Subgroups — C₃×#79867 #11860666

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#5545	C₂	1	2	yes	maximal, complemented
3	C₃²×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#213	C₂	1	2	yes	maximal, complemented
6	C₃×#4869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4860	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4770	C₂	1	2	yes	maximal, complemented
9	C₃×#4756	C₂	1	2	yes	maximal, complemented
10	C₃×#4711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2948	—	3	1	no	maximal
13	#79867	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
15	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
16	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
17	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₃×#213	C₂²	1	2	yes	—
19	C₃×C₄×#67	—	2	2	no	—
20	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
21	C₃×D₃×D₈	C₄	1	8	yes	complemented
22	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₃×#893	C₂²	1	2	yes	complemented
26	C₃×#892	C₂²	1	2	yes	—
27	C₃×#67⋊C₄	—	2	2	no	—
28	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
29	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
30	C₃×#872	C₂²	1	1	yes	characteristic
31	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#102	C₂²	1	2	yes	complemented
33	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
34	C₃×#832	C₂²	1	2	yes	complemented
35	C₃×#821	C₂²	1	2	yes	complemented
36	C₃×#817	C₂²	1	1	yes	characteristic, complemented
37	C₃×#815	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₃×#809	C₂²	1	2	yes	complemented
40	C₃×#807	C₂²	1	2	yes	complemented
41	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₃×D₈	—	3	1	no	—
43	C₃×#518	—	3	2	no	—
44	C₂×D₃×D₈	C₂×C₃	1	1	yes	characteristic
45	#5545	C₂×C₃	1	2	yes	complemented
46	C₃×#442	—	2	1	no	—
47	C₃×#442	—	3	1	no	—
48	C₃×#442	—	3	1	no	—
49	C₃×#442	—	3	1	no	—
50	C₃×#442	D₃	1	1	yes	characteristic, complemented
51	C₃×#442	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×C₄×D₈	—	3	2	no	—
53	C₃×C₄×D₈	—	3	2	no	—
54	C₃×#427	—	3	1	no	—
55	C₃×#418	—	3	2	no	—
56	C₃×#405	—	3	1	no	—
57	#5152	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×#213	C₂×C₃	1	2	yes	complemented
59	#4869	C₂×C₃	1	1	yes	characteristic, complemented
60	#4860	C₂×C₃	1	1	yes	characteristic, complemented
61	#4770	C₂×C₃	1	2	yes	complemented
62	#4756	C₂×C₃	1	2	yes	complemented
63	#4711	C₂×C₃	1	1	yes	characteristic, complemented
64	#4708	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂³×C₃×D₃	—	2	2	no	—
66	C₂×C₃²×D₄	C₂³	1	2	yes	—
67	C₂²×C₃²×C₄	—	2	2	no	—
68	C₂×C₃×#67	—	2	2	no	—
69	C₂²×C₃×Dic₃	—	2	2	no	—
70	C₃×D₃×D₄	—	2	4	no	—
71	C₃×D₃×D₄	C₂×C₄	1	8	yes	complemented
72	C₂×C₃×D₁₂	C₂³	1	2	yes	—
73	C₂×C₃×C₄×D₃	—	2	2	no	—
74	C₂×C₃×C₄×D₃	—	2	2	no	—
75	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
76	C₃²×D₈	C₂×C₄	1	4	yes	complemented
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₂²⋊C₄	—	2	2	no	—
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#217	—	2	2	no	—
83	C₃×#213	C₂×C₄	1	8	yes	complemented
84	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
