Subgroups — C₉×#3106 #11767827

Order 1152.

651 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#482	C₂	1	2	yes	maximal, complemented
4	C₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#449	C₂	1	2	yes	maximal, complemented
9	C₄×C₉×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×D₈	C₂	1	2	yes	maximal, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3106	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	—	2	1	no	—
14	C₂×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₉×D₈	C₂²	1	2	yes	—
17	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₉×#127	C₂²	1	1	yes	characteristic
19	C₉×#124	—	2	1	no	—
20	C₉×#121	—	2	1	no	—
21	C₉×#121	C₂²	1	2	yes	—
22	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
23	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₉	—	2	1	no	—
25	C₄×D₄×C₉	—	2	1	no	—
26	C₄×D₄×C₉	—	2	1	no	—
27	C₄×D₄×C₉	C₂²	1	2	yes	—
28	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
30	C₉×#117	—	2	1	no	—
31	C₉×#117	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	—	2	1	no	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#107	C₂²	1	2	yes	—
35	C₉×#106	C₂²	1	2	yes	—
36	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#532	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
46	C₃×#482	C₂×C₃	1	2	yes	—
47	C₃×#477	C₂×C₃	1	1	yes	characteristic
48	C₃×#476	C₂×C₃	1	1	yes	characteristic
49	C₃×#460	C₂×C₃	1	1	yes	characteristic
50	C₃×#459	C₂×C₃	1	1	yes	characteristic
51	C₃×#449	C₂×C₃	1	2	yes	—
52	C₃×C₄×SD₁₆	C₂×C₃	1	2	yes	—
53	C₃×C₄×D₈	C₂×C₃	1	2	yes	—
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₉×#41	—	2	2	no	—
56	C₉×#41	—	2	2	no	—
57	C₉×#41	—	4	4	no	—
58	C₂×Q₈×C₉	—	2	1	no	—
59	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	—	2	2	no	—
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	—	2	1	no	—
64	C₂×D₄×C₉	C₂³	1	2	yes	—
65	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	—	2	1	no	—
67	C₂²×C₄×C₉	—	2	1	no	—
68	C₂²×C₄×C₉	—	2	1	no	—
69	C₂²×C₄×C₉	—	2	2	no	—
70	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
71	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₉×SD₁₆	—	2	4	no	—
74	C₉×D₈	—	2	4	no	—
75	C₂×C₈×C₉	C₂³	1	2	yes	—
76	C₂×C₈×C₉	C₂³	1	2	yes	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₄⋊C₄	—	2	1	no	—
80	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₉×C₄⋊C₄	C₂³	1	2	yes	—
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	1	no	—
85	C₉×C₂²⋊C₄	—	2	1	no	—
86	C₉×C₂²⋊C₄	—	2	2	no	—
87	C₉×C₂²⋊C₄	—	2	2	no	—
88	C₄²×C₉	—	2	1	no	—
89	C₄²×C₉	—	2	1	no	—
90	C₄²×C₉	—	2	1	no	—
91	C₄²×C₉	D₄	1	1	yes	characteristic
92	C₄²×C₉	D₄	1	1	yes	characteristic
93	C₄²×C₉	C₂³	1	1	yes	characteristic
94	C₄²×C₉	C₂³	1	1	yes	characteristic
95	#3106	C₉	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×C₃×#41	—	2	1	no	—
97	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
100	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₃×#127	C₂²×C₃	1	1	yes	characteristic
102	C₃×#124	—	2	1	no	—
103	C₃×#121	—	2	1	no	—
104	C₃×#121	C₂²×C₃	1	2	yes	—
105	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄×D₄	—	2	1	no	—
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	—	2	1	no	—
110	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
111	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
112	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
113	C₃×#117	—	2	1	no	—
114	C₃×#117	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄²	—	2	1	no	—
116	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
117	C₃×#107	C₂²×C₃	1	2	yes	—
118	C₃×#106	C₂²×C₃	1	2	yes	—
119	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#102	C₂²×C₃	1	2	yes	—
