Subgroups — #11859088

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#3697	C₂	1	1	yes	maximal, characteristic
2	C₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588605	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588521	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588519	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588517	C₂	1	1	yes	maximal, characteristic, complemented
7	D₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10588409	C₂	1	2	yes	maximal
9	#10588400	C₂	1	2	yes	maximal, complemented
10	#10588390	C₂	1	2	yes	maximal, complemented
11	#10588389	C₂	1	2	yes	maximal, complemented
12	#79334	—	3	1	no	maximal
13	C₂×#3697	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₄×#611	C₄	1	1	yes	characteristic
16	C₄×#611	C₄	1	1	yes	characteristic
17	C₄×#611	C₄	1	1	yes	characteristic
18	C₄×#611	C₄	1	1	yes	characteristic
19	#63488	C₂²	1	1	yes	characteristic
20	C₂×#3663	C₂²	1	2	yes	—
21	C₂×C₈×D₉	C₂²	1	2	yes	—
22	C₄×D₃₆	C₄	1	1	yes	characteristic
23	C₄×D₃₆	C₄	1	1	yes	characteristic
24	#63434	C₂²	1	1	yes	characteristic
25	#63434	C₂²	1	1	yes	characteristic
26	C₄²×D₉	C₂²	1	1	yes	characteristic
27	C₄²×D₉	C₂²	1	1	yes	characteristic
28	C₄×Dic₁₈	C₄	1	1	yes	characteristic
29	C₄×Dic₁₈	C₄	1	1	yes	characteristic
30	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₉×#97	C₂²	1	2	yes	—
34	#63389	C₂²	1	2	yes	—
35	(C₂×D₉)⋊C₈	C₂²	1	2	yes	—
36	(C₂×D₉)⋊C₈	C₂²	1	2	yes	—
37	#63375	C₂²	1	2	yes	—
38	Dic₉⋊C₈	C₂²	1	2	yes	—
39	Dic₉⋊C₈	C₂²	1	2	yes	—
40	C₈×Dic₉	C₂²	1	2	yes	—
41	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
42	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
43	C₄×C₉⋊C₈	C₂²	1	2	yes	—
44	C₄×#235	—	3	1	no	—
45	C₃×#432	D₃	1	1	yes	characteristic
46	#4925	—	3	1	no	—
47	#4837	—	3	1	no	—
48	#4835	—	3	1	no	—
49	#4833	—	3	1	no	—
50	D₃×C₄⋊C₈	—	3	1	no	—
51	#4727	—	3	2	no	—
52	#4720	—	3	2	no	—
53	#4709	—	3	2	no	—
54	#4708	—	3	2	no	—
55	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×#611	C₂×C₄	1	1	yes	characteristic
59	C₂×#611	C₂×C₄	1	1	yes	characteristic
60	#3697	—	2	2	no	—
61	#3697	—	2	2	no	—
62	C₂×D₃₆	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
69	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
73	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
74	C₄²×C₉	C₂³	1	1	yes	characteristic
75	C₄²×C₉	C₂³	1	1	yes	characteristic
76	#3676	C₂×C₄	1	1	yes	characteristic
77	#3676	C₂×C₄	1	1	yes	characteristic
78	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
83	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
84	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
85	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
86	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
87	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₉	C₂³	1	1	yes	characteristic
93	C₄×Dic₉	C₂³	1	1	yes	characteristic
94	C₂×C₉⋊C₈	C₂³	1	2	yes	—
95	C₂×C₉⋊C₈	C₂³	1	2	yes	—
96	#3663	—	2	4	no	—
97	C₈×D₉	—	2	4	no	—