87	C₃×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
88	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
89	C₃×Dic₃⋊C₄	D₄	1	2	yes	—
90	C₃×C₄×Dic₃	—	2	2	no	—
91	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
95	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
96	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
97	#2948	—	3	1	no	Sylow
98	C₂²×C₃×D₄	—	3	2	no	—
99	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×D₈	—	2	1	no	—
101	C₂×C₃×D₈	—	3	2	no	—
102	C₂×C₃×D₈	—	3	8	no	—
103	C₂×C₃×D₈	—	3	1	no	—
104	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
105	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×M₁₆	—	3	1	no	—
107	C₂²×C₃×C₈	—	3	1	no	—
108	C₃×C₄×D₄	—	2	2	no	—
109	C₃×C₄×D₄	—	3	2	no	—
110	C₃×C₄×D₄	—	3	2	no	—
111	C₃×C₄×D₄	—	3	2	no	—
112	C₃×C₄×D₄	—	6	2	no	—
113	C₃×C₄×D₄	—	6	2	no	—
114	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
115	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
116	C₃×#117	—	3	1	no	—
117	C₃×#117	—	3	2	no	—
118	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
119	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
120	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
121	C₂×#213	C₂²×C₃	1	2	yes	—
122	C₄×#67	—	2	2	no	—
123	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
124	D₃×D₈	C₃×C₄	1	8	yes	complemented
125	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
127	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
128	#893	C₂²×C₃	1	2	yes	complemented
129	#892	C₂²×C₃	1	2	yes	—
130	#67⋊C₄	—	2	2	no	—
131	D₃×C₂²⋊C₄	—	2	2	no	—
132	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
133	#872	C₂²×C₃	1	1	yes	characteristic
134	C₃×#107	—	3	2	no	—
135	C₃×#106	—	2	1	no	—
136	C₃×#106	—	3	1	no	—
137	C₃×#106	C₂×D₃	1	1	yes	characteristic, complemented
138	C₃×#106	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃×#102	—	2	2	no	—
140	C₃×#102	—	3	2	no	—
141	C₃×#102	—	3	2	no	—
142	C₃×#102	—	3	2	no	—
143	C₃×#102	C₂×D₃	1	2	yes	complemented
144	C₃×#102	C₂²×C₃	1	2	yes	complemented
145	C₃×#97	—	2	1	no	—
146	C₃×#97	—	3	1	no	—
147	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
148	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₃×C₄×C₈	—	3	1	no	—
150	C₃×C₄×C₈	—	3	1	no	—
151	#832	C₂²×C₃	1	2	yes	complemented
152	#821	C₂²×C₃	1	2	yes	complemented
153	#817	C₂²×C₃	1	1	yes	characteristic, complemented
154	#815	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
156	#809	C₂²×C₃	1	2	yes	complemented
157	#807	C₂²×C₃	1	2	yes	complemented
158	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂³×C₃²	—	2	2	no	—
160	C₂²×C₃×D₃	—	2	2	no	—
161	C₂²×C₃×D₃	—	2	8	no	—
162	C₂²×C₃×D₃	—	8	2	no	—
163	C₂²×C₃×D₃	—	8	2	no	—
164	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
165	C₃²×D₄	—	2	2	no	—
166	C₃²×D₄	C₂²×C₄	1	4	yes	—
167	C₂×C₃²×C₄	—	2	2	no	—
168	C₂×C₃²×C₄	—	8	2	no	—
169	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
170	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
171	C₃×#67	—	2	8	no	—
172	C₂×C₃×Dic₃	—	2	2	no	—
173	C₂×C₃×Dic₃	—	8	2	no	—
174	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
