Subgroups — C₉×#3285 #11768006

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 411 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#548	C₂	1	2	yes	maximal, complemented
4	C₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	2	yes	maximal, complemented
8	C₉×#452	C₂	1	2	yes	maximal, complemented
9	C₉×#448	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3285	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂²×Q₈×C₉	C₂²	1	2	yes	—
15	C₉×#135	—	2	4	no	—
16	C₂×C₉×Q₁₆	—	2	4	no	—
17	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
21	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
22	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
25	C₉×#124	—	2	2	no	—
26	C₉×#124	C₂²	1	2	yes	—
27	C₉×C₂²⋊Q₈	—	2	2	no	—
28	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₉×#121	—	2	2	no	—
30	C₉×#121	C₂²	1	2	yes	—
31	C₄×Q₈×C₉	C₂²	1	2	yes	—
32	C₄×D₄×C₉	—	2	2	no	—
33	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
34	C₉×#107	C₂²	1	1	yes	characteristic
35	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₉×#103	C₂²	1	2	yes	—
37	C₉×#103	C₂²	1	2	yes	—
38	C₉×#102	C₂²	1	2	yes	—
39	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
42	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
43	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic
44	C₃×#548	C₂×C₃	1	2	yes	—
45	C₃×#495	C₂×C₃	1	1	yes	characteristic
46	C₃×#467	C₂×C₃	1	1	yes	characteristic
47	C₃×#466	C₂×C₃	1	1	yes	characteristic
48	C₃×#464	C₂×C₃	1	2	yes	—
49	C₃×#452	C₂×C₃	1	2	yes	—
50	C₃×#448	C₂×C₃	1	2	yes	—
51	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic
52	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic
53	C₉×#41	—	2	4	no	—
54	C₉×#41	—	4	2	no	—
55	C₂×Q₈×C₉	—	2	2	no	—
56	C₂×Q₈×C₉	—	2	4	no	—
57	C₂×Q₈×C₉	—	4	2	no	—
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×Q₈×C₉	C₂³	1	2	yes	—
60	C₂×D₄×C₉	—	2	2	no	—
61	C₂×D₄×C₉	—	2	2	no	—
62	C₂×D₄×C₉	D₄	1	1	yes	characteristic
63	C₂×D₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	—	2	2	no	—
65	C₂²×C₄×C₉	—	2	2	no	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×Q₁₆	—	2	4	no	—
69	C₉×Q₁₆	—	2	2	no	—
70	C₉×Q₁₆	D₄	1	4	yes	complemented
71	C₉×SD₁₆	—	2	4	no	—
72	C₉×SD₁₆	—	4	2	no	—
73	C₉×D₈	—	2	2	no	—
74	C₂×C₈×C₉	—	2	2	no	—
75	C₂×C₈×C₉	—	2	2	no	—
76	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
77	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
78	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
80	C₉×C₄⋊C₄	—	2	2	no	—
81	C₉×C₄⋊C₄	—	2	2	no	—
82	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₉×C₄⋊C₄	C₂³	1	2	yes	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	—	2	2	no	—
87	C₉×C₂²⋊C₄	—	2	2	no	—
88	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
89	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₄²×C₉	—	2	2	no	—
91	C₄²×C₉	C₂³	1	1	yes	characteristic
92	#3285	C₉	1	1	yes	characteristic, direct product factor, Sylow
93	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
95	C₃×#135	—	2	4	no	—
96	C₂×C₃×Q₁₆	—	2	4	no	—
97	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
98	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
105	C₃×#124	—	2	2	no	—
106	C₃×#124	C₂²×C₃	1	2	yes	—
107	C₃×C₂²⋊Q₈	—	2	2	no	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
109	C₃×#121	—	2	2	no	—
110	C₃×#121	C₂²×C₃	1	2	yes	—
111	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
112	C₃×C₄×D₄	—	2	2	no	—
113	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
114	C₃×#107	C₂²×C₃	1	1	yes	characteristic
115	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₃×#103	C₂²×C₃	1	2	yes	—
117	C₃×#103	C₂²×C₃	1	2	yes	—
118	C₃×#102	C₂²×C₃	1	2	yes	—
119	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₂³×C₉	—	2	2	no	—
123	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
