Subgroups — #11859509

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#63464	C₂	1	1	yes	maximal, characteristic, complemented
3	#10589650	C₂	1	1	yes	maximal, characteristic
4	C₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588809	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588792	C₂	1	1	yes	maximal, characteristic, complemented
7	#10588688	C₂	1	1	yes	maximal, characteristic, complemented
8	#10588521	C₂	1	1	yes	maximal, characteristic, complemented
9	#10588520	C₂	1	1	yes	maximal, characteristic, complemented
10	#10588412	C₂	1	1	yes	maximal, characteristic, complemented
11	#10588410	C₂	1	1	yes	maximal, characteristic, complemented
12	#10588409	C₂	1	1	yes	maximal, characteristic, complemented
13	#10588409	C₂	1	1	yes	maximal, characteristic, complemented
14	#10588387	C₂	1	1	yes	maximal, characteristic, complemented
15	D₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	#79480	—	3	1	no	maximal
17	C₂×#3697	C₂²	1	1	yes	characteristic
18	C₂×#3697	C₂²	1	1	yes	characteristic
19	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
21	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
22	#63502	C₄	1	1	yes	characteristic
23	#63500	C₄	1	1	yes	characteristic
24	C₄×#611	C₂²	1	1	yes	characteristic
25	C₄×#611	C₂²	1	1	yes	characteristic
26	C₂×#3667	C₂²	1	1	yes	characteristic
27	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
28	#63469	—	2	4	no	—
29	#63464	—	2	4	no	—
30	C₂×#3663	C₂²	1	1	yes	characteristic
31	C₂×#3663	C₂²	1	1	yes	characteristic
32	C₂×#3663	C₂²	1	1	yes	characteristic
33	C₂×#3663	C₂²	1	1	yes	characteristic
34	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
38	#63457	C₄	1	1	yes	characteristic
39	#63450	C₄	1	1	yes	characteristic
40	#63447	C₄	1	1	yes	characteristic
41	#63447	C₄	1	1	yes	characteristic
42	#63446	C₄	1	1	yes	characteristic
43	#63446	C₄	1	1	yes	characteristic
44	C₄×D₃₆	C₂²	1	1	yes	characteristic
45	C₄²×D₉	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₉×#97	C₂²	1	1	yes	characteristic
50	#63389	C₂²	1	1	yes	characteristic
51	#63389	C₂²	1	1	yes	characteristic
52	(C₂×D₉)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₉)⋊C₈	C₂²	1	1	yes	characteristic
54	(C₂×D₉)⋊C₈	C₂²	1	1	yes	characteristic
55	(C₂×D₉)⋊C₈	C₂²	1	1	yes	characteristic
56	#63375	C₂²	1	1	yes	characteristic
57	#63375	C₂²	1	1	yes	characteristic
58	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
59	Dic₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
61	#63362	C₂²	1	1	yes	characteristic
62	C₂×#907	—	3	1	no	—
63	C₂×#901	—	3	1	no	—
64	#5548	—	3	1	no	—
65	C₃×#435	D₃	1	1	yes	characteristic
66	#5127	—	3	1	no	—
67	#5111	—	3	1	no	—
68	#5011	—	3	1	no	—
69	#4837	—	3	1	no	—
70	#4836	—	3	1	no	—
71	#4730	—	3	1	no	—
72	#4728	—	3	1	no	—
73	#4727	—	3	1	no	—
74	#4727	—	3	1	no	—
