Subgroups — D₄×C₉×SD₁₆ #11768002

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×SD₁₆	C₂	1	2	yes	maximal, complemented
2	D₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄²×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#465	C₂	1	2	yes	maximal, complemented
6	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#450	C₂	1	2	yes	maximal, complemented
9	C₉×#448	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×D₄×SD₁₆	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	2	yes	complemented
14	C₂²×D₄×C₉	—	2	1	no	—
15	C₂²×D₄×C₉	C₂²	1	2	yes	—
16	C₂×C₉×SD₁₆	—	2	8	no	—
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
21	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₈×C₉	C₂²	1	2	yes	complemented
23	C₉×C₄⋊Q₈	—	2	1	no	—
24	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₉×#127	C₂²	1	1	yes	characteristic
26	C₉×C₂²⋊Q₈	—	2	2	no	—
27	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₉×#121	—	2	1	no	—
29	C₉×#121	C₂²	1	2	yes	—
30	C₉×#120	—	2	2	no	—
31	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₄×C₉	—	2	1	no	—
33	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
35	C₉×#106	C₂²	1	1	yes	characteristic, complemented
36	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₉×#103	C₂²	1	1	yes	characteristic, complemented
38	C₉×#103	C₂²	1	2	yes	complemented
39	C₉×#102	C₂²	1	1	yes	characteristic
40	C₉×#102	C₂²	1	2	yes	complemented
41	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
42	C₄×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₃×SD₁₆	C₂×C₃	1	2	yes	—
44	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
45	C₃×D₄²	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×#461	C₂×C₃	1	1	yes	characteristic
49	C₃×#460	C₂×C₃	1	1	yes	characteristic
50	C₃×#450	C₂×C₃	1	2	yes	—
51	C₃×#448	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	C₂⁴×C₉	—	2	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	1	yes	characteristic
60	C₂×D₄×C₉	—	2	4	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	—	4	2	no	—
66	C₂×D₄×C₉	—	4	4	no	—
67	C₂×D₄×C₉	D₄	1	1	yes	characteristic
68	C₂×D₄×C₉	C₂³	1	2	yes	—
69	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	—	2	2	no	—
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	C₂³	1	2	yes	—
73	C₉×SD₁₆	—	2	4	no	—
74	C₉×SD₁₆	—	2	4	no	—
75	C₉×SD₁₆	—	2	4	no	—
76	C₉×SD₁₆	—	4	2	no	—
77	C₉×SD₁₆	D₄	1	4	yes	direct product factor
78	C₂×C₈×C₉	—	2	4	no	—
79	C₂×C₈×C₉	C₂³	1	2	yes	—
80	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
82	C₉×C₄⋊C₄	—	2	1	no	—
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	—	2	2	no	—
86	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₉×C₂²⋊C₄	—	2	2	no	—
90	C₉×C₂²⋊C₄	—	2	1	no	—
91	C₉×C₂²⋊C₄	—	2	2	no	—
92	C₉×C₂²⋊C₄	D₄	1	2	yes	—
93	C₄²×C₉	—	2	1	no	—
94	C₄²×C₉	C₂³	1	1	yes	characteristic
95	D₄×SD₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
96	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×D₄	—	2	1	no	—
98	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×SD₁₆	—	2	8	no	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
104	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
105	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
106	C₃×C₄⋊Q₈	—	2	1	no	—
107	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₃×#127	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₂²⋊Q₈	—	2	2	no	—
110	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
111	C₃×#121	—	2	1	no	—
112	C₃×#121	C₂²×C₃	1	2	yes	—
113	C₃×#120	—	2	2	no	—
114	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₃×C₄×D₄	—	2	1	no	—
116	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₃×#106	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×#103	C₂²×C₃	1	1	yes	characteristic
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#102	C₂²×C₃	1	1	yes	characteristic
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
125	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	—	4	4	no	—
129	C₂³×C₉	—	4	4	no	—
130	C₂³×C₉	—	8	2	no	—
131	C₂³×C₉	C₂×D₄	1	2	yes	—
132	Q₈×C₉	—	2	1	no	—
133	Q₈×C₉	—	2	2	no	—
134	Q₈×C₉	—	2	2	no	—
135	Q₈×C₉	—	4	4	no	—
136	Q₈×C₉	C₂×D₄	1	2	yes	complemented
137	D₄×C₉	—	2	2	no	—
138	D₄×C₉	—	2	1	no	—
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	4	4	no	—
141	D₄×C₉	—	4	4	no	—
142	D₄×C₉	—	4	2	no	—
143	D₄×C₉	—	8	1	no	—
144	D₄×C₉	SD₁₆	1	4	yes	direct product factor
