Subgroups — D₃×#435 #79477

Order 384.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	#5127	C₂	1	1	yes	maximal, characteristic, complemented
6	#5111	C₂	1	1	yes	maximal, characteristic, complemented
7	#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	#4836	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#4730	C₂	1	1	yes	maximal, characteristic, complemented
11	#4728	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#4706	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#435	—	3	1	no	maximal, Sylow
17	C₂×D₃×D₄	C₄	1	1	yes	characteristic
18	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
23	D₄×Dic₃	C₄	1	1	yes	characteristic
24	C₄×#67	C₂²	1	1	yes	characteristic
25	C₄×#67	C₂²	1	1	yes	characteristic
26	C₂×#208	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	D₃×M₁₆	—	2	4	no	—
29	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
30	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×C₈	—	2	4	no	—
32	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
33	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
34	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
38	#893	C₄	1	1	yes	characteristic
39	D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
40	#67⋊C₄	C₄	1	1	yes	characteristic
41	#67⋊C₄	C₄	1	1	yes	characteristic
42	D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
43	D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
44	C₄×D₁₂	C₂²	1	1	yes	characteristic
45	C₄²×D₃	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×#97	C₂²	1	1	yes	characteristic, complemented
50	#830	C₂²	1	1	yes	characteristic, complemented
51	#830	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	#815	C₂²	1	1	yes	characteristic, complemented
57	#815	C₂²	1	1	yes	characteristic, complemented
58	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	#803	C₂²	1	1	yes	characteristic, complemented
62	C₂²×M₁₆	—	3	1	no	—
63	C₂³×C₈	—	3	1	no	—
64	C₂×C₄×D₄	—	3	1	no	—
65	#435	—	3	1	no	—
66	#435	—	3	1	no	—
67	#435	—	3	1	no	—
68	#435	—	3	1	no	—
69	#435	—	3	1	no	—
70	#435	—	3	1	no	—
71	#435	—	3	1	no	—
72	#435	D₃	1	1	yes	characteristic, direct product factor
73	C₂×C₄⋊C₈	—	3	1	no	—
74	C₂×C₂²⋊C₈	—	3	1	no	—
75	C₂×C₂²⋊C₈	—	3	1	no	—
76	C₂×#97	—	3	1	no	—
77	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×D₄	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
82	C₂×#67	C₂×C₄	1	1	yes	characteristic
83	C₂×#67	C₂×C₄	1	1	yes	characteristic
84	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
86	D₃×D₄	—	2	4	no	—
87	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×D₃	—	2	2	no	—
89	C₂×C₄×D₃	—	2	2	no	—
90	C₂×C₄×D₃	—	2	2	no	—
91	C₂×C₄×D₃	—	2	2	no	—
92	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
101	C₃×M₁₆	—	2	2	no	—
102	C₂×C₃×C₈	—	2	2	no	—
103	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
107	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×C₄²	C₂³	1	1	yes	characteristic
111	#217	C₂×C₄	1	1	yes	characteristic
112	#217	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