75	#4706	—	3	1	no	—
76	D₃×#97	—	3	1	no	—
77	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂×#611	C₂×C₄	1	1	yes	characteristic
81	C₂×#611	C₂×C₄	1	1	yes	characteristic
82	C₂×#611	C₂×C₄	1	1	yes	characteristic
83	C₂×#611	C₂×C₄	1	1	yes	characteristic
84	C₂×#611	C₂×C₄	1	1	yes	characteristic
85	C₂×#611	C₂×C₄	1	1	yes	characteristic
86	#3697	—	2	2	no	—
87	#3697	—	2	2	no	—
88	#3697	—	2	2	no	—
89	#3697	—	2	2	no	—
90	C₂×D₃₆	C₂×C₄	1	1	yes	characteristic
91	C₂×D₃₆	C₂×C₄	1	1	yes	characteristic
92	C₂×D₃₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
98	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
99	C₂×Dic₁₈	C₂×C₄	1	1	yes	characteristic
100	C₉×M₁₆	—	2	2	no	—
101	C₂×C₈×C₉	—	2	2	no	—
102	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
103	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
104	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
105	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
106	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₉×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₉×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄²×C₉	C₂³	1	1	yes	characteristic
110	#3676	C₂×C₄	1	1	yes	characteristic
111	#3676	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₄⋊Dic₉	C₂×C₄	1	1	yes	characteristic
117	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
118	Dic₉⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
120	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
121	C₄×Dic₉	C₂³	1	1	yes	characteristic
122	#3667	—	2	2	no	—
123	C₂×C₉⋊C₈	—	2	2	no	—
124	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
128	#3663	—	2	2	no	—
129	#3663	—	2	2	no	—
130	#3663	—	2	2	no	—
131	#3663	—	2	2	no	—
132	C₈×D₉	—	2	2	no	—
133	C₈×D₉	—	2	2	no	—
134	C₈×D₉	—	2	2	no	—
135	C₈×D₉	D₄	1	4	yes	complemented
136	#2932	—	9	1	no	Sylow
137	C₂×#235	—	3	1	no	—
138	C₂×#235	—	3	1	no	—
139	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
141	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
142	#940	—	3	1	no	—
143	#938	—	3	1	no	—
144	C₄×#67	—	3	1	no	—
145	C₄×#67	—	3	1	no	—
146	C₂×#208	—	3	1	no	—
147	C₂²×C₃⋊C₈	—	3	1	no	—
148	#907	—	6	4	no	—
149	#901	—	6	4	no	—
150	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
151	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
152	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
153	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
154	C₂×D₃×C₈	—	3	1	no	—
155	C₂×D₃×C₈	—	3	1	no	—
156	C₂×D₃×C₈	—	3	1	no	—
157	C₂×D₃×C₈	—	3	1	no	—
158	#895	—	3	1	no	—
159	#888	—	3	1	no	—
160	#885	—	3	1	no	—
161	#885	—	3	1	no	—
162	#884	—	3	1	no	—
163	#884	—	3	1	no	—
164	C₄×D₁₂	—	3	1	no	—
165	C₄²×D₃	—	3	1	no	—
166	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
167	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
