Subgroups — C₉×#3100 #11767821

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 363 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	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#480	C₂	1	2	yes	maximal, complemented
4	C₉×#474	C₂	1	2	yes	maximal, complemented
5	C₉×#459	C₂	1	2	yes	maximal, complemented
6	C₉×#447	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×D₈	C₂	1	4	yes	maximal, complemented
8	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3100	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#41	—	2	1	no	—
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	—	2	1	no	—
13	C₂×C₉×D₈	C₂²	1	4	yes	—
14	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₉×#127	C₂²	1	1	yes	characteristic, complemented
16	C₉×#124	—	2	1	no	—
17	C₉×#121	—	2	1	no	—
18	C₉×#121	C₂²	1	2	yes	—
19	C₄×D₄×C₉	—	2	1	no	—
20	C₄×D₄×C₉	—	2	1	no	—
21	C₄×D₄×C₉	—	2	1	no	—
22	C₄×D₄×C₉	C₂²	1	2	yes	—
23	C₄×D₄×C₉	C₂²	1	2	yes	—
24	C₄×D₄×C₉	C₂²	1	2	yes	complemented
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₉×#107	C₂²	1	4	yes	complemented
29	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₉×#102	C₂²	1	4	yes	—
31	C₉×#102	C₂²	1	4	yes	complemented
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₄×C₈×C₉	C₂²	1	2	yes	complemented
34	C₃×#532	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
36	C₃×#480	C₂×C₃	1	2	yes	—
37	C₃×#474	C₂×C₃	1	2	yes	—
38	C₃×#459	C₂×C₃	1	2	yes	—
39	C₃×#447	C₂×C₃	1	2	yes	—
40	C₃×C₄×D₈	C₂×C₃	1	4	yes	—
41	C₃×#431	C₂×C₃	1	1	yes	characteristic
42	C₂⁴×C₉	—	2	1	no	—
43	C₉×#41	—	4	4	no	—
44	C₂×Q₈×C₉	—	2	1	no	—
45	C₂×D₄×C₉	—	2	4	no	—
46	C₂×D₄×C₉	—	2	2	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	—	2	1	no	—
50	C₂×D₄×C₉	C₂³	1	2	yes	—
51	C₂×D₄×C₉	C₂³	1	2	yes	—
52	C₂²×C₄×C₉	—	2	1	no	—
53	C₂²×C₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	4	4	no	—
57	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×D₈	—	2	8	no	—
61	C₂×C₈×C₉	C₂³	1	4	yes	—
62	C₉×C₄⋊C₄	—	2	1	no	—
63	C₉×C₄⋊C₄	—	2	1	no	—
64	C₉×C₄⋊C₄	C₂³	1	2	yes	—
65	C₉×C₄⋊C₄	C₂³	1	2	yes	—
66	C₉×C₂²⋊C₄	—	2	2	no	—
67	C₉×C₂²⋊C₄	—	2	2	no	—
68	C₉×C₂²⋊C₄	—	2	2	no	—
69	C₉×C₂²⋊C₄	—	2	2	no	—
70	C₄²×C₉	D₄	1	1	yes	characteristic
71	C₄²×C₉	D₄	1	1	yes	characteristic
72	C₄²×C₉	C₂³	1	1	yes	characteristic
73	C₄²×C₉	C₂³	1	1	yes	characteristic
74	#3100	C₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×C₃×#41	—	2	1	no	—
76	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	—	2	1	no	—
78	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
79	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₃×#127	C₂²×C₃	1	1	yes	characteristic
81	C₃×#124	—	2	1	no	—
82	C₃×#121	—	2	1	no	—
83	C₃×#121	C₂²×C₃	1	2	yes	—
84	C₃×C₄×D₄	—	2	1	no	—
85	C₃×C₄×D₄	—	2	1	no	—
86	C₃×C₄×D₄	—	2	1	no	—
87	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
88	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
89	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
93	C₃×#107	C₂²×C₃	1	4	yes	—
94	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
95	C₃×#102	C₂²×C₃	1	4	yes	—
96	C₃×#102	C₂²×C₃	1	4	yes	—
97	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
98	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
99	C₂³×C₉	—	2	4	no	—
100	C₂³×C₉	—	2	2	no	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	4	2	no	—
103	C₂³×C₉	—	4	2	no	—
104	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
105	Q₈×C₉	—	4	2	no	—
106	D₄×C₉	—	2	4	no	—
107	D₄×C₉	—	2	2	no	—
108	D₄×C₉	—	2	4	no	—
109	D₄×C₉	—	4	2	no	—
110	D₄×C₉	—	4	4	no	—
111	D₄×C₉	—	4	2	no	—
112	D₄×C₉	#41	1	4	yes	complemented
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	4	1	no	—
