Subgroups — C₃×#79334 #11859090

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	C₃²×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4837	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4727	C₂	1	2	yes	maximal
9	C₃×#4720	C₂	1	2	yes	maximal, complemented
10	C₃×#4709	C₂	1	2	yes	maximal, complemented
11	C₃×#4708	C₂	1	2	yes	maximal, complemented
12	C₃×#2925	—	3	1	no	maximal
13	#79334	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₃×C₄×#67	C₄	1	1	yes	characteristic
17	C₃×C₄×#67	C₄	1	1	yes	characteristic
18	C₃×C₄×#67	C₄	1	1	yes	characteristic
19	C₃×C₄×#67	C₄	1	1	yes	characteristic
20	C₃×#926	C₂²	1	1	yes	characteristic
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
22	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
23	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
24	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
25	C₃×#872	C₂²	1	1	yes	characteristic
26	C₃×#872	C₂²	1	1	yes	characteristic
27	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
28	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
30	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
31	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃²×#97	C₂²	1	2	yes	—
35	C₃×#830	C₂²	1	2	yes	—
36	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
37	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
38	C₃×#815	C₂²	1	2	yes	—
39	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
40	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
41	C₃×C₈×Dic₃	C₂²	1	2	yes	—
42	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
45	C₃×C₄×#41	—	3	1	no	—
46	C₄×#235	C₂×C₃	1	1	yes	characteristic
47	C₃×#433	—	3	2	no	—
48	C₃×#433	—	3	2	no	—
49	C₃×#432	—	2	1	no	—
50	C₃×#432	—	3	1	no	—
51	C₃×#432	D₃	1	1	yes	characteristic, complemented
52	C₃×#432	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#431	—	3	1	no	—
54	C₃×#431	—	3	1	no	—
55	C₃×#423	—	3	1	no	—
56	C₂×C₃×C₄⋊C₈	—	3	1	no	—
57	C₃×#408	—	3	2	no	—
58	C₃×#405	—	3	2	no	—
59	#4925	C₂×C₃	1	1	yes	characteristic, complemented
60	#4837	C₂×C₃	1	1	yes	characteristic, complemented
61	#4835	C₂×C₃	1	1	yes	characteristic, complemented
62	#4833	C₂×C₃	1	1	yes	characteristic, complemented
63	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
64	#4727	C₂×C₃	1	2	yes	—
65	#4720	C₂×C₃	1	2	yes	complemented
66	#4709	C₂×C₃	1	2	yes	complemented
67	#4708	C₂×C₃	1	2	yes	complemented
68	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
71	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
73	C₃×#235	—	2	2	no	—
74	C₃×#235	—	2	2	no	—
75	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃²×C₈	C₂³	1	2	yes	—
84	C₂×C₃²×C₈	C₂³	1	2	yes	—
85	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
86	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
87	C₃²×C₄²	C₂³	1	1	yes	characteristic
88	C₃²×C₄²	C₂³	1	1	yes	characteristic
89	C₃×#217	C₂×C₄	1	1	yes	characteristic
90	C₃×#217	C₂×C₄	1	1	yes	characteristic
91	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
97	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
103	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
106	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
108	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
109	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
110	C₃×D₃×C₈	—	2	4	no	—
111	#2925	—	3	1	no	Sylow
112	C₂×C₃×#41	—	3	1	no	—
113	C₂×#235	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×M₁₆	—	3	2	no	—
115	C₂²×C₃×C₈	—	3	2	no	—
116	C₃×C₄×Q₈	—	3	1	no	—
117	C₃×C₄×Q₈	—	3	1	no	—
118	C₃×C₄×D₄	—	3	1	no	—
119	C₃×C₄×D₄	—	3	1	no	—
120	C₃×C₄×D₄	—	3	1	no	—
121	C₃×C₄×D₄	—	3	1	no	—
122	C₃×C₄×D₄	—	3	1	no	—
123	C₃×C₄×D₄	—	3	1	no	—
124	C₃×#117	—	3	1	no	—
125	C₃×#117	—	3	1	no	—
