Subgroups — C₃×#79899 #11861192

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#5750	C₂	1	2	yes	maximal, complemented
3	C₃²×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5197	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5144	C₂	1	2	yes	maximal, complemented
6	C₃×#4894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4824	C₂	1	2	yes	maximal, complemented
9	C₃×#4821	C₂	1	2	yes	maximal, complemented
10	C₃×#4717	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2957	—	3	1	no	maximal
13	#79899	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×D₃×#41	C₂²	1	2	yes	—
15	C₃²×#135	C₂²	1	1	yes	characteristic
16	C₃²×#131	C₂²	1	2	yes	complemented
17	C₃×#950	C₂²	1	2	yes	—
18	C₃×#948	C₂²	1	2	yes	complemented
19	C₃×#919	C₄	1	1	yes	characteristic, complemented
20	C₃×D₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
21	C₃×#916	C₄	1	2	yes	complemented
22	C₃×D₃×SD₁₆	C₄	1	2	yes	complemented
23	C₃×#912	C₄	1	1	yes	characteristic, complemented
24	C₃×D₃×D₈	C₄	1	1	yes	characteristic, complemented
25	C₃×#907	—	2	2	no	—
26	C₃×#907	C₂²	1	2	yes	complemented
27	C₃×D₃×M₁₆	—	2	2	no	—
28	C₃×D₃×M₁₆	C₂²	1	2	yes	—
29	C₃×#904	C₂²	1	1	yes	characteristic
30	C₃×#901	—	2	2	no	—
31	C₃×#901	C₂²	1	2	yes	complemented
32	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
33	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
34	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₃×#872	C₂²	1	1	yes	characteristic
36	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
37	C₃²×#104	C₂²	1	2	yes	complemented
38	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
39	C₃×#837	C₂²	1	2	yes	complemented
40	C₃×#825	C₂²	1	2	yes	complemented
41	C₃×#822	C₂²	1	2	yes	complemented
42	C₃×#819	C₂²	1	1	yes	characteristic, complemented
43	C₃×#815	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₃×#805	C₂²	1	2	yes	complemented
46	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#135	—	3	1	no	—
48	C₃×#568	—	3	2	no	—
49	D₃×#135	C₂×C₃	1	1	yes	characteristic
50	#5750	C₂×C₃	1	2	yes	complemented
51	C₃×#444	—	2	1	no	—
52	C₃×#444	—	3	1	no	—
53	C₃×#444	—	3	1	no	—
54	C₃×#444	—	3	1	no	—
55	C₃×#444	D₃	1	1	yes	characteristic, complemented
56	C₃×#444	C₂×C₃	1	1	yes	characteristic, complemented
57	C₃×#443	—	3	2	no	—
58	C₃×#443	—	3	2	no	—
59	C₂×C₃×#108	—	3	1	no	—
60	C₃×#421	—	3	2	no	—
61	C₃×#405	—	3	1	no	—
62	#5197	C₂×C₃	1	1	yes	characteristic, complemented
63	#5144	C₂×C₃	1	2	yes	complemented
64	#4894	C₂×C₃	1	1	yes	characteristic, complemented
65	D₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
66	#4824	C₂×C₃	1	2	yes	complemented
67	#4821	C₂×C₃	1	2	yes	complemented
68	#4717	C₂×C₃	1	1	yes	characteristic, complemented
