Subgroups — C₃×#21138 #10639745

Order 768.

772 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2943	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×#1778	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	#21138	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×#442	C₄	1	2	yes	complemented
18	C₃×#441	C₄	1	2	yes	complemented
19	C₃×#440	C₄	1	2	yes	complemented
20	C₃×#440	C₄	1	2	yes	complemented
21	C₃×#433	—	2	1	no	—
22	C₃×#433	—	2	1	no	—
23	C₃×#431	—	2	2	no	—
24	C₂×C₃×#108	C₂²	1	2	yes	—
25	C₃×#427	C₂²	1	1	yes	characteristic
26	C₃×#424	C₂²	1	2	yes	—
27	C₂×C₃×#104	C₂²	1	2	yes	—
28	C₂×C₃×#104	C₂²	1	2	yes	—
29	C₃×#416	C₂²	1	1	yes	characteristic
30	C₃×#416	C₂²	1	1	yes	characteristic
31	C₃×#408	C₂²	1	2	yes	—
32	C₃×#405	—	2	2	no	—
33	C₃×#405	C₂²	1	2	yes	—
34	C₃×C₄×M₁₆	—	2	1	no	—
35	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
36	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×C₈	—	2	1	no	—
39	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
40	C₃×#376	C₂²	1	1	yes	characteristic
41	C₃×#341	C₂²	1	2	yes	—
42	C₃×#339	C₂²	1	2	yes	—
43	C₃×#339	C₂²	1	2	yes	—
44	C₃×#336	C₂²	1	2	yes	—
45	C₃×#336	C₂²	1	2	yes	—
46	#2943	C₂×C₃	1	1	yes	characteristic
47	#2922	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×#131	C₂×C₃	1	1	yes	characteristic, complemented
49	#1929	C₂×C₃	1	2	yes	complemented
50	#1922	C₂×C₃	1	2	yes	complemented
51	#1876	C₂×C₃	1	2	yes	—
52	#1866	C₂×C₃	1	2	yes	complemented
53	#1778	C₂×C₃	1	1	yes	characteristic, complemented
54	#1759	C₂×C₃	1	1	yes	characteristic, complemented
55	#1759	C₂×C₃	1	1	yes	characteristic, complemented
56	#1746	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×#41	C₂³	1	1	yes	characteristic
58	C₂×C₃×#41	C₂³	1	1	yes	characteristic
59	C₃×#135	—	2	4	no	—
60	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
64	C₃×#131	—	2	4	no	—
65	C₃×#131	—	2	4	no	—
66	C₂×C₃×M₁₆	—	2	2	no	—
67	C₂×C₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₃×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₃×C₈	—	2	2	no	—
70	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂³	1	2	yes	—
73	C₃×C₄×Q₈	C₂×C₄	1	2	yes	—
74	C₃×C₄×Q₈	C₂×C₄	1	2	yes	—
75	C₃×C₄×D₄	—	2	2	no	—
76	C₃×C₄×D₄	—	2	2	no	—
77	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
78	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
79	C₃×#117	—	2	1	no	—
80	C₃×#117	—	2	1	no	—
81	C₃×#117	C₂³	1	1	yes	characteristic
82	C₃×#117	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	—	2	1	no	—
85	C₂×C₃×C₄²	C₂³	1	2	yes	—
86	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
87	C₃×#108	—	2	4	no	—
88	C₃×#107	C₂×C₄	1	2	yes	—
89	C₃×#106	C₂×C₄	1	2	yes	—
90	C₃×C₄⋊C₈	—	2	2	no	—
91	C₃×C₄⋊C₈	—	2	2	no	—
92	C₃×#104	—	2	4	no	—
93	C₃×#104	—	2	4	no	—
94	C₃×#103	C₂×C₄	1	2	yes	—
95	C₃×#103	C₂×C₄	1	2	yes	—
96	C₃×#102	C₂×C₄	1	2	yes	—
97	C₃×#102	C₂×C₄	1	2	yes	—
98	C₃×C₂²⋊C₈	—	2	2	no	—
99	C₃×C₂²⋊C₈	—	2	2	no	—
100	C₃×#97	—	2	2	no	—
101	C₃×#97	—	2	1	no	—
102	C₃×#97	—	2	1	no	—
103	C₃×#97	C₂×C₄	1	2	yes	—
104	C₃×#97	C₂×C₄	1	2	yes	—
105	C₃×C₄×C₈	—	2	2	no	—
106	C₃×C₄×C₈	—	2	1	no	—
107	C₃×C₄×C₈	—	2	1	no	—
108	C₃×C₄×C₈	D₄	1	1	yes	characteristic
109	C₃×C₄×C₈	D₄	1	1	yes	characteristic
110	C₃×C₄×C₈	D₄	1	2	yes	—
111	C₃×#95	—	2	2	no	—
112	C₂×#135	C₂²×C₃	1	1	yes	characteristic
113	C₂×#131	C₂²×C₃	1	2	yes	—
114	C₄×#41	C₂²×C₃	1	1	yes	characteristic
115	C₄×#41	C₂²×C₃	1	1	yes	characteristic
116	#442	C₃×C₄	1	2	yes	complemented
117	#441	C₃×C₄	1	2	yes	complemented
118	#440	C₃×C₄	1	2	yes	complemented
119	#440	C₃×C₄	1	2	yes	complemented
120	#433	—	2	1	no	—
121	#433	—	2	1	no	—
122	#431	—	2	2	no	—
123	C₂×#108	C₂²×C₃	1	2	yes	—
