Subgroups — C₉×#3069 #11767790

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 429 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
2	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#473	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×#101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3069	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×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₉×#137	—	2	2	no	—
15	C₉×#137	—	2	1	no	—
16	C₉×#137	—	2	2	no	—
17	C₉×#137	—	2	2	no	—
18	C₉×#137	C₂²	1	4	yes	—
19	C₉×#137	C₂²	1	2	yes	—
20	C₉×AGL(1,ℤ/8)	—	2	1	no	—
21	C₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₉×#135	—	2	2	no	—
23	C₂×C₉×Q₁₆	—	2	1	no	—
24	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
25	C₂×C₉×SD₁₆	—	2	1	no	—
26	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
27	C₉×#131	—	2	2	no	—
28	C₉×#131	C₂²	1	4	yes	—
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	4	yes	complemented
36	C₉×#101	C₂²	1	2	yes	complemented
37	C₉×#100	C₂²	1	2	yes	complemented
38	C₃×#575	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
41	C₃×#568	C₂×C₃	1	1	yes	characteristic
42	C₃×#473	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×#101	C₂×C₃	1	1	yes	characteristic
47	C₉×#41	—	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	D₄	1	2	yes	—
54	C₉×#41	C₂³	1	2	yes	—
55	C₂×Q₈×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	—	2	1	no	—
57	C₂×Q₈×C₉	—	2	1	no	—
58	C₂×Q₈×C₉	—	2	1	no	—
59	C₂×Q₈×C₉	—	2	1	no	—
60	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
61	C₂×Q₈×C₉	C₂³	1	2	yes	—
62	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₉	—	2	1	no	—
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	4	no	—
72	C₉×Q₁₆	—	2	2	no	—
73	C₉×Q₁₆	—	2	4	no	—
74	C₉×SD₁₆	—	2	2	no	—
75	C₉×SD₁₆	—	2	4	no	—
76	C₉×SD₁₆	—	2	2	no	—
77	C₉×SD₁₆	—	2	4	no	—
78	C₉×D₈	—	2	2	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	#3069	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×Q₈	C₂²×C₃	1	1	yes	characteristic
97	C₃×#137	—	2	2	no	—
98	C₃×#137	—	2	1	no	—
99	C₃×#137	—	2	2	no	—
100	C₃×#137	—	2	2	no	—
101	C₃×#137	C₂²×C₃	1	4	yes	—
102	C₃×#137	C₂²×C₃	1	2	yes	—
103	C₃×AGL(1,ℤ/8)	—	2	1	no	—
104	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
105	C₃×#135	—	2	2	no	—
106	C₂×C₃×Q₁₆	—	2	1	no	—
107	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₃×SD₁₆	—	2	1	no	—
109	C₂×C₃×SD₁₆	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	4	yes	—
119	C₃×#101	C₂²×C₃	1	2	yes	—
120	C₃×#100	C₂²×C₃	1	2	yes	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	#41	1	1	yes	characteristic
124	Q₈×C₉	—	2	1	no	—
125	Q₈×C₉	—	2	2	no	—
126	Q₈×C₉	—	2	2	no	—
127	Q₈×C₉	—	2	1	no	—
128	Q₈×C₉	—	2	1	no	—
129	Q₈×C₉	—	4	1	no	—
130	Q₈×C₉	—	4	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	1	no	—
137	D₄×C₉	—	4	1	no	—
138	D₄×C₉	—	4	1	no	—
139	D₄×C₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	4	1	no	—
146	C₂×C₄×C₉	—	4	1	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	4	1	no	—
149	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
155	C₈×C₉	—	2	2	no	—
156	C₈×C₉	—	2	2	no	—
157	C₈×C₉	—	2	2	no	—
158	C₈×C₉	C₂×D₄	1	4	yes	—
159	#575	C₂×C₉	1	1	yes	characteristic
160	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
161	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
162	#568	C₂×C₉	1	1	yes	characteristic, complemented
163	#473	C₂×C₉	1	4	yes	complemented
