Subgroups — C₂×D₉×#208 #13150015

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#88532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88413	C₂	1	2	yes	maximal, complemented
5	D₉×#208	C₂	1	8	yes	maximal, direct product factor
6	C₂×D₉×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂×D₃×#208	—	3	1	no	maximal
8	C₂×M₁₆×D₉	—	3	1	no	maximal
9	C₂³×C₃×D₉	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₉	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×D₉	C₄	1	1	yes	characteristic
13	C₂×C₃×C₄×D₉	C₄	1	4	yes	—
14	C₂×C₃×C₄×D₉	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
18	#88532	C₂²	1	4	yes	complemented
19	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	2	yes	complemented
20	C₉×#208	C₂²	1	4	yes	complemented
21	C₂×C₉×C₃⋊C₈	C₂²	1	2	yes	complemented
22	#88413	C₂²	1	8	yes	complemented
23	D₉×C₃⋊C₈	C₂²	1	8	yes	complemented
24	C₂²×C₃×C₄×D₃	—	3	1	no	—
25	C₂×#3748	—	3	1	no	—
26	C₂×C₃×#208	D₃	1	1	yes	characteristic
27	C₂×#3711	—	3	2	no	—
28	D₃×#208	—	3	8	no	—
29	C₂×D₃×C₃⋊C₈	—	3	2	no	—
30	C₂²×C₄×D₉	D₃	1	1	yes	characteristic
31	C₂×C₉×M₁₆	—	3	1	no	—
32	C₂×#3667	—	3	1	no	—
33	C₂×#3667	—	6	1	no	—
34	M₁₆×D₉	—	3	8	no	—
35	C₂×#3663	—	3	2	no	—
36	C₂×C₈×D₉	—	3	2	no	—
37	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×D₉	—	2	4	no	—
39	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×D₉	C₂×C₄	1	4	yes	—
41	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
46	C₂×C₃×Dic₉	C₂×C₄	1	4	yes	—
47	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄×D₉	C₂×C₄	1	4	yes	—
50	C₃×C₄×D₉	C₂×C₄	1	2	yes	—
51	C₃×C₄×D₉	C₂×C₄	1	2	yes	—
52	C₃×C₄×D₉	C₂×C₄	1	4	yes	—
53	C₃×C₄×D₉	C₂³	1	2	yes	—
54	C₃×C₄×D₉	C₂³	1	2	yes	—
55	C₃⋊(C₉⋊C₈)	C₂³	1	4	yes	complemented
56	C₉×C₃⋊C₈	C₂³	1	4	yes	complemented
57	C₂²×#208	—	9	1	no	—
58	C₂×D₃×M₁₆	—	9	1	no	—
59	C₂³×C₃×D₃	—	3	1	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃×Dic₃	—	3	1	no	—
62	C₂×C₃×C₄×D₃	—	3	1	no	—
63	C₂×C₃×C₄×D₃	—	3	4	no	—
64	C₂×C₃×C₄×D₃	—	3	1	no	—
65	C₂×C₃×C₄×D₃	—	3	1	no	—
66	C₂×C₃×C₄×D₃	—	3	4	no	—
67	C₂×C₃×C₄×D₃	—	3	1	no	—
68	C₂³×D₉	Dic₃	1	1	yes	characteristic
69	#3748	—	3	4	no	—
70	C₂×C₃⋊(C₃⋊C₈)	—	3	2	no	—
71	C₃×#208	C₂×D₃	1	4	yes	—
72	C₂×C₃×C₃⋊C₈	C₂×D₃	1	2	yes	—
73	#3711	—	3	8	no	—
74	D₃×C₃⋊C₈	—	3	8	no	—
75	C₂²×C₄×C₉	—	2	1	no	—
76	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
77	C₂²×Dic₉	Dic₃	1	1	yes	characteristic
78	C₂×C₄×D₉	Dic₃	1	4	yes	—
79	C₂×C₄×D₉	Dic₃	1	1	yes	characteristic
80	C₂×C₄×D₉	Dic₃	1	1	yes	characteristic
81	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
82	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄×D₉	C₂×D₃	1	4	yes	—
