Subgroups — #11861373

Order 1152.

522 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10589680	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588701	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588523	C₂	1	1	yes	maximal, characteristic
5	#10588523	C₂	1	1	yes	maximal, characteristic
6	#10588521	C₂	1	1	yes	maximal, characteristic
7	#10588510	C₂	1	1	yes	maximal, characteristic, complemented
8	#10588510	C₂	1	1	yes	maximal, characteristic, complemented
9	#10588509	C₂	1	1	yes	maximal, characteristic, complemented
10	#10588389	C₂	1	1	yes	maximal, characteristic
11	D₉×#97	C₂	1	1	yes	maximal, characteristic
12	#10588381	C₂	1	1	yes	maximal, characteristic, complemented
13	#10588381	C₂	1	1	yes	maximal, characteristic, complemented
14	#10588371	C₂	1	1	yes	maximal, characteristic
15	#10588359	C₂	1	1	yes	maximal, characteristic, complemented
16	#79959	—	3	1	no	maximal
17	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
18	#63508	C₄	1	1	yes	characteristic
19	#63506	C₄	1	1	yes	characteristic
20	C₂×#3663	C₂²	1	1	yes	characteristic
21	C₂×#3663	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
24	#63459	C₄	1	1	yes	characteristic
25	#63458	C₄	1	1	yes	characteristic
26	#63458	C₄	1	1	yes	characteristic
27	#63451	C₄	1	1	yes	characteristic
28	#63451	C₄	1	1	yes	characteristic
29	#63450	C₄	1	1	yes	characteristic
30	#63434	C₂²	1	1	yes	characteristic
31	#63434	C₂²	1	1	yes	characteristic
32	C₄²×D₉	C₂²	1	1	yes	characteristic
33	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
34	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
35	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
36	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₉×#97	C₂²	1	1	yes	characteristic
40	C₉×#97	C₂²	1	1	yes	characteristic
41	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
42	#63375	C₂²	1	1	yes	characteristic
43	#63375	C₂²	1	1	yes	characteristic
44	#63375	C₂²	1	1	yes	characteristic
45	#63375	C₂²	1	1	yes	characteristic
46	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
47	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
48	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
49	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
50	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
51	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
52	C₈×Dic₉	C₂²	1	1	yes	characteristic
53	C₈×Dic₉	C₂²	1	1	yes	characteristic
54	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
55	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
56	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
57	#63362	C₂²	1	1	yes	characteristic
58	#63362	C₂²	1	1	yes	characteristic
59	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
60	#5578	—	3	1	no	—
61	C₃×#446	D₃	1	1	yes	characteristic
