Subgroups — C₂×C₉×#554 #11768193

Order 1152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#554	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#125	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×D₄×C₉	C₂	1	2	yes	maximal
8	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#554	C₃	1	1	yes	maximal, characteristic
11	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₉	C₂²	1	2	yes	—
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₉	C₂²	1	4	yes	—
16	C₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
17	C₉×#125	C₂²	1	16	yes	complemented
18	C₉×C₂²⋊Q₈	C₂²	1	32	yes	complemented
19	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
20	C₄×Q₈×C₉	C₂²	1	8	yes	complemented
21	C₄×D₄×C₉	C₂²	1	16	yes	—
22	C₄×D₄×C₉	C₂²	1	8	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
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	2	yes	—
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	16	yes	complemented
31	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	2	yes	—
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₃×#554	C₂×C₃	1	16	yes	—
36	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×#125	C₂×C₃	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
40	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂×C₃	1	2	yes	—
42	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
43	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
44	C₂⁴×C₉	C₂³	1	2	yes	—
45	C₂×Q₈×C₉	—	2	4	no	—
46	C₂×Q₈×C₉	—	4	4	no	—
47	C₂×Q₈×C₉	C₂³	1	4	yes	—
48	C₂×Q₈×C₉	C₂³	1	8	yes	—
49	C₂×D₄×C₉	Q₈	1	8	yes	complemented
50	C₂×D₄×C₉	C₂³	1	4	yes	—
51	C₂²×C₄×C₉	—	2	8	no	—
52	C₂²×C₄×C₉	—	4	8	no	—
53	C₂²×C₄×C₉	C₂³	1	8	yes	—
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
58	C₂²×C₄×C₉	C₂³	1	4	yes	—
59	C₂²×C₄×C₉	C₂³	1	16	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₉×C₄⋊C₄	C₂³	1	4	yes	—
63	C₉×C₄⋊C₄	C₂³	1	16	yes	—
64	C₉×C₄⋊C₄	C₂³	1	8	yes	—
65	C₉×C₄⋊C₄	C₂³	1	4	yes	—
66	C₉×C₄⋊C₄	C₂³	1	8	yes	—
67	C₉×C₄⋊C₄	C₂³	1	8	yes	—
68	C₉×C₄⋊C₄	C₂³	1	16	yes	—
69	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
70	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₄²×C₉	C₂³	1	8	yes	—
72	C₄²×C₉	C₂³	1	4	yes	—
73	C₂×#554	C₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
76	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
78	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
79	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
80	C₃×#125	C₂²×C₃	1	16	yes	—
81	C₃×C₂²⋊Q₈	C₂²×C₃	1	32	yes	—
82	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
83	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
84	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
85	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
95	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
98	C₂³×C₉	—	2	4	no	—
99	C₂³×C₉	—	2	4	no	—
100	C₂³×C₉	C₂×Q₈	1	8	yes	—
101	C₂³×C₉	C₂⁴	1	4	yes	—
102	C₂³×C₉	C₂⁴	1	1	yes	characteristic
103	Q₈×C₉	—	2	8	no	—
104	Q₈×C₉	—	4	8	no	—
105	D₄×C₉	C₂×Q₈	1	16	yes	complemented
106	C₂×C₄×C₉	—	2	4	no	—
107	C₂×C₄×C₉	—	2	4	no	—
108	C₂×C₄×C₉	—	2	4	no	—
109	C₂×C₄×C₉	—	2	8	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	16	no	—
112	C₂×C₄×C₉	—	4	16	no	—
113	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
114	C₂×C₄×C₉	#41	1	4	yes	—
115	C₂×C₄×C₉	C₂⁴	1	4	yes	—
116	C₂×C₄×C₉	C₂⁴	1	2	yes	—
117	C₂×C₄×C₉	C₂⁴	1	4	yes	—
118	C₂×C₄×C₉	C₂⁴	1	4	yes	—
119	C₂×C₄×C₉	C₂⁴	1	8	yes	—
120	C₂×C₄×C₉	C₂⁴	1	2	yes	—
121	C₂×C₄×C₉	C₂⁴	1	2	yes	—
122	#554	C₂×C₉	1	16	yes	direct product factor
123	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂×#125	C₂×C₉	1	2	yes	complemented
125	C₂×C₂²⋊Q₈	C₂×C₉	1	4	yes	complemented
126	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
127	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂×C₄×D₄	C₂×C₉	1	2	yes	—
129	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
131	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
132	C₂×C₃×Q₈	—	2	4	no	—
133	C₂×C₃×Q₈	—	4	4	no	—
134	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
