C₄⋊Q₈	C₂²×C₃²	1	2	yes	complemented
263	C₄⋊Q₈	C₂²×C₃²	1	2	yes	complemented
264	#127	C₂²×C₃²	1	2	yes	—
265	#126	C₂²×C₃²	1	8	yes	complemented
266	#126	C₂²×C₃²	1	8	yes	complemented
267	#125	C₂²×C₃²	1	2	yes	complemented
268	#124	C₂²×C₃²	1	2	yes	—
269	#124	C₂²×C₃²	1	2	yes	—
270	#124	C₂²×C₃²	1	4	yes	—
271	#124	C₂²×C₃²	1	2	yes	—
272	#124	C₂²×C₃²	1	2	yes	complemented
273	#124	C₂²×C₃²	1	8	yes	complemented
274	#123	C₂²×C₃²	1	4	yes	—
275	#123	C₂²×C₃²	1	8	yes	complemented
276	#123	C₂²×C₃²	1	8	yes	complemented
277	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
278	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
279	C₂²⋊Q₈	C₂²×C₃²	1	8	yes	complemented
280	#121	C₂²×C₃²	1	4	yes	—
281	#120	C₂²×C₃²	1	4	yes	—
282	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
283	C₄×Q₈	C₂²×C₃²	1	4	yes	complemented
284	C₄×Q₈	C₂²×C₃²	1	4	yes	complemented
285	C₄×Q₈	C₂²×C₃²	1	4	yes	complemented
286	C₄×D₄	C₂²×C₃²	1	4	yes	—
287	C₄×D₄	C₂²×C₃²	1	4	yes	—
288	C₄×D₄	C₂²×C₃²	1	4	yes	—
289	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
290	C₄×D₄	C₂²×C₃²	1	8	yes	complemented
291	#117	C₂²×C₃²	1	1	yes	characteristic
292	#117	C₂²×C₃²	1	1	yes	characteristic
293	#117	C₂²×C₃²	1	1	yes	characteristic
294	#117	C₂²×C₃²	1	4	yes	—
295	#117	C₂²×C₃²	1	2	yes	complemented
296	#117	C₂²×C₃²	1	8	yes	complemented
297	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	—
299	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
300	C₂×C₄²	C₂²×C₃²	1	2	yes	complemented
301	C₂³×C₃	—	2	16	no	—
302	C₂³×C₃	—	4	16	no	—
303	C₂³×C₃	C₂⁴×C₃	1	16	yes	—
304	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
305	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
306	C₃×Q₈	—	2	16	no	—
307	C₃×Q₈	—	2	16	no	—
308	C₃×Q₈	—	2	8	no	—
309	C₃×Q₈	—	4	16	no	—
310	C₃×D₄	—	2	16	no	—
311	C₃×D₄	—	2	16	no	—
312	C₃×D₄	—	2	16	no	—
313	C₃×D₄	—	2	8	no	—
314	C₃×D₄	—	4	32	no	—
315	C₂×C₃×C₄	—	2	16	no	—
316	C₂×C₃×C₄	—	2	16	no	—
317	C₂×C₃×C₄	—	4	16	no	—
318	C₂×C₃×C₄	—	4	32	no	—
319	C₂×C₃×C₄	—	4	8	no	—
320	C₂×C₃×C₄	C₃×#41	1	16	yes	—
321	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
322	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
323	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
324	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
325	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
326	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
327	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
328	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
329	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
330	C₂×C₃²	—	2	2	no	—
331	C₂×C₃²	—	4	2	no	—
332	C₂×C₃²	—	4	4	no	—
333	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
334	C₂×C₃²	#585	1	2	yes	—
335	C₂⁴	C₂³×C₃²	1	2	yes	—
336	#41	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	C₂³×C₃²	1	2	yes	—
339	C₂×Q₈	C₂³×C₃²	1	2	yes	—
340	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
341	C₂×Q₈	C₂³×C₃²	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	C₂³×C₃²	1	2	yes	—
344	C₂×D₄	C₂³×C₃²	1	2	yes	—
345	C₂×D₄	C₂³×C₃²	1	2	yes	—
346	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
347	C₂×D₄	C₂³×C₃²	1	8	yes	—
348	C₂²×C₄	C₂³×C₃²	1	2	yes	—
349	C₂²×C₄	C₂³×C₃²	1	2	yes	—
350	C₂²×C₄	C₂³×C₃²	1	2	yes	—
351	C₂²×C₄	C₂³×C₃²	1	4	yes	—
352	C₂²×C₄	C₂³×C₃²	1	8	yes	—