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
126	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	—	2	2	no	—
129	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
130	Q₈×C₉	—	2	1	no	—
131	Q₈×C₉	—	4	2	no	—
132	Q₈×C₉	#41	1	2	yes	complemented
133	D₄×C₉	—	2	4	no	—
134	D₄×C₉	—	2	1	no	—
135	D₄×C₉	—	2	2	no	—
136	D₄×C₉	—	2	2	no	—
137	D₄×C₉	—	4	2	no	—
138	D₄×C₉	—	4	4	no	—
139	D₄×C₉	—	4	2	no	—
140	D₄×C₉	#41	1	2	yes	complemented
141	C₂×C₄×C₉	—	2	4	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	4	2	no	—
151	C₂×C₄×C₉	—	4	2	no	—
152	C₂×C₄×C₉	—	4	4	no	—
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
159	C₈×C₉	—	2	2	no	—
160	C₈×C₉	—	2	2	no	—
161	#532	C₂×C₉	1	1	yes	characteristic, complemented
162	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
163	#482	C₂×C₉	1	2	yes	complemented
164	#477	C₂×C₉	1	1	yes	characteristic, complemented
165	#476	C₂×C₉	1	1	yes	characteristic, complemented
166	#460	C₂×C₉	1	1	yes	characteristic, complemented
167	#459	C₂×C₉	1	1	yes	characteristic, complemented
168	#449	C₂×C₉	1	2	yes	complemented
169	C₄×SD₁₆	C₂×C₉	1	2	yes	complemented
170	C₄×D₈	C₂×C₉	1	2	yes	complemented
171	#431	C₂×C₉	1	1	yes	characteristic, complemented
172	C₃×#41	—	2	2	no	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	4	4	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×D₄	—	2	1	no	—
178	C₂×C₃×D₄	—	2	2	no	—
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	—	2	1	no	—
181	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₃×SD₁₆	—	2	4	no	—
191	C₃×D₈	—	2	4	no	—
192	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
193	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×C₂²⋊C₄	—	2	1	no	—
203	C₃×C₂²⋊C₄	—	2	2	no	—
204	C₃×C₂²⋊C₄	—	2	2	no	—
205	C₃×C₄²	—	2	1	no	—
206	C₃×C₄²	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
209	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
210	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
211	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	2	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	2	1	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	4	1	no	—
218	C₂²×C₉	—	4	2	no	—
219	C₂²×C₉	—	4	2	no	—
220	C₂²×C₉	—	4	2	no	—
221	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
222	C₄×C₉	—	2	1	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	2	1	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	1	no	—
228	C₄×C₉	—	4	2	no	—
229	C₄×C₉	#135	1	2	yes	—
230	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	—
231	C₄×C₉	C₂×#41	1	1	yes	characteristic
232	C₄×C₉	C₂×#41	1	1	yes	characteristic
233	C₂×#41	—	2	1	no	—
234	C₂×#41	C₂²×C₉	1	1	yes	characteristic
235	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
236	C₂×D₈	C₂²×C₉	1	2	yes	—
237	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
238	#127	C₂²×C₉	1	1	yes	characteristic
239	#124	—	2	1	no	—
240	#121	—	2	1	no	—
241	#121	C₂²×C₉	1	2	yes	—
242	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
243	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
248	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
249	C₄×D₄	C₂²×C₉	1	2	yes	—
250	#117	—	2	1	no	—
251	#117	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
254	#107	C₂²×C₉	1	2	yes	—
255	#106	C₂²×C₉	1	2	yes	—
256	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
257	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
258	#103	C₂²×C₉	1	2	yes	—
259	#102	C₂²×C₉	1	2	yes	—
260	#102	C₂²×C₉	1	2	yes	—
261	#102	C₂²×C₉	1	2	yes	—
262	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
263	C₄×C₈	C₂²×C₉	1	2	yes	—
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