126	C₃×#117	—	3	1	no	—
127	C₂×C₃×C₄²	—	2	1	no	—
128	C₂×C₃×C₄²	—	3	1	no	—
129	C₂×C₃×C₄²	—	3	1	no	—
130	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
132	C₄×#67	C₃×C₄	1	1	yes	characteristic
133	C₄×#67	C₃×C₄	1	1	yes	characteristic
134	C₄×#67	C₃×C₄	1	1	yes	characteristic
135	C₄×#67	C₃×C₄	1	1	yes	characteristic
136	#926	C₂²×C₃	1	1	yes	characteristic
137	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
138	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
139	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
140	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
141	#872	C₂²×C₃	1	1	yes	characteristic
142	#872	C₂²×C₃	1	1	yes	characteristic
143	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
144	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
145	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
146	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
147	C₃×C₄⋊C₈	—	2	1	no	—
148	C₃×C₄⋊C₈	—	2	1	no	—
149	C₃×C₄⋊C₈	—	3	2	no	—
150	C₃×C₄⋊C₈	—	3	2	no	—
151	C₃×C₄⋊C₈	—	3	1	no	—
152	C₃×C₄⋊C₈	—	3	1	no	—
153	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
154	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
155	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₂²⋊C₈	—	2	2	no	—
158	C₃×C₂²⋊C₈	—	3	2	no	—
159	C₃×C₂²⋊C₈	—	3	2	no	—
160	C₃×C₂²⋊C₈	—	3	2	no	—
161	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
162	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
163	C₃×#97	—	2	2	no	—
164	C₃×#97	—	3	2	no	—
165	C₃×#97	C₂×D₃	1	2	yes	—
166	C₃×#97	C₂²×C₃	1	2	yes	—
167	C₃×C₄×C₈	—	3	2	no	—
168	C₃×C₄×C₈	—	3	2	no	—
169	#830	C₂²×C₃	1	2	yes	—
170	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
171	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
172	#815	C₂²×C₃	1	2	yes	—
173	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
174	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
175	C₈×Dic₃	C₂²×C₃	1	2	yes	—
176	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
177	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
178	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
179	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	—	2	2	no	—
183	C₂×C₃²×C₄	—	2	1	no	—
184	C₂×C₃²×C₄	—	2	1	no	—
185	C₂×C₃²×C₄	—	4	1	no	—
186	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
192	C₃×#67	—	2	2	no	—
193	C₃×#67	—	2	2	no	—
194	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₃×D₁₂	—	2	2	no	—
201	C₃×C₄×D₃	—	2	2	no	—
202	C₃×C₄×D₃	—	2	2	no	—
203	C₃×C₄×D₃	—	2	1	no	—
204	C₃×C₄×D₃	—	2	1	no	—
205	C₃×C₄×D₃	—	4	1	no	—
206	C₃×C₄×D₃	—	4	1	no	—
207	C₃×C₄×D₃	#41	1	2	yes	—
208	C₃×C₄×D₃	#41	1	2	yes	—
209	C₃×Dic₆	—	2	2	no	—
210	C₃²×C₈	—	2	2	no	—
211	C₃²×C₈	—	2	2	no	—
212	C₃×C₃⋊C₈	—	2	2	no	—
213	C₃×C₃⋊C₈	—	2	2	no	—
214	C₄×#41	—	3	1	no	—
215	#433	—	3	2	no	—
216	#433	—	3	2	no	—
217	#432	—	3	1	no	—
218	#432	C₃×D₃	1	1	yes	characteristic, complemented
219	#431	—	3	1	no	—
220	#431	—	3	1	no	—
221	#423	—	3	1	no	—
222	C₂×C₄⋊C₈	—	3	1	no	—
223	#408	—	3	2	no	—
224	#405	—	3	2	no	—
225	C₃×#41	—	6	2	no	—
226	C₃×#41	—	6	2	no	—
227	C₂×C₃×Q₈	—	3	1	no	—
228	C₂×C₃×D₄	—	3	1	no	—
229	C₂×C₃×D₄	—	3	1	no	—
230	C₂×C₃×D₄	—	3	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	—	3	1	no	—
235	C₂²×C₃×C₄	—	3	1	no	—
236	C₂²×C₃×C₄	—	3	1	no	—
237	C₂²×C₃×C₄	—	3	1	no	—
238	C₂²×C₃×C₄	—	3	1	no	—
239	C₂²×C₃×C₄	—	3	1	no	—
240	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
247	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
248	#235	—	2	2	no	—
249	#235	—	2	2	no	—
250	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
251	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
253	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
257	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
