Subgroups — C₉×#3200 #11767921

Order 1152.

615 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₉×#485	C₂	1	2	yes	maximal, complemented
4	C₉×#482	C₂	1	2	yes	maximal, complemented
5	C₉×#468	C₂	1	2	yes	maximal, complemented
6	C₉×#465	C₂	1	2	yes	maximal, complemented
7	C₉×#450	C₂	1	2	yes	maximal, complemented
8	C₉×#448	C₂	1	2	yes	maximal, complemented
9	C₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3200	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₉×C₄⋊Q₈	—	2	1	no	—
19	C₉×#127	—	2	1	no	—
20	C₉×#124	—	2	1	no	—
21	C₉×#124	—	2	1	no	—
22	C₉×#123	—	2	1	no	—
23	C₉×#123	—	2	1	no	—
24	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₉×#121	C₂²	1	2	yes	—
27	C₉×#121	C₂²	1	2	yes	—
28	C₉×#120	—	2	1	no	—
29	C₉×#120	—	2	1	no	—
30	C₉×#117	C₂²	1	1	yes	characteristic
31	C₉×#117	C₂²	1	1	yes	characteristic, complemented
32	C₉×#107	C₂²	1	2	yes	complemented
33	C₉×#106	C₂²	1	2	yes	complemented
34	C₉×#103	C₂²	1	2	yes	complemented
35	C₉×#103	C₂²	1	2	yes	complemented
36	C₉×#102	C₂²	1	2	yes	—
37	C₉×#102	C₂²	1	2	yes	—
38	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
40	C₃×#536	C₂×C₃	1	1	yes	characteristic
41	C₃×#535	C₂×C₃	1	1	yes	characteristic
42	C₃×#485	C₂×C₃	1	2	yes	—
43	C₃×#482	C₂×C₃	1	2	yes	—
44	C₃×#468	C₂×C₃	1	2	yes	—
45	C₃×#465	C₂×C₃	1	2	yes	—
46	C₃×#450	C₂×C₃	1	2	yes	—
47	C₃×#448	C₂×C₃	1	2	yes	—
48	C₃×#408	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	—	2	1	no	—
50	C₉×#41	—	4	1	no	—
51	C₉×#41	—	4	1	no	—
52	C₂×Q₈×C₉	—	2	1	no	—
53	C₂×Q₈×C₉	—	4	1	no	—
54	C₂×Q₈×C₉	—	4	1	no	—
55	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
56	C₂×Q₈×C₉	C₂³	1	2	yes	—
57	C₂×D₄×C₉	—	2	2	no	—
58	C₂×D₄×C₉	—	2	2	no	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	—	4	1	no	—
61	C₂×D₄×C₉	—	4	1	no	—
62	C₂×D₄×C₉	D₄	1	1	yes	characteristic
63	C₂×D₄×C₉	D₄	1	1	yes	characteristic
64	C₂×D₄×C₉	D₄	1	1	yes	characteristic
65	C₂×D₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	—	2	1	no	—
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×SD₁₆	—	4	2	no	—
71	C₉×SD₁₆	—	4	2	no	—
72	C₉×M₁₆	—	4	1	no	—
73	C₂×C₈×C₉	—	4	1	no	—
74	C₂×C₈×C₉	C₂³	1	2	yes	—
75	C₂×C₈×C₉	C₂³	1	2	yes	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	C₂³	1	2	yes	—
79	C₉×C₄⋊C₄	C₂³	1	2	yes	—
80	C₉×C₂²⋊C₄	—	2	1	no	—
81	C₉×C₂²⋊C₄	—	2	1	no	—
82	C₉×C₂²⋊C₄	—	2	2	no	—
83	C₉×C₂²⋊C₄	—	2	2	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₄²×C₉	—	2	1	no	—
87	C₄²×C₉	—	2	1	no	—
88	#3200	C₉	1	1	yes	characteristic, direct product factor, Sylow
89	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
93	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
94	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
96	C₃×C₄⋊Q₈	—	2	1	no	—
97	C₃×#127	—	2	1	no	—
98	C₃×#124	—	2	1	no	—
99	C₃×#124	—	2	1	no	—
100	C₃×#123	—	2	1	no	—
101	C₃×#123	—	2	1	no	—
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
103	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₃×#121	C₂²×C₃	1	2	yes	—
105	C₃×#121	C₂²×C₃	1	2	yes	—
106	C₃×#120	—	2	1	no	—
107	C₃×#120	—	2	1	no	—
108	C₃×#117	C₂²×C₃	1	1	yes	characteristic
109	C₃×#117	C₂²×C₃	1	1	yes	characteristic
110	C₃×#107	C₂²×C₃	1	2	yes	—
111	C₃×#106	C₂²×C₃	1	2	yes	—
112	C₃×#103	C₂²×C₃	1	2	yes	—
113	C₃×#103	C₂²×C₃	1	2	yes	—
114	C₃×#102	C₂²×C₃	1	2	yes	—
115	C₃×#102	C₂²×C₃	1	2	yes	—
116	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
117	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
118	C₂³×C₉	—	2	2	no	—