164	#471	C₂×C₉	1	4	yes	complemented
165	#430	C₂×C₉	1	1	yes	characteristic, complemented
166	#413	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂×#101	C₂×C₉	1	1	yes	characteristic, complemented
168	C₃×#41	—	2	1	no	—
169	C₃×#41	—	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	C₃×D₄	1	2	yes	—
175	C₃×#41	C₂³×C₃	1	2	yes	—
176	C₂×C₃×Q₈	—	2	1	no	—
177	C₂×C₃×Q₈	—	2	1	no	—
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
182	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
183	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
187	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₃×Q₁₆	—	2	4	no	—
193	C₃×Q₁₆	—	2	2	no	—
194	C₃×Q₁₆	—	2	4	no	—
195	C₃×SD₁₆	—	2	2	no	—
196	C₃×SD₁₆	—	2	4	no	—
197	C₃×SD₁₆	—	2	2	no	—
198	C₃×SD₁₆	—	2	4	no	—
199	C₃×D₈	—	2	2	no	—
200	C₃×M₁₆	—	2	1	no	—
201	C₃×M₁₆	—	2	1	no	—
202	C₃×M₁₆	—	2	1	no	—
203	C₃×M₁₆	—	2	4	no	—
204	C₃×M₁₆	C₃×D₄	1	2	yes	—
205	C₃×M₁₆	C₃×D₄	1	2	yes	—
206	C₃×M₁₆	C₂³×C₃	1	2	yes	—
207	C₃×M₁₆	C₂³×C₃	1	2	yes	—
208	C₃×M₁₆	C₂³×C₃	1	2	yes	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	4	no	—
213	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
214	C₂²×C₉	—	2	2	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	8	1	no	—
218	C₂²×C₉	—	8	1	no	—
219	C₂²×C₉	#121	1	1	yes	characteristic
220	C₂²×C₉	#121	1	1	yes	characteristic
221	C₂²×C₉	C₂×#41	1	1	yes	characteristic
222	C₄×C₉	—	2	2	no	—
223	C₄×C₉	—	4	1	no	—
224	C₄×C₉	—	4	2	no	—
225	C₄×C₉	#121	1	1	yes	characteristic
226	C₄×C₉	#121	1	1	yes	characteristic
227	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
228	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×#41	C₂²×C₉	1	1	yes	characteristic
230	C₂×#41	C₂²×C₉	1	1	yes	characteristic
231	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
232	#137	—	2	2	no	—
233	#137	—	2	1	no	—
234	#137	—	2	2	no	—
235	#137	—	2	2	no	—
236	#137	C₂²×C₉	1	4	yes	—
237	#137	C₂²×C₉	1	2	yes	—
238	AGL(1,ℤ/8)	—	2	1	no	—
239	AGL(1,ℤ/8)	C₂²×C₉	1	2	yes	—
240	#135	—	2	2	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
245	#131	—	2	2	no	—
246	#131	C₂²×C₉	1	4	yes	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
249	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
250	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
251	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
252	#108	C₂²×C₉	1	4	yes	complemented
253	#101	C₂²×C₉	1	4	yes	complemented
254	#101	C₂²×C₉	1	2	yes	complemented
255	#100	C₂²×C₉	1	2	yes	complemented
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	C₃×#41	1	1	yes	characteristic
259	C₃×Q₈	—	2	1	no	—
260	C₃×Q₈	—	2	2	no	—
261	C₃×Q₈	—	2	2	no	—
262	C₃×Q₈	—	2	1	no	—
263	C₃×Q₈	—	2	1	no	—
264	C₃×Q₈	—	4	1	no	—
265	C₃×Q₈	—	4	1	no	—
266	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	2	1	no	—
270	C₃×D₄	—	2	1	no	—
271	C₃×D₄	—	2	1	no	—
272	C₃×D₄	—	4	1	no	—
273	C₃×D₄	—	4	1	no	—
274	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
294	C₂×C₉	—	2	1	no	—
295	C₂×C₉	—	2	1	no	—
296	C₂×C₉	—	2	1	no	—
297	C₂×C₉	—	4	2	no	—
298	C₂×C₉	—	8	1	no	—
299	C₂×C₉	C₂×#121	1	1	yes	characteristic
300	#41	—	2	1	no	—
301	#41	—	2	1	no	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	2	1	no	—
305	#41	—	2	1	no	—
306	#41	D₄×C₉	1	2	yes	—
307	#41	C₂³×C₉	1	2	yes	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
314	C₂×Q₈	C₂³×C₉	1	2	yes	—
315	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	D₄×C₉	1	1	yes	characteristic
