Subgroups — C₉×#3194 #11767915

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#482	C₂	1	2	yes	maximal, complemented
5	C₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#469	C₂	1	2	yes	maximal, complemented
7	C₉×#468	C₂	1	2	yes	maximal, complemented
8	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#449	C₂	1	2	yes	maximal, complemented
10	C₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3194	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂²×D₄×C₉	—	2	1	no	—
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₉×D₈	C₂²	1	2	yes	complemented
19	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
20	C₉×#123	—	2	1	no	—
21	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₉×#121	—	2	1	no	—
24	C₉×#121	—	2	1	no	—
25	C₉×#121	C₂²	1	2	yes	—
26	C₉×#121	C₂²	1	2	yes	—
27	C₉×#121	C₂²	1	1	yes	characteristic
28	C₉×#121	C₂²	1	1	yes	characteristic, complemented
29	C₉×#120	—	2	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	—	2	1	no	—
32	C₉×#117	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
35	C₉×#107	C₂²	1	2	yes	complemented
36	C₉×#106	C₂²	1	2	yes	complemented
37	C₉×#103	C₂²	1	2	yes	complemented
38	C₉×#102	C₂²	1	2	yes	complemented
39	C₉×#102	C₂²	1	2	yes	complemented
40	C₉×#102	C₂²	1	2	yes	complemented
41	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
44	C₃×#525	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
46	C₃×#483	C₂×C₃	1	1	yes	characteristic
47	C₃×#482	C₂×C₃	1	2	yes	—
48	C₃×#480	C₂×C₃	1	1	yes	characteristic
49	C₃×#469	C₂×C₃	1	2	yes	—
50	C₃×#468	C₂×C₃	1	2	yes	—
51	C₃×#450	C₂×C₃	1	1	yes	characteristic
52	C₃×#449	C₂×C₃	1	2	yes	—
53	C₃×#447	C₂×C₃	1	1	yes	characteristic
54	C₃×#407	C₂×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	—	2	1	no	—
56	C₂⁴×C₉	D₄	1	1	yes	characteristic
57	C₉×#41	—	4	2	no	—
58	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	—	2	2	no	—
63	C₂×D₄×C₉	—	2	2	no	—
64	C₂×D₄×C₉	—	2	1	no	—
65	C₂×D₄×C₉	—	4	2	no	—
66	C₂×D₄×C₉	—	4	4	no	—
67	C₂×D₄×C₉	C₂³	1	2	yes	—
68	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	4	2	no	—
72	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
73	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
74	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₉×SD₁₆	—	4	2	no	—
79	C₉×D₈	—	4	2	no	—
80	C₉×M₁₆	—	4	2	no	—
81	C₂×C₈×C₉	C₂³	1	2	yes	—
82	C₂×C₈×C₉	C₂³	1	2	yes	—
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	—	2	1	no	—
86	C₉×C₄⋊C₄	C₂³	1	2	yes	—
87	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₉×C₂²⋊C₄	—	2	1	no	—
90	C₉×C₂²⋊C₄	—	2	1	no	—
91	C₉×C₂²⋊C₄	—	2	1	no	—
92	C₉×C₂²⋊C₄	—	2	2	no	—
93	C₉×C₂²⋊C₄	—	2	2	no	—
94	C₉×C₂²⋊C₄	—	2	1	no	—
95	C₉×C₂²⋊C₄	—	2	1	no	—
96	C₄²×C₉	—	2	1	no	—
97	#3194	C₉	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃×D₄	—	2	1	no	—
100	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
104	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
105	C₃×#123	—	2	1	no	—
106	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₃×#121	—	2	1	no	—
109	C₃×#121	—	2	1	no	—
110	C₃×#121	C₂²×C₃	1	1	yes	characteristic
111	C₃×#121	C₂²×C₃	1	2	yes	—
112	C₃×#121	C₂²×C₃	1	2	yes	—
113	C₃×#121	C₂²×C₃	1	1	yes	characteristic
114	C₃×#120	—	2	1	no	—
115	C₃×C₄×D₄	—	2	1	no	—
116	C₃×C₄×D₄	—	2	1	no	—
117	C₃×#117	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
120	C₃×#107	C₂²×C₃	1	2	yes	—
121	C₃×#106	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×#102	C₂²×C₃	1	2	yes	—
126	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
128	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
129	C₂³×C₉	—	2	2	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	—	2	2	no	—
132	C₂³×C₉	—	4	1	no	—
133	C₂³×C₉	—	4	1	no	—
134	C₂³×C₉	—	4	2	no	—
135	C₂³×C₉	—	4	2	no	—
136	C₂³×C₉	—	4	2	no	—
137	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
140	Q₈×C₉	—	2	2	no	—
141	D₄×C₉	—	2	2	no	—
142	D₄×C₉	—	2	2	no	—
143	D₄×C₉	—	2	2	no	—
144	D₄×C₉	—	4	2	no	—
145	D₄×C₉	—	4	2	no	—
146	D₄×C₉	—	4	4	no	—
147	D₄×C₉	—	4	4	no	—
148	D₄×C₉	—	4	2	no	—
149	D₄×C₉	—	4	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	4	1	no	—
158	C₂×C₄×C₉	—	4	1	no	—