258	C₃×M₁₆	—	6	4	no	—
259	C₂×C₃×C₈	—	2	2	no	—
260	C₂×C₃×C₈	—	2	2	no	—
261	C₂×C₃×C₈	—	3	2	no	—
262	C₂×C₃×C₈	—	3	2	no	—
263	C₂×C₃×C₈	—	6	4	no	—
264	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
265	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
266	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
267	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
268	C₃×C₄⋊C₄	—	3	1	no	—
269	C₃×C₄⋊C₄	—	3	1	no	—
270	C₃×C₄⋊C₄	—	3	1	no	—
271	C₃×C₄⋊C₄	—	3	1	no	—
272	C₃×C₄⋊C₄	—	3	1	no	—
273	C₃×C₄⋊C₄	—	3	1	no	—
274	C₃×C₂²⋊C₄	—	3	1	no	—
275	C₃×C₂²⋊C₄	—	3	1	no	—
276	C₃×C₂²⋊C₄	—	3	1	no	—
277	C₃×C₂²⋊C₄	—	3	1	no	—
278	C₃×C₂²⋊C₄	—	3	1	no	—
279	C₃×C₂²⋊C₄	—	3	1	no	—
280	C₃×C₄²	—	2	1	no	—
281	C₃×C₄²	—	2	1	no	—
282	C₃×C₄²	—	2	1	no	—
283	C₃×C₄²	—	2	1	no	—
284	C₃×C₄²	—	3	1	no	—
285	C₃×C₄²	—	3	1	no	—
286	C₃×C₄²	—	3	1	no	—
287	C₃×C₄²	—	3	1	no	—
288	C₃×C₄²	—	3	1	no	—
289	C₃×C₄²	—	3	1	no	—
290	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
291	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
292	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
293	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
294	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
295	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
296	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
297	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
298	#217	C₂×C₃×C₄	1	1	yes	characteristic
299	#217	C₂×C₃×C₄	1	1	yes	characteristic
300	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
301	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
303	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
304	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
305	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
306	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
307	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
308	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
309	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
310	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
311	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
312	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
313	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
314	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
315	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
317	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
318	ΓL(1,𝔽₂₅)	—	2	4	no	—
319	D₃×C₈	—	2	4	no	—
320	C₂²×C₃²	—	2	1	no	—
321	C₂²×C₃²	—	2	1	no	—
322	C₂²×C₃²	—	2	1	no	—
323	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
324	C₂×C₃×D₃	—	2	1	no	—
325	C₂×C₃×D₃	—	2	1	no	—
326	C₂×C₃×D₃	—	2	1	no	—
327	C₂×C₃×D₃	—	2	1	no	—
328	C₂×C₃×D₃	—	2	1	no	—
329	C₂×C₃×D₃	#117	1	2	yes	—
330	C₃²×C₄	—	2	1	no	—
331	C₃²×C₄	—	2	1	no	—
332	C₃²×C₄	—	2	1	no	—
333	C₃²×C₄	—	2	1	no	—
334	C₃²×C₄	#131	1	2	yes	—
335	C₃²×C₄	C₂×#41	1	1	yes	characteristic
336	C₃²×C₄	C₂×#41	1	1	yes	characteristic
337	C₃×Dic₃	—	2	1	no	—
338	C₃×Dic₃	—	2	1	no	—
339	C₃×Dic₃	—	2	1	no	—
340	C₃×Dic₃	—	2	1	no	—
341	C₃×Dic₃	—	2	1	no	—
342	C₃×Dic₃	#117	1	2	yes	—
343	C₂×#41	—	3	1	no	—
344	C₂×M₁₆	—	3	2	no	—
345	C₂²×C₈	—	3	2	no	—
346	C₄×Q₈	—	3	1	no	—
347	C₄×Q₈	—	3	1	no	—
348	C₄×D₄	—	3	1	no	—
349	C₄×D₄	—	3	1	no	—
350	C₄×D₄	—	3	1	no	—
351	C₄×D₄	—	3	1	no	—
352	C₄×D₄	—	3	1	no	—
353	C₄×D₄	—	3	1	no	—
354	#117	—	3	1	no	—
355	#117	—	3	1	no	—
356	#117	—	3	1	no	—
357	C₂×C₄²	—	3	1	no	—
358	C₂×C₄²	—	3	1	no	—
359	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
360	C₄⋊C₈	—	3	2	no	—
361	C₄⋊C₈	—	3	2	no	—
362	C₄⋊C₈	—	3	1	no	—
363	C₄⋊C₈	—	3	1	no	—
364	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
365	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
366	C₂²⋊C₈	—	3	2	no	—
