Subgroups — C₂×C₉×#552 #11768191

Order 1152.

1686 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#552	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×#125	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#123	C₂	1	2	yes	maximal
6	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
10	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×#117	C₂	1	2	yes	maximal, complemented
12	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#552	C₃	1	1	yes	maximal, characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	2	yes	—
19	C₉×#126	C₂²	1	16	yes	complemented
20	C₉×#125	C₂²	1	16	yes	complemented
21	C₉×#125	C₂²	1	8	yes	complemented
22	C₉×#123	C₂²	1	16	yes	—
23	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
24	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
25	C₄×Q₈×C₉	C₂²	1	8	yes	complemented
26	C₄×D₄×C₉	C₂²	1	8	yes	—
27	C₉×#117	C₂²	1	8	yes	complemented
28	C₉×#117	C₂²	1	16	yes	complemented
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	2	yes	—
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
38	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₄⋊C₄	C₂²	1	8	yes	complemented
40	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₉	C₂²	1	2	yes	—
46	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	C₂²	1	2	yes	—
48	C₃×#552	C₂×C₃	1	16	yes	—
49	C₂×C₃×#126	C₂×C₃	1	2	yes	—
50	C₂×C₃×#125	C₂×C₃	1	2	yes	—
51	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
52	C₂×C₃×#123	C₂×C₃	1	2	yes	—
53	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×#117	C₂×C₃	1	2	yes	—
59	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₂⁴×C₉	C₂³	1	1	yes	characteristic
61	C₂⁴×C₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₉	—	2	4	no	—
63	C₂×Q₈×C₉	C₂³	1	4	yes	—
64	C₂×D₄×C₉	—	2	4	no	—
65	C₂×D₄×C₉	C₂³	1	4	yes	—
66	C₂²×C₄×C₉	—	2	8	no	—
67	C₂²×C₄×C₉	—	2	4	no	—
68	C₂²×C₄×C₉	—	2	4	no	—
69	C₂²×C₄×C₉	C₂³	1	8	yes	—
70	C₂²×C₄×C₉	C₂³	1	4	yes	—
71	C₂²×C₄×C₉	C₂³	1	4	yes	—
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	2	yes	—
75	C₂²×C₄×C₉	C₂³	1	2	yes	—
76	C₂²×C₄×C₉	C₂³	1	2	yes	—
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	2	yes	—
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	C₂³	1	4	yes	—
82	C₉×C₄⋊C₄	C₂³	1	4	yes	—
83	C₉×C₄⋊C₄	C₂³	1	8	yes	—
84	C₉×C₄⋊C₄	C₂³	1	8	yes	—
85	C₉×C₄⋊C₄	C₂³	1	4	yes	—
86	C₉×C₄⋊C₄	C₂³	1	8	yes	—
87	C₉×C₄⋊C₄	C₂³	1	4	yes	—
88	C₉×C₄⋊C₄	C₂³	1	8	yes	—
89	C₉×C₄⋊C₄	C₂³	1	8	yes	—
90	C₉×C₄⋊C₄	C₂³	1	8	yes	—
91	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₄²×C₉	C₂³	1	8	yes	—
97	C₄²×C₉	C₂³	1	8	yes	—
98	C₄²×C₉	C₂³	1	4	yes	—
99	C₂×#552	C₉	1	1	yes	characteristic, direct product factor, Sylow
100	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
103	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃×#126	C₂²×C₃	1	16	yes	—
106	C₃×#125	C₂²×C₃	1	16	yes	—
107	C₃×#125	C₂²×C₃	1	8	yes	—
108	C₃×#123	C₂²×C₃	1	16	yes	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
110	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
111	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
112	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
113	C₃×#117	C₂²×C₃	1	8	yes	—
114	C₃×#117	C₂²×C₃	1	16	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
131	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
133	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
134	C₂³×C₉	—	2	2	no	—
135	C₂³×C₉	—	2	2	no	—
136	C₂³×C₉	—	2	2	no	—
137	C₂³×C₉	—	2	2	no	—
138	C₂³×C₉	—	2	2	no	—
139	C₂³×C₉	#41	1	4	yes	—
140	C₂³×C₉	C₂⁴	1	2	yes	—
141	C₂³×C₉	C₂⁴	1	2	yes	—
142	C₂³×C₉	C₂⁴	1	1	yes	characteristic
143	Q₈×C₉	—	2	8	no	—
144	D₄×C₉	—	2	8	no	—
145	C₂×C₄×C₉	—	2	16	no	—
146	C₂×C₄×C₉	—	2	4	no	—
147	C₂×C₄×C₉	—	2	4	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	4	no	—
154	C₂×C₄×C₉	—	2	8	no	—
155	C₂×C₄×C₉	—	2	8	no	—
156	C₂×C₄×C₉	#41	1	4	yes	—
157	C₂×C₄×C₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₉	C₂⁴	1	4	yes	—
160	C₂×C₄×C₉	C₂⁴	1	4	yes	—
161	C₂×C₄×C₉	C₂⁴	1	4	yes	—
162	C₂×C₄×C₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₉	C₂⁴	1	4	yes	—
165	C₂×C₄×C₉	C₂⁴	1	2	yes	—
166	#552	C₂×C₉	1	16	yes	direct product factor
167	C₂×#126	C₂×C₉	1	2	yes	complemented
168	C₂×#125	C₂×C₉	1	2	yes	complemented
169	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
170	C₂×#123	C₂×C₉	1	2	yes	—
171	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
172	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
