Subgroups — C₃×#69789 #11784069

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5113	C₂	1	1	yes	maximal, characteristic
4	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#805	C₂	1	1	yes	maximal, characteristic
6	C₃×#4552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1764	—	3	1	no	maximal
9	#69789	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×#926	C₂²	1	1	yes	characteristic
15	C₂×C₃×#208	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	1	yes	characteristic
17	C₃×#901	—	2	2	no	—
18	C₃×#901	C₄	1	4	yes	complemented
19	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
20	C₂×C₃×D₃×C₈	—	2	1	no	—
21	C₃²×C₄×C₈	—	2	2	no	—
22	C₃×#821	C₄	1	2	yes	complemented
23	C₃×#816	C₄	1	2	yes	complemented
24	C₃×#815	—	2	1	no	—
25	C₃×C₈×Dic₃	—	2	1	no	—
26	C₃×#805	C₄	1	4	yes	complemented
27	C₂×C₃×#131	—	3	1	no	—
28	C₂×#901	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#104	—	3	1	no	—
30	C₃×#416	—	3	1	no	—
31	C₃×#405	—	3	1	no	—
32	C₂×C₃×C₄×C₈	—	2	1	no	—
33	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
35	#5113	C₂×C₃	1	1	yes	characteristic
36	#5101	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#805	C₂×C₃	1	1	yes	characteristic
38	C₃×#341	—	3	1	no	—
39	C₃×#339	—	3	1	no	—
40	#4552	C₂×C₃	1	1	yes	characteristic, complemented
41	#4523	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×C₃²×C₄	—	2	1	no	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃×#67	—	2	1	no	—
45	C₃×#235	—	2	1	no	—
46	C₃×#235	—	2	1	no	—
47	C₃×#235	C₂×C₄	1	2	yes	—
48	C₃×#235	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₃	—	2	1	no	—
51	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃²×C₈	—	2	1	no	—
53	C₂×C₃²×C₈	—	2	1	no	—
54	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
55	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
56	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
57	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
58	C₂×C₃²×C₈	D₄	1	2	yes	—
59	C₃²×C₄²	—	2	1	no	—
60	C₃²×C₄²	C₂×C₄	1	2	yes	—
61	C₃×#217	—	2	1	no	—
62	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
63	C₃×C₄×Dic₃	—	2	1	no	—
64	C₃×#208	—	2	1	no	—
65	C₃×#208	—	2	1	no	—
66	C₃×#208	C₂×C₄	1	2	yes	—
67	C₃×#208	C₂×C₄	1	2	yes	—
68	C₂×C₃×C₃⋊C₈	—	2	1	no	—
69	C₂×C₃×C₃⋊C₈	—	2	1	no	—
70	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
71	C₃×D₃×C₈	—	2	4	no	—
72	#1764	—	3	1	no	Sylow
73	C₂×C₃×#41	—	3	1	no	—
74	C₂×#235	C₂²×C₃	1	1	yes	characteristic
75	C₃×#131	—	3	4	no	—
76	C₃×#131	—	6	2	no	—
77	C₂×C₃×M₁₆	—	3	1	no	—
78	C₂×C₃×M₁₆	—	3	1	no	—
79	C₂×C₃×M₁₆	—	6	1	no	—
80	C₂²×C₃×C₈	—	2	1	no	—
81	C₂²×C₃×C₈	—	2	1	no	—
82	C₂²×C₃×C₈	—	6	1	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
87	C₃×#117	—	3	1	no	—
88	C₂×C₃×C₄²	—	2	1	no	—
89	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
91	#926	C₂²×C₃	1	1	yes	characteristic
92	C₂×#208	C₂²×C₃	1	1	yes	characteristic
93	C₂×#208	C₂²×C₃	1	1	yes	characteristic
94	#901	—	2	2	no	—
95	#901	C₃×C₄	1	4	yes	complemented
96	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
97	C₂×D₃×C₈	—	2	1	no	—
98	C₃×#104	—	3	4	no	—
99	C₃×#103	—	3	2	no	—
100	C₃×#102	—	3	2	no	—
101	C₃×#97	—	6	1	no	—
102	C₃×C₄×C₈	—	2	4	no	—
103	C₃×C₄×C₈	—	2	2	no	—
104	C₃×C₄×C₈	—	2	2	no	—