135	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
136	C₂×C₃×D₄	C₃×Q₈	1	8	yes	—
137	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
138	C₂²×C₃×C₄	—	2	8	no	—
139	C₂²×C₃×C₄	—	4	8	no	—
140	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
141	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
143	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
144	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
145	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
146	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
150	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
151	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
152	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
153	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
154	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
155	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
156	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
157	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
158	C₃×C₄²	C₂³×C₃	1	8	yes	—
159	C₃×C₄²	C₂³×C₃	1	4	yes	—
160	C₂²×C₉	—	2	16	no	—
161	C₂²×C₉	—	2	4	no	—
162	C₂²×C₉	—	2	4	no	—
163	C₂²×C₉	C₂²×Q₈	1	8	yes	—
164	C₂²×C₉	C₂²×Q₈	1	2	yes	—
165	C₂²×C₉	C₂×#41	1	2	yes	—
166	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
167	C₂²×C₉	C₂⁵	1	1	yes	characteristic
168	C₄×C₉	—	2	4	no	—
169	C₄×C₉	—	2	4	no	—
170	C₄×C₉	—	2	4	no	—
171	C₄×C₉	—	2	8	no	—
172	C₄×C₉	—	2	2	no	—
173	C₄×C₉	C₂²×Q₈	1	4	yes	—
174	C₄×C₉	C₂×#41	1	4	yes	—
175	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
176	C₂²×Q₈	C₂²×C₉	1	2	yes	—
177	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
178	C₂³×C₄	C₂²×C₉	1	2	yes	—
179	C₂³×C₄	C₂²×C₉	1	4	yes	—
180	C₄⋊Q₈	C₂²×C₉	1	8	yes	complemented
181	#125	C₂²×C₉	1	16	yes	complemented
182	C₂²⋊Q₈	C₂²×C₉	1	32	yes	complemented
183	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
184	C₄×Q₈	C₂²×C₉	1	8	yes	complemented
185	C₄×D₄	C₂²×C₉	1	16	yes	—
186	C₄×D₄	C₂²×C₉	1	8	yes	—
187	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
189	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
190	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
192	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
193	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
194	C₂×C₄⋊C₄	C₂²×C₉	1	16	yes	complemented
195	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
196	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
197	C₂×C₄²	C₂²×C₉	1	2	yes	—
198	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
199	C₂³×C₃	—	2	4	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	C₂×C₃×Q₈	1	8	yes	—
202	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
203	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
204	C₃×Q₈	—	2	8	no	—
205	C₃×Q₈	—	4	8	no	—
206	C₃×D₄	C₂×C₃×Q₈	1	16	yes	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	4	no	—
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	16	no	—
213	C₂×C₃×C₄	—	4	16	no	—
214	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
215	C₂×C₃×C₄	C₃×#41	1	4	yes	—
216	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
217	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
218	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
219	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
220	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
221	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
222	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
223	C₂×C₉	—	2	8	no	—
224	C₂×C₉	#554	1	4	yes	direct product factor
225	C₂×C₉	C₂³×Q₈	1	1	yes	characteristic
226	C₂×C₉	C₂²×#41	1	1	yes	characteristic
227	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂⁴	C₂³×C₉	1	2	yes	—
229	C₂×Q₈	—	2	4	no	—
230	C₂×Q₈	—	4	4	no	—
231	C₂×Q₈	C₂³×C₉	1	4	yes	—
232	C₂×Q₈	C₂³×C₉	1	8	yes	—
233	C₂×D₄	Q₈×C₉	1	8	yes	complemented
234	C₂×D₄	C₂³×C₉	1	4	yes	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	4	8	no	—
237	C₂²×C₄	C₂³×C₉	1	2	yes	—
238	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
