Subgroups — C₃×#79959 #11861375

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5578	C₂	1	1	yes	maximal, characteristic
2	C₃²×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4839	C₂	1	1	yes	maximal, characteristic
5	C₃×#4839	C₂	1	1	yes	maximal, characteristic
6	C₃×#4837	C₂	1	1	yes	maximal, characteristic
7	C₃×#4831	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4828	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4828	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4708	C₂	1	1	yes	maximal, characteristic
11	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic
12	C₃×#4701	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4701	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4689	C₂	1	1	yes	maximal, characteristic
15	C₃×#4679	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2961	—	3	1	no	maximal
17	#79959	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
19	C₃×#946	C₄	1	1	yes	characteristic
20	C₃×#944	C₄	1	1	yes	characteristic
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₃×#897	C₄	1	1	yes	characteristic
26	C₃×#896	C₄	1	1	yes	characteristic
27	C₃×#896	C₄	1	1	yes	characteristic
28	C₃×#889	C₄	1	1	yes	characteristic
29	C₃×#889	C₄	1	1	yes	characteristic
30	C₃×#888	C₄	1	1	yes	characteristic
31	C₃×#872	C₂²	1	1	yes	characteristic
32	C₃×#872	C₂²	1	1	yes	characteristic
33	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₃²×#97	C₂²	1	1	yes	characteristic
41	C₃²×#97	C₂²	1	1	yes	characteristic
42	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
43	C₃×#815	C₂²	1	1	yes	characteristic
44	C₃×#815	C₂²	1	1	yes	characteristic
45	C₃×#815	C₂²	1	1	yes	characteristic
46	C₃×#815	C₂²	1	1	yes	characteristic
47	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
49	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
51	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
54	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
55	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
56	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
58	C₃×#803	C₂²	1	1	yes	characteristic
59	C₃×#803	C₂²	1	1	yes	characteristic
60	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×#533	—	3	1	no	—
62	#5578	C₂×C₃	1	1	yes	characteristic
63	C₃×#446	—	2	1	no	—
64	C₃×#446	—	3	1	no	—
65	C₃×#446	—	3	1	no	—
66	C₃×#446	—	3	1	no	—
67	C₃×#446	—	3	1	no	—
68	C₃×#446	—	3	1	no	—
69	C₃×#446	—	3	1	no	—
70	C₃×#446	—	3	1	no	—
71	C₃×#446	D₃	1	1	yes	characteristic, complemented
72	C₃×#446	C₂×C₃	1	1	yes	characteristic, complemented
73	C₃×#424	—	3	1	no	—
74	C₃×#424	—	3	1	no	—
75	C₃×#423	—	3	1	no	—
76	C₃×#405	—	3	1	no	—
77	C₃×#405	—	3	1	no	—
78	C₂×C₃×#97	—	3	1	no	—
79	#5024	C₂×C₃	1	1	yes	characteristic, complemented
80	#4839	C₂×C₃	1	1	yes	characteristic
81	#4839	C₂×C₃	1	1	yes	characteristic
82	#4837	C₂×C₃	1	1	yes	characteristic
83	#4831	C₂×C₃	1	1	yes	characteristic, complemented
84	#4828	C₂×C₃	1	1	yes	characteristic, complemented
85	#4828	C₂×C₃	1	1	yes	characteristic, complemented
86	#4708	C₂×C₃	1	1	yes	characteristic
87	D₃×#97	C₂×C₃	1	1	yes	characteristic
88	#4701	C₂×C₃	1	1	yes	characteristic, complemented
89	#4701	C₂×C₃	1	1	yes	characteristic, complemented
90	#4689	C₂×C₃	1	1	yes	characteristic
91	#4679	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
103	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₃²×C₄²	C₂³	1	1	yes	characteristic
107	C₃²×C₄²	C₂³	1	1	yes	characteristic
108	C₃²×C₄²	C₂³	1	1	yes	characteristic
109	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