105	C₃×C₄×C₈	—	6	1	no	—
106	#821	C₃×C₄	1	2	yes	complemented
107	#816	C₃×C₄	1	2	yes	complemented
108	#815	—	2	1	no	—
109	C₈×Dic₃	—	2	1	no	—
110	#805	C₃×C₄	1	4	yes	complemented
111	C₂³×C₃²	#41	1	1	yes	characteristic
112	C₂²×C₃×D₃	—	2	1	no	—
113	C₂×C₃²×C₄	—	2	4	no	—
114	C₂×C₃²×C₄	—	2	2	no	—
115	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃²×C₄	#41	1	1	yes	characteristic
121	C₃×#67	—	2	2	no	—
122	C₃×#67	—	2	2	no	—
123	C₂×C₃×Dic₃	—	2	1	no	—
124	C₂×C₃×Dic₃	—	2	2	no	—
125	C₃×D₁₂	—	2	1	no	—
126	C₃×D₁₂	C₄²	1	2	yes	—
127	C₃×C₄×D₃	—	2	2	no	—
128	C₃×C₄×D₃	—	2	2	no	—
129	C₃×Dic₆	—	2	1	no	—
130	C₃×Dic₆	C₄²	1	2	yes	—
131	C₃²×C₈	—	2	2	no	—
132	C₃²×C₈	C₂²⋊C₄	1	2	yes	—
133	C₃²×C₈	C₂²⋊C₄	1	2	yes	—
134	C₃×C₃⋊C₈	—	2	2	no	—
135	C₃×C₃⋊C₈	—	2	2	no	—
136	C₂×#131	—	3	1	no	—
137	C₂×#104	—	3	1	no	—
138	#416	—	3	1	no	—
139	#405	—	3	1	no	—
140	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
141	#341	—	3	1	no	—
142	#339	—	3	1	no	—
143	C₃×#41	—	3	2	no	—
144	C₃×#41	—	3	2	no	—
145	C₃×#41	—	6	1	no	—
146	C₃×#41	—	6	1	no	—
147	C₂×C₃×Q₈	—	3	1	no	—
148	C₂×C₃×D₄	—	3	1	no	—
149	C₂×C₃×D₄	—	6	1	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	6	1	no	—
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×#67	—	2	1	no	—
158	#235	—	2	1	no	—
159	#235	—	2	1	no	—
160	#235	C₂×C₃×C₄	1	2	yes	—
161	#235	C₂×C₃×C₄	1	2	yes	—
162	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
163	C₂×C₄×D₃	—	2	1	no	—
164	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
165	C₃×M₁₆	—	3	2	no	—
166	C₃×M₁₆	—	3	2	no	—
167	C₃×M₁₆	—	6	1	no	—
168	C₃×M₁₆	—	6	1	no	—
169	C₃×M₁₆	—	6	4	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	6	1	no	—
182	C₂×C₃×C₈	—	6	1	no	—
183	C₂×C₃×C₈	—	6	4	no	—
184	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
185	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
186	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
187	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
188	C₂×C₃×C₈	#67	1	2	yes	—
189	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
190	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
191	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
192	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
193	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
194	C₃×C₄⋊C₄	—	3	2	no	—
195	C₃×C₂²⋊C₄	—	6	1	no	—
196	C₃×C₄²	—	2	2	no	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	2	no	—
200	C₃×C₄²	—	6	1	no	—
201	C₃×C₄²	C₄×D₃	1	2	yes	—
202	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
203	#217	—	2	1	no	—
204	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
205	C₄×Dic₃	—	2	1	no	—
206	#208	—	2	1	no	—
207	#208	—	2	1	no	—
208	#208	C₂×C₃×C₄	1	2	yes	—
209	#208	C₂×C₃×C₄	1	2	yes	—
210	C₂×C₃⋊C₈	—	2	1	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	ΓL(1,𝔽₂₅)	—	2	4	no	—
213	D₃×C₈	—	2	4	no	—
214	C₂²×C₃²	—	2	2	no	—
215	C₂²×C₃²	#117	1	1	yes	characteristic
216	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
217	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
218	C₂×C₃×D₃	—	2	2	no	—
219	C₂×C₃×D₃	—	4	2	no	—
220	C₃²×C₄	—	2	4	no	—
221	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
222	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
