Subgroups — C₄×C₉×C₂²⋊Q₈ #11767023

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#387	C₂	1	2	yes	maximal, complemented
7	C₉×#385	C₂	1	2	yes	maximal
8	C₉×#380	C₂	1	1	yes	maximal, characteristic
9	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
12	C₃×C₄×C₂²⋊Q₈	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₉×C₂²⋊Q₈	C₄	1	8	yes	direct product factor
18	C₄×Q₈×C₉	—	2	4	no	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₄²×C₉	—	2	4	no	—
28	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₉	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	C₂²	1	2	yes	—
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
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	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
42	C₃×#391	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	1	yes	characteristic
44	C₃×#387	C₂×C₃	1	2	yes	—
45	C₃×#385	C₂×C₃	1	2	yes	—
46	C₃×#380	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
48	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	—	2	2	no	—
53	C₂×Q₈×C₉	C₂×C₄	1	4	yes	complemented
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	2	2	no	—
57	C₂²×C₄×C₉	—	2	2	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	2	2	no	—
60	C₂²×C₄×C₉	—	2	2	no	—
61	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
62	C₂²×C₄×C₉	Q₈	1	4	yes	complemented
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₉×C₄⋊C₄	—	2	4	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	2	4	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
78	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
79	C₉×C₂²⋊C₄	—	2	4	no	—
80	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
81	C₄²×C₉	—	2	2	no	—
82	C₄²×C₉	—	2	2	no	—
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	2	4	no	—
85	C₄²×C₉	—	2	4	no	—
86	C₄²×C₉	D₄	1	4	yes	—
87	C₄×C₂²⋊Q₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₃×C₂²⋊Q₈	C₃×C₄	1	8	yes	—
93	C₃×C₄×Q₈	—	2	4	no	—
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	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	2	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄²	—	2	4	no	—
103	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	2	yes	—
111	C₃×#95	C₂²×C₃	1	2	yes	—
112	C₃×#95	C₂²×C₃	1	2	yes	—
113	C₃×#95	C₂²×C₃	1	2	yes	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	2	1	no	—
117	C₂³×C₉	—	2	1	no	—
118	C₂³×C₉	C₂²×C₄	1	2	yes	—
119	C₂³×C₉	C₂×Q₈	1	2	yes	—
120	C₂³×C₉	#41	1	2	yes	—
121	C₂³×C₉	C₂⁴	1	1	yes	characteristic
122	Q₈×C₉	—	2	8	no	—
123	C₂×C₄×C₉	—	2	8	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	8	no	—
137	C₂×C₄×C₉	—	2	8	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
145	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
146	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
147	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
148	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
150	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
151	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
152	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
153	C₂×C₄×C₉	#41	1	2	yes	—
154	C₂×C₄×C₉	#41	1	2	yes	—
155	C₂×C₄×C₉	#41	1	2	yes	—
156	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
158	C₂²×C₄²	C₂×C₉	1	1	yes	characteristic
159	#391	C₂×C₉	1	1	yes	characteristic, complemented
160	#389	C₂×C₉	1	1	yes	characteristic, complemented
161	#387	C₂×C₉	1	2	yes	complemented
162	#385	C₂×C₉	1	2	yes	—
163	#380	C₂×C₉	1	1	yes	characteristic
164	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
165	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
166	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	—
167	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₃×Q₈	—	2	2	no	—
169	C₂×C₃×Q₈	—	2	2	no	—
170	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	2	2	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
179	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	2	2	no	—
194	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
195	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
196	C₃×C₂²⋊C₄	—	2	4	no	—
197	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
198	C₃×C₄²	—	2	2	no	—
199	C₃×C₄²	—	2	2	no	—
200	C₃×C₄²	—	2	2	no	—
201	C₃×C₄²	—	2	4	no	—
202	C₃×C₄²	—	2	4	no	—
203	C₃×C₄²	C₃×D₄	1	4	yes	—
204	C₂²×C₉	—	2	2	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	2	no	—
209	C₂²×C₉	—	2	2	no	—
210	C₂²×C₉	C₄×Q₈	1	4	yes	complemented
211	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
212	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
213	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
214	C₂²×C₉	C₂×#41	1	1	yes	characteristic
215	C₂²×C₉	C₂×#41	1	1	yes	characteristic
216	C₂²×C₉	C₂×#41	1	1	yes	characteristic
217	C₂²×C₉	C₂×#41	1	1	yes	characteristic
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	4	no	—
220	C₄×C₉	—	2	4	no	—
221	C₄×C₉	—	2	2	no	—
222	C₄×C₉	—	2	2	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	4	2	no	—
225	C₄×C₉	—	4	2	no	—
226	C₄×C₉	C₄×D₄	1	4	yes	—
227	C₄×C₉	C₂²⋊Q₈	1	4	yes	direct product factor
228	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
229	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
230	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
231	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
232	C₂²⋊Q₈	C₄×C₉	1	8	yes	direct product factor
233	C₄×Q₈	—	2	4	no	—
234	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
239	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
242	C₂×C₄²	—	2	4	no	—
243	C₂×C₄²	C₂²×C₉	1	2	yes	—
244	C₂×C₄²	C₂²×C₉	1	2	yes	—
