Subgroups — D₃×(C₂×D₃)⋊C₁₆ #11795960

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10589373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×(C₂×D₃)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#10589108	C₂	1	1	yes	maximal, characteristic, complemented
7	(C₂×D₃)⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×(C₂×D₃)⋊C₁₆	—	3	1	no	maximal
9	D₃×C₂²⋊C₁₆	—	3	1	no	maximal
10	C₂×C₄×D₃²	C₄	1	1	yes	characteristic
11	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
14	C₂×#3710	C₄	1	1	yes	characteristic
15	C₂×D₃×C₃⋊C₈	C₄	1	1	yes	characteristic
16	C₂×D₃×C₃⋊C₈	C₄	1	1	yes	characteristic
17	D₃²×C₈	—	2	2	no	—
18	D₃²×C₈	—	2	2	no	—
19	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×D₃×C₁₆	—	2	2	no	—
24	D₃×C₃⋊C₁₆	—	2	2	no	—
25	C₂²×D₃×C₈	—	3	1	no	—
26	C₂²×D₃×C₈	—	3	1	no	—
27	C₂²×C₃×C₁₆	—	3	1	no	—
28	C₂²×C₃⋊C₁₆	—	3	1	no	—
29	C₂×D₃×C₁₆	—	3	1	no	—
30	C₂×D₃×C₁₆	D₃	1	1	yes	characteristic, complemented
31	C₃×C₂²⋊C₁₆	—	3	1	no	—
32	#4549	—	3	1	no	—
33	(C₂×D₃)⋊C₁₆	—	3	1	no	—
34	(C₂×D₃)⋊C₁₆	—	3	1	no	—
35	(C₂×D₃)⋊C₁₆	—	3	1	no	—
36	(C₂×D₃)⋊C₁₆	—	3	1	no	—
37	(C₂×D₃)⋊C₁₆	—	3	1	no	—
38	(C₂×D₃)⋊C₁₆	—	6	1	no	—
39	(C₂×D₃)⋊C₁₆	D₃	1	1	yes	characteristic, direct product factor
40	C₂²×D₃²	C₈	1	1	yes	characteristic
41	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#624	C₈	1	1	yes	characteristic
45	C₂×D₃×Dic₃	C₈	1	1	yes	characteristic
46	C₂×D₃×Dic₃	C₈	1	1	yes	characteristic
47	C₄×D₃²	—	2	2	no	—
48	C₄×D₃²	—	2	2	no	—
49	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
51	C₈×C₃⋊D₃	—	2	1	no	—
52	C₈×C₃⋊D₃	—	2	1	no	—
53	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₃×D₃×C₈	—	2	1	no	—
56	C₃×D₃×C₈	—	2	1	no	—
57	C₃×D₃×C₈	D₄	1	2	yes	—
58	C₃×D₃×C₈	D₄	1	2	yes	—
59	#3710	—	2	2	no	—
60	D₃×C₃⋊C₈	—	2	2	no	—
61	D₃×C₃⋊C₈	—	2	2	no	—
62	C₃²×C₁₆	—	2	1	no	—
63	C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
64	C₃×C₃⋊C₁₆	—	2	1	no	—
65	C₃×C₃⋊C₁₆	—	2	1	no	—
66	C₂×C₂²⋊C₁₆	—	9	1	no	Sylow
67	C₂²×C₄×D₃	—	3	1	no	—
68	C₂²×C₄×D₃	—	3	1	no	—
69	C₂²×C₃×C₈	—	3	1	no	—
70	C₂²×C₃×C₈	—	3	1	no	—
71	C₂²×C₃⋊C₈	—	3	1	no	—
72	C₂²×C₃⋊C₈	—	3	1	no	—
73	C₂×D₃×C₈	—	3	1	no	—
74	C₂×D₃×C₈	—	3	1	no	—
75	C₂×D₃×C₈	—	3	1	no	—
76	C₂×D₃×C₈	—	3	1	no	—
77	C₂×D₃×C₈	—	3	1	no	—
78	C₂×D₃×C₈	—	3	1	no	—
79	C₂×D₃×C₈	—	6	1	no	—
80	C₂×D₃×C₈	—	6	2	no	—
81	C₂×D₃×C₈	—	6	2	no	—
82	C₂×D₃×C₈	—	6	2	no	—
83	C₂×D₃×C₈	—	6	2	no	—
84	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
86	C₂×C₃×C₁₆	—	2	1	no	—
87	C₂×C₃×C₁₆	—	3	1	no	—
88	C₂×C₃×C₁₆	—	3	1	no	—
89	C₂×C₃×C₁₆	—	6	2	no	—
90	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
