Subgroups — C₉×#3056 #11767777

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#525	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#470	C₂	1	2	yes	maximal, complemented
6	C₉×#468	C₂	1	2	yes	maximal, complemented
7	C₉×#467	C₂	1	2	yes	maximal, complemented
8	C₉×#465	C₂	1	2	yes	maximal, complemented
9	C₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3056	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₉×#137	—	2	4	no	—
17	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₉×M₁₆	—	2	4	no	—
20	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×M₁₆	C₂²	1	2	yes	—
22	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₉	C₂²	1	2	yes	—
24	C₉×#123	—	2	1	no	—
25	C₉×C₂²⋊Q₈	—	2	1	no	—
26	C₉×C₂²⋊Q₈	—	2	1	no	—
27	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₉×#121	C₂²	1	1	yes	characteristic
32	C₉×#121	C₂²	1	1	yes	characteristic
33	C₉×#120	—	2	1	no	—
34	C₄×D₄×C₉	—	2	1	no	—
35	C₄×D₄×C₉	—	2	1	no	—
36	C₉×#117	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₄⋊C₄	—	2	1	no	—
38	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
40	C₉×#107	C₂²	1	2	yes	complemented
41	C₉×#106	C₂²	1	2	yes	complemented
42	C₉×#103	C₂²	1	2	yes	complemented
43	C₉×#103	C₂²	1	2	yes	complemented
44	C₉×#103	C₂²	1	2	yes	complemented
45	C₉×#102	C₂²	1	2	yes	complemented
46	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
47	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
48	C₃×#525	C₂×C₃	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
50	C₃×#470	C₂×C₃	1	2	yes	—
51	C₃×#468	C₂×C₃	1	2	yes	—
52	C₃×#467	C₂×C₃	1	2	yes	—
53	C₃×#465	C₂×C₃	1	2	yes	—
54	C₃×#428	C₂×C₃	1	1	yes	characteristic
55	C₃×#419	C₂×C₃	1	1	yes	characteristic
56	C₃×#417	C₂×C₃	1	1	yes	characteristic
57	C₂⁴×C₉	D₄	1	1	yes	characteristic
58	C₉×#41	—	2	2	no	—
59	C₉×#41	—	2	2	no	—
60	C₂×Q₈×C₉	—	2	1	no	—
61	C₂×Q₈×C₉	—	2	2	no	—
62	C₂×Q₈×C₉	—	2	2	no	—
63	C₂×Q₈×C₉	C₂³	1	2	yes	—
64	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₉	—	2	1	no	—
66	C₂×D₄×C₉	—	2	1	no	—
67	C₂×D₄×C₉	—	2	1	no	—
68	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	2	2	no	—
70	C₂²×C₄×C₉	—	2	2	no	—
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	—	2	1	no	—
73	C₂²×C₄×C₉	—	2	1	no	—
74	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
75	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
76	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₉×Q₁₆	—	2	4	no	—
81	C₉×SD₁₆	—	2	4	no	—
82	C₉×M₁₆	—	2	2	no	—
83	C₉×M₁₆	—	2	4	no	—
84	C₉×M₁₆	D₄	1	4	yes	complemented
85	C₂×C₈×C₉	—	2	4	no	—
86	C₂×C₈×C₉	C₂³	1	2	yes	—
87	C₂×C₈×C₉	C₂³	1	2	yes	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	—	2	1	no	—
91	C₉×C₄⋊C₄	—	2	1	no	—
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	C₂³	1	2	yes	—
94	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₉×C₂²⋊C₄	—	2	2	no	—
97	C₉×C₂²⋊C₄	—	2	2	no	—
98	C₉×C₂²⋊C₄	—	2	1	no	—
99	C₉×C₂²⋊C₄	—	2	1	no	—
100	C₉×C₂²⋊C₄	—	2	1	no	—
101	C₉×C₂²⋊C₄	—	2	1	no	—
102	C₉×C₂²⋊C₄	—	2	1	no	—
103	C₄²×C₉	—	2	1	no	—
104	#3056	C₉	1	1	yes	characteristic, direct product factor, Sylow
105	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
108	C₃×#137	—	2	4	no	—
109	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
111	C₂×C₃×M₁₆	—	2	4	no	—
112	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
114	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
116	C₃×#123	—	2	1	no	—
117	C₃×C₂²⋊Q₈	—	2	1	no	—
118	C₃×C₂²⋊Q₈	—	2	1	no	—
119	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
120	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
122	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×#121	C₂²×C₃	1	1	yes	characteristic
124	C₃×#121	C₂²×C₃	1	1	yes	characteristic
125	C₃×#120	—	2	1	no	—
126	C₃×C₄×D₄	—	2	1	no	—
127	C₃×C₄×D₄	—	2	1	no	—
128	C₃×#117	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
132	C₃×#107	C₂²×C₃	1	2	yes	—
133	C₃×#106	C₂²×C₃	1	2	yes	—
134	C₃×#103	C₂²×C₃	1	2	yes	—
135	C₃×#103	C₂²×C₃	1	2	yes	—
136	C₃×#103	C₂²×C₃	1	2	yes	—
137	C₃×#102	C₂²×C₃	1	2	yes	—
138	C₂³×C₉	—	2	2	no	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	1	no	—
141	C₂³×C₉	—	4	1	no	—
142	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
145	Q₈×C₉	—	2	2	no	—
146	Q₈×C₉	—	2	1	no	—
147	Q₈×C₉	—	2	2	no	—
148	Q₈×C₉	—	2	1	no	—
149	Q₈×C₉	—	4	2	no	—
150	D₄×C₉	—	2	1	no	—
151	D₄×C₉	—	2	1	no	—
152	D₄×C₉	—	4	2	no	—