117	C₂×C₄×C₉	—	4	2	no	—
118	C₂×C₄×C₉	—	4	4	no	—
119	C₂×C₄×C₉	—	4	4	no	—
120	C₂×C₄×C₉	—	4	4	no	—
121	C₂×C₄×C₉	D₈	1	4	yes	complemented
122	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
128	C₈×C₉	—	2	4	no	—
129	#532	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
131	#480	C₂×C₉	1	2	yes	complemented
132	#474	C₂×C₉	1	2	yes	complemented
133	#459	C₂×C₉	1	2	yes	complemented
134	#447	C₂×C₉	1	2	yes	complemented
135	C₄×D₈	C₂×C₉	1	4	yes	complemented
136	#431	C₂×C₉	1	1	yes	characteristic, complemented
137	C₂⁴×C₃	—	2	1	no	—
138	C₃×#41	—	4	4	no	—
139	C₂×C₃×Q₈	—	2	1	no	—
140	C₂×C₃×D₄	—	2	4	no	—
141	C₂×C₃×D₄	—	2	2	no	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	1	no	—
144	C₂×C₃×D₄	—	2	1	no	—
145	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
146	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	4	4	no	—
152	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₃×D₈	—	2	8	no	—
156	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
157	C₃×C₄⋊C₄	—	2	1	no	—
158	C₃×C₄⋊C₄	—	2	1	no	—
159	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
160	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
161	C₃×C₂²⋊C₄	—	2	2	no	—
162	C₃×C₂²⋊C₄	—	2	2	no	—
163	C₃×C₂²⋊C₄	—	2	2	no	—
164	C₃×C₂²⋊C₄	—	2	2	no	—
165	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
166	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
167	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
168	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₉	—	2	1	no	—
170	C₂²×C₉	—	2	1	no	—
171	C₂²×C₉	—	2	4	no	—
172	C₂²×C₉	—	4	8	no	—
173	C₂²×C₉	—	4	2	no	—
174	C₂²×C₉	—	4	2	no	—
175	C₂²×C₉	—	4	2	no	—
176	C₂²×C₉	—	4	2	no	—
177	C₂²×C₉	—	4	2	no	—
178	C₂²×C₉	C₂×D₈	1	2	yes	—
179	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
180	C₄×C₉	—	2	1	no	—
181	C₄×C₉	—	2	1	no	—
182	C₄×C₉	—	2	1	no	—
183	C₄×C₉	—	4	2	no	—
184	C₄×C₉	—	4	2	no	—
185	C₄×C₉	C₂×D₈	1	2	yes	—
186	C₄×C₉	C₂×D₈	1	2	yes	—
187	C₄×C₉	C₂×#41	1	2	yes	—
188	C₂×#41	—	2	1	no	—
189	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
190	C₂³×C₄	—	2	1	no	—
191	C₂×D₈	C₂²×C₉	1	4	yes	—
192	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
193	#127	C₂²×C₉	1	1	yes	characteristic, complemented
194	#124	—	2	1	no	—
195	#121	—	2	1	no	—
196	#121	C₂²×C₉	1	2	yes	—
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	—	2	1	no	—
199	C₄×D₄	—	2	1	no	—
200	C₄×D₄	C₂²×C₉	1	2	yes	—
201	C₄×D₄	C₂²×C₉	1	2	yes	—
202	C₄×D₄	C₂²×C₉	1	2	yes	complemented
203	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
206	#107	C₂²×C₉	1	4	yes	complemented
207	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
208	#102	C₂²×C₉	1	4	yes	—
209	#102	C₂²×C₉	1	4	yes	complemented
210	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
211	C₄×C₈	C₂²×C₉	1	2	yes	complemented
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	4	2	no	—
216	C₂³×C₃	—	4	2	no	—
217	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
218	C₃×Q₈	—	4	2	no	—
219	C₃×D₄	—	2	4	no	—
220	C₃×D₄	—	2	2	no	—
221	C₃×D₄	—	2	4	no	—
222	C₃×D₄	—	4	2	no	—
223	C₃×D₄	—	4	4	no	—
224	C₃×D₄	—	4	2	no	—
225	C₃×D₄	C₃×#41	1	4	yes	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	—	4	4	no	—
232	C₂×C₃×C₄	—	4	4	no	—
233	C₂×C₃×C₄	—	4	4	no	—
234	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
235	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
241	C₃×C₈	—	2	4	no	—
242	C₂×C₉	—	2	2	no	—
243	C₂×C₉	—	4	4	no	—
244	C₂×C₉	—	8	2	no	—
245	C₂×C₉	#525	1	1	yes	characteristic
246	C₂×C₉	C₂²×D₈	1	1	yes	characteristic
247	C₂×C₉	#575	1	1	yes	characteristic
248	C₂⁴	—	2	1	no	—
249	#41	—	4	4	no	—