114	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
116	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
127	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
128	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
129	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
130	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
136	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
137	C₃×D₃×C₈	—	2	2	no	—
138	C₃×D₃×C₈	Q₈	1	4	yes	complemented
139	#2961	—	3	1	no	Sylow
140	C₂×C₃×M₁₆	—	3	1	no	—
141	C₂×C₃×M₁₆	—	3	1	no	—
142	C₂²×C₃×C₈	—	3	1	no	—
143	C₂²×C₃×C₈	—	3	1	no	—
144	C₃×C₄⋊Q₈	—	3	1	no	—
145	C₃×C₄⋊Q₈	—	3	1	no	—
146	C₃×#125	—	3	1	no	—
147	C₃×#125	—	3	1	no	—
148	C₃×C₂²⋊Q₈	—	3	1	no	—
149	C₃×C₂²⋊Q₈	—	3	1	no	—
150	C₃×C₂²⋊Q₈	—	3	1	no	—
151	C₃×C₂²⋊Q₈	—	3	1	no	—
152	C₃×C₄×Q₈	—	2	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×Q₈	—	3	1	no	—
155	C₃×C₄×Q₈	—	3	1	no	—
156	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
157	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×#117	—	3	1	no	—
159	C₃×#117	—	3	1	no	—
160	C₂×C₃×C₄²	—	3	1	no	—
161	#946	C₃×C₄	1	1	yes	characteristic
162	#944	C₃×C₄	1	1	yes	characteristic
163	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
164	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
165	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
166	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
167	#897	C₃×C₄	1	1	yes	characteristic
168	#896	C₃×C₄	1	1	yes	characteristic
169	#896	C₃×C₄	1	1	yes	characteristic
170	#889	C₃×C₄	1	1	yes	characteristic
171	#889	C₃×C₄	1	1	yes	characteristic
172	#888	C₃×C₄	1	1	yes	characteristic
173	#872	C₂²×C₃	1	1	yes	characteristic
174	#872	C₂²×C₃	1	1	yes	characteristic
175	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
176	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
177	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
178	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
179	C₃×C₄⋊C₈	—	2	1	no	—
180	C₃×C₄⋊C₈	—	2	1	no	—
181	C₃×C₄⋊C₈	—	2	1	no	—
182	C₃×C₄⋊C₈	—	3	1	no	—
183	C₃×C₄⋊C₈	—	3	1	no	—
184	C₃×C₄⋊C₈	—	3	1	no	—
185	C₃×C₄⋊C₈	—	3	1	no	—
186	C₃×C₄⋊C₈	—	3	1	no	—
187	C₃×C₄⋊C₈	—	3	1	no	—
188	C₃×C₄⋊C₈	—	3	1	no	—
189	C₃×C₄⋊C₈	—	3	1	no	—
190	C₃×C₄⋊C₈	—	3	1	no	—
191	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
192	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
193	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
194	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
195	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
196	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
197	C₃×#97	—	2	1	no	—
198	C₃×#97	—	2	1	no	—
199	C₃×#97	—	3	1	no	—
200	C₃×#97	—	3	1	no	—
201	C₃×#97	—	3	1	no	—
202	C₃×#97	—	3	1	no	—
203	C₃×#97	—	3	1	no	—
204	C₃×#97	—	3	1	no	—
205	C₃×#97	C₂×D₃	1	1	yes	characteristic
206	C₃×#97	C₂×D₃	1	1	yes	characteristic
207	C₃×#97	C₂²×C₃	1	1	yes	characteristic
208	C₃×#97	C₂²×C₃	1	1	yes	characteristic
209	C₃×C₄×C₈	—	2	1	no	—
210	C₃×C₄×C₈	—	3	1	no	—
211	C₃×C₄×C₈	—	3	1	no	—
212	C₃×C₄×C₈	—	3	1	no	—
213	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
214	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
215	#815	C₂²×C₃	1	1	yes	characteristic
216	#815	C₂²×C₃	1	1	yes	characteristic
217	#815	C₂²×C₃	1	1	yes	characteristic
218	#815	C₂²×C₃	1	1	yes	characteristic
219	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
220	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
221	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