91	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
92	C₂×C₃⋊C₁₆	—	3	1	no	—
93	C₂×C₃⋊C₁₆	—	3	1	no	—
94	C₂×C₃⋊C₁₆	—	6	1	no	—
95	C₂×C₃⋊C₁₆	—	6	2	no	—
96	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
97	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
98	D₃×C₁₆	—	2	2	no	—
99	D₃×C₁₆	—	6	2	no	—
100	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
101	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
103	C₂×D₃²	—	2	2	no	—
104	C₂×D₃²	—	2	2	no	—
105	C₂×D₃²	C₁₆	1	4	yes	complemented
106	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃⋊Dic₃	C₂×C₈	1	1	yes	characteristic
108	C₄×C₃⋊D₃	—	2	1	no	—
109	C₄×C₃⋊D₃	—	2	1	no	—
110	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
111	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
112	C₃×C₄×D₃	—	2	1	no	—
113	C₃×C₄×D₃	—	2	1	no	—
114	C₃×C₄×D₃	C₂²⋊C₄	1	2	yes	—
115	C₃×C₄×D₃	M₁₆	1	2	yes	—
116	#624	—	2	2	no	—
117	D₃×Dic₃	—	2	2	no	—
118	D₃×Dic₃	—	2	2	no	—
119	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
121	C₃⋊(C₃⋊C₈)	—	2	1	no	—
122	C₃×C₃⋊C₈	—	2	1	no	—
123	C₃×C₃⋊C₈	C₂²⋊C₄	1	2	yes	—
124	C₂³×C₈	—	9	1	no	—
125	C₂²×C₁₆	—	3	1	no	—
126	C₂²×C₁₆	—	9	1	no	—
127	C₂²⋊C₁₆	—	3	1	no	—
128	C₂²⋊C₁₆	—	9	1	no	—
129	C₂²⋊C₁₆	—	9	1	no	—
130	C₂²⋊C₁₆	—	9	1	no	—
131	C₂³×D₃	—	3	1	no	—
132	C₂³×D₃	—	3	1	no	—
133	C₂²×C₃×C₄	—	3	1	no	—
134	C₂²×C₃×C₄	—	3	1	no	—
135	C₂²×Dic₃	—	3	1	no	—
136	C₂²×Dic₃	—	3	1	no	—
137	C₂×C₄×D₃	—	3	1	no	—
138	C₂×C₄×D₃	—	3	1	no	—
139	C₂×C₄×D₃	—	3	1	no	—
140	C₂×C₄×D₃	—	3	1	no	—
141	C₂×C₄×D₃	—	3	1	no	—
142	C₂×C₄×D₃	—	3	1	no	—
143	C₂×C₄×D₃	—	6	1	no	—
144	C₂×C₄×D₃	—	6	2	no	—
145	C₂×C₄×D₃	—	6	2	no	—
146	C₂×C₄×D₃	—	6	2	no	—
147	C₂×C₄×D₃	—	6	2	no	—
148	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
149	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
150	C₂×C₃×C₈	—	2	1	no	—
151	C₂×C₃×C₈	—	3	1	no	—
152	C₂×C₃×C₈	—	3	2	no	—
153	C₂×C₃×C₈	—	3	2	no	—
154	C₂×C₃×C₈	—	3	1	no	—
155	C₂×C₃×C₈	—	6	1	no	—
156	C₂×C₃×C₈	—	6	1	no	—
157	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₃⋊C₈	—	3	1	no	—
160	C₂×C₃⋊C₈	—	3	1	no	—
161	C₂×C₃⋊C₈	—	6	1	no	—
162	C₂×C₃⋊C₈	—	6	2	no	—
163	C₂×C₃⋊C₈	—	6	2	no	—
164	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
165	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
166	D₃×C₈	—	2	1	no	—
167	D₃×C₈	—	2	1	no	—
168	D₃×C₈	—	6	2	no	—
169	D₃×C₈	—	6	2	no	—
170	D₃×C₈	—	6	2	no	—
171	D₃×C₈	—	6	1	no	—
172	D₃×C₈	—	6	1	no	—
173	D₃×C₈	—	6	1	no	—
174	D₃×C₈	—	6	1	no	—
175	D₃×C₈	—	6	2	no	—
176	D₃×C₈	—	12	1	no	—
177	D₃×C₈	—	12	1	no	—
178	D₃×C₈	D₁₂	1	2	yes	—
179	D₃×C₈	#67	1	2	yes	—
180	C₃×C₁₆	—	2	1	no	—
181	C₃×C₁₆	—	2	1	no	—