224	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
225	C₃×Dic₃	—	2	2	no	—
226	C₃×Dic₃	—	4	2	no	—
227	C₂×#41	—	3	1	no	—
228	#131	—	3	4	no	—
229	#131	—	6	2	no	—
230	C₂×M₁₆	—	3	1	no	—
231	C₂×M₁₆	—	3	1	no	—
232	C₂×M₁₆	—	6	1	no	—
233	C₂²×C₈	—	6	1	no	—
234	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
236	#117	—	3	1	no	—
237	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
238	#104	—	3	4	no	—
239	#103	—	3	2	no	—
240	#102	—	3	2	no	—
241	#97	—	6	1	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	—	6	1	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	6	1	no	—
246	C₂³×C₃	#235	1	1	yes	characteristic
247	C₂³×C₃	C₃×#41	1	1	yes	characteristic
248	C₂²×D₃	—	2	1	no	—
249	C₃×Q₈	—	3	2	no	—
250	C₃×Q₈	—	6	1	no	—
251	C₃×D₄	—	3	2	no	—
252	C₃×D₄	—	6	2	no	—
253	C₃×D₄	—	6	2	no	—
254	C₃×D₄	—	6	1	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	6	1	no	—
268	C₂×C₃×C₄	—	6	2	no	—
269	C₂×C₃×C₄	—	6	2	no	—
270	C₂×C₃×C₄	—	6	2	no	—
271	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
275	C₂×C₃×C₄	#235	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
283	#67	—	2	2	no	—
284	#67	—	2	2	no	—
285	C₂×Dic₃	—	2	1	no	—
286	C₂×Dic₃	—	2	2	no	—
287	D₁₂	—	2	1	no	—
288	D₁₂	C₃×C₄²	1	2	yes	—
289	C₄×D₃	—	2	2	no	—
290	C₄×D₃	—	2	2	no	—
291	Dic₆	—	2	1	no	—
292	Dic₆	C₃×C₄²	1	2	yes	—
293	C₃×C₈	—	2	4	no	—
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	2	no	—
298	C₃×C₈	—	6	2	no	—
299	C₃×C₈	—	6	2	no	—
300	C₃×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
301	C₃×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
302	C₃×C₈	C₃×C₂²⋊C₄	1	2	yes	—
303	C₃×C₈	C₃×C₂²⋊C₄	1	2	yes	—
304	C₃⋊C₈	—	2	2	no	—
305	C₃⋊C₈	—	2	2	no	—
306	C₂×C₃²	—	2	1	no	—
307	C₂×C₃²	—	2	1	no	—
308	C₂×C₃²	C₄×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₃²	#443	1	2	yes	—
310	C₃×D₃	—	4	2	no	—
311	#41	—	3	2	no	—
312	#41	—	3	2	no	—
313	#41	—	6	1	no	—
314	#41	—	6	1	no	—
315	C₂×Q₈	—	3	1	no	—
316	C₂×D₄	—	3	1	no	—
317	C₂×D₄	—	6	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	6	1	no	—
320	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
321	M₁₆	—	3	2	no	—
322	M₁₆	—	3	2	no	—
323	M₁₆	—	6	1	no	—
324	M₁₆	—	6	1	no	—
325	M₁₆	—	6	4	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	6	1	no	—
329	C₂×C₈	—	6	1	no	—
330	C₂×C₈	—	6	4	no	—
331	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
332	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
333	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
334	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
335	C₂×C₈	C₃×#67	1	2	yes	—
336	C₄⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	6	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	6	1	no	—
340	C₄²	C₃×C₄×D₃	1	2	yes	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	6	2	no	—
348	C₂²×C₃	—	12	2	no	—
349	C₂²×C₃	#872	1	1	yes	characteristic
350	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
351	C₂²×C₃	C₄×#67	1	1	yes	characteristic
352	C₂²×C₃	C₃×#117	1	1	yes	characteristic
353	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
354	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	4	2	no	—
357	C₃×C₄	—	2	8	no	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	6	2	no	—
365	C₃×C₄	—	12	2	no	—
366	C₃×C₄	C₄²×D₃	1	1	yes	characteristic
