Subgroups — C₃×#21137 #10639744

Order 768.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1929	C₂	1	2	yes	maximal, complemented
5	C₃×#1922	C₂	1	2	yes	maximal, complemented
6	C₃×#1876	C₂	1	2	yes	maximal
7	C₃×#1866	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#104	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×#104	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	#21137	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₃×#131	C₂²	1	2	yes	—
15	C₃×C₄×#41	C₂²	1	1	yes	characteristic
16	C₃×C₄×#41	C₂²	1	1	yes	characteristic
17	C₃×C₄×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₃×C₄×Q₁₆	C₄	1	1	yes	characteristic, complemented
19	C₃×C₄×SD₁₆	C₄	1	1	yes	characteristic, complemented
20	C₃×C₄×SD₁₆	C₄	1	1	yes	characteristic, complemented
21	C₃×C₄×SD₁₆	C₄	1	1	yes	characteristic, complemented
22	C₃×C₄×SD₁₆	C₄	1	1	yes	characteristic, complemented
23	C₃×C₄×D₈	C₄	1	1	yes	characteristic, complemented
24	C₃×C₄×D₈	C₄	1	1	yes	characteristic, complemented
25	C₃×#433	—	2	2	no	—
26	C₃×#431	—	2	1	no	—
27	C₃×#431	—	2	1	no	—
28	C₂×C₃×#108	C₂²	1	2	yes	—
29	C₃×#427	C₂²	1	1	yes	characteristic
30	C₃×#424	C₂²	1	2	yes	—
31	C₂×C₃×#104	C₂²	1	2	yes	—
32	C₂×C₃×#104	C₂²	1	2	yes	—
33	C₃×#416	C₂²	1	1	yes	characteristic
34	C₃×#416	C₂²	1	1	yes	characteristic
35	C₃×#408	C₂²	1	2	yes	—
36	C₃×#405	—	2	2	no	—
37	C₃×#405	C₂²	1	2	yes	—
38	C₃×C₄×M₁₆	—	2	1	no	—
39	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
40	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×C₈	—	2	1	no	—
42	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
44	C₃×C₄³	C₂²	1	1	yes	characteristic
45	C₃×#341	C₂²	1	2	yes	—
46	C₃×#339	C₂²	1	2	yes	—
47	C₃×#339	C₂²	1	2	yes	—
48	C₃×#336	C₂²	1	2	yes	—
49	C₃×#336	C₂²	1	2	yes	—
50	C₄×#135	C₂×C₃	1	1	yes	characteristic
51	#2922	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×#131	C₂×C₃	1	1	yes	characteristic, complemented
53	#1929	C₂×C₃	1	2	yes	complemented
54	#1922	C₂×C₃	1	2	yes	complemented
55	#1876	C₂×C₃	1	2	yes	—
56	#1866	C₂×C₃	1	2	yes	complemented
57	C₄×#108	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×#104	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×#104	C₂×C₃	1	1	yes	characteristic, complemented
60	#1744	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×C₃×#41	C₂³	1	1	yes	characteristic
62	C₂×C₃×#41	C₂³	1	1	yes	characteristic
63	C₃×#135	—	2	4	no	—
64	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
68	C₃×#131	—	2	4	no	—
69	C₃×#131	—	2	4	no	—
70	C₂×C₃×M₁₆	—	2	2	no	—
71	C₂×C₃×M₁₆	C₂³	1	2	yes	—
72	C₂×C₃×M₁₆	C₂³	1	2	yes	—
73	C₂²×C₃×C₈	—	2	2	no	—
74	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	2	yes	—
77	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×D₄	—	2	1	no	—
82	C₃×C₄×D₄	—	2	1	no	—
83	C₃×C₄×D₄	—	2	1	no	—
84	C₃×C₄×D₄	—	2	1	no	—
85	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
86	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
87	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
89	C₃×#117	—	2	1	no	—
90	C₃×#117	—	2	1	no	—
91	C₃×#117	C₂³	1	1	yes	characteristic
92	C₃×#117	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄²	—	2	1	no	—
94	C₂×C₃×C₄²	—	2	1	no	—
95	C₂×C₃×C₄²	—	2	1	no	—
96	C₂×C₃×C₄²	—	2	1	no	—
97	C₂×C₃×C₄²	C₂³	1	2	yes	—
98	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
99	C₃×#108	—	2	4	no	—
100	C₃×#107	C₂×C₄	1	1	yes	characteristic
101	C₃×#107	C₂×C₄	1	1	yes	characteristic
102	C₃×#106	C₂×C₄	1	1	yes	characteristic
103	C₃×#106	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄⋊C₈	—	2	2	no	—
105	C₃×C₄⋊C₈	—	2	2	no	—
106	C₃×#104	—	2	4	no	—
107	C₃×#104	—	2	4	no	—
108	C₃×#103	C₂×C₄	1	1	yes	characteristic
109	C₃×#103	C₂×C₄	1	1	yes	characteristic
110	C₃×#103	C₂×C₄	1	1	yes	characteristic
