Subgroups — C₃×#87090 #11910509

Order 1152.

2802 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5679	C₂	1	3	yes	maximal, complemented
3	C₃×#5678	C₂	1	6	yes	maximal, complemented
4	C₃×#5676	C₂	1	6	yes	maximal, complemented
5	C₃×#5674	C₂	1	3	yes	maximal, complemented
6	C₃×#5595	C₂	1	3	yes	maximal, complemented
7	C₃×#5590	C₂	1	3	yes	maximal, complemented
8	C₃×#5589	C₂	1	3	yes	maximal, complemented
9	C₃×D₃×#120	C₂	1	3	yes	maximal, complemented
10	C₃×#3532	—	3	1	no	maximal
11	#87090	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×#67	C₂²	1	3	yes	complemented
14	C₂×C₃×#239	C₂²	1	3	yes	complemented
15	C₂×C₃×D₃×D₄	C₂²	1	3	yes	complemented
16	C₂×C₃×D₃×D₄	C₂²	1	6	yes	complemented
17	C₃²×#124	C₂²	1	3	yes	complemented
18	C₃²×#124	C₂²	1	6	yes	complemented
19	C₃²×#120	C₂²	1	3	yes	complemented
20	C₃²×#120	C₂²	1	3	yes	complemented
21	C₃×#953	C₂²	1	3	yes	complemented
22	C₃×#953	C₂²	1	1	yes	characteristic, complemented
23	C₃×#947	C₂²	1	3	yes	complemented
24	C₃×#946	C₂²	1	6	yes	complemented
25	C₃×#940	C₂²	1	3	yes	complemented
26	C₃×#939	C₂²	1	6	yes	complemented
27	C₃×#938	C₂²	1	6	yes	complemented
28	C₃×#937	C₂²	1	3	yes	—
29	C₃×#937	C₂²	1	6	yes	complemented
30	C₃×#935	C₂²	1	3	yes	complemented
31	C₃×#886	C₂²	1	3	yes	complemented
32	C₃×#884	C₂²	1	6	yes	complemented
33	C₃×#884	C₂²	1	6	yes	complemented
34	C₃×#884	C₂²	1	6	yes	complemented
35	C₃×#883	C₂²	1	6	yes	complemented
36	C₃×#883	C₂²	1	6	yes	complemented
37	C₃×#882	C₂²	1	6	yes	complemented
38	C₃×#882	C₂²	1	3	yes	complemented
39	C₃×#882	C₂²	1	6	yes	complemented
40	C₃×#67⋊C₄	C₂²	1	6	yes	complemented
41	C₃×D₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
42	C₃×D₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
43	C₃×D₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
44	C₃×#879	C₂²	1	6	yes	complemented
45	C₃×#876	C₂²	1	2	yes	complemented
46	C₃×#874	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
48	C₃×#872	C₂²	1	3	yes	complemented
49	C₃×H(3,𝔽₄)	—	2	1	no	—
50	C₃×H(3,𝔽₄)	D₃	1	1	yes	characteristic, complemented
51	C₃×H(3,𝔽₄)	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#560	—	3	3	no	—
53	C₃×#551	—	3	3	no	—
54	C₃×#546	—	3	6	no	—
55	C₃×D₄²	—	3	3	no	—
56	C₃×#538	—	3	6	no	—
57	C₃×#535	—	3	3	no	—
58	C₃×#534	—	3	3	no	—
59	C₂×C₃×#120	—	3	3	no	—
60	#5679	C₂×C₃	1	3	yes	complemented
61	#5678	C₂×C₃	1	6	yes	complemented
62	#5676	C₂×C₃	1	6	yes	complemented
63	#5674	C₂×C₃	1	3	yes	complemented
64	#5595	C₂×C₃	1	3	yes	complemented
65	#5590	C₂×C₃	1	3	yes	complemented
66	#5589	C₂×C₃	1	3	yes	complemented
67	D₃×#120	C₂×C₃	1	3	yes	complemented
68	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
69	C₂⁴×C₃²	C₂³	1	1	yes	characteristic, complemented
70	C₂³×C₃×D₃	—	4	6	no	—
71	C₂³×C₃×D₃	C₂³	1	3	yes	—
72	C₂³×C₃×D₃	C₂³	1	3	yes	—
73	C₂³×C₃×D₃	C₂³	1	3	yes	—
74	C₂×C₃²×Q₈	C₂³	1	3	yes	complemented
75	C₂×C₃²×D₄	C₂³	1	3	yes	—
76	C₂×C₃²×D₄	C₂³	1	6	yes	—
77	C₂×C₃×#67	—	4	6	no	—
78	C₂×C₃×#67	C₂³	1	6	yes	—
79	C₂×C₃×#67	C₂³	1	6	yes	—
80	C₂×C₃×#67	C₂³	1	3	yes	—
81	C₂×C₃×#67	C₂³	1	3	yes	—
82	C₂×C₃×#67	C₂³	1	6	yes	complemented
