Subgroups — C₃×#79312 #11878704

Order 1152.

915 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5477	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4841	C₂	1	4	yes	maximal, complemented
5	C₃×#4738	C₂	1	4	yes	maximal, complemented
6	C₃×#4693	C₂	1	2	yes	maximal, complemented
7	C₃×#4681	C₂	1	2	yes	maximal, complemented
8	C₃×#3206	—	3	1	no	maximal
9	#79312	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	—	2	1	no	—
11	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₃×#930	—	2	1	no	—
14	C₃×#930	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₃×#204	C₂²	1	8	yes	—
18	C₃×#875	—	2	1	no	—
19	C₃×#874	C₂²	1	1	yes	characteristic
20	C₃×C₄×D₁₂	—	2	1	no	—
21	C₃×C₄×D₁₂	C₂²	1	2	yes	—
22	C₃×#869	—	2	1	no	—
23	C₃×#869	—	2	1	no	—
24	C₃×#869	C₂²	1	2	yes	—
25	C₃×#869	C₂²	1	2	yes	—
26	C₃×#869	C₂²	1	1	yes	characteristic
27	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
28	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃²×C₄×C₈	C₂²	1	2	yes	—
30	C₃×#816	C₂²	1	8	yes	—
31	C₃×#532	—	3	1	no	—
32	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
33	#5477	C₂×C₃	1	1	yes	characteristic
34	C₂×#869	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#492	—	3	2	no	—
36	C₃×#487	—	3	2	no	—
37	C₃×#461	—	3	4	no	—
38	C₃×#448	—	3	4	no	—
39	C₃×#431	—	2	1	no	—
40	C₃×#431	D₃	1	1	yes	characteristic, complemented
41	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
42	#4841	C₂×C₃	1	4	yes	complemented
43	#4738	C₂×C₃	1	4	yes	complemented
44	#4693	C₂×C₃	1	2	yes	complemented
45	#4681	C₂×C₃	1	2	yes	complemented
46	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
47	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	2	no	—
50	C₂²×C₃×Dic₃	—	2	2	no	—
51	C₃×#235	—	4	4	no	—
52	C₂×C₃×D₁₂	—	2	1	no	—
53	C₂×C₃×D₁₂	—	2	1	no	—
54	C₂×C₃×D₁₂	C₂³	1	2	yes	—
55	C₂×C₃×C₄×D₃	—	2	2	no	—
56	C₂×C₃×Dic₆	—	2	2	no	—
57	C₂×C₃×Dic₆	—	2	1	no	—
58	C₂×C₃×Dic₆	—	4	4	no	—
59	C₂×C₃×Dic₆	C₂³	1	4	yes	—
60	C₂×C₃²×C₈	C₂³	1	4	yes	—
61	C₃²×C₄²	D₄	1	1	yes	characteristic
62	C₃²×C₄²	D₄	1	1	yes	characteristic
63	C₃²×C₄²	C₂³	1	1	yes	characteristic
64	C₃²×C₄²	C₂³	1	1	yes	characteristic
65	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
66	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
67	C₃×C₄⋊Dic₃	—	2	2	no	—
68	C₃×C₄⋊Dic₃	—	2	2	no	—
69	C₃×C₄⋊Dic₃	—	2	2	no	—
70	C₃×C₄⋊Dic₃	—	2	2	no	—
71	C₃×C₄⋊Dic₃	—	2	1	no	—
72	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₃×#204	—	4	8	no	—
74	#3206	—	3	1	no	Sylow
75	C₂×C₃×#41	—	6	1	no	—
76	C₂²×C₃×Q₈	—	3	2	no	—
77	C₂×#235	—	2	1	no	—
78	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
79	C₂×C₃×SD₁₆	—	3	8	no	—
80	C₃×C₄⋊Q₈	—	3	1	no	—
81	C₃×C₄⋊Q₈	—	3	2	no	—
82	C₃×C₄⋊Q₈	—	3	2	no	—
83	C₃×C₄⋊Q₈	—	6	1	no	—
84	C₃×C₄⋊Q₈	—	6	1	no	—
85	C₃×#127	—	3	1	no	—
86	C₃×#124	—	6	1	no	—
87	C₃×#121	—	3	2	no	—
88	C₃×#121	—	6	1	no	—
89	C₃×C₄×D₄	—	3	2	no	—
90	C₃×C₄×D₄	—	6	1	no	—
91	C₂×C₃×C₄⋊C₄	—	6	1	no	—
92	C₂×C₃×C₄⋊C₄	—	6	1	no	—
93	C₂×C₃×C₄²	—	2	1	no	—
94	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
95	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
96	#930	—	2	1	no	—
97	#930	C₂²×C₃	1	2	yes	—
98	C₂×C₄⋊Dic₃	—	2	1	no	—
99	C₂×C₄⋊Dic₃	—	2	1	no	—
100	C₂×#204	C₂²×C₃	1	8	yes	—
101	#875	—	2	1	no	—
102	#874	C₂²×C₃	1	1	yes	characteristic
