Subgroups — C₉×#2451 #11767172

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#398	C₂	1	2	yes	maximal
4	C₉×#395	C₂	1	2	yes	maximal
5	C₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₉×#391	C₂	1	1	yes	maximal, characteristic
7	C₉×#391	C₂	1	2	yes	maximal
8	C₉×#389	C₂	1	1	yes	maximal, characteristic
9	C₉×#389	C₂	1	1	yes	maximal, characteristic
10	C₉×#387	C₂	1	2	yes	maximal
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2451	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	2	yes	—
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₉×C₄⋊Q₈	—	2	4	no	—
16	C₄×Q₈×C₉	—	2	4	no	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₉	C₂²	1	2	yes	—
30	C₉×#95	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	2	yes	—
33	C₉×#95	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
40	C₃×#398	C₂×C₃	1	2	yes	—
41	C₃×#395	C₂×C₃	1	2	yes	—
42	C₃×#391	C₂×C₃	1	2	yes	—
43	C₃×#391	C₂×C₃	1	1	yes	characteristic
44	C₃×#391	C₂×C₃	1	1	yes	characteristic
45	C₃×#389	C₂×C₃	1	1	yes	characteristic
46	C₃×#389	C₂×C₃	1	1	yes	characteristic
47	C₃×#387	C₂×C₃	1	2	yes	—
48	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₂×Q₈×C₉	—	2	2	no	—
50	C₂×Q₈×C₉	—	2	4	no	—
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	—	2	4	no	—
53	C₂×Q₈×C₉	—	4	2	no	—
54	C₂×Q₈×C₉	Q₈	1	4	yes	complemented
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
58	C₂²×C₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₉×C₄⋊C₄	—	2	4	no	—
67	C₉×C₄⋊C₄	—	2	4	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₄⋊C₄	—	2	2	no	—
71	C₉×C₄⋊C₄	—	4	2	no	—
72	C₉×C₄⋊C₄	—	4	2	no	—
73	C₉×C₄⋊C₄	D₄	1	4	yes	—
74	C₉×C₄⋊C₄	Q₈	1	4	yes	complemented
75	C₄²×C₉	—	2	4	no	—
76	C₄²×C₉	—	2	2	no	—
77	C₄²×C₉	—	2	2	no	—
78	C₄²×C₉	—	2	2	no	—
79	#2451	C₉	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
81	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₃×C₄⋊Q₈	—	2	4	no	—
83	C₃×C₄×Q₈	—	2	4	no	—
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
97	C₃×#95	C₂²×C₃	1	1	yes	characteristic
98	C₃×#95	C₂²×C₃	1	1	yes	characteristic
99	C₃×#95	C₂²×C₃	1	2	yes	—
100	C₃×#95	C₂²×C₃	1	2	yes	—
101	C₃×#95	C₂²×C₃	1	2	yes	—
102	C₃×#95	C₂²×C₃	1	2	yes	—
103	C₃×#95	C₂²×C₃	1	2	yes	—
104	C₃×#95	C₂²×C₃	1	2	yes	—
105	C₂³×C₉	C₂⁴	1	1	yes	characteristic
106	Q₈×C₉	—	2	8	no	—
107	Q₈×C₉	—	4	8	no	—
108	C₂×C₄×C₉	—	2	1	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	1	no	—
112	C₂×C₄×C₉	—	2	1	no	—
113	C₂×C₄×C₉	—	2	1	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	1	no	—
118	C₂×C₄×C₉	—	2	1	no	—
119	C₂×C₄×C₉	—	2	1	no	—
120	C₂×C₄×C₉	—	2	1	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
133	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
135	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
136	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
137	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
138	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
139	C₂×C₄×C₉	#41	1	2	yes	—
140	C₂×C₄×C₉	#41	1	2	yes	—
141	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
142	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic
143	#398	C₂×C₉	1	2	yes	—
144	#395	C₂×C₉	1	2	yes	—
145	#391	C₂×C₉	1	2	yes	—
146	#391	C₂×C₉	1	1	yes	characteristic
147	#391	C₂×C₉	1	1	yes	characteristic
148	#389	C₂×C₉	1	1	yes	characteristic
149	#389	C₂×C₉	1	1	yes	characteristic
150	#387	C₂×C₉	1	2	yes	—
151	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
152	C₂×C₃×Q₈	—	2	2	no	—
153	C₂×C₃×Q₈	—	2	4	no	—
154	C₂×C₃×Q₈	—	2	2	no	—
155	C₂×C₃×Q₈	—	2	4	no	—
156	C₂×C₃×Q₈	—	4	2	no	—
157	C₂×C₃×Q₈	C₃×Q₈	1	4	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	4	2	no	—
175	C₃×C₄⋊C₄	—	4	2	no	—
176	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
177	C₃×C₄⋊C₄	C₃×Q₈	1	4	yes	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	—	2	2	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×C₉	C₂×#41	1	1	yes	characteristic
186	C₂²×C₉	C₂×#41	1	1	yes	characteristic
187	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₄×C₉	—	2	4	no	—
190	C₄×C₉	—	2	2	no	—
191	C₄×C₉	—	2	4	no	—
192	C₄×C₉	—	2	2	no	—
193	C₄×C₉	—	2	2	no	—
194	C₄×C₉	—	2	2	no	—
195	C₄×C₉	—	4	1	no	—
196	C₄×C₉	—	4	2	no	—