222	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
223	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
224	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
225	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
226	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
227	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
228	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
229	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
230	#803	C₂²×C₃	1	1	yes	characteristic
231	#803	C₂²×C₃	1	1	yes	characteristic
232	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
233	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
234	C₃²×Q₈	—	4	1	no	—
235	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
242	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
249	C₃×C₄×D₃	—	4	1	no	—
250	C₃×C₄×D₃	—	4	1	no	—
251	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
252	C₃×C₄×D₃	#41	1	2	yes	—
253	C₃×Dic₆	—	4	1	no	—
254	C₃×Dic₆	—	4	1	no	—
255	C₃×Dic₆	—	4	1	no	—
256	C₃²×C₈	—	2	1	no	—
257	C₃²×C₈	—	2	1	no	—
258	C₃²×C₈	—	2	1	no	—
259	C₃²×C₈	C₂×Q₈	1	2	yes	—
260	C₃×C₃⋊C₈	—	2	1	no	—
261	C₃×C₃⋊C₈	—	2	1	no	—
262	C₃×C₃⋊C₈	—	2	1	no	—
263	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	—
264	#533	—	3	1	no	—
265	#446	—	3	1	no	—
266	#446	—	3	1	no	—
267	#446	—	3	1	no	—
268	#446	—	3	1	no	—
269	#446	—	3	1	no	—
270	#446	—	3	1	no	—
271	#446	—	3	1	no	—
272	#446	C₃×D₃	1	1	yes	characteristic, complemented
273	#424	—	3	1	no	—
274	#424	—	3	1	no	—
275	#423	—	3	1	no	—
276	#405	—	3	1	no	—
277	#405	—	3	1	no	—
278	C₂×#97	—	3	1	no	—
279	C₂×C₃×Q₈	—	2	1	no	—
280	C₂×C₃×Q₈	—	3	1	no	—
281	C₂×C₃×Q₈	—	3	1	no	—
282	C₂×C₃×Q₈	—	3	1	no	—
283	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
284	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
285	C₂²×C₃×C₄	—	3	1	no	—
286	C₂²×C₃×C₄	—	3	1	no	—
287	C₂²×C₃×C₄	—	3	1	no	—
288	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
289	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
291	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
292	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
293	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
294	C₃×M₁₆	—	6	2	no	—
295	C₃×M₁₆	—	6	2	no	—
296	C₂×C₃×C₈	—	2	1	no	—
297	C₂×C₃×C₈	—	2	1	no	—
298	C₂×C₃×C₈	—	2	1	no	—
299	C₂×C₃×C₈	—	2	1	no	—
300	C₂×C₃×C₈	—	3	1	no	—
301	C₂×C₃×C₈	—	3	4	no	—
302	C₂×C₃×C₈	—	3	1	no	—
303	C₂×C₃×C₈	—	3	1	no	—
304	C₂×C₃×C₈	—	3	1	no	—
305	C₂×C₃×C₈	—	6	2	no	—
306	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
308	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
314	C₃×C₄⋊C₄	—	2	1	no	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	2	1	no	—
317	C₃×C₄⋊C₄	—	3	1	no	—
318	C₃×C₄⋊C₄	—	3	1	no	—
319	C₃×C₄⋊C₄	—	3	1	no	—
320	C₃×C₄⋊C₄	—	3	1	no	—
321	C₃×C₄⋊C₄	—	3	1	no	—
322	C₃×C₄⋊C₄	—	3	1	no	—
323	C₃×C₄⋊C₄	—	3	1	no	—
324	C₃×C₄⋊C₄	—	3	1	no	—
325	C₃×C₄⋊C₄	—	3	1	no	—
326	C₃×C₄⋊C₄	—	3	1	no	—
327	C₃×C₄⋊C₄	—	3	1	no	—
328	C₃×C₄⋊C₄	—	3	1	no	—
329	C₃×C₄⋊C₄	—	3	1	no	—
330	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
331	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
332	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
333	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
334	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
336	C₃×C₂²⋊C₄	—	3	1	no	—
337	C₃×C₂²⋊C₄	—	3	1	no	—
338	C₃×C₂²⋊C₄	—	3	1	no	—
339	C₃×C₂²⋊C₄	—	3	1	no	—
340	C₃×C₄²	—	2	1	no	—
341	C₃×C₄²	—	2	1	no	—
342	C₃×C₄²	—	2	1	no	—
343	C₃×C₄²	—	3	1	no	—