168	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
169	C₃×#97	C₂×D₃	1	1	yes	characteristic
170	#830	—	3	1	no	—
171	#830	—	3	1	no	—
172	(C₂×D₃)⋊C₈	—	3	1	no	—
173	(C₂×D₃)⋊C₈	—	3	1	no	—
174	(C₂×D₃)⋊C₈	—	3	1	no	—
175	(C₂×D₃)⋊C₈	—	3	1	no	—
176	#815	—	3	1	no	—
177	#815	—	3	1	no	—
178	Dic₃⋊C₈	—	3	1	no	—
179	Dic₃⋊C₈	—	3	1	no	—
180	C₄⋊(C₃⋊C₈)	—	3	1	no	—
181	#803	—	3	1	no	—
182	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
183	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×D₉	C₂²×C₄	1	1	yes	characteristic
187	D₄×C₉	—	4	1	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
197	#611	—	2	2	no	—
198	#611	—	2	2	no	—
199	#611	—	2	2	no	—
200	#611	—	2	2	no	—
201	#611	—	4	1	no	—
202	#611	—	4	1	no	—
203	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
204	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
205	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
206	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
207	C₂×Dic₉	C₂²×C₄	1	1	yes	characteristic
208	D₃₆	—	2	2	no	—
209	D₃₆	—	2	2	no	—
210	D₃₆	—	4	1	no	—
211	C₄×D₉	—	2	1	no	—
212	C₄×D₉	—	2	1	no	—
213	C₄×D₉	—	2	1	no	—
214	C₄×D₉	—	2	1	no	—
215	C₄×D₉	—	4	1	no	—
216	C₄×D₉	—	4	1	no	—
217	C₄×D₉	C₂×D₄	1	2	yes	—
218	C₄×D₉	#41	1	2	yes	—
219	Dic₁₈	—	2	2	no	—
220	Dic₁₈	—	2	2	no	—
221	C₈×C₉	—	2	1	no	—
222	C₈×C₉	—	2	1	no	—
223	C₈×C₉	—	2	1	no	—
224	C₈×C₉	C₂×D₄	1	2	yes	—
225	C₉⋊C₈	—	2	1	no	—
226	C₉⋊C₈	—	2	1	no	—
227	C₉⋊C₈	—	2	1	no	—
228	C₉⋊C₈	C₂×D₄	1	2	yes	—
229	C₂×#131	—	9	1	no	—
230	C₂×#131	—	9	1	no	—
231	#532	—	9	1	no	—
232	#435	—	9	1	no	—
233	#435	—	9	1	no	—
234	#435	—	9	1	no	—
235	#435	—	9	1	no	—
236	#435	—	9	1	no	—
237	#435	—	9	1	no	—
238	#435	—	9	1	no	—
239	#435	D₉	1	1	yes	characteristic, complemented
240	#423	—	9	1	no	—
241	#408	—	9	1	no	—
242	#408	—	9	1	no	—
243	C₂×#97	—	9	1	no	—
244	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
247	C₂×#67	—	3	1	no	—
248	C₂×#67	—	3	1	no	—
249	C₂×#67	—	3	1	no	—
250	C₂×#67	—	3	1	no	—
251	C₂×#67	—	3	1	no	—
252	C₂×#67	—	3	1	no	—
253	#235	—	6	2	no	—
254	#235	—	6	2	no	—
255	#235	—	6	2	no	—
256	#235	—	6	2	no	—
257	C₂×D₁₂	—	3	1	no	—
258	C₂×D₁₂	—	3	1	no	—
259	C₂×D₁₂	—	3	1	no	—
260	C₂×C₄×D₃	—	3	1	no	—
261	C₂×C₄×D₃	—	3	1	no	—
262	C₂×C₄×D₃	—	3	1	no	—
263	C₂×C₄×D₃	—	3	1	no	—
264	C₂×C₄×D₃	—	3	1	no	—
265	C₂×Dic₆	—	3	1	no	—
266	C₂×Dic₆	—	3	1	no	—
267	C₃×M₁₆	—	2	2	no	—
268	C₂×C₃×C₈	—	2	2	no	—
269	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
274	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
275	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
276	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
277	#217	—	3	1	no	—
278	#217	—	3	1	no	—
279	(C₂×D₃)⋊C₄	—	3	1	no	—
280	(C₂×D₃)⋊C₄	—	3	1	no	—
281	(C₂×D₃)⋊C₄	—	3	1	no	—
282	(C₂×D₃)⋊C₄	—	3	1	no	—
283	C₄⋊Dic₃	—	3	1	no	—