250	C₂×Q₈	—	2	1	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	C₂³×C₉	1	2	yes	—
257	C₂×D₄	C₂³×C₉	1	2	yes	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
264	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
266	D₈	—	2	8	no	—
267	C₂×C₈	C₂³×C₉	1	4	yes	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	C₂³×C₉	1	2	yes	—
271	C₄⋊C₄	C₂³×C₉	1	2	yes	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	—	2	2	no	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₄²	D₄×C₉	1	1	yes	characteristic
277	C₄²	D₄×C₉	1	1	yes	characteristic
278	C₄²	C₂³×C₉	1	1	yes	characteristic
279	C₄²	C₂³×C₉	1	1	yes	characteristic
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	4	8	no	—
284	C₂²×C₃	—	4	2	no	—
285	C₂²×C₃	—	4	2	no	—
286	C₂²×C₃	—	4	2	no	—
287	C₂²×C₃	—	4	2	no	—
288	C₂²×C₃	—	4	2	no	—
289	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
290	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	1	no	—
294	C₃×C₄	—	4	2	no	—
295	C₃×C₄	—	4	2	no	—
296	C₃×C₄	C₂×C₃×D₈	1	2	yes	—
297	C₃×C₄	C₂×C₃×D₈	1	2	yes	—
298	C₃×C₄	C₂×C₃×#41	1	2	yes	—
299	C₉	#3100	1	1	yes	characteristic, direct product factor, Sylow
300	C₂³	—	2	4	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
306	Q₈	—	4	2	no	—
307	D₄	—	2	4	no	—
308	D₄	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	2	no	—
313	D₄	C₉×#41	1	4	yes	complemented
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₉×D₈	1	4	yes	complemented
323	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
324	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
325	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
326	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
328	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₂×C₃	—	2	2	no	—
331	C₂×C₃	—	4	4	no	—
332	C₂×C₃	—	8	2	no	—
333	C₂×C₃	C₃×#525	1	1	yes	characteristic
334	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
335	C₂×C₃	C₃×#575	1	1	yes	characteristic
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	C₂×C₉×D₈	1	2	yes	—
346	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	C₂×C₉×D₈	1	2	yes	—
353	C₄	C₂×C₉×D₈	1	2	yes	—
354	C₄	C₂×C₉×#41	1	2	yes	—
355	C₃	C₃×#3100	1	1	yes	characteristic
356	C₂	—	2	2	no	—
357	C₂	—	4	4	no	—
358	C₂	—	8	2	no	—
359	C₂	C₉×#525	1	1	yes	characteristic
360	C₂	C₂²×C₉×D₈	1	1	yes	characteristic
361	C₂	C₉×#575	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×#3100	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. C₂×C₄×D₄×C₉	C₂	semidirect
3. C₉×#480	C₂	semidirect
4. C₉×#474	C₂	semidirect
5. C₉×#459	C₂	semidirect
6. C₉×#447	C₂	semidirect
7. C₄×C₉×D₈	C₂	semidirect
8. C₉×#431	C₂	semidirect
14. C₉×C₄⋊Q₈	C₂²	semidirect
15. C₉×#127	C₂²	semidirect
24. C₄×D₄×C₉	C₂²	semidirect
28. C₉×#107	C₂²	semidirect
29. C₉×C₄⋊C₈	C₂²	semidirect
31. C₉×#102	C₂²	semidirect
33. C₄×C₈×C₉	C₂²	semidirect
74. #3100	C₉	direct (N × H)
112. D₄×C₉	#41	semidirect
121. C₂×C₄×C₉	D₈	semidirect
129. #532	C₂×C₉	semidirect
130. C₂×C₄×D₄	C₂×C₉	semidirect
131. #480	C₂×C₉	semidirect
132. #474	C₂×C₉	semidirect
133. #459	C₂×C₉	semidirect
134. #447	C₂×C₉	semidirect
135. C₄×D₈	C₂×C₉	semidirect
136. #431	C₂×C₉	semidirect
192. C₄⋊Q₈	C₂²×C₉	semidirect
193. #127	C₂²×C₉	semidirect
202. C₄×D₄	C₂²×C₉	semidirect
206. #107	C₂²×C₉	semidirect
207. C₄⋊C₈	C₂²×C₉	semidirect
209. #102	C₂²×C₉	semidirect
211. C₄×C₈	C₂²×C₉	semidirect
299. C₉	#3100	direct (N × H)
313. D₄	C₉×#41	semidirect
322. C₂×C₄	C₉×D₈	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
C₂×C₄×D₄×C₉	2
C₉×#480	2
C₉×#474	2
C₉×#459	2
C₉×#447	2
C₄×C₉×D₈	2
C₉×#431	2
C₃×#3100	3

Subgroups — C9×#3100 #11767821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3100 #11767821