98	#2925	—	9	1	no	Sylow
99	C₂×#235	—	3	1	no	—
100	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
101	C₄×#67	—	3	1	no	—
102	C₄×#67	—	3	1	no	—
103	C₄×#67	—	3	1	no	—
104	C₄×#67	—	3	1	no	—
105	#926	—	3	1	no	—
106	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
107	C₂×D₃×C₈	—	3	2	no	—
108	C₄×D₁₂	—	3	1	no	—
109	C₄×D₁₂	—	3	1	no	—
110	#872	—	3	1	no	—
111	#872	—	3	1	no	—
112	C₄²×D₃	—	3	1	no	—
113	C₄²×D₃	—	3	1	no	—
114	C₄×Dic₆	—	3	1	no	—
115	C₄×Dic₆	—	3	1	no	—
116	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
117	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
118	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
119	C₃×#97	C₂×D₃	1	2	yes	—
120	#830	—	3	2	no	—
121	(C₂×D₃)⋊C₈	—	3	2	no	—
122	(C₂×D₃)⋊C₈	—	3	2	no	—
123	#815	—	3	2	no	—
124	Dic₃⋊C₈	—	3	2	no	—
125	Dic₃⋊C₈	—	3	2	no	—
126	C₈×Dic₃	—	3	2	no	—
127	C₄⋊(C₃⋊C₈)	—	3	1	no	—
128	C₄⋊(C₃⋊C₈)	—	3	1	no	—
129	C₄×C₃⋊C₈	—	3	2	no	—
130	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	4	1	no	—
137	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
143	#611	—	2	2	no	—
144	#611	—	2	2	no	—
145	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
151	D₃₆	—	2	2	no	—
152	C₄×D₉	—	2	2	no	—
153	C₄×D₉	—	2	2	no	—
154	C₄×D₉	—	2	1	no	—
155	C₄×D₉	—	2	1	no	—
156	C₄×D₉	—	4	1	no	—
157	C₄×D₉	—	4	1	no	—
158	C₄×D₉	#41	1	2	yes	—
159	C₄×D₉	#41	1	2	yes	—
160	Dic₁₈	—	2	2	no	—
161	C₈×C₉	—	2	2	no	—
162	C₈×C₉	—	2	2	no	—
163	C₉⋊C₈	—	2	2	no	—
164	C₉⋊C₈	—	2	2	no	—
165	C₄×#41	—	9	1	no	—
166	#433	—	9	2	no	—
167	#433	—	9	2	no	—
168	#432	—	9	1	no	—
169	#432	D₉	1	1	yes	characteristic, complemented
170	#431	—	9	1	no	—
171	#431	—	9	1	no	—
172	#423	—	9	1	no	—
173	C₂×C₄⋊C₈	—	9	1	no	—
174	#408	—	9	2	no	—
175	#405	—	9	2	no	—
176	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
179	C₂×#67	—	3	1	no	—
180	C₂×#67	—	3	1	no	—
181	#235	—	6	2	no	—
182	#235	—	6	2	no	—
183	C₂×D₁₂	—	3	1	no	—
184	C₂×C₄×D₃	—	3	1	no	—
185	C₂×C₄×D₃	—	3	1	no	—
186	C₂×C₄×D₃	—	3	1	no	—
187	C₂×C₄×D₃	—	3	1	no	—
188	C₂×C₄×D₃	—	3	1	no	—
189	C₂×C₄×D₃	—	3	1	no	—
190	C₂×Dic₆	—	3	1	no	—
191	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
192	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
193	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
194	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
195	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
196	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
197	#217	—	3	1	no	—
198	#217	—	3	1	no	—
199	(C₂×D₃)⋊C₄	—	3	1	no	—
200	(C₂×D₃)⋊C₄	—	3	1	no	—
201	(C₂×D₃)⋊C₄	—	3	1	no	—
202	(C₂×D₃)⋊C₄	—	3	1	no	—
203	C₄⋊Dic₃	—	3	1	no	—
204	C₄⋊Dic₃	—	3	1	no	—
205	Dic₃⋊C₄	—	3	1	no	—
206	Dic₃⋊C₄	—	3	1	no	—
207	Dic₃⋊C₄	—	3	1	no	—
208	Dic₃⋊C₄	—	3	1	no	—
209	C₄×Dic₃	—	3	1	no	—
210	C₄×Dic₃	—	3	1	no	—
211	C₄×Dic₃	—	3	1	no	—
212	C₄×Dic₃	—	3	1	no	—
213	C₄×Dic₃	—	3	1	no	—
214	C₄×Dic₃	—	3	1	no	—
215	C₂×C₃⋊C₈	—	3	2	no	—
216	C₂×C₃⋊C₈	—	3	2	no	—
217	ΓL(1,𝔽₂₅)	—	6	4	no	—
218	D₃×C₈	—	6	4	no	—