174	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
175	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂×#117	C₂×C₉	1	2	yes	complemented
177	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
178	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
179	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×Q₈	—	2	4	no	—
181	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
184	C₂²×C₃×C₄	—	2	8	no	—
185	C₂²×C₃×C₄	—	2	4	no	—
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
195	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
196	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
197	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
200	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
201	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
202	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
203	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
204	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
207	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
208	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
209	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
210	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
211	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
212	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
213	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
214	C₃×C₄²	C₂³×C₃	1	8	yes	—
215	C₃×C₄²	C₂³×C₃	1	8	yes	—
216	C₃×C₄²	C₂³×C₃	1	4	yes	—
217	C₂²×C₉	—	2	8	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	2	2	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	4	4	no	—
224	C₂²×C₉	C₂×#41	1	4	yes	—
225	C₂²×C₉	C₂×#41	1	2	yes	—
226	C₂²×C₉	C₂×#41	1	2	yes	—
227	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
228	C₂²×C₉	C₂⁵	1	1	yes	characteristic
229	C₄×C₉	—	2	4	no	—
230	C₄×C₉	—	2	4	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	—	2	4	no	—
235	C₄×C₉	—	2	2	no	—
236	C₄×C₉	—	2	4	no	—
237	C₄×C₉	C₂×#41	1	4	yes	—
238	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
239	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
240	C₂³×C₄	C₂²×C₉	1	2	yes	—
241	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
242	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
243	#126	C₂²×C₉	1	16	yes	complemented
244	#125	C₂²×C₉	1	16	yes	complemented
245	#125	C₂²×C₉	1	8	yes	complemented
246	#123	C₂²×C₉	1	16	yes	—
247	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
248	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
249	C₄×Q₈	C₂²×C₉	1	8	yes	complemented
250	C₄×D₄	C₂²×C₉	1	8	yes	—
251	#117	C₂²×C₉	1	8	yes	complemented
252	#117	C₂²×C₉	1	16	yes	complemented
253	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
261	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂²×C₉	1	8	yes	complemented
264	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
269	C₂×C₄²	C₂²×C₉	1	2	yes	—
270	C₂×C₄²	C₂²×C₉	1	2	yes	—
271	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	C₃×#41	1	4	yes	—
278	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
279	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
280	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
281	C₃×Q₈	—	2	8	no	—
282	C₃×D₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	16	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	8	no	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	C₃×#41	1	4	yes	—
295	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
296	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
297	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
298	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
299	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
300	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
301	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
303	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
304	C₂×C₉	—	2	4	no	—
305	C₂×C₉	—	4	2	no	—
306	C₂×C₉	#552	1	4	yes	direct product factor
307	C₂×C₉	C₂²×#41	1	1	yes	characteristic
308	C₂×C₉	C₂²×#41	1	1	yes	characteristic
309	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂⁴	C₂³×C₉	1	1	yes	characteristic
311	C₂⁴	C₂³×C₉	1	1	yes	characteristic
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	C₂³×C₉	1	4	yes	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	C₂³×C₉	1	4	yes	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₉	1	2	yes	—
322	C₂²×C₄	C₂³×C₉	1	2	yes	—
323	C₂²×C₄	C₂³×C₉	1	2	yes	—