84	C₉×M₁₆	—	3	4	no	—
85	C₂×C₈×C₉	—	3	2	no	—
86	#3667	—	3	4	no	—
87	#3667	—	6	4	no	—
88	C₂×C₉⋊C₈	—	3	2	no	—
89	C₂×C₉⋊C₈	—	6	2	no	—
90	#3663	—	3	8	no	—
91	C₈×D₉	—	3	8	no	—
92	C₂²×C₃×C₉	—	2	2	no	—
93	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×D₉	—	2	2	no	—
96	C₂×C₃×D₉	—	2	8	no	—
97	C₂×C₃×D₉	M₁₆	1	4	yes	complemented
98	C₂×C₃×D₉	C₂²×C₄	1	2	yes	—
99	C₂×C₃×D₉	C₂²×C₄	1	2	yes	—
100	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
101	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
102	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
103	C₃×Dic₉	C₂²×C₄	1	2	yes	—
104	C₃×Dic₉	C₂²×C₄	1	2	yes	—
105	C₂³×C₃×C₄	—	9	1	no	—
106	C₂²×C₄×D₃	—	3	1	no	—
107	C₂×C₃×M₁₆	—	3	1	no	—
108	C₂×#208	—	9	1	no	—
109	C₂×#208	—	9	1	no	—
110	C₂×#208	—	9	8	no	—
111	C₂×#208	—	9	2	no	—
112	C₂×#208	—	18	1	no	—
113	C₂×#208	D₉	1	1	yes	characteristic, direct product factor
114	C₂²×C₃⋊C₈	—	9	2	no	—
115	D₃×M₁₆	—	9	8	no	—
116	C₂×ΓL(1,𝔽₂₅)	—	9	2	no	—
117	C₂×D₃×C₈	—	9	2	no	—
118	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	3	1	no	—
120	C₂²×C₃×D₃	—	3	4	no	—
121	C₂²×C₃×D₃	—	3	1	no	—
122	C₂²×C₃×D₃	—	6	4	no	—
123	C₂×C₃²×C₄	C₄×D₃	1	2	yes	—
124	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
127	C₂×C₃×Dic₃	—	3	4	no	—
128	C₂×C₃×Dic₃	—	3	1	no	—
129	C₂×C₃×Dic₃	—	3	1	no	—
130	C₃×C₄×D₃	—	3	2	no	—
131	C₃×C₄×D₃	—	3	4	no	—
132	C₃×C₄×D₃	—	3	4	no	—
133	C₃×C₄×D₃	—	3	2	no	—
134	C₃×C₄×D₃	—	3	2	no	—
135	C₃×C₄×D₃	—	3	2	no	—
136	C₂³×C₉	—	2	1	no	—
137	C₂³×C₉	C₂×Dic₃	1	1	yes	characteristic
138	C₂²×D₉	—	2	4	no	—
139	C₂²×D₉	C₂×Dic₃	1	1	yes	characteristic
140	C₂²×D₉	C₂×Dic₃	1	4	yes	—
141	C₂²×D₉	C₂×Dic₃	1	1	yes	characteristic
142	C₃⋊(C₃⋊C₈)	—	3	4	no	—
143	C₃×C₃⋊C₈	C₂²×D₃	1	4	yes	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	C₂×Dic₃	1	2	yes	—
149	C₂×C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
152	C₂×Dic₉	C₂×Dic₃	1	4	yes	—
153	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
154	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
155	C₄×D₉	C₂×Dic₃	1	2	yes	—
156	C₄×D₉	C₂×Dic₃	1	4	yes	—
157	C₄×D₉	C₂×Dic₃	1	2	yes	—
158	C₄×D₉	C₂×Dic₃	1	4	yes	—
159	C₄×D₉	C₂²×D₃	1	2	yes	—
160	C₄×D₉	C₂²×D₃	1	2	yes	—
161	C₈×C₉	—	3	4	no	—
162	C₉⋊C₈	—	3	4	no	—
163	C₉⋊C₈	—	6	4	no	—
164	C₂²×M₁₆	—	27	1	no	Sylow
165	C₂×C₃×C₉	—	2	2	no	—
166	C₂×C₃×C₉	C₂×M₁₆	1	2	yes	complemented
167	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
168	C₃×D₉	—	2	2	no	—
169	C₃×D₉	C₂×M₁₆	1	4	yes	complemented
170	C₂⁴×C₃	—	9	1	no	—
171	C₂³×D₃	—	3	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	9	1	no	—