118	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
119	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
121	C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
122	C₄×Dic₃	C₂³	1	1	yes	characteristic
123	#208	—	2	2	no	—
124	C₂×C₃⋊C₈	—	2	2	no	—
125	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
129	ΓL(1,𝔽₂₅)	—	2	2	no	—
130	ΓL(1,𝔽₂₅)	—	2	2	no	—
131	D₃×C₈	—	2	2	no	—
132	D₃×C₈	—	2	2	no	—
133	D₃×C₈	—	2	2	no	—
134	D₃×C₈	—	2	2	no	—
135	D₃×C₈	—	2	2	no	—
136	D₃×C₈	D₄	1	4	yes	complemented
137	C₂²×D₄	—	3	1	no	—
138	C₂³×C₄	—	3	1	no	—
139	C₂³×C₄	—	3	1	no	—
140	C₂×M₁₆	—	3	1	no	—
141	C₂×M₁₆	—	3	1	no	—
142	C₂×M₁₆	—	3	1	no	—
143	C₂×M₁₆	—	6	4	no	—
144	C₂×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
145	C₂²×C₈	—	3	1	no	—
146	C₂²×C₈	—	3	1	no	—
147	C₂²×C₈	—	3	1	no	—
148	C₂²×C₈	—	3	1	no	—
149	C₂²×C₈	—	3	1	no	—
150	C₂²×C₈	—	3	1	no	—
151	C₂²×C₈	—	3	1	no	—
152	C₂²×C₈	—	6	4	no	—
153	C₂²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
154	C₄×D₄	—	3	1	no	—
155	C₄×D₄	—	3	1	no	—
156	C₄×D₄	—	3	1	no	—
157	C₄×D₄	—	3	1	no	—
158	C₄×D₄	—	3	1	no	—
159	C₄×D₄	—	3	1	no	—
160	C₄×D₄	—	3	1	no	—
161	C₄×D₄	C₂×D₃	1	1	yes	characteristic
162	C₂×C₄⋊C₄	—	3	1	no	—
163	C₂×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₄²	—	3	1	no	—
166	C₄⋊C₈	—	3	1	no	—
167	C₄⋊C₈	—	3	1	no	—
168	C₄⋊C₈	—	3	1	no	—
169	C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
170	C₂²⋊C₈	—	3	1	no	—
171	C₂²⋊C₈	—	3	1	no	—
172	C₂²⋊C₈	—	3	1	no	—
173	C₂²⋊C₈	—	3	1	no	—
174	C₂²⋊C₈	—	3	1	no	—
175	C₂²⋊C₈	—	3	1	no	—
176	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
177	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
178	#97	—	3	1	no	—
179	#97	—	3	1	no	—
180	#97	—	3	1	no	—
181	#97	C₂×D₃	1	1	yes	characteristic, complemented
182	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
183	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×D₃	—	2	2	no	—
185	C₂²×D₃	—	2	2	no	—
186	C₂²×D₃	—	2	2	no	—
187	C₂²×D₃	—	2	2	no	—
188	C₂²×D₃	—	2	2	no	—
189	C₂²×D₃	M₁₆	1	4	yes	complemented
190	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
193	C₃×D₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	1	no	—
195	C₂×C₃×C₄	—	2	1	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
203	#67	—	2	2	no	—
204	#67	—	2	2	no	—
205	C₂×Dic₃	—	2	2	no	—
206	C₂×Dic₃	—	2	2	no	—
207	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
209	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
210	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
211	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
212	D₁₂	—	2	2	no	—
213	C₄×D₃	—	2	2	no	—
214	C₄×D₃	—	2	2	no	—
215	C₄×D₃	—	2	2	no	—
216	C₄×D₃	—	2	2	no	—
217	C₄×D₃	—	2	1	no	—
218	C₄×D₃	—	2	1	no	—
219	C₄×D₃	—	2	1	no	—
220	C₄×D₃	—	2	1	no	—
221	C₄×D₃	—	2	2	no	—
222	C₄×D₃	—	2	2	no	—
223	C₄×D₃	C₂×D₄	1	2	yes	—
224	C₄×D₃	#41	1	2	yes	—
225	C₃×C₈	—	2	1	no	—
226	C₃×C₈	—	2	1	no	—
227	C₃×C₈	—	2	1	no	—
228	C₃×C₈	C₂×D₄	1	2	yes	complemented
229	C₃⋊C₈	—	2	1	no	—
230	C₃⋊C₈	—	2	1	no	—
231	C₃⋊C₈	—	2	1	no	—
232	C₃⋊C₈	C₂×D₄	1	2	yes	complemented
233	C₂⁴	—	3	1	no	—
234	C₂⁴	—	3	1	no	—