324	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₉	1	2	yes	—
327	C₂²×C₄	C₂³×C₉	1	8	yes	—
328	C₂²×C₄	C₂³×C₉	1	4	yes	—
329	C₂²×C₄	C₂³×C₉	1	4	yes	—
330	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂³×C₉	1	4	yes	—
332	C₄⋊C₄	C₂³×C₉	1	4	yes	—
333	C₄⋊C₄	C₂³×C₉	1	8	yes	—
334	C₄⋊C₄	C₂³×C₉	1	8	yes	—
335	C₄⋊C₄	C₂³×C₉	1	4	yes	—
336	C₄⋊C₄	C₂³×C₉	1	8	yes	—
337	C₄⋊C₄	C₂³×C₉	1	4	yes	—
338	C₄⋊C₄	C₂³×C₉	1	8	yes	—
339	C₄⋊C₄	C₂³×C₉	1	8	yes	—
340	C₄⋊C₄	C₂³×C₉	1	8	yes	—
341	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
342	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
343	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
344	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
345	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
346	C₄²	C₂³×C₉	1	8	yes	—
347	C₄²	C₂³×C₉	1	8	yes	—
348	C₄²	C₂³×C₉	1	4	yes	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	8	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	4	4	no	—
356	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
357	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
358	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
359	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
360	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	4	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	4	no	—
369	C₃×C₄	C₂×C₃×#41	1	4	yes	—
370	C₉	C₂×#552	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	C₉×#41	1	4	yes	—
377	C₂³	C₂⁴×C₉	1	2	yes	—
378	C₂³	C₂⁴×C₉	1	2	yes	—
379	C₂³	C₂⁴×C₉	1	1	yes	characteristic
380	Q₈	—	2	8	no	—
381	D₄	—	2	8	no	—
382	C₂×C₄	—	2	16	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	C₉×#41	1	4	yes	—
394	C₂×C₄	C₂⁴×C₉	1	2	yes	—
395	C₂×C₄	C₂⁴×C₉	1	2	yes	—
396	C₂×C₄	C₂⁴×C₉	1	4	yes	—
397	C₂×C₄	C₂⁴×C₉	1	4	yes	—
398	C₂×C₄	C₂⁴×C₉	1	4	yes	—
399	C₂×C₄	C₂⁴×C₉	1	2	yes	—
400	C₂×C₄	C₂⁴×C₉	1	2	yes	—
401	C₂×C₄	C₂⁴×C₉	1	4	yes	—
402	C₂×C₄	C₂⁴×C₉	1	2	yes	—
403	C₂×C₃	—	2	4	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	C₃×#552	1	4	yes	—
406	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
407	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
408	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²	—	2	8	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	C₂×C₉×#41	1	4	yes	—
417	C₂²	C₂×C₉×#41	1	2	yes	—
418	C₂²	C₂×C₉×#41	1	2	yes	—
419	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
420	C₂²	C₂⁵×C₉	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	4	no	—
429	C₄	C₂×C₉×#41	1	4	yes	—
430	C₃	C₂×C₃×#552	1	1	yes	characteristic
431	C₂	—	2	4	no	—
432	C₂	—	4	2	no	—
433	C₂	C₉×#552	1	4	yes	direct product factor
434	C₂	C₂²×C₉×#41	1	1	yes	characteristic
435	C₂	C₂²×C₉×#41	1	1	yes	characteristic
436	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	C₂²×C₃×D₄	C₂²×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. C₉×#552	C₂	direct (N × H)
2. C₂×C₉×#126	C₂	semidirect
3. C₂×C₉×#125	C₂	semidirect
4. C₂×C₉×#125	C₂	semidirect
6. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
7. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₄×Q₈×C₉	C₂	semidirect
10. C₂×C₉×#117	C₂	semidirect
11. C₂×C₉×#117	C₂	semidirect
12. C₂²×C₉×C₄⋊C₄	C₂	semidirect
19. C₉×#126	C₂²	semidirect
20. C₉×#125	C₂²	semidirect
21. C₉×#125	C₂²	semidirect
23. C₉×C₂²⋊Q₈	C₂²	semidirect
24. C₉×C₂²⋊Q₈	C₂²	semidirect
25. C₄×Q₈×C₉	C₂²	semidirect
27. C₉×#117	C₂²	semidirect
28. C₉×#117	C₂²	semidirect
39. C₂×C₉×C₄⋊C₄	C₂²	semidirect
99. C₂×#552	C₉	direct (N × H)
166. #552	C₂×C₉	direct (N × H)
167. C₂×#126	C₂×C₉	semidirect
168. C₂×#125	C₂×C₉	semidirect
169. C₂×#125	C₂×C₉	semidirect
171. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
172. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
173. C₂×C₄×Q₈	C₂×C₉	semidirect
175. C₂×#117	C₂×C₉	semidirect
176. C₂×#117	C₂×C₉	semidirect
177. C₂²×C₄⋊C₄	C₂×C₉	semidirect
243. #126	C₂²×C₉	semidirect
244. #125	C₂²×C₉	semidirect
245. #125	C₂²×C₉	semidirect
247. C₂²⋊Q₈	C₂²×C₉	semidirect
248. C₂²⋊Q₈	C₂²×C₉	semidirect
249. C₄×Q₈	C₂²×C₉	semidirect
251. #117	C₂²×C₉	semidirect
252. #117	C₂²×C₉	semidirect
263. C₂×C₄⋊C₄	C₂²×C₉	semidirect
306. C₂×C₉	#552	direct (N × H)
370. C₉	C₂×#552	direct (N × H)
433. C₂	C₉×#552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#552	2
C₂×C₉×#126	2
C₂×C₉×#125	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂²×C₉×C₄⋊C₄	2
C₂×C₃×#552	3

Subgroups — C2×C9×#552 #11768191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#552 #11768191