Subgroups — C₉×#3136 #11767857

Order 1152.

606 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₉×#490	C₂	1	2	yes	maximal, complemented
4	C₉×#489	C₂	1	2	yes	maximal, complemented
5	C₉×#488	C₂	1	2	yes	maximal, complemented
6	C₉×#486	C₂	1	2	yes	maximal, complemented
7	C₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3136	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₉×C₄⋊Q₈	—	2	1	no	—
18	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₉×#127	C₂²	1	2	yes	—
20	C₉×#125	—	2	1	no	—
21	C₉×#125	C₂²	1	2	yes	complemented
22	C₉×#124	C₂²	1	2	yes	—
23	C₉×C₂²⋊Q₈	—	2	2	no	—
24	C₉×#121	—	2	1	no	—
25	C₉×#121	—	2	1	no	—
26	C₉×#120	—	2	2	no	—
27	C₉×#117	C₂²	1	1	yes	characteristic
28	C₉×#117	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₉×#103	C₂²	1	1	yes	characteristic, complemented
31	C₉×#103	C₂²	1	1	yes	characteristic, complemented
32	C₉×#103	C₂²	1	2	yes	complemented
33	C₉×#102	C₂²	1	2	yes	—
34	C₉×#102	C₂²	1	2	yes	—
35	C₉×#102	C₂²	1	2	yes	—
36	C₉×#102	C₂²	1	2	yes	—
37	C₉×#102	C₂²	1	1	yes	characteristic, complemented
38	C₉×#102	C₂²	1	1	yes	characteristic, complemented
39	C₉×#102	C₂²	1	2	yes	complemented
40	C₉×#97	C₂²	1	2	yes	complemented
41	C₄×C₈×C₉	C₂²	1	2	yes	complemented
42	C₃×#544	C₂×C₃	1	1	yes	characteristic
43	C₃×#535	C₂×C₃	1	1	yes	characteristic
44	C₃×#490	C₂×C₃	1	2	yes	—
45	C₃×#489	C₂×C₃	1	2	yes	—
46	C₃×#488	C₂×C₃	1	2	yes	—
47	C₃×#486	C₂×C₃	1	2	yes	—
48	C₃×#418	C₂×C₃	1	1	yes	characteristic
49	C₃×#417	C₂×C₃	1	1	yes	characteristic
50	C₃×#416	C₂×C₃	1	1	yes	characteristic
51	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
52	C₃×#405	C₂×C₃	1	1	yes	characteristic
53	C₂⁴×C₉	—	2	1	no	—
54	C₉×#41	—	2	2	no	—
55	C₉×#41	—	2	2	no	—
56	C₂×Q₈×C₉	—	2	2	no	—
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	—	2	2	no	—
61	C₂×D₄×C₉	—	2	2	no	—
62	C₂×D₄×C₉	—	2	2	no	—
63	C₂×D₄×C₉	—	2	2	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	C₂³	1	1	yes	characteristic
69	C₉×M₁₆	—	2	2	no	—
70	C₂×C₈×C₉	—	2	2	no	—
71	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₉	C₂³	1	2	yes	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	2	yes	—
81	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	D₄	1	2	yes	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	C₂³	1	2	yes	—
89	#3136	C₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Q₈	—	2	1	no	—
95	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₃×#127	C₂²×C₃	1	2	yes	—
97	C₃×#125	—	2	1	no	—
98	C₃×#125	C₂²×C₃	1	2	yes	—
99	C₃×#124	C₂²×C₃	1	2	yes	—
100	C₃×C₂²⋊Q₈	—	2	2	no	—
101	C₃×#121	—	2	1	no	—
102	C₃×#121	—	2	1	no	—
103	C₃×#120	—	2	2	no	—
104	C₃×#117	C₂²×C₃	1	1	yes	characteristic
105	C₃×#117	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃×#103	C₂²×C₃	1	1	yes	characteristic
108	C₃×#103	C₂²×C₃	1	1	yes	characteristic
109	C₃×#103	C₂²×C₃	1	2	yes	—
110	C₃×#102	C₂²×C₃	1	2	yes	—
111	C₃×#102	C₂²×C₃	1	2	yes	—
112	C₃×#102	C₂²×C₃	1	2	yes	—
113	C₃×#102	C₂²×C₃	1	2	yes	—
114	C₃×#102	C₂²×C₃	1	1	yes	characteristic
115	C₃×#102	C₂²×C₃	1	1	yes	characteristic
116	C₃×#102	C₂²×C₃	1	2	yes	—
117	C₃×#97	C₂²×C₃	1	2	yes	—
118	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	1	no	—
121	C₂³×C₉	—	4	2	no	—
122	C₂³×C₉	—	8	1	no	—
123	C₂³×C₉	—	8	1	no	—
124	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
125	Q₈×C₉	—	2	1	no	—
126	Q₈×C₉	—	2	1	no	—
127	Q₈×C₉	—	8	2	no	—
128	D₄×C₉	—	2	2	no	—
129	D₄×C₉	—	2	2	no	—
130	D₄×C₉	—	2	1	no	—
131	D₄×C₉	—	2	1	no	—
132	D₄×C₉	—	4	2	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	2	no	—
140	C₂×C₄×C₉	—	4	2	no	—
141	C₂×C₄×C₉	—	8	1	no	—
142	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
143	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