175	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
176	C₃×D₁₂	—	2	2	no	—
177	C₃×D₁₂	C₂²×C₄	1	4	yes	—
178	C₃×C₄×D₃	—	8	2	no	—
179	C₃×C₄×D₃	—	8	2	no	—
180	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
181	C₃×C₄×D₃	#41	1	2	yes	—
182	C₃²×C₈	—	2	1	no	—
183	C₃²×C₈	C₂²×C₄	1	2	yes	—
184	C₃×C₃⋊C₈	—	2	1	no	—
185	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
186	C₂²×D₈	—	3	1	no	—
187	#518	—	3	2	no	—
188	#442	—	3	1	no	—
189	#442	—	3	1	no	—
190	#442	—	3	1	no	—
191	#442	C₃×D₃	1	1	yes	characteristic, complemented
192	C₄×D₈	—	3	2	no	—
193	C₄×D₈	—	3	2	no	—
194	#427	—	3	1	no	—
195	#418	—	3	2	no	—
196	#405	—	3	1	no	—
197	C₂⁴×C₃	—	6	2	no	—
198	C₂³×D₃	—	2	2	no	—
199	C₂×C₃×D₄	—	2	2	no	—
200	C₂×C₃×D₄	—	3	8	no	—
201	C₂×C₃×D₄	—	3	2	no	—
202	C₂×C₃×D₄	—	6	4	no	—
203	C₂×C₃×D₄	—	6	2	no	—
204	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
205	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	4	2	no	—
210	C₂²×C₃×C₄	—	6	2	no	—
211	C₂²×C₃×C₄	—	6	2	no	—
212	C₂²×C₃×C₄	—	6	2	no	—
213	C₂×#67	—	2	2	no	—
214	C₂²×Dic₃	—	2	2	no	—
215	D₃×D₄	—	2	4	no	—
216	D₃×D₄	C₂×C₃×C₄	1	8	yes	complemented
217	C₂×D₁₂	C₂³×C₃	1	2	yes	—
218	C₂×C₄×D₃	—	2	2	no	—
219	C₂×C₄×D₃	—	2	2	no	—
220	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
221	C₃×D₈	—	2	4	no	—
222	C₃×D₈	—	3	8	no	—
223	C₃×D₈	—	3	4	no	—
224	C₃×D₈	C₄×D₃	1	4	yes	complemented
225	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
226	C₃×M₁₆	—	6	2	no	—
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	—	2	1	no	—
229	C₂×C₃×C₈	—	3	1	no	—
230	C₂×C₃×C₈	—	3	4	no	—
231	C₂×C₃×C₈	—	3	1	no	—
232	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	3	2	no	—
238	C₃×C₄⋊C₄	—	3	2	no	—
239	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
240	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
241	C₃×C₂²⋊C₄	—	2	2	no	—
242	C₃×C₂²⋊C₄	—	2	2	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	4	2	no	—
245	C₃×C₂²⋊C₄	—	6	2	no	—
246	C₃×C₂²⋊C₄	—	6	2	no	—
247	C₃×C₂²⋊C₄	—	6	2	no	—
248	C₃×C₂²⋊C₄	—	6	2	no	—
249	C₃×C₄²	—	2	1	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	6	2	no	—
252	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
253	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
254	#217	—	2	2	no	—
255	#213	C₂×C₃×C₄	1	8	yes	complemented
256	(C₂×D₃)⋊C₄	—	2	2	no	—
257	(C₂×D₃)⋊C₄	—	2	2	no	—
258	(C₂×D₃)⋊C₄	—	2	2	no	—
259	(C₂×D₃)⋊C₄	C₃×D₄	1	2	yes	—
260	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
261	Dic₃⋊C₄	C₃×D₄	1	2	yes	—
262	C₄×Dic₃	—	2	2	no	—
263	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
266	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
267	ΓL(1,𝔽₂₅)	—	2	2	no	—
268	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
269	C₂²×C₃²	—	2	4	no	—
270	C₂²×C₃²	—	4	2	no	—
271	C₂²×C₃²	—	4	2	no	—
272	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₃×D₃	—	2	2	no	—
274	C₂×C₃×D₃	—	2	4	no	—
275	C₂×C₃×D₃	—	4	2	no	—
276	C₂×C₃×D₃	—	4	2	no	—
277	C₂×C₃×D₃	—	8	8	no	—
278	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
279	C₃²×C₄	—	2	2	no	—
280	C₃²×C₄	—	4	2	no	—
281	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
282	C₃²×C₄	C₂×#41	1	1	yes	characteristic