284	Dic₃⋊C₄	—	3	1	no	—
285	Dic₃⋊C₄	—	3	1	no	—
286	C₄×Dic₃	—	3	1	no	—
287	C₄×Dic₃	—	3	1	no	—
288	C₄×Dic₃	—	3	1	no	—
289	#208	—	6	2	no	—
290	C₂×C₃⋊C₈	—	3	1	no	—
291	C₂×C₃⋊C₈	—	3	1	no	—
292	C₂×C₃⋊C₈	—	3	1	no	—
293	C₂×C₃⋊C₈	—	3	1	no	—
294	C₂×C₃⋊C₈	—	6	2	no	—
295	ΓL(1,𝔽₂₅)	—	6	2	no	—
296	ΓL(1,𝔽₂₅)	—	6	2	no	—
297	ΓL(1,𝔽₂₅)	—	6	2	no	—
298	ΓL(1,𝔽₂₅)	—	6	2	no	—
299	D₃×C₈	—	3	4	no	—
300	D₃×C₈	—	6	2	no	—
301	D₃×C₈	—	6	2	no	—
302	D₃×C₈	—	6	2	no	—
303	C₂²×C₉	—	2	1	no	—
304	C₂²×C₉	—	2	1	no	—
305	C₂²×C₉	—	2	1	no	—
306	C₂²×C₉	—	2	1	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
310	C₂×D₉	—	2	1	no	—
311	C₂×D₉	—	2	1	no	—
312	C₂×D₉	—	2	1	no	—
313	C₂×D₉	—	2	1	no	—
314	C₂×D₉	—	2	1	no	—
315	C₂×D₉	—	2	1	no	—
316	C₂×D₉	—	2	1	no	—
317	C₂×D₉	—	2	1	no	—
318	C₂×D₉	C₄×D₄	1	2	yes	—
319	C₄×C₉	—	2	1	no	—
320	C₄×C₉	—	2	1	no	—
321	C₄×C₉	—	2	1	no	—
322	C₄×C₉	—	2	1	no	—
323	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
324	C₄×C₉	C₂×#41	1	1	yes	characteristic
325	Dic₉	—	2	1	no	—
326	Dic₉	—	2	1	no	—
327	Dic₉	—	2	1	no	—
328	Dic₉	—	2	1	no	—
329	Dic₉	C₄×D₄	1	2	yes	—
330	C₂×#41	—	9	1	no	—
331	C₂×#41	—	9	1	no	—
332	#131	—	18	4	no	—
333	#131	—	18	4	no	—
334	C₂×M₁₆	—	9	1	no	—
335	C₂×M₁₆	—	9	1	no	—
336	C₂×M₁₆	—	9	1	no	—
337	C₂×M₁₆	—	9	1	no	—
338	C₂×M₁₆	—	9	1	no	—
339	C₂×M₁₆	C₂×D₉	1	1	yes	characteristic
340	C₂²×C₈	—	9	1	no	—
341	C₂²×C₈	—	9	1	no	—
342	C₂²×C₈	—	9	1	no	—
343	C₂²×C₈	—	9	1	no	—
344	C₂²×C₈	—	9	1	no	—
345	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
346	C₄⋊Q₈	—	9	1	no	—
347	#127	—	9	1	no	—
348	#124	—	9	1	no	—
349	#124	—	9	1	no	—
350	#121	—	9	1	no	—
351	#121	—	9	1	no	—
352	#121	—	9	1	no	—
353	#121	—	9	1	no	—
354	C₄×D₄	—	9	1	no	—
355	C₄×D₄	—	9	1	no	—
356	C₄×D₄	—	9	1	no	—
357	C₄×D₄	C₂×D₉	1	1	yes	characteristic
358	C₂×C₄²	—	9	1	no	—
359	C₄⋊C₈	—	9	1	no	—
360	C₄⋊C₈	—	9	1	no	—
361	C₄⋊C₈	—	9	1	no	—
362	C₄⋊C₈	C₂×D₉	1	1	yes	characteristic
363	C₂²⋊C₈	—	9	1	no	—
364	C₂²⋊C₈	—	9	1	no	—
365	C₂²⋊C₈	—	9	1	no	—
366	C₂²⋊C₈	—	9	1	no	—
367	C₂²⋊C₈	—	9	1	no	—
368	C₂²⋊C₈	—	9	1	no	—
369	C₂²⋊C₈	C₂×D₉	1	1	yes	characteristic
370	C₂²⋊C₈	C₂×D₉	1	1	yes	characteristic
371	#97	—	9	1	no	—
372	#97	—	9	1	no	—
373	#97	—	9	1	no	—
374	#97	C₂×D₉	1	1	yes	characteristic
375	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
376	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
377	C₂²×D₃	—	3	1	no	—
378	C₂²×D₃	—	3	1	no	—
379	C₂²×D₃	—	3	1	no	—
380	C₃×D₄	—	4	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
390	#67	—	6	2	no	—
391	#67	—	6	2	no	—
392	#67	—	6	2	no	—
393	#67	—	6	2	no	—
394	#67	—	12	1	no	—
395	#67	—	12	1	no	—
396	C₂×Dic₃	—	3	1	no	—
397	C₂×Dic₃	—	3	1	no	—
398	C₂×Dic₃	—	3	1	no	—
399	C₂×Dic₃	—	3	1	no	—
400	C₂×Dic₃	—	3	1	no	—
401	D₁₂	—	6	2	no	—
402	D₁₂	—	6	2	no	—
403	D₁₂	—	12	1	no	—
404	C₄×D₃	—	3	2	no	—
