Subgroups — C₂×C₉×#547 #11768185

Order 1152.

2448 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#41	C₂	1	2	yes	maximal, complemented
2	C₉×#547	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#123	C₂	1	4	yes	maximal, complemented
5	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×#121	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#547	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	—	2	16	no	—
12	C₂×C₉×#41	C₂²	1	16	yes	complemented
13	C₂²×Q₈×C₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₉	C₂²	1	4	yes	—
16	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	2	yes	—
18	C₂³×C₄×C₉	C₂²	1	2	yes	—
19	C₂³×C₄×C₉	C₂²	1	4	yes	—
20	C₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
21	C₉×#123	C₂²	1	32	yes	complemented
22	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
23	C₉×#121	C₂²	1	16	yes	complemented
24	C₄×D₄×C₉	C₂²	1	8	yes	complemented
25	C₄×D₄×C₉	C₂²	1	8	yes	complemented
26	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
29	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	16	yes	complemented
32	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
33	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₂²×C₃×#41	C₂×C₃	1	2	yes	—
37	C₃×#547	C₂×C₃	1	16	yes	—
38	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#123	C₂×C₃	1	4	yes	—
40	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
41	C₂×C₃×#121	C₂×C₃	1	2	yes	—
42	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
44	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
45	C₂⁴×C₉	C₂³	1	2	yes	—
46	C₂⁴×C₉	C₂³	1	2	yes	—
47	C₉×#41	—	2	64	no	—
48	C₂×Q₈×C₉	—	2	8	no	—
49	C₂×Q₈×C₉	C₂³	1	8	yes	—
50	C₂×D₄×C₉	—	2	16	no	—
51	C₂×D₄×C₉	—	2	4	no	—
52	C₂×D₄×C₉	D₄	1	8	yes	complemented
53	C₂×D₄×C₉	C₂³	1	4	yes	—
54	C₂×D₄×C₉	C₂³	1	16	yes	—
55	C₂×D₄×C₉	C₂³	1	4	yes	—
56	C₂²×C₄×C₉	—	2	16	no	—
57	C₂²×C₄×C₉	—	2	8	no	—
58	C₂²×C₄×C₉	—	2	8	no	—
59	C₂²×C₄×C₉	C₂³	1	8	yes	—
60	C₂²×C₄×C₉	C₂³	1	16	yes	—
61	C₂²×C₄×C₉	C₂³	1	8	yes	—
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	C₂³	1	4	yes	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×C₄⋊C₄	C₂³	1	4	yes	—
69	C₉×C₄⋊C₄	C₂³	1	8	yes	—
70	C₉×C₄⋊C₄	C₂³	1	16	yes	—
71	C₉×C₄⋊C₄	C₂³	1	4	yes	—
72	C₉×C₄⋊C₄	C₂³	1	8	yes	—
73	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₄²×C₉	C₂³	1	4	yes	—
77	C₂×#547	C₉	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₃×#41	—	2	16	no	—
79	C₂×C₃×#41	C₂²×C₃	1	16	yes	—
80	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
81	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
82	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
85	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
86	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
87	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
88	C₃×#123	C₂²×C₃	1	32	yes	—
89	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
90	C₃×#121	C₂²×C₃	1	16	yes	—
91	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
92	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
102	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
103	C₂³×C₉	—	2	4	no	—
104	C₂³×C₉	—	2	4	no	—
105	C₂³×C₉	—	2	4	no	—
106	C₂³×C₉	—	2	4	no	—
107	C₂³×C₉	—	2	4	no	—
108	C₂³×C₉	C₂×D₄	1	8	yes	—
109	C₂³×C₉	C₂⁴	1	4	yes	—
110	C₂³×C₉	C₂⁴	1	4	yes	—
111	C₂³×C₉	C₂⁴	1	1	yes	characteristic
112	Q₈×C₉	—	2	16	no	—
113	D₄×C₉	—	2	32	no	—
114	D₄×C₉	—	2	8	no	—
115	D₄×C₉	C₂×D₄	1	16	yes	complemented
116	C₂×C₄×C₉	—	2	4	no	—
117	C₂×C₄×C₉	—	2	8	no	—
118	C₂×C₄×C₉	—	2	32	no	—
119	C₂×C₄×C₉	—	2	4	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	16	no	—
122	C₂×C₄×C₉	—	2	16	no	—
123	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
124	C₂×C₄×C₉	#41	1	4	yes	complemented
125	C₂×C₄×C₉	C₂⁴	1	2	yes	—
126	C₂×C₄×C₉	C₂⁴	1	4	yes	—
127	C₂×C₄×C₉	C₂⁴	1	4	yes	—
128	C₂×C₄×C₉	C₂⁴	1	8	yes	—
129	C₂×C₄×C₉	C₂⁴	1	2	yes	—
130	C₂×C₄×C₉	C₂⁴	1	2	yes	—
131	C₂²×#41	C₂×C₉	1	2	yes	complemented
132	#547	C₂×C₉	1	16	yes	direct product factor
133	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
134	C₂×#123	C₂×C₉	1	4	yes	complemented
135	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
136	C₂×#121	C₂×C₉	1	2	yes	complemented
137	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
