Subgroups — C₉×#3041 #11767762

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#463	C₂	1	4	yes	maximal, complemented
6	C₉×#459	C₂	1	4	yes	maximal, complemented
7	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3041	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	C₂²	1	1	yes	characteristic
12	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₉×AGL(1,ℤ/8)	—	2	4	no	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₉×D₈	—	2	4	no	—
17	C₂×C₉×D₈	C₂²	1	4	yes	—
18	C₂×C₉×D₈	C₂²	1	2	yes	complemented
19	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
21	C₉×#127	C₂²	1	2	yes	complemented
22	C₉×#124	C₂²	1	2	yes	complemented
23	C₉×#121	—	2	2	no	—
24	C₉×#120	—	2	2	no	—
25	C₄×D₄×C₉	—	2	2	no	—
26	C₄×D₄×C₉	C₂²	1	4	yes	complemented
27	C₉×#117	C₂²	1	1	yes	characteristic
28	C₉×#117	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
30	C₉×C₄⋊C₈	C₂²	1	4	yes	complemented
31	C₉×#103	C₂²	1	2	yes	complemented
32	C₉×#102	C₂²	1	2	yes	complemented
33	C₉×#102	C₂²	1	4	yes	complemented
34	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
35	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
36	C₃×#535	C₂×C₃	1	1	yes	characteristic
37	C₃×#518	C₂×C₃	1	1	yes	characteristic
38	C₃×#463	C₂×C₃	1	4	yes	—
39	C₃×#459	C₂×C₃	1	4	yes	—
40	C₃×#424	C₂×C₃	1	1	yes	characteristic
41	C₃×#418	C₂×C₃	1	1	yes	characteristic
42	C₃×#416	C₂×C₃	1	1	yes	characteristic
43	C₂⁴×C₉	—	2	1	no	—
44	C₂⁴×C₉	—	2	1	no	—
45	C₉×#41	—	2	2	no	—
46	C₉×#41	—	2	2	no	—
47	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	—	2	1	no	—
50	C₂×D₄×C₉	—	2	2	no	—
51	C₂×D₄×C₉	—	2	1	no	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	D₄	1	4	yes	complemented
56	C₂×D₄×C₉	C₂³	1	2	yes	—
57	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	—	2	1	no	—
60	C₂²×C₄×C₉	—	2	4	no	—
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₉×SD₁₆	—	2	4	no	—
63	C₉×D₈	—	2	8	no	—
64	C₉×D₈	—	2	4	no	—
65	C₉×M₁₆	—	2	2	no	—
66	C₂×C₈×C₉	—	2	2	no	—
67	C₂×C₈×C₉	C₂³	1	2	yes	—
68	C₂×C₈×C₉	C₂³	1	2	yes	—
69	C₉×C₄⋊C₄	D₄	1	2	yes	—
70	C₉×C₄⋊C₄	C₂³	1	2	yes	—
71	C₉×C₂²⋊C₄	—	2	1	no	—
72	C₉×C₂²⋊C₄	—	2	4	no	—
73	C₉×C₂²⋊C₄	—	2	4	no	—
74	C₉×C₂²⋊C₄	D₄	1	2	yes	—
75	C₄²×C₉	—	2	1	no	—
76	C₄²×C₉	C₂³	1	2	yes	—
77	#3041	C₉	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₃×AGL(1,ℤ/8)	—	2	4	no	—
82	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
83	C₂×C₃×D₈	—	2	4	no	—
84	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
85	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
86	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
88	C₃×#127	C₂²×C₃	1	2	yes	—
89	C₃×#124	C₂²×C₃	1	2	yes	—
90	C₃×#121	—	2	2	no	—
91	C₃×#120	—	2	2	no	—
92	C₃×C₄×D₄	—	2	2	no	—
93	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
94	C₃×#117	C₂²×C₃	1	1	yes	characteristic
95	C₃×#117	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
98	C₃×#103	C₂²×C₃	1	2	yes	—
99	C₃×#102	C₂²×C₃	1	2	yes	—
100	C₃×#102	C₂²×C₃	1	4	yes	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	2	4	no	—
103	C₂³×C₉	—	2	2	no	—
104	C₂³×C₉	—	2	1	no	—
105	C₂³×C₉	—	4	2	no	—
106	C₂³×C₉	—	8	2	no	—
107	C₂³×C₉	—	8	2	no	—
108	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
109	Q₈×C₉	—	2	1	no	—
110	Q₈×C₉	—	2	1	no	—
111	D₄×C₉	—	2	4	no	—
112	D₄×C₉	—	2	2	no	—
113	D₄×C₉	—	2	1	no	—
114	D₄×C₉	—	2	2	no	—
115	D₄×C₉	—	2	2	no	—
116	D₄×C₉	—	2	1	no	—
117	D₄×C₉	—	4	2	no	—
118	D₄×C₉	—	4	2	no	—
119	D₄×C₉	—	8	4	no	—
120	D₄×C₉	C₂×D₄	1	4	yes	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	4	2	no	—
124	C₂×C₄×C₉	—	8	4	no	—
125	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
126	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
128	C₂×C₄×C₉	#41	1	2	yes	—
129	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
130	C₈×C₉	—	2	2	no	—
131	C₈×C₉	—	2	2	no	—
132	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
133	C₂²×D₈	C₂×C₉	1	1	yes	characteristic, complemented