182	C₃×C₁₆	—	4	1	no	—
183	C₃×C₁₆	—	6	1	no	—
184	C₃×C₁₆	—	6	1	no	—
185	C₃⋊C₁₆	—	2	1	no	—
186	C₃⋊C₁₆	—	2	1	no	—
187	C₃⋊C₁₆	—	6	1	no	—
188	C₃⋊C₁₆	—	6	1	no	—
189	C₃⋊C₁₆	—	12	1	no	—
190	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₃⋊D₃	—	2	1	no	—
192	C₂×C₃⋊D₃	—	2	1	no	—
193	C₂×C₃⋊D₃	C₂×C₁₆	1	2	yes	complemented
194	C₂×C₃×D₃	—	2	1	no	—
195	C₂×C₃×D₃	—	2	1	no	—
196	C₂×C₃×D₃	C₂²⋊C₈	1	2	yes	—
197	C₂×C₃×D₃	C₂×C₁₆	1	2	yes	—
198	C₂×C₃×D₃	C₂×C₁₆	1	2	yes	complemented
199	C₂×C₃×D₃	M₃₂	1	2	yes	—
200	D₃²	—	2	8	no	—
201	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
203	C₃⋊Dic₃	—	2	1	no	—
204	C₃×Dic₃	—	2	1	no	—
205	C₃×Dic₃	C₂²⋊C₈	1	2	yes	—
206	C₂³×C₄	—	9	1	no	—
207	C₂²×C₈	—	3	1	no	—
208	C₂²×C₈	—	3	1	no	—
209	C₂²×C₈	—	9	1	no	—
210	C₂²×C₈	—	9	1	no	—
211	C₂²×C₈	—	9	1	no	—
212	C₂²×C₈	—	9	1	no	—
213	C₂²×C₈	—	18	2	no	—
214	C₂²×C₈	—	18	2	no	—
215	C₂×C₁₆	—	3	1	no	—
216	C₂×C₁₆	—	3	1	no	—
217	C₂×C₁₆	—	6	2	no	—
218	C₂×C₁₆	—	9	1	no	—
219	C₂×C₁₆	—	18	2	no	—
220	C₂×C₁₆	D₃²	1	1	yes	characteristic, complemented
221	C₂³×C₃	—	3	1	no	—
222	C₂³×C₃	—	3	1	no	—
223	C₂²×D₃	—	3	1	no	—
224	C₂²×D₃	—	3	1	no	—
225	C₂²×D₃	—	3	4	no	—
226	C₂²×D₃	—	3	4	no	—
227	C₂²×D₃	—	6	1	no	—
228	C₂²×D₃	—	6	2	no	—
229	C₂²×D₃	—	6	2	no	—
230	C₂²×D₃	—	6	2	no	—
231	C₂²×D₃	—	6	2	no	—
232	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
233	C₂²×D₃	D₃×C₈	1	1	yes	characteristic
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	3	1	no	—
236	C₂×C₃×C₄	—	3	2	no	—
237	C₂×C₃×C₄	—	3	2	no	—
238	C₂×C₃×C₄	—	3	1	no	—
239	C₂×C₃×C₄	—	6	1	no	—
240	C₂×C₃×C₄	—	6	1	no	—
241	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×Dic₃	—	3	1	no	—
244	C₂×Dic₃	—	3	1	no	—
245	C₂×Dic₃	—	6	1	no	—
246	C₂×Dic₃	—	6	2	no	—
247	C₂×Dic₃	—	6	2	no	—
248	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
249	C₂×Dic₃	D₃×C₈	1	1	yes	characteristic
250	C₄×D₃	—	2	1	no	—
251	C₄×D₃	—	2	1	no	—
252	C₄×D₃	—	6	2	no	—
253	C₄×D₃	—	6	2	no	—
254	C₄×D₃	—	6	2	no	—
255	C₄×D₃	—	6	1	no	—
256	C₄×D₃	—	6	1	no	—
257	C₄×D₃	—	6	1	no	—
258	C₄×D₃	—	6	1	no	—
259	C₄×D₃	—	6	2	no	—
260	C₄×D₃	—	12	1	no	—
261	C₄×D₃	—	12	1	no	—
262	C₄×D₃	ΓL(1,𝔽₂₅)	1	2	yes	—
263	C₄×D₃	(C₂×D₃)⋊C₄	1	2	yes	—
264	C₃×C₈	—	2	1	no	—
265	C₃×C₈	—	2	1	no	—
266	C₃×C₈	—	3	2	no	—
267	C₃×C₈	—	6	1	no	—
268	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
269	C₃×C₈	D₃×D₄	1	1	yes	characteristic
270	C₃×C₈	D₃×D₄	1	1	yes	characteristic
271	C₃×C₈	C₂×#67	1	1	yes	characteristic
272	C₃⋊C₈	—	2	1	no	—
273	C₃⋊C₈	—	6	1	no	—
274	C₃⋊C₈	—	6	1	no	—
275	C₃⋊C₈	—	12	1	no	—
276	C₃⋊C₈	(C₂×D₃)⋊C₄	1	2	yes	—
277	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