111	C₃×#103	C₂×C₄	1	1	yes	characteristic
112	C₃×#102	C₂×C₄	1	1	yes	characteristic
113	C₃×#102	C₂×C₄	1	1	yes	characteristic
114	C₃×#102	C₂×C₄	1	1	yes	characteristic
115	C₃×#102	C₂×C₄	1	1	yes	characteristic
116	C₃×C₂²⋊C₈	—	2	2	no	—
117	C₃×C₂²⋊C₈	—	2	2	no	—
118	C₃×#97	—	2	2	no	—
119	C₃×#97	—	2	1	no	—
120	C₃×#97	—	2	1	no	—
121	C₃×C₄×C₈	—	2	2	no	—
122	C₃×C₄×C₈	—	2	1	no	—
123	C₃×C₄×C₈	—	2	1	no	—
124	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
125	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
126	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
127	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
128	C₃×C₄×C₈	D₄	1	2	yes	—
129	C₃×C₄×C₈	D₄	1	1	yes	characteristic
130	C₃×C₄×C₈	D₄	1	1	yes	characteristic
131	C₂×#135	C₂²×C₃	1	1	yes	characteristic
132	C₂×#131	C₂²×C₃	1	2	yes	—
133	C₄×#41	C₂²×C₃	1	1	yes	characteristic
134	C₄×#41	C₂²×C₃	1	1	yes	characteristic
135	C₄×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
136	C₄×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
137	C₄×SD₁₆	C₃×C₄	1	1	yes	characteristic, complemented
138	C₄×SD₁₆	C₃×C₄	1	1	yes	characteristic, complemented
139	C₄×SD₁₆	C₃×C₄	1	1	yes	characteristic, complemented
140	C₄×SD₁₆	C₃×C₄	1	1	yes	characteristic, complemented
141	C₄×D₈	C₃×C₄	1	1	yes	characteristic, complemented
142	C₄×D₈	C₃×C₄	1	1	yes	characteristic, complemented
143	#433	—	2	2	no	—
144	#431	—	2	1	no	—
145	#431	—	2	1	no	—
146	C₂×#108	C₂²×C₃	1	2	yes	—
147	#427	C₂²×C₃	1	1	yes	characteristic
148	#424	C₂²×C₃	1	2	yes	—
149	C₂×#104	C₂²×C₃	1	2	yes	—
150	C₂×#104	C₂²×C₃	1	2	yes	—
151	#416	C₂²×C₃	1	1	yes	characteristic
152	#416	C₂²×C₃	1	1	yes	characteristic
153	#408	C₂²×C₃	1	2	yes	—
154	#405	—	2	2	no	—
155	#405	C₂²×C₃	1	2	yes	—
156	C₄×M₁₆	—	2	1	no	—
157	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
158	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄×C₈	—	2	1	no	—
160	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
162	C₄³	C₂²×C₃	1	1	yes	characteristic
163	#341	C₂²×C₃	1	2	yes	—
164	#339	C₂²×C₃	1	2	yes	—
165	#339	C₂²×C₃	1	2	yes	—
166	#336	C₂²×C₃	1	2	yes	—
167	#336	C₂²×C₃	1	2	yes	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	2	no	—
171	C₃×#41	#41	1	4	yes	—
172	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	#41	1	1	yes	characteristic
186	C₂²×C₃×C₄	#41	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
188	C₃×Q₁₆	—	2	2	no	—
189	C₃×SD₁₆	—	2	2	no	—
190	C₃×SD₁₆	—	2	2	no	—
191	C₃×D₈	—	2	2	no	—
192	C₃×M₁₆	—	2	8	no	—
193	C₃×M₁₆	—	2	2	no	—
194	C₃×M₁₆	—	2	2	no	—
195	C₃×M₁₆	—	2	2	no	—
196	C₃×M₁₆	#41	1	4	yes	—
197	C₂×C₃×C₈	—	2	8	no	—
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	2	2	no	—
200	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	2	2	no	—
202	C₂×C₃×C₈	—	2	2	no	—
203	C₂×C₃×C₈	—	2	2	no	—
204	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
209	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
215	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
216	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
217	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
218	C₃×C₂²⋊C₄	—	2	1	no	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₂²⋊C₄	—	2	1	no	—
221	C₃×C₂²⋊C₄	—	2	1	no	—
222	C₃×C₂²⋊C₄	—	2	1	no	—
223	C₃×C₂²⋊C₄	—	2	1	no	—
224	C₃×C₄²	—	2	4	no	—
225	C₃×C₄²	—	2	1	no	—
226	C₃×C₄²	—	2	1	no	—
227	C₃×C₄²	—	2	1	no	—
228	C₃×C₄²	—	2	1	no	—
229	C₃×C₄²	—	2	1	no	—
230	C₃×C₄²	—	2	1	no	—
231	C₃×C₄²	—	2	2	no	—
232	C₃×C₄²	—	2	2	no	—
233	C₃×C₄²	—	4	2	no	—
234	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
235	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
236	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
237	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
238	C₂×#41	C₂³×C₃	1	1	yes	characteristic