344	C₃×C₄²	—	3	1	no	—
345	C₃×C₄²	—	3	1	no	—
346	C₃×C₄²	—	3	1	no	—
347	C₃×C₄²	—	3	1	no	—
348	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
349	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
350	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
351	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
352	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
353	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
355	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
356	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
357	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
358	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
359	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
360	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
369	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
371	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
372	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
373	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
374	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
375	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
378	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
380	ΓL(1,𝔽₂₅)	—	2	2	no	—
381	ΓL(1,𝔽₂₅)	—	2	2	no	—
382	D₃×C₈	—	2	2	no	—
383	D₃×C₈	C₃×Q₈	1	4	yes	complemented
384	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
385	C₂×C₃×D₃	—	2	1	no	—
386	C₂×C₃×D₃	—	2	1	no	—
387	C₂×C₃×D₃	C₄×Q₈	1	2	yes	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	—	2	1	no	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	—	2	1	no	—
393	C₃²×C₄	—	2	1	no	—
394	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
395	C₃²×C₄	C₂×#41	1	1	yes	characteristic
396	C₃×Dic₃	—	2	1	no	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	2	1	no	—
399	C₃×Dic₃	—	2	1	no	—
400	C₃×Dic₃	—	2	1	no	—
401	C₃×Dic₃	—	2	1	no	—
402	C₃×Dic₃	C₄×Q₈	1	2	yes	—
403	C₂×M₁₆	—	3	1	no	—
404	C₂×M₁₆	—	3	1	no	—
405	C₂²×C₈	—	3	1	no	—
406	C₂²×C₈	—	3	1	no	—
407	C₄⋊Q₈	—	3	1	no	—
408	C₄⋊Q₈	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	C₂²⋊Q₈	—	3	1	no	—
412	C₂²⋊Q₈	—	3	1	no	—
413	C₂²⋊Q₈	—	3	1	no	—
414	C₂²⋊Q₈	—	3	1	no	—
415	C₄×Q₈	—	3	1	no	—
416	C₄×Q₈	—	3	1	no	—
417	C₄×Q₈	—	3	1	no	—
418	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
419	#117	—	3	1	no	—
420	#117	—	3	1	no	—
421	C₂×C₄²	—	3	1	no	—
422	C₄⋊C₈	—	3	1	no	—
423	C₄⋊C₈	—	3	1	no	—
424	C₄⋊C₈	—	3	1	no	—
425	C₄⋊C₈	—	3	1	no	—
426	C₄⋊C₈	—	3	1	no	—
427	C₄⋊C₈	—	3	1	no	—
428	C₄⋊C₈	—	3	1	no	—
429	C₄⋊C₈	—	3	1	no	—
430	C₄⋊C₈	—	3	1	no	—
431	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
432	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
433	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
434	#97	—	3	1	no	—
435	#97	—	3	1	no	—
436	#97	—	3	1	no	—
437	#97	—	3	1	no	—
438	#97	—	3	1	no	—
439	#97	—	3	1	no	—
440	#97	C₂×C₃×D₃	1	1	yes	characteristic
441	#97	C₂×C₃×D₃	1	1	yes	characteristic
442	C₄×C₈	—	3	1	no	—
443	C₄×C₈	—	3	1	no	—
444	C₄×C₈	—	3	1	no	—
445	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
446	C₂³×C₃	—	3	1	no	—
447	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
448	C₃×Q₈	—	4	1	no	—
449	C₃×Q₈	—	4	1	no	—
450	C₃×Q₈	—	4	2	no	—
451	C₃×Q₈	—	12	1	no	—
452	C₃×Q₈	—	12	1	no	—
453	C₃×Q₈	—	12	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	3	1	no	—
462	C₂×C₃×C₄	—	3	2	no	—
463	C₂×C₃×C₄	—	3	2	no	—
464	C₂×C₃×C₄	—	3	1	no	—
465	C₂×C₃×C₄	—	3	1	no	—
466	C₂×C₃×C₄	—	3	1	no	—
467	C₂×C₃×C₄	—	3	1	no	—
468	C₂×C₃×C₄	—	3	1	no	—
469	C₂×C₃×C₄	—	3	1	no	—