145	D₄×C₉	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	4	4	no	—
153	C₂×C₄×C₉	—	4	2	no	—
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
156	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
158	C₈×C₉	—	2	2	no	—
159	C₈×C₉	—	2	1	no	—
160	C₈×C₉	C₂×D₄	1	2	yes	complemented
161	C₂²×SD₁₆	C₂×C₉	1	2	yes	complemented
162	D₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
163	D₄²	C₂×C₉	1	1	yes	characteristic
164	#492	C₂×C₉	1	1	yes	characteristic, complemented
165	#465	C₂×C₉	1	2	yes	complemented
166	#461	C₂×C₉	1	1	yes	characteristic, complemented
167	#460	C₂×C₉	1	1	yes	characteristic, complemented
168	#450	C₂×C₉	1	2	yes	complemented
169	#448	C₂×C₉	1	2	yes	complemented
170	C₄×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
171	C₈×D₄	C₂×C₉	1	1	yes	characteristic, complemented
172	C₂⁴×C₃	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	—	4	2	no	—
176	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
177	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	2	no	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	1	no	—
182	C₂×C₃×D₄	—	2	1	no	—
183	C₂×C₃×D₄	—	4	2	no	—
184	C₂×C₃×D₄	—	4	4	no	—
185	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
186	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
187	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
191	C₃×SD₁₆	—	2	4	no	—
192	C₃×SD₁₆	—	2	4	no	—
193	C₃×SD₁₆	—	2	4	no	—
194	C₃×SD₁₆	—	4	2	no	—
195	C₃×SD₁₆	C₃×D₄	1	4	yes	—
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
199	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	—	2	1	no	—
202	C₃×C₄⋊C₄	—	2	1	no	—
203	C₃×C₄⋊C₄	—	2	2	no	—
204	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	—	2	2	no	—
208	C₃×C₂²⋊C₄	—	2	1	no	—
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₉	—	2	2	no	—
214	C₂²×C₉	—	2	2	no	—
215	C₂²×C₉	—	2	2	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	—	4	1	no	—
218	C₂²×C₉	—	4	2	no	—
219	C₂²×C₉	—	4	2	no	—
220	C₂²×C₉	—	4	2	no	—
221	C₂²×C₉	—	8	8	no	—
222	C₂²×C₉	C₂×SD₁₆	1	4	yes	complemented
223	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
224	C₄×C₉	—	2	2	no	—
225	C₄×C₉	—	2	2	no	—
226	C₄×C₉	—	2	1	no	—
227	C₄×C₉	—	4	2	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	—	4	1	no	—
230	C₄×C₉	C₂×SD₁₆	1	2	yes	complemented
231	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂²×Q₈	C₂²×C₉	1	2	yes	complemented
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂²×C₉	1	2	yes	—
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
238	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
239	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
240	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
241	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
242	C₂²×C₈	C₂²×C₉	1	2	yes	complemented
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
245	#127	C₂²×C₉	1	1	yes	characteristic
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
248	#121	—	2	1	no	—
249	#121	C₂²×C₉	1	2	yes	—
250	#120	—	2	2	no	—
251	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
254	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
255	#106	C₂²×C₉	1	1	yes	characteristic, complemented
256	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
257	#103	C₂²×C₉	1	1	yes	characteristic, complemented
258	#103	C₂²×C₉	1	2	yes	complemented
259	#102	C₂²×C₉	1	1	yes	characteristic
260	#102	C₂²×C₉	1	2	yes	complemented
261	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
262	C₄×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	2	2	no	—
265	C₂³×C₃	—	4	4	no	—
266	C₂³×C₃	—	4	4	no	—
267	C₂³×C₃	—	8	2	no	—
268	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
269	C₃×Q₈	—	2	1	no	—
270	C₃×Q₈	—	2	2	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	4	4	no	—
273	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
274	C₃×D₄	—	2	2	no	—
275	C₃×D₄	—	2	1	no	—
276	C₃×D₄	—	2	2	no	—
277	C₃×D₄	—	4	4	no	—
278	C₃×D₄	—	4	4	no	—
279	C₃×D₄	—	4	2	no	—
280	C₃×D₄	—	8	1	no	—
281	C₃×D₄	C₃×SD₁₆	1	4	yes	—
282	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	4	4	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₉	—	2	4	no	—
299	C₂×C₉	—	4	2	no	—
300	C₂×C₉	—	8	2	no	—
301	C₂×C₉	D₄²	1	1	yes	characteristic
302	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
303	C₂×C₉	#577	1	1	yes	characteristic
304	C₂⁴	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	C₂³×C₉	1	2	yes	—