69	#4708	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃²×#41	C₂³	1	2	yes	—
71	C₃×#239	C₂×C₄	1	2	yes	—
72	C₃×D₃×Q₈	C₂×C₄	1	2	yes	—
73	C₃×#237	—	2	2	no	—
74	C₃×#237	C₂×C₄	1	2	yes	—
75	C₃×D₃×D₄	—	2	2	no	—
76	C₃×D₃×D₄	C₂×C₄	1	2	yes	—
77	C₃×#235	—	2	2	no	—
78	C₃×#235	C₂³	1	2	yes	—
79	C₂×C₃×C₄×D₃	—	2	2	no	—
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₃²×Q₁₆	C₂×C₄	1	1	yes	characteristic
82	C₃²×SD₁₆	C₂×C₄	1	2	yes	—
83	C₃²×D₈	C₂×C₄	1	1	yes	characteristic
84	C₃²×M₁₆	—	2	2	no	—
85	C₃²×M₁₆	C₂³	1	2	yes	—
86	C₂×C₃²×C₈	—	2	2	no	—
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
89	C₃²×C₄²	C₂³	1	1	yes	characteristic
90	C₃×#216	C₂×C₄	1	2	yes	—
91	C₃×#215	C₂×C₄	1	2	yes	—
92	C₃×#214	C₂×C₄	1	2	yes	—
93	C₃×#213	C₂×C₄	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
95	C₃×Dic₃⋊C₄	—	2	1	no	—
96	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
97	C₃×#208	—	2	2	no	—
98	C₃×#208	C₂³	1	2	yes	—
99	C₂×C₃×C₃⋊C₈	—	2	2	no	—
100	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₃×Dic₁₂	C₂×C₄	1	1	yes	characteristic
103	C₃×D₂₄	C₂×C₄	1	1	yes	characteristic
104	C₃×#204	C₂×C₄	1	2	yes	—
105	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
106	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
107	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
108	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
109	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
110	C₃×D₃×C₈	—	2	2	no	—
111	C₃×D₃×C₈	—	2	2	no	—
112	C₃×D₃×C₈	—	2	2	no	—
113	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
114	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
115	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
116	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
117	#2957	—	3	1	no	Sylow
118	C₂×C₃×#41	—	3	2	no	—
119	D₃×#41	C₂²×C₃	1	2	yes	—
120	C₃×#135	—	2	1	no	—
121	C₃×#135	—	3	2	no	—
122	C₃×#135	—	3	1	no	—
123	C₃×#135	—	3	2	no	—
124	C₃×#135	—	3	1	no	—
125	C₃×#135	—	3	1	no	—
126	C₃×#135	C₂×D₃	1	1	yes	characteristic
127	C₃×#135	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×Q₁₆	—	3	1	no	—
129	C₂×C₃×SD₁₆	—	3	2	no	—
130	C₂×C₃×D₈	—	3	1	no	—
131	C₃×#131	—	2	2	no	—
132	C₃×#131	—	3	2	no	—
133	C₃×#131	—	3	2	no	—
134	C₃×#131	—	3	2	no	—
135	C₃×#131	—	6	2	no	—
136	C₃×#131	—	6	2	no	—
137	C₃×#131	C₂×D₃	1	2	yes	complemented
138	C₃×#131	C₂²×C₃	1	2	yes	complemented
139	C₂×C₃×M₁₆	—	3	1	no	—
140	C₂×C₃×M₁₆	—	3	2	no	—
141	C₂×C₃×M₁₆	—	6	2	no	—
142	C₂×C₃×M₁₆	—	6	2	no	—
143	C₂²×C₃×C₈	—	3	1	no	—
144	C₃×#117	—	3	1	no	—
145	#950	C₂²×C₃	1	2	yes	—
146	#948	C₂²×C₃	1	2	yes	complemented
147	#919	C₃×C₄	1	1	yes	characteristic, complemented
148	D₃×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
149	#916	C₃×C₄	1	2	yes	complemented
150	D₃×SD₁₆	C₃×C₄	1	2	yes	complemented