144	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₉	#41	1	2	yes	—
146	C₂×C₄×C₉	#41	1	2	yes	—
147	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
148	C₈×C₉	—	2	1	no	—
149	C₈×C₉	—	2	1	no	—
150	C₈×C₉	—	2	2	no	—
151	#544	C₂×C₉	1	1	yes	characteristic, complemented
152	#535	C₂×C₉	1	1	yes	characteristic
153	#490	C₂×C₉	1	2	yes	complemented
154	#489	C₂×C₉	1	2	yes	complemented
155	#488	C₂×C₉	1	2	yes	complemented
156	#486	C₂×C₉	1	2	yes	complemented
157	#418	C₂×C₉	1	1	yes	characteristic, complemented
158	#417	C₂×C₉	1	1	yes	characteristic, complemented
159	#416	C₂×C₉	1	1	yes	characteristic, complemented
160	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
161	#405	C₂×C₉	1	1	yes	characteristic, complemented
162	C₂⁴×C₃	—	2	1	no	—
163	C₃×#41	—	2	2	no	—
164	C₃×#41	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	—	2	1	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
174	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₃×M₁₆	—	2	2	no	—
179	C₂×C₃×C₈	—	2	2	no	—
180	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
182	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	2	no	—
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	C₂³×C₃	1	2	yes	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	2	1	no	—
200	C₂²×C₉	—	4	1	no	—
201	C₂²×C₉	—	4	2	no	—
202	C₂²×C₉	—	4	1	no	—
203	C₂²×C₉	—	4	2	no	—
204	C₂²×C₉	—	4	1	no	—
205	C₂²×C₉	—	4	2	no	—
206	C₂²×C₉	—	8	4	no	—
207	C₂²×C₉	#124	1	2	yes	—
208	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	2	no	—
211	C₄×C₉	—	4	1	no	—
212	C₄×C₉	—	4	2	no	—
213	C₄×C₉	—	4	1	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	#124	1	2	yes	—
216	C₄×C₉	C₂×#41	1	1	yes	characteristic
217	C₄×C₉	C₂×#41	1	1	yes	characteristic
218	C₂×#41	C₂²×C₉	1	1	yes	characteristic
219	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
220	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
221	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
222	C₄⋊Q₈	—	2	1	no	—
223	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
224	#127	C₂²×C₉	1	2	yes	—
225	#125	—	2	1	no	—
226	#125	C₂²×C₉	1	2	yes	complemented
227	#124	C₂²×C₉	1	2	yes	—
228	C₂²⋊Q₈	—	2	2	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#120	—	2	2	no	—
232	#117	C₂²×C₉	1	1	yes	characteristic
233	#117	C₂²×C₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	#103	C₂²×C₉	1	1	yes	characteristic, complemented
236	#103	C₂²×C₉	1	1	yes	characteristic, complemented
237	#103	C₂²×C₉	1	2	yes	complemented
238	#102	C₂²×C₉	1	2	yes	—
239	#102	C₂²×C₉	1	2	yes	—
240	#102	C₂²×C₉	1	2	yes	—
241	#102	C₂²×C₉	1	2	yes	—
242	#102	C₂²×C₉	1	1	yes	characteristic, complemented
243	#102	C₂²×C₉	1	1	yes	characteristic, complemented
244	#102	C₂²×C₉	1	2	yes	complemented
245	#97	C₂²×C₉	1	2	yes	complemented
246	C₄×C₈	C₂²×C₉	1	2	yes	complemented
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	4	2	no	—
250	C₂³×C₃	—	8	1	no	—
251	C₂³×C₃	—	8	1	no	—
252	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
253	C₃×Q₈	—	2	1	no	—
254	C₃×Q₈	—	2	1	no	—
255	C₃×Q₈	—	8	2	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	—	2	1	no	—
260	C₃×D₄	—	4	2	no	—
261	C₃×D₄	—	4	2	no	—
262	C₃×D₄	—	8	2	no	—
263	C₃×D₄	—	8	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	8	1	no	—
270	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₃×#41	1	2	yes	—
274	C₂×C₃×C₄	C₃×#41	1	2	yes	—
275	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
276	C₃×C₈	—	2	1	no	—
277	C₃×C₈	—	2	1	no	—
278	C₃×C₈	—	2	2	no	—
279	C₂×C₉	—	2	2	no	—
280	C₂×C₉	—	8	1	no	—
281	C₂×C₉	—	8	2	no	—
282	C₂×C₉	C₂×#124	1	1	yes	characteristic
283	C₂×C₉	#576	1	1	yes	characteristic
284	C₂×C₉	#577	1	1	yes	characteristic
285	C₂⁴	—	2	1	no	—
286	#41	—	2	2	no	—
287	#41	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	C₂³×C₉	1	2	yes	—