283	C₃×Dic₃	—	2	2	no	—
284	C₃×Dic₃	—	4	2	no	—
285	C₃×Dic₃	C₄×D₄	1	2	yes	—
286	C₂²×D₄	—	3	2	no	—
287	C₂×D₈	—	3	2	no	—
288	C₂×D₈	—	3	8	no	—
289	C₂×D₈	—	3	1	no	—
290	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
291	C₂×M₁₆	—	3	1	no	—
292	C₂²×C₈	—	3	1	no	—
293	C₄×D₄	—	3	2	no	—
294	C₄×D₄	—	3	2	no	—
295	C₄×D₄	—	3	2	no	—
296	C₄×D₄	—	6	2	no	—
297	C₄×D₄	—	6	2	no	—
298	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
299	#117	—	3	1	no	—
300	#117	—	3	2	no	—
301	C₂×C₂²⋊C₄	—	6	2	no	—
302	C₂×C₂²⋊C₄	—	6	2	no	—
303	#107	—	3	2	no	—
304	#106	—	3	1	no	—
305	#106	C₂×C₃×D₃	1	1	yes	characteristic, complemented
306	#102	—	3	2	no	—
307	#102	—	3	2	no	—
308	#102	—	3	2	no	—
309	#102	C₂×C₃×D₃	1	2	yes	complemented
310	#97	—	3	1	no	—
311	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
312	C₄×C₈	—	3	1	no	—
313	C₄×C₈	—	3	1	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	2	2	no	—
316	C₂³×C₃	—	3	1	no	—
317	C₂³×C₃	—	4	2	no	—
318	C₂³×C₃	—	6	8	no	—
319	C₂³×C₃	—	6	2	no	—
320	C₂³×C₃	—	24	2	no	—
321	C₂³×C₃	—	24	2	no	—
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	—	2	8	no	—
324	C₂²×D₃	—	8	2	no	—
325	C₂²×D₃	—	8	2	no	—
326	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	4	no	—
330	C₃×D₄	—	3	4	no	—
331	C₃×D₄	—	4	2	no	—
332	C₃×D₄	—	6	8	no	—
333	C₃×D₄	—	6	2	no	—
334	C₃×D₄	C₂×C₄×D₃	1	4	yes	—
335	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	3	1	no	—
341	C₂×C₃×C₄	—	3	2	no	—
342	C₂×C₃×C₄	—	3	2	no	—
343	C₂×C₃×C₄	—	3	2	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	6	2	no	—
346	C₂×C₃×C₄	—	8	2	no	—
347	C₂×C₃×C₄	—	8	2	no	—
348	C₂×C₃×C₄	—	8	4	no	—
349	C₂×C₃×C₄	—	24	2	no	—
350	C₂×C₃×C₄	—	24	2	no	—
351	C₂×C₃×C₄	—	24	2	no	—
352	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
353	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
354	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
356	#67	—	2	8	no	—
357	C₂×Dic₃	—	2	2	no	—
358	C₂×Dic₃	—	8	2	no	—
359	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
360	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
361	D₁₂	—	2	2	no	—
362	D₁₂	C₂²×C₃×C₄	1	4	yes	—
363	C₄×D₃	—	8	2	no	—
364	C₄×D₃	—	8	2	no	—
365	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
366	C₄×D₃	C₃×#41	1	2	yes	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	1	no	—
369	C₃×C₈	—	2	2	no	—
370	C₃×C₈	—	3	2	no	—
371	C₃×C₈	—	4	1	no	—
372	C₃×C₈	—	6	1	no	—
373	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
374	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
375	C₃⋊C₈	—	2	1	no	—
376	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
377	C₂×C₃²	—	4	4	no	—
378	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
379	C₂×C₃²	#576	1	2	yes	—
380	C₃×D₃	—	2	2	no	—
381	C₃×D₃	—	4	4	no	—
382	C₂⁴	—	6	2	no	—
383	C₂×D₄	—	3	8	no	—
384	C₂×D₄	—	3	2	no	—
385	C₂×D₄	—	6	4	no	—
386	C₂×D₄	—	6	2	no	—
387	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	6	2	no	—
391	C₂²×C₄	—	6	2	no	—
392	C₂²×C₄	—	6	2	no	—
393	D₈	—	3	8	no	—
394	D₈	—	3	4	no	—
395	D₈	C₃×C₄×D₃	1	4	yes	complemented
396	M₁₆	—	6	2	no	—
397	C₂×C₈	—	3	1	no	—
398	C₂×C₈	—	3	4	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