367	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
368	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
369	C₃×C₄	C₄×#67	1	1	yes	characteristic
370	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
371	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
372	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
373	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
374	Dic₃	—	2	2	no	—
375	Dic₃	—	4	2	no	—
376	C₃²	#1764	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	6	1	no	—
378	C₂³	C₃×#235	1	1	yes	characteristic
379	Q₈	—	3	2	no	—
380	Q₈	—	6	1	no	—
381	D₄	—	3	2	no	—
382	D₄	—	6	2	no	—
383	D₄	—	6	2	no	—
384	D₄	—	6	1	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	6	1	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
393	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
395	C₂×C₄	C₃×#235	1	1	yes	characteristic
396	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	6	2	no	—
399	C₈	—	6	2	no	—
400	C₈	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
401	C₈	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	2	1	no	—
406	C₂×C₃	—	2	1	no	—
407	C₂×C₃	—	2	1	no	—
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	2	2	no	—
410	C₂×C₃	—	12	2	no	—
411	C₂×C₃	#4700	1	2	yes	—
412	C₂×C₃	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
413	C₂×C₃	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
414	C₂×C₃	C₃×#443	1	2	yes	—
415	D₃	—	4	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	6	2	no	—
418	C₂²	—	12	2	no	—
419	C₂²	C₃×#872	1	1	yes	characteristic
420	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
421	C₂²	C₃×C₄×#67	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	6	2	no	—
424	C₄	—	12	2	no	—
425	C₄	C₃×C₄²×D₃	1	1	yes	characteristic
426	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
427	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
428	C₄	C₃×C₄×#67	1	1	yes	characteristic
429	C₃	—	2	1	no	—
430	C₃	#69789	1	1	yes	characteristic, direct product factor
431	C₃	C₃×#1764	1	1	yes	characteristic, complemented
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	12	2	no	—
435	C₂	C₃×#4700	1	2	yes	—
436	C₂	C₃×C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	D₁₂
commutator	C₃×C₄	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#1764
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄×C₈	C₂	semidirect
4. C₃×#5101	C₂	semidirect
6. C₃×#4552	C₂	semidirect
7. C₃×#4523	C₂	semidirect
9. #69789	C₃	direct (N × H)
18. C₃×#901	C₄	semidirect
22. C₃×#821	C₄	semidirect
23. C₃×#816	C₄	semidirect
26. C₃×#805	C₄	semidirect
33. C₂×C₃×C₄×C₈	D₃	semidirect
34. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
36. #5101	C₂×C₃	semidirect
40. #4552	C₂×C₃	semidirect
41. #4523	C₂×C₃	semidirect
95. #901	C₃×C₄	semidirect
106. #821	C₃×C₄	semidirect
107. #816	C₃×C₄	semidirect
110. #805	C₃×C₄	semidirect
140. C₂×C₄×C₈	C₃×D₃	semidirect
376. C₃²	#1764	semidirect
430. C₃	#69789	direct (N × H)
431. C₃	C₃×#1764	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₂×C₃²×C₄×C₈	2
C₃×#5113	2
C₃×#5101	2
C₂×C₃×#805	2
C₃×#4552	2
C₃×#4523	2
C₃×#1764	3
#69789	3

Subgroups — C3×#69789 #11784069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69789 #11784069