103	C₄×D₁₂	—	2	1	no	—
104	C₄×D₁₂	C₂²×C₃	1	2	yes	—
105	#869	—	2	1	no	—
106	#869	—	2	1	no	—
107	#869	C₂²×C₃	1	2	yes	—
108	#869	C₂²×C₃	1	2	yes	—
109	#869	C₂²×C₃	1	1	yes	characteristic
110	C₃×C₄⋊C₈	—	2	2	no	—
111	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
112	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
113	C₃×#103	—	3	8	no	—
114	C₃×C₂²⋊C₈	—	2	2	no	—
115	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
116	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
117	C₃×C₄×C₈	—	2	2	no	—
118	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
119	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
120	#816	C₂²×C₃	1	8	yes	—
121	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₃×D₃	—	2	2	no	—
123	C₂×C₃²×C₄	—	2	2	no	—
124	C₂×C₃²×C₄	—	2	2	no	—
125	C₂×C₃²×C₄	SD₁₆	1	4	yes	complemented
126	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
132	C₃×#67	—	4	4	no	—
133	C₂×C₃×Dic₃	—	2	4	no	—
134	C₂×C₃×Dic₃	—	2	2	no	—
135	C₂×C₃×Dic₃	—	4	4	no	—
136	C₃×D₁₂	—	2	4	no	—
137	C₃×D₁₂	—	4	2	no	—
138	C₃×D₁₂	—	4	2	no	—
139	C₃×C₄×D₃	—	4	4	no	—
140	C₃×Dic₆	—	2	8	no	—
141	C₃×Dic₆	—	4	4	no	—
142	C₃×Dic₆	—	4	2	no	—
143	C₃²×C₈	—	2	4	no	—
144	#532	—	3	1	no	—
145	C₂×C₄⋊Q₈	—	3	1	no	—
146	#492	—	3	2	no	—
147	#487	—	3	2	no	—
148	#461	—	3	4	no	—
149	#448	—	3	4	no	—
150	#431	C₃×D₃	1	1	yes	characteristic, complemented
151	C₃×#41	—	12	4	no	—
152	C₂×C₃×Q₈	—	3	4	no	—
153	C₂×C₃×Q₈	—	6	1	no	—
154	C₂×C₃×Q₈	—	6	2	no	—
155	C₂×C₃×Q₈	—	12	4	no	—
156	C₂×C₃×D₄	—	3	2	no	—
157	C₂×C₃×D₄	—	6	2	no	—
158	C₂×C₃×D₄	—	6	1	no	—
159	C₂×C₃×D₄	—	6	1	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	—	6	2	no	—
164	C₂²×C₃×C₄	—	6	2	no	—
165	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
166	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂×#67	—	2	2	no	—
172	C₂²×Dic₃	—	2	2	no	—
173	#235	—	4	4	no	—
174	C₂×D₁₂	—	2	1	no	—
175	C₂×D₁₂	—	2	1	no	—
176	C₂×D₁₂	C₂³×C₃	1	2	yes	—
177	C₂×C₄×D₃	—	2	2	no	—
178	C₂×Dic₆	—	2	2	no	—
179	C₂×Dic₆	—	2	1	no	—
180	C₂×Dic₆	—	4	4	no	—
181	C₂×Dic₆	C₂³×C₃	1	4	yes	—
182	C₃×SD₁₆	—	12	8	no	—
183	C₂×C₃×C₈	—	2	4	no	—
184	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
185	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
186	C₃×C₄⋊C₄	—	3	2	no	—
187	C₃×C₄⋊C₄	—	6	2	no	—
188	C₃×C₄⋊C₄	—	6	2	no	—
189	C₃×C₄⋊C₄	—	6	2	no	—
190	C₃×C₄⋊C₄	—	6	2	no	—
191	C₃×C₄⋊C₄	—	6	1	no	—
192	C₃×C₂²⋊C₄	—	6	2	no	—
193	C₃×C₂²⋊C₄	—	6	2	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	D₁₂	1	1	yes	characteristic
199	C₃×C₄²	D₁₂	1	1	yes	characteristic
200	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
201	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
202	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
203	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
204	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
205	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
206	(C₂×D₃)⋊C₄	—	2	2	no	—
207	(C₂×D₃)⋊C₄	—	2	2	no	—
208	C₄⋊Dic₃	—	2	2	no	—
209	C₄⋊Dic₃	—	2	2	no	—
210	C₄⋊Dic₃	—	2	2	no	—
211	C₄⋊Dic₃	—	2	2	no	—
212	C₄⋊Dic₃	—	2	1	no	—
213	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
214	#204	—	4	8	no	—
215	C₂²×C₃²	—	2	1	no	—
216	C₂²×C₃²	—	2	1	no	—
217	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