401	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
402	C₄⋊C₄	—	3	2	no	—
403	C₄⋊C₄	—	3	2	no	—
404	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	3	2	no	—
407	C₂²⋊C₄	—	6	2	no	—
408	C₂²⋊C₄	—	6	2	no	—
409	C₂²⋊C₄	—	6	2	no	—
410	C₂²⋊C₄	—	6	2	no	—
411	C₄²	—	3	1	no	—
412	C₄²	—	6	2	no	—
413	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
414	C₂²×C₃	—	2	4	no	—
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	3	2	no	—
418	C₂²×C₃	—	4	4	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	—	4	2	no	—
423	C₂²×C₃	—	6	2	no	—
424	C₂²×C₃	—	6	4	no	—
425	C₂²×C₃	—	8	2	no	—
426	C₂²×C₃	—	8	2	no	—
427	C₂²×C₃	—	12	2	no	—
428	C₂²×C₃	—	12	2	no	—
429	C₂²×C₃	—	24	8	no	—
430	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
431	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
432	C₂×D₃	—	2	2	no	—
433	C₂×D₃	—	2	4	no	—
434	C₂×D₃	—	4	2	no	—
435	C₂×D₃	—	4	2	no	—
436	C₂×D₃	—	8	8	no	—
437	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	1	no	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	3	2	no	—
443	C₃×C₄	—	4	2	no	—
444	C₃×C₄	—	4	2	no	—
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	6	2	no	—
447	C₃×C₄	—	8	2	no	—
448	C₃×C₄	—	12	2	no	—
449	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
450	C₃×C₄	D₃×#41	1	1	yes	characteristic
451	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
452	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
453	Dic₃	—	2	2	no	—
454	Dic₃	—	4	2	no	—
455	Dic₃	C₃×C₄×D₄	1	2	yes	—
456	C₃²	#2948	1	1	yes	characteristic, complemented, Sylow
457	C₂³	—	2	2	no	—
458	C₂³	—	3	1	no	—
459	C₂³	—	6	8	no	—
460	C₂³	—	6	2	no	—
461	C₂³	—	24	2	no	—
462	C₂³	—	24	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	3	4	no	—
465	D₄	—	6	8	no	—
466	D₄	—	6	2	no	—
467	D₄	C₂×C₃×C₄×D₃	1	4	yes	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	3	1	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	3	2	no	—
472	C₂×C₄	—	3	2	no	—
473	C₂×C₄	—	6	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	—	24	2	no	—
476	C₂×C₄	—	24	2	no	—
477	C₂×C₄	—	24	2	no	—
478	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
479	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
480	C₈	—	2	1	no	—
481	C₈	—	3	2	no	—
482	C₈	—	6	1	no	—
483	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
484	C₂×C₃	—	2	2	no	—
485	C₂×C₃	—	2	1	no	—
486	C₂×C₃	—	4	4	no	—
487	C₂×C₃	—	4	4	no	—
488	C₂×C₃	—	6	2	no	—
489	C₂×C₃	—	8	4	no	—
490	C₂×C₃	—	12	4	no	—
491	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
492	C₂×C₃	#5774	1	2	yes	—
493	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
494	C₂×C₃	C₃×#576	1	2	yes	—
495	D₃	—	2	2	no	—
496	D₃	—	4	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	3	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	6	2	no	—
502	C₂²	—	6	4	no	—
503	C₂²	—	12	2	no	—
504	C₂²	—	12	2	no	—
505	C₂²	—	24	8	no	—
506	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	3	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	6	2	no	—
511	C₄	—	12	2	no	—
512	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
513	C₄	C₃×D₃×#41	1	1	yes	characteristic
