Subgroups — C₃×#5609 #10595706

Order 576.

903 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃×D₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#937	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#884	C₂	1	2	yes	maximal, complemented
11	C₃×#882	C₂	1	2	yes	maximal, complemented
12	C₃×D₄²	—	3	1	no	maximal
13	#5609	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃×D₃	C₂²	1	2	yes	complemented
15	C₂³×C₃×D₃	C₂²	1	2	yes	complemented
16	C₂×C₃²×D₄	C₂²	1	2	yes	complemented
17	C₂×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#67	C₂²	1	1	yes	characteristic
20	C₂×C₃×#67	C₂²	1	2	yes	complemented
21	C₂×C₃×#67	C₂²	1	2	yes	complemented
22	C₂×C₃×#67	C₂²	1	2	yes	complemented
23	C₃×D₃×D₄	—	2	8	no	—
24	C₃×D₃×D₄	—	2	4	no	—
25	C₂×C₃×D₁₂	—	2	4	no	—
26	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₁₂	C₂²	1	2	yes	complemented
28	C₂×C₃×D₁₂	C₂²	1	2	yes	complemented
29	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₃	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₃×#217	C₂²	1	1	yes	characteristic, complemented
35	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
38	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₃×D₄	—	3	2	no	—
41	C₂²×C₃×D₄	—	3	1	no	—
42	C₂²×C₃×D₄	—	3	1	no	—
43	C₂×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×D₃×D₄	C₂×C₃	1	2	yes	complemented
45	C₂²×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#127	—	3	1	no	—
47	C₃×#121	—	2	1	no	—
48	C₃×#121	—	3	1	no	—
49	C₃×#121	—	3	2	no	—
50	C₃×#121	D₃	1	1	yes	characteristic, complemented
51	C₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#120	—	3	2	no	—
53	C₃×#120	—	3	2	no	—
54	C₃×C₄×D₄	—	3	1	no	—
55	C₃×C₄×D₄	—	3	1	no	—
56	#940	C₂×C₃	1	1	yes	characteristic, complemented
57	#937	C₂×C₃	1	2	yes	complemented
58	C₄×#67	C₂×C₃	1	1	yes	characteristic, complemented
59	#895	C₂×C₃	1	1	yes	characteristic, complemented
60	#893	C₂×C₃	1	1	yes	characteristic, complemented
61	#884	C₂×C₃	1	2	yes	complemented
62	#882	C₂×C₃	1	2	yes	complemented
63	C₂³×C₃²	C₂³	1	2	yes	—
64	C₂³×C₃²	C₂³	1	1	yes	characteristic
65	C₂²×C₃×D₃	—	2	4	no	—
66	C₂²×C₃×D₃	—	2	4	no	—
67	C₂²×C₃×D₃	—	2	4	no	—
68	C₂²×C₃×D₃	—	2	4	no	—
69	C₂²×C₃×D₃	—	4	2	no	—
70	C₂²×C₃×D₃	—	4	2	no	—
71	C₂²×C₃×D₃	C₂³	1	2	yes	—
72	C₂²×C₃×D₃	C₂³	1	2	yes	—
73	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
74	C₃²×D₄	—	2	4	no	—
75	C₃²×D₄	—	2	2	no	—
76	C₂×C₃²×C₄	—	2	2	no	—
77	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₄	C₂³	1	2	yes	—
79	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