218	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₃×D₃	—	4	2	no	—
220	C₂×C₃×D₃	—	4	2	no	—
221	C₂×C₃×D₃	—	4	2	no	—
222	C₃²×C₄	—	2	1	no	—
223	C₃²×C₄	—	2	1	no	—
224	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
225	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
226	C₃²×C₄	#137	1	2	yes	—
227	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
228	C₃×Dic₃	—	4	4	no	—
229	C₃×Dic₃	—	4	2	no	—
230	C₂×#41	—	6	1	no	—
231	C₂²×Q₈	—	3	2	no	—
232	C₂×SD₁₆	—	3	8	no	—
233	C₄⋊Q₈	—	3	1	no	—
234	C₄⋊Q₈	—	3	2	no	—
235	C₄⋊Q₈	—	3	2	no	—
236	C₄⋊Q₈	—	6	1	no	—
237	C₄⋊Q₈	—	6	1	no	—
238	#127	—	3	1	no	—
239	#124	—	6	1	no	—
240	#121	—	3	2	no	—
241	#121	—	6	1	no	—
242	C₄×D₄	—	3	2	no	—
243	C₄×D₄	—	6	1	no	—
244	C₂×C₄⋊C₄	—	6	1	no	—
245	C₂×C₄⋊C₄	—	6	1	no	—
246	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
247	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
248	#103	—	3	8	no	—
249	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
250	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	6	2	no	—
253	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
254	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂²×D₃	—	2	2	no	—
256	C₃×Q₈	—	6	8	no	—
257	C₃×Q₈	—	12	4	no	—
258	C₃×Q₈	—	12	2	no	—
259	C₃×D₄	—	6	4	no	—
260	C₃×D₄	—	12	4	no	—
261	C₃×D₄	—	12	2	no	—
262	C₃×D₄	—	12	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	—	6	4	no	—
278	C₂×C₃×C₄	—	12	4	no	—
279	C₂×C₃×C₄	—	12	4	no	—
280	C₂×C₃×C₄	#204	1	4	yes	complemented
281	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	complemented
282	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
294	#67	—	4	4	no	—
295	C₂×Dic₃	—	2	4	no	—
296	C₂×Dic₃	—	2	2	no	—
297	C₂×Dic₃	—	4	4	no	—
298	D₁₂	—	2	4	no	—
299	D₁₂	—	4	2	no	—
300	D₁₂	—	4	2	no	—
301	C₄×D₃	—	4	4	no	—
302	Dic₆	—	2	8	no	—
303	Dic₆	—	4	4	no	—
304	Dic₆	—	4	2	no	—
305	C₃×C₈	—	2	4	no	—
306	C₃×C₈	—	2	4	no	—
307	C₃×C₈	—	4	4	no	—
308	C₂×C₃²	—	2	2	no	—
309	C₂×C₃²	#535	1	1	yes	characteristic
310	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
311	C₂×C₃²	C₂×#137	1	1	yes	characteristic
312	C₃×D₃	—	8	2	no	—
313	#41	—	12	4	no	—
314	C₂×Q₈	—	3	4	no	—
315	C₂×Q₈	—	6	1	no	—
316	C₂×Q₈	—	6	2	no	—
317	C₂×Q₈	—	12	4	no	—
318	C₂×D₄	—	3	2	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	1	no	—
321	C₂×D₄	—	6	1	no	—
322	C₂²×C₄	—	6	2	no	—
323	C₂²×C₄	—	6	2	no	—
324	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
325	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
327	SD₁₆	—	12	8	no	—
328	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
329	C₄⋊C₄	—	3	2	no	—
330	C₄⋊C₄	—	6	2	no	—
331	C₄⋊C₄	—	6	2	no	—
332	C₄⋊C₄	—	6	2	no	—
333	C₄⋊C₄	—	6	2	no	—
334	C₄⋊C₄	—	6	1	no	—
335	C₂²⋊C₄	—	6	2	no	—
336	C₂²⋊C₄	—	6	2	no	—
337	C₄²	C₃×D₁₂	1	1	yes	characteristic
338	C₄²	C₃×D₁₂	1	1	yes	characteristic
339	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
341	C₂²×C₃	—	2	1	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	12	2	no	—
350	C₂²×C₃	—	12	2	no	—
351	C₂²×C₃	—	12	2	no	—
352	C₂²×C₃	C₂×#204	1	2	yes	—
353	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
354	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
355	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
356	C₂×D₃	—	4	2	no	—
357	C₂×D₃	—	4	2	no	—