353	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
354	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
355	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
356	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
357	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
358	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
359	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
360	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
361	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
362	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
363	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
364	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
365	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
366	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
367	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
368	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
369	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
370	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
371	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
372	C₄²	C₂³×C₃²	1	1	yes	characteristic
373	C₄²	C₂³×C₃²	1	1	yes	characteristic
374	C₄²	C₂³×C₃²	1	2	yes	—
375	C₄²	C₂³×C₃²	1	2	yes	—
376	C₄²	C₂³×C₃²	1	4	yes	—
377	C₄²	C₂³×C₃²	1	8	yes	—
378	C₄²	C₂³×C₃²	1	2	yes	—
379	C₄²	C₂³×C₃²	1	2	yes	—
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	8	no	—
382	C₂²×C₃	—	2	16	no	—
383	C₂²×C₃	—	2	16	no	—
384	C₂²×C₃	—	2	32	no	—
385	C₂²×C₃	—	8	16	no	—
386	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
387	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
388	C₃×C₄	—	2	8	no	—
389	C₃×C₄	—	2	16	no	—
390	C₃×C₄	—	2	8	no	—
391	C₃×C₄	—	2	16	no	—
392	C₃×C₄	—	2	16	no	—
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	—	2	16	no	—
395	C₃×C₄	C₂×C₃×#41	1	8	yes	—
396	C₃×C₄	C₂×C₃×#41	1	8	yes	—
397	C₃²	#3510	1	1	yes	characteristic, direct product factor, Sylow
398	C₂³	—	2	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	C₂⁴×C₃²	1	4	yes	—
401	C₂³	C₂⁴×C₃²	1	2	yes	—
402	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	8	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₃²×#41	1	4	yes	—
418	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
419	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
420	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
421	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
422	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
423	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
424	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
425	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
426	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
427	C₂×C₃	—	2	8	no	—
428	C₂×C₃	—	4	16	no	—
429	C₂×C₃	—	4	8	no	—
430	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
431	C₂×C₃	C₃×#585	1	8	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	8	4	no	—
438	C₂²	C₂×C₃²×#41	1	2	yes	—
439	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	C₂×C₃²×#41	1	2	yes	—
448	C₄	C₂×C₃²×#41	1	2	yes	—
449	C₃	C₃×#3510	1	4	yes	direct product factor
450	C₂	—	2	2	no	—
451	C₂	—	4	4	no	—
452	C₂	—	4	2	no	—
453	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
454	C₂	C₃²×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