405	C₄×D₃	—	3	2	no	—
406	C₄×D₃	—	6	1	no	—
407	C₄×D₃	—	6	1	no	—
408	C₄×D₃	—	6	1	no	—
409	C₄×D₃	—	6	1	no	—
410	C₄×D₃	—	12	1	no	—
411	C₄×D₃	—	12	1	no	—
412	Dic₆	—	6	2	no	—
413	Dic₆	—	6	2	no	—
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	—	2	1	no	—
416	C₃×C₈	—	2	1	no	—
417	C₃×C₈	D₃×D₄	1	2	yes	—
418	C₃⋊C₈	—	3	2	no	—
419	C₃⋊C₈	—	6	1	no	—
420	C₃⋊C₈	—	6	1	no	—
421	C₃⋊C₈	—	6	1	no	—
422	C₂×C₉	—	4	1	no	—
423	C₂×C₉	—	4	1	no	—
424	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂×C₉	#568	1	1	yes	characteristic
426	C₂×C₉	#568	1	1	yes	characteristic
427	D₉	—	2	2	no	—
428	D₉	—	4	1	no	—
429	D₉	—	4	1	no	—
430	#41	—	18	2	no	—
431	#41	—	18	2	no	—
432	#41	—	18	2	no	—
433	#41	—	18	2	no	—
434	C₂×Q₈	—	9	1	no	—
435	C₂×Q₈	—	9	1	no	—
436	C₂×D₄	—	9	1	no	—
437	C₂×D₄	—	9	1	no	—
438	C₂×D₄	—	9	1	no	—
439	C₂×D₄	—	9	1	no	—
440	C₂×D₄	—	9	1	no	—
441	C₂×D₄	—	9	1	no	—
442	C₂×D₄	—	9	1	no	—
443	C₂×D₄	—	9	1	no	—
444	C₂×D₄	—	9	1	no	—
445	C₂×D₄	C₄×D₉	1	1	yes	characteristic
446	C₂²×C₄	—	9	1	no	—
447	C₂²×C₄	—	9	1	no	—
448	C₂²×C₄	—	9	1	no	—
449	C₂²×C₄	—	9	1	no	—
450	C₂²×C₄	—	9	1	no	—
451	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
453	M₁₆	—	2	2	no	—
454	M₁₆	—	18	2	no	—
455	M₁₆	—	18	2	no	—
456	M₁₆	—	18	2	no	—
457	M₁₆	—	18	2	no	—
458	M₁₆	—	18	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	9	1	no	—
461	C₂×C₈	—	9	4	no	—
462	C₂×C₈	—	9	1	no	—
463	C₂×C₈	—	9	1	no	—
464	C₂×C₈	—	9	1	no	—
465	C₂×C₈	—	18	2	no	—
466	C₂×C₈	—	18	2	no	—
467	C₂×C₈	—	18	2	no	—
468	C₂×C₈	—	18	2	no	—
469	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
470	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
471	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
472	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
473	C₄⋊C₄	—	9	1	no	—
474	C₄⋊C₄	—	9	1	no	—
475	C₄⋊C₄	—	9	1	no	—
476	C₄⋊C₄	C₄×D₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	9	1	no	—
478	C₂²⋊C₄	—	9	1	no	—
479	C₂²⋊C₄	—	9	1	no	—
480	C₂²⋊C₄	—	9	1	no	—
481	C₂²⋊C₄	—	9	1	no	—
482	C₂²⋊C₄	—	9	1	no	—
483	C₂²⋊C₄	C₄×D₉	1	1	yes	characteristic
484	C₂²⋊C₄	C₄×D₉	1	1	yes	characteristic
485	C₄²	—	9	1	no	—
486	C₄²	—	9	1	no	—
487	C₄²	—	9	1	no	—
488	C₄²	C₂²×D₉	1	1	yes	characteristic
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
496	C₂×D₃	—	3	2	no	—
497	C₂×D₃	—	6	1	no	—
498	C₂×D₃	—	6	1	no	—
499	C₂×D₃	—	6	1	no	—
500	C₂×D₃	—	6	1	no	—
501	C₂×D₃	—	6	1	no	—
502	C₂×D₃	—	6	1	no	—
503	C₂×D₃	—	6	1	no	—
504	C₂×D₃	—	6	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
510	C₃×C₄	D₃×#41	1	1	yes	characteristic
511	Dic₃	—	3	2	no	—
512	Dic₃	—	6	1	no	—
513	Dic₃	—	6	1	no	—
514	Dic₃	—	6	1	no	—
515	Dic₃	—	6	1	no	—
516	C₉	#2932	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	9	1	no	—
518	C₂³	—	9	1	no	—
519	C₂³	—	9	1	no	—
520	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