267	C₃×Q₈	—	2	1	no	—
268	C₃×Q₈	—	4	2	no	—
269	C₃×Q₈	C₃×#41	1	2	yes	—
270	C₃×D₄	—	2	4	no	—
271	C₃×D₄	—	2	1	no	—
272	C₃×D₄	—	2	2	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	4	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₃×D₄	—	4	2	no	—
277	C₃×D₄	C₃×#41	1	2	yes	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	4	4	no	—
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	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	2	no	—
298	C₂×C₉	—	4	1	no	—
299	C₂×C₉	—	4	2	no	—
300	C₂×C₉	—	8	2	no	—
301	C₂×C₉	#525	1	1	yes	characteristic
302	C₂×C₉	C₂×#135	1	1	yes	characteristic
303	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	4	4	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂³×C₉	1	2	yes	—
314	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
320	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
322	SD₁₆	—	2	4	no	—
323	D₈	—	2	4	no	—
324	C₂×C₈	C₂³×C₉	1	2	yes	—
325	C₂×C₈	C₂³×C₉	1	2	yes	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂³×C₉	1	2	yes	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	D₄×C₉	1	1	yes	characteristic
341	C₄²	D₄×C₉	1	1	yes	characteristic
342	C₄²	C₂³×C₉	1	1	yes	characteristic
343	C₄²	C₂³×C₉	1	1	yes	characteristic
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	4	1	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	C₃×#135	1	2	yes	—
362	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
363	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
364	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
365	C₉	#3106	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	C₉×#41	1	2	yes	complemented
372	D₄	—	2	4	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	2	no	—
379	D₄	C₉×#41	1	2	yes	complemented
380	C₂×C₄	—	2	4	no	—
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	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₂×C₃	—	4	1	no	—
401	C₂×C₃	—	4	2	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	C₃×#525	1	1	yes	characteristic
404	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
405	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	1	no	—
423	C₄	C₉×#135	1	2	yes	—
424	C₄	C₉×AGL(1,ℤ/8)	1	2	yes	—
425	C₄	C₂×C₉×#41	1	1	yes	characteristic
426	C₄	C₂×C₉×#41	1	1	yes	characteristic
427	C₃	C₃×#3106	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	2	no	—
431	C₂	C₉×#525	1	1	yes	characteristic
432	C₂	C₂×C₉×#135	1	1	yes	characteristic
433	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3106	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#532	C₂	semidirect
2. C₄×C₉×#41	C₂	semidirect
3. C₉×#482	C₂	semidirect
4. C₉×#477	C₂	semidirect
5. C₉×#476	C₂	semidirect
6. C₉×#460	C₂	semidirect
7. C₉×#459	C₂	semidirect
8. C₉×#449	C₂	semidirect
9. C₄×C₉×SD₁₆	C₂	semidirect
10. C₄×C₉×D₈	C₂	semidirect
11. C₉×#431	C₂	semidirect
95. #3106	C₉	direct (N × H)
132. Q₈×C₉	#41	semidirect
140. D₄×C₉	#41	semidirect
161. #532	C₂×C₉	semidirect
162. C₄×#41	C₂×C₉	semidirect
163. #482	C₂×C₉	semidirect
164. #477	C₂×C₉	semidirect
165. #476	C₂×C₉	semidirect
166. #460	C₂×C₉	semidirect
167. #459	C₂×C₉	semidirect
168. #449	C₂×C₉	semidirect
169. C₄×SD₁₆	C₂×C₉	semidirect
170. C₄×D₈	C₂×C₉	semidirect
171. #431	C₂×C₉	semidirect
365. C₉	#3106	direct (N × H)
371. Q₈	C₉×#41	semidirect
379. D₄	C₉×#41	semidirect

Maximal subgroups

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

subgroup	index
C₉×#532	2
C₄×C₉×#41	2
C₉×#482	2
C₉×#477	2
C₉×#476	2
C₉×#460	2
C₉×#459	2
C₉×#449	2
C₄×C₉×SD₁₆	2
C₄×C₉×D₈	2
C₉×#431	2
C₃×#3106	3

Subgroups — C9×#3106 #11767827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3106 #11767827