Subgroups — C₃×D₃×#137 #10595873

Order 576.

546 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#942	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#918	C₂	1	2	yes	maximal, complemented
7	C₃×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₃×#915	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×#909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#137	—	3	1	no	maximal
13	D₃×#137	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×#239	C₂²	1	1	yes	characteristic
17	C₃×D₃×Q₈	—	2	1	no	—
18	C₃×D₃×Q₈	—	2	1	no	—
19	C₃×D₃×Q₈	C₂²	1	2	yes	—
20	C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
21	C₃×D₃×Q₈	C₂²	1	2	yes	complemented
22	C₃×#237	—	2	1	no	—
23	C₃×#237	C₂²	1	1	yes	characteristic
24	C₃×D₃×D₄	—	2	1	no	—
25	C₃×D₃×D₄	C₂²	1	1	yes	characteristic
26	C₃×#235	—	2	1	no	—
27	C₃×#235	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₃	—	2	1	no	—
29	C₂×C₃×C₄×D₃	—	2	1	no	—
30	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×Dic₆	—	2	1	no	—
32	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
33	C₃²×Q₁₆	C₂²	1	2	yes	complemented
34	C₃²×SD₁₆	C₂²	1	2	yes	complemented
35	C₃²×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₃×#216	C₂²	1	2	yes	complemented
37	C₃×#216	C₂²	1	2	yes	complemented
38	C₃×#215	C₂²	1	2	yes	complemented
39	C₃×#214	C₂²	1	2	yes	complemented
40	C₃×#208	C₂²	1	1	yes	characteristic, complemented
41	C₃×Dic₁₂	C₂²	1	2	yes	complemented
42	C₃×#204	C₂²	1	2	yes	complemented
43	C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
44	C₃×D₃×C₈	C₂²	1	2	yes	—
45	C₂×C₃×#41	—	3	1	no	—
46	C₂²×C₃×Q₈	—	3	1	no	—
47	D₃×#41	C₂×C₃	1	1	yes	characteristic
48	C₂×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#137	—	2	1	no	—
50	C₃×#137	—	3	1	no	—
51	C₃×#137	—	3	1	no	—
52	C₃×#137	—	3	2	no	—
53	C₃×#137	—	3	2	no	—
54	C₃×#137	—	3	1	no	—
55	C₃×#137	D₃	1	1	yes	characteristic, direct product factor
56	C₃×#137	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×Q₁₆	—	3	2	no	—
58	C₂×C₃×SD₁₆	—	3	2	no	—
59	C₂×C₃×M₁₆	—	3	1	no	—
60	#951	C₂×C₃	1	1	yes	characteristic, complemented
61	#942	C₂×C₃	1	1	yes	characteristic, complemented
62	#918	C₂×C₃	1	2	yes	complemented
63	D₃×Q₁₆	C₂×C₃	1	2	yes	complemented
64	#915	C₂×C₃	1	2	yes	complemented
65	D₃×SD₁₆	C₂×C₃	1	2	yes	complemented
66	#909	C₂×C₃	1	1	yes	characteristic, complemented
67	D₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂²×C₃×D₃	—	2	1	no	—
69	C₂²×C₃×D₃	D₄	1	1	yes	characteristic
70	C₃²×Q₈	—	2	1	no	—
71	C₃²×Q₈	C₂³	1	2	yes	—
72	C₃²×Q₈	C₂³	1	1	yes	characteristic
73	C₃²×D₄	—	2	1	no	—
74	C₃²×D₄	C₂³	1	1	yes	characteristic
75	C₂×C₃²×C₄	—	2	1	no	—
76	C₂×C₃²×C₄	—	2	1	no	—
77	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
78	C₃×#67	—	2	1	no	—
79	C₃×#67	—	2	1	no	—
80	C₃×#67	—	2	1	no	—
81	C₂×C₃×Dic₃	—	2	1	no	—
82	C₂×C₃×Dic₃	—	2	1	no	—
83	C₂×C₃×Dic₃	D₄	1	1	yes	characteristic
84	C₃×D₁₂	—	2	1	no	—
85	C₃×D₁₂	C₂³	1	1	yes	characteristic