197	C₄×C₉	—	4	1	no	—
198	C₄×C₉	—	4	2	no	—
199	C₄×C₉	C₂²⋊Q₈	1	4	yes	—
200	C₂²×Q₈	C₂²×C₉	1	2	yes	—
201	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
202	C₄⋊Q₈	—	2	4	no	—
203	C₄×Q₈	—	2	4	no	—
204	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
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	2	yes	—
211	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₄²	C₂²×C₉	1	2	yes	—
215	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
217	#95	C₂²×C₉	1	1	yes	characteristic
218	#95	C₂²×C₉	1	1	yes	characteristic
219	#95	C₂²×C₉	1	2	yes	—
220	#95	C₂²×C₉	1	2	yes	—
221	#95	C₂²×C₉	1	2	yes	—
222	#95	C₂²×C₉	1	2	yes	—
223	#95	C₂²×C₉	1	2	yes	—
224	#95	C₂²×C₉	1	2	yes	—
225	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
226	C₃×Q₈	—	2	8	no	—
227	C₃×Q₈	—	4	8	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
253	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
259	C₂×C₃×C₄	C₃×#41	1	2	yes	—
260	C₂×C₃×C₄	C₃×#41	1	2	yes	—
261	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₉	#533	1	1	yes	characteristic
263	C₂×C₉	#542	1	1	yes	characteristic
264	C₂×C₉	#546	1	1	yes	characteristic
265	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
266	C₂×C₉	#557	1	1	yes	characteristic
267	C₂×C₉	Q₈²	1	1	yes	characteristic
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	Q₈×C₉	1	4	yes	complemented
274	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₉	1	2	yes	—
276	C₂²×C₄	C₂³×C₉	1	2	yes	—
277	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₉	1	2	yes	—
279	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₉	1	2	yes	—
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	D₄×C₉	1	4	yes	—
293	C₄⋊C₄	Q₈×C₉	1	4	yes	complemented
294	C₄²	—	2	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
299	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
300	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
302	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
303	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	4	1	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
316	C₉	#2451	1	1	yes	characteristic, direct product factor, Sylow
317	C₂³	C₂⁴×C₉	1	1	yes	characteristic
318	Q₈	—	2	8	no	—
319	Q₈	—	4	8	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
345	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
346	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
347	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
348	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
349	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
350	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
351	C₂×C₄	C₉×#41	1	2	yes	—
352	C₂×C₄	C₉×#41	1	2	yes	—
353	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂×C₃	C₃×#533	1	1	yes	characteristic
355	C₂×C₃	C₃×#542	1	1	yes	characteristic
356	C₂×C₃	C₃×#546	1	1	yes	characteristic
357	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
358	C₂×C₃	C₃×#557	1	1	yes	characteristic
359	C₂×C₃	C₃×Q₈²	1	1	yes	characteristic
360	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
361	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
362	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
363	C₂²	C₂×C₉×#41	1	1	yes	characteristic
364	C₂²	C₂×C₉×#41	1	1	yes	characteristic
365	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	1	no	—
377	C₄	C₉×C₂²⋊Q₈	1	4	yes	—
378	C₃	C₃×#2451	1	1	yes	characteristic
379	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂	C₉×#533	1	1	yes	characteristic
381	C₂	C₉×#542	1	1	yes	characteristic
382	C₂	C₉×#546	1	1	yes	characteristic
383	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
384	C₂	C₉×#557	1	1	yes	characteristic
385	C₂	Q₈²×C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
54. C₂×Q₈×C₉	Q₈	semidirect
74. C₉×C₄⋊C₄	Q₈	semidirect
79. #2451	C₉	direct (N × H)
273. C₂×Q₈	Q₈×C₉	semidirect
293. C₄⋊C₄	Q₈×C₉	semidirect
316. C₉	#2451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₄⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₉×#398	2
C₉×#395	2
C₉×#391	2
C₉×#389	2
C₉×#387	2
C₄×C₉×C₄⋊C₄	2
C₃×#2451	3

Subgroups — C9×#2451 #11767172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2451 #11767172