151	#912	C₃×C₄	1	1	yes	characteristic, complemented
152	D₃×D₈	C₃×C₄	1	1	yes	characteristic, complemented
153	#907	—	2	2	no	—
154	#907	C₂²×C₃	1	2	yes	complemented
155	D₃×M₁₆	—	2	2	no	—
156	D₃×M₁₆	C₂²×C₃	1	2	yes	—
157	#904	C₂²×C₃	1	1	yes	characteristic
158	#901	—	2	2	no	—
159	#901	C₂²×C₃	1	2	yes	complemented
160	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
161	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
162	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
163	#872	C₂²×C₃	1	1	yes	characteristic
164	C₃×#108	—	2	1	no	—
165	C₃×#108	—	3	2	no	—
166	C₃×#108	—	3	1	no	—
167	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
168	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₃×#104	—	2	2	no	—
170	C₃×#104	—	3	2	no	—
171	C₃×#104	—	3	2	no	—
172	C₃×#104	—	3	2	no	—
173	C₃×#104	C₂×D₃	1	2	yes	complemented
174	C₃×#104	C₂²×C₃	1	2	yes	complemented
175	C₃×#97	—	2	1	no	—
176	C₃×#97	—	3	1	no	—
177	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
178	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₃×C₄×C₈	—	3	1	no	—
180	C₃×C₄×C₈	—	3	1	no	—
181	#837	C₂²×C₃	1	2	yes	complemented
182	#825	C₂²×C₃	1	2	yes	complemented
183	#822	C₂²×C₃	1	2	yes	complemented
184	#819	C₂²×C₃	1	1	yes	characteristic, complemented
185	#815	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
187	#805	C₂²×C₃	1	2	yes	complemented
188	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂²×C₃×D₃	—	2	2	no	—
190	C₂²×C₃×D₃	#41	1	1	yes	characteristic
191	C₃²×Q₈	C₂²×C₄	1	2	yes	—
192	C₃²×D₄	—	2	2	no	—
193	C₃²×D₄	C₂²×C₄	1	2	yes	—
194	C₂×C₃²×C₄	—	2	2	no	—
195	C₂×C₃²×C₄	—	2	1	no	—
196	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
197	C₃×#67	—	2	2	no	—
198	C₃×#67	—	2	2	no	—
199	C₃×#67	—	2	2	no	—
200	C₂×C₃×Dic₃	—	2	2	no	—
201	C₂×C₃×Dic₃	—	2	1	no	—
202	C₂×C₃×Dic₃	#41	1	1	yes	characteristic
203	C₃×D₁₂	—	2	2	no	—
204	C₃×D₁₂	C₂²×C₄	1	2	yes	—
205	C₃×C₄×D₃	—	2	2	no	—
206	C₃×C₄×D₃	—	2	2	no	—
207	C₃×C₄×D₃	—	2	2	no	—
208	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
209	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
210	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
211	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
212	C₃×Dic₆	—	2	2	no	—
213	C₃×Dic₆	C₂²×C₄	1	2	yes	—
214	C₃²×C₈	—	2	2	no	—
215	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
216	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
217	C₃²×C₈	C₂×D₄	1	2	yes	—
218	C₃×C₃⋊C₈	—	2	2	no	—
219	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
222	C₂×#135	—	3	1	no	—
223	#568	—	3	2	no	—
224	#444	—	3	1	no	—
225	#444	—	3	1	no	—
226	#444	—	3	1	no	—
227	#444	C₃×D₃	1	1	yes	characteristic, complemented
228	#443	—	3	2	no	—
229	#443	—	3	2	no	—
230	C₂×#108	—	3	1	no	—
231	#421	—	3	2	no	—