62	#5024	—	3	1	no	—
63	#4839	—	3	1	no	—
64	#4839	—	3	1	no	—
65	#4837	—	3	1	no	—
66	#4831	—	3	1	no	—
67	#4828	—	3	1	no	—
68	#4828	—	3	1	no	—
69	#4708	—	3	1	no	—
70	D₃×#97	—	3	1	no	—
71	#4701	—	3	1	no	—
72	#4701	—	3	1	no	—
73	#4689	—	3	1	no	—
74	#4679	—	3	1	no	—
75	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
79	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
80	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
86	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₄²×C₉	C₂³	1	1	yes	characteristic
90	C₄²×C₉	C₂³	1	1	yes	characteristic
91	C₄²×C₉	C₂³	1	1	yes	characteristic
92	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
97	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
98	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
99	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
100	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
101	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
105	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
106	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
107	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
108	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
110	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
111	C₄×Dic₉	C₂³	1	1	yes	characteristic
112	C₄×Dic₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₉	C₂³	1	1	yes	characteristic
114	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
115	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
118	#3663	—	2	2	no	—
119	#3663	—	2	2	no	—
120	C₈×D₉	—	2	2	no	—
121	C₈×D₉	Q₈	1	4	yes	complemented
122	#2961	—	9	1	no	Sylow
123	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
124	#946	—	3	1	no	—
125	#944	—	3	1	no	—
126	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
127	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
128	C₂×D₃×C₈	—	3	1	no	—
129	C₂×D₃×C₈	—	3	1	no	—
130	#897	—	3	1	no	—
131	#896	—	3	1	no	—
132	#896	—	3	1	no	—
133	#889	—	3	1	no	—
134	#889	—	3	1	no	—
135	#888	—	3	1	no	—
136	#872	—	3	1	no	—
137	#872	—	3	1	no	—
138	C₄²×D₃	—	3	1	no	—
139	C₄×Dic₆	—	3	1	no	—
140	C₄×Dic₆	—	3	1	no	—
141	C₄×Dic₆	—	3	1	no	—
142	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
143	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
144	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
145	C₃×#97	C₂×D₃	1	1	yes	characteristic
146	C₃×#97	C₂×D₃	1	1	yes	characteristic
147	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
148	#815	—	3	1	no	—
149	#815	—	3	1	no	—
150	#815	—	3	1	no	—
151	#815	—	3	1	no	—
152	Dic₃⋊C₈	—	3	1	no	—
153	Dic₃⋊C₈	—	3	1	no	—
154	Dic₃⋊C₈	—	3	1	no	—
155	Dic₃⋊C₈	—	3	1	no	—
156	Dic₃⋊C₈	—	3	1	no	—
157	Dic₃⋊C₈	—	3	1	no	—
158	C₈×Dic₃	—	3	1	no	—
159	C₈×Dic₃	—	3	1	no	—
160	C₄⋊(C₃⋊C₈)	—	3	1	no	—
161	C₄⋊(C₃⋊C₈)	—	3	1	no	—