86	C₃×C₄×D₃	—	2	1	no	—
87	C₃×C₄×D₃	—	2	2	no	—
88	C₃×C₄×D₃	—	2	2	no	—
89	C₃×C₄×D₃	—	2	1	no	—
90	C₃×C₄×D₃	—	2	1	no	—
91	C₃×C₄×D₃	D₄	1	1	yes	characteristic
92	C₃×C₄×D₃	D₄	1	1	yes	characteristic
93	C₃×C₄×D₃	C₂³	1	1	yes	characteristic
94	C₃×C₄×D₃	C₂³	1	1	yes	characteristic
95	C₃×Dic₆	—	2	1	no	—
96	C₃×Dic₆	—	2	2	no	—
97	C₃×Dic₆	—	2	2	no	—
98	C₃×Dic₆	—	2	1	no	—
99	C₃×Dic₆	C₂³	1	2	yes	—
100	C₃×Dic₆	C₂³	1	1	yes	characteristic
101	C₃²×C₈	C₂³	1	2	yes	—
102	C₃×C₃⋊C₈	C₂³	1	2	yes	—
103	C₂×#137	—	3	1	no	Sylow
104	C₃×#41	—	2	1	no	—
105	C₃×#41	—	3	1	no	—
106	C₃×#41	—	3	1	no	—
107	C₃×#41	—	3	1	no	—
108	C₃×#41	—	6	1	no	—
109	C₃×#41	—	6	1	no	—
110	C₃×#41	C₂×D₃	1	1	yes	characteristic
111	C₃×#41	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×Q₈	—	2	1	no	—
113	C₂×C₃×Q₈	—	3	2	no	—
114	C₂×C₃×Q₈	—	3	1	no	—
115	C₂×C₃×Q₈	—	3	2	no	—
116	C₂×C₃×Q₈	—	3	1	no	—
117	C₂×C₃×Q₈	—	6	1	no	—
118	C₂×C₃×Q₈	—	6	1	no	—
119	C₂×C₃×Q₈	—	6	1	no	—
120	C₂×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₂×C₃×D₄	—	3	1	no	—
123	C₂×C₃×D₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	3	1	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	1	no	—
127	#239	C₂²×C₃	1	1	yes	characteristic
128	D₃×Q₈	—	2	1	no	—
129	D₃×Q₈	—	2	1	no	—
130	D₃×Q₈	C₂²×C₃	1	2	yes	—
131	D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
132	D₃×Q₈	C₂²×C₃	1	2	yes	complemented
133	#237	—	2	1	no	—
134	#237	C₂²×C₃	1	1	yes	characteristic
135	D₃×D₄	—	2	1	no	—
136	D₃×D₄	C₂²×C₃	1	1	yes	characteristic
137	#235	—	2	1	no	—
138	#235	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₄×D₃	—	2	1	no	—
140	C₂×C₄×D₃	—	2	1	no	—
141	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
142	C₂×Dic₆	—	2	1	no	—
143	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₃×Q₁₆	—	2	2	no	—
145	C₃×Q₁₆	—	3	2	no	—
146	C₃×Q₁₆	—	3	2	no	—
147	C₃×Q₁₆	—	3	2	no	—
148	C₃×Q₁₆	C₂×D₃	1	2	yes	complemented
149	C₃×Q₁₆	C₂²×C₃	1	2	yes	complemented
150	C₃×SD₁₆	—	2	2	no	—
151	C₃×SD₁₆	—	3	2	no	—
152	C₃×SD₁₆	—	3	2	no	—
153	C₃×SD₁₆	—	3	2	no	—
154	C₃×SD₁₆	C₂×D₃	1	2	yes	complemented
155	C₃×SD₁₆	C₂²×C₃	1	2	yes	complemented
156	C₃×M₁₆	—	2	1	no	—
157	C₃×M₁₆	—	3	1	no	—
158	C₃×M₁₆	—	3	2	no	—
159	C₃×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
160	C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×C₃×C₈	—	3	2	no	—
162	#216	C₂²×C₃	1	2	yes	complemented
163	#216	C₂²×C₃	1	2	yes	complemented
164	#215	C₂²×C₃	1	2	yes	complemented
165	#214	C₂²×C₃	1	2	yes	complemented
166	#208	C₂²×C₃	1	1	yes	characteristic, complemented
167	Dic₁₂	C₂²×C₃	1	2	yes	complemented
168	#204	C₂²×C₃	1	2	yes	complemented
169	ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	complemented
170	D₃×C₈	C₂²×C₃	1	2	yes	—
171	C₂²×C₃²	—	2	1	no	—
172	C₂²×C₃²	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃×D₃	—	2	2	no	—
174	C₂×C₃×D₃	—	2	1	no	—
175	C₂×C₃×D₃	—	4	2	no	—
176	C₂×C₃×D₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×D₃	C₂×D₄	1	1	yes	characteristic