83	C₂²×C₃×Dic₃	C₂³	1	3	yes	complemented
84	C₃×#239	—	4	6	no	—
85	C₃×D₃×D₄	—	4	6	no	—
86	C₃×D₃×D₄	—	4	12	no	—
87	C₂×C₃×D₁₂	C₂³	1	6	yes	—
88	C₂×C₃×D₁₂	C₂³	1	3	yes	—
89	C₂×C₃×D₁₂	C₂³	1	3	yes	complemented
90	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
91	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
92	C₂×C₃×C₄×D₃	C₂³	1	6	yes	complemented
93	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
94	C₃²×C₂²⋊C₄	C₂³	1	3	yes	—
95	C₃²×C₂²⋊C₄	C₂³	1	3	yes	complemented
96	C₃²×C₂²⋊C₄	C₂³	1	6	yes	complemented
97	C₃²×C₄²	C₂³	1	1	yes	characteristic, complemented
98	C₃²×C₄²	C₂³	1	2	yes	complemented
99	C₃×#217	C₂³	1	3	yes	—
100	C₃×#217	C₂³	1	6	yes	—
101	C₃×#217	C₂³	1	3	yes	complemented
102	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
103	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
105	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	complemented
106	C₃×C₄⋊Dic₃	C₂³	1	6	yes	complemented
107	C₃×Dic₃⋊C₄	C₂³	1	6	yes	complemented
108	C₃×Dic₃⋊C₄	C₂³	1	6	yes	complemented
109	C₃×C₄×Dic₃	C₂³	1	3	yes	complemented
110	#3532	—	3	1	no	Sylow
111	C₂⁵×C₃	—	3	1	no	—
112	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₃×#41	—	3	3	no	—
114	C₂²×C₃×D₄	—	3	3	no	—
115	C₂²×C₃×D₄	—	3	3	no	—
116	C₂²×C₃×D₄	—	3	6	no	—
117	C₂²×#67	C₂²×C₃	1	3	yes	complemented
118	C₂×#239	C₂²×C₃	1	3	yes	complemented
119	C₂×D₃×D₄	C₂²×C₃	1	3	yes	complemented
120	C₂×D₃×D₄	C₂²×C₃	1	6	yes	complemented
121	C₃×#127	—	3	3	no	—
122	C₃×#127	—	3	1	no	—
123	C₃×#126	—	3	6	no	—
124	C₃×#126	—	3	2	no	—
125	C₃×#124	—	2	3	no	—
126	C₃×#124	—	2	6	no	—
127	C₃×#124	—	3	3	no	—
128	C₃×#124	C₂×D₃	1	3	yes	complemented
129	C₃×#124	C₂×D₃	1	6	yes	complemented
130	C₃×#124	C₂²×C₃	1	3	yes	complemented
131	C₃×#124	C₂²×C₃	1	6	yes	complemented
132	C₃×#123	—	3	3	no	—
133	C₃×#123	—	3	6	no	—
134	C₃×#123	—	3	6	no	—
135	C₃×#123	—	3	3	no	—
136	C₃×C₂²⋊Q₈	—	3	6	no	—
137	C₃×#121	—	3	6	no	—
138	C₃×#121	—	3	6	no	—
139	C₃×#121	—	3	6	no	—
140	C₃×#121	—	3	6	no	—
141	C₃×#121	—	3	6	no	—
142	C₃×#120	—	2	3	no	—
143	C₃×#120	—	2	3	no	—
144	C₃×#120	—	3	3	no	—
145	C₃×#120	—	3	1	no	—
146	C₃×#120	—	3	3	no	—
147	C₃×#120	—	3	6	no	—
148	C₃×#120	—	3	6	no	—
149	C₃×#120	—	3	3	no	—
150	C₃×#120	—	3	6	no	—
151	C₃×#120	C₂×D₃	1	3	yes	complemented
152	C₃×#120	C₂×D₃	1	3	yes	complemented
153	C₃×#120	C₂²×C₃	1	3	yes	complemented
154	C₃×#120	C₂²×C₃	1	3	yes	complemented
155	C₃×C₄×D₄	—	3	6	no	—
156	C₃×C₄×D₄	—	3	6	no	—
157	C₃×#117	—	3	3	no	—
158	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
159	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
160	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
161	#953	C₂²×C₃	1	3	yes	complemented
162	#953	C₂²×C₃	1	1	yes	characteristic, complemented
163	#947	C₂²×C₃	1	3	yes	complemented
164	#946	C₂²×C₃	1	6	yes	complemented
165	#940	C₂²×C₃	1	3	yes	complemented
166	#939	C₂²×C₃	1	6	yes	complemented
167	#938	C₂²×C₃	1	6	yes	complemented
168	#937	C₂²×C₃	1	3	yes	—
169	#937	C₂²×C₃	1	6	yes	complemented
170	#935	C₂²×C₃	1	3	yes	complemented
171	#886	C₂²×C₃	1	3	yes	complemented
172	#884	C₂²×C₃	1	6	yes	complemented