153	D₄×C₉	—	4	2	no	—
154	D₄×C₉	—	4	2	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	2	2	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	2	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	2	no	—
167	C₂×C₄×C₉	—	4	2	no	—
168	C₂×C₄×C₉	—	4	2	no	—
169	C₂×C₄×C₉	—	4	2	no	—
170	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
174	C₂×C₄×C₉	#41	1	2	yes	—
175	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
176	C₈×C₉	—	2	2	no	—
177	C₈×C₉	C₂×D₄	1	4	yes	—
178	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
179	C₂²×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
180	#525	C₂×C₉	1	1	yes	characteristic
181	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
182	#470	C₂×C₉	1	2	yes	complemented
183	#468	C₂×C₉	1	2	yes	complemented
184	#467	C₂×C₉	1	2	yes	complemented
185	#465	C₂×C₉	1	2	yes	complemented
186	#428	C₂×C₉	1	1	yes	characteristic, complemented
187	#419	C₂×C₉	1	1	yes	characteristic, complemented
188	#417	C₂×C₉	1	1	yes	characteristic, complemented
189	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
190	C₃×#41	—	2	2	no	—
191	C₃×#41	—	2	2	no	—
192	C₂×C₃×Q₈	—	2	1	no	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	—	2	2	no	—
195	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
196	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₃×D₄	—	2	1	no	—
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	—	2	1	no	—
200	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	—	2	2	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
212	C₃×Q₁₆	—	2	4	no	—
213	C₃×SD₁₆	—	2	4	no	—
214	C₃×M₁₆	—	2	2	no	—
215	C₃×M₁₆	—	2	4	no	—
216	C₃×M₁₆	C₃×D₄	1	4	yes	—
217	C₂×C₃×C₈	—	2	4	no	—
218	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
219	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
226	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
228	C₃×C₂²⋊C₄	—	2	2	no	—
229	C₃×C₂²⋊C₄	—	2	2	no	—
230	C₃×C₂²⋊C₄	—	2	1	no	—
231	C₃×C₂²⋊C₄	—	2	1	no	—
232	C₃×C₂²⋊C₄	—	2	1	no	—
233	C₃×C₂²⋊C₄	—	2	1	no	—
234	C₃×C₂²⋊C₄	—	2	1	no	—
235	C₃×C₄²	—	2	1	no	—
236	C₂²×C₉	—	2	1	no	—
237	C₂²×C₉	—	2	1	no	—
238	C₂²×C₉	—	2	1	no	—
239	C₂²×C₉	—	2	1	no	—
240	C₂²×C₉	—	2	1	no	—
241	C₂²×C₉	—	2	1	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	4	4	no	—
244	C₂²×C₉	—	4	1	no	—
245	C₂²×C₉	—	4	1	no	—
246	C₂²×C₉	—	4	1	no	—
247	C₂²×C₉	#121	1	2	yes	—
248	C₂²×C₉	#137	1	2	yes	complemented
249	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
250	C₄×C₉	—	2	1	no	—
251	C₄×C₉	—	2	1	no	—
252	C₄×C₉	—	4	1	no	—
253	C₄×C₉	—	4	2	no	—
254	C₄×C₉	—	4	1	no	—
255	C₄×C₉	—	4	2	no	—
256	C₄×C₉	—	4	1	no	—
257	C₄×C₉	#121	1	2	yes	—
258	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
259	C₄×C₉	C₂×#41	1	1	yes	characteristic
260	C₂×#41	C₂²×C₉	1	1	yes	characteristic
261	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
262	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
263	#137	—	2	4	no	—
264	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
265	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
268	C₂×M₁₆	C₂²×C₉	1	2	yes	—
269	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
270	C₂²×C₈	C₂²×C₉	1	2	yes	—
271	#123	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
275	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
276	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
277	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
278	#121	C₂²×C₉	1	1	yes	characteristic
279	#121	C₂²×C₉	1	1	yes	characteristic
280	#120	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	#117	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	#107	C₂²×C₉	1	2	yes	complemented
288	#106	C₂²×C₉	1	2	yes	complemented
289	#103	C₂²×C₉	1	2	yes	complemented
290	#103	C₂²×C₉	1	2	yes	complemented
291	#103	C₂²×C₉	1	2	yes	complemented
292	#102	C₂²×C₉	1	2	yes	complemented
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	1	no	—
296	C₂³×C₃	—	4	1	no	—
297	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
300	C₃×Q₈	—	2	2	no	—
301	C₃×Q₈	—	2	1	no	—
302	C₃×Q₈	—	2	2	no	—
303	C₃×Q₈	—	2	1	no	—
304	C₃×Q₈	—	4	2	no	—
305	C₃×D₄	—	2	1	no	—
306	C₃×D₄	—	2	1	no	—
307	C₃×D₄	—	4	2	no	—
308	C₃×D₄	—	4	2	no	—
309	C₃×D₄	—	4	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	4	2	no	—
323	C₂×C₃×C₄	—	4	2	no	—
324	C₂×C₃×C₄	—	4	2	no	—
325	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