232	#405	—	3	1	no	—
233	C₃×#41	—	2	2	no	—
234	C₃×#41	—	3	2	no	—
235	C₃×#41	—	3	2	no	—
236	C₃×#41	—	3	2	no	—
237	C₃×#41	—	6	2	no	—
238	C₃×#41	—	6	2	no	—
239	C₃×#41	C₂²×D₃	1	2	yes	—
240	C₃×#41	C₂³×C₃	1	2	yes	—
241	C₂×C₃×Q₈	—	3	2	no	—
242	C₂×C₃×D₄	—	3	2	no	—
243	C₂×C₃×D₄	—	6	2	no	—
244	C₂²×C₃×C₄	—	3	1	no	—
245	C₂²×C₃×C₄	—	6	2	no	—
246	#239	C₂×C₃×C₄	1	2	yes	—
247	D₃×Q₈	C₂×C₃×C₄	1	2	yes	—
248	#237	—	2	2	no	—
249	#237	C₂×C₃×C₄	1	2	yes	—
250	D₃×D₄	—	2	2	no	—
251	D₃×D₄	C₂×C₃×C₄	1	2	yes	—
252	#235	—	2	2	no	—
253	#235	C₂³×C₃	1	2	yes	—
254	C₂×C₄×D₃	—	2	2	no	—
255	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
256	C₃×Q₁₆	—	2	1	no	—
257	C₃×Q₁₆	—	3	2	no	—
258	C₃×Q₁₆	—	3	1	no	—
259	C₃×Q₁₆	C₄×D₃	1	1	yes	characteristic
260	C₃×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
261	C₃×SD₁₆	—	2	2	no	—
262	C₃×SD₁₆	—	3	2	no	—
263	C₃×SD₁₆	—	3	2	no	—
264	C₃×SD₁₆	—	3	2	no	—
265	C₃×SD₁₆	C₄×D₃	1	2	yes	—
266	C₃×SD₁₆	C₂×C₃×C₄	1	2	yes	—
267	C₃×D₈	—	2	1	no	—
268	C₃×D₈	—	3	2	no	—
269	C₃×D₈	—	3	1	no	—
270	C₃×D₈	C₄×D₃	1	1	yes	characteristic
271	C₃×D₈	C₂×C₃×C₄	1	1	yes	characteristic
272	C₃×M₁₆	—	2	2	no	—
273	C₃×M₁₆	—	2	2	no	—
274	C₃×M₁₆	—	2	2	no	—
275	C₃×M₁₆	—	3	2	no	—
276	C₃×M₁₆	—	3	2	no	—
277	C₃×M₁₆	—	3	2	no	—
278	C₃×M₁₆	—	4	2	no	—
279	C₃×M₁₆	—	6	2	no	—
280	C₃×M₁₆	—	6	2	no	—
281	C₃×M₁₆	—	6	2	no	—
282	C₃×M₁₆	—	6	2	no	—
283	C₃×M₁₆	C₂²×D₃	1	2	yes	—
284	C₃×M₁₆	C₂³×C₃	1	2	yes	—
285	C₂×C₃×C₈	—	2	2	no	—
286	C₂×C₃×C₈	—	2	2	no	—
287	C₂×C₃×C₈	—	2	1	no	—
288	C₂×C₃×C₈	—	2	1	no	—
289	C₂×C₃×C₈	—	3	1	no	—
290	C₂×C₃×C₈	—	3	1	no	—
291	C₂×C₃×C₈	—	3	1	no	—
292	C₂×C₃×C₈	—	3	1	no	—
293	C₂×C₃×C₈	—	3	1	no	—
294	C₂×C₃×C₈	—	3	1	no	—
295	C₂×C₃×C₈	—	4	2	no	—
296	C₂×C₃×C₈	—	6	2	no	—
297	C₂×C₃×C₈	—	6	2	no	—
298	C₂×C₃×C₈	—	6	2	no	—
299	C₂×C₃×C₈	—	6	2	no	—
300	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
302	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
304	C₃×C₄⋊C₄	—	6	1	no	—
305	C₃×C₂²⋊C₄	—	6	1	no	—
306	C₃×C₄²	—	2	1	no	—
307	C₃×C₄²	—	3	1	no	—
308	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
309	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
310	#216	C₂×C₃×C₄	1	2	yes	—
311	#215	C₂×C₃×C₄	1	2	yes	—
312	#214	C₂×C₃×C₄	1	2	yes	—
313	#213	C₂×C₃×C₄	1	2	yes	—
314	(C₂×D₃)⋊C₄	—	2	1	no	—
315	Dic₃⋊C₄	—	2	1	no	—
316	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
317	#208	—	2	2	no	—
318	#208	C₂³×C₃	1	2	yes	—
319	C₂×C₃⋊C₈	—	2	2	no	—
320	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
321	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
322	Dic₁₂	C₂×C₃×C₄	1	1	yes	characteristic
323	D₂₄	C₂×C₃×C₄	1	1	yes	characteristic
324	#204	C₂×C₃×C₄	1	2	yes	—
325	ΓL(1,𝔽₂₅)	—	2	2	no	—
326	ΓL(1,𝔽₂₅)	—	2	2	no	—
327	ΓL(1,𝔽₂₅)	—	2	2	no	—