159	C₂×C₄×C₉	—	4	1	no	—
160	C₂×C₄×C₉	—	4	2	no	—
161	C₂×C₄×C₉	—	4	2	no	—
162	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
166	C₈×C₉	—	2	2	no	—
167	C₈×C₉	—	2	2	no	—
168	#525	C₂×C₉	1	1	yes	characteristic, complemented
169	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
170	#483	C₂×C₉	1	1	yes	characteristic, complemented
171	#482	C₂×C₉	1	2	yes	complemented
172	#480	C₂×C₉	1	1	yes	characteristic, complemented
173	#469	C₂×C₉	1	2	yes	complemented
174	#468	C₂×C₉	1	2	yes	complemented
175	#450	C₂×C₉	1	1	yes	characteristic, complemented
176	#449	C₂×C₉	1	2	yes	complemented
177	#447	C₂×C₉	1	1	yes	characteristic, complemented
178	#407	C₂×C₉	1	1	yes	characteristic, complemented
179	C₂⁴×C₃	—	2	1	no	—
180	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
181	C₃×#41	—	4	2	no	—
182	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	—	2	2	no	—
188	C₂×C₃×D₄	—	2	1	no	—
189	C₂×C₃×D₄	—	4	2	no	—
190	C₂×C₃×D₄	—	4	4	no	—
191	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	4	2	no	—
196	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×SD₁₆	—	4	2	no	—
203	C₃×D₈	—	4	2	no	—
204	C₃×M₁₆	—	4	2	no	—
205	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
206	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
207	C₃×C₄⋊C₄	—	2	1	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
211	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₂²⋊C₄	—	2	1	no	—
215	C₃×C₂²⋊C₄	—	2	1	no	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	2	2	no	—
218	C₃×C₂²⋊C₄	—	2	1	no	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	2	1	no	—
223	C₂²×C₉	—	2	1	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	—	2	1	no	—
226	C₂²×C₉	—	2	1	no	—
227	C₂²×C₉	—	2	1	no	—
228	C₂²×C₉	—	2	1	no	—
229	C₂²×C₉	—	4	4	no	—
230	C₂²×C₉	—	4	1	no	—
231	C₂²×C₉	—	4	2	no	—
232	C₂²×C₉	—	4	2	no	—
233	C₂²×C₉	—	4	1	no	—
234	C₂²×C₉	—	4	1	no	—
235	C₂²×C₉	—	4	2	no	—
236	C₂²×C₉	—	8	4	no	—
237	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
238	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	—	2	1	no	—
241	C₄×C₉	—	2	1	no	—
242	C₄×C₉	—	4	1	no	—
243	C₄×C₉	—	4	2	no	—
244	C₄×C₉	—	4	1	no	—
245	C₄×C₉	—	4	1	no	—
246	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
247	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
250	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
252	C₂×D₈	C₂²×C₉	1	2	yes	complemented
253	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
254	#123	—	2	1	no	—
255	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
256	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	C₂²×C₉	1	2	yes	—
260	#121	C₂²×C₉	1	2	yes	—
261	#121	C₂²×C₉	1	1	yes	characteristic
262	#121	C₂²×C₉	1	1	yes	characteristic, complemented
263	#120	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	#117	C₂²×C₉	1	1	yes	characteristic, complemented
267	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	#107	C₂²×C₉	1	2	yes	complemented
270	#106	C₂²×C₉	1	2	yes	complemented
271	#103	C₂²×C₉	1	2	yes	complemented
272	#102	C₂²×C₉	1	2	yes	complemented
273	#102	C₂²×C₉	1	2	yes	complemented
274	#102	C₂²×C₉	1	2	yes	complemented
275	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
276	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
277	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	1	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	4	1	no	—
282	C₂³×C₃	—	4	1	no	—
283	C₂³×C₃	—	4	2	no	—
284	C₂³×C₃	—	4	2	no	—
285	C₂³×C₃	—	4	2	no	—
286	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
289	C₃×Q₈	—	2	2	no	—
290	C₃×D₄	—	2	2	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	4	2	no	—
294	C₃×D₄	—	4	2	no	—
295	C₃×D₄	—	4	4	no	—
296	C₃×D₄	—	4	4	no	—
297	C₃×D₄	—	4	2	no	—
298	C₃×D₄	—	4	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	1	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	2	no	—
310	C₂×C₃×C₄	—	4	2	no	—
311	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
315	C₃×C₈	—	2	2	no	—
316	C₃×C₈	—	2	2	no	—
317	C₂×C₉	—	2	2	no	—
318	C₂×C₉	—	4	1	no	—
319	C₂×C₉	—	4	1	no	—
320	C₂×C₉	—	8	1	no	—
321	C₂×C₉	—	8	2	no	—
322	C₂×C₉	#534	1	1	yes	characteristic