139	C₂²×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
140	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
141	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
142	C₃×#41	—	2	64	no	—
143	C₂×C₃×Q₈	—	2	8	no	—
144	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
145	C₂×C₃×D₄	—	2	16	no	—
146	C₂×C₃×D₄	—	2	4	no	—
147	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
148	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
149	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
150	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
151	C₂²×C₃×C₄	—	2	16	no	—
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	—	2	8	no	—
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
164	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
165	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
166	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
167	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
168	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
169	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
170	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
171	C₃×C₄²	C₂³×C₃	1	4	yes	—
172	C₂²×C₉	—	2	16	no	—
173	C₂²×C₉	—	2	4	no	—
174	C₂²×C₉	—	2	4	no	—
175	C₂²×C₉	—	2	4	no	—
176	C₂²×C₉	—	2	4	no	—
177	C₂²×C₉	—	2	4	no	—
178	C₂²×C₉	—	4	8	no	—
179	C₂²×C₉	C₂²×D₄	1	8	yes	—
180	C₂²×C₉	C₂²×D₄	1	2	yes	—
181	C₂²×C₉	C₂×#41	1	2	yes	—
182	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
183	C₂²×C₉	C₂⁵	1	1	yes	characteristic
184	C₄×C₉	—	2	4	no	—
185	C₄×C₉	—	2	8	no	—
186	C₄×C₉	—	2	4	no	—
187	C₄×C₉	—	2	2	no	—
188	C₄×C₉	C₂²×D₄	1	4	yes	—
189	C₄×C₉	C₂×#41	1	4	yes	complemented
190	C₂×#41	—	2	16	no	—
191	C₂×#41	C₂²×C₉	1	16	yes	complemented
192	C₂²×Q₈	C₂²×C₉	1	2	yes	—
193	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
194	C₂²×D₄	C₂²×C₉	1	4	yes	—
195	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
196	C₂³×C₄	C₂²×C₉	1	2	yes	—
197	C₂³×C₄	C₂²×C₉	1	4	yes	—
198	C₂³×C₄	C₂²×C₉	1	2	yes	—
199	C₄⋊Q₈	C₂²×C₉	1	8	yes	complemented
200	#123	C₂²×C₉	1	32	yes	complemented
201	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
202	#121	C₂²×C₉	1	16	yes	complemented
203	C₄×D₄	C₂²×C₉	1	8	yes	complemented
204	C₄×D₄	C₂²×C₉	1	8	yes	complemented
205	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
208	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
210	C₂×C₄⋊C₄	C₂²×C₉	1	16	yes	complemented
211	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
214	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
221	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
222	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
223	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
224	C₃×Q₈	—	2	16	no	—
225	C₃×D₄	—	2	32	no	—
226	C₃×D₄	—	2	8	no	—
227	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	—	2	32	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	16	no	—
234	C₂×C₃×C₄	—	2	16	no	—
235	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
236	C₂×C₃×C₄	C₃×#41	1	4	yes	—
237	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
238	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
239	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
240	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
241	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
242	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
243	C₂×C₉	—	2	8	no	—
244	C₂×C₉	—	4	4	no	—
245	C₂×C₉	#547	1	4	yes	direct product factor
246	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
247	C₂×C₉	C₂²×#41	1	1	yes	characteristic
248	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
249	C₂⁴	C₂³×C₉	1	2	yes	—
250	C₂⁴	C₂³×C₉	1	2	yes	—
251	#41	—	2	64	no	—
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	C₂³×C₉	1	8	yes	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	D₄×C₉	1	8	yes	complemented
257	C₂×D₄	C₂³×C₉	1	4	yes	—
258	C₂×D₄	C₂³×C₉	1	16	yes	—
259	C₂×D₄	C₂³×C₉	1	4	yes	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₉	1	2	yes	—
265	C₂²×C₄	C₂³×C₉	1	2	yes	—
266	C₂²×C₄	C₂³×C₉	1	4	yes	—
267	C₂²×C₄	C₂³×C₉	1	8	yes	—
268	C₂²×C₄	C₂³×C₉	1	16	yes	—
269	C₂²×C₄	C₂³×C₉	1	8	yes	—
270	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
272	C₄⋊C₄	C₂³×C₉	1	4	yes	—