219	C₂²×C₉	—	2	1	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
223	C₂×D₉	—	2	1	no	—
224	C₂×D₉	—	2	1	no	—
225	C₂×D₉	—	2	1	no	—
226	C₂×D₉	—	2	1	no	—
227	C₂×D₉	—	2	1	no	—
228	C₂×D₉	#117	1	2	yes	—
229	C₄×C₉	—	2	1	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	#131	1	2	yes	—
234	C₄×C₉	C₂×#41	1	1	yes	characteristic
235	C₄×C₉	C₂×#41	1	1	yes	characteristic
236	Dic₉	—	2	1	no	—
237	Dic₉	—	2	1	no	—
238	Dic₉	—	2	1	no	—
239	Dic₉	—	2	1	no	—
240	Dic₉	—	2	1	no	—
241	Dic₉	#117	1	2	yes	—
242	C₂×#41	—	9	1	no	—
243	C₂×M₁₆	—	9	2	no	—
244	C₂²×C₈	—	9	2	no	—
245	C₄×Q₈	—	9	1	no	—
246	C₄×Q₈	—	9	1	no	—
247	C₄×D₄	—	9	1	no	—
248	C₄×D₄	—	9	1	no	—
249	C₄×D₄	—	9	1	no	—
250	C₄×D₄	—	9	1	no	—
251	C₄×D₄	—	9	1	no	—
252	C₄×D₄	—	9	1	no	—
253	#117	—	9	1	no	—
254	#117	—	9	1	no	—
255	#117	—	9	1	no	—
256	C₂×C₄²	—	9	1	no	—
257	C₂×C₄²	—	9	1	no	—
258	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
259	C₄⋊C₈	—	9	2	no	—
260	C₄⋊C₈	—	9	2	no	—
261	C₄⋊C₈	—	9	1	no	—
262	C₄⋊C₈	—	9	1	no	—
263	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
264	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
265	C₂²⋊C₈	—	9	2	no	—
266	C₂²⋊C₈	—	9	2	no	—
267	C₂²⋊C₈	—	9	2	no	—
268	C₂²⋊C₈	C₂×D₉	1	2	yes	—
269	#97	—	9	2	no	—
270	#97	C₂×D₉	1	2	yes	—
271	C₄×C₈	—	9	2	no	—
272	C₄×C₈	—	9	2	no	—
273	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
274	C₂²×D₃	—	3	1	no	—
275	C₂²×D₃	—	3	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
286	#67	—	6	2	no	—
287	#67	—	6	2	no	—
288	C₂×Dic₃	—	3	1	no	—
289	C₂×Dic₃	—	3	1	no	—
290	C₂×Dic₃	—	3	1	no	—
291	C₂×Dic₃	—	3	1	no	—
292	C₂×Dic₃	—	3	1	no	—
293	C₂×Dic₃	—	3	1	no	—
294	D₁₂	—	6	2	no	—
295	C₄×D₃	—	3	2	no	—
296	C₄×D₃	—	3	2	no	—
297	C₄×D₃	—	6	2	no	—
298	C₄×D₃	—	6	2	no	—
299	C₄×D₃	—	6	1	no	—
300	C₄×D₃	—	6	1	no	—
301	C₄×D₃	—	12	1	no	—
302	C₄×D₃	—	12	1	no	—
303	Dic₆	—	6	2	no	—
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	—	2	2	no	—
306	C₃⋊C₈	—	6	2	no	—
307	C₃⋊C₈	—	6	2	no	—
308	C₂×C₉	—	4	1	no	—
309	C₂×C₉	C₂×#117	1	1	yes	characteristic
310	C₂×C₉	C₂×#131	1	1	yes	characteristic
311	C₂×C₉	#568	1	1	yes	characteristic
312	D₉	—	2	2	no	—
313	D₉	—	4	1	no	—
314	#41	—	18	2	no	—
315	#41	—	18	2	no	—
316	C₂×Q₈	—	9	1	no	—
317	C₂×D₄	—	9	1	no	—
318	C₂×D₄	—	9	1	no	—
319	C₂×D₄	—	9	1	no	—
320	C₂²×C₄	—	9	1	no	—
321	C₂²×C₄	—	9	1	no	—
322	C₂²×C₄	—	9	1	no	—
323	C₂²×C₄	—	9	1	no	—
324	C₂²×C₄	—	9	1	no	—
325	C₂²×C₄	—	9	1	no	—
326	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
327	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
329	M₁₆	—	18	4	no	—
330	C₂×C₈	—	9	2	no	—
331	C₂×C₈	—	9	2	no	—
332	C₂×C₈	—	18	4	no	—
333	C₂×C₈	C₂²×D₉	1	2	yes	—
334	C₂×C₈	C₂²×D₉	1	2	yes	—
335	C₄⋊C₄	—	9	1	no	—
336	C₄⋊C₄	—	9	1	no	—
337	C₄⋊C₄	—	9	1	no	—
338	C₄⋊C₄	—	9	1	no	—
339	C₄⋊C₄	—	9	1	no	—
340	C₄⋊C₄	—	9	1	no	—
341	C₂²⋊C₄	—	9	1	no	—
342	C₂²⋊C₄	—	9	1	no	—
343	C₂²⋊C₄	—	9	1	no	—
344	C₂²⋊C₄	—	9	1	no	—
345	C₂²⋊C₄	—	9	1	no	—
346	C₂²⋊C₄	—	9	1	no	—
347	C₄²	—	9	1	no	—
348	C₄²	—	9	1	no	—
