Subgroups — C₉×#3284 #11768005

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#135	C₂	1	2	yes	maximal, complemented
2	C₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#465	C₂	1	2	yes	maximal, complemented
6	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#452	C₂	1	2	yes	maximal, complemented
9	C₉×#449	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3284	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂×C₉×#41	C₂²	1	2	yes	—
15	C₉×#135	—	2	8	no	—
16	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₉×D₈	C₂²	1	2	yes	—
21	C₂²×C₈×C₉	C₂²	1	2	yes	—
22	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₉×#127	—	2	1	no	—
24	C₉×#127	C₂²	1	1	yes	characteristic
25	C₉×#123	—	2	2	no	—
26	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₉×#121	—	2	1	no	—
28	C₉×#121	—	2	2	no	—
29	C₉×#121	C₂²	1	2	yes	—
30	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₉	—	2	1	no	—
32	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₄⋊C₄	—	2	1	no	—
35	C₉×#106	C₂²	1	1	yes	characteristic
36	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₉×#103	C₂²	1	1	yes	characteristic
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#102	C₂²	1	1	yes	characteristic
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
43	C₂×C₃×#135	C₂×C₃	1	2	yes	—
44	C₃×#550	C₂×C₃	1	1	yes	characteristic
45	C₃×#547	C₂×C₃	1	1	yes	characteristic
46	C₃×#492	C₂×C₃	1	1	yes	characteristic
47	C₃×#465	C₂×C₃	1	2	yes	—
48	C₃×#462	C₂×C₃	1	1	yes	characteristic
49	C₃×#459	C₂×C₃	1	1	yes	characteristic
50	C₃×#452	C₂×C₃	1	2	yes	—
51	C₃×#449	C₂×C₃	1	2	yes	—
52	C₃×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic
53	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic
54	C₉×#41	—	2	4	no	—
55	C₉×#41	—	2	4	no	—
56	C₉×#41	—	4	2	no	—
57	C₉×#41	—	4	2	no	—
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
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	1	no	—
64	C₂×D₄×C₉	—	2	1	no	—
65	C₂×D₄×C₉	D₄	1	1	yes	characteristic
66	C₂×D₄×C₉	C₂³	1	2	yes	—
67	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	—	2	1	no	—
69	C₂²×C₄×C₉	—	2	2	no	—
70	C₂²×C₄×C₉	—	2	2	no	—
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₉×Q₁₆	—	2	4	no	—
73	C₉×SD₁₆	—	2	4	no	—
74	C₉×SD₁₆	—	4	2	no	—
75	C₉×SD₁₆	D₄	1	4	yes	complemented
76	C₉×D₈	—	2	4	no	—
77	C₂×C₈×C₉	—	2	4	no	—
78	C₂×C₈×C₉	C₂³	1	2	yes	—
79	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	—	2	1	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	—	2	2	no	—
90	C₉×C₂²⋊C₄	—	2	1	no	—
91	C₉×C₂²⋊C₄	D₄	1	2	yes	—
92	C₄²×C₉	—	2	1	no	—
93	C₄²×C₉	C₂³	1	1	yes	characteristic
94	#3284	C₉	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
96	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
97	C₃×#135	—	2	8	no	—
98	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
103	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
104	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₃×#127	—	2	1	no	—
106	C₃×#127	C₂²×C₃	1	1	yes	characteristic
107	C₃×#123	—	2	2	no	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
109	C₃×#121	—	2	1	no	—
110	C₃×#121	—	2	2	no	—
111	C₃×#121	C₂²×C₃	1	2	yes	—
112	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×D₄	—	2	1	no	—
114	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	—	2	1	no	—
117	C₃×#106	C₂²×C₃	1	1	yes	characteristic
118	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₃×#103	C₂²×C₃	1	1	yes	characteristic
120	C₃×#103	C₂²×C₃	1	2	yes	—
121	C₃×#102	C₂²×C₃	1	1	yes	characteristic
122	C₃×#102	C₂²×C₃	1	2	yes	—
123	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
124	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	C₂×D₄	1	2	yes	—
128	Q₈×C₉	—	2	1	no	—
129	Q₈×C₉	—	2	2	no	—
130	Q₈×C₉	—	2	2	no	—
131	Q₈×C₉	C₂×D₄	1	2	yes	—
132	D₄×C₉	—	2	2	no	—
133	D₄×C₉	—	2	2	no	—
134	D₄×C₉	—	2	1	no	—
135	D₄×C₉	—	2	2	no	—