124	#427	C₂²×C₃	1	1	yes	characteristic
125	#424	C₂²×C₃	1	2	yes	—
126	C₂×#104	C₂²×C₃	1	2	yes	—
127	C₂×#104	C₂²×C₃	1	2	yes	—
128	#416	C₂²×C₃	1	1	yes	characteristic
129	#416	C₂²×C₃	1	1	yes	characteristic
130	#408	C₂²×C₃	1	2	yes	—
131	#405	—	2	2	no	—
132	#405	C₂²×C₃	1	2	yes	—
133	C₄×M₁₆	—	2	1	no	—
134	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
135	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
136	C₂×#97	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₄×C₈	—	2	1	no	—
138	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
139	#376	C₂²×C₃	1	1	yes	characteristic
140	#341	C₂²×C₃	1	2	yes	—
141	#339	C₂²×C₃	1	2	yes	—
142	#339	C₂²×C₃	1	2	yes	—
143	#336	C₂²×C₃	1	2	yes	—
144	#336	C₂²×C₃	1	2	yes	—
145	C₃×#41	—	2	2	no	—
146	C₃×#41	—	2	2	no	—
147	C₃×#41	—	2	2	no	—
148	C₃×#41	#41	1	4	yes	—
149	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×D₄	—	2	1	no	—
152	C₂×C₃×D₄	—	2	1	no	—
153	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	#41	1	2	yes	—
161	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
162	C₃×Q₁₆	—	2	2	no	—
163	C₃×SD₁₆	—	2	2	no	—
164	C₃×SD₁₆	—	2	2	no	—
165	C₃×D₈	—	2	2	no	—
166	C₃×M₁₆	—	2	8	no	—
167	C₃×M₁₆	—	2	2	no	—
168	C₃×M₁₆	—	2	2	no	—
169	C₃×M₁₆	—	2	2	no	—
170	C₃×M₁₆	#41	1	4	yes	—
171	C₂×C₃×C₈	—	2	8	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₂×C₃×C₈	—	2	2	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
182	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
183	C₃×C₄⋊C₄	—	2	2	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
186	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₄²	—	2	2	no	—
192	C₃×C₄²	—	2	2	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	—	2	2	no	—
197	C₃×C₄²	C₂²×C₄	1	2	yes	—
198	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
199	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
200	C₂×#41	C₂³×C₃	1	1	yes	characteristic
201	C₂×#41	C₂³×C₃	1	1	yes	characteristic
202	#135	—	2	4	no	—
203	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
207	#131	—	2	4	no	—
208	#131	—	2	4	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	C₂³×C₃	1	2	yes	—
211	C₂×M₁₆	C₂³×C₃	1	2	yes	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₃	1	2	yes	—
216	C₄×Q₈	C₂×C₃×C₄	1	2	yes	—
217	C₄×Q₈	C₂×C₃×C₄	1	2	yes	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	C₂×C₃×C₄	1	2	yes	—
221	C₄×D₄	C₂×C₃×C₄	1	2	yes	—
222	#117	—	2	1	no	—
223	#117	—	2	1	no	—
224	#117	C₂³×C₃	1	1	yes	characteristic
225	#117	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₄²	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	C₂³×C₃	1	2	yes	—
229	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
230	#108	—	2	4	no	—
231	#107	C₂×C₃×C₄	1	2	yes	—
232	#106	C₂×C₃×C₄	1	2	yes	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	#104	—	2	4	no	—
236	#104	—	2	4	no	—
237	#103	C₂×C₃×C₄	1	2	yes	—
238	#103	C₂×C₃×C₄	1	2	yes	—
239	#102	C₂×C₃×C₄	1	2	yes	—
240	#102	C₂×C₃×C₄	1	2	yes	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	#97	—	2	2	no	—
244	#97	—	2	1	no	—
245	#97	—	2	1	no	—
246	#97	C₂×C₃×C₄	1	2	yes	—
247	#97	C₂×C₃×C₄	1	2	yes	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	C₃×D₄	1	1	yes	characteristic
252	C₄×C₈	C₃×D₄	1	1	yes	characteristic
253	C₄×C₈	C₃×D₄	1	2	yes	—
254	#95	—	2	2	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	C₂×#41	1	1	yes	characteristic
258	C₃×Q₈	—	2	1	no	—
259	C₃×Q₈	—	2	1	no	—
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	#117	1	2	yes	—
262	C₃×D₄	—	2	4	no	—
263	C₃×D₄	—	2	1	no	—
264	C₃×D₄	—	2	1	no	—
265	C₃×D₄	—	2	1	no	—
266	C₃×D₄	—	4	2	no	—
267	C₃×D₄	#117	1	2	yes	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	—	4	4	no	—