134	#535	C₂×C₉	1	1	yes	characteristic, complemented
135	#518	C₂×C₉	1	1	yes	characteristic, complemented
136	#463	C₂×C₉	1	4	yes	complemented
137	#459	C₂×C₉	1	4	yes	complemented
138	#424	C₂×C₉	1	1	yes	characteristic, complemented
139	#418	C₂×C₉	1	1	yes	characteristic, complemented
140	#416	C₂×C₉	1	1	yes	characteristic, complemented
141	C₂⁴×C₃	—	2	1	no	—
142	C₂⁴×C₃	—	2	1	no	—
143	C₃×#41	—	2	2	no	—
144	C₃×#41	—	2	2	no	—
145	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₃×D₄	—	2	1	no	—
147	C₂×C₃×D₄	—	2	1	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	—	2	1	no	—
150	C₂×C₃×D₄	—	2	4	no	—
151	C₂×C₃×D₄	—	2	2	no	—
152	C₂×C₃×D₄	—	2	2	no	—
153	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
154	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
155	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
157	C₂²×C₃×C₄	—	2	1	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₃×SD₁₆	—	2	4	no	—
161	C₃×D₈	—	2	8	no	—
162	C₃×D₈	—	2	4	no	—
163	C₃×M₁₆	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
166	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
167	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
168	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
169	C₃×C₂²⋊C₄	—	2	1	no	—
170	C₃×C₂²⋊C₄	—	2	4	no	—
171	C₃×C₂²⋊C₄	—	2	4	no	—
172	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
173	C₃×C₄²	—	2	1	no	—
174	C₃×C₄²	C₂³×C₃	1	2	yes	—
175	C₂²×C₉	—	2	2	no	—
176	C₂²×C₉	—	2	4	no	—
177	C₂²×C₉	—	4	4	no	—
178	C₂²×C₉	—	4	1	no	—
179	C₂²×C₉	—	4	2	no	—
180	C₂²×C₉	—	4	2	no	—
181	C₂²×C₉	—	4	4	no	—
182	C₂²×C₉	—	8	4	no	—
183	C₂²×C₉	—	8	4	no	—
184	C₂²×C₉	#121	1	2	yes	—
185	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
186	C₄×C₉	—	2	4	no	—
187	C₄×C₉	—	4	1	no	—
188	C₄×C₉	—	4	2	no	—
189	C₄×C₉	#121	1	2	yes	—
190	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₉	C₂×#41	1	1	yes	characteristic
192	C₂×#41	C₂²×C₉	1	1	yes	characteristic
193	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
194	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
195	AGL(1,ℤ/8)	—	2	4	no	—
196	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
197	C₂×D₈	—	2	4	no	—
198	C₂×D₈	C₂²×C₉	1	4	yes	—
199	C₂×D₈	C₂²×C₉	1	2	yes	complemented
200	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
201	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
202	#127	C₂²×C₉	1	2	yes	complemented
203	#124	C₂²×C₉	1	2	yes	complemented
204	#121	—	2	2	no	—
205	#120	—	2	2	no	—
206	C₄×D₄	—	2	2	no	—
207	C₄×D₄	C₂²×C₉	1	4	yes	complemented
208	#117	C₂²×C₉	1	1	yes	characteristic
209	#117	C₂²×C₉	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	—	2	2	no	—
211	C₄⋊C₈	C₂²×C₉	1	4	yes	complemented
212	#103	C₂²×C₉	1	2	yes	complemented
213	#102	C₂²×C₉	1	2	yes	complemented
214	#102	C₂²×C₉	1	4	yes	complemented
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	4	2	no	—
220	C₂³×C₃	—	8	2	no	—
221	C₂³×C₃	—	8	2	no	—
222	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
223	C₃×Q₈	—	2	1	no	—
224	C₃×Q₈	—	2	1	no	—
225	C₃×D₄	—	2	4	no	—
226	C₃×D₄	—	2	2	no	—
227	C₃×D₄	—	2	1	no	—
228	C₃×D₄	—	2	2	no	—
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	2	1	no	—
231	C₃×D₄	—	4	2	no	—
232	C₃×D₄	—	4	2	no	—
233	C₃×D₄	—	8	4	no	—
234	C₃×D₄	C₂×C₃×D₄	1	4	yes	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	8	4	no	—
239	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
240	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₃×#41	1	2	yes	—
243	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
244	C₃×C₈	—	2	2	no	—
245	C₃×C₈	—	2	2	no	—
246	C₂×C₉	—	2	2	no	—
247	C₂×C₉	—	4	4	no	—
248	C₂×C₉	—	8	1	no	—
249	C₂×C₉	—	8	2	no	—
250	C₂×C₉	C₂×#121	1	1	yes	characteristic
251	C₂×C₉	#576	1	2	yes	—
252	C₂⁴	—	2	1	no	—
253	C₂⁴	—	2	1	no	—
254	#41	—	2	2	no	—
255	#41	—	2	2	no	—
256	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	D₄×C₉	1	4	yes	complemented