178	C₃²×C₄	—	2	2	no	—
179	C₃²×C₄	—	2	1	no	—
180	C₃²×C₄	C₂×D₄	1	1	yes	characteristic
181	C₃²×C₄	C₂⁴	1	1	yes	characteristic
182	C₃×Dic₃	—	2	2	no	—
183	C₃×Dic₃	—	2	1	no	—
184	C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
185	C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
186	C₂×#41	—	3	1	no	—
187	C₂²×Q₈	—	3	1	no	—
188	#137	—	3	1	no	—
189	#137	—	3	1	no	—
190	#137	—	3	2	no	—
191	#137	—	3	2	no	—
192	#137	—	3	1	no	—
193	#137	C₃×D₃	1	1	yes	characteristic, direct product factor
194	C₂×Q₁₆	—	3	2	no	—
195	C₂×SD₁₆	—	3	2	no	—
196	C₂×M₁₆	—	3	1	no	—
197	C₂³×C₃	—	3	1	no	—
198	C₂³×C₃	—	6	1	no	—
199	C₂²×D₃	—	2	1	no	—
200	C₂²×D₃	C₃×D₄	1	1	yes	characteristic
201	C₃×Q₈	—	2	1	no	—
202	C₃×Q₈	—	2	1	no	—
203	C₃×Q₈	—	2	2	no	—
204	C₃×Q₈	—	2	1	no	—
205	C₃×Q₈	—	3	2	no	—
206	C₃×Q₈	—	3	1	no	—
207	C₃×Q₈	—	4	1	no	—
208	C₃×Q₈	—	6	2	no	—
209	C₃×Q₈	—	6	2	no	—
210	C₃×Q₈	—	6	1	no	—
211	C₃×Q₈	—	6	1	no	—
212	C₃×Q₈	C₂²×D₃	1	2	yes	—
213	C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
214	C₃×Q₈	C₂³×C₃	1	2	yes	—
215	C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₃×D₄	—	2	1	no	—
217	C₃×D₄	—	2	1	no	—
218	C₃×D₄	—	2	1	no	—
219	C₃×D₄	—	3	1	no	—
220	C₃×D₄	—	4	1	no	—
221	C₃×D₄	—	6	1	no	—
222	C₃×D₄	—	6	1	no	—
223	C₃×D₄	—	6	1	no	—
224	C₃×D₄	—	6	1	no	—
225	C₃×D₄	C₂²×D₃	1	1	yes	characteristic
226	C₃×D₄	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	3	1	no	—
233	C₂×C₃×C₄	—	3	1	no	—
234	C₂×C₃×C₄	—	3	1	no	—
235	C₂×C₃×C₄	—	3	1	no	—
236	C₂×C₃×C₄	—	3	1	no	—
237	C₂×C₃×C₄	—	4	1	no	—
238	C₂×C₃×C₄	—	4	1	no	—
239	C₂×C₃×C₄	—	6	1	no	—
240	C₂×C₃×C₄	—	6	1	no	—
241	C₂×C₃×C₄	—	6	2	no	—
242	C₂×C₃×C₄	—	6	2	no	—
243	C₂×C₃×C₄	—	6	1	no	—
244	C₂×C₃×C₄	—	6	1	no	—
245	C₂×C₃×C₄	—	6	1	no	—
246	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
248	#67	—	2	1	no	—
249	#67	—	2	1	no	—
250	#67	—	2	1	no	—
251	C₂×Dic₃	—	2	1	no	—
252	C₂×Dic₃	—	2	1	no	—
253	C₂×Dic₃	C₃×D₄	1	1	yes	characteristic
254	D₁₂	—	2	1	no	—
255	D₁₂	C₂³×C₃	1	1	yes	characteristic
256	C₄×D₃	—	2	1	no	—
257	C₄×D₃	—	2	2	no	—
258	C₄×D₃	—	2	2	no	—
259	C₄×D₃	—	2	1	no	—
260	C₄×D₃	—	2	1	no	—
261	C₄×D₃	C₃×D₄	1	1	yes	characteristic
262	C₄×D₃	C₃×D₄	1	1	yes	characteristic
263	C₄×D₃	C₂³×C₃	1	1	yes	characteristic
264	C₄×D₃	C₂³×C₃	1	1	yes	characteristic
265	Dic₆	—	2	1	no	—
266	Dic₆	—	2	2	no	—
267	Dic₆	—	2	2	no	—
268	Dic₆	—	2	1	no	—
269	Dic₆	C₂³×C₃	1	2	yes	—
270	Dic₆	C₂³×C₃	1	1	yes	characteristic
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	3	2	no	—
273	C₃×C₈	C₂²×D₃	1	2	yes	—
274	C₃×C₈	C₂³×C₃	1	2	yes	—
275	C₃⋊C₈	C₂³×C₃	1	2	yes	—
276	C₂×C₃²	—	2	1	no	—
277	C₂×C₃²	—	4	1	no	—
278	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
279	C₃×D₃	—	2	1	no	—
280	C₃×D₃	—	4	1	no	—
281	C₃×D₃	#137	1	2	yes	direct product factor
282	#41	—	3	1	no	—
283	#41	—	3	1	no	—
284	#41	—	3	1	no	—
285	#41	—	6	1	no	—
286	#41	—	6	1	no	—
287	#41	C₂×C₃×D₃	1	1	yes	characteristic