136	D₄×C₉	—	4	4	no	—
137	D₄×C₉	—	4	4	no	—
138	D₄×C₉	—	4	2	no	—
139	D₄×C₉	—	8	1	no	—
140	D₄×C₉	—	8	2	no	—
141	D₄×C₉	C₂×D₄	1	2	yes	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	4	4	no	—
149	C₂×C₄×C₉	—	4	4	no	—
150	C₂×C₄×C₉	—	4	2	no	—
151	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
155	C₈×C₉	—	2	2	no	—
156	C₈×C₉	—	2	1	no	—
157	C₈×C₉	C₂×D₄	1	2	yes	—
158	C₂×#135	C₂×C₉	1	2	yes	complemented
159	#550	C₂×C₉	1	1	yes	characteristic, complemented
160	#547	C₂×C₉	1	1	yes	characteristic, complemented
161	#492	C₂×C₉	1	1	yes	characteristic, complemented
162	#465	C₂×C₉	1	2	yes	complemented
163	#462	C₂×C₉	1	1	yes	characteristic, complemented
164	#459	C₂×C₉	1	1	yes	characteristic, complemented
165	#452	C₂×C₉	1	2	yes	complemented
166	#449	C₂×C₉	1	2	yes	complemented
167	C₄×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
168	C₈×D₄	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#41	—	2	4	no	—
170	C₃×#41	—	2	4	no	—
171	C₃×#41	—	4	2	no	—
172	C₃×#41	—	4	2	no	—
173	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
174	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	—	2	2	no	—
178	C₂×C₃×D₄	—	2	1	no	—
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
181	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	2	2	no	—
186	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
187	C₃×Q₁₆	—	2	4	no	—
188	C₃×SD₁₆	—	2	4	no	—
189	C₃×SD₁₆	—	4	2	no	—
190	C₃×SD₁₆	C₃×D₄	1	4	yes	—
191	C₃×D₈	—	2	4	no	—
192	C₂×C₃×C₈	—	2	4	no	—
193	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
195	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₄⋊C₄	—	2	1	no	—
200	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
201	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	2	2	no	—
204	C₃×C₂²⋊C₄	—	2	2	no	—
205	C₃×C₂²⋊C₄	—	2	1	no	—
206	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
209	C₂²×C₉	—	2	2	no	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	2	no	—
212	C₂²×C₉	—	2	2	no	—
213	C₂²×C₉	—	4	1	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	2	no	—
216	C₂²×C₉	—	4	2	no	—
217	C₂²×C₉	—	4	2	no	—
218	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	2	2	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	4	2	no	—
223	C₄×C₉	—	4	1	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	#135	1	2	yes	complemented
226	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
227	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×#41	C₂²×C₉	1	2	yes	—
229	C₂×#41	C₂²×C₉	1	2	yes	—
230	#135	—	2	8	no	—
231	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
232	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
233	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
234	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
235	C₂×D₈	C₂²×C₉	1	2	yes	—
236	C₂²×C₈	C₂²×C₉	1	2	yes	—
237	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
238	#127	—	2	1	no	—
239	#127	C₂²×C₉	1	1	yes	characteristic
240	#123	—	2	2	no	—
241	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
242	#121	—	2	1	no	—
243	#121	—	2	2	no	—
244	#121	C₂²×C₉	1	2	yes	—
245	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
248	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	—	2	1	no	—
250	#106	C₂²×C₉	1	1	yes	characteristic
251	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
252	#103	C₂²×C₉	1	1	yes	characteristic
253	#103	C₂²×C₉	1	2	yes	—
254	#102	C₂²×C₉	1	1	yes	characteristic
255	#102	C₂²×C₉	1	2	yes	—
256	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
257	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
261	C₃×Q₈	—	2	1	no	—
262	C₃×Q₈	—	2	2	no	—
263	C₃×Q₈	—	2	2	no	—
264	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
265	C₃×D₄	—	2	2	no	—
266	C₃×D₄	—	2	2	no	—
267	C₃×D₄	—	2	1	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	4	4	no	—