173	#884	C₂²×C₃	1	6	yes	complemented
174	#884	C₂²×C₃	1	6	yes	complemented
175	#883	C₂²×C₃	1	6	yes	complemented
176	#883	C₂²×C₃	1	6	yes	complemented
177	#882	C₂²×C₃	1	6	yes	complemented
178	#882	C₂²×C₃	1	3	yes	complemented
179	#882	C₂²×C₃	1	6	yes	complemented
180	#67⋊C₄	C₂²×C₃	1	6	yes	complemented
181	D₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	complemented
182	D₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
183	D₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
184	#879	C₂²×C₃	1	6	yes	complemented
185	#876	C₂²×C₃	1	2	yes	complemented
186	#874	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
188	#872	C₂²×C₃	1	3	yes	complemented
189	C₂³×C₃²	—	4	3	no	—
190	C₂³×C₃²	—	4	3	no	—
191	C₂³×C₃²	C₂⁴	1	3	yes	—
192	C₂³×C₃²	C₂⁴	1	3	yes	—
193	C₂²×C₃×D₃	—	2	12	no	—
194	C₂²×C₃×D₃	—	2	6	no	—
195	C₂²×C₃×D₃	—	2	6	no	—
196	C₂²×C₃×D₃	—	4	3	no	—
197	C₂²×C₃×D₃	—	4	6	no	—
198	C₂²×C₃×D₃	—	4	6	no	—
199	C₂²×C₃×D₃	—	4	16	no	—
200	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₃×D₃	C₂⁴	1	3	yes	—
202	C₂²×C₃×D₃	C₂⁴	1	3	yes	—
203	C₃²×Q₈	—	4	3	no	—
204	C₃²×D₄	—	4	3	no	—
205	C₃²×D₄	—	4	6	no	—
206	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
207	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
208	C₃×#67	—	2	12	no	—
209	C₃×#67	—	4	3	no	—
210	C₃×#67	—	4	3	no	—
211	C₃×#67	—	4	6	no	—
212	C₃×#67	—	4	6	no	—
213	C₂×C₃×Dic₃	—	4	3	no	—
214	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
215	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
216	C₃×D₁₂	—	2	12	no	—
217	C₃×D₁₂	—	4	3	no	—
218	C₃×D₁₂	—	4	3	no	—
219	C₃×C₄×D₃	—	2	6	no	—
220	C₃×C₄×D₃	—	4	6	no	—
221	C₃×C₄×D₃	—	4	6	no	—
222	H(3,𝔽₄)	C₃×D₃	1	1	yes	characteristic, complemented
223	#560	—	3	3	no	—
224	#551	—	3	3	no	—
225	#546	—	3	6	no	—
226	D₄²	—	3	3	no	—
227	#538	—	3	6	no	—
228	#535	—	3	3	no	—
229	#534	—	3	3	no	—
230	C₂×#120	—	3	3	no	—
231	C₂⁴×C₃	—	2	1	no	—
232	C₂⁴×C₃	—	2	1	no	—
233	C₂⁴×C₃	—	3	3	no	—
234	C₂⁴×C₃	—	3	3	no	—
235	C₂⁴×C₃	—	3	3	no	—
236	C₂⁴×C₃	—	12	6	no	—
237	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
238	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic, complemented
239	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
240	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic, complemented
241	C₂³×D₃	—	4	6	no	—
242	C₂³×D₃	C₂³×C₃	1	3	yes	—
243	C₂³×D₃	C₂³×C₃	1	3	yes	—
244	C₂³×D₃	C₂³×C₃	1	3	yes	—
245	C₃×#41	—	12	6	no	—
246	C₂×C₃×Q₈	—	2	3	no	—
247	C₂×C₃×Q₈	C₂²×D₃	1	3	yes	complemented
248	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	complemented
249	C₂×C₃×D₄	—	2	6	no	—
250	C₂×C₃×D₄	—	2	3	no	—
251	C₂×C₃×D₄	—	3	6	no	—
252	C₂×C₃×D₄	—	3	3	no	—
253	C₂×C₃×D₄	—	3	3	no	—
254	C₂×C₃×D₄	—	3	6	no	—
255	C₂×C₃×D₄	—	3	6	no	—
256	C₂×C₃×D₄	—	3	6	no	—
257	C₂×C₃×D₄	—	3	3	no	—
258	C₂×C₃×D₄	—	3	3	no	—
259	C₂×C₃×D₄	—	12	6	no	—
260	C₂×C₃×D₄	—	12	12	no	—
261	C₂×C₃×D₄	—	12	6	no	—
262	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
263	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
264	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