80	C₃×#67	—	2	4	no	—
81	C₃×#67	—	2	4	no	—
82	C₃×#67	—	4	2	no	—
83	C₃×#67	D₄	1	4	yes	complemented
84	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
87	C₃×D₁₂	—	2	4	no	—
88	C₃×D₁₂	—	2	4	no	—
89	C₃×D₁₂	—	2	2	no	—
90	C₃×D₁₂	D₄	1	4	yes	complemented
91	C₃×C₄×D₃	—	2	2	no	—
92	C₃×C₄×D₃	—	2	4	no	—
93	D₄²	—	3	1	no	Sylow
94	C₂⁴×C₃	—	3	2	no	—
95	C₂⁴×C₃	—	3	2	no	—
96	C₂³×D₃	C₂²×C₃	1	2	yes	complemented
97	C₂³×D₃	C₂²×C₃	1	2	yes	complemented
98	C₂×C₃×D₄	—	2	2	no	—
99	C₂×C₃×D₄	—	2	1	no	—
100	C₂×C₃×D₄	—	3	1	no	—
101	C₂×C₃×D₄	—	3	2	no	—
102	C₂×C₃×D₄	—	3	2	no	—
103	C₂×C₃×D₄	—	3	2	no	—
104	C₂×C₃×D₄	—	3	1	no	—
105	C₂×C₃×D₄	—	3	2	no	—
106	C₂×C₃×D₄	—	3	2	no	—
107	C₂×C₃×D₄	—	3	1	no	—
108	C₂×C₃×D₄	—	6	4	no	—
109	C₂×C₃×D₄	—	6	8	no	—
110	C₂×C₃×D₄	—	6	4	no	—
111	C₂×C₃×D₄	C₂×D₃	1	2	yes	complemented
112	C₂×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂×C₃×D₄	C₂²×C₃	1	2	yes	complemented
114	C₂×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂²×C₃×C₄	—	2	1	no	—
116	C₂²×C₃×C₄	—	3	2	no	—
117	C₂²×C₃×C₄	—	3	1	no	—
118	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
119	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₂×#67	C₂²×C₃	1	1	yes	characteristic
121	C₂×#67	C₂²×C₃	1	2	yes	complemented
122	C₂×#67	C₂²×C₃	1	2	yes	complemented
123	C₂×#67	C₂²×C₃	1	2	yes	complemented
124	D₃×D₄	—	2	8	no	—
125	D₃×D₄	—	2	4	no	—
126	C₂×D₁₂	—	2	4	no	—
127	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
128	C₂×D₁₂	C₂²×C₃	1	2	yes	complemented
129	C₂×D₁₂	C₂²×C₃	1	2	yes	complemented
130	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂×C₄×D₃	C₂²×C₃	1	2	yes	complemented
132	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₃×C₄⋊C₄	—	2	1	no	—
134	C₃×C₄⋊C₄	—	3	1	no	—
135	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
136	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₃×C₂²⋊C₄	—	2	2	no	—
138	C₃×C₂²⋊C₄	—	3	1	no	—
139	C₃×C₂²⋊C₄	—	3	2	no	—
140	C₃×C₂²⋊C₄	—	3	1	no	—
141	C₃×C₂²⋊C₄	—	3	2	no	—
142	C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
143	C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
144	C₃×C₄²	—	3	1	no	—
145	#217	C₂²×C₃	1	1	yes	characteristic, complemented
146	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
147	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
148	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
149	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₂²×C₃²	—	2	1	no	—
152	C₂²×C₃²	—	2	1	no	—
153	C₂²×C₃²	—	2	2	no	—
154	C₂²×C₃²	—	2	2	no	—
155	C₂²×C₃²	—	2	2	no	—
156	C₂²×C₃²	C₂×D₄	1	2	yes	complemented