125	Q₈×C₉	—	2	2	no	—
126	Q₈×C₉	—	2	2	no	—
127	Q₈×C₉	—	2	2	no	—
128	Q₈×C₉	—	4	4	no	—
129	Q₈×C₉	C₂×D₄	1	4	yes	—
130	D₄×C₉	—	2	2	no	—
131	D₄×C₉	—	2	2	no	—
132	D₄×C₉	—	2	2	no	—
133	D₄×C₉	—	4	4	no	—
134	D₄×C₉	—	4	4	no	—
135	C₂×C₄×C₉	—	2	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	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	4	4	no	—
143	C₂×C₄×C₉	—	4	4	no	—
144	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
149	C₈×C₉	—	2	1	no	—
150	C₈×C₉	—	2	1	no	—
151	C₈×C₉	—	2	1	no	—
152	C₈×C₉	C₂×D₄	1	2	yes	—
153	C₂×#135	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂²×Q₁₆	C₂×C₉	1	1	yes	characteristic, complemented
155	#548	C₂×C₉	1	2	yes	complemented
156	#495	C₂×C₉	1	1	yes	characteristic, complemented
157	#467	C₂×C₉	1	1	yes	characteristic, complemented
158	#466	C₂×C₉	1	1	yes	characteristic, complemented
159	#464	C₂×C₉	1	2	yes	complemented
160	#452	C₂×C₉	1	2	yes	complemented
161	#448	C₂×C₉	1	2	yes	complemented
162	C₄×Q₁₆	C₂×C₉	1	1	yes	characteristic, complemented
163	C₈×D₄	C₂×C₉	1	1	yes	characteristic, complemented
164	C₃×#41	—	2	4	no	—
165	C₃×#41	—	4	2	no	—
166	C₂×C₃×Q₈	—	2	2	no	—
167	C₂×C₃×Q₈	—	2	4	no	—
168	C₂×C₃×Q₈	—	4	2	no	—
169	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
170	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
174	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₃×Q₁₆	—	2	4	no	—
180	C₃×Q₁₆	—	2	2	no	—
181	C₃×Q₁₆	C₃×D₄	1	4	yes	—
182	C₃×SD₁₆	—	2	4	no	—
183	C₃×SD₁₆	—	4	2	no	—
184	C₃×D₈	—	2	2	no	—
185	C₂×C₃×C₈	—	2	2	no	—
186	C₂×C₃×C₈	—	2	2	no	—
187	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
195	C₃×C₂²⋊C₄	—	2	2	no	—
196	C₃×C₂²⋊C₄	—	2	2	no	—
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₂²⋊C₄	—	2	2	no	—
199	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
201	C₃×C₄²	—	2	2	no	—
202	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	4	2	no	—
209	C₂²×C₉	—	4	2	no	—
210	C₂²×C₉	—	4	2	no	—
211	C₂²×C₉	#135	1	2	yes	complemented
212	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	4	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	2	1	no	—
218	C₄×C₉	—	4	2	no	—
219	C₄×C₉	—	4	2	no	—
220	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
221	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×#41	C₂²×C₉	1	2	yes	—
223	C₂²×Q₈	C₂²×C₉	1	2	yes	—
224	#135	—	2	4	no	—
225	C₂×Q₁₆	—	2	4	no	—
226	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
227	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
228	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
229	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
230	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
231	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
232	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
233	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
234	#124	—	2	2	no	—
235	#124	C₂²×C₉	1	2	yes	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
238	#121	—	2	2	no	—
239	#121	C₂²×C₉	1	2	yes	—
240	C₄×Q₈	C₂²×C₉	1	2	yes	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
243	#107	C₂²×C₉	1	1	yes	characteristic
244	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
245	#103	C₂²×C₉	1	2	yes	—
246	#103	C₂²×C₉	1	2	yes	—
247	#102	C₂²×C₉	1	2	yes	—
248	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
249	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
250	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
251	C₂³×C₃	—	2	2	no	—
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	—	2	2	no	—
257	C₃×Q₈	—	4	4	no	—
258	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
259	C₃×D₄	—	2	2	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	—	2	2	no	—
262	C₃×D₄	—	4	4	no	—