265	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
266	C₂²×C₃×C₄	—	3	3	no	—
267	C₂²×C₃×C₄	—	3	3	no	—
268	C₂²×C₃×C₄	—	3	6	no	—
269	C₂²×C₃×C₄	—	3	6	no	—
270	C₂×#67	—	4	6	no	—
271	C₂×#67	C₂³×C₃	1	6	yes	—
272	C₂×#67	C₂³×C₃	1	6	yes	—
273	C₂×#67	C₂³×C₃	1	3	yes	—
274	C₂×#67	C₂³×C₃	1	3	yes	—
275	C₂×#67	C₂³×C₃	1	6	yes	complemented
276	C₂²×Dic₃	C₂³×C₃	1	3	yes	complemented
277	#239	—	4	6	no	—
278	D₃×D₄	—	4	6	no	—
279	D₃×D₄	—	4	12	no	—
280	C₂×D₁₂	C₂³×C₃	1	6	yes	—
281	C₂×D₁₂	C₂³×C₃	1	3	yes	—
282	C₂×D₁₂	C₂³×C₃	1	3	yes	complemented
283	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
284	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
285	C₂×C₄×D₃	C₂³×C₃	1	6	yes	complemented
286	C₃×C₄⋊C₄	—	3	6	no	—
287	C₃×C₄⋊C₄	—	3	6	no	—
288	C₃×C₄⋊C₄	—	3	6	no	—
289	C₃×C₂²⋊C₄	—	2	6	no	—
290	C₃×C₂²⋊C₄	—	2	3	no	—
291	C₃×C₂²⋊C₄	—	2	3	no	—
292	C₃×C₂²⋊C₄	—	2	6	no	—
293	C₃×C₂²⋊C₄	—	3	3	no	—
294	C₃×C₂²⋊C₄	—	3	6	no	—
295	C₃×C₂²⋊C₄	—	3	3	no	—
296	C₃×C₂²⋊C₄	—	3	6	no	—
297	C₃×C₂²⋊C₄	—	3	6	no	—
298	C₃×C₂²⋊C₄	—	3	6	no	—
299	C₃×C₂²⋊C₄	—	3	6	no	—
300	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
301	C₃×C₂²⋊C₄	C₂²×D₃	1	3	yes	—
302	C₃×C₂²⋊C₄	C₂²×D₃	1	3	yes	complemented
303	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	complemented
304	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
305	C₃×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
306	C₃×C₂²⋊C₄	C₂³×C₃	1	3	yes	complemented
307	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	complemented
308	C₃×C₄²	—	2	1	no	—
309	C₃×C₄²	—	2	2	no	—
310	C₃×C₄²	—	3	3	no	—
311	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic, complemented
312	C₃×C₄²	C₂²×D₃	1	2	yes	complemented
313	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic, complemented
314	C₃×C₄²	C₂³×C₃	1	2	yes	complemented
315	#217	C₂³×C₃	1	3	yes	—
316	#217	C₂³×C₃	1	6	yes	—
317	#217	C₂³×C₃	1	3	yes	complemented
318	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
320	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
321	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	complemented
322	C₄⋊Dic₃	C₂³×C₃	1	6	yes	complemented
323	Dic₃⋊C₄	C₂³×C₃	1	6	yes	complemented
324	Dic₃⋊C₄	C₂³×C₃	1	6	yes	complemented
325	C₄×Dic₃	C₂³×C₃	1	3	yes	complemented
326	C₂²×C₃²	—	2	3	no	—
327	C₂²×C₃²	—	2	6	no	—
328	C₂²×C₃²	—	2	3	no	—
329	C₂²×C₃²	—	2	6	no	—
330	C₂²×C₃²	—	4	4	no	—
331	C₂²×C₃²	—	8	2	no	—
332	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
333	C₂×C₃×D₃	—	2	6	no	—
334	C₂×C₃×D₃	—	2	6	no	—
335	C₂×C₃×D₃	—	2	3	no	—
336	C₂×C₃×D₃	—	2	3	no	—
337	C₂×C₃×D₃	—	4	12	no	—
338	C₂×C₃×D₃	—	4	12	no	—
339	C₂×C₃×D₃	—	8	6	no	—
340	C₂×C₃×D₃	H(5,𝔽₂)	1	6	yes	—
341	C₃²×C₄	—	2	3	no	—
342	C₃²×C₄	—	2	6	no	—
343	C₃×Dic₃	—	2	3	no	—
344	C₃×Dic₃	—	2	6	no	—
345	C₂⁵	—	3	1	no	—
346	C₂×#41	—	3	3	no	—
347	C₂²×D₄	—	3	3	no	—
348	C₂²×D₄	—	3	3	no	—
349	C₂²×D₄	—	3	6	no	—
350	#127	—	3	3	no	—
351	#127	—	3	1	no	—
352	#126	—	3	6	no	—
353	#126	—	3	2	no	—
354	#124	—	3	3	no	—
355	#124	C₂×C₃×D₃	1	3	yes	complemented
356	#124	C₂×C₃×D₃	1	6	yes	complemented
357	#123	—	3	3	no	—
358	#123	—	3	6	no	—