162	C₄⋊(C₃⋊C₈)	—	3	1	no	—
163	#803	—	3	1	no	—
164	#803	—	3	1	no	—
165	C₄×C₃⋊C₈	—	3	1	no	—
166	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
167	Q₈×C₉	—	4	1	no	—
168	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
177	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
178	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
182	C₄×D₉	—	4	1	no	—
183	C₄×D₉	—	4	1	no	—
184	C₄×D₉	C₂×Q₈	1	2	yes	—
185	C₄×D₉	#41	1	2	yes	—
186	Dic₁₈	—	4	1	no	—
187	Dic₁₈	—	4	1	no	—
188	Dic₁₈	—	4	1	no	—
189	C₈×C₉	—	2	1	no	—
190	C₈×C₉	—	2	1	no	—
191	C₈×C₉	—	2	1	no	—
192	C₈×C₉	C₂×Q₈	1	2	yes	—
193	C₉⋊C₈	—	2	1	no	—
194	C₉⋊C₈	—	2	1	no	—
195	C₉⋊C₈	—	2	1	no	—
196	C₉⋊C₈	C₂×Q₈	1	2	yes	—
197	#533	—	9	1	no	—
198	#446	—	9	1	no	—
199	#446	—	9	1	no	—
200	#446	—	9	1	no	—
201	#446	—	9	1	no	—
202	#446	—	9	1	no	—
203	#446	—	9	1	no	—
204	#446	—	9	1	no	—
205	#446	D₉	1	1	yes	characteristic, complemented
206	#424	—	9	1	no	—
207	#424	—	9	1	no	—
208	#423	—	9	1	no	—
209	#405	—	9	1	no	—
210	#405	—	9	1	no	—
211	C₂×#97	—	9	1	no	—
212	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
213	C₂×C₄×D₃	—	3	1	no	—
214	C₂×C₄×D₃	—	3	1	no	—
215	C₂×C₄×D₃	—	3	1	no	—
216	C₂×Dic₆	—	3	1	no	—
217	C₂×Dic₆	—	3	1	no	—
218	C₂×Dic₆	—	3	1	no	—
219	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
221	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
223	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
224	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
225	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
226	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
227	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
228	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
229	(C₂×D₃)⋊C₄	—	3	1	no	—
230	(C₂×D₃)⋊C₄	—	3	1	no	—
231	(C₂×D₃)⋊C₄	—	3	1	no	—
232	(C₂×D₃)⋊C₄	—	3	1	no	—
233	C₄⋊Dic₃	—	3	1	no	—
234	C₄⋊Dic₃	—	3	1	no	—
235	C₄⋊Dic₃	—	3	1	no	—
236	Dic₃⋊C₄	—	3	1	no	—
237	Dic₃⋊C₄	—	3	1	no	—
238	Dic₃⋊C₄	—	3	1	no	—
239	Dic₃⋊C₄	—	3	1	no	—
240	Dic₃⋊C₄	—	3	1	no	—
241	Dic₃⋊C₄	—	3	1	no	—
242	Dic₃⋊C₄	—	3	1	no	—
243	Dic₃⋊C₄	—	3	1	no	—
244	Dic₃⋊C₄	—	3	1	no	—
245	Dic₃⋊C₄	—	3	1	no	—
246	C₄×Dic₃	—	3	1	no	—
247	C₄×Dic₃	—	3	1	no	—
248	C₄×Dic₃	—	3	1	no	—
249	C₄×Dic₃	—	3	1	no	—
250	C₄×Dic₃	—	3	1	no	—
251	C₂×C₃⋊C₈	—	3	1	no	—
252	C₂×C₃⋊C₈	—	3	1	no	—
253	C₂×C₃⋊C₈	—	3	1	no	—
254	C₂×C₃⋊C₈	—	3	1	no	—
255	ΓL(1,𝔽₂₅)	—	6	2	no	—
256	ΓL(1,𝔽₂₅)	—	6	2	no	—
257	D₃×C₈	—	3	4	no	—
258	D₃×C₈	—	6	2	no	—
259	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
260	C₂×D₉	—	2	1	no	—
261	C₂×D₉	—	2	1	no	—
262	C₂×D₉	C₄×Q₈	1	2	yes	—
263	C₄×C₉	—	2	1	no	—
264	C₄×C₉	—	2	1	no	—
265	C₄×C₉	—	2	1	no	—
266	C₄×C₉	—	2	1	no	—
267	C₄×C₉	—	2	1	no	—
268	C₄×C₉	—	2	1	no	—
269	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
270	C₄×C₉	C₂×#41	1	1	yes	characteristic
271	Dic₉	—	2	1	no	—