297	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
301	M₁₆	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
304	C₂×C₈	C₂³×C₉	1	2	yes	—
305	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
311	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
312	C₄⋊C₄	C₂³×C₉	1	2	yes	—
313	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
314	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	D₄×C₉	1	2	yes	—
319	C₄²	—	2	1	no	—
320	C₄²	C₂³×C₉	1	2	yes	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	—	4	2	no	—
327	C₂²×C₃	—	4	1	no	—
328	C₂²×C₃	—	4	2	no	—
329	C₂²×C₃	—	8	4	no	—
330	C₂²×C₃	C₃×#124	1	2	yes	—
331	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	4	1	no	—
336	C₃×C₄	—	4	1	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	C₃×#124	1	2	yes	—
339	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
340	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
341	C₉	#3136	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	2	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	1	no	—
346	C₂³	—	8	1	no	—
347	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
348	Q₈	—	2	1	no	—
349	Q₈	—	2	1	no	—
350	Q₈	—	8	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
366	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
367	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
368	C₂×C₄	C₉×#41	1	2	yes	—
369	C₂×C₄	C₉×#41	1	2	yes	—
370	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	2	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	8	2	no	—
376	C₂×C₃	—	8	1	no	—
377	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
378	C₂×C₃	C₃×#576	1	1	yes	characteristic
379	C₂×C₃	C₃×#577	1	1	yes	characteristic
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	4	no	—
389	C₂²	C₉×#124	1	2	yes	—
390	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	C₉×#124	1	2	yes	—
398	C₄	C₂×C₉×#41	1	1	yes	characteristic
399	C₄	C₂×C₉×#41	1	1	yes	characteristic
400	C₃	C₃×#3136	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	1	no	—
404	C₂	C₂×C₉×#124	1	1	yes	characteristic
405	C₂	C₉×#576	1	1	yes	characteristic
406	C₂	C₉×#577	1	1	yes	characteristic

	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 ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#544	C₂	semidirect
3. C₉×#490	C₂	semidirect
4. C₉×#489	C₂	semidirect
5. C₉×#488	C₂	semidirect
6. C₉×#486	C₂	semidirect
7. C₉×#418	C₂	semidirect
8. C₉×#417	C₂	semidirect
9. C₉×#416	C₂	semidirect
10. C₂×C₉×#102	C₂	semidirect
11. C₉×#405	C₂	semidirect
18. C₉×C₄⋊Q₈	C₂²	semidirect
21. C₉×#125	C₂²	semidirect
30. C₉×#103	C₂²	semidirect
31. C₉×#103	C₂²	semidirect
32. C₉×#103	C₂²	semidirect
37. C₉×#102	C₂²	semidirect
38. C₉×#102	C₂²	semidirect
39. C₉×#102	C₂²	semidirect
40. C₉×#97	C₂²	semidirect
41. C₄×C₈×C₉	C₂²	semidirect
89. #3136	C₉	direct (N × H)
151. #544	C₂×C₉	semidirect
153. #490	C₂×C₉	semidirect
154. #489	C₂×C₉	semidirect
155. #488	C₂×C₉	semidirect
156. #486	C₂×C₉	semidirect
157. #418	C₂×C₉	semidirect
158. #417	C₂×C₉	semidirect
159. #416	C₂×C₉	semidirect
160. C₂×#102	C₂×C₉	semidirect
161. #405	C₂×C₉	semidirect
223. C₄⋊Q₈	C₂²×C₉	semidirect
226. #125	C₂²×C₉	semidirect
235. #103	C₂²×C₉	semidirect
236. #103	C₂²×C₉	semidirect
237. #103	C₂²×C₉	semidirect
242. #102	C₂²×C₉	semidirect
243. #102	C₂²×C₉	semidirect
244. #102	C₂²×C₉	semidirect
245. #97	C₂²×C₉	semidirect
246. C₄×C₈	C₂²×C₉	semidirect
341. C₉	#3136	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×#544	2
C₉×#535	2
C₉×#490	2
C₉×#489	2
C₉×#488	2
C₉×#486	2
C₉×#418	2
C₉×#417	2
C₉×#416	2
C₂×C₉×#102	2
C₉×#405	2
C₃×#3136	3

Subgroups — C9×#3136 #11767857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3136 #11767857