359	#123	—	3	3	no	—
360	#123	—	3	6	no	—
361	C₂²⋊Q₈	—	3	6	no	—
362	#121	—	3	6	no	—
363	#121	—	3	6	no	—
364	#121	—	3	6	no	—
365	#121	—	3	6	no	—
366	#121	—	3	6	no	—
367	#120	—	3	3	no	—
368	#120	—	3	1	no	—
369	#120	—	3	6	no	—
370	#120	—	3	3	no	—
371	#120	—	3	6	no	—
372	#120	—	3	3	no	—
373	#120	—	3	6	no	—
374	#120	C₂×C₃×D₃	1	3	yes	complemented
375	#120	C₂×C₃×D₃	1	3	yes	complemented
376	C₄×D₄	—	3	6	no	—
377	C₄×D₄	—	3	6	no	—
378	#117	—	3	3	no	—
379	C₂×C₂²⋊C₄	—	3	3	no	—
380	C₂×C₂²⋊C₄	—	3	6	no	—
381	C₂×C₂²⋊C₄	—	3	3	no	—
382	C₂³×C₃	—	2	3	no	—
383	C₂³×C₃	—	2	3	no	—
384	C₂³×C₃	—	3	3	no	—
385	C₂³×C₃	—	3	1	no	—
386	C₂³×C₃	—	3	3	no	—
387	C₂³×C₃	—	4	3	no	—
388	C₂³×C₃	—	4	3	no	—
389	C₂³×C₃	—	4	3	no	—
390	C₂³×C₃	—	4	3	no	—
391	C₂³×C₃	—	6	12	no	—
392	C₂³×C₃	—	6	6	no	—
393	C₂³×C₃	—	6	6	no	—
394	C₂³×C₃	—	8	3	no	—
395	C₂³×C₃	—	8	3	no	—
396	C₂³×C₃	—	12	3	no	—
397	C₂³×C₃	—	12	6	no	—
398	C₂³×C₃	—	12	6	no	—
399	C₂³×C₃	—	12	16	no	—
400	C₂³×C₃	C₂³×D₃	1	3	yes	—
401	C₂³×C₃	C₂³×D₃	1	3	yes	—
402	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
403	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
404	C₂²×D₃	—	2	12	no	—
405	C₂²×D₃	—	2	6	no	—
406	C₂²×D₃	—	2	6	no	—
407	C₂²×D₃	—	4	3	no	—
408	C₂²×D₃	—	4	6	no	—
409	C₂²×D₃	—	4	6	no	—
410	C₂²×D₃	—	4	16	no	—
411	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
412	C₂²×D₃	C₂⁴×C₃	1	3	yes	—
413	C₂²×D₃	C₂⁴×C₃	1	3	yes	—
414	C₃×Q₈	—	4	3	no	—
415	C₃×Q₈	—	4	3	no	—
416	C₃×Q₈	—	8	3	no	—
417	C₃×D₄	—	4	3	no	—
418	C₃×D₄	—	4	6	no	—
419	C₃×D₄	—	4	3	no	—
420	C₃×D₄	—	4	6	no	—
421	C₃×D₄	—	6	12	no	—
422	C₃×D₄	—	6	12	no	—
423	C₃×D₄	—	8	3	no	—
424	C₃×D₄	—	8	6	no	—
425	C₃×D₄	—	12	3	no	—
426	C₃×D₄	—	12	3	no	—
427	C₃×D₄	—	12	3	no	—
428	C₃×D₄	—	12	3	no	—
429	C₃×D₄	—	12	6	no	—
430	C₃×D₄	—	12	6	no	—
431	C₂×C₃×C₄	—	2	3	no	—
432	C₂×C₃×C₄	—	2	6	no	—
433	C₂×C₃×C₄	—	3	6	no	—
434	C₂×C₃×C₄	—	3	3	no	—
435	C₂×C₃×C₄	—	6	6	no	—
436	C₂×C₃×C₄	—	12	6	no	—
437	C₂×C₃×C₄	—	12	6	no	—
438	C₂×C₃×C₄	—	12	3	no	—
439	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
440	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
441	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
442	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
443	#67	—	2	12	no	—
444	#67	—	4	3	no	—
445	#67	—	4	3	no	—
446	#67	—	4	6	no	—
447	#67	—	4	6	no	—
448	C₂×Dic₃	—	4	3	no	—
449	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
450	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
451	D₁₂	—	2	12	no	—
452	D₁₂	—	4	3	no	—
453	D₁₂	—	4	3	no	—
454	C₄×D₃	—	2	6	no	—
455	C₄×D₃	—	4	6	no	—
456	C₄×D₃	—	4	6	no	—
457	C₂×C₃²	—	4	3	no	—
458	C₂×C₃²	—	4	3	no	—
459	C₂×C₃²	C₂×H(5,𝔽₂)	1	3	yes	—
460	C₃×D₃	—	2	6	no	—
461	C₃×D₃	—	4	1	no	—
462	C₃×D₃	—	4	3	no	—
463	C₂⁴	—	3	3	no	—
464	C₂⁴	—	3	3	no	—
465	C₂⁴	—	3	3	no	—
466	C₂⁴	—	12	6	no	—
467	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
468	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
469	#41	—	12	6	no	—
470	C₂×Q₈	C₂²×C₃×D₃	1	3	yes	complemented
471	C₂×D₄	—	3	6	no	—
472	C₂×D₄	—	3	3	no	—
473	C₂×D₄	—	3	3	no	—
474	C₂×D₄	—	3	6	no	—
475	C₂×D₄	—	3	6	no	—