272	Dic₉	—	2	1	no	—
273	Dic₉	—	2	1	no	—
274	Dic₉	—	2	1	no	—
275	Dic₉	—	2	1	no	—
276	Dic₉	—	2	1	no	—
277	Dic₉	C₄×Q₈	1	2	yes	—
278	C₂×M₁₆	—	9	1	no	—
279	C₂×M₁₆	—	9	1	no	—
280	C₂²×C₈	—	9	1	no	—
281	C₂²×C₈	—	9	1	no	—
282	C₄⋊Q₈	—	9	1	no	—
283	C₄⋊Q₈	—	9	1	no	—
284	#125	—	9	1	no	—
285	#125	—	9	1	no	—
286	C₂²⋊Q₈	—	9	1	no	—
287	C₂²⋊Q₈	—	9	1	no	—
288	C₂²⋊Q₈	—	9	1	no	—
289	C₂²⋊Q₈	—	9	1	no	—
290	C₄×Q₈	—	9	1	no	—
291	C₄×Q₈	—	9	1	no	—
292	C₄×Q₈	—	9	1	no	—
293	C₄×Q₈	C₂×D₉	1	1	yes	characteristic
294	#117	—	9	1	no	—
295	#117	—	9	1	no	—
296	C₂×C₄²	—	9	1	no	—
297	C₄⋊C₈	—	9	1	no	—
298	C₄⋊C₈	—	9	1	no	—
299	C₄⋊C₈	—	9	1	no	—
300	C₄⋊C₈	—	9	1	no	—
301	C₄⋊C₈	—	9	1	no	—
302	C₄⋊C₈	—	9	1	no	—
303	C₄⋊C₈	—	9	1	no	—
304	C₄⋊C₈	—	9	1	no	—
305	C₄⋊C₈	—	9	1	no	—
306	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
309	#97	—	9	1	no	—
310	#97	—	9	1	no	—
311	#97	—	9	1	no	—
312	#97	—	9	1	no	—
313	#97	—	9	1	no	—
314	#97	—	9	1	no	—
315	#97	C₂×D₉	1	1	yes	characteristic
316	#97	C₂×D₉	1	1	yes	characteristic
317	C₄×C₈	—	9	1	no	—
318	C₄×C₈	—	9	1	no	—
319	C₄×C₈	—	9	1	no	—
320	C₄×C₈	C₂×D₉	1	1	yes	characteristic
321	C₂²×D₃	—	3	1	no	—
322	C₃×Q₈	—	4	1	no	—
323	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
330	C₂×Dic₃	—	3	1	no	—
331	C₂×Dic₃	—	3	1	no	—
332	C₂×Dic₃	—	3	1	no	—
333	C₂×Dic₃	—	3	1	no	—
334	C₂×Dic₃	—	3	1	no	—
335	C₂×Dic₃	—	3	1	no	—
336	C₂×Dic₃	—	3	1	no	—
337	C₄×D₃	—	3	2	no	—
338	C₄×D₃	—	3	2	no	—
339	C₄×D₃	—	12	1	no	—
340	C₄×D₃	—	12	1	no	—
341	Dic₆	—	12	1	no	—
342	Dic₆	—	12	1	no	—
343	Dic₆	—	12	1	no	—
344	C₃×C₈	—	2	1	no	—
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	D₃×Q₈	1	2	yes	—
348	C₃⋊C₈	—	3	2	no	—
349	C₃⋊C₈	—	6	1	no	—
350	C₃⋊C₈	—	6	1	no	—
351	C₃⋊C₈	—	6	1	no	—
352	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
353	C₂×C₉	#568	1	1	yes	characteristic
354	C₂×C₉	#568	1	1	yes	characteristic
355	D₉	—	2	2	no	—
356	C₂×Q₈	—	9	1	no	—
357	C₂×Q₈	—	9	1	no	—
358	C₂×Q₈	—	9	1	no	—
359	C₂×Q₈	C₄×D₉	1	1	yes	characteristic
360	C₂²×C₄	—	9	1	no	—
361	C₂²×C₄	—	9	1	no	—
362	C₂²×C₄	—	9	1	no	—
363	M₁₆	—	18	2	no	—
364	M₁₆	—	18	2	no	—
365	C₂×C₈	—	9	1	no	—
366	C₂×C₈	—	9	4	no	—
367	C₂×C₈	—	9	1	no	—
368	C₂×C₈	—	9	1	no	—
369	C₂×C₈	—	9	1	no	—
370	C₂×C₈	—	18	2	no	—
371	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
372	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
373	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
374	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
375	C₄⋊C₄	—	9	1	no	—
376	C₄⋊C₄	—	9	1	no	—
377	C₄⋊C₄	—	9	1	no	—
378	C₄⋊C₄	—	9	1	no	—
379	C₄⋊C₄	—	9	1	no	—
380	C₄⋊C₄	—	9	1	no	—
381	C₄⋊C₄	—	9	1	no	—
382	C₄⋊C₄	—	9	1	no	—
383	C₄⋊C₄	—	9	1	no	—
384	C₄⋊C₄	—	9	1	no	—
385	C₄⋊C₄	—	9	1	no	—
386	C₄⋊C₄	—	9	1	no	—
387	C₄⋊C₄	—	9	1	no	—
388	C₄⋊C₄	C₄×D₉	1	1	yes	characteristic
389	C₄⋊C₄	C₄×D₉	1	1	yes	characteristic