239	C₂×#41	C₂³×C₃	1	1	yes	characteristic
240	#135	—	2	4	no	—
241	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
242	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
244	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
245	#131	—	2	4	no	—
246	#131	—	2	4	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	C₂³×C₃	1	2	yes	—
249	C₂×M₁₆	C₂³×C₃	1	2	yes	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₃	1	2	yes	—
254	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
255	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
256	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
257	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
263	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
264	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
265	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
266	#117	—	2	1	no	—
267	#117	—	2	1	no	—
268	#117	C₂³×C₃	1	1	yes	characteristic
269	#117	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₃	1	2	yes	—
275	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
276	#108	—	2	4	no	—
277	#107	C₂×C₃×C₄	1	1	yes	characteristic
278	#107	C₂×C₃×C₄	1	1	yes	characteristic
279	#106	C₂×C₃×C₄	1	1	yes	characteristic
280	#106	C₂×C₃×C₄	1	1	yes	characteristic
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	#104	—	2	4	no	—
284	#104	—	2	4	no	—
285	#103	C₂×C₃×C₄	1	1	yes	characteristic
286	#103	C₂×C₃×C₄	1	1	yes	characteristic
287	#103	C₂×C₃×C₄	1	1	yes	characteristic
288	#103	C₂×C₃×C₄	1	1	yes	characteristic
289	#102	C₂×C₃×C₄	1	1	yes	characteristic
290	#102	C₂×C₃×C₄	1	1	yes	characteristic
291	#102	C₂×C₃×C₄	1	1	yes	characteristic
292	#102	C₂×C₃×C₄	1	1	yes	characteristic
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	#97	—	2	2	no	—
296	#97	—	2	1	no	—
297	#97	—	2	1	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
302	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
303	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
304	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
305	C₄×C₈	C₃×D₄	1	1	yes	characteristic
306	C₄×C₈	C₃×D₄	1	1	yes	characteristic
307	C₄×C₈	C₃×D₄	1	2	yes	—
308	C₂³×C₃	—	2	1	no	—
309	C₂³×C₃	—	2	1	no	—
310	C₂³×C₃	C₂×#41	1	1	yes	characteristic
311	C₃×Q₈	—	2	1	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	#117	1	2	yes	—
315	C₃×D₄	—	2	4	no	—
316	C₃×D₄	—	2	1	no	—
317	C₃×D₄	—	2	1	no	—
318	C₃×D₄	—	2	1	no	—
319	C₃×D₄	—	4	2	no	—
320	C₃×D₄	#117	1	2	yes	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	4	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	4	2	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	4	2	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	4	2	no	—
336	C₂×C₃×C₄	—	4	2	no	—
337	C₂×C₃×C₄	—	4	2	no	—
338	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂×#41	1	2	yes	—
345	C₂×C₃×C₄	C₂×#41	1	2	yes	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	—	2	1	no	—
348	C₃×C₈	—	2	1	no	—
349	C₃×C₈	—	2	1	no	—
350	C₃×C₈	—	2	2	no	—
351	C₃×C₈	—	2	4	no	—
352	C₃×C₈	—	2	2	no	—
353	C₃×C₈	—	4	2	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	C₃×#41	1	4	yes	—
358	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
359	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
363	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	C₃×#41	1	1	yes	characteristic
372	C₂²×C₄	C₃×#41	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
374	Q₁₆	—	2	2	no	—
375	SD₁₆	—	2	2	no	—
376	SD₁₆	—	2	2	no	—
377	D₈	—	2	2	no	—
378	M₁₆	—	2	8	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	C₃×#41	1	4	yes	—
383	C₂×C₈	—	2	8	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
391	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
392	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
393	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