476	C₂×D₄	—	3	6	no	—
477	C₂×D₄	—	3	3	no	—
478	C₂×D₄	—	3	3	no	—
479	C₂×D₄	—	12	6	no	—
480	C₂×D₄	—	12	12	no	—
481	C₂×D₄	—	12	6	no	—
482	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
483	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
484	C₂²×C₄	—	3	3	no	—
485	C₂²×C₄	—	3	3	no	—
486	C₂²×C₄	—	3	6	no	—
487	C₂²×C₄	—	3	6	no	—
488	C₄⋊C₄	—	3	6	no	—
489	C₄⋊C₄	—	3	6	no	—
490	C₄⋊C₄	—	3	6	no	—
491	C₂²⋊C₄	—	3	3	no	—
492	C₂²⋊C₄	—	3	6	no	—
493	C₂²⋊C₄	—	3	3	no	—
494	C₂²⋊C₄	—	3	6	no	—
495	C₂²⋊C₄	—	3	6	no	—
496	C₂²⋊C₄	—	3	6	no	—
497	C₂²⋊C₄	—	3	6	no	—
498	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
499	C₂²⋊C₄	C₂²×C₃×D₃	1	3	yes	—
500	C₂²⋊C₄	C₂²×C₃×D₃	1	3	yes	complemented
501	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	complemented
502	C₄²	—	3	3	no	—
503	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
504	C₄²	C₂²×C₃×D₃	1	2	yes	complemented
505	C₂²×C₃	—	2	3	no	—
506	C₂²×C₃	—	2	6	no	—
507	C₂²×C₃	—	2	3	no	—
508	C₂²×C₃	—	2	6	no	—
509	C₂²×C₃	—	2	3	no	—
510	C₂²×C₃	—	2	6	no	—
511	C₂²×C₃	—	2	3	no	—
512	C₂²×C₃	—	2	6	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	3	6	no	—
515	C₂²×C₃	—	4	3	no	—
516	C₂²×C₃	—	4	6	no	—
517	C₂²×C₃	—	4	3	no	—
518	C₂²×C₃	—	4	6	no	—
519	C₂²×C₃	—	4	4	no	—
520	C₂²×C₃	—	4	4	no	—
521	C₂²×C₃	—	6	6	no	—
522	C₂²×C₃	—	6	6	no	—
523	C₂²×C₃	—	6	3	no	—
524	C₂²×C₃	—	6	3	no	—
525	C₂²×C₃	—	8	4	no	—
526	C₂²×C₃	—	8	2	no	—
527	C₂²×C₃	—	8	2	no	—
528	C₂²×C₃	—	8	4	no	—
529	C₂²×C₃	—	12	12	no	—
530	C₂²×C₃	—	12	12	no	—
531	C₂²×C₃	—	24	6	no	—
532	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
533	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
534	C₂×D₃	—	2	6	no	—
535	C₂×D₃	—	2	6	no	—
536	C₂×D₃	—	2	3	no	—
537	C₂×D₃	—	2	3	no	—
538	C₂×D₃	—	4	12	no	—
539	C₂×D₃	—	4	12	no	—
540	C₂×D₃	—	8	6	no	—
541	C₂×D₃	C₃×H(5,𝔽₂)	1	6	yes	—
542	C₃×C₄	—	2	3	no	—
543	C₃×C₄	—	2	6	no	—
544	C₃×C₄	—	2	3	no	—
545	C₃×C₄	—	2	6	no	—
546	C₃×C₄	—	4	3	no	—
547	C₃×C₄	—	4	6	no	—
548	C₃×C₄	—	6	3	no	—
549	C₃×C₄	—	6	6	no	—
550	Dic₃	—	2	3	no	—
551	Dic₃	—	2	6	no	—
552	C₃²	#3532	1	1	yes	characteristic, complemented, Sylow
553	C₂³	—	3	3	no	—
554	C₂³	—	3	1	no	—
555	C₂³	—	3	3	no	—
556	C₂³	—	4	3	no	—
557	C₂³	—	4	3	no	—
558	C₂³	—	6	12	no	—
559	C₂³	—	6	6	no	—
560	C₂³	—	6	6	no	—
561	C₂³	—	12	3	no	—
562	C₂³	—	12	6	no	—
563	C₂³	—	12	6	no	—
564	C₂³	—	12	16	no	—
565	C₂³	C₂³×C₃×D₃	1	3	yes	—
566	C₂³	C₂³×C₃×D₃	1	3	yes	—
567	Q₈	—	4	3	no	—
568	D₄	—	4	3	no	—
569	D₄	—	4	6	no	—
570	D₄	—	6	12	no	—
571	D₄	—	6	12	no	—
572	D₄	—	12	3	no	—
573	D₄	—	12	3	no	—
574	D₄	—	12	3	no	—
575	D₄	—	12	3	no	—
576	D₄	—	12	6	no	—
577	D₄	—	12	6	no	—
578	C₂×C₄	—	3	6	no	—
579	C₂×C₄	—	3	3	no	—
580	C₂×C₄	—	6	6	no	—
581	C₂×C₄	—	12	6	no	—
582	C₂×C₄	—	12	6	no	—
583	C₂×C₄	—	12	3	no	—
584	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
585	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
586	C₂×C₃	—	2	3	no	—
587	C₂×C₃	—	4	3	no	—
588	C₂×C₃	—	4	3	no	—
589	C₂×C₃	—	4	3	no	—
590	C₂×C₃	—	4	3	no	—
591	C₂×C₃	—	6	6	no	—
592	C₂×C₃	—	8	3	no	—
593	C₂×C₃	—	8	3	no	—
594	C₂×C₃	—	12	1	no	—
595	C₂×C₃	—	12	3	no	—