119	C₂³×C₉	—	4	2	no	—
120	C₂³×C₉	—	8	2	no	—
121	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
122	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
123	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
124	Q₈×C₉	—	2	2	no	—
125	Q₈×C₉	—	2	2	no	—
126	Q₈×C₉	—	4	1	no	—
127	Q₈×C₉	—	4	2	no	—
128	D₄×C₉	—	2	2	no	—
129	D₄×C₉	—	2	2	no	—
130	D₄×C₉	—	4	1	no	—
131	D₄×C₉	—	4	1	no	—
132	D₄×C₉	—	4	1	no	—
133	D₄×C₉	—	4	2	no	—
134	D₄×C₉	—	8	2	no	—
135	D₄×C₉	—	8	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	4	2	no	—
146	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
150	C₈×C₉	—	2	2	no	—
151	C₈×C₉	—	2	2	no	—
152	#536	C₂×C₉	1	1	yes	characteristic, complemented
153	#535	C₂×C₉	1	1	yes	characteristic
154	#485	C₂×C₉	1	2	yes	complemented
155	#482	C₂×C₉	1	2	yes	complemented
156	#468	C₂×C₉	1	2	yes	complemented
157	#465	C₂×C₉	1	2	yes	complemented
158	#450	C₂×C₉	1	2	yes	complemented
159	#448	C₂×C₉	1	2	yes	complemented
160	#408	C₂×C₉	1	1	yes	characteristic, complemented
161	C₂⁴×C₃	—	2	1	no	—
162	C₃×#41	—	4	1	no	—
163	C₃×#41	—	4	1	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	—	4	1	no	—
166	C₂×C₃×Q₈	—	4	1	no	—
167	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
168	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	1	no	—
172	C₂×C₃×D₄	—	4	1	no	—
173	C₂×C₃×D₄	—	4	1	no	—
174	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
175	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
176	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₃×SD₁₆	—	4	2	no	—
183	C₃×SD₁₆	—	4	2	no	—
184	C₃×M₁₆	—	4	1	no	—
185	C₂×C₃×C₈	—	4	1	no	—
186	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
187	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	1	no	—
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	2	2	no	—
196	C₃×C₂²⋊C₄	—	2	2	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	2	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	4	2	no	—
207	C₂²×C₉	—	4	2	no	—
208	C₂²×C₉	—	4	2	no	—
209	C₂²×C₉	—	8	4	no	—
210	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	4	2	no	—
215	C₄×C₉	—	4	2	no	—
216	C₄×C₉	—	4	2	no	—
217	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×#41	C₂²×C₉	1	1	yes	characteristic
220	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
221	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
222	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
223	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
224	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
225	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
226	C₄⋊Q₈	—	2	1	no	—
227	#127	—	2	1	no	—
228	#124	—	2	1	no	—
229	#124	—	2	1	no	—
230	#123	—	2	1	no	—
231	#123	—	2	1	no	—
232	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
233	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
234	#121	C₂²×C₉	1	2	yes	—
235	#121	C₂²×C₉	1	2	yes	—
236	#120	—	2	1	no	—
237	#120	—	2	1	no	—
238	#117	C₂²×C₉	1	1	yes	characteristic
239	#117	C₂²×C₉	1	1	yes	characteristic, complemented
240	#107	C₂²×C₉	1	2	yes	complemented
241	#106	C₂²×C₉	1	2	yes	complemented
242	#103	C₂²×C₉	1	2	yes	complemented
243	#103	C₂²×C₉	1	2	yes	complemented
244	#102	C₂²×C₉	1	2	yes	—
245	#102	C₂²×C₉	1	2	yes	—
246	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
247	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	4	2	no	—
250	C₂³×C₃	—	8	2	no	—
251	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	—	4	1	no	—
257	C₃×Q₈	—	4	2	no	—
258	C₃×D₄	—	2	2	no	—