235	C₂×D₄	—	3	1	no	—
236	C₂×D₄	—	3	1	no	—
237	C₂×D₄	—	3	1	no	—
238	C₂×D₄	—	6	4	no	—
239	C₂×D₄	C₄×D₃	1	1	yes	characteristic
240	C₂²×C₄	—	3	1	no	—
241	C₂²×C₄	—	3	1	no	—
242	C₂²×C₄	—	3	1	no	—
243	C₂²×C₄	—	3	1	no	—
244	C₂²×C₄	—	3	1	no	—
245	C₂²×C₄	—	3	1	no	—
246	C₂²×C₄	—	3	1	no	—
247	C₂²×C₄	—	3	1	no	—
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	3	1	no	—
250	C₂²×C₄	—	3	1	no	—
251	C₂²×C₄	—	6	2	no	—
252	C₂²×C₄	—	6	2	no	—
253	C₂²×C₄	—	6	2	no	—
254	C₂²×C₄	—	6	2	no	—
255	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
257	M₁₆	—	2	2	no	—
258	M₁₆	—	6	2	no	—
259	M₁₆	—	6	2	no	—
260	M₁₆	—	6	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	3	1	no	—
263	C₂×C₈	—	3	4	no	—
264	C₂×C₈	—	3	1	no	—
265	C₂×C₈	—	3	1	no	—
266	C₂×C₈	—	3	1	no	—
267	C₂×C₈	—	6	2	no	—
268	C₂×C₈	—	6	2	no	—
269	C₂×C₈	—	6	2	no	—
270	C₂×C₈	—	6	2	no	—
271	C₂×C₈	—	6	2	no	—
272	C₂×C₈	—	6	2	no	—
273	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
275	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
277	C₄⋊C₄	—	3	1	no	—
278	C₄⋊C₄	—	3	1	no	—
279	C₄⋊C₄	—	3	1	no	—
280	C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
281	C₂²⋊C₄	—	3	1	no	—
282	C₂²⋊C₄	—	3	1	no	—
283	C₂²⋊C₄	—	3	1	no	—
284	C₂²⋊C₄	—	3	1	no	—
285	C₂²⋊C₄	—	3	1	no	—
286	C₂²⋊C₄	—	3	1	no	—
287	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
288	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
289	C₄²	—	3	1	no	—
290	C₄²	—	3	1	no	—
291	C₄²	—	3	1	no	—
292	C₄²	C₂²×D₃	1	1	yes	characteristic
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	C₂×M₁₆	1	2	yes	complemented
299	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
300	C₂×D₃	—	2	1	no	—
301	C₂×D₃	—	2	1	no	—
302	C₂×D₃	—	2	8	no	—
303	C₂×D₃	—	2	1	no	—
304	C₂×D₃	—	2	1	no	—
305	C₂×D₃	—	2	1	no	—
306	C₂×D₃	—	4	4	no	—
307	C₂×D₃	C₄×D₄	1	2	yes	—
308	C₂×D₃	C₂×M₁₆	1	2	yes	—
309	C₂×D₃	C₂×M₁₆	1	2	yes	complemented
310	C₂×D₃	#131	1	2	yes	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
316	C₃×C₄	C₂×#41	1	1	yes	characteristic
317	Dic₃	—	2	1	no	—
318	Dic₃	—	2	1	no	—
319	Dic₃	—	2	1	no	—
320	Dic₃	—	2	1	no	—
321	Dic₃	C₄×D₄	1	2	yes	—
322	C₂³	—	3	1	no	—
323	C₂³	—	3	4	no	—
324	C₂³	—	3	1	no	—
325	C₂³	—	3	1	no	—
326	C₂³	—	6	2	no	—
327	C₂³	—	6	2	no	—
328	C₂³	—	6	2	no	—
329	C₂³	—	6	2	no	—
330	C₂³	—	6	2	no	—
331	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
333	D₄	—	2	2	no	—
334	D₄	—	6	2	no	—
335	D₄	—	6	2	no	—
336	D₄	—	6	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	3	2	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	3	1	no	—
346	C₂×C₄	—	3	1	no	—
347	C₂×C₄	—	3	1	no	—
348	C₂×C₄	—	6	2	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	6	2	no	—
352	C₂×C₄	—	6	2	no	—
353	C₂×C₄	—	6	2	no	—
354	C₂×C₄	—	6	2	no	—
355	C₂×C₄	—	6	2	no	—
356	C₂×C₄	—	6	1	no	—
357	C₂×C₄	—	6	1	no	—
358	C₂×C₄	—	6	1	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
364	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	3	2	no	—
369	C₈	—	6	1	no	—
370	C₈	—	6	1	no	—
371	C₈	—	6	1	no	—
372	C₈	D₃×D₄	1	2	yes	complemented
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	4	1	no	—
