Subgroups — C₂×C₉×#542 #11768175

Order 1152.

1698 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#542	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#124	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
7	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#542	C₃	1	1	yes	maximal, characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₉	C₂²	1	2	yes	—
16	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₉	C₂²	1	2	yes	—
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	2	yes	—
20	C₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
21	C₉×#126	C₂²	1	16	yes	complemented
22	C₉×#124	C₂²	1	8	yes	complemented
23	C₉×#124	C₂²	1	16	yes	complemented
24	C₉×#123	C₂²	1	16	yes	complemented
25	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
26	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
27	C₉×#121	C₂²	1	8	yes	—
28	C₄×Q₈×C₉	C₂²	1	8	yes	complemented
29	C₄×D₄×C₉	C₂²	1	8	yes	complemented
30	C₉×#117	C₂²	1	8	yes	complemented
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
38	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
45	C₂×C₄²×C₉	C₂²	1	2	yes	—
46	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
48	C₃×#542	C₂×C₃	1	16	yes	—
49	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
50	C₂×C₃×#126	C₂×C₃	1	2	yes	—
51	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
52	C₂×C₃×#124	C₂×C₃	1	2	yes	—
53	C₂×C₃×#123	C₂×C₃	1	2	yes	—
54	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
55	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
59	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
60	C₂⁴×C₉	C₂³	1	1	yes	characteristic
61	C₂⁴×C₉	C₂³	1	2	yes	—
62	C₂×Q₈×C₉	—	2	4	no	—
63	C₂×Q₈×C₉	—	4	4	no	—
64	C₂×Q₈×C₉	C₂³	1	4	yes	—
65	C₂×Q₈×C₉	C₂³	1	8	yes	—
66	C₂×D₄×C₉	—	2	4	no	—
67	C₂×D₄×C₉	—	4	4	no	—
68	C₂×D₄×C₉	C₂³	1	4	yes	—
69	C₂×D₄×C₉	C₂³	1	8	yes	—
70	C₂²×C₄×C₉	—	2	4	no	—
71	C₂²×C₄×C₉	—	4	4	no	—
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	2	yes	—
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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	2	yes	—
81	C₂²×C₄×C₉	C₂³	1	8	yes	—
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₉×C₄⋊C₄	C₂³	1	4	yes	—
84	C₉×C₄⋊C₄	C₂³	1	4	yes	—
85	C₉×C₄⋊C₄	C₂³	1	4	yes	—
86	C₉×C₄⋊C₄	C₂³	1	4	yes	—
87	C₉×C₄⋊C₄	C₂³	1	8	yes	—
88	C₉×C₄⋊C₄	C₂³	1	8	yes	—
89	C₉×C₄⋊C₄	C₂³	1	8	yes	—
90	C₉×C₂²⋊C₄	C₂³	1	4	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	8	yes	—
95	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₄²×C₉	C₂³	1	4	yes	—
98	C₄²×C₉	C₂³	1	4	yes	—
99	C₄²×C₉	C₂³	1	8	yes	—
100	C₂×#542	C₉	1	1	yes	characteristic, direct product factor, Sylow
101	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
103	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
105	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
107	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
108	C₃×#126	C₂²×C₃	1	16	yes	—
109	C₃×#124	C₂²×C₃	1	8	yes	—
110	C₃×#124	C₂²×C₃	1	16	yes	—
111	C₃×#123	C₂²×C₃	1	16	yes	—
112	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
113	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
114	C₃×#121	C₂²×C₃	1	8	yes	—
115	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
116	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
117	C₃×#117	C₂²×C₃	1	8	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
135	C₂³×C₉	—	2	2	no	—
136	C₂³×C₉	—	2	4	no	—
137	C₂³×C₉	—	2	4	no	—
138	C₂³×C₉	—	2	2	no	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	4	no	—
141	C₂³×C₉	C₂⁴	1	2	yes	—
142	C₂³×C₉	C₂⁴	1	4	yes	—
143	C₂³×C₉	C₂⁴	1	1	yes	characteristic
144	Q₈×C₉	—	2	8	no	—
145	Q₈×C₉	—	4	8	no	—
146	D₄×C₉	—	2	8	no	—
147	D₄×C₉	—	4	8	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	8	no	—
157	C₂×C₄×C₉	—	4	8	no	—
158	C₂×C₄×C₉	#41	1	4	yes	—
159	C₂×C₄×C₉	C₂⁴	1	2	yes	—
160	C₂×C₄×C₉	C₂⁴	1	2	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	C₂×C₄×C₉	C₂⁴	1	4	yes	—
167	C₂×C₄×C₉	C₂⁴	1	2	yes	—
168	#542	C₂×C₉	1	16	yes	direct product factor
169	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
170	C₂×#126	C₂×C₉	1	2	yes	complemented
171	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
172	C₂×#124	C₂×C₉	1	2	yes	complemented
173	C₂×#123	C₂×C₉	1	2	yes	complemented
174	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
175	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂×#121	C₂×C₉	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
178	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