329	C₂×C₃×C₄	C₃×#41	1	2	yes	—
330	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
331	C₃×C₈	—	2	2	no	—
332	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
333	C₂×C₉	—	2	2	no	—
334	C₂×C₉	—	2	2	no	—
335	C₂×C₉	—	4	1	no	—
336	C₂×C₉	—	8	1	no	—
337	C₂×C₉	C₂×#121	1	1	yes	characteristic
338	C₂×C₉	C₂×#137	1	1	yes	characteristic
339	C₂×C₉	#575	1	1	yes	characteristic
340	C₂⁴	D₄×C₉	1	1	yes	characteristic
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	C₂³×C₉	1	2	yes	—
347	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
358	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
360	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
361	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
362	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
363	Q₁₆	—	2	4	no	—
364	SD₁₆	—	2	4	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	D₄×C₉	1	4	yes	complemented
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	C₂³×C₉	1	2	yes	—
370	C₂×C₈	C₂³×C₉	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	C₂³×C₉	1	2	yes	—
377	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	4	4	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	C₃×#121	1	2	yes	—
399	C₂²×C₃	C₃×#137	1	2	yes	—
400	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	4	1	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	4	1	no	—
406	C₃×C₄	—	4	1	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	C₃×#121	1	2	yes	—
409	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
410	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
411	C₉	#3056	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
417	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
418	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	1	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
445	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
448	C₂×C₄	C₉×#41	1	2	yes	—
449	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	C₂×D₄×C₉	1	4	yes	—
452	C₂×C₃	—	2	2	no	—
453	C₂×C₃	—	2	2	no	—
454	C₂×C₃	—	4	1	no	—
455	C₂×C₃	—	8	1	no	—
456	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
457	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
458	C₂×C₃	C₃×#575	1	1	yes	characteristic
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	C₉×#121	1	2	yes	—
471	C₂²	C₉×#137	1	2	yes	complemented
472	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	C₉×#121	1	2	yes	—
481	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
482	C₄	C₂×C₉×#41	1	1	yes	characteristic
483	C₃	C₃×#3056	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	2	2	no	—
486	C₂	—	4	1	no	—
487	C₂	—	8	1	no	—
488	C₂	C₂×C₉×#121	1	1	yes	characteristic
489	C₂	C₂×C₉×#137	1	1	yes	characteristic
490	C₂	C₉×#575	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×#525	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
2. C₂²×C₉×M₁₆	C₂	semidirect
4. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
5. C₉×#470	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#467	C₂	semidirect
8. C₉×#465	C₂	semidirect
9. C₉×#428	C₂	semidirect
10. C₉×#419	C₂	semidirect
11. C₉×#417	C₂	semidirect
17. C₂×C₉×Q₁₆	C₂²	semidirect
18. C₂×C₉×SD₁₆	C₂²	semidirect
40. C₉×#107	C₂²	semidirect
41. C₉×#106	C₂²	semidirect
42. C₉×#103	C₂²	semidirect
43. C₉×#103	C₂²	semidirect
44. C₉×#103	C₂²	semidirect
45. C₉×#102	C₂²	semidirect
84. C₉×M₁₆	D₄	semidirect
104. #3056	C₉	direct (N × H)
178. C₂×#137	C₂×C₉	semidirect
179. C₂²×M₁₆	C₂×C₉	semidirect
181. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
182. #470	C₂×C₉	semidirect
183. #468	C₂×C₉	semidirect
184. #467	C₂×C₉	semidirect
185. #465	C₂×C₉	semidirect
186. #428	C₂×C₉	semidirect
187. #419	C₂×C₉	semidirect
188. #417	C₂×C₉	semidirect
248. C₂²×C₉	#137	semidirect
264. C₂×Q₁₆	C₂²×C₉	semidirect
265. C₂×SD₁₆	C₂²×C₉	semidirect
287. #107	C₂²×C₉	semidirect
288. #106	C₂²×C₉	semidirect
289. #103	C₂²×C₉	semidirect
290. #103	C₂²×C₉	semidirect
291. #103	C₂²×C₉	semidirect
292. #102	C₂²×C₉	semidirect
367. M₁₆	D₄×C₉	semidirect
411. C₉	#3056	direct (N × H)
471. C₂²	C₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#137	2
C₂²×C₉×M₁₆	2
C₉×#525	2
C₂×C₉×C₂²⋊Q₈	2
C₉×#470	2
C₉×#468	2
C₉×#467	2
C₉×#465	2
C₉×#428	2
C₉×#419	2
C₉×#417	2
C₃×#3056	3

Subgroups — C9×#3056 #11767777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3056 #11767777