328	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
329	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
330	D₃×C₈	—	2	2	no	—
331	D₃×C₈	—	2	2	no	—
332	D₃×C₈	—	2	2	no	—
333	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
334	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
335	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
336	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
337	C₂²×C₃²	—	2	2	no	—
338	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
339	C₂×C₃×D₃	—	2	2	no	—
340	C₂×C₃×D₃	—	4	1	no	—
341	C₂×C₃×D₃	—	8	2	no	—
342	C₂×C₃×D₃	C₄×D₄	1	1	yes	characteristic
343	C₂×C₃×D₃	C₄×D₄	1	1	yes	characteristic
344	C₃²×C₄	—	2	2	no	—
345	C₃²×C₄	—	4	1	no	—
346	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
347	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
348	C₃×Dic₃	—	2	2	no	—
349	C₃×Dic₃	—	4	1	no	—
350	C₃×Dic₃	C₄×D₄	1	1	yes	characteristic
351	C₃×Dic₃	C₄×D₄	1	1	yes	characteristic
352	C₂×#41	—	3	2	no	—
353	#135	—	3	2	no	—
354	#135	—	3	1	no	—
355	#135	—	3	2	no	—
356	#135	—	3	1	no	—
357	#135	—	3	1	no	—
358	#135	C₂×C₃×D₃	1	1	yes	characteristic
359	C₂×Q₁₆	—	3	1	no	—
360	C₂×SD₁₆	—	3	2	no	—
361	C₂×D₈	—	3	1	no	—
362	#131	—	3	2	no	—
363	#131	—	3	2	no	—
364	#131	—	3	2	no	—
365	#131	—	6	2	no	—
366	#131	—	6	2	no	—
367	#131	C₂×C₃×D₃	1	2	yes	complemented
368	C₂×M₁₆	—	3	1	no	—
369	C₂×M₁₆	—	3	2	no	—
370	C₂×M₁₆	—	6	2	no	—
371	C₂×M₁₆	—	6	2	no	—
372	C₂²×C₈	—	3	1	no	—
373	#117	—	3	1	no	—
374	#108	—	3	2	no	—
375	#108	—	3	1	no	—
376	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
377	#104	—	3	2	no	—
378	#104	—	3	2	no	—
379	#104	—	3	2	no	—
380	#104	C₂×C₃×D₃	1	2	yes	complemented
381	#97	—	3	1	no	—
382	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
383	C₄×C₈	—	3	1	no	—
384	C₄×C₈	—	3	1	no	—
385	C₂³×C₃	—	3	1	no	—
386	C₂³×C₃	—	6	2	no	—
387	C₂²×D₃	—	2	2	no	—
388	C₂²×D₃	C₃×#41	1	1	yes	characteristic
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	3	2	no	—
391	C₃×Q₈	—	6	2	no	—
392	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
393	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
394	C₃×D₄	—	2	2	no	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	3	2	no	—
398	C₃×D₄	—	4	2	no	—
399	C₃×D₄	—	6	2	no	—
400	C₃×D₄	—	6	2	no	—
401	C₃×D₄	—	6	2	no	—
402	C₃×D₄	—	6	2	no	—
403	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
404	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	3	1	no	—
411	C₂×C₃×C₄	—	3	1	no	—
412	C₂×C₃×C₄	—	3	1	no	—
413	C₂×C₃×C₄	—	3	1	no	—
414	C₂×C₃×C₄	—	3	1	no	—
415	C₂×C₃×C₄	—	4	2	no	—
416	C₂×C₃×C₄	—	4	1	no	—
417	C₂×C₃×C₄	—	6	2	no	—
418	C₂×C₃×C₄	—	6	2	no	—
419	C₂×C₃×C₄	—	6	2	no	—
420	C₂×C₃×C₄	—	6	2	no	—
421	C₂×C₃×C₄	—	6	1	no	—
422	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
