Subgroups — C₉×#3193 #11767914

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
3	C₉×#484	C₂	1	2	yes	maximal, complemented
4	C₉×#480	C₂	1	2	yes	maximal, complemented
5	C₉×#468	C₂	1	4	yes	maximal, complemented
6	C₉×#450	C₂	1	2	yes	maximal, complemented
7	C₉×#448	C₂	1	2	yes	maximal, complemented
8	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3193	C₃	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₄×C₉	—	2	1	no	—
12	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×SD₁₆	C₂²	1	4	yes	complemented
15	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
16	C₉×C₂²⋊Q₈	—	2	1	no	—
17	C₉×C₂²⋊Q₈	—	2	1	no	—
18	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
20	C₉×#121	—	2	1	no	—
21	C₉×#121	—	2	1	no	—
22	C₉×#121	C₂²	1	2	yes	—
23	C₉×#121	C₂²	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	—	2	1	no	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
29	C₉×#107	C₂²	1	4	yes	complemented
30	C₉×#103	C₂²	1	4	yes	complemented
31	C₉×#102	C₂²	1	4	yes	complemented
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
36	C₃×#484	C₂×C₃	1	2	yes	—
37	C₃×#480	C₂×C₃	1	2	yes	—
38	C₃×#468	C₂×C₃	1	4	yes	—
39	C₃×#450	C₂×C₃	1	2	yes	—
40	C₃×#448	C₂×C₃	1	2	yes	—
41	C₃×#407	C₂×C₃	1	1	yes	characteristic
42	C₂⁴×C₉	—	2	1	no	—
43	C₂⁴×C₉	D₄	1	1	yes	characteristic
44	C₂×Q₈×C₉	—	2	1	no	—
45	C₂×Q₈×C₉	—	4	2	no	—
46	C₂×Q₈×C₉	C₂³	1	2	yes	—
47	C₂×D₄×C₉	—	2	2	no	—
48	C₂×D₄×C₉	—	2	2	no	—
49	C₂×D₄×C₉	—	2	1	no	—
50	C₂×D₄×C₉	—	4	2	no	—
51	C₂×D₄×C₉	—	4	4	no	—
52	C₂×D₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	—	2	1	no	—
54	C₂²×C₄×C₉	—	2	1	no	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	—	4	2	no	—
57	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
59	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₉×SD₁₆	—	4	4	no	—
64	C₉×M₁₆	—	4	2	no	—
65	C₂×C₈×C₉	C₂³	1	4	yes	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	1	no	—
69	C₉×C₄⋊C₄	—	2	1	no	—
70	C₉×C₄⋊C₄	C₂³	1	2	yes	—
71	C₉×C₄⋊C₄	C₂³	1	2	yes	—
72	C₉×C₂²⋊C₄	—	2	2	no	—
73	C₉×C₂²⋊C₄	—	2	2	no	—
74	C₉×C₂²⋊C₄	—	2	2	no	—
75	C₉×C₂²⋊C₄	—	2	2	no	—
76	#3193	C₉	1	1	yes	characteristic, direct product factor, Sylow
77	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃×D₄	—	2	1	no	—
79	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
82	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
83	C₃×C₂²⋊Q₈	—	2	1	no	—
84	C₃×C₂²⋊Q₈	—	2	1	no	—
85	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
86	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
87	C₃×#121	—	2	1	no	—
88	C₃×#121	—	2	1	no	—
89	C₃×#121	C₂²×C₃	1	2	yes	—
90	C₃×#121	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
96	C₃×#107	C₂²×C₃	1	4	yes	—
97	C₃×#103	C₂²×C₃	1	4	yes	—
98	C₃×#102	C₂²×C₃	1	4	yes	—
99	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
100	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	2	2	no	—
103	C₂³×C₉	—	2	2	no	—
104	C₂³×C₉	—	4	1	no	—
105	C₂³×C₉	—	4	2	no	—
106	C₂³×C₉	—	4	2	no	—
107	C₂³×C₉	—	4	2	no	—
108	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
109	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
111	Q₈×C₉	—	2	4	no	—
112	Q₈×C₉	—	4	2	no	—
113	D₄×C₉	—	2	4	no	—
114	D₄×C₉	—	4	2	no	—
115	D₄×C₉	—	4	4	no	—
116	D₄×C₉	—	4	4	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	4	1	no	—