275	C₂×C₃×C₄	—	4	4	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	—	4	4	no	—
278	C₂×C₃×C₄	—	4	2	no	—
279	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
281	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×#41	1	2	yes	—
284	C₂×C₃×C₄	C₂×#41	1	2	yes	—
285	C₃×C₈	—	2	1	no	—
286	C₃×C₈	—	2	1	no	—
287	C₃×C₈	—	2	2	no	—
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	2	4	no	—
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	4	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	C₃×#41	1	4	yes	—
296	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
297	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₃×#41	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
309	Q₁₆	—	2	2	no	—
310	SD₁₆	—	2	2	no	—
311	SD₁₆	—	2	2	no	—
312	D₈	—	2	2	no	—
313	M₁₆	—	2	8	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	C₃×#41	1	4	yes	—
318	C₂×C₈	—	2	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
326	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
329	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
333	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	C₂²×C₃×C₄	1	2	yes	—
345	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
346	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₃	#529	1	2	yes	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	—	4	1	no	—
360	C₃×C₄	—	8	2	no	—
361	C₃×C₄	C₂×#117	1	1	yes	characteristic
362	C₃×C₄	C₄×#41	1	1	yes	characteristic
363	C₃×C₄	#525	1	2	yes	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	C₂×C₃×#41	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	C₃×#117	1	2	yes	—
371	D₄	—	2	4	no	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	2	no	—
376	D₄	C₃×#117	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
389	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
390	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₃×#41	1	2	yes	—
393	C₂×C₄	C₂×C₃×#41	1	2	yes	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	4	no	—
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	4	2	no	—
403	C₂×C₃	—	8	1	no	—
404	C₂×C₃	#2290	1	1	yes	characteristic
405	C₂×C₃	#2955	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
412	C₂²	C₃×#529	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₂×C₃×#117	1	1	yes	characteristic
421	C₄	C₃×C₄×#41	1	1	yes	characteristic
422	C₄	C₃×#525	1	2	yes	—
423	C₃	#21138	1	1	yes	characteristic, direct product factor, Sylow
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	C₃×#2290	1	1	yes	characteristic
428	C₂	C₃×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×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 ◁ C₂×C₃×C₄ ◁ 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×#1778	C₂	semidirect
9. C₃×#1759	C₂	semidirect
10. C₃×#1759	C₂	semidirect
11. C₃×#1746	C₂	semidirect
12. #21138	C₃	direct (N × H)
17. C₃×#442	C₄	semidirect
18. C₃×#441	C₄	semidirect
19. C₃×#440	C₄	semidirect
20. C₃×#440	C₄	semidirect
47. #2922	C₂×C₃	semidirect
48. C₄×#131	C₂×C₃	semidirect
49. #1929	C₂×C₃	semidirect
50. #1922	C₂×C₃	semidirect
52. #1866	C₂×C₃	semidirect
53. #1778	C₂×C₃	semidirect
54. #1759	C₂×C₃	semidirect
55. #1759	C₂×C₃	semidirect
56. #1746	C₂×C₃	semidirect
116. #442	C₃×C₄	semidirect
117. #441	C₃×C₄	semidirect
118. #440	C₃×C₄	semidirect
119. #440	C₃×C₄	semidirect
423. C₃	#21138	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×#2943	2
C₃×#2922	2
C₃×C₄×#131	2
C₃×#1929	2
C₃×#1922	2
C₃×#1876	2
C₃×#1866	2
C₃×#1778	2
C₃×#1759	2
C₃×#1746	2
#21138	3

Subgroups — C3×#21138 #10639745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21138 #10639745