309	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	D₄×C₉	1	1	yes	characteristic
318	C₂×D₄	C₂³×C₉	1	2	yes	—
319	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂³×C₉	1	2	yes	—
323	SD₁₆	—	2	4	no	—
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	2	4	no	—
326	SD₁₆	—	4	2	no	—
327	SD₁₆	D₄×C₉	1	4	yes	direct product factor
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
330	C₂×C₈	C₂³×C₉	1	2	yes	—
331	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	D₄×C₉	1	2	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	C₂³×C₉	1	1	yes	characteristic
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	8	8	no	—
354	C₂²×C₃	C₂×C₃×SD₁₆	1	4	yes	—
355	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	4	1	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	C₂×C₃×SD₁₆	1	2	yes	—
363	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₉	D₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	8	2	no	—
371	C₂³	C₂×D₄×C₉	1	2	yes	—
372	Q₈	—	2	1	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	C₂×D₄×C₉	1	2	yes	complemented
377	D₄	—	2	2	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	1	no	—
384	D₄	C₉×SD₁₆	1	4	yes	direct product factor
385	D₄	C₂×D₄×C₉	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
396	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	C₂×D₄×C₉	1	2	yes	complemented
401	C₂×C₃	—	2	4	no	—
402	C₂×C₃	—	4	2	no	—
403	C₂×C₃	—	8	2	no	—
404	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
405	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
406	C₂×C₃	C₃×#577	1	1	yes	characteristic
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	8	no	—
416	C₂²	C₂×C₉×SD₁₆	1	4	yes	complemented
417	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	C₂×C₉×SD₁₆	1	2	yes	complemented
425	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
426	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
427	C₃	C₃×D₄×SD₁₆	1	1	yes	characteristic
428	C₂	—	2	4	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	2	no	—
431	C₂	D₄²×C₉	1	1	yes	characteristic
432	C₂	C₂²×C₉×SD₁₆	1	1	yes	characteristic
433	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×D₄²	C₂×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. C₂²×C₉×SD₁₆	C₂	semidirect
2. D₄×Q₈×C₉	C₂	semidirect
4. C₉×#492	C₂	semidirect
5. C₉×#465	C₂	semidirect
6. C₉×#461	C₂	semidirect
7. C₉×#460	C₂	semidirect
8. C₉×#450	C₂	semidirect
9. C₉×#448	C₂	semidirect
10. C₄×C₉×SD₁₆	C₂	semidirect
11. C₈×D₄×C₉	C₂	semidirect
13. C₂²×Q₈×C₉	C₂²	semidirect
19. C₂×C₉×SD₁₆	C₂²	semidirect
20. C₂×C₉×SD₁₆	C₂²	semidirect
21. C₂×C₉×SD₁₆	C₂²	semidirect
22. C₂²×C₈×C₉	C₂²	semidirect
24. C₉×C₄⋊Q₈	C₂²	semidirect
27. C₉×C₂²⋊Q₈	C₂²	semidirect
31. C₄×Q₈×C₉	C₂²	semidirect
35. C₉×#106	C₂²	semidirect
36. C₉×C₄⋊C₈	C₂²	semidirect
37. C₉×#103	C₂²	semidirect
38. C₉×#103	C₂²	semidirect
40. C₉×#102	C₂²	semidirect
41. C₉×C₂²⋊C₈	C₂²	semidirect
42. C₄×C₈×C₉	C₂²	semidirect
77. C₉×SD₁₆	D₄	direct (N × H)
95. D₄×SD₁₆	C₉	direct (N × H)
136. Q₈×C₉	C₂×D₄	semidirect
144. D₄×C₉	SD₁₆	direct (N × H)
160. C₈×C₉	C₂×D₄	semidirect
161. C₂²×SD₁₆	C₂×C₉	semidirect
162. D₄×Q₈	C₂×C₉	semidirect
164. #492	C₂×C₉	semidirect
165. #465	C₂×C₉	semidirect
166. #461	C₂×C₉	semidirect
167. #460	C₂×C₉	semidirect
168. #450	C₂×C₉	semidirect
169. #448	C₂×C₉	semidirect
170. C₄×SD₁₆	C₂×C₉	semidirect
171. C₈×D₄	C₂×C₉	semidirect
222. C₂²×C₉	C₂×SD₁₆	semidirect
230. C₄×C₉	C₂×SD₁₆	semidirect
233. C₂²×Q₈	C₂²×C₉	semidirect
239. C₂×SD₁₆	C₂²×C₉	semidirect
240. C₂×SD₁₆	C₂²×C₉	semidirect
241. C₂×SD₁₆	C₂²×C₉	semidirect
242. C₂²×C₈	C₂²×C₉	semidirect
244. C₄⋊Q₈	C₂²×C₉	semidirect
247. C₂²⋊Q₈	C₂²×C₉	semidirect
251. C₄×Q₈	C₂²×C₉	semidirect
255. #106	C₂²×C₉	semidirect
256. C₄⋊C₈	C₂²×C₉	semidirect
257. #103	C₂²×C₉	semidirect
258. #103	C₂²×C₉	semidirect
260. #102	C₂²×C₉	semidirect
261. C₂²⋊C₈	C₂²×C₉	semidirect
262. C₄×C₈	C₂²×C₉	semidirect
327. SD₁₆	D₄×C₉	direct (N × H)
365. C₉	D₄×SD₁₆	direct (N × H)
376. Q₈	C₂×D₄×C₉	semidirect
384. D₄	C₉×SD₁₆	direct (N × H)
400. C₈	C₂×D₄×C₉	semidirect
416. C₂²	C₂×C₉×SD₁₆	semidirect
424. C₄	C₂×C₉×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×SD₁₆	2
D₄×Q₈×C₉	2
D₄²×C₉	2
C₉×#492	2
C₉×#465	2
C₉×#461	2
C₉×#460	2
C₉×#450	2
C₉×#448	2
C₄×C₉×SD₁₆	2
C₈×D₄×C₉	2
C₃×D₄×SD₁₆	3

Subgroups — D4×C9×SD16 #11768002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₉×SD₁₆ #11768002