514	C₃	—	2	1	no	—
515	C₃	#79867	1	1	yes	characteristic, direct product factor
516	C₃	C₃×#2948	1	1	yes	characteristic, complemented
517	C₂	—	4	4	no	—
518	C₂	—	6	2	no	—
519	C₂	—	12	4	no	—
520	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
521	C₂	C₃×#5774	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#442	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#442	D₃
hypocenter	C₃	C₃×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#442

Complements

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

N	H ≅ G/N	type
2. C₃×#5545	C₂	semidirect
3. C₃²×#442	C₂	semidirect
4. C₃×#5152	C₂	semidirect
5. C₃×C₄×#213	C₂	semidirect
6. C₃×#4869	C₂	semidirect
7. C₃×#4860	C₂	semidirect
8. C₃×#4770	C₂	semidirect
9. C₃×#4756	C₂	semidirect
10. C₃×#4711	C₂	semidirect
11. C₃×#4708	C₂	semidirect
13. #79867	C₃	direct (N × H)
16. C₃²×C₄×D₄	C₂²	semidirect
17. C₃×D₄×Dic₃	C₂²	semidirect
21. C₃×D₃×D₈	C₄	semidirect
25. C₃×#893	C₂²	semidirect
29. C₃×C₄×D₁₂	C₂²	semidirect
31. C₃²×#106	C₂²	semidirect
32. C₃²×#102	C₂²	semidirect
33. C₃²×#97	C₂²	semidirect
34. C₃×#832	C₂²	semidirect
35. C₃×#821	C₂²	semidirect
36. C₃×#817	C₂²	semidirect
37. C₃×#815	C₂²	semidirect
38. C₃×C₈×Dic₃	C₂²	semidirect
39. C₃×#809	C₂²	semidirect
40. C₃×#807	C₂²	semidirect
41. C₃×C₄×C₃⋊C₈	C₂²	semidirect
45. #5545	C₂×C₃	semidirect
50. C₃×#442	D₃	semidirect
51. C₃×#442	C₂×C₃	semidirect
57. #5152	C₂×C₃	semidirect
58. C₄×#213	C₂×C₃	semidirect
59. #4869	C₂×C₃	semidirect
60. #4860	C₂×C₃	semidirect
61. #4770	C₂×C₃	semidirect
62. #4756	C₂×C₃	semidirect
63. #4711	C₂×C₃	semidirect
64. #4708	C₂×C₃	semidirect
71. C₃×D₃×D₄	C₂×C₄	semidirect
76. C₃²×D₈	C₂×C₄	semidirect
83. C₃×#213	C₂×C₄	semidirect
94. C₃×D₂₄	C₂×C₄	semidirect
96. C₃×D₃×C₈	C₂×C₄	semidirect
114. C₃×C₄×D₄	C₂×D₃	semidirect
115. C₃×C₄×D₄	C₂²×C₃	semidirect
120. D₄×Dic₃	C₂²×C₃	semidirect
124. D₃×D₈	C₃×C₄	semidirect
128. #893	C₂²×C₃	semidirect
132. C₄×D₁₂	C₂²×C₃	semidirect
137. C₃×#106	C₂×D₃	semidirect
138. C₃×#106	C₂²×C₃	semidirect
143. C₃×#102	C₂×D₃	semidirect
144. C₃×#102	C₂²×C₃	semidirect
147. C₃×#97	C₂×D₃	semidirect
148. C₃×#97	C₂²×C₃	semidirect
151. #832	C₂²×C₃	semidirect
152. #821	C₂²×C₃	semidirect
153. #817	C₂²×C₃	semidirect
154. #815	C₂²×C₃	semidirect
155. C₈×Dic₃	C₂²×C₃	semidirect
156. #809	C₂²×C₃	semidirect
157. #807	C₂²×C₃	semidirect
158. C₄×C₃⋊C₈	C₂²×C₃	semidirect
191. #442	C₃×D₃	semidirect
216. D₃×D₄	C₂×C₃×C₄	semidirect
224. C₃×D₈	C₄×D₃	semidirect
225. C₃×D₈	C₂×C₃×C₄	semidirect
255. #213	C₂×C₃×C₄	semidirect
266. D₂₄	C₂×C₃×C₄	semidirect
268. D₃×C₈	C₂×C₃×C₄	semidirect
298. C₄×D₄	C₂×C₃×D₃	semidirect
305. #106	C₂×C₃×D₃	semidirect
309. #102	C₂×C₃×D₃	semidirect
311. #97	C₂×C₃×D₃	semidirect
395. D₈	C₃×C₄×D₃	semidirect
456. C₃²	#2948	semidirect
515. C₃	#79867	direct (N × H)
516. C₃	C₃×#2948	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×D₈	2
C₃×#5545	2
C₃²×#442	2
C₃×#5152	2
C₃×C₄×#213	2
C₃×#4869	2
C₃×#4860	2
C₃×#4770	2
C₃×#4756	2
C₃×#4711	2
C₃×#4708	2
C₃×#2948	3
#79867	3

Subgroups — C3×#79867 #11860666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79867 #11860666