263	C₃×D₄	—	4	4	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	1	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	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	4	4	no	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
278	C₃×C₈	—	2	1	no	—
279	C₃×C₈	—	2	1	no	—
280	C₃×C₈	—	2	1	no	—
281	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₉	—	2	2	no	—
283	C₂×C₉	—	4	1	no	—
284	C₂×C₉	—	8	2	no	—
285	C₂×C₉	D₄²	1	1	yes	characteristic
286	C₂×C₉	C₂×#135	1	1	yes	characteristic
287	C₂×C₉	#578	1	1	yes	characteristic
288	#41	—	2	4	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂³×C₉	1	2	yes	—
294	C₂×Q₈	C₂³×C₉	1	2	yes	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	D₄×C₉	1	1	yes	characteristic
298	C₂×D₄	C₂³×C₉	1	2	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
303	Q₁₆	—	2	4	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	D₄×C₉	1	4	yes	complemented
306	SD₁₆	—	2	4	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
312	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
313	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
314	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
318	C₄⋊C₄	C₂³×C₉	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
324	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
325	C₄²	—	2	2	no	—
326	C₄²	C₂³×C₉	1	1	yes	characteristic
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	4	2	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	C₃×#135	1	2	yes	—
336	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	2	no	—
344	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
345	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₉	#3285	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
349	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	4	no	—
354	Q₈	C₂×D₄×C₉	1	4	yes	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
370	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
371	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
373	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂×D₄×C₉	1	2	yes	—
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	4	1	no	—
380	C₂×C₃	—	8	2	no	—
381	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
382	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
383	C₂×C₃	C₃×#578	1	1	yes	characteristic
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₉×#135	1	2	yes	complemented
393	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	4	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
402	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
403	C₃	C₃×#3285	1	1	yes	characteristic
404	C₂	—	2	2	no	—
405	C₂	—	4	1	no	—
406	C₂	—	8	2	no	—
407	C₂	D₄²×C₉	1	1	yes	characteristic
408	C₂	C₂×C₉×#135	1	1	yes	characteristic
409	C₂	C₉×#578	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×#3285	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. C₂²×C₉×Q₁₆	C₂	semidirect
3. C₉×#548	C₂	semidirect
4. C₉×#495	C₂	semidirect
5. C₉×#467	C₂	semidirect
6. C₉×#466	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#452	C₂	semidirect
9. C₉×#448	C₂	semidirect
10. C₄×C₉×Q₁₆	C₂	semidirect
11. C₈×D₄×C₉	C₂	semidirect
70. C₉×Q₁₆	D₄	semidirect
92. #3285	C₉	direct (N × H)
153. C₂×#135	C₂×C₉	semidirect
154. C₂²×Q₁₆	C₂×C₉	semidirect
155. #548	C₂×C₉	semidirect
156. #495	C₂×C₉	semidirect
157. #467	C₂×C₉	semidirect
158. #466	C₂×C₉	semidirect
159. #464	C₂×C₉	semidirect
160. #452	C₂×C₉	semidirect
161. #448	C₂×C₉	semidirect
162. C₄×Q₁₆	C₂×C₉	semidirect
163. C₈×D₄	C₂×C₉	semidirect
211. C₂²×C₉	#135	semidirect
305. Q₁₆	D₄×C₉	semidirect
346. C₉	#3285	direct (N × H)
392. C₂²	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
C₂²×C₉×Q₁₆	2
C₉×#548	2
C₉×#495	2
C₉×#467	2
C₉×#466	2
C₉×#464	2
C₉×#452	2
C₉×#448	2
C₄×C₉×Q₁₆	2
C₈×D₄×C₉	2
C₃×#3285	3

Subgroups — C9×#3285 #11768006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3285 #11768006