375	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
376	C₂×C₃	C₂²×M₁₆	1	1	yes	characteristic
377	C₂×C₃	C₂×#131	1	1	yes	characteristic
378	D₃	—	2	2	no	—
379	D₃	—	4	1	no	—
380	D₃	#435	1	4	yes	direct product factor
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	3	2	no	—
387	C₂²	—	3	2	no	—
388	C₂²	—	3	2	no	—
389	C₂²	—	3	2	no	—
390	C₂²	—	6	8	no	—
391	C₂²	—	6	1	no	—
392	C₂²	—	6	1	no	—
393	C₂²	—	6	1	no	—
394	C₂²	—	6	1	no	—
395	C₂²	—	6	1	no	—
396	C₂²	—	12	4	no	—
397	C₂²	D₃×M₁₆	1	2	yes	complemented
398	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	3	2	no	—
404	C₄	—	6	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	1	no	—
407	C₄	—	6	1	no	—
408	C₄	C₂×D₃×D₄	1	1	yes	characteristic
409	C₄	D₃×#41	1	1	yes	characteristic
410	C₃	C₂×#435	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	3	4	no	—
413	C₂	—	4	1	no	—
414	C₂	—	6	2	no	—
415	C₂	—	12	1	no	—
416	C₂	C₄×D₃×D₄	1	1	yes	characteristic
417	C₂	C₂×D₃×M₁₆	1	1	yes	characteristic
418	C₂	D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#435	C₂
prime radical	C₂×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#435	D₃
hypocenter	C₃	C₂×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×M₁₆	C₂	semidirect
2. C₂²×D₃×C₈	C₂	semidirect
4. C₃×#435	C₂	semidirect
5. #5127	C₂	semidirect
6. #5111	C₂	semidirect
7. #5011	C₂	semidirect
8. #4836	C₂	semidirect
9. D₃×C₄⋊C₈	C₂	semidirect
10. #4730	C₂	semidirect
11. #4728	C₂	semidirect
12. D₃×C₂²⋊C₈	C₂	semidirect
13. D₃×C₂²⋊C₈	C₂	semidirect
14. #4706	C₂	semidirect
15. D₃×#97	C₂	semidirect
20. C₂×C₃×M₁₆	C₂²	semidirect
21. C₂²×C₃×C₈	C₂²	semidirect
26. C₂×#208	C₂²	semidirect
27. C₂²×C₃⋊C₈	C₂²	semidirect
29. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
30. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
36. C₂×D₃×C₈	C₂²	semidirect
37. C₂×D₃×C₈	C₂²	semidirect
46. C₃×C₄⋊C₈	C₂²	semidirect
47. C₃×C₂²⋊C₈	C₂²	semidirect
48. C₃×C₂²⋊C₈	C₂²	semidirect
49. C₃×#97	C₂²	semidirect
50. #830	C₂²	semidirect
51. #830	C₂²	semidirect
52. (C₂×D₃)⋊C₈	C₂²	semidirect
53. (C₂×D₃)⋊C₈	C₂²	semidirect
54. (C₂×D₃)⋊C₈	C₂²	semidirect
55. (C₂×D₃)⋊C₈	C₂²	semidirect
56. #815	C₂²	semidirect
57. #815	C₂²	semidirect
58. Dic₃⋊C₈	C₂²	semidirect
59. Dic₃⋊C₈	C₂²	semidirect
60. C₄⋊(C₃⋊C₈)	C₂²	semidirect
61. #803	C₂²	semidirect
72. #435	D₃	direct (N × H)
136. D₃×C₈	D₄	semidirect
144. C₂×M₁₆	C₂×D₃	semidirect
153. C₂²×C₈	C₂×D₃	semidirect
169. C₄⋊C₈	C₂×D₃	semidirect
176. C₂²⋊C₈	C₂×D₃	semidirect
177. C₂²⋊C₈	C₂×D₃	semidirect
181. #97	C₂×D₃	semidirect
189. C₂²×D₃	M₁₆	semidirect
228. C₃×C₈	C₂×D₄	semidirect
232. C₃⋊C₈	C₂×D₄	semidirect
298. C₂²×C₃	C₂×M₁₆	semidirect
309. C₂×D₃	C₂×M₁₆	semidirect
372. C₈	D₃×D₄	semidirect
380. D₃	#435	direct (N × H)
397. C₂²	D₃×M₁₆	semidirect
410. C₃	C₂×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×M₁₆	2
C₂²×D₃×C₈	2
C₄×D₃×D₄	2
C₃×#435	2
#5127	2
#5111	2
#5011	2
#4836	2
D₃×C₄⋊C₈	2
#4730	2
#4728	2
D₃×C₂²⋊C₈	2
#4706	2
D₃×#97	2
C₂×#435	3

Subgroups — D3×#435 #79477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#435 #79477