288	C₂×Q₈	—	3	2	no	—
289	C₂×Q₈	—	3	1	no	—
290	C₂×Q₈	—	3	2	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×Q₈	—	6	1	no	—
293	C₂×Q₈	—	6	1	no	—
294	C₂×Q₈	—	6	1	no	—
295	C₂×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
296	C₂×D₄	—	3	1	no	—
297	C₂×D₄	—	6	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	—	6	1	no	—
300	C₂²×C₄	—	6	1	no	—
301	Q₁₆	—	3	2	no	—
302	Q₁₆	—	3	2	no	—
303	Q₁₆	—	3	2	no	—
304	Q₁₆	C₂×C₃×D₃	1	2	yes	complemented
305	SD₁₆	—	3	2	no	—
306	SD₁₆	—	3	2	no	—
307	SD₁₆	—	3	2	no	—
308	SD₁₆	C₂×C₃×D₃	1	2	yes	complemented
309	M₁₆	—	3	1	no	—
310	M₁₆	—	3	2	no	—
311	M₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
312	C₂×C₈	—	3	2	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	3	1	no	—
317	C₂²×C₃	—	3	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	—	6	2	no	—
320	C₂²×C₃	—	6	1	no	—
321	C₂²×C₃	—	12	2	no	—
322	C₂²×C₃	D₃×D₄	1	1	yes	characteristic
323	C₂²×C₃	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	1	no	—
326	C₂×D₃	—	4	2	no	—
327	C₂×D₃	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂×D₃	C₂×C₃×D₄	1	1	yes	characteristic
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	3	1	no	—
336	C₃×C₄	—	3	1	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	—	6	1	no	—
340	C₃×C₄	—	6	2	no	—
341	C₃×C₄	D₃×D₄	1	1	yes	characteristic
342	C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
343	C₃×C₄	C₂³×D₃	1	1	yes	characteristic
344	C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
345	Dic₃	—	2	2	no	—
346	Dic₃	—	2	1	no	—
347	Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
348	Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
349	C₃²	C₂×#137	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	3	1	no	—
351	C₂³	—	6	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	3	2	no	—
354	Q₈	—	3	1	no	—
355	Q₈	—	6	2	no	—
356	Q₈	—	6	2	no	—
357	Q₈	—	6	1	no	—
358	Q₈	—	6	1	no	—
359	Q₈	C₂²×C₃×D₃	1	2	yes	—
360	Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
361	D₄	—	2	1	no	—
362	D₄	—	3	1	no	—
363	D₄	—	6	1	no	—
364	D₄	—	6	1	no	—
365	D₄	—	6	1	no	—
366	D₄	—	6	1	no	—
367	D₄	C₂²×C₃×D₃	1	1	yes	characteristic
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	3	1	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	1	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	6	2	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
383	C₈	—	3	2	no	—
384	C₈	C₂²×C₃×D₃	1	2	yes	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	3	2	no	—
389	C₂×C₃	—	4	1	no	—
390	C₂×C₃	—	4	1	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	6	1	no	—
393	C₂×C₃	—	8	1	no	—
394	C₂×C₃	—	12	1	no	—
395	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
396	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
397	D₃	—	2	1	no	—
398	D₃	—	4	1	no	—
399	D₃	C₃×#137	1	2	yes	direct product factor
400	C₂²	—	2	1	no	—
401	C₂²	—	3	1	no	—
402	C₂²	—	3	1	no	—
403	C₂²	—	6	2	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	12	2	no	—