179	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
180	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
181	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
182	C₂×C₃×Q₈	—	2	4	no	—
183	C₂×C₃×Q₈	—	4	4	no	—
184	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
185	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	—	4	4	no	—
188	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
189	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	4	4	no	—
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	1	yes	characteristic
196	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
201	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
202	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
203	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
204	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
207	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
208	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
209	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
210	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
211	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
212	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
213	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
214	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
215	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
216	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
217	C₃×C₄²	C₂³×C₃	1	4	yes	—
218	C₃×C₄²	C₂³×C₃	1	4	yes	—
219	C₃×C₄²	C₂³×C₃	1	8	yes	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	4	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	2	4	no	—
226	C₂²×C₉	—	4	4	no	—
227	C₂²×C₉	—	4	8	no	—
228	C₂²×C₉	C₂×#41	1	2	yes	—
229	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
230	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
231	C₂²×C₉	C₂⁵	1	1	yes	characteristic
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	2	4	no	—
236	C₄×C₉	—	2	4	no	—
237	C₄×C₉	—	2	2	no	—
238	C₄×C₉	—	2	2	no	—
239	C₄×C₉	—	2	2	no	—
240	C₄×C₉	C₂×#41	1	4	yes	—
241	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
242	C₂²×Q₈	C₂²×C₉	1	2	yes	—
243	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
244	C₂²×D₄	C₂²×C₉	1	2	yes	—
245	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
246	C₂³×C₄	C₂²×C₉	1	2	yes	—
247	C₄⋊Q₈	C₂²×C₉	1	8	yes	complemented
248	#126	C₂²×C₉	1	16	yes	complemented
249	#124	C₂²×C₉	1	8	yes	complemented
250	#124	C₂²×C₉	1	16	yes	complemented
251	#123	C₂²×C₉	1	16	yes	complemented
252	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
253	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
254	#121	C₂²×C₉	1	8	yes	—
255	C₄×Q₈	C₂²×C₉	1	8	yes	complemented
256	C₄×D₄	C₂²×C₉	1	8	yes	complemented
257	#117	C₂²×C₉	1	8	yes	complemented
258	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
272	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
273	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
274	C₂×C₄²	C₂²×C₉	1	2	yes	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	4	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
282	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
283	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
284	C₃×Q₈	—	2	8	no	—
285	C₃×Q₈	—	4	8	no	—
286	C₃×D₄	—	2	8	no	—
287	C₃×D₄	—	4	8	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	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	8	no	—
297	C₂×C₃×C₄	—	4	8	no	—
298	C₂×C₃×C₄	C₃×#41	1	4	yes	—
299	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
300	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
301	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
302	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
303	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
304	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
306	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
307	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
308	C₂×C₉	—	4	2	no	—
309	C₂×C₉	—	4	4	no	—
310	C₂×C₉	#542	1	4	yes	direct product factor
311	C₂×C₉	C₂²×#41	1	1	yes	characteristic
312	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂⁴	C₂³×C₉	1	1	yes	characteristic
315	C₂⁴	C₂³×C₉	1	2	yes	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	C₂³×C₉	1	4	yes	—
319	C₂×Q₈	C₂³×C₉	1	8	yes	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	C₂³×C₉	1	4	yes	—
323	C₂×D₄	C₂³×C₉	1	8	yes	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₉	1	2	yes	—