394	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
395	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	2	no	—
420	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
421	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
422	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
423	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
424	C₂²×C₃	—	2	1	no	—
425	C₂²×C₃	—	2	1	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	4	1	no	—
428	C₂²×C₃	—	4	1	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	1	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
433	C₂²×C₃	#529	1	2	yes	—
434	C₃×C₄	—	2	1	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	4	4	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	#443	1	2	yes	—
444	C₃×C₄	#444	1	2	yes	—
445	C₃×C₄	C₂×#117	1	1	yes	characteristic
446	C₃×C₄	C₄×#41	1	1	yes	characteristic
447	C₃×C₄	#525	1	2	yes	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	C₂×C₃×#41	1	1	yes	characteristic
451	Q₈	—	2	1	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	1	no	—
454	Q₈	C₃×#117	1	2	yes	—
455	D₄	—	2	4	no	—
456	D₄	—	2	1	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	4	2	no	—
460	D₄	C₃×#117	1	2	yes	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
479	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
480	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
481	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₃×#41	1	2	yes	—
485	C₂×C₄	C₂×C₃×#41	1	2	yes	—
486	C₈	—	2	1	no	—
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	4	no	—
492	C₈	—	2	2	no	—
493	C₈	—	4	2	no	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	—	8	1	no	—
497	C₂×C₃	#2290	1	1	yes	characteristic
498	C₂×C₃	C₂×#443	1	1	yes	characteristic
499	C₂×C₃	C₂×#444	1	1	yes	characteristic
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
509	C₂²	C₃×#529	1	2	yes	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	C₃×#443	1	2	yes	—
520	C₄	C₃×#444	1	2	yes	—
521	C₄	C₂×C₃×#117	1	1	yes	characteristic
522	C₄	C₃×C₄×#41	1	1	yes	characteristic
523	C₄	C₃×#525	1	2	yes	—
524	C₃	#21137	1	1	yes	characteristic, direct product factor, Sylow
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	1	no	—
528	C₂	C₃×#2290	1	1	yes	characteristic
529	C₂	C₂×C₃×#443	1	1	yes	characteristic
530	C₂	C₂×C₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₂×C₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2922	C₂	semidirect
3. C₃×C₄×#131	C₂	semidirect
4. C₃×#1929	C₂	semidirect
5. C₃×#1922	C₂	semidirect
7. C₃×#1866	C₂	semidirect
8. C₃×C₄×#108	C₂	semidirect
9. C₃×C₄×#104	C₂	semidirect
10. C₃×C₄×#104	C₂	semidirect
11. C₃×#1744	C₂	semidirect
12. #21137	C₃	direct (N × H)
17. C₃×C₄×Q₁₆	C₄	semidirect
18. C₃×C₄×Q₁₆	C₄	semidirect
19. C₃×C₄×SD₁₆	C₄	semidirect
20. C₃×C₄×SD₁₆	C₄	semidirect
21. C₃×C₄×SD₁₆	C₄	semidirect
22. C₃×C₄×SD₁₆	C₄	semidirect
23. C₃×C₄×D₈	C₄	semidirect
24. C₃×C₄×D₈	C₄	semidirect
51. #2922	C₂×C₃	semidirect
52. C₄×#131	C₂×C₃	semidirect
53. #1929	C₂×C₃	semidirect
54. #1922	C₂×C₃	semidirect
56. #1866	C₂×C₃	semidirect
57. C₄×#108	C₂×C₃	semidirect
58. C₄×#104	C₂×C₃	semidirect
59. C₄×#104	C₂×C₃	semidirect
60. #1744	C₂×C₃	semidirect
135. C₄×Q₁₆	C₃×C₄	semidirect
136. C₄×Q₁₆	C₃×C₄	semidirect
137. C₄×SD₁₆	C₃×C₄	semidirect
138. C₄×SD₁₆	C₃×C₄	semidirect
139. C₄×SD₁₆	C₃×C₄	semidirect
140. C₄×SD₁₆	C₃×C₄	semidirect
141. C₄×D₈	C₃×C₄	semidirect
142. C₄×D₈	C₃×C₄	semidirect
524. C₃	#21137	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#135	2
C₃×#2922	2
C₃×C₄×#131	2
C₃×#1929	2
C₃×#1922	2
C₃×#1876	2
C₃×#1866	2
C₃×C₄×#108	2
C₃×C₄×#104	2
C₃×#1744	2
#21137	3

Subgroups — C3×#21137 #10639744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21137 #10639744