273	C₄⋊C₄	C₂³×C₉	1	8	yes	—
274	C₄⋊C₄	C₂³×C₉	1	16	yes	—
275	C₄⋊C₄	C₂³×C₉	1	4	yes	—
276	C₄⋊C₄	C₂³×C₉	1	8	yes	—
277	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
278	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
279	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
280	C₄²	C₂³×C₉	1	4	yes	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	2	16	no	—
284	C₂²×C₃	—	2	4	no	—
285	C₂²×C₃	—	2	4	no	—
286	C₂²×C₃	—	2	4	no	—
287	C₂²×C₃	—	4	8	no	—
288	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
289	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
290	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
291	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
293	C₃×C₄	—	2	4	no	—
294	C₃×C₄	—	2	8	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
298	C₃×C₄	C₂×C₃×#41	1	4	yes	—
299	C₉	C₂×#547	1	1	yes	characteristic, direct product factor, Sylow
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	C₂×D₄×C₉	1	8	yes	—
306	C₂³	C₂⁴×C₉	1	4	yes	—
307	C₂³	C₂⁴×C₉	1	4	yes	—
308	C₂³	C₂⁴×C₉	1	1	yes	characteristic
309	Q₈	—	2	16	no	—
310	D₄	—	2	32	no	—
311	D₄	—	2	8	no	—
312	D₄	C₂×D₄×C₉	1	16	yes	complemented
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	32	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	16	no	—
320	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
321	C₂×C₄	C₉×#41	1	4	yes	complemented
322	C₂×C₄	C₂⁴×C₉	1	2	yes	—
323	C₂×C₄	C₂⁴×C₉	1	4	yes	—
324	C₂×C₄	C₂⁴×C₉	1	4	yes	—
325	C₂×C₄	C₂⁴×C₉	1	8	yes	—
326	C₂×C₄	C₂⁴×C₉	1	2	yes	—
327	C₂×C₄	C₂⁴×C₉	1	2	yes	—
328	C₂×C₃	—	2	8	no	—
329	C₂×C₃	—	4	4	no	—
330	C₂×C₃	C₃×#547	1	4	yes	—
331	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
332	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
333	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
334	C₂²	—	2	16	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	4	8	no	—
341	C₂²	C₂²×D₄×C₉	1	8	yes	—
342	C₂²	C₂²×D₄×C₉	1	2	yes	—
343	C₂²	C₂×C₉×#41	1	2	yes	—
344	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
345	C₂²	C₂⁵×C₉	1	1	yes	characteristic
346	C₄	—	2	4	no	—
347	C₄	—	2	8	no	—
348	C₄	—	2	4	no	—
349	C₄	—	2	2	no	—
350	C₄	C₂²×D₄×C₉	1	4	yes	—
351	C₄	C₂×C₉×#41	1	4	yes	complemented
352	C₃	C₂×C₃×#547	1	1	yes	characteristic
353	C₂	—	2	8	no	—
354	C₂	—	4	4	no	—
355	C₂	C₉×#547	1	4	yes	direct product factor
356	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
357	C₂	C₂²×C₉×#41	1	1	yes	characteristic
358	C₂	C₂×C₉×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#547	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#41	C₂	semidirect
2. C₉×#547	C₂	direct (N × H)
3. C₂×C₉×C₄⋊Q₈	C₂	semidirect
4. C₂×C₉×#123	C₂	semidirect
5. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₉×#121	C₂	semidirect
7. C₂×C₄×D₄×C₉	C₂	semidirect
8. C₂×C₄×D₄×C₉	C₂	semidirect
9. C₂²×C₉×C₄⋊C₄	C₂	semidirect
12. C₂×C₉×#41	C₂²	semidirect
20. C₉×C₄⋊Q₈	C₂²	semidirect
21. C₉×#123	C₂²	semidirect
22. C₉×C₂²⋊Q₈	C₂²	semidirect
23. C₉×#121	C₂²	semidirect
24. C₄×D₄×C₉	C₂²	semidirect
25. C₄×D₄×C₉	C₂²	semidirect
31. C₂×C₉×C₄⋊C₄	C₂²	semidirect
52. C₂×D₄×C₉	D₄	semidirect
77. C₂×#547	C₉	direct (N × H)
115. D₄×C₉	C₂×D₄	semidirect
124. C₂×C₄×C₉	#41	semidirect
131. C₂²×#41	C₂×C₉	semidirect
132. #547	C₂×C₉	direct (N × H)
133. C₂×C₄⋊Q₈	C₂×C₉	semidirect
134. C₂×#123	C₂×C₉	semidirect
135. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
136. C₂×#121	C₂×C₉	semidirect
137. C₂×C₄×D₄	C₂×C₉	semidirect
138. C₂×C₄×D₄	C₂×C₉	semidirect
139. C₂²×C₄⋊C₄	C₂×C₉	semidirect
189. C₄×C₉	C₂×#41	semidirect
191. C₂×#41	C₂²×C₉	semidirect
199. C₄⋊Q₈	C₂²×C₉	semidirect
200. #123	C₂²×C₉	semidirect
201. C₂²⋊Q₈	C₂²×C₉	semidirect
202. #121	C₂²×C₉	semidirect
203. C₄×D₄	C₂²×C₉	semidirect
204. C₄×D₄	C₂²×C₉	semidirect
210. C₂×C₄⋊C₄	C₂²×C₉	semidirect
245. C₂×C₉	#547	direct (N × H)
256. C₂×D₄	D₄×C₉	semidirect
299. C₉	C₂×#547	direct (N × H)
312. D₄	C₂×D₄×C₉	semidirect
321. C₂×C₄	C₉×#41	semidirect
351. C₄	C₂×C₉×#41	semidirect
355. C₂	C₉×#547	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×#41	2
C₉×#547	2
C₂×C₉×C₄⋊Q₈	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₄⋊C₄	2
C₂×C₃×#547	3

Subgroups — C2×C9×#547 #11768185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#547 #11768185