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂²×C₄	C₂³×C₉	1	2	yes	—
332	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₉	1	2	yes	—
334	C₂²×C₄	C₂³×C₉	1	4	yes	—
335	C₂²×C₄	C₂³×C₉	1	8	yes	—
336	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₉	1	4	yes	—
338	C₄⋊C₄	C₂³×C₉	1	4	yes	—
339	C₄⋊C₄	C₂³×C₉	1	4	yes	—
340	C₄⋊C₄	C₂³×C₉	1	4	yes	—
341	C₄⋊C₄	C₂³×C₉	1	8	yes	—
342	C₄⋊C₄	C₂³×C₉	1	8	yes	—
343	C₄⋊C₄	C₂³×C₉	1	8	yes	—
344	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
345	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
346	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
347	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
348	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
349	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
350	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
351	C₄²	C₂³×C₉	1	4	yes	—
352	C₄²	C₂³×C₉	1	4	yes	—
353	C₄²	C₂³×C₉	1	8	yes	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	4	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	—	4	8	no	—
362	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
363	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
364	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
365	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	4	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	4	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	C₂×C₃×#41	1	4	yes	—
375	C₉	C₂×#542	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	C₂⁴×C₉	1	2	yes	—
383	C₂³	C₂⁴×C₉	1	4	yes	—
384	C₂³	C₂⁴×C₉	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	4	8	no	—
387	D₄	—	2	8	no	—
388	D₄	—	4	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	C₉×#41	1	4	yes	—
400	C₂×C₄	C₂⁴×C₉	1	2	yes	—
401	C₂×C₄	C₂⁴×C₉	1	2	yes	—
402	C₂×C₄	C₂⁴×C₉	1	4	yes	—
403	C₂×C₄	C₂⁴×C₉	1	2	yes	—
404	C₂×C₄	C₂⁴×C₉	1	2	yes	—
405	C₂×C₄	C₂⁴×C₉	1	4	yes	—
406	C₂×C₄	C₂⁴×C₉	1	2	yes	—
407	C₂×C₄	C₂⁴×C₉	1	4	yes	—
408	C₂×C₄	C₂⁴×C₉	1	2	yes	—
409	C₂×C₃	—	4	2	no	—
410	C₂×C₃	—	4	4	no	—
411	C₂×C₃	C₃×#542	1	4	yes	—
412	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
413	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	8	no	—
423	C₂²	C₂×C₉×#41	1	2	yes	—
424	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
425	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
426	C₂²	C₂⁵×C₉	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	C₂×C₉×#41	1	4	yes	—
436	C₃	C₂×C₃×#542	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	—	4	4	no	—
439	C₂	C₉×#542	1	4	yes	direct product factor
440	C₂	C₂²×C₉×#41	1	1	yes	characteristic
441	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic
442	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×#121	C₂×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×#542	C₂	direct (N × H)
2. C₂×C₉×C₄⋊Q₈	C₂	semidirect
3. C₂×C₉×#126	C₂	semidirect
4. C₂×C₉×#124	C₂	semidirect
5. C₂×C₉×#124	C₂	semidirect
6. C₂×C₉×#123	C₂	semidirect
7. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
10. C₂×C₄×Q₈×C₉	C₂	semidirect
11. C₂×C₄×D₄×C₉	C₂	semidirect
12. C₂×C₉×#117	C₂	semidirect
20. C₉×C₄⋊Q₈	C₂²	semidirect
21. C₉×#126	C₂²	semidirect
22. C₉×#124	C₂²	semidirect
23. C₉×#124	C₂²	semidirect
24. C₉×#123	C₂²	semidirect
25. C₉×C₂²⋊Q₈	C₂²	semidirect
26. C₉×C₂²⋊Q₈	C₂²	semidirect
28. C₄×Q₈×C₉	C₂²	semidirect
29. C₄×D₄×C₉	C₂²	semidirect
30. C₉×#117	C₂²	semidirect
100. C₂×#542	C₉	direct (N × H)
168. #542	C₂×C₉	direct (N × H)
169. C₂×C₄⋊Q₈	C₂×C₉	semidirect
170. C₂×#126	C₂×C₉	semidirect
171. C₂×#124	C₂×C₉	semidirect
172. C₂×#124	C₂×C₉	semidirect
173. C₂×#123	C₂×C₉	semidirect
174. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
175. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
177. C₂×C₄×Q₈	C₂×C₉	semidirect
178. C₂×C₄×D₄	C₂×C₉	semidirect
179. C₂×#117	C₂×C₉	semidirect
247. C₄⋊Q₈	C₂²×C₉	semidirect
248. #126	C₂²×C₉	semidirect
249. #124	C₂²×C₉	semidirect
250. #124	C₂²×C₉	semidirect
251. #123	C₂²×C₉	semidirect
252. C₂²⋊Q₈	C₂²×C₉	semidirect
253. C₂²⋊Q₈	C₂²×C₉	semidirect
255. C₄×Q₈	C₂²×C₉	semidirect
256. C₄×D₄	C₂²×C₉	semidirect
257. #117	C₂²×C₉	semidirect
310. C₂×C₉	#542	direct (N × H)
375. C₉	C₂×#542	direct (N × H)
439. C₂	C₉×#542	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×#542	2
C₂×C₉×C₄⋊Q₈	2
C₂×C₉×#126	2
C₂×C₉×#124	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂×C₃×#542	3

Subgroups — C2×C9×#542 #11768175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#542 #11768175