323	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₂×C₉	#575	1	1	yes	characteristic
325	C₂⁴	—	2	1	no	—
326	C₂⁴	D₄×C₉	1	1	yes	characteristic
327	#41	—	4	2	no	—
328	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	C₂³×C₉	1	2	yes	—
338	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
343	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
344	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
345	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
347	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
348	SD₁₆	—	4	2	no	—
349	D₈	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	C₂×C₈	C₂³×C₉	1	2	yes	—
352	C₂×C₈	C₂³×C₉	1	2	yes	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
357	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
358	C₄⋊C₄	C₂³×C₉	1	2	yes	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₂²×C₃	—	2	1	no	—
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	2	1	no	—
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	4	4	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	4	1	no	—
378	C₂²×C₃	—	4	1	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	1	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	8	4	no	—
383	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
384	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	4	1	no	—
390	C₃×C₄	—	4	1	no	—
391	C₃×C₄	—	4	1	no	—
392	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
393	C₉	#3194	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
403	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
404	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
430	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	4	1	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	—	8	2	no	—
437	C₂×C₃	—	8	1	no	—
438	C₂×C₃	C₃×#534	1	1	yes	characteristic
439	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₃	C₃×#575	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
458	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
467	C₃	C₃×#3194	1	1	yes	characteristic
468	C₂	—	2	2	no	—
469	C₂	—	4	1	no	—
470	C₂	—	4	1	no	—
471	C₂	—	8	2	no	—
472	C₂	—	8	1	no	—
473	C₂	C₉×#534	1	1	yes	characteristic
474	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
475	C₂	C₉×#575	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×#3194	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. C₉×#525	C₂	semidirect
2. C₂×C₉×#121	C₂	semidirect
3. C₉×#483	C₂	semidirect
4. C₉×#482	C₂	semidirect
5. C₉×#480	C₂	semidirect
6. C₉×#469	C₂	semidirect
7. C₉×#468	C₂	semidirect
8. C₉×#450	C₂	semidirect
9. C₉×#449	C₂	semidirect
10. C₉×#447	C₂	semidirect
11. C₉×#407	C₂	semidirect
13. C₂×C₉×#41	C₂²	semidirect
17. C₂×C₉×SD₁₆	C₂²	semidirect
18. C₂×C₉×D₈	C₂²	semidirect
19. C₂×C₉×M₁₆	C₂²	semidirect
22. C₉×C₂²⋊Q₈	C₂²	semidirect
28. C₉×#121	C₂²	semidirect
32. C₉×#117	C₂²	semidirect
35. C₉×#107	C₂²	semidirect
36. C₉×#106	C₂²	semidirect
37. C₉×#103	C₂²	semidirect
38. C₉×#102	C₂²	semidirect
39. C₉×#102	C₂²	semidirect
40. C₉×#102	C₂²	semidirect
43. C₉×C₂²⋊C₈	C₂²	semidirect
97. #3194	C₉	direct (N × H)
168. #525	C₂×C₉	semidirect
169. C₂×#121	C₂×C₉	semidirect
170. #483	C₂×C₉	semidirect
171. #482	C₂×C₉	semidirect
172. #480	C₂×C₉	semidirect
173. #469	C₂×C₉	semidirect
174. #468	C₂×C₉	semidirect
175. #450	C₂×C₉	semidirect
176. #449	C₂×C₉	semidirect
177. #447	C₂×C₉	semidirect
178. #407	C₂×C₉	semidirect
247. C₂×#41	C₂²×C₉	semidirect
251. C₂×SD₁₆	C₂²×C₉	semidirect
252. C₂×D₈	C₂²×C₉	semidirect
253. C₂×M₁₆	C₂²×C₉	semidirect
256. C₂²⋊Q₈	C₂²×C₉	semidirect
262. #121	C₂²×C₉	semidirect
266. #117	C₂²×C₉	semidirect
269. #107	C₂²×C₉	semidirect
270. #106	C₂²×C₉	semidirect
271. #103	C₂²×C₉	semidirect
272. #102	C₂²×C₉	semidirect
273. #102	C₂²×C₉	semidirect
274. #102	C₂²×C₉	semidirect
277. C₂²⋊C₈	C₂²×C₉	semidirect
393. C₉	#3194	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×#525	2
C₂×C₉×#121	2
C₉×#483	2
C₉×#482	2
C₉×#480	2
C₉×#469	2
C₉×#468	2
C₉×#450	2
C₉×#449	2
C₉×#447	2
C₉×#407	2
C₃×#3194	3

Subgroups — C9×#3194 #11767915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3194 #11767915