174	C₂²×C₃×C₄	—	9	1	no	—
175	C₂²×C₃×C₄	—	9	4	no	—
176	C₂²×C₃×C₄	—	9	1	no	—
177	C₂²×C₃×C₄	—	9	1	no	—
178	C₂²×C₃×C₄	—	9	4	no	—
179	C₂²×C₃×C₄	—	9	1	no	—
180	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
181	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
182	C₂²×Dic₃	—	3	1	no	—
183	C₂×C₄×D₃	—	3	1	no	—
184	C₂×C₄×D₃	—	3	4	no	—
185	C₂×C₄×D₃	—	3	1	no	—
186	C₂×C₄×D₃	—	3	1	no	—
187	C₂×C₄×D₃	—	3	1	no	—
188	C₂×C₄×D₃	—	3	4	no	—
189	C₃×M₁₆	—	3	4	no	—
190	C₂×C₃×C₈	—	3	2	no	—
191	#208	—	9	4	no	—
192	#208	—	9	4	no	—
193	#208	—	9	8	no	—
194	#208	—	18	4	no	—
195	#208	C₂×D₉	1	4	yes	direct product factor
196	C₂×C₃⋊C₈	—	9	2	no	—
197	C₂×C₃⋊C₈	—	9	2	no	—
198	C₂×C₃⋊C₈	—	9	8	no	—
199	C₂×C₃⋊C₈	—	18	2	no	—
200	C₂×C₃⋊C₈	C₂×D₉	1	2	yes	complemented
201	ΓL(1,𝔽₂₅)	—	9	8	no	—
202	D₃×C₈	—	9	8	no	—
203	C₂²×C₃²	—	2	2	no	—
204	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
205	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
206	C₂×C₃×D₃	—	3	4	no	—
207	C₂×C₃×D₃	—	3	2	no	—
208	C₂×C₃×D₃	—	3	2	no	—
209	C₂×C₃×D₃	—	6	8	no	—
210	C₂×C₃×D₃	—	6	2	no	—
211	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
212	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
213	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
214	C₃×Dic₃	—	3	2	no	—
215	C₃×Dic₃	—	3	2	no	—
216	C₂²×C₉	—	2	2	no	—
217	C₂²×C₉	—	2	1	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	—	4	2	no	—
220	C₂²×C₉	C₂²×Dic₃	1	2	yes	—
221	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
222	C₂×D₉	—	2	2	no	—
223	C₂×D₉	—	2	8	no	—
224	C₂×D₉	#208	1	4	yes	direct product factor
225	C₂×D₉	C₂²×Dic₃	1	2	yes	—
226	C₂×D₉	C₂²×Dic₃	1	2	yes	—
227	C₄×C₉	—	2	1	no	—
228	C₄×C₉	—	2	1	no	—
229	C₄×C₉	—	2	2	no	—
230	C₄×C₉	C₂²×Dic₃	1	1	yes	characteristic
231	C₄×C₉	C₂²×Dic₃	1	2	yes	—
232	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
233	Dic₉	C₂²×Dic₃	1	2	yes	—
234	Dic₉	C₂²×Dic₃	1	2	yes	—
235	C₂³×C₄	—	9	1	no	—
236	C₂×M₁₆	—	3	1	no	—
237	C₂×M₁₆	—	27	2	no	—
238	C₂×M₁₆	—	27	8	no	—
239	C₂×M₁₆	—	27	1	no	—
240	C₂²×C₈	—	27	2	no	—
241	C₃×C₉	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	—	9	1	no	—
244	C₂³×C₃	—	9	4	no	—
245	C₂³×C₃	—	9	1	no	—
246	C₂³×C₃	—	18	4	no	—
247	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
248	C₂³×C₃	D₃×Dic₃	1	1	yes	characteristic
249	C₂²×D₃	—	3	1	no	—
250	C₂²×D₃	—	3	4	no	—
251	C₂²×D₃	—	3	1	no	—
252	C₂²×D₃	—	6	4	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	9	4	no	—
258	C₂×C₃×C₄	—	9	1	no	—
259	C₂×C₃×C₄	—	9	1	no	—
260	C₂×C₃×C₄	—	9	2	no	—
261	C₂×C₃×C₄	—	9	4	no	—
262	C₂×C₃×C₄	—	9	4	no	—
263	C₂×C₃×C₄	—	9	2	no	—
