Subgroups — C₉×#3068 #11767789

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#472	C₂	1	4	yes	maximal, complemented
6	C₉×#471	C₂	1	4	yes	maximal, complemented
7	C₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3068	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	C₂²	1	1	yes	characteristic
12	C₂×C₉×#41	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₉×#137	—	2	1	no	—
15	C₉×#137	C₂²	1	2	yes	complemented
16	C₉×AGL(1,ℤ/8)	—	2	2	no	—
17	C₉×AGL(1,ℤ/8)	—	2	1	no	—
18	C₉×AGL(1,ℤ/8)	—	2	2	no	—
19	C₉×AGL(1,ℤ/8)	—	2	2	no	—
20	C₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
21	C₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₉×#135	—	2	2	no	—
23	C₂×C₉×SD₁₆	—	2	1	no	—
24	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
25	C₂×C₉×D₈	—	2	1	no	—
26	C₂×C₉×D₈	C₂²	1	2	yes	complemented
27	C₉×#131	—	2	2	no	—
28	C₉×#131	C₂²	1	4	yes	complemented
29	C₂×C₉×M₁₆	—	2	2	no	—
30	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
34	C₉×#108	C₂²	1	4	yes	complemented
35	C₉×#101	C₂²	1	2	yes	complemented
36	C₉×#100	C₂²	1	4	yes	complemented
37	C₉×#100	C₂²	1	2	yes	complemented
38	C₃×#575	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
41	C₃×#568	C₂×C₃	1	1	yes	characteristic
42	C₃×#472	C₂×C₃	1	4	yes	—
43	C₃×#471	C₂×C₃	1	4	yes	—
44	C₃×#430	C₂×C₃	1	1	yes	characteristic
45	C₃×#413	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃×#100	C₂×C₃	1	1	yes	characteristic
47	C₂⁴×C₉	—	2	1	no	—
48	C₉×#41	—	2	1	no	—
49	C₉×#41	—	2	1	no	—
50	C₉×#41	—	2	1	no	—
51	C₉×#41	—	2	1	no	—
52	C₉×#41	—	2	1	no	—
53	C₉×#41	—	2	1	no	—
54	C₉×#41	D₄	1	2	yes	—
55	C₉×#41	C₂³	1	2	yes	—
56	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	—	2	1	no	—
64	C₂×D₄×C₉	—	2	1	no	—
65	C₂×D₄×C₉	D₄	1	1	yes	characteristic
66	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	—	2	1	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₉×Q₁₆	—	2	2	no	—
72	C₉×SD₁₆	—	2	4	no	—
73	C₉×SD₁₆	—	2	2	no	—
74	C₉×SD₁₆	—	2	2	no	—
75	C₉×SD₁₆	—	2	4	no	—
76	C₉×D₈	—	2	4	no	—
77	C₉×D₈	—	2	2	no	—
78	C₉×D₈	—	2	4	no	—
79	C₉×M₁₆	—	2	1	no	—
80	C₉×M₁₆	—	2	1	no	—
81	C₉×M₁₆	—	2	1	no	—
82	C₉×M₁₆	—	2	4	no	—
83	C₉×M₁₆	D₄	1	2	yes	—
84	C₉×M₁₆	D₄	1	2	yes	—
85	C₉×M₁₆	C₂³	1	2	yes	—
86	C₉×M₁₆	C₂³	1	2	yes	—
87	C₉×M₁₆	C₂³	1	2	yes	—
88	C₂×C₈×C₉	—	2	1	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	—	2	1	no	—
91	C₂×C₈×C₉	—	2	4	no	—
92	C₂×C₈×C₉	C₂³	1	2	yes	—
93	#3068	C₉	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₃×#137	—	2	1	no	—
98	C₃×#137	C₂²×C₃	1	2	yes	—
99	C₃×AGL(1,ℤ/8)	—	2	2	no	—
100	C₃×AGL(1,ℤ/8)	—	2	1	no	—
101	C₃×AGL(1,ℤ/8)	—	2	2	no	—
102	C₃×AGL(1,ℤ/8)	—	2	2	no	—
103	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	—
104	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
105	C₃×#135	—	2	2	no	—
106	C₂×C₃×SD₁₆	—	2	1	no	—
107	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₃×D₈	—	2	1	no	—
109	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
110	C₃×#131	—	2	2	no	—
111	C₃×#131	C₂²×C₃	1	4	yes	—
112	C₂×C₃×M₁₆	—	2	2	no	—
113	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