157	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
158	C₂×C₃×D₃	—	2	1	no	—
159	C₂×C₃×D₃	—	2	2	no	—
160	C₂×C₃×D₃	—	2	2	no	—
161	C₂×C₃×D₃	—	2	1	no	—
162	C₂×C₃×D₃	—	2	2	no	—
163	C₂×C₃×D₃	—	2	2	no	—
164	C₂×C₃×D₃	—	2	2	no	—
165	C₂×C₃×D₃	—	4	8	no	—
166	C₂×C₃×D₃	—	4	8	no	—
167	C₂×C₃×D₃	C₂×D₄	1	2	yes	complemented
168	C₂×C₃×D₃	C₂×D₄	1	4	yes	complemented
169	C₃²×C₄	—	2	2	no	—
170	C₃²×C₄	—	2	1	no	—
171	C₃²×C₄	C₂×D₄	1	2	yes	complemented
172	C₃×Dic₃	—	2	1	no	—
173	C₃×Dic₃	—	2	1	no	—
174	C₃×Dic₃	C₂×D₄	1	2	yes	complemented
175	C₂²×D₄	—	3	2	no	—
176	C₂²×D₄	—	3	1	no	—
177	C₂²×D₄	—	3	1	no	—
178	#127	—	3	1	no	—
179	#121	—	3	1	no	—
180	#121	—	3	2	no	—
181	#121	C₃×D₃	1	1	yes	characteristic, complemented
182	#120	—	3	2	no	—
183	#120	—	3	2	no	—
184	C₄×D₄	—	3	1	no	—
185	C₄×D₄	—	3	1	no	—
186	C₂³×C₃	—	2	1	no	—
187	C₂³×C₃	—	2	2	no	—
188	C₂³×C₃	—	3	2	no	—
189	C₂³×C₃	—	3	1	no	—
190	C₂³×C₃	—	3	2	no	—
191	C₂³×C₃	—	6	4	no	—
192	C₂³×C₃	—	6	4	no	—
193	C₂³×C₃	—	6	4	no	—
194	C₂³×C₃	—	6	4	no	—
195	C₂³×C₃	—	12	2	no	—
196	C₂³×C₃	—	12	2	no	—
197	C₂³×C₃	C₂²×D₃	1	2	yes	—
198	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
199	C₂³×C₃	C₂³×C₃	1	2	yes	—
200	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
201	C₂²×D₃	—	2	4	no	—
202	C₂²×D₃	—	2	4	no	—
203	C₂²×D₃	—	2	4	no	—
204	C₂²×D₃	—	2	4	no	—
205	C₂²×D₃	—	4	2	no	—
206	C₂²×D₃	—	4	2	no	—
207	C₂²×D₃	C₂³×C₃	1	2	yes	—
208	C₂²×D₃	C₂³×C₃	1	2	yes	—
209	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
210	C₃×D₄	—	2	4	no	—
211	C₃×D₄	—	2	4	no	—
212	C₃×D₄	—	2	2	no	—
213	C₃×D₄	—	2	2	no	—
214	C₃×D₄	—	3	4	no	—
215	C₃×D₄	—	3	4	no	—
216	C₃×D₄	—	4	2	no	—
217	C₃×D₄	—	4	4	no	—
218	C₃×D₄	—	6	4	no	—
219	C₃×D₄	—	6	4	no	—
220	C₃×D₄	—	6	4	no	—
221	C₃×D₄	—	6	4	no	—
222	C₃×D₄	—	6	2	no	—
223	C₃×D₄	—	12	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	3	1	no	—
230	C₂×C₃×C₄	—	3	1	no	—
231	C₂×C₃×C₄	—	3	1	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	6	4	no	—
234	C₂×C₃×C₄	—	6	2	no	—
235	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
236	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
240	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
241	#67	—	2	4	no	—
242	#67	—	2	4	no	—
243	#67	—	4	2	no	—
244	#67	C₃×D₄	1	4	yes	complemented
245	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
246	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
247	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
248	D₁₂	—	2	4	no	—
249	D₁₂	—	2	4	no	—
250	D₁₂	—	2	2	no	—
251	D₁₂	C₃×D₄	1	4	yes	complemented
252	C₄×D₃	—	2	2	no	—