124	C₂×C₄×C₉	—	4	1	no	—
125	C₂×C₄×C₉	—	4	1	no	—
126	C₂×C₄×C₉	—	4	2	no	—
127	C₂×C₄×C₉	—	4	2	no	—
128	C₂×C₄×C₉	—	4	2	no	—
129	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
133	C₈×C₉	—	2	4	no	—
134	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
135	C₂×#121	C₂×C₉	1	1	yes	characteristic
136	#484	C₂×C₉	1	2	yes	complemented
137	#480	C₂×C₉	1	2	yes	complemented
138	#468	C₂×C₉	1	4	yes	complemented
139	#450	C₂×C₉	1	2	yes	complemented
140	#448	C₂×C₉	1	2	yes	complemented
141	#407	C₂×C₉	1	1	yes	characteristic, complemented
142	C₂⁴×C₃	—	2	1	no	—
143	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
144	C₂×C₃×Q₈	—	2	1	no	—
145	C₂×C₃×Q₈	—	4	2	no	—
146	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	—	2	1	no	—
150	C₂×C₃×D₄	—	4	2	no	—
151	C₂×C₃×D₄	—	4	4	no	—
152	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂²×C₃×C₄	—	4	2	no	—
157	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₃×SD₁₆	—	4	4	no	—
164	C₃×M₁₆	—	4	2	no	—
165	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	—	2	1	no	—
170	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
171	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
172	C₃×C₂²⋊C₄	—	2	2	no	—
173	C₃×C₂²⋊C₄	—	2	2	no	—
174	C₃×C₂²⋊C₄	—	2	2	no	—
175	C₃×C₂²⋊C₄	—	2	2	no	—
176	C₂²×C₉	—	2	1	no	—
177	C₂²×C₉	—	2	1	no	—
178	C₂²×C₉	—	2	1	no	—
179	C₂²×C₉	—	2	1	no	—
180	C₂²×C₉	—	2	1	no	—
181	C₂²×C₉	—	2	1	no	—
182	C₂²×C₉	—	2	1	no	—
183	C₂²×C₉	—	4	4	no	—
184	C₂²×C₉	—	4	2	no	—
185	C₂²×C₉	—	4	2	no	—
186	C₂²×C₉	—	4	2	no	—
187	C₂²×C₉	—	8	4	no	—
188	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂²×C₉	#137	1	2	yes	—
190	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₉	—	2	1	no	—
192	C₄×C₉	—	2	1	no	—
193	C₄×C₉	—	2	1	no	—
194	C₄×C₉	—	4	2	no	—
195	C₄×C₉	—	4	2	no	—
196	C₄×C₉	—	4	2	no	—
197	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
198	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
199	C₂²×D₄	—	2	1	no	—
200	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
201	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
202	C₂×SD₁₆	C₂²×C₉	1	4	yes	complemented
203	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
207	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	C₂²×C₉	1	2	yes	—
211	#121	C₂²×C₉	1	2	yes	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
215	C₂×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₂²⋊C₄	—	2	1	no	—
217	#107	C₂²×C₉	1	4	yes	complemented
218	#103	C₂²×C₉	1	4	yes	complemented
219	#102	C₂²×C₉	1	4	yes	complemented
220	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
221	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
222	C₂³×C₃	—	2	2	no	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	4	1	no	—
226	C₂³×C₃	—	4	2	no	—
227	C₂³×C₃	—	4	2	no	—
228	C₂³×C₃	—	4	2	no	—
229	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
232	C₃×Q₈	—	2	4	no	—
233	C₃×Q₈	—	4	2	no	—
234	C₃×D₄	—	2	4	no	—
235	C₃×D₄	—	4	2	no	—
236	C₃×D₄	—	4	4	no	—
237	C₃×D₄	—	4	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	—	4	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	4	2	no	—
249	C₂×C₃×C₄	—	4	2	no	—
250	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
254	C₃×C₈	—	2	4	no	—
255	C₂×C₉	—	2	2	no	—
256	C₂×C₉	—	2	2	no	—
257	C₂×C₉	—	4	1	no	—