424	#67	—	2	2	no	—
425	#67	—	2	2	no	—
426	#67	—	2	2	no	—
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	C₃×#41	1	1	yes	characteristic
430	D₁₂	—	2	2	no	—
431	D₁₂	C₂²×C₃×C₄	1	2	yes	—
432	C₄×D₃	—	2	2	no	—
433	C₄×D₃	—	2	2	no	—
434	C₄×D₃	—	2	2	no	—
435	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
436	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
437	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
438	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
439	Dic₆	—	2	2	no	—
440	Dic₆	C₂²×C₃×C₄	1	2	yes	—
441	C₃×C₈	—	2	2	no	—
442	C₃×C₈	—	2	2	no	—
443	C₃×C₈	—	2	1	no	—
444	C₃×C₈	—	2	1	no	—
445	C₃×C₈	—	2	2	no	—
446	C₃×C₈	—	3	1	no	—
447	C₃×C₈	—	3	1	no	—
448	C₃×C₈	—	3	2	no	—
449	C₃×C₈	—	4	2	no	—
450	C₃×C₈	—	6	2	no	—
451	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
452	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
453	C₃×C₈	D₃×D₄	1	2	yes	—
454	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
456	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
457	C₃⋊C₈	—	2	2	no	—
458	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
459	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
460	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
461	C₂×C₃²	—	2	1	no	—
462	C₂×C₃²	—	4	2	no	—
463	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
464	C₃×D₃	—	2	1	no	—
465	C₃×D₃	—	2	1	no	—
466	C₃×D₃	—	4	2	no	—
467	#41	—	3	2	no	—
468	#41	—	3	2	no	—
469	#41	—	3	2	no	—
470	#41	—	6	2	no	—
471	#41	—	6	2	no	—
472	#41	C₂²×C₃×D₃	1	2	yes	—
473	C₂×Q₈	—	3	2	no	—
474	C₂×D₄	—	3	2	no	—
475	C₂×D₄	—	6	2	no	—
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	6	2	no	—
478	Q₁₆	—	3	2	no	—
479	Q₁₆	—	3	1	no	—
480	Q₁₆	C₃×C₄×D₃	1	1	yes	characteristic
481	SD₁₆	—	3	2	no	—
482	SD₁₆	—	3	2	no	—
483	SD₁₆	—	3	2	no	—
484	SD₁₆	C₃×C₄×D₃	1	2	yes	—
485	D₈	—	3	2	no	—
486	D₈	—	3	1	no	—
487	D₈	C₃×C₄×D₃	1	1	yes	characteristic
488	M₁₆	—	2	2	no	—
489	M₁₆	—	3	2	no	—
490	M₁₆	—	3	2	no	—
491	M₁₆	—	3	2	no	—
492	M₁₆	—	6	2	no	—
493	M₁₆	—	6	2	no	—
494	M₁₆	—	6	2	no	—
495	M₁₆	—	6	2	no	—
496	M₁₆	C₂²×C₃×D₃	1	2	yes	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	3	1	no	—
499	C₂×C₈	—	3	1	no	—
500	C₂×C₈	—	3	1	no	—
501	C₂×C₈	—	3	1	no	—
502	C₂×C₈	—	3	1	no	—
503	C₂×C₈	—	3	1	no	—
504	C₂×C₈	—	6	2	no	—
505	C₂×C₈	—	6	2	no	—
506	C₂×C₈	—	6	2	no	—
507	C₂×C₈	—	6	2	no	—
508	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
509	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
510	C₄⋊C₄	—	6	1	no	—
511	C₂²⋊C₄	—	6	1	no	—
512	C₄²	—	3	1	no	—
513	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	3	1	no	—
518	C₂²×C₃	—	3	1	no	—
519	C₂²×C₃	—	4	2	no	—
520	C₂²×C₃	—	6	2	no	—
521	C₂²×C₃	—	12	1	no	—
522	C₂²×C₃	—	24	2	no	—
523	C₂²×C₃	D₃×#41	1	1	yes	characteristic