521	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
522	Q₈	—	18	2	no	—
523	Q₈	—	18	2	no	—
524	D₄	—	4	1	no	—
525	D₄	—	18	2	no	—
526	D₄	—	18	2	no	—
527	D₄	—	18	2	no	—
528	D₄	—	18	2	no	—
529	D₄	—	18	2	no	—
530	D₄	—	18	2	no	—
531	D₄	—	36	1	no	—
532	D₄	—	36	1	no	—
533	D₄	—	36	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	9	1	no	—
539	C₂×C₄	—	9	2	no	—
540	C₂×C₄	—	9	2	no	—
541	C₂×C₄	—	9	1	no	—
542	C₂×C₄	—	9	1	no	—
543	C₂×C₄	—	9	1	no	—
544	C₂×C₄	—	9	1	no	—
545	C₂×C₄	—	18	1	no	—
546	C₂×C₄	—	18	1	no	—
547	C₂×C₄	—	18	1	no	—
548	C₂×C₄	—	18	1	no	—
549	C₂×C₄	—	36	1	no	—
550	C₂×C₄	—	36	1	no	—
551	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
552	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
553	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
554	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	9	2	no	—
560	C₈	—	18	1	no	—
561	C₈	—	18	1	no	—
562	C₈	—	18	1	no	—
563	C₈	D₄×D₉	1	2	yes	—
564	C₂×C₃	—	4	1	no	—
565	C₂×C₃	—	4	1	no	—
566	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
567	C₂×C₃	#5745	1	1	yes	characteristic
568	C₂×C₃	#5750	1	1	yes	characteristic
569	D₃	—	6	2	no	—
570	D₃	—	12	1	no	—
571	D₃	—	12	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	9	2	no	—
579	C₂²	—	18	1	no	—
580	C₂²	—	18	1	no	—
581	C₂²	—	18	1	no	—
582	C₂²	—	18	1	no	—
583	C₂²	—	18	1	no	—
584	C₂²	—	18	1	no	—
585	C₂²	—	18	1	no	—
586	C₂²	—	18	1	no	—
587	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	9	2	no	—
593	C₄	—	18	1	no	—
594	C₄	—	18	1	no	—
595	C₄	—	18	1	no	—
596	C₄	—	18	1	no	—
597	C₄	C₂×D₄×D₉	1	1	yes	characteristic
598	C₄	#41×D₉	1	1	yes	characteristic
599	C₃	#79480	1	1	yes	characteristic
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	18	2	no	—
603	C₂	—	36	1	no	—
604	C₂	—	36	1	no	—
605	C₂	C₄×D₄×D₉	1	1	yes	characteristic
606	C₂	#10589847	1	1	yes	characteristic
607	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×#435	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	#10589650	C₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#435	D₉
hypocenter	C₉	#2932
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#63469	C₂	semidirect
2. C₂×#63464	C₂	semidirect
4. C₉×#435	C₂	semidirect
5. #10588809	C₂	semidirect
6. #10588792	C₂	semidirect
7. #10588688	C₂	semidirect
8. #10588521	C₂	semidirect
9. #10588520	C₂	semidirect
10. #10588412	C₂	semidirect
11. #10588410	C₂	semidirect
12. #10588409	C₂	semidirect
13. #10588409	C₂	semidirect
14. #10588387	C₂	semidirect
15. D₉×#97	C₂	semidirect
135. C₈×D₉	D₄	semidirect
239. #435	D₉	semidirect
516. C₉	#2932	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63469	2
C₂×#63464	2
#10589650	2
C₉×#435	2
#10588809	2
#10588792	2
#10588688	2
#10588521	2
#10588520	2
#10588412	2
#10588410	2
#10588409	2
#10588387	2
D₉×#97	2
#79480	3