117	C₃×#108	C₂²×C₃	1	4	yes	—
118	C₃×#101	C₂²×C₃	1	2	yes	—
119	C₃×#100	C₂²×C₃	1	4	yes	—
120	C₃×#100	C₂²×C₃	1	2	yes	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	—	2	2	no	—
124	C₂³×C₉	—	4	1	no	—
125	C₂³×C₉	—	4	1	no	—
126	C₂³×C₉	—	8	2	no	—
127	C₂³×C₉	#41	1	1	yes	characteristic
128	Q₈×C₉	—	2	1	no	—
129	Q₈×C₉	—	2	1	no	—
130	Q₈×C₉	—	2	1	no	—
131	Q₈×C₉	C₂×D₄	1	2	yes	—
132	D₄×C₉	—	2	2	no	—
133	D₄×C₉	—	2	2	no	—
134	D₄×C₉	—	2	1	no	—
135	D₄×C₉	—	2	1	no	—
136	D₄×C₉	—	2	2	no	—
137	D₄×C₉	—	2	2	no	—
138	D₄×C₉	—	2	1	no	—
139	D₄×C₉	—	4	1	no	—
140	D₄×C₉	—	4	1	no	—
141	D₄×C₉	—	4	1	no	—
142	D₄×C₉	—	4	1	no	—
143	D₄×C₉	C₂×D₄	1	2	yes	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	4	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	#41	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
156	C₈×C₉	—	2	2	no	—
157	C₈×C₉	—	2	2	no	—
158	C₈×C₉	—	2	2	no	—
159	C₈×C₉	C₂×D₄	1	4	yes	—
160	#575	C₂×C₉	1	1	yes	characteristic, complemented
161	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
162	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
163	#568	C₂×C₉	1	1	yes	characteristic, complemented
164	#472	C₂×C₉	1	4	yes	complemented
165	#471	C₂×C₉	1	4	yes	complemented
166	#430	C₂×C₉	1	1	yes	characteristic, complemented
167	#413	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂×#100	C₂×C₉	1	1	yes	characteristic, complemented
169	C₂⁴×C₃	—	2	1	no	—
170	C₃×#41	—	2	1	no	—
171	C₃×#41	—	2	1	no	—
172	C₃×#41	—	2	1	no	—
173	C₃×#41	—	2	1	no	—
174	C₃×#41	—	2	1	no	—
175	C₃×#41	—	2	1	no	—
176	C₃×#41	C₃×D₄	1	2	yes	—
177	C₃×#41	C₂³×C₃	1	2	yes	—
178	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
179	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×D₄	—	2	1	no	—
181	C₂×C₃×D₄	—	2	1	no	—
182	C₂×C₃×D₄	—	2	1	no	—
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	—	2	1	no	—
187	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
188	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₃×Q₁₆	—	2	2	no	—
194	C₃×SD₁₆	—	2	4	no	—
195	C₃×SD₁₆	—	2	2	no	—
196	C₃×SD₁₆	—	2	2	no	—
197	C₃×SD₁₆	—	2	4	no	—
198	C₃×D₈	—	2	4	no	—
199	C₃×D₈	—	2	2	no	—
200	C₃×D₈	—	2	4	no	—
201	C₃×M₁₆	—	2	1	no	—
202	C₃×M₁₆	—	2	1	no	—
203	C₃×M₁₆	—	2	1	no	—
204	C₃×M₁₆	—	2	4	no	—
205	C₃×M₁₆	C₃×D₄	1	2	yes	—
206	C₃×M₁₆	C₃×D₄	1	2	yes	—
207	C₃×M₁₆	C₂³×C₃	1	2	yes	—
208	C₃×M₁₆	C₂³×C₃	1	2	yes	—
209	C₃×M₁₆	C₂³×C₃	1	2	yes	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	4	no	—
214	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
215	C₂²×C₉	—	2	2	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	4	1	no	—
218	C₂²×C₉	—	4	2	no	—
219	C₂²×C₉	—	8	1	no	—
220	C₂²×C₉	—	8	1	no	—
221	C₂²×C₉	—	8	2	no	—
222	C₂²×C₉	—	8	2	no	—
223	C₂²×C₉	—	8	2	no	—
224	C₂²×C₉	#121	1	1	yes	characteristic
225	C₂²×C₉	#121	1	1	yes	characteristic
226	C₂²×C₉	C₂×#41	1	1	yes	characteristic
227	C₄×C₉	—	2	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	#121	1	1	yes	characteristic
230	C₄×C₉	#121	1	1	yes	characteristic
231	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×#41	C₂²×C₉	1	1	yes	characteristic