390	C₄⋊C₄	C₄×D₉	1	1	yes	characteristic
391	C₂²⋊C₄	—	9	1	no	—
392	C₂²⋊C₄	—	9	1	no	—
393	C₂²⋊C₄	—	9	1	no	—
394	C₂²⋊C₄	—	9	1	no	—
395	C₄²	—	9	1	no	—
396	C₄²	—	9	1	no	—
397	C₄²	—	9	1	no	—
398	C₄²	—	9	1	no	—
399	C₄²	—	9	1	no	—
400	C₄²	C₂²×D₉	1	1	yes	characteristic
401	C₄²	C₂²×D₉	1	1	yes	characteristic
402	C₄²	C₂²×D₉	1	1	yes	characteristic
403	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
404	C₂×D₃	—	3	2	no	—
405	C₂×D₃	—	6	1	no	—
406	C₂×D₃	—	6	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
414	C₃×C₄	D₃×#41	1	1	yes	characteristic
415	Dic₃	—	3	2	no	—
416	Dic₃	—	6	1	no	—
417	Dic₃	—	6	1	no	—
418	Dic₃	—	6	1	no	—
419	Dic₃	—	6	1	no	—
420	Dic₃	—	6	1	no	—
421	Dic₃	—	6	1	no	—
422	C₉	#2961	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	9	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	36	1	no	—
426	Q₈	—	36	1	no	—
427	Q₈	—	36	1	no	—
428	C₂×C₄	—	9	1	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	9	2	no	—
431	C₂×C₄	—	9	1	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	1	no	—
434	C₂×C₄	—	9	1	no	—
435	C₂×C₄	—	9	1	no	—
436	C₂×C₄	—	9	1	no	—
437	C₂×C₄	—	36	1	no	—
438	C₂×C₄	—	36	1	no	—
439	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
441	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	9	2	no	—
450	C₈	—	18	1	no	—
451	C₈	—	18	1	no	—
452	C₈	—	18	1	no	—
453	C₈	Q₈×D₉	1	2	yes	—
454	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
455	C₂×C₃	#5745	1	1	yes	characteristic
456	C₂×C₃	#5750	1	1	yes	characteristic
457	D₃	—	6	2	no	—
458	C₂²	—	9	2	no	—
459	C₂²	—	18	1	no	—
460	C₂²	—	18	1	no	—
461	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	9	2	no	—
469	C₄	—	18	1	no	—
470	C₄	—	18	1	no	—
471	C₄	—	18	1	no	—
472	C₄	—	18	1	no	—
473	C₄	—	18	1	no	—
474	C₄	—	18	1	no	—
475	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
476	C₄	#41×D₉	1	1	yes	characteristic
477	C₃	#79959	1	1	yes	characteristic
478	C₂	—	18	2	no	—
479	C₂	C₄×Q₈×D₉	1	1	yes	characteristic
480	C₂	#10589847	1	1	yes	characteristic
481	C₂	#10589852	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×#446	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	C₂²×D₉	C₂²×C₄
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#446	D₉
hypocenter	C₉	#2961
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
3. #10588701	C₂	semidirect
7. #10588510	C₂	semidirect
8. #10588510	C₂	semidirect
9. #10588509	C₂	semidirect
12. #10588381	C₂	semidirect
13. #10588381	C₂	semidirect
15. #10588359	C₂	semidirect
121. C₈×D₉	Q₈	semidirect
205. #446	D₉	semidirect
422. C₉	#2961	semidirect

Maximal subgroups

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

subgroup	index
#10589680	2
C₉×#446	2
#10588701	2
#10588523	2
#10588521	2
#10588510	2
#10588509	2
#10588389	2
D₉×#97	2
#10588381	2
#10588371	2
#10588359	2
#79959	3