259	C₃×D₄	—	2	2	no	—
260	C₃×D₄	—	4	1	no	—
261	C₃×D₄	—	4	1	no	—
262	C₃×D₄	—	4	1	no	—
263	C₃×D₄	—	4	2	no	—
264	C₃×D₄	—	8	2	no	—
265	C₃×D₄	—	8	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
280	C₃×C₈	—	2	2	no	—
281	C₃×C₈	—	2	2	no	—
282	C₂×C₉	—	4	1	no	—
283	C₂×C₉	—	4	1	no	—
284	C₂×C₉	—	4	1	no	—
285	C₂×C₉	—	8	2	no	—
286	C₂×C₉	#534	1	1	yes	characteristic
287	C₂×C₉	#577	1	2	yes	—
288	C₂⁴	—	2	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
295	C₂×Q₈	C₂³×C₉	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	D₄×C₉	1	1	yes	characteristic
302	C₂×D₄	D₄×C₉	1	1	yes	characteristic
303	C₂×D₄	D₄×C₉	1	1	yes	characteristic
304	C₂×D₄	C₂³×C₉	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
309	SD₁₆	—	4	2	no	—
310	SD₁₆	—	4	2	no	—
311	M₁₆	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	C₂³×C₉	1	2	yes	—
314	C₂×C₈	C₂³×C₉	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₂³×C₉	1	2	yes	—
318	C₄⋊C₄	C₂³×C₉	1	2	yes	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	8	4	no	—
337	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	2	no	—
344	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₉	#3200	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
351	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
352	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
353	Q₈	—	2	2	no	—
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
377	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
378	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₂×C₃	—	4	1	no	—
382	C₂×C₃	—	4	1	no	—
383	C₂×C₃	—	4	1	no	—
384	C₂×C₃	—	8	2	no	—
385	C₂×C₃	C₃×#534	1	1	yes	characteristic
386	C₂×C₃	C₃×#577	1	2	yes	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	4	no	—
397	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
405	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
406	C₃	C₃×#3200	1	1	yes	characteristic
407	C₂	—	4	1	no	—
408	C₂	—	4	1	no	—
409	C₂	—	4	1	no	—
410	C₂	—	8	2	no	—
411	C₂	C₉×#534	1	1	yes	characteristic
412	C₂	C₉×#577	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×#535	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#536	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#482	C₂	semidirect
5. C₉×#468	C₂	semidirect
6. C₉×#465	C₂	semidirect
7. C₉×#450	C₂	semidirect
8. C₉×#448	C₂	semidirect
9. C₉×#408	C₂	semidirect
12. C₂²×Q₈×C₉	C₂²	semidirect
16. C₂×C₉×M₁₆	C₂²	semidirect
17. C₂²×C₈×C₉	C₂²	semidirect
25. C₉×C₂²⋊Q₈	C₂²	semidirect
31. C₉×#117	C₂²	semidirect
32. C₉×#107	C₂²	semidirect
33. C₉×#106	C₂²	semidirect
34. C₉×#103	C₂²	semidirect
35. C₉×#103	C₂²	semidirect
39. C₉×C₂²⋊C₈	C₂²	semidirect
88. #3200	C₉	direct (N × H)
152. #536	C₂×C₉	semidirect
154. #485	C₂×C₉	semidirect
155. #482	C₂×C₉	semidirect
156. #468	C₂×C₉	semidirect
157. #465	C₂×C₉	semidirect
158. #450	C₂×C₉	semidirect
159. #448	C₂×C₉	semidirect
160. #408	C₂×C₉	semidirect
220. C₂²×Q₈	C₂²×C₉	semidirect
224. C₂×M₁₆	C₂²×C₉	semidirect
225. C₂²×C₈	C₂²×C₉	semidirect
233. C₂²⋊Q₈	C₂²×C₉	semidirect
239. #117	C₂²×C₉	semidirect
240. #107	C₂²×C₉	semidirect
241. #106	C₂²×C₉	semidirect
242. #103	C₂²×C₉	semidirect
243. #103	C₂²×C₉	semidirect
247. C₂²⋊C₈	C₂²×C₉	semidirect
346. C₉	#3200	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×#536	2
C₉×#535	2
C₉×#485	2
C₉×#482	2
C₉×#468	2
C₉×#465	2
C₉×#450	2
C₉×#448	2
C₉×#408	2
C₃×#3200	3

Subgroups — C9×#3200 #11767921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3200 #11767921