253	C₄×D₃	—	2	4	no	—
254	C₂×C₃²	—	2	2	no	—
255	C₂×C₃²	—	4	2	no	—
256	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
259	C₃×D₃	—	2	2	no	—
260	C₃×D₃	—	2	4	no	—
261	C₃×D₃	—	4	2	no	—
262	C₂⁴	—	3	2	no	—
263	C₂⁴	—	3	2	no	—
264	C₂×D₄	—	3	1	no	—
265	C₂×D₄	—	3	2	no	—
266	C₂×D₄	—	3	2	no	—
267	C₂×D₄	—	3	2	no	—
268	C₂×D₄	—	3	1	no	—
269	C₂×D₄	—	3	2	no	—
270	C₂×D₄	—	3	2	no	—
271	C₂×D₄	—	3	1	no	—
272	C₂×D₄	—	6	4	no	—
273	C₂×D₄	—	6	8	no	—
274	C₂×D₄	—	6	4	no	—
275	C₂×D₄	C₂×C₃×D₃	1	2	yes	complemented
276	C₂×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
277	C₂²×C₄	—	3	2	no	—
278	C₂²×C₄	—	3	1	no	—
279	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
280	C₄⋊C₄	—	3	1	no	—
281	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
282	C₂²⋊C₄	—	3	1	no	—
283	C₂²⋊C₄	—	3	2	no	—
284	C₂²⋊C₄	—	3	1	no	—
285	C₂²⋊C₄	—	3	2	no	—
286	C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
287	C₄²	—	3	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	3	2	no	—
301	C₂²×C₃	—	3	4	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	4	1	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	2	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	6	2	no	—
308	C₂²×C₃	—	6	1	no	—
309	C₂²×C₃	—	6	2	no	—
310	C₂²×C₃	—	6	1	no	—
311	C₂²×C₃	—	6	2	no	—
312	C₂²×C₃	—	6	2	no	—
313	C₂²×C₃	—	6	2	no	—
314	C₂²×C₃	—	12	8	no	—
315	C₂²×C₃	—	12	8	no	—
316	C₂²×C₃	D₃×D₄	1	2	yes	complemented
317	C₂²×C₃	C₂×C₃×D₄	1	2	yes	complemented
318	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
319	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
320	C₂×D₃	—	2	1	no	—
321	C₂×D₃	—	2	2	no	—
322	C₂×D₃	—	2	2	no	—
323	C₂×D₃	—	2	1	no	—
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	2	no	—
326	C₂×D₃	—	2	2	no	—
327	C₂×D₃	—	4	8	no	—
328	C₂×D₃	—	4	8	no	—
329	C₂×D₃	C₂×C₃×D₄	1	2	yes	complemented
330	C₂×D₃	C₂×C₃×D₄	1	4	yes	complemented
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	3	2	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	—	6	1	no	—
340	C₃×C₄	—	6	1	no	—
341	C₃×C₄	D₃×D₄	1	2	yes	complemented
342	C₃×C₄	C₂×C₃×D₄	1	2	yes	complemented
343	Dic₃	—	2	1	no	—
344	Dic₃	—	2	1	no	—
345	Dic₃	C₂×C₃×D₄	1	2	yes	complemented
346	C₃²	D₄²	1	1	yes	characteristic, complemented, Sylow
347	C₂³	—	3	1	no	—
348	C₂³	—	3	2	no	—
349	C₂³	—	3	2	no	—
350	C₂³	—	6	4	no	—
351	C₂³	—	6	4	no	—
352	C₂³	—	6	4	no	—
353	C₂³	—	6	4	no	—
354	C₂³	—	12	2	no	—
355	C₂³	—	12	2	no	—
356	C₂³	C₂²×C₃×D₃	1	2	yes	—
357	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
358	D₄	—	2	4	no	—
359	D₄	—	2	2	no	—
360	D₄	—	3	4	no	—