406	C₂²	C₃×D₃×D₄	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	—	3	1	no	—
410	C₄	—	3	1	no	—
411	C₄	—	6	1	no	—
412	C₄	—	6	2	no	—
413	C₄	C₃×D₃×D₄	1	1	yes	characteristic
414	C₄	C₂³×C₃×D₃	1	1	yes	characteristic
415	C₃	—	2	1	no	—
416	C₃	D₃×#137	1	1	yes	characteristic, direct product factor
417	C₃	C₂×C₃×#137	1	1	yes	characteristic, complemented
418	C₂	—	2	1	no	—
419	C₂	—	3	2	no	—
420	C₂	—	4	1	no	—
421	C₂	—	6	1	no	—
422	C₂	—	12	1	no	—
423	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×D₃
Fitting	C₃²×#137	C₂
socle	C₂×C₃²	C₂²×D₄
prime radical	C₃×D₃×#41	C₂
hypercenter	C₃×#137	D₃
hypocenter	C₃	C₂×C₃×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×D₃×Q₈	C₂	semidirect
3. C₃²×#137	C₂	semidirect
4. C₃×#951	C₂	semidirect
5. C₃×#942	C₂	semidirect
6. C₃×#918	C₂	semidirect
7. C₃×D₃×Q₁₆	C₂	semidirect
8. C₃×#915	C₂	semidirect
9. C₃×D₃×SD₁₆	C₂	semidirect
10. C₃×#909	C₂	semidirect
11. C₃×D₃×M₁₆	C₂	semidirect
13. D₃×#137	C₃	direct (N × H)
15. C₂×C₃²×Q₈	C₂²	semidirect
21. C₃×D₃×Q₈	C₂²	semidirect
32. C₂×C₃×Dic₆	C₂²	semidirect
33. C₃²×Q₁₆	C₂²	semidirect
34. C₃²×SD₁₆	C₂²	semidirect
35. C₃²×M₁₆	C₂²	semidirect
36. C₃×#216	C₂²	semidirect
37. C₃×#216	C₂²	semidirect
38. C₃×#215	C₂²	semidirect
39. C₃×#214	C₂²	semidirect
40. C₃×#208	C₂²	semidirect
41. C₃×Dic₁₂	C₂²	semidirect
42. C₃×#204	C₂²	semidirect
43. C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
48. C₂×D₃×Q₈	C₂×C₃	semidirect
55. C₃×#137	D₃	direct (N × H)
56. C₃×#137	C₂×C₃	semidirect
60. #951	C₂×C₃	semidirect
61. #942	C₂×C₃	semidirect
62. #918	C₂×C₃	semidirect
63. D₃×Q₁₆	C₂×C₃	semidirect
64. #915	C₂×C₃	semidirect
65. D₃×SD₁₆	C₂×C₃	semidirect
66. #909	C₂×C₃	semidirect
67. D₃×M₁₆	C₂×C₃	semidirect
120. C₂×C₃×Q₈	C₂×D₃	semidirect
121. C₂×C₃×Q₈	C₂²×C₃	semidirect
132. D₃×Q₈	C₂²×C₃	semidirect
143. C₂×Dic₆	C₂²×C₃	semidirect
148. C₃×Q₁₆	C₂×D₃	semidirect
149. C₃×Q₁₆	C₂²×C₃	semidirect
154. C₃×SD₁₆	C₂×D₃	semidirect
155. C₃×SD₁₆	C₂²×C₃	semidirect
159. C₃×M₁₆	C₂×D₃	semidirect
160. C₃×M₁₆	C₂²×C₃	semidirect
162. #216	C₂²×C₃	semidirect
163. #216	C₂²×C₃	semidirect
164. #215	C₂²×C₃	semidirect
165. #214	C₂²×C₃	semidirect
166. #208	C₂²×C₃	semidirect
167. Dic₁₂	C₂²×C₃	semidirect
168. #204	C₂²×C₃	semidirect
169. ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
193. #137	C₃×D₃	direct (N × H)
281. C₃×D₃	#137	direct (N × H)
295. C₂×Q₈	C₂×C₃×D₃	semidirect
304. Q₁₆	C₂×C₃×D₃	semidirect
308. SD₁₆	C₂×C₃×D₃	semidirect
311. M₁₆	C₂×C₃×D₃	semidirect
349. C₃²	C₂×#137	semidirect
399. D₃	C₃×#137	direct (N × H)
416. C₃	D₃×#137	direct (N × H)
417. C₃	C₂×C₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#41	2
C₂×C₃×D₃×Q₈	2
C₃²×#137	2
C₃×#951	2
C₃×#942	2
C₃×#918	2
C₃×D₃×Q₁₆	2
C₃×#915	2
C₃×D₃×SD₁₆	2
C₃×#909	2
C₃×D₃×M₁₆	2
C₂×C₃×#137	3
D₃×#137	3

Subgroups — C3×D3×#137 #10595873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#137 #10595873