319	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
324	Q₁₆	—	2	4	no	—
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	2	4	no	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	2	4	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	2	1	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	2	1	no	—
335	M₁₆	—	2	4	no	—
336	M₁₆	D₄×C₉	1	2	yes	—
337	M₁₆	D₄×C₉	1	2	yes	—
338	M₁₆	C₂³×C₉	1	2	yes	—
339	M₁₆	C₂³×C₉	1	2	yes	—
340	M₁₆	C₂³×C₉	1	2	yes	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	C₂³×C₉	1	2	yes	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	8	1	no	—
350	C₂²×C₃	—	8	1	no	—
351	C₂²×C₃	C₃×#121	1	1	yes	characteristic
352	C₂²×C₃	C₃×#121	1	1	yes	characteristic
353	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	4	1	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	C₃×#121	1	1	yes	characteristic
358	C₃×C₄	C₃×#121	1	1	yes	characteristic
359	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
360	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₉	#3069	1	1	yes	characteristic, direct product factor, Sylow
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	C₉×#41	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	1	no	—
372	Q₈	C₂×D₄×C₉	1	2	yes	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	1	no	—
376	D₄	—	2	1	no	—
377	D₄	—	2	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	C₂×D₄×C₉	1	2	yes	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
394	C₂×C₄	C₉×#41	1	1	yes	characteristic
395	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	C₂×D₄×C₉	1	4	yes	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	4	2	no	—
404	C₂×C₃	—	8	1	no	—
405	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
406	C₂²	—	2	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	C₉×#121	1	1	yes	characteristic
412	C₂²	C₉×#121	1	1	yes	characteristic
413	C₂²	C₂×C₉×#41	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	2	no	—
417	C₄	C₉×#121	1	1	yes	characteristic
418	C₄	C₉×#121	1	1	yes	characteristic
419	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
420	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
421	C₃	C₃×#3069	1	1	yes	characteristic
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	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×#575	C₂×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
2. C₂×C₉×#137	C₂	semidirect
3. C₂×C₉×#137	C₂	semidirect
4. C₉×#568	C₂	semidirect
5. C₉×#473	C₂	semidirect
6. C₉×#471	C₂	semidirect
7. C₉×#430	C₂	semidirect
8. C₉×#413	C₂	semidirect
9. C₂×C₉×#101	C₂	semidirect
24. C₂×C₉×Q₁₆	C₂²	semidirect
26. C₂×C₉×SD₁₆	C₂²	semidirect
34. C₉×#108	C₂²	semidirect
35. C₉×#101	C₂²	semidirect
36. C₉×#101	C₂²	semidirect
37. C₉×#100	C₂²	semidirect
93. #3069	C₉	direct (N × H)
160. C₂×#137	C₂×C₉	semidirect
161. C₂×#137	C₂×C₉	semidirect
162. #568	C₂×C₉	semidirect
163. #473	C₂×C₉	semidirect
164. #471	C₂×C₉	semidirect
165. #430	C₂×C₉	semidirect
166. #413	C₂×C₉	semidirect
167. C₂×#101	C₂×C₉	semidirect
242. C₂×Q₁₆	C₂²×C₉	semidirect
244. C₂×SD₁₆	C₂²×C₉	semidirect
252. #108	C₂²×C₉	semidirect
253. #101	C₂²×C₉	semidirect
254. #101	C₂²×C₉	semidirect
255. #100	C₂²×C₉	semidirect
361. C₉	#3069	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×#137	2
C₉×#568	2
C₉×#473	2
C₉×#471	2
C₉×#430	2
C₉×#413	2
C₂×C₉×#101	2
C₃×#3069	3

Subgroups — C9×#3069 #11767790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3069 #11767790