361	D₄	—	3	4	no	—
362	D₄	—	6	4	no	—
363	D₄	—	6	4	no	—
364	D₄	—	6	4	no	—
365	D₄	—	6	4	no	—
366	D₄	—	6	2	no	—
367	D₄	—	12	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	3	1	no	—
370	C₂×C₄	—	3	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	6	4	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
375	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	—	4	2	no	—
384	C₂×C₃	—	4	2	no	—
385	C₂×C₃	—	6	4	no	—
386	C₂×C₃	—	6	2	no	—
387	C₂×C₃	—	8	2	no	—
388	C₂×C₃	—	12	2	no	—
389	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
390	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
391	C₂×C₃	#1009	1	1	yes	characteristic
392	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
393	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
394	C₂×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
395	D₃	—	2	2	no	—
396	D₃	—	2	4	no	—
397	D₃	—	4	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	3	2	no	—
404	C₂²	—	3	4	no	—
405	C₂²	—	6	2	no	—
406	C₂²	—	6	1	no	—
407	C₂²	—	6	2	no	—
408	C₂²	—	6	1	no	—
409	C₂²	—	6	2	no	—
410	C₂²	—	6	2	no	—
411	C₂²	—	6	2	no	—
412	C₂²	—	12	8	no	—
413	C₂²	—	12	8	no	—
414	C₂²	C₃×D₃×D₄	1	2	yes	complemented
415	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	—	3	2	no	—
419	C₄	—	6	1	no	—
420	C₄	—	6	1	no	—
421	C₄	C₃×D₃×D₄	1	2	yes	complemented
422	C₃	—	2	1	no	—
423	C₃	#5609	1	1	yes	characteristic, direct product factor
424	C₃	C₃×D₄²	1	1	yes	characteristic, complemented
425	C₂	—	2	2	no	—
426	C₂	—	4	2	no	—
427	C₂	—	6	4	no	—
428	C₂	—	6	2	no	—
429	C₂	—	12	2	no	—
430	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
431	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
432	C₂	C₃×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#121	C₂
socle	C₂²×C₃²	C₂⁴
hypercenter	C₃×#121	D₃
hypocenter	C₃	C₃×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×D₄	C₂	semidirect
2. C₂×C₃×D₃×D₄	C₂	semidirect
3. C₂²×C₃×D₁₂	C₂	semidirect
4. C₃²×#121	C₂	semidirect
5. C₃×#940	C₂	semidirect
6. C₃×#937	C₂	semidirect
7. C₃×C₄×#67	C₂	semidirect
8. C₃×#895	C₂	semidirect
9. C₃×#893	C₂	semidirect
10. C₃×#884	C₂	semidirect
11. C₃×#882	C₂	semidirect
13. #5609	C₃	direct (N × H)
14. C₂³×C₃×D₃	C₂²	semidirect
15. C₂³×C₃×D₃	C₂²	semidirect
16. C₂×C₃²×D₄	C₂²	semidirect
17. C₂×C₃²×D₄	C₂²	semidirect
18. C₂²×C₃²×C₄	C₂²	semidirect
20. C₂×C₃×#67	C₂²	semidirect
21. C₂×C₃×#67	C₂²	semidirect
22. C₂×C₃×#67	C₂²	semidirect
27. C₂×C₃×D₁₂	C₂²	semidirect
28. C₂×C₃×D₁₂	C₂²	semidirect
29. C₂×C₃×D₁₂	C₂²	semidirect
30. C₂×C₃×C₄×D₃	C₂²	semidirect