470	C₂×C₃×C₄	—	12	1	no	—
471	C₂×C₃×C₄	—	12	1	no	—
472	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
474	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
476	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
477	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
478	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
486	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
487	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
488	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
489	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
490	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
491	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
492	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
493	C₄×D₃	—	4	1	no	—
494	C₄×D₃	—	4	1	no	—
495	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
496	C₄×D₃	C₃×#41	1	2	yes	—
497	Dic₆	—	4	1	no	—
498	Dic₆	—	4	1	no	—
499	Dic₆	—	4	1	no	—
500	C₃×C₈	—	2	1	no	—
501	C₃×C₈	—	2	1	no	—
502	C₃×C₈	—	2	1	no	—
503	C₃×C₈	—	2	1	no	—
504	C₃×C₈	—	2	1	no	—
505	C₃×C₈	—	2	1	no	—
506	C₃×C₈	—	2	2	no	—
507	C₃×C₈	—	3	2	no	—
508	C₃×C₈	—	4	1	no	—
509	C₃×C₈	—	4	1	no	—
510	C₃×C₈	—	4	1	no	—
511	C₃×C₈	—	6	1	no	—
512	C₃×C₈	—	6	1	no	—
513	C₃×C₈	—	6	1	no	—
514	C₃×C₈	D₃×Q₈	1	2	yes	—
515	C₃×C₈	C₂×C₃×Q₈	1	2	yes	—
516	C₃⋊C₈	—	2	1	no	—
517	C₃⋊C₈	—	2	1	no	—
518	C₃⋊C₈	—	2	1	no	—
519	C₃⋊C₈	C₂×C₃×Q₈	1	2	yes	—
520	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
521	C₂×C₃²	#568	1	1	yes	characteristic
522	C₂×C₃²	#568	1	1	yes	characteristic
523	C₃×D₃	—	2	2	no	—
524	C₂×Q₈	—	3	1	no	—
525	C₂×Q₈	—	3	1	no	—
526	C₂×Q₈	—	3	1	no	—
527	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
528	C₂²×C₄	—	3	1	no	—
529	C₂²×C₄	—	3	1	no	—
530	C₂²×C₄	—	3	1	no	—
531	M₁₆	—	6	2	no	—
532	M₁₆	—	6	2	no	—
533	C₂×C₈	—	3	1	no	—
534	C₂×C₈	—	3	4	no	—
535	C₂×C₈	—	3	1	no	—
536	C₂×C₈	—	3	1	no	—
537	C₂×C₈	—	3	1	no	—
538	C₂×C₈	—	6	2	no	—
539	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
540	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
541	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
542	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
543	C₄⋊C₄	—	3	1	no	—
544	C₄⋊C₄	—	3	1	no	—
545	C₄⋊C₄	—	3	1	no	—
546	C₄⋊C₄	—	3	1	no	—
547	C₄⋊C₄	—	3	1	no	—
548	C₄⋊C₄	—	3	1	no	—
549	C₄⋊C₄	—	3	1	no	—
550	C₄⋊C₄	—	3	1	no	—
551	C₄⋊C₄	—	3	1	no	—
552	C₄⋊C₄	—	3	1	no	—
553	C₄⋊C₄	—	3	1	no	—
554	C₄⋊C₄	—	3	1	no	—
555	C₄⋊C₄	—	3	1	no	—
556	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
557	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
558	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
559	C₂²⋊C₄	—	3	1	no	—
560	C₂²⋊C₄	—	3	1	no	—
561	C₂²⋊C₄	—	3	1	no	—
562	C₂²⋊C₄	—	3	1	no	—
563	C₄²	—	3	1	no	—
564	C₄²	—	3	1	no	—
565	C₄²	—	3	1	no	—
566	C₄²	—	3	1	no	—
567	C₄²	—	3	1	no	—
568	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
569	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
570	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	3	2	no	—
573	C₂²×C₃	—	6	1	no	—
574	C₂²×C₃	—	6	1	no	—
575	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
576	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
577	C₂×D₃	—	2	1	no	—
578	C₂×D₃	—	2	1	no	—
579	C₂×D₃	C₃×C₄×Q₈	1	2	yes	—
580	C₃×C₄	—	2	2	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	2	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	3	2	no	—
596	C₃×C₄	—	4	1	no	—
597	C₃×C₄	—	4	1	no	—
598	C₃×C₄	—	4	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	—	6	1	no	—