265	C₂×D₄	C₂³×C₉	1	2	yes	—
266	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
267	C₂×D₄	C₂³×C₉	1	2	yes	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
271	SD₁₆	—	2	4	no	—
272	D₈	—	2	8	no	—
273	D₈	—	2	4	no	—
274	M₁₆	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	C₂³×C₉	1	2	yes	—
277	C₂×C₈	C₂³×C₉	1	2	yes	—
278	C₄⋊C₄	D₄×C₉	1	2	yes	—
279	C₄⋊C₄	C₂³×C₉	1	2	yes	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	4	no	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₂²⋊C₄	D₄×C₉	1	2	yes	—
284	C₄²	—	2	1	no	—
285	C₄²	C₂³×C₉	1	2	yes	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	4	4	no	—
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	—	4	4	no	—
291	C₂²×C₃	—	4	1	no	—
292	C₂²×C₃	—	4	2	no	—
293	C₂²×C₃	—	8	4	no	—
294	C₂²×C₃	—	8	4	no	—
295	C₂²×C₃	C₃×#121	1	2	yes	—
296	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	4	2	no	—
299	C₃×C₄	—	4	1	no	—
300	C₃×C₄	C₃×#121	1	2	yes	—
301	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
302	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
303	C₉	#3041	1	1	yes	characteristic, direct product factor, Sylow
304	C₂³	—	2	2	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	—	8	2	no	—
311	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
312	Q₈	—	2	1	no	—
313	Q₈	—	2	1	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	D₄	—	2	1	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	1	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	8	4	no	—
323	D₄	C₂×D₄×C₉	1	4	yes	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
329	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
331	C₂×C₄	C₉×#41	1	2	yes	—
332	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
333	C₈	—	2	2	no	—
334	C₈	—	2	2	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	—	4	4	no	—
337	C₂×C₃	—	8	2	no	—
338	C₂×C₃	—	8	1	no	—
339	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
340	C₂×C₃	C₃×#576	1	2	yes	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	8	4	no	—
349	C₂²	—	8	4	no	—
350	C₂²	C₉×#121	1	2	yes	—
351	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	2	no	—
355	C₄	C₉×#121	1	2	yes	—
356	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
357	C₄	C₂×C₉×#41	1	1	yes	characteristic
358	C₃	C₃×#3041	1	1	yes	characteristic
359	C₂	—	2	2	no	—
360	C₂	—	4	4	no	—
361	C₂	—	8	2	no	—
362	C₂	—	8	1	no	—
363	C₂	C₂×C₉×#121	1	1	yes	characteristic
364	C₂	C₉×#576	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3041	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₉×D₈	C₂	semidirect
3. C₉×#535	C₂	semidirect
4. C₉×#518	C₂	semidirect
5. C₉×#463	C₂	semidirect
6. C₉×#459	C₂	semidirect
7. C₉×#424	C₂	semidirect
8. C₉×#418	C₂	semidirect
9. C₉×#416	C₂	semidirect
15. C₂×C₉×SD₁₆	C₂²	semidirect
18. C₂×C₉×D₈	C₂²	semidirect
21. C₉×#127	C₂²	semidirect
22. C₉×#124	C₂²	semidirect
26. C₄×D₄×C₉	C₂²	semidirect
30. C₉×C₄⋊C₈	C₂²	semidirect
31. C₉×#103	C₂²	semidirect
32. C₉×#102	C₂²	semidirect
33. C₉×#102	C₂²	semidirect
55. C₂×D₄×C₉	D₄	semidirect
77. #3041	C₉	direct (N × H)
132. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
133. C₂²×D₈	C₂×C₉	semidirect
134. #535	C₂×C₉	semidirect
135. #518	C₂×C₉	semidirect
136. #463	C₂×C₉	semidirect
137. #459	C₂×C₉	semidirect
138. #424	C₂×C₉	semidirect
139. #418	C₂×C₉	semidirect
140. #416	C₂×C₉	semidirect
196. C₂×SD₁₆	C₂²×C₉	semidirect
199. C₂×D₈	C₂²×C₉	semidirect
202. #127	C₂²×C₉	semidirect
203. #124	C₂²×C₉	semidirect
207. C₄×D₄	C₂²×C₉	semidirect
211. C₄⋊C₈	C₂²×C₉	semidirect
212. #103	C₂²×C₉	semidirect
213. #102	C₂²×C₉	semidirect
214. #102	C₂²×C₉	semidirect
264. C₂×D₄	D₄×C₉	semidirect
303. C₉	#3041	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×AGL(1,ℤ/8)	2
C₂²×C₉×D₈	2
C₉×#535	2
C₉×#518	2
C₉×#463	2
C₉×#459	2
C₉×#424	2
C₉×#418	2
C₉×#416	2
C₃×#3041	3

Subgroups — C9×#3041 #11767762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3041 #11767762