31. C₂×C₃×C₄×D₃	C₂²	semidirect
32. C₃²×C₄⋊C₄	C₂²	semidirect
33. C₃²×C₂²⋊C₄	C₂²	semidirect
34. C₃×#217	C₂²	semidirect
35. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
38. C₃×Dic₃⋊C₄	C₂²	semidirect
39. C₃×C₄×Dic₃	C₂²	semidirect
43. C₂×D₃×D₄	C₂×C₃	semidirect
44. C₂×D₃×D₄	C₂×C₃	semidirect
45. C₂²×D₁₂	C₂×C₃	semidirect
50. C₃×#121	D₃	semidirect
51. C₃×#121	C₂×C₃	semidirect
56. #940	C₂×C₃	semidirect
57. #937	C₂×C₃	semidirect
58. C₄×#67	C₂×C₃	semidirect
59. #895	C₂×C₃	semidirect
60. #893	C₂×C₃	semidirect
61. #884	C₂×C₃	semidirect
62. #882	C₂×C₃	semidirect
83. C₃×#67	D₄	semidirect
90. C₃×D₁₂	D₄	semidirect
96. C₂³×D₃	C₂²×C₃	semidirect
97. C₂³×D₃	C₂²×C₃	semidirect
111. C₂×C₃×D₄	C₂×D₃	semidirect
112. C₂×C₃×D₄	C₂×D₃	semidirect
113. C₂×C₃×D₄	C₂²×C₃	semidirect
114. C₂×C₃×D₄	C₂²×C₃	semidirect
118. C₂²×C₃×C₄	C₂×D₃	semidirect
119. C₂²×C₃×C₄	C₂²×C₃	semidirect
121. C₂×#67	C₂²×C₃	semidirect
122. C₂×#67	C₂²×C₃	semidirect
123. C₂×#67	C₂²×C₃	semidirect
128. C₂×D₁₂	C₂²×C₃	semidirect
129. C₂×D₁₂	C₂²×C₃	semidirect
130. C₂×D₁₂	C₂²×C₃	semidirect
131. C₂×C₄×D₃	C₂²×C₃	semidirect
132. C₂×C₄×D₃	C₂²×C₃	semidirect
135. C₃×C₄⋊C₄	C₂×D₃	semidirect
136. C₃×C₄⋊C₄	C₂²×C₃	semidirect
142. C₃×C₂²⋊C₄	C₂×D₃	semidirect
143. C₃×C₂²⋊C₄	C₂²×C₃	semidirect
145. #217	C₂²×C₃	semidirect
146. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
147. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
148. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
149. Dic₃⋊C₄	C₂²×C₃	semidirect
150. C₄×Dic₃	C₂²×C₃	semidirect
156. C₂²×C₃²	C₂×D₄	semidirect
167. C₂×C₃×D₃	C₂×D₄	semidirect
168. C₂×C₃×D₃	C₂×D₄	semidirect
171. C₃²×C₄	C₂×D₄	semidirect
174. C₃×Dic₃	C₂×D₄	semidirect
181. #121	C₃×D₃	semidirect
244. #67	C₃×D₄	semidirect
251. D₁₂	C₃×D₄	semidirect
275. C₂×D₄	C₂×C₃×D₃	semidirect
276. C₂×D₄	C₂×C₃×D₃	semidirect
279. C₂²×C₄	C₂×C₃×D₃	semidirect
281. C₄⋊C₄	C₂×C₃×D₃	semidirect
286. C₂²⋊C₄	C₂×C₃×D₃	semidirect
316. C₂²×C₃	D₃×D₄	semidirect
317. C₂²×C₃	C₂×C₃×D₄	semidirect
329. C₂×D₃	C₂×C₃×D₄	semidirect
330. C₂×D₃	C₂×C₃×D₄	semidirect
341. C₃×C₄	D₃×D₄	semidirect
342. C₃×C₄	C₂×C₃×D₄	semidirect
345. Dic₃	C₂×C₃×D₄	semidirect
346. C₃²	D₄²	semidirect
414. C₂²	C₃×D₃×D₄	semidirect
421. C₄	C₃×D₃×D₄	semidirect
423. C₃	#5609	direct (N × H)
424. C₃	C₃×D₄²	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×D₄	2
C₂²×C₃×D₁₂	2
C₃²×#121	2
C₃×#940	2
C₃×#937	2
C₃×C₄×#67	2
C₃×#895	2
C₃×#893	2
C₃×#884	2
C₃×#882	2
C₃×D₄²	3
#5609	3

Subgroups — C3×#5609 #10595706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5609 #10595706