603	C₃×C₄	—	6	1	no	—
604	C₃×C₄	—	6	1	no	—
605	C₃×C₄	—	6	1	no	—
606	C₃×C₄	—	6	1	no	—
607	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
608	C₃×C₄	D₃×#41	1	1	yes	characteristic
609	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
610	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
611	Dic₃	—	2	1	no	—
612	Dic₃	—	2	1	no	—
613	Dic₃	—	2	1	no	—
614	Dic₃	—	2	1	no	—
615	Dic₃	—	2	1	no	—
616	Dic₃	—	2	1	no	—
617	Dic₃	C₃×C₄×Q₈	1	2	yes	—
618	C₃²	#2961	1	1	yes	characteristic, complemented, Sylow
619	C₂³	—	3	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	12	1	no	—
622	Q₈	—	12	1	no	—
623	Q₈	—	12	1	no	—
624	C₂×C₄	—	3	1	no	—
625	C₂×C₄	—	3	2	no	—
626	C₂×C₄	—	3	2	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	3	1	no	—
633	C₂×C₄	—	12	1	no	—
634	C₂×C₄	—	12	1	no	—
635	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
636	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
637	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
638	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
639	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
640	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
641	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	3	2	no	—
646	C₈	—	6	1	no	—
647	C₈	—	6	1	no	—
648	C₈	—	6	1	no	—
649	C₈	C₃×D₃×Q₈	1	2	yes	—
650	C₂×C₃	—	2	1	no	—
651	C₂×C₃	—	2	1	no	—
652	C₂×C₃	—	2	1	no	—
653	C₂×C₃	—	6	2	no	—
654	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
655	C₂×C₃	#5745	1	1	yes	characteristic
656	C₂×C₃	#5750	1	1	yes	characteristic
657	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
658	C₂×C₃	C₃×#568	1	1	yes	characteristic
659	C₂×C₃	C₃×#568	1	1	yes	characteristic
660	D₃	—	2	2	no	—
661	C₂²	—	3	2	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	3	2	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	1	no	—
677	C₄	—	6	1	no	—
678	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
679	C₄	C₃×D₃×#41	1	1	yes	characteristic
680	C₃	—	2	1	no	—
681	C₃	#79959	1	1	yes	characteristic, direct product factor
682	C₃	C₃×#2961	1	1	yes	characteristic, complemented
683	C₂	—	6	2	no	—
684	C₂	C₃×C₄×D₃×Q₈	1	1	yes	characteristic
685	C₂	C₃×#5745	1	1	yes	characteristic
686	C₂	C₃×#5750	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×#446	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂²×C₃×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#446	D₃
hypocenter	C₃	C₃×#2961
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#446

Complements

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

N	H ≅ G/N	type
2. C₃²×#446	C₂	semidirect
3. C₃×#5024	C₂	semidirect
7. C₃×#4831	C₂	semidirect
8. C₃×#4828	C₂	semidirect
9. C₃×#4828	C₂	semidirect
12. C₃×#4701	C₂	semidirect
13. C₃×#4701	C₂	semidirect
15. C₃×#4679	C₂	semidirect
17. #79959	C₃	direct (N × H)
71. C₃×#446	D₃	semidirect
72. C₃×#446	C₂×C₃	semidirect
79. #5024	C₂×C₃	semidirect
83. #4831	C₂×C₃	semidirect
84. #4828	C₂×C₃	semidirect
85. #4828	C₂×C₃	semidirect
88. #4701	C₂×C₃	semidirect
89. #4701	C₂×C₃	semidirect
91. #4679	C₂×C₃	semidirect
138. C₃×D₃×C₈	Q₈	semidirect
272. #446	C₃×D₃	semidirect
383. D₃×C₈	C₃×Q₈	semidirect
618. C₃²	#2961	semidirect
681. C₃	#79959	direct (N × H)
682. C₃	C₃×#2961	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5578	2
C₃²×#446	2
C₃×#5024	2
C₃×#4839	2
C₃×#4837	2
C₃×#4831	2
C₃×#4828	2
C₃×#4708	2
C₃×D₃×#97	2
C₃×#4701	2
C₃×#4689	2
C₃×#4679	2
C₃×#2961	3
#79959	3

Subgroups — C3×#79959 #11861375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79959 #11861375