524	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	4	1	no	—
527	C₂×D₃	—	8	2	no	—
528	C₂×D₃	C₃×C₄×D₄	1	1	yes	characteristic
529	C₂×D₃	C₃×C₄×D₄	1	1	yes	characteristic
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	2	2	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	3	1	no	—
535	C₃×C₄	—	3	1	no	—
536	C₃×C₄	—	4	2	no	—
537	C₃×C₄	—	4	1	no	—
538	C₃×C₄	—	4	1	no	—
539	C₃×C₄	—	6	2	no	—
540	C₃×C₄	—	8	1	no	—
541	C₃×C₄	—	12	1	no	—
542	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
543	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
544	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
545	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
546	Dic₃	—	2	2	no	—
547	Dic₃	—	4	1	no	—
548	Dic₃	C₃×C₄×D₄	1	1	yes	characteristic
549	Dic₃	C₃×C₄×D₄	1	1	yes	characteristic
550	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
551	C₂³	—	3	1	no	—
552	C₂³	—	6	2	no	—
553	Q₈	—	3	2	no	—
554	Q₈	—	6	2	no	—
555	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
556	D₄	—	2	2	no	—
557	D₄	—	3	2	no	—
558	D₄	—	6	2	no	—
559	D₄	—	6	2	no	—
560	D₄	—	6	2	no	—
561	D₄	—	6	2	no	—
562	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	1	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	6	2	no	—
571	C₂×C₄	—	6	2	no	—
572	C₂×C₄	—	6	2	no	—
573	C₂×C₄	—	6	2	no	—
574	C₂×C₄	—	6	1	no	—
575	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	3	1	no	—
578	C₈	—	3	1	no	—
579	C₈	—	3	2	no	—
580	C₈	—	6	2	no	—
581	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
582	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
583	C₈	C₃×D₃×D₄	1	2	yes	—
584	C₂×C₃	—	2	1	no	—
585	C₂×C₃	—	2	1	no	—
586	C₂×C₃	—	2	1	no	—
587	C₂×C₃	—	4	1	no	—
588	C₂×C₃	—	4	2	no	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	6	1	no	—
591	C₂×C₃	—	6	1	no	—
592	C₂×C₃	—	8	2	no	—
593	C₂×C₃	—	12	2	no	—
594	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
595	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
596	D₃	—	2	1	no	—
597	D₃	—	2	1	no	—
598	D₃	—	4	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	3	1	no	—
601	C₂²	—	3	1	no	—
602	C₂²	—	6	2	no	—
603	C₂²	—	12	1	no	—
604	C₂²	—	24	2	no	—
605	C₂²	C₃×D₃×#41	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	3	1	no	—
608	C₄	—	3	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	6	2	no	—
611	C₄	—	12	1	no	—
612	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
613	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
614	C₃	—	2	1	no	—
615	C₃	#79899	1	1	yes	characteristic, direct product factor
616	C₃	C₃×#2957	1	1	yes	characteristic, complemented
617	C₂	—	2	1	no	—
618	C₂	—	4	2	no	—
619	C₂	—	6	1	no	—
620	C₂	—	6	1	no	—
621	C₂	—	12	2	no	—