234	C₂×#41	C₂²×C₉	1	1	yes	characteristic
235	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
236	#137	—	2	1	no	—
237	#137	C₂²×C₉	1	2	yes	complemented
238	AGL(1,ℤ/8)	—	2	2	no	—
239	AGL(1,ℤ/8)	—	2	1	no	—
240	AGL(1,ℤ/8)	—	2	2	no	—
241	AGL(1,ℤ/8)	—	2	2	no	—
242	AGL(1,ℤ/8)	C₂²×C₉	1	4	yes	—
243	AGL(1,ℤ/8)	C₂²×C₉	1	2	yes	complemented
244	#135	—	2	2	no	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	C₂²×C₉	1	2	yes	complemented
249	#131	—	2	2	no	—
250	#131	C₂²×C₉	1	4	yes	complemented
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
253	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
254	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
255	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
256	#108	C₂²×C₉	1	4	yes	complemented
257	#101	C₂²×C₉	1	2	yes	complemented
258	#100	C₂²×C₉	1	4	yes	complemented
259	#100	C₂²×C₉	1	2	yes	complemented
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	4	1	no	—
264	C₂³×C₃	—	4	1	no	—
265	C₂³×C₃	—	8	2	no	—
266	C₂³×C₃	C₃×#41	1	1	yes	characteristic
267	C₃×Q₈	—	2	1	no	—
268	C₃×Q₈	—	2	1	no	—
269	C₃×Q₈	—	2	1	no	—
270	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
271	C₃×D₄	—	2	2	no	—
272	C₃×D₄	—	2	2	no	—
273	C₃×D₄	—	2	1	no	—
274	C₃×D₄	—	2	1	no	—
275	C₃×D₄	—	2	2	no	—
276	C₃×D₄	—	2	2	no	—
277	C₃×D₄	—	2	1	no	—
278	C₃×D₄	—	4	1	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	4	1	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	—	4	1	no	—
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	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	2	no	—
298	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	—	2	1	no	—
302	C₂×C₉	—	4	2	no	—
303	C₂×C₉	—	8	1	no	—
304	C₂×C₉	—	8	2	no	—
305	C₂×C₉	C₂×#121	1	1	yes	characteristic
306	C₂⁴	—	2	1	no	—
307	#41	—	2	1	no	—
308	#41	—	2	1	no	—
309	#41	—	2	1	no	—
310	#41	—	2	1	no	—
311	#41	—	2	1	no	—
312	#41	—	2	1	no	—
313	#41	D₄×C₉	1	2	yes	—
314	#41	C₂³×C₉	1	2	yes	—
315	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
316	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	D₄×C₉	1	1	yes	characteristic
325	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
326	C₂×D₄	C₂³×C₉	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	SD₁₆	—	2	4	no	—
332	SD₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	4	no	—
335	D₈	—	2	4	no	—
336	D₈	—	2	2	no	—
337	D₈	—	2	4	no	—
338	M₁₆	—	2	1	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	D₄×C₉	1	2	yes	—
343	M₁₆	D₄×C₉	1	2	yes	—
344	M₁₆	C₂³×C₉	1	2	yes	—
345	M₁₆	C₂³×C₉	1	2	yes	—
346	M₁₆	C₂³×C₉	1	2	yes	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	C₂³×C₉	1	2	yes	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	—	4	1	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	8	1	no	—
357	C₂²×C₃	—	8	2	no	—
358	C₂²×C₃	—	8	1	no	—
359	C₂²×C₃	—	8	2	no	—
360	C₂²×C₃	—	8	2	no	—
361	C₂²×C₃	C₃×#121	1	1	yes	characteristic
362	C₂²×C₃	C₃×#121	1	1	yes	characteristic
363	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	4	1	no	—
366	C₃×C₄	C₃×#121	1	1	yes	characteristic