264	C₂×C₃×C₄	—	9	2	no	—
265	C₂×C₃×C₄	—	9	2	no	—
266	C₂×C₃×C₄	C₄×D₉	1	2	yes	—
267	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
269	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
270	C₂×C₃×C₄	D₃×Dic₃	1	2	yes	—
271	C₂×C₃×C₄	D₃×Dic₃	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×D₃²	1	2	yes	—
273	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
274	C₂×Dic₃	—	3	4	no	—
275	C₂×Dic₃	—	3	1	no	—
276	C₂×Dic₃	—	3	1	no	—
277	C₄×D₃	—	3	2	no	—
278	C₄×D₃	—	3	2	no	—
279	C₄×D₃	—	3	2	no	—
280	C₄×D₃	—	3	4	no	—
281	C₄×D₃	—	3	2	no	—
282	C₄×D₃	—	3	4	no	—
283	C₃×C₈	—	3	4	no	—
284	C₃⋊C₈	—	9	4	no	—
285	C₃⋊C₈	—	9	4	no	—
286	C₃⋊C₈	—	18	4	no	—
287	C₃⋊C₈	C₂²×D₉	1	4	yes	complemented
288	C₂×C₃²	—	2	2	no	—
289	C₂×C₃²	D₃×M₁₆	1	2	yes	—
290	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
291	C₃×D₃	—	3	4	no	—
292	C₃×D₃	—	6	2	no	—
293	C₂×C₉	—	2	2	no	—
294	C₂×C₉	—	2	1	no	—
295	C₂×C₉	—	2	2	no	—
296	C₂×C₉	—	4	2	no	—
297	C₂×C₉	C₂×#208	1	2	yes	complemented
298	C₂×C₉	C₂³×Dic₃	1	1	yes	characteristic
299	D₉	—	2	2	no	—
300	D₉	C₂×#208	1	4	yes	direct product factor
301	C₂⁴	—	9	1	no	—
302	C₂²×C₄	—	9	1	no	—
303	C₂²×C₄	—	9	1	no	—
304	C₂²×C₄	—	9	4	no	—
305	C₂²×C₄	—	9	1	no	—
306	C₂²×C₄	—	9	4	no	—
307	C₂²×C₄	—	9	1	no	—
308	C₂²×C₄	—	9	1	no	—
309	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
310	M₁₆	—	3	4	no	—
311	M₁₆	—	27	8	no	—
312	M₁₆	—	27	4	no	—
313	C₂×C₈	—	3	2	no	—
314	C₂×C₈	—	27	8	no	—
315	C₂×C₈	—	27	2	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	9	2	no	—
322	C₂²×C₃	—	9	4	no	—
323	C₂²×C₃	—	9	2	no	—
324	C₂²×C₃	—	18	8	no	—
325	C₂²×C₃	—	18	2	no	—
326	C₂²×C₃	C₂×C₄×D₉	1	2	yes	—
327	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
328	C₂²×C₃	C₂×D₃×Dic₃	1	2	yes	—
329	C₂²×C₃	C₂×D₃×Dic₃	1	1	yes	characteristic
330	C₂×D₃	—	3	2	no	—
331	C₂×D₃	—	3	4	no	—
332	C₂×D₃	—	3	2	no	—
333	C₂×D₃	—	6	8	no	—
334	C₂×D₃	—	6	2	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	9	2	no	—
339	C₃×C₄	—	9	2	no	—
340	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
341	C₃×C₄	C₂×C₄×D₉	1	1	yes	characteristic
342	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
343	C₃×C₄	C₂×D₃×Dic₃	1	2	yes	—
344	C₃×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
345	C₃×C₄	C₂²×D₃²	1	1	yes	characteristic
346	Dic₃	—	3	2	no	—
347	Dic₃	—	3	2	no	—
348	C₃²	C₂×D₃×M₁₆	1	1	yes	characteristic
349	C₉	—	2	1	no	—
350	C₉	C₂²×#208	1	1	yes	characteristic, complemented
351	C₂³	—	9	1	no	—
352	C₂³	—	9	4	no	—
353	C₂³	—	9	1	no	—
354	C₂³	—	18	4	no	—
355	C₂³	Dic₃×D₉	1	1	yes	characteristic
356	C₂×C₄	—	9	4	no	—
357	C₂×C₄	—	9	1	no	—
358	C₂×C₄	—	9	1	no	—