367	C₂²⋊C₈	—	3	2	no	—
368	C₂²⋊C₈	—	3	2	no	—
369	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
370	#97	—	3	2	no	—
371	#97	C₂×C₃×D₃	1	2	yes	—
372	C₄×C₈	—	3	2	no	—
373	C₄×C₈	—	3	2	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	—	3	1	no	—
376	C₂³×C₃	—	3	1	no	—
377	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
378	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
379	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
380	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
381	C₃×Q₈	—	6	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	6	2	no	—
384	C₃×D₄	—	6	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	3	1	no	—
398	C₂×C₃×C₄	—	3	2	no	—
399	C₂×C₃×C₄	—	3	2	no	—
400	C₂×C₃×C₄	—	3	1	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	1	no	—
403	C₂×C₃×C₄	—	3	1	no	—
404	C₂×C₃×C₄	—	3	1	no	—
405	C₂×C₃×C₄	—	4	2	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	4	1	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	—	6	2	no	—
413	C₂×C₃×C₄	—	6	1	no	—
414	C₂×C₃×C₄	—	6	1	no	—
415	C₂×C₃×C₄	—	12	1	no	—
416	C₂×C₃×C₄	—	12	1	no	—
417	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
429	#67	—	2	2	no	—
430	#67	—	2	2	no	—
431	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
432	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
433	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
434	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
435	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
436	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
437	D₁₂	—	2	2	no	—
438	C₄×D₃	—	2	2	no	—
439	C₄×D₃	—	2	2	no	—
440	C₄×D₃	—	2	1	no	—
441	C₄×D₃	—	2	1	no	—
442	C₄×D₃	—	4	1	no	—
443	C₄×D₃	—	4	1	no	—
444	C₄×D₃	C₃×#41	1	2	yes	—
445	C₄×D₃	C₃×#41	1	2	yes	—
446	Dic₆	—	2	2	no	—
447	C₃×C₈	—	2	2	no	—
448	C₃×C₈	—	2	2	no	—
449	C₃×C₈	—	2	2	no	—
450	C₃×C₈	—	2	2	no	—
451	C₃×C₈	—	4	2	no	—
452	C₃×C₈	—	4	2	no	—
453	C₃×C₈	—	6	2	no	—
454	C₃×C₈	—	6	2	no	—
455	C₃⋊C₈	—	2	2	no	—
456	C₃⋊C₈	—	2	2	no	—
457	C₂×C₃²	—	4	1	no	—
458	C₂×C₃²	C₂×#117	1	1	yes	characteristic
459	C₂×C₃²	C₂×#131	1	1	yes	characteristic
460	C₂×C₃²	#568	1	1	yes	characteristic
461	C₃×D₃	—	2	2	no	—
462	C₃×D₃	—	4	1	no	—
463	#41	—	6	2	no	—
464	#41	—	6	2	no	—
465	C₂×Q₈	—	3	1	no	—
466	C₂×D₄	—	3	1	no	—
467	C₂×D₄	—	3	1	no	—
468	C₂×D₄	—	3	1	no	—
469	C₂²×C₄	—	3	1	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	1	no	—
472	C₂²×C₄	—	3	1	no	—
473	C₂²×C₄	—	3	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
476	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
478	M₁₆	—	6	4	no	—
479	C₂×C₈	—	3	2	no	—
480	C₂×C₈	—	3	2	no	—
481	C₂×C₈	—	6	4	no	—
482	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
483	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
484	C₄⋊C₄	—	3	1	no	—
485	C₄⋊C₄	—	3	1	no	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₄²	—	3	1	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₄²	—	3	1	no	—
501	C₄²	—	3	1	no	—
502	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
503	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
504	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
505	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	3	2	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	6	1	no	—
518	C₂²×C₃	—	6	1	no	—
519	C₂²×C₃	—	6	1	no	—
520	C₂²×C₃	—	6	1	no	—
521	C₂²×C₃	—	6	1	no	—
522	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
523	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
524	C₂×D₃	—	2	1	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	C₃×#117	1	2	yes	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	3	2	no	—
542	C₃×C₄	—	4	1	no	—
543	C₃×C₄	—	4	1	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	—	4	1	no	—
546	C₃×C₄	—	6	1	no	—