596	C₂×C₃	D₃×H(5,𝔽₂)	1	3	yes	—
597	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
598	D₃	—	2	6	no	—
599	D₃	—	4	1	no	—
600	D₃	—	4	3	no	—
601	C₂²	—	2	3	no	—
602	C₂²	—	2	6	no	—
603	C₂²	—	2	3	no	—
604	C₂²	—	2	6	no	—
605	C₂²	—	3	6	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	6	6	no	—
608	C₂²	—	6	6	no	—
609	C₂²	—	6	3	no	—
610	C₂²	—	6	3	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	12	12	no	—
613	C₂²	—	12	12	no	—
614	C₂²	—	24	6	no	—
615	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
616	C₄	—	2	3	no	—
617	C₄	—	2	6	no	—
618	C₄	—	6	3	no	—
619	C₄	—	6	6	no	—
620	C₃	—	2	1	no	—
621	C₃	#87090	1	1	yes	characteristic, direct product factor
622	C₃	C₃×#3532	1	1	yes	characteristic, complemented
623	C₂	—	4	3	no	—
624	C₂	—	4	3	no	—
625	C₂	—	6	6	no	—
626	C₂	—	12	1	no	—
627	C₂	—	12	3	no	—
628	C₂	C₃×D₃×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×H(3,𝔽₄)	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×H(3,𝔽₄)	D₃
hypocenter	C₃	C₃×#3532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. C₃²×H(3,𝔽₄)	C₂	semidirect
2. C₃×#5679	C₂	semidirect
3. C₃×#5678	C₂	semidirect
4. C₃×#5676	C₂	semidirect
5. C₃×#5674	C₂	semidirect
6. C₃×#5595	C₂	semidirect
7. C₃×#5590	C₂	semidirect
8. C₃×#5589	C₂	semidirect
9. C₃×D₃×#120	C₂	semidirect
11. #87090	C₃	direct (N × H)
12. C₂⁴×C₃×D₃	C₂²	semidirect
13. C₂²×C₃×#67	C₂²	semidirect
14. C₂×C₃×#239	C₂²	semidirect
15. C₂×C₃×D₃×D₄	C₂²	semidirect
16. C₂×C₃×D₃×D₄	C₂²	semidirect
17. C₃²×#124	C₂²	semidirect
18. C₃²×#124	C₂²	semidirect
19. C₃²×#120	C₂²	semidirect
20. C₃²×#120	C₂²	semidirect
21. C₃×#953	C₂²	semidirect
22. C₃×#953	C₂²	semidirect
23. C₃×#947	C₂²	semidirect
24. C₃×#946	C₂²	semidirect
25. C₃×#940	C₂²	semidirect
26. C₃×#939	C₂²	semidirect
27. C₃×#938	C₂²	semidirect
29. C₃×#937	C₂²	semidirect
30. C₃×#935	C₂²	semidirect
31. C₃×#886	C₂²	semidirect
32. C₃×#884	C₂²	semidirect
33. C₃×#884	C₂²	semidirect
34. C₃×#884	C₂²	semidirect
35. C₃×#883	C₂²	semidirect
36. C₃×#883	C₂²	semidirect
37. C₃×#882	C₂²	semidirect
38. C₃×#882	C₂²	semidirect
39. C₃×#882	C₂²	semidirect
40. C₃×#67⋊C₄	C₂²	semidirect
41. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
42. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
43. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
44. C₃×#879	C₂²	semidirect
45. C₃×#876	C₂²	semidirect
46. C₃×#874	C₂²	semidirect
47. C₃×C₄×D₁₂	C₂²	semidirect
48. C₃×#872	C₂²	semidirect
50. C₃×H(3,𝔽₄)	D₃	semidirect
51. C₃×H(3,𝔽₄)	C₂×C₃	semidirect
60. #5679	C₂×C₃	semidirect
61. #5678	C₂×C₃	semidirect
62. #5676	C₂×C₃	semidirect
63. #5674	C₂×C₃	semidirect
64. #5595	C₂×C₃	semidirect
65. #5590	C₂×C₃	semidirect
66. #5589	C₂×C₃	semidirect
67. D₃×#120	C₂×C₃	semidirect
69. C₂⁴×C₃²	C₂³	semidirect
74. C₂×C₃²×Q₈	C₂³	semidirect
82. C₂×C₃×#67	C₂³	semidirect
83. C₂²×C₃×Dic₃	C₂³	semidirect
89. C₂×C₃×D₁₂	C₂³	semidirect
92. C₂×C₃×C₄×D₃	C₂³	semidirect
95. C₃²×C₂²⋊C₄	C₂³	semidirect
96. C₃²×C₂²⋊C₄	C₂³	semidirect
97. C₃²×C₄²	C₂³	semidirect
98. C₃²×C₄²	C₂³	semidirect
101. C₃×#217	C₂³	semidirect
105. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
106. C₃×C₄⋊Dic₃	C₂³	semidirect
107. C₃×Dic₃⋊C₄	C₂³	semidirect
108. C₃×Dic₃⋊C₄	C₂³	semidirect
109. C₃×C₄×Dic₃	C₂³	semidirect
112. C₂⁴×D₃	C₂²×C₃	semidirect
117. C₂²×#67	C₂²×C₃	semidirect
118. C₂×#239	C₂²×C₃	semidirect
119. C₂×D₃×D₄	C₂²×C₃	semidirect
120. C₂×D₃×D₄	C₂²×C₃	semidirect
128. C₃×#124	C₂×D₃	semidirect
129. C₃×#124	C₂×D₃	semidirect
130. C₃×#124	C₂²×C₃	semidirect
131. C₃×#124	C₂²×C₃	semidirect
151. C₃×#120	C₂×D₃	semidirect
152. C₃×#120	C₂×D₃	semidirect
153. C₃×#120	C₂²×C₃	semidirect
154. C₃×#120	C₂²×C₃	semidirect
161. #953	C₂²×C₃	semidirect
162. #953	C₂²×C₃	semidirect
163. #947	C₂²×C₃	semidirect
164. #946	C₂²×C₃	semidirect
165. #940	C₂²×C₃	semidirect
166. #939	C₂²×C₃	semidirect
167. #938	C₂²×C₃	semidirect
169. #937	C₂²×C₃	semidirect
170. #935	C₂²×C₃	semidirect
171. #886	C₂²×C₃	semidirect
172. #884	C₂²×C₃	semidirect
173. #884	C₂²×C₃	semidirect
174. #884	C₂²×C₃	semidirect
175. #883	C₂²×C₃	semidirect
176. #883	C₂²×C₃	semidirect
177. #882	C₂²×C₃	semidirect
178. #882	C₂²×C₃	semidirect
179. #882	C₂²×C₃	semidirect
180. #67⋊C₄	C₂²×C₃	semidirect
181. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
182. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
183. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
184. #879	C₂²×C₃	semidirect
185. #876	C₂²×C₃	semidirect
186. #874	C₂²×C₃	semidirect
187. C₄×D₁₂	C₂²×C₃	semidirect
188. #872	C₂²×C₃	semidirect
222. H(3,𝔽₄)	C₃×D₃	semidirect
238. C₂⁴×C₃	C₂²×D₃	semidirect
240. C₂⁴×C₃	C₂³×C₃	semidirect
247. C₂×C₃×Q₈	C₂²×D₃	semidirect
248. C₂×C₃×Q₈	C₂³×C₃	semidirect
275. C₂×#67	C₂³×C₃	semidirect
276. C₂²×Dic₃	C₂³×C₃	semidirect
282. C₂×D₁₂	C₂³×C₃	semidirect
285. C₂×C₄×D₃	C₂³×C₃	semidirect
302. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
303. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
306. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
307. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
311. C₃×C₄²	C₂²×D₃	semidirect
312. C₃×C₄²	C₂²×D₃	semidirect
313. C₃×C₄²	C₂³×C₃	semidirect
314. C₃×C₄²	C₂³×C₃	semidirect
317. #217	C₂³×C₃	semidirect
321. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
322. C₄⋊Dic₃	C₂³×C₃	semidirect
323. Dic₃⋊C₄	C₂³×C₃	semidirect
324. Dic₃⋊C₄	C₂³×C₃	semidirect
325. C₄×Dic₃	C₂³×C₃	semidirect
355. #124	C₂×C₃×D₃	semidirect
356. #124	C₂×C₃×D₃	semidirect
374. #120	C₂×C₃×D₃	semidirect
375. #120	C₂×C₃×D₃	semidirect
468. C₂⁴	C₂²×C₃×D₃	semidirect
470. C₂×Q₈	C₂²×C₃×D₃	semidirect
500. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
501. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
503. C₄²	C₂²×C₃×D₃	semidirect
504. C₄²	C₂²×C₃×D₃	semidirect
552. C₃²	#3532	semidirect
621. C₃	#87090	direct (N × H)
622. C₃	C₃×#3532	semidirect

Maximal subgroups

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

subgroup	index
C₃²×H(3,𝔽₄)	2
C₃×#5679	2
C₃×#5678	2
C₃×#5676	2
C₃×#5674	2
C₃×#5595	2
C₃×#5590	2
C₃×#5589	2
C₃×D₃×#120	2
C₃×#3532	3
#87090	3

Subgroups — C3×#87090 #11910509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87090 #11910509