prime radical	C₃²×#535	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×#556	C₂	semidirect
3. C₃²×#551	C₂	semidirect
4. C₃²×#542	C₂	semidirect
5. C₃²×#536	C₂	semidirect
7. C₃²×#533	C₂	semidirect
8. C₃²×#529	C₂	semidirect
9. C₂×C₃²×#124	C₂	semidirect
10. C₃²×#519	C₂	semidirect
11. C₃²×#518	C₂	semidirect
12. C₃²×C₄×#41	C₂	semidirect
13. C₃×#3510	C₃	direct (N × H)
17. C₃²×C₄⋊Q₈	C₂²	semidirect
18. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×#126	C₂²	semidirect
21. C₃²×#126	C₂²	semidirect
22. C₃²×#125	C₂²	semidirect
27. C₃²×#124	C₂²	semidirect
28. C₃²×#124	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×#123	C₂²	semidirect
33. C₃²×C₂²⋊Q₈	C₂²	semidirect
34. C₃²×C₂²⋊Q₈	C₂²	semidirect
37. C₃²×C₄×Q₈	C₂²	semidirect
38. C₃²×C₄×Q₈	C₂²	semidirect
39. C₃²×C₄×Q₈	C₂²	semidirect
40. C₃²×C₄×Q₈	C₂²	semidirect
44. C₃²×C₄×D₄	C₂²	semidirect
45. C₃²×C₄×D₄	C₂²	semidirect
50. C₃²×#117	C₂²	semidirect
51. C₃²×#117	C₂²	semidirect
55. C₂×C₃²×C₄²	C₂²	semidirect
56. C₃×#559	C₂×C₃	semidirect
57. C₃×#556	C₂×C₃	semidirect
58. C₃×#551	C₂×C₃	semidirect
59. C₃×#542	C₂×C₃	semidirect
60. C₃×#536	C₂×C₃	semidirect
62. C₃×#533	C₂×C₃	semidirect
63. C₃×#529	C₂×C₃	semidirect
64. C₂×C₃×#124	C₂×C₃	semidirect
65. C₃×#519	C₂×C₃	semidirect
66. C₃×#518	C₂×C₃	semidirect
67. C₃×C₄×#41	C₂×C₃	semidirect
113. #3510	C₃²	direct (N × H)
117. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
118. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
120. C₃×#126	C₂²×C₃	semidirect
121. C₃×#126	C₂²×C₃	semidirect
122. C₃×#125	C₂²×C₃	semidirect
127. C₃×#124	C₂²×C₃	semidirect
128. C₃×#124	C₂²×C₃	semidirect
130. C₃×#123	C₂²×C₃	semidirect
131. C₃×#123	C₂²×C₃	semidirect
133. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
134. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
137. C₃×C₄×Q₈	C₂²×C₃	semidirect
138. C₃×C₄×Q₈	C₂²×C₃	semidirect
139. C₃×C₄×Q₈	C₂²×C₃	semidirect
140. C₃×C₄×Q₈	C₂²×C₃	semidirect
144. C₃×C₄×D₄	C₂²×C₃	semidirect
145. C₃×C₄×D₄	C₂²×C₃	semidirect
150. C₃×#117	C₂²×C₃	semidirect
151. C₃×#117	C₂²×C₃	semidirect
155. C₂×C₃×C₄²	C₂²×C₃	semidirect
185. #559	C₂×C₃²	semidirect
186. #556	C₂×C₃²	semidirect
187. #551	C₂×C₃²	semidirect
188. #542	C₂×C₃²	semidirect
189. #536	C₂×C₃²	semidirect
191. #533	C₂×C₃²	semidirect
192. #529	C₂×C₃²	semidirect
193. C₂×#124	C₂×C₃²	semidirect
194. #519	C₂×C₃²	semidirect
195. #518	C₂×C₃²	semidirect
196. C₄×#41	C₂×C₃²	semidirect
262. C₄⋊Q₈	C₂²×C₃²	semidirect
263. C₄⋊Q₈	C₂²×C₃²	semidirect
265. #126	C₂²×C₃²	semidirect
266. #126	C₂²×C₃²	semidirect
267. #125	C₂²×C₃²	semidirect
272. #124	C₂²×C₃²	semidirect
273. #124	C₂²×C₃²	semidirect
275. #123	C₂²×C₃²	semidirect
276. #123	C₂²×C₃²	semidirect
278. C₂²⋊Q₈	C₂²×C₃²	semidirect
279. C₂²⋊Q₈	C₂²×C₃²	semidirect
282. C₄×Q₈	C₂²×C₃²	semidirect
283. C₄×Q₈	C₂²×C₃²	semidirect
284. C₄×Q₈	C₂²×C₃²	semidirect
285. C₄×Q₈	C₂²×C₃²	semidirect
289. C₄×D₄	C₂²×C₃²	semidirect
290. C₄×D₄	C₂²×C₃²	semidirect
295. #117	C₂²×C₃²	semidirect
296. #117	C₂²×C₃²	semidirect
300. C₂×C₄²	C₂²×C₃²	semidirect
397. C₃²	#3510	direct (N × H)
449. C₃	C₃×#3510	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×#556	2
C₃²×#551	2
C₃²×#542	2
C₃²×#536	2
C₃²×#535	2
C₃²×#533	2
C₃²×#529	2
C₂×C₃²×#124	2
C₃²×#519	2
C₃²×#518	2
C₃²×C₄×#41	2
C₃×#3510	3

Subgroups — C32×#3510 #11770559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3510 #11770559