270	C₃×D₄	—	4	4	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	8	1	no	—
273	C₃×D₄	—	8	2	no	—
274	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	4	4	no	—
282	C₂×C₃×C₄	—	4	4	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	2	1	no	—
290	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
291	C₂×C₉	—	4	2	no	—
292	C₂×C₉	—	4	2	no	—
293	C₂×C₉	—	8	2	no	—
294	C₂×C₉	D₄²	1	1	yes	characteristic
295	C₂×C₉	C₂×#135	1	1	yes	characteristic
296	C₂×C₉	#577	1	1	yes	characteristic
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	4	2	no	—
300	#41	—	4	2	no	—
301	C₂×Q₈	C₂³×C₉	1	2	yes	—
302	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	D₄×C₉	1	1	yes	characteristic
309	C₂×D₄	C₂³×C₉	1	2	yes	—
310	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	C₂³×C₉	1	2	yes	—
315	Q₁₆	—	2	4	no	—
316	SD₁₆	—	2	4	no	—
317	SD₁₆	—	4	2	no	—
318	SD₁₆	D₄×C₉	1	4	yes	complemented
319	D₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
322	C₂×C₈	C₂³×C₉	1	2	yes	—
323	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
329	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	D₄×C₉	1	2	yes	—
335	C₄²	—	2	1	no	—
336	C₄²	C₂³×C₉	1	1	yes	characteristic
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	—	4	1	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	4	1	no	—
351	C₃×C₄	—	4	1	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	C₃×#135	1	2	yes	—
354	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
356	C₉	#3284	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	C₂×D₄×C₉	1	2	yes	—
360	Q₈	—	2	1	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	C₂×D₄×C₉	1	2	yes	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	8	1	no	—
372	D₄	—	8	2	no	—
373	D₄	C₂×D₄×C₉	1	2	yes	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
384	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
385	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
386	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	1	no	—
389	C₈	C₂×D₄×C₉	1	2	yes	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	—	4	2	no	—
392	C₂×C₃	—	8	2	no	—
393	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
394	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
395	C₂×C₃	C₃×#577	1	1	yes	characteristic
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	C₉×#135	1	2	yes	complemented
413	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
414	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
415	C₃	C₃×#3284	1	1	yes	characteristic
416	C₂	—	4	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	8	2	no	—
419	C₂	D₄²×C₉	1	1	yes	characteristic
420	C₂	C₂×C₉×#135	1	1	yes	characteristic
421	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×#3284	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×D₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#135	C₂	semidirect
2. C₉×#550	C₂	semidirect
3. C₉×#547	C₂	semidirect
4. C₉×#492	C₂	semidirect
5. C₉×#465	C₂	semidirect
6. C₉×#462	C₂	semidirect
7. C₉×#459	C₂	semidirect
8. C₉×#452	C₂	semidirect
9. C₉×#449	C₂	semidirect
10. C₄×C₉×SD₁₆	C₂	semidirect
11. C₈×D₄×C₉	C₂	semidirect
75. C₉×SD₁₆	D₄	semidirect
94. #3284	C₉	direct (N × H)
158. C₂×#135	C₂×C₉	semidirect
159. #550	C₂×C₉	semidirect
160. #547	C₂×C₉	semidirect
161. #492	C₂×C₉	semidirect
162. #465	C₂×C₉	semidirect
163. #462	C₂×C₉	semidirect
164. #459	C₂×C₉	semidirect
165. #452	C₂×C₉	semidirect
166. #449	C₂×C₉	semidirect
167. C₄×SD₁₆	C₂×C₉	semidirect
168. C₈×D₄	C₂×C₉	semidirect
225. C₄×C₉	#135	semidirect
318. SD₁₆	D₄×C₉	semidirect
356. C₉	#3284	direct (N × H)
412. C₄	C₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#135	2
C₉×#550	2
C₉×#547	2
C₉×#492	2
C₉×#465	2
C₉×#462	2
C₉×#459	2
C₉×#452	2
C₉×#449	2
C₄×C₉×SD₁₆	2
C₈×D₄×C₉	2
C₃×#3284	3

Subgroups — C9×#3284 #11768005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3284 #11768005