547	C₃×C₄	—	6	1	no	—
548	C₃×C₄	—	6	1	no	—
549	C₃×C₄	—	6	1	no	—
550	C₃×C₄	—	6	1	no	—
551	C₃×C₄	#907	1	2	yes	—
552	C₃×C₄	C₃×#131	1	2	yes	—
553	C₃×C₄	D₃×#41	1	1	yes	characteristic
554	C₃×C₄	D₃×#41	1	1	yes	characteristic
555	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
556	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	1	no	—
561	Dic₃	—	2	1	no	—
562	Dic₃	C₃×#117	1	2	yes	—
563	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	3	1	no	—
565	C₂³	—	3	1	no	—
566	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
567	Q₈	—	6	2	no	—
568	D₄	—	6	2	no	—
569	D₄	—	6	2	no	—
570	D₄	—	6	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	3	2	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	6	2	no	—
584	C₂×C₄	—	6	2	no	—
585	C₂×C₄	—	6	1	no	—
586	C₂×C₄	—	6	1	no	—
587	C₂×C₄	—	12	1	no	—
588	C₂×C₄	—	12	1	no	—
589	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
590	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
591	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
592	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
593	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
594	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	6	2	no	—
598	C₈	—	6	2	no	—
599	C₂×C₃	—	2	1	no	—
600	C₂×C₃	—	2	1	no	—
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	4	2	no	—
603	C₂×C₃	—	4	1	no	—
604	C₂×C₃	—	4	1	no	—
605	C₂×C₃	—	6	2	no	—
606	C₂×C₃	—	12	1	no	—
607	C₂×C₃	D₃×#117	1	1	yes	characteristic
608	C₂×C₃	C₂×#907	1	1	yes	characteristic
609	C₂×C₃	#5745	1	1	yes	characteristic
610	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
611	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
612	C₂×C₃	C₃×#568	1	1	yes	characteristic
613	D₃	—	2	2	no	—
614	D₃	—	4	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	3	2	no	—
619	C₂²	—	6	1	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	1	no	—
622	C₂²	—	6	1	no	—
623	C₂²	—	6	1	no	—
624	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	3	2	no	—
630	C₄	—	6	1	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	1	no	—
633	C₄	—	6	1	no	—
634	C₄	—	6	1	no	—
635	C₄	C₃×#907	1	2	yes	—
636	C₄	C₃×D₃×#41	1	1	yes	characteristic
637	C₄	C₃×D₃×#41	1	1	yes	characteristic
638	C₃	—	2	1	no	—
639	C₃	#79334	1	1	yes	characteristic, direct product factor
640	C₃	C₃×#2925	1	1	yes	characteristic, complemented
641	C₂	—	4	1	no	—
642	C₂	—	6	2	no	—
643	C₂	—	12	1	no	—
644	C₂	C₃×D₃×#117	1	1	yes	characteristic
645	C₂	C₂×C₃×#907	1	1	yes	characteristic
646	C₂	C₃×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#432	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#432	D₃
hypocenter	C₃	C₃×#2925
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#432

Complements

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

N	H ≅ G/N	type
2. C₃²×#432	C₂	semidirect
3. C₃×#4925	C₂	semidirect
4. C₃×#4837	C₂	semidirect
5. C₃×#4835	C₂	semidirect
6. C₃×#4833	C₂	semidirect
7. C₃×D₃×C₄⋊C₈	C₂	semidirect
9. C₃×#4720	C₂	semidirect
10. C₃×#4709	C₂	semidirect
11. C₃×#4708	C₂	semidirect
13. #79334	C₃	direct (N × H)
51. C₃×#432	D₃	semidirect
52. C₃×#432	C₂×C₃	semidirect
59. #4925	C₂×C₃	semidirect
60. #4837	C₂×C₃	semidirect
61. #4835	C₂×C₃	semidirect
62. #4833	C₂×C₃	semidirect
63. D₃×C₄⋊C₈	C₂×C₃	semidirect
65. #4720	C₂×C₃	semidirect
66. #4709	C₂×C₃	semidirect
67. #4708	C₂×C₃	semidirect
218. #432	C₃×D₃	semidirect
563. C₃²	#2925	semidirect
639. C₃	#79334	direct (N × H)
640. C₃	C₃×#2925	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
C₃²×#432	2
C₃×#4925	2
C₃×#4837	2
C₃×#4835	2
C₃×#4833	2
C₃×D₃×C₄⋊C₈	2
C₃×#4727	2
C₃×#4720	2
C₃×#4709	2
C₃×#4708	2
C₃×#2925	3
#79334	3

Subgroups — C3×#79334 #11859090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79334 #11859090