367	C₃×C₄	C₃×#121	1	1	yes	characteristic
368	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
370	C₉	#3068	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	8	2	no	—
377	C₂³	C₉×#41	1	1	yes	characteristic
378	Q₈	—	2	1	no	—
379	Q₈	—	2	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	C₂×D₄×C₉	1	2	yes	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	1	no	—
385	D₄	—	2	1	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	C₂×D₄×C₉	1	2	yes	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
402	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
404	C₂×C₄	C₉×#41	1	1	yes	characteristic
405	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	C₂×D₄×C₉	1	4	yes	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	4	2	no	—
414	C₂×C₃	—	8	2	no	—
415	C₂×C₃	—	8	1	no	—
416	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
417	C₂²	—	2	2	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₉×#121	1	1	yes	characteristic
427	C₂²	C₉×#121	1	1	yes	characteristic
428	C₂²	C₂×C₉×#41	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	C₉×#121	1	1	yes	characteristic
432	C₄	C₉×#121	1	1	yes	characteristic
433	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
434	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
435	C₃	C₃×#3068	1	1	yes	characteristic
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	4	2	no	—
440	C₂	—	8	2	no	—
441	C₂	—	8	1	no	—
442	C₂	C₂×C₉×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×#121
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂×C₃	C₂×C₃×#121
prime radical	C₃×#3068	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#575	C₂	semidirect
2. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
4. C₉×#568	C₂	semidirect
5. C₉×#472	C₂	semidirect
6. C₉×#471	C₂	semidirect
7. C₉×#430	C₂	semidirect
8. C₉×#413	C₂	semidirect
9. C₂×C₉×#100	C₂	semidirect
15. C₉×#137	C₂²	semidirect
21. C₉×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₉×SD₁₆	C₂²	semidirect
26. C₂×C₉×D₈	C₂²	semidirect
28. C₉×#131	C₂²	semidirect
34. C₉×#108	C₂²	semidirect
35. C₉×#101	C₂²	semidirect
36. C₉×#100	C₂²	semidirect
37. C₉×#100	C₂²	semidirect
93. #3068	C₉	direct (N × H)
160. #575	C₂×C₉	semidirect
161. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
162. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
163. #568	C₂×C₉	semidirect
164. #472	C₂×C₉	semidirect
165. #471	C₂×C₉	semidirect
166. #430	C₂×C₉	semidirect
167. #413	C₂×C₉	semidirect
168. C₂×#100	C₂×C₉	semidirect
237. #137	C₂²×C₉	semidirect
243. AGL(1,ℤ/8)	C₂²×C₉	semidirect
246. C₂×SD₁₆	C₂²×C₉	semidirect
248. C₂×D₈	C₂²×C₉	semidirect
250. #131	C₂²×C₉	semidirect
256. #108	C₂²×C₉	semidirect
257. #101	C₂²×C₉	semidirect
258. #100	C₂²×C₉	semidirect
259. #100	C₂²×C₉	semidirect
370. C₉	#3068	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#575	2
C₂×C₉×AGL(1,ℤ/8)	2
C₉×#568	2
C₉×#472	2
C₉×#471	2
C₉×#430	2
C₉×#413	2
C₂×C₉×#100	2
C₃×#3068	3

Subgroups — C9×#3068 #11767789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3068 #11767789