239	C₂²×C₄	C₂³×C₉	1	2	yes	—
240	C₂²×C₄	C₂³×C₉	1	2	yes	—
241	C₂²×C₄	C₂³×C₉	1	4	yes	—
242	C₂²×C₄	C₂³×C₉	1	8	yes	—
243	C₂²×C₄	C₂³×C₉	1	16	yes	—
244	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
246	C₄⋊C₄	C₂³×C₉	1	4	yes	—
247	C₄⋊C₄	C₂³×C₉	1	16	yes	—
248	C₄⋊C₄	C₂³×C₉	1	8	yes	—
249	C₄⋊C₄	C₂³×C₉	1	4	yes	—
250	C₄⋊C₄	C₂³×C₉	1	8	yes	—
251	C₄⋊C₄	C₂³×C₉	1	8	yes	—
252	C₄⋊C₄	C₂³×C₉	1	16	yes	—
253	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
254	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
255	C₄²	C₂³×C₉	1	8	yes	—
256	C₄²	C₂³×C₉	1	4	yes	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	2	16	no	—
260	C₂²×C₃	C₂²×C₃×Q₈	1	8	yes	—
261	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
262	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
263	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
264	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	2	4	no	—
267	C₃×C₄	—	2	4	no	—
268	C₃×C₄	—	2	8	no	—
269	C₃×C₄	—	2	2	no	—
270	C₃×C₄	C₂²×C₃×Q₈	1	4	yes	—
271	C₃×C₄	C₂×C₃×#41	1	4	yes	—
272	C₉	C₂×#554	1	1	yes	characteristic, direct product factor, Sylow
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	C₂×Q₈×C₉	1	8	yes	—
276	C₂³	C₂⁴×C₉	1	4	yes	—
277	C₂³	C₂⁴×C₉	1	1	yes	characteristic
278	Q₈	—	2	8	no	—
279	Q₈	—	4	8	no	—
280	D₄	C₂×Q₈×C₉	1	16	yes	complemented
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	16	no	—
287	C₂×C₄	—	4	16	no	—
288	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
289	C₂×C₄	C₉×#41	1	4	yes	—
290	C₂×C₄	C₂⁴×C₉	1	4	yes	—
291	C₂×C₄	C₂⁴×C₉	1	2	yes	—
292	C₂×C₄	C₂⁴×C₉	1	4	yes	—
293	C₂×C₄	C₂⁴×C₉	1	4	yes	—
294	C₂×C₄	C₂⁴×C₉	1	8	yes	—
295	C₂×C₄	C₂⁴×C₉	1	2	yes	—
296	C₂×C₄	C₂⁴×C₉	1	2	yes	—
297	C₂×C₃	—	2	8	no	—
298	C₂×C₃	C₃×#554	1	4	yes	—
299	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
300	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
301	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂²	—	2	16	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	4	no	—
305	C₂²	C₂²×Q₈×C₉	1	8	yes	—
306	C₂²	C₂²×Q₈×C₉	1	2	yes	—
307	C₂²	C₂×C₉×#41	1	2	yes	—
308	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
309	C₂²	C₂⁵×C₉	1	1	yes	characteristic
310	C₄	—	2	4	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	4	no	—
313	C₄	—	2	8	no	—
314	C₄	—	2	2	no	—
315	C₄	C₂²×Q₈×C₉	1	4	yes	—
316	C₄	C₂×C₉×#41	1	4	yes	—
317	C₃	C₂×C₃×#554	1	1	yes	characteristic
318	C₂	—	2	8	no	—
319	C₂	C₉×#554	1	4	yes	direct product factor
320	C₂	C₂³×Q₈×C₉	1	1	yes	characteristic
321	C₂	C₂²×C₉×#41	1	1	yes	characteristic
322	C₂	C₂×C₉×H(5,𝔽₂)	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×#554	C₂	direct (N × H)
2. C₂×C₉×C₄⋊Q₈	C₂	semidirect
3. C₂×C₉×#125	C₂	semidirect
4. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
5. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₄×Q₈×C₉	C₂	semidirect
9. C₂²×C₉×C₄⋊C₄	C₂	semidirect
16. C₉×C₄⋊Q₈	C₂²	semidirect
17. C₉×#125	C₂²	semidirect
18. C₉×C₂²⋊Q₈	C₂²	semidirect
19. C₉×C₂²⋊Q₈	C₂²	semidirect
20. C₄×Q₈×C₉	C₂²	semidirect
30. C₂×C₉×C₄⋊C₄	C₂²	semidirect
49. C₂×D₄×C₉	Q₈	semidirect
73. C₂×#554	C₉	direct (N × H)
105. D₄×C₉	C₂×Q₈	semidirect
122. #554	C₂×C₉	direct (N × H)
123. C₂×C₄⋊Q₈	C₂×C₉	semidirect
124. C₂×#125	C₂×C₉	semidirect
125. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
126. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
127. C₂×C₄×Q₈	C₂×C₉	semidirect
130. C₂²×C₄⋊C₄	C₂×C₉	semidirect
180. C₄⋊Q₈	C₂²×C₉	semidirect
181. #125	C₂²×C₉	semidirect
182. C₂²⋊Q₈	C₂²×C₉	semidirect
183. C₂²⋊Q₈	C₂²×C₉	semidirect
184. C₄×Q₈	C₂²×C₉	semidirect
194. C₂×C₄⋊C₄	C₂²×C₉	semidirect
224. C₂×C₉	#554	direct (N × H)
233. C₂×D₄	Q₈×C₉	semidirect
272. C₉	C₂×#554	direct (N × H)
280. D₄	C₂×Q₈×C₉	semidirect
319. C₂	C₉×#554	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×#554	2
C₂×C₉×C₄⋊Q₈	2
C₂×C₉×#125	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₄⋊C₄	2
C₂×C₃×#554	3

Subgroups — C2×C9×#554 #11768193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#554 #11768193