258	C₂×C₉	—	8	2	no	—
259	C₂×C₉	#534	1	1	yes	characteristic
260	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂×C₉	C₂×#137	1	1	yes	characteristic
262	C₂⁴	—	2	1	no	—
263	C₂⁴	D₄×C₉	1	1	yes	characteristic
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	C₂³×C₉	1	2	yes	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	C₂³×C₉	1	2	yes	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
278	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
279	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
283	SD₁₆	—	4	4	no	—
284	M₁₆	—	4	2	no	—
285	C₂×C₈	C₂³×C₉	1	4	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	C₂³×C₉	1	2	yes	—
291	C₄⋊C₄	C₂³×C₉	1	2	yes	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	2	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	8	4	no	—
308	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
309	C₂²×C₃	C₃×#137	1	2	yes	—
310	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	2	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
318	C₉	#3193	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
327	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
328	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
349	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
350	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	4	1	no	—
355	C₂×C₃	—	8	2	no	—
356	C₂×C₃	C₃×#534	1	1	yes	characteristic
357	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
358	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	8	4	no	—
371	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
372	C₂²	C₉×#137	1	2	yes	—
373	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
381	C₃	C₃×#3193	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	4	1	no	—
385	C₂	—	8	2	no	—
386	C₂	C₉×#534	1	1	yes	characteristic
387	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂	C₂×C₉×#137	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	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
3. C₉×#484	C₂	semidirect
4. C₉×#480	C₂	semidirect
5. C₉×#468	C₂	semidirect
6. C₉×#450	C₂	semidirect
7. C₉×#448	C₂	semidirect
8. C₉×#407	C₂	semidirect
10. C₂²×Q₈×C₉	C₂²	semidirect
14. C₂×C₉×SD₁₆	C₂²	semidirect
15. C₂×C₉×M₁₆	C₂²	semidirect
19. C₉×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₉×C₄⋊C₄	C₂²	semidirect
29. C₉×#107	C₂²	semidirect
30. C₉×#103	C₂²	semidirect
31. C₉×#102	C₂²	semidirect
33. C₉×C₂²⋊C₈	C₂²	semidirect
76. #3193	C₉	direct (N × H)
134. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
136. #484	C₂×C₉	semidirect
137. #480	C₂×C₉	semidirect
138. #468	C₂×C₉	semidirect
139. #450	C₂×C₉	semidirect
140. #448	C₂×C₉	semidirect
141. #407	C₂×C₉	semidirect
198. C₂²×Q₈	C₂²×C₉	semidirect
202. C₂×SD₁₆	C₂²×C₉	semidirect
203. C₂×M₁₆	C₂²×C₉	semidirect
207. C₂²⋊Q₈	C₂²×C₉	semidirect
214. C₂×C₄⋊C₄	C₂²×C₉	semidirect
217. #107	C₂²×C₉	semidirect
218. #103	C₂²×C₉	semidirect
219. #102	C₂²×C₉	semidirect
221. C₂²⋊C₈	C₂²×C₉	semidirect
318. C₉	#3193	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×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₉×#484	2
C₉×#480	2
C₉×#468	2
C₉×#450	2
C₉×#448	2
C₉×#407	2
C₃×#3193	3

Subgroups — C9×#3193 #11767914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3193 #11767914