245	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
249	#95	C₂²×C₉	1	2	yes	—
250	#95	C₂²×C₉	1	2	yes	—
251	#95	C₂²×C₉	1	2	yes	—
252	#95	C₂²×C₉	1	2	yes	—
253	#95	C₂²×C₉	1	2	yes	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
259	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
260	C₂³×C₃	C₃×#41	1	2	yes	—
261	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
262	C₃×Q₈	—	2	8	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
286	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
287	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
289	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
290	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
291	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
293	C₂×C₃×C₄	C₃×#41	1	2	yes	—
294	C₂×C₃×C₄	C₃×#41	1	2	yes	—
295	C₂×C₃×C₄	C₃×#41	1	2	yes	—
296	C₂×C₉	—	2	4	no	—
297	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
299	C₂×C₉	C₄×#41	1	1	yes	characteristic
300	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
301	C₂×C₉	#525	1	1	yes	characteristic
302	C₂×C₉	#529	1	1	yes	characteristic
303	C₂×C₉	#533	1	1	yes	characteristic
304	C₂⁴	C₂³×C₉	1	1	yes	characteristic
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	C₂×C₄×C₉	1	4	yes	complemented
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
316	C₂²×C₄	Q₈×C₉	1	4	yes	complemented
317	C₂²×C₄	C₂³×C₉	1	2	yes	—
318	C₂²×C₄	C₂³×C₉	1	2	yes	—
319	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₉	1	2	yes	—
321	C₂²×C₄	C₂³×C₉	1	2	yes	—
322	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
332	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	4	no	—
340	C₄²	D₄×C₉	1	4	yes	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	C₃×C₄×Q₈	1	4	yes	—
348	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
349	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
350	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
351	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
352	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
353	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
354	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	4	no	—
357	C₃×C₄	—	2	4	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
364	C₃×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
365	C₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	C₂²×C₄×C₉	1	2	yes	—
371	C₂³	C₂×Q₈×C₉	1	2	yes	—
372	C₂³	C₉×#41	1	2	yes	—
373	C₂³	C₂⁴×C₉	1	1	yes	characteristic
374	Q₈	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
397	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
398	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
399	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
400	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
401	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
402	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
403	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
404	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
405	C₂×C₄	C₉×#41	1	2	yes	—
406	C₂×C₄	C₉×#41	1	2	yes	—
407	C₂×C₄	C₉×#41	1	2	yes	—
408	C₂×C₃	—	2	4	no	—
409	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
410	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
411	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
412	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
413	C₂×C₃	C₃×#525	1	1	yes	characteristic
414	C₂×C₃	C₃×#529	1	1	yes	characteristic
415	C₂×C₃	C₃×#533	1	1	yes	characteristic
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₄×Q₈×C₉	1	4	yes	complemented
423	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
424	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
425	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
426	C₂²	C₂×C₉×#41	1	1	yes	characteristic
427	C₂²	C₂×C₉×#41	1	1	yes	characteristic
428	C₂²	C₂×C₉×#41	1	1	yes	characteristic
429	C₂²	C₂×C₉×#41	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	C₄×D₄×C₉	1	4	yes	—
439	C₄	C₉×C₂²⋊Q₈	1	4	yes	direct product factor
440	C₃	C₃×C₄×C₂²⋊Q₈	1	1	yes	characteristic
441	C₂	—	2	4	no	—
442	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
443	C₂	C₂×C₄×Q₈×C₉	1	1	yes	characteristic
444	C₂	C₄×C₉×#41	1	1	yes	characteristic
445	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
446	C₂	C₉×#525	1	1	yes	characteristic
447	C₂	C₉×#529	1	1	yes	characteristic
448	C₂	C₉×#533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×C₉	C₂	semidirect
4. C₉×#391	C₂	semidirect
5. C₉×#389	C₂	semidirect
6. C₉×#387	C₂	semidirect
9. C₄×C₉×C₄⋊C₄	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
17. C₉×C₂²⋊Q₈	C₄	direct (N × H)
53. C₂×Q₈×C₉	C₂×C₄	semidirect
62. C₂²×C₄×C₉	Q₈	semidirect
77. C₉×C₄⋊C₄	C₂×C₄	semidirect
78. C₉×C₄⋊C₄	C₂×C₄	semidirect
87. C₄×C₂²⋊Q₈	C₉	direct (N × H)
157. C₂×C₄×Q₈	C₂×C₉	semidirect
159. #391	C₂×C₉	semidirect
160. #389	C₂×C₉	semidirect
161. #387	C₂×C₉	semidirect
164. C₄×C₄⋊C₄	C₂×C₉	semidirect
165. C₄×C₄⋊C₄	C₂×C₉	semidirect
210. C₂²×C₉	C₄×Q₈	semidirect
227. C₄×C₉	C₂²⋊Q₈	direct (N × H)
232. C₂²⋊Q₈	C₄×C₉	direct (N × H)
307. C₂×Q₈	C₂×C₄×C₉	semidirect
316. C₂²×C₄	Q₈×C₉	semidirect
331. C₄⋊C₄	C₂×C₄×C₉	semidirect
332. C₄⋊C₄	C₂×C₄×C₉	semidirect
365. C₉	C₄×C₂²⋊Q₈	direct (N × H)
422. C₂²	C₄×Q₈×C₉	semidirect
439. C₄	C₉×C₂²⋊Q₈	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×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₂²×C₄²×C₉	2
C₉×#391	2
C₉×#389	2
C₉×#387	2
C₉×#385	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×C₄×C₂²⋊Q₈	3

Subgroups — C4×C9×C22⋊Q8 #11767023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₂²⋊Q₈ #11767023