278	C₂×C₃²	C₂²×C₁₆	1	1	yes	characteristic
279	C₂×C₃²	C₂×M₃₂	1	1	yes	characteristic
280	C₃⋊D₃	—	2	2	no	—
281	C₃×D₃	—	2	2	no	—
282	C₃×D₃	C₂²⋊C₁₆	1	4	yes	complemented
283	C₂⁴	—	9	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	9	1	no	—
287	C₂²×C₄	—	9	1	no	—
288	C₂²×C₄	—	9	1	no	—
289	C₂²×C₄	—	9	1	no	—
290	C₂²×C₄	—	18	2	no	—
291	C₂²×C₄	—	18	2	no	—
292	C₂×C₈	—	3	1	no	—
293	C₂×C₈	—	3	2	no	—
294	C₂×C₈	—	3	2	no	—
295	C₂×C₈	—	3	1	no	—
296	C₂×C₈	—	6	1	no	—
297	C₂×C₈	—	6	1	no	—
298	C₂×C₈	—	9	1	no	—
299	C₂×C₈	—	18	2	no	—
300	C₂×C₈	—	18	2	no	—
301	C₂×C₈	—	18	2	no	—
302	C₂×C₈	—	18	1	no	—
303	C₂×C₈	—	18	1	no	—
304	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
305	C₁₆	—	2	1	no	—
306	C₁₆	—	6	1	no	—
307	C₁₆	—	6	1	no	—
308	C₁₆	—	18	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	3	2	no	—
311	C₂²×C₃	—	3	2	no	—
312	C₂²×C₃	—	3	2	no	—
313	C₂²×C₃	—	3	2	no	—
314	C₂²×C₃	—	6	1	no	—
315	C₂²×C₃	—	6	1	no	—
316	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
317	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
318	C₂×D₃	—	2	1	no	—
319	C₂×D₃	—	2	1	no	—
320	C₂×D₃	—	3	2	no	—
321	C₂×D₃	—	3	2	no	—
322	C₂×D₃	—	6	2	no	—
323	C₂×D₃	—	6	8	no	—
324	C₂×D₃	—	6	1	no	—
325	C₂×D₃	—	6	1	no	—
326	C₂×D₃	—	6	1	no	—
327	C₂×D₃	—	6	1	no	—
328	C₂×D₃	—	6	8	no	—
329	C₂×D₃	—	12	1	no	—
330	C₂×D₃	—	12	1	no	—
331	C₂×D₃	D₃×C₁₆	1	2	yes	—
332	C₂×D₃	D₃×C₁₆	1	2	yes	complemented
333	C₂×D₃	#798	1	2	yes	—
334	C₂×D₃	(C₂×D₃)⋊C₈	1	2	yes	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	3	2	no	—
338	C₃×C₄	—	6	1	no	—
339	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
340	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
341	C₃×C₄	D₃×M₁₆	1	1	yes	characteristic
342	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	Dic₃	—	2	1	no	—
344	Dic₃	—	6	1	no	—
345	Dic₃	—	6	1	no	—
346	Dic₃	—	12	1	no	—
347	Dic₃	(C₂×D₃)⋊C₈	1	2	yes	—
348	C₃²	C₂×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	3	1	no	—
350	C₂³	—	3	1	no	—
351	C₂³	—	9	4	no	—
352	C₂³	—	9	1	no	—
353	C₂³	—	18	2	no	—
354	C₂³	—	18	2	no	—
355	C₂×C₄	—	3	1	no	—
356	C₂×C₄	—	3	2	no	—
357	C₂×C₄	—	3	2	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	—	6	1	no	—
361	C₂×C₄	—	9	1	no	—
362	C₂×C₄	—	18	2	no	—
363	C₂×C₄	—	18	2	no	—
364	C₂×C₄	—	18	2	no	—
365	C₂×C₄	—	18	1	no	—
366	C₂×C₄	—	18	1	no	—
367	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
368	C₈	—	3	2	no	—
369	C₈	—	6	1	no	—
370	C₈	—	18	1	no	—
371	C₈	D₃×D₁₂	1	1	yes	characteristic
372	C₈	D₃×#67	1	1	yes	characteristic
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	3	4	no	—
377	C₂×C₃	—	6	2	no	—