349	C₄²	—	9	1	no	—
350	C₄²	—	9	1	no	—
351	C₄²	—	9	1	no	—
352	C₄²	—	9	1	no	—
353	C₄²	C₄×D₉	1	1	yes	characteristic
354	C₄²	C₄×D₉	1	1	yes	characteristic
355	C₄²	C₂²×D₉	1	1	yes	characteristic
356	C₄²	C₂²×D₉	1	1	yes	characteristic
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
361	C₂×D₃	—	3	2	no	—
362	C₂×D₃	—	6	1	no	—
363	C₂×D₃	—	6	1	no	—
364	C₂×D₃	—	6	1	no	—
365	C₂×D₃	—	6	1	no	—
366	C₂×D₃	—	6	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	#907	1	2	yes	—
372	C₃×C₄	D₃×#41	1	1	yes	characteristic
373	C₃×C₄	D₃×#41	1	1	yes	characteristic
374	Dic₃	—	3	2	no	—
375	Dic₃	—	6	1	no	—
376	Dic₃	—	6	1	no	—
377	Dic₃	—	6	1	no	—
378	Dic₃	—	6	1	no	—
379	Dic₃	—	6	1	no	—
380	C₉	#2925	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	9	1	no	—
382	C₂³	—	9	1	no	—
383	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
384	Q₈	—	18	2	no	—
385	D₄	—	18	2	no	—
386	D₄	—	18	2	no	—
387	D₄	—	18	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	9	1	no	—
393	C₂×C₄	—	9	2	no	—
394	C₂×C₄	—	9	2	no	—
395	C₂×C₄	—	9	1	no	—
396	C₂×C₄	—	9	1	no	—
397	C₂×C₄	—	9	1	no	—
398	C₂×C₄	—	9	1	no	—
399	C₂×C₄	—	9	1	no	—
400	C₂×C₄	—	18	1	no	—
401	C₂×C₄	—	18	1	no	—
402	C₂×C₄	—	18	2	no	—
403	C₂×C₄	—	18	2	no	—
404	C₂×C₄	—	36	1	no	—
405	C₂×C₄	—	36	1	no	—
406	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	18	2	no	—
415	C₈	—	18	2	no	—
416	C₂×C₃	—	4	1	no	—
417	C₂×C₃	D₃×#117	1	1	yes	characteristic
418	C₂×C₃	C₂×#907	1	1	yes	characteristic
419	C₂×C₃	#5745	1	1	yes	characteristic
420	D₃	—	6	2	no	—
421	D₃	—	12	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	9	2	no	—
426	C₂²	—	18	1	no	—
427	C₂²	—	18	1	no	—
428	C₂²	—	18	1	no	—
429	C₂²	—	18	1	no	—
430	C₂²	—	18	1	no	—
431	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	9	2	no	—
437	C₄	—	18	1	no	—
438	C₄	—	18	1	no	—
439	C₄	—	18	1	no	—
440	C₄	—	18	1	no	—
441	C₄	—	18	1	no	—
442	C₄	#63469	1	2	yes	—
443	C₄	#41×D₉	1	1	yes	characteristic
444	C₄	#41×D₉	1	1	yes	characteristic
445	C₃	#79334	1	1	yes	characteristic
446	C₂	—	4	1	no	—
447	C₂	—	18	2	no	—
448	C₂	—	36	1	no	—
449	C₂	D₉×#117	1	1	yes	characteristic
450	C₂	C₂×#63469	1	1	yes	characteristic
451	C₂	#10589847	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#432	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	C₂×#3697	C₂²
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#432	D₉
hypocenter	C₉	#2925
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
2. C₉×#432	C₂	semidirect
3. #10588605	C₂	semidirect
4. #10588521	C₂	semidirect
5. #10588519	C₂	semidirect
6. #10588517	C₂	semidirect
7. D₉×C₄⋊C₈	C₂	semidirect
9. #10588400	C₂	semidirect
10. #10588390	C₂	semidirect
11. #10588389	C₂	semidirect
169. #432	D₉	semidirect
380. C₉	#2925	semidirect

Maximal subgroups

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

subgroup	index
C₄×#3697	2
C₉×#432	2
#10588605	2
#10588521	2
#10588519	2
#10588517	2
D₉×C₄⋊C₈	2
#10588409	2
#10588400	2
#10588390	2
#10588389	2
#79334	3