622	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#444	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₃×D₃×#135	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#444	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#444

Complements

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

N	H ≅ G/N	type
2. C₃×#5750	C₂	semidirect
3. C₃²×#444	C₂	semidirect
4. C₃×#5197	C₂	semidirect
5. C₃×#5144	C₂	semidirect
6. C₃×#4894	C₂	semidirect
7. C₃×D₃×#108	C₂	semidirect
8. C₃×#4824	C₂	semidirect
9. C₃×#4821	C₂	semidirect
10. C₃×#4717	C₂	semidirect
11. C₃×#4708	C₂	semidirect
13. #79899	C₃	direct (N × H)
16. C₃²×#131	C₂²	semidirect
18. C₃×#948	C₂²	semidirect
19. C₃×#919	C₄	semidirect
20. C₃×D₃×Q₁₆	C₄	semidirect
21. C₃×#916	C₄	semidirect
22. C₃×D₃×SD₁₆	C₄	semidirect
23. C₃×#912	C₄	semidirect
24. C₃×D₃×D₈	C₄	semidirect
26. C₃×#907	C₂²	semidirect
31. C₃×#901	C₂²	semidirect
36. C₃²×#108	C₂²	semidirect
37. C₃²×#104	C₂²	semidirect
38. C₃²×#97	C₂²	semidirect
39. C₃×#837	C₂²	semidirect
40. C₃×#825	C₂²	semidirect
41. C₃×#822	C₂²	semidirect
42. C₃×#819	C₂²	semidirect
43. C₃×#815	C₂²	semidirect
44. C₃×C₈×Dic₃	C₂²	semidirect
45. C₃×#805	C₂²	semidirect
46. C₃×C₄×C₃⋊C₈	C₂²	semidirect
50. #5750	C₂×C₃	semidirect
55. C₃×#444	D₃	semidirect
56. C₃×#444	C₂×C₃	semidirect
62. #5197	C₂×C₃	semidirect
63. #5144	C₂×C₃	semidirect
64. #4894	C₂×C₃	semidirect
65. D₃×#108	C₂×C₃	semidirect
66. #4824	C₂×C₃	semidirect
67. #4821	C₂×C₃	semidirect
68. #4717	C₂×C₃	semidirect
69. #4708	C₂×C₃	semidirect
137. C₃×#131	C₂×D₃	semidirect
138. C₃×#131	C₂²×C₃	semidirect
146. #948	C₂²×C₃	semidirect
147. #919	C₃×C₄	semidirect
148. D₃×Q₁₆	C₃×C₄	semidirect
149. #916	C₃×C₄	semidirect
150. D₃×SD₁₆	C₃×C₄	semidirect
151. #912	C₃×C₄	semidirect
152. D₃×D₈	C₃×C₄	semidirect
154. #907	C₂²×C₃	semidirect
159. #901	C₂²×C₃	semidirect
167. C₃×#108	C₂×D₃	semidirect
168. C₃×#108	C₂²×C₃	semidirect
173. C₃×#104	C₂×D₃	semidirect
174. C₃×#104	C₂²×C₃	semidirect
177. C₃×#97	C₂×D₃	semidirect
178. C₃×#97	C₂²×C₃	semidirect
181. #837	C₂²×C₃	semidirect
182. #825	C₂²×C₃	semidirect
183. #822	C₂²×C₃	semidirect
184. #819	C₂²×C₃	semidirect
185. #815	C₂²×C₃	semidirect
186. C₈×Dic₃	C₂²×C₃	semidirect
187. #805	C₂²×C₃	semidirect
188. C₄×C₃⋊C₈	C₂²×C₃	semidirect
227. #444	C₃×D₃	semidirect
367. #131	C₂×C₃×D₃	semidirect
376. #108	C₂×C₃×D₃	semidirect
380. #104	C₂×C₃×D₃	semidirect
382. #97	C₂×C₃×D₃	semidirect
550. C₃²	#2957	semidirect
615. C₃	#79899	direct (N × H)
616. C₃	C₃×#2957	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#135	2
C₃×#5750	2
C₃²×#444	2
C₃×#5197	2
C₃×#5144	2
C₃×#4894	2
C₃×D₃×#108	2
C₃×#4824	2
C₃×#4821	2
C₃×#4717	2
C₃×#4708	2
C₃×#2957	3
#79899	3

Subgroups — C3×#79899 #11861192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79899 #11861192