358	C₂×D₃	—	4	2	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	4	1	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	12	2	no	—
370	C₃×C₄	—	12	4	no	—
371	C₃×C₄	C₂×#204	1	2	yes	—
372	C₃×C₄	C₂×#204	1	2	yes	—
373	C₃×C₄	#909	1	2	yes	—
374	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
375	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
376	C₃×C₄	C₃×#137	1	2	yes	—
377	C₃×C₄	#1009	1	2	yes	—
378	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
379	Dic₃	—	4	2	no	—
380	Dic₃	—	4	4	no	—
381	C₃²	#3206	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	6	2	no	—
383	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
384	Q₈	—	6	8	no	—
385	Q₈	—	12	4	no	—
386	Q₈	—	12	2	no	—
387	D₄	—	6	4	no	—
388	D₄	—	12	4	no	—
389	D₄	—	12	2	no	—
390	D₄	—	12	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	6	4	no	—
395	C₂×C₄	—	12	4	no	—
396	C₂×C₄	—	12	4	no	—
397	C₂×C₄	C₃×#204	1	4	yes	complemented
398	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
399	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
400	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
402	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
403	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₂×C₃	—	2	2	no	—
406	C₂×C₃	—	2	2	no	—
407	C₂×C₃	—	2	1	no	—
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	4	2	no	—
411	C₂×C₃	—	24	2	no	—
412	C₂×C₃	#5525	1	1	yes	characteristic
413	C₂×C₃	C₂²×#204	1	1	yes	characteristic
414	C₂×C₃	C₂×#909	1	1	yes	characteristic
415	C₂×C₃	C₃×#535	1	1	yes	characteristic
416	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
417	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
418	D₃	—	8	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	12	2	no	—
422	C₂²	—	12	2	no	—
423	C₂²	—	12	2	no	—
424	C₂²	C₂×C₃×#204	1	2	yes	—
425	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	12	4	no	—
429	C₄	—	12	2	no	—
430	C₄	C₂×C₃×#204	1	2	yes	—
431	C₄	C₂×C₃×#204	1	2	yes	—
432	C₄	C₃×#909	1	2	yes	—
433	C₄	C₃×#1009	1	2	yes	—
434	C₃	—	2	1	no	—
435	C₃	#79312	1	1	yes	characteristic, direct product factor
436	C₃	C₃×#3206	1	1	yes	characteristic, complemented
437	C₂	—	2	2	no	—
438	C₂	—	24	2	no	—
439	C₂	C₃×#5525	1	1	yes	characteristic
440	C₂	C₂²×C₃×#204	1	1	yes	characteristic
441	C₂	C₂×C₃×#909	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃×#5477	C₂
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#3206
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#869	C₂	semidirect
3. C₃²×#431	C₂	semidirect
4. C₃×#4841	C₂	semidirect
5. C₃×#4738	C₂	semidirect
6. C₃×#4693	C₂	semidirect
7. C₃×#4681	C₂	semidirect
9. #79312	C₃	direct (N × H)
34. C₂×#869	C₂×C₃	semidirect
40. C₃×#431	D₃	semidirect
41. C₃×#431	C₂×C₃	semidirect
42. #4841	C₂×C₃	semidirect
43. #4738	C₂×C₃	semidirect
44. #4693	C₂×C₃	semidirect
45. #4681	C₂×C₃	semidirect
125. C₂×C₃²×C₄	SD₁₆	semidirect
150. #431	C₃×D₃	semidirect
280. C₂×C₃×C₄	#204	semidirect
281. C₂×C₃×C₄	C₃×SD₁₆	semidirect
381. C₃²	#3206	semidirect
397. C₂×C₄	C₃×#204	semidirect
435. C₃	#79312	direct (N × H)
436. C₃	C₃×#3206	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5477	2
C₂×C₃×#869	2
C₃²×#431	2
C₃×#4841	2
C₃×#4738	2
C₃×#4693	2
C₃×#4681	2
C₃×#3206	3
#79312	3

Subgroups — C3×#79312 #11878704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79312 #11878704