359	C₂×C₄	—	9	2	no	—
360	C₂×C₄	—	9	2	no	—
361	C₂×C₄	—	9	4	no	—
362	C₂×C₄	—	9	4	no	—
363	C₂×C₄	—	9	2	no	—
364	C₂×C₄	—	9	2	no	—
365	C₂×C₄	Dic₃×D₉	1	1	yes	characteristic
366	C₂×C₄	Dic₃×D₉	1	2	yes	—
367	C₂×C₄	C₂×D₃×D₉	1	2	yes	—
368	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
369	C₈	—	3	4	no	—
370	C₈	—	27	4	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	4	2	no	—
376	C₂×C₃	—	9	4	no	—
377	C₂×C₃	—	18	2	no	—
378	C₂×C₃	M₁₆×D₉	1	2	yes	complemented
379	C₂×C₃	C₂²×C₄×D₉	1	1	yes	characteristic
380	C₂×C₃	D₃×#208	1	2	yes	—
381	C₂×C₃	C₂²×D₃×Dic₃	1	1	yes	characteristic
382	D₃	—	3	4	no	—
383	D₃	—	6	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	9	2	no	—
386	C₂²	—	9	4	no	—
387	C₂²	—	9	2	no	—
388	C₂²	—	18	8	no	—
389	C₂²	—	18	2	no	—
390	C₂²	C₂×Dic₃×D₉	1	2	yes	—
391	C₂²	C₂×Dic₃×D₉	1	1	yes	characteristic
392	C₄	—	9	2	no	—
393	C₄	—	9	2	no	—
394	C₄	C₂×Dic₃×D₉	1	2	yes	—
395	C₄	C₂×Dic₃×D₉	1	1	yes	characteristic
396	C₄	C₂²×D₃×D₉	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×M₁₆×D₉	1	1	yes	characteristic, complemented
399	C₃	C₂×D₃×#208	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	9	4	no	—
402	C₂	—	18	2	no	—
403	C₂	D₉×#208	1	2	yes	direct product factor
404	C₂	C₂²×Dic₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂×C₃×C₉	C₂³×C₄
Frattini	C₃×C₄	C₂²×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂³×C₃×D₉	C₄
cosocle	C₃×C₄×C₉	C₂⁴
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₂²×M₁₆
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#88532	C₂	semidirect
3. C₂×C₉×#208	C₂	semidirect
4. C₂×#88413	C₂	semidirect
5. D₉×#208	C₂	direct (N × H)
6. C₂×D₉×C₃⋊C₈	C₂	semidirect
18. #88532	C₂²	semidirect
19. C₂×C₃⋊(C₉⋊C₈)	C₂²	semidirect
20. C₉×#208	C₂²	semidirect
21. C₂×C₉×C₃⋊C₈	C₂²	semidirect
22. #88413	C₂²	semidirect
23. D₉×C₃⋊C₈	C₂²	semidirect
55. C₃⋊(C₉⋊C₈)	C₂³	semidirect
56. C₉×C₃⋊C₈	C₂³	semidirect
97. C₂×C₃×D₉	M₁₆	semidirect
113. C₂×#208	D₉	direct (N × H)
166. C₂×C₃×C₉	C₂×M₁₆	semidirect
169. C₃×D₉	C₂×M₁₆	semidirect
195. #208	C₂×D₉	direct (N × H)
200. C₂×C₃⋊C₈	C₂×D₉	semidirect
224. C₂×D₉	#208	direct (N × H)
241. C₃×C₉	C₂²×M₁₆	semidirect
287. C₃⋊C₈	C₂²×D₉	semidirect
297. C₂×C₉	C₂×#208	semidirect
300. D₉	C₂×#208	direct (N × H)
350. C₉	C₂²×#208	semidirect
378. C₂×C₃	M₁₆×D₉	semidirect
398. C₃	C₂×M₁₆×D₉	semidirect
403. C₂	D₉×#208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×D₉	2
C₂×#88532	2
C₂×C₉×#208	2
C₂×#88413	2
D₉×#208	2
C₂×D₉×C₃⋊C₈	2
C₂×D₃×#208	3
C₂×M₁₆×D₉	3

Subgroups — C2×D9×#208 #13150015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×#208 #13150015