378	C₂×C₃	D₃×C₂²⋊C₈	1	1	yes	characteristic
379	C₂×C₃	C₂×D₃×C₁₆	1	1	yes	characteristic
380	C₂×C₃	C₂×D₃×C₁₆	1	1	yes	characteristic
381	C₂×C₃	C₂×#798	1	1	yes	characteristic
382	C₂×C₃	D₃×M₃₂	1	1	yes	characteristic
383	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
384	D₃	—	2	2	no	—
385	D₃	—	6	2	no	—
386	D₃	—	6	2	no	—
387	D₃	—	12	2	no	—
388	D₃	(C₂×D₃)⋊C₁₆	1	4	yes	direct product factor
389	C₂²	—	3	2	no	—
390	C₂²	—	3	2	no	—
391	C₂²	—	3	2	no	—
392	C₂²	—	3	2	no	—
393	C₂²	—	6	1	no	—
394	C₂²	—	6	1	no	—
395	C₂²	—	9	2	no	—
396	C₂²	—	18	8	no	—
397	C₂²	—	18	1	no	—
398	C₂²	—	18	1	no	—
399	C₂²	D₃²×C₈	1	1	yes	characteristic
400	C₄	—	3	2	no	—
401	C₄	—	6	1	no	—
402	C₄	—	18	1	no	—
403	C₄	D₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
404	C₄	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
405	C₃	—	2	1	no	—
406	C₃	D₃×C₂²⋊C₁₆	1	1	yes	characteristic, complemented
407	C₃	C₂×(C₂×D₃)⋊C₁₆	1	1	yes	characteristic, complemented
408	C₂	—	3	4	no	—
409	C₂	—	6	2	no	—
410	C₂	—	18	2	no	—
411	C₂	D₃²×C₁₆	1	1	yes	characteristic
412	C₂	D₃×#798	1	1	yes	characteristic
413	C₂	D₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂²×C₁₆
Fitting	C₂×C₃²×C₁₆	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂²×D₃²	C₈
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂×C₁₆	D₃²
hypocenter	C₃²	C₂×C₂²⋊C₁₆
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×D₃×C₁₆	C₂	semidirect
3. C₂×D₃×C₃⋊C₁₆	C₂	semidirect
4. #10589373	C₂	semidirect
5. C₃×(C₂×D₃)⋊C₁₆	C₂	semidirect
6. #10589108	C₂	semidirect
7. (C₂×D₃)⋊(C₃⋊C₁₆)	C₂	semidirect
19. C₂×C₃²×C₁₆	C₂²	semidirect
20. C₂×C₃⋊(C₃⋊C₁₆)	C₂²	semidirect
21. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
22. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
30. C₂×D₃×C₁₆	D₃	semidirect
39. (C₂×D₃)⋊C₁₆	D₃	direct (N × H)
90. C₂×C₃×C₁₆	C₂×D₃	semidirect
91. C₂×C₃×C₁₆	C₂×D₃	semidirect
96. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
97. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
105. C₂×D₃²	C₁₆	semidirect
193. C₂×C₃⋊D₃	C₂×C₁₆	semidirect
198. C₂×C₃×D₃	C₂×C₁₆	semidirect
220. C₂×C₁₆	D₃²	semidirect
282. C₃×D₃	C₂²⋊C₁₆	semidirect
332. C₂×D₃	D₃×C₁₆	semidirect
348. C₃²	C₂×C₂²⋊C₁₆	semidirect
388. D₃	(C₂×D₃)⋊C₁₆	direct (N × H)
406. C₃	D₃×C₂²⋊C₁₆	semidirect
407. C₃	C₂×(C₂×D₃)⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃²×C₈	2
C₂×C₃×D₃×C₁₆	2
C₂×D₃×C₃⋊C₁₆	2
#10589373	2
C₃×(C₂×D₃)⋊C₁₆	2
#10589108	2
(C₂×D₃)⋊(C₃⋊C₁₆)	2
C₂×(C₂×D₃)⋊C₁₆	3
D₃×C₂²⋊C₁₆	3

Subgroups — D3×(C2×D3)⋊C16 #11795960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×(C₂×D₃)⋊C₁₆ #11795960