Subgroups — C₉×#3046 #11767767

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#135	C₂	1	1	yes	maximal, characteristic
3	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#464	C₂	1	2	yes	maximal, complemented
6	C₉×#463	C₂	1	2	yes	maximal, complemented
7	C₉×#462	C₂	1	2	yes	maximal, complemented
8	C₉×#461	C₂	1	2	yes	maximal, complemented
9	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3046	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
16	C₉×#137	—	2	4	no	—
17	C₉×#135	—	2	4	no	—
18	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
20	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
23	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
26	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₉×#124	C₂²	1	2	yes	—
28	C₉×#123	—	2	2	no	—
29	C₉×C₂²⋊Q₈	—	2	1	no	—
30	C₉×C₂²⋊Q₈	—	2	1	no	—
31	C₄×Q₈×C₉	C₂²	1	2	yes	—
32	C₄×D₄×C₉	—	2	2	no	—
33	C₄×D₄×C₉	C₂²	1	2	yes	—
34	C₉×#117	—	2	1	no	—
35	C₉×#117	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₄⋊C₄	—	2	1	no	—
37	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×C₄⋊C₈	C₂²	1	2	yes	—
39	C₉×C₄⋊C₈	C₂²	1	2	yes	—
40	C₉×#103	C₂²	1	2	yes	—
41	C₉×#103	C₂²	1	2	yes	—
42	C₉×#103	C₂²	1	2	yes	—
43	C₉×#102	C₂²	1	2	yes	—
44	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
46	C₃×#536	C₂×C₃	1	1	yes	characteristic
47	C₃×#520	C₂×C₃	1	1	yes	characteristic
48	C₃×#464	C₂×C₃	1	2	yes	—
49	C₃×#463	C₂×C₃	1	2	yes	—
50	C₃×#462	C₂×C₃	1	2	yes	—
51	C₃×#461	C₂×C₃	1	2	yes	—
52	C₃×#424	C₂×C₃	1	1	yes	characteristic
53	C₃×#417	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
55	C₉×#41	—	2	2	no	—
56	C₉×#41	—	2	2	no	—
57	C₉×#41	—	2	2	no	—
58	C₉×#41	D₄	1	4	yes	—
59	C₂×Q₈×C₉	—	2	1	no	—
60	C₂×Q₈×C₉	—	2	2	no	—
61	C₂×Q₈×C₉	—	2	2	no	—
62	C₂×Q₈×C₉	C₂³	1	2	yes	—
63	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
64	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₉	—	2	1	no	—
66	C₂×D₄×C₉	—	2	1	no	—
67	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	—	2	1	no	—
73	C₂²×C₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×Q₁₆	—	2	2	no	—
76	C₉×Q₁₆	—	2	4	no	—
77	C₉×SD₁₆	—	2	2	no	—
78	C₉×SD₁₆	—	2	2	no	—
79	C₉×SD₁₆	—	2	4	no	—
80	C₉×D₈	—	2	2	no	—
81	C₉×M₁₆	—	2	2	no	—
82	C₂×C₈×C₉	—	2	2	no	—
83	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₉	C₂³	1	2	yes	—
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₉×C₄⋊C₄	C₂³	1	2	yes	—
93	C₉×C₂²⋊C₄	—	2	2	no	—
94	C₉×C₂²⋊C₄	—	2	2	no	—
95	C₉×C₂²⋊C₄	—	2	2	no	—
96	C₉×C₂²⋊C₄	D₄	1	2	yes	—
97	C₄²×C₉	—	2	2	no	—
98	C₄²×C₉	C₂³	1	2	yes	—
99	#3046	C₉	1	1	yes	characteristic, direct product factor, Sylow
100	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₃×#137	—	2	4	no	—
104	C₃×#135	—	2	4	no	—
105	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
107	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
112	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
114	C₃×#124	C₂²×C₃	1	2	yes	—
115	C₃×#123	—	2	2	no	—
116	C₃×C₂²⋊Q₈	—	2	1	no	—
117	C₃×C₂²⋊Q₈	—	2	1	no	—
118	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
119	C₃×C₄×D₄	—	2	2	no	—
120	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
121	C₃×#117	—	2	1	no	—
122	C₃×#117	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
126	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
127	C₃×#103	C₂²×C₃	1	2	yes	—
128	C₃×#103	C₂²×C₃	1	2	yes	—
129	C₃×#103	C₂²×C₃	1	2	yes	—
130	C₃×#102	C₂²×C₃	1	2	yes	—
131	C₂³×C₉	—	2	1	no	—
132	C₂³×C₉	—	2	1	no	—
133	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
134	Q₈×C₉	—	2	1	no	—
135	Q₈×C₉	—	2	2	no	—
136	Q₈×C₉	—	2	1	no	—
137	Q₈×C₉	—	2	2	no	—
138	Q₈×C₉	—	2	1	no	—
139	Q₈×C₉	—	4	2	no	—
140	Q₈×C₉	C₂×D₄	1	2	yes	—
141	D₄×C₉	—	2	4	no	—
142	D₄×C₉	—	2	1	no	—
143	D₄×C₉	—	2	1	no	—
144	D₄×C₉	—	2	1	no	—
145	D₄×C₉	—	4	2	no	—
146	D₄×C₉	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	4	2	no	—
153	C₂×C₄×C₉	—	4	2	no	—
154	C₂×C₄×C₉	—	8	2	no	—
155	C₂×C₄×C₉	—	8	1	no	—
156	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
157	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₉	#41	1	2	yes	—
161	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
162	C₈×C₉	—	2	1	no	—
163	C₈×C₉	—	2	1	no	—
164	C₈×C₉	—	2	2	no	—
165	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂×#135	C₂×C₉	1	1	yes	characteristic
167	#536	C₂×C₉	1	1	yes	characteristic, complemented
168	#520	C₂×C₉	1	1	yes	characteristic, complemented
169	#464	C₂×C₉	1	2	yes	complemented
170	#463	C₂×C₉	1	2	yes	complemented
171	#462	C₂×C₉	1	2	yes	complemented
172	#461	C₂×C₉	1	2	yes	complemented
173	#424	C₂×C₉	1	1	yes	characteristic, complemented
174	#417	C₂×C₉	1	1	yes	characteristic, complemented
175	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
176	C₃×#41	—	2	2	no	—
177	C₃×#41	—	2	2	no	—
178	C₃×#41	—	2	2	no	—
179	C₃×#41	C₃×D₄	1	4	yes	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	—	2	2	no	—
182	C₂×C₃×Q₈	—	2	2	no	—
183	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
184	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	1	no	—
187	C₂×C₃×D₄	—	2	1	no	—
188	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₃×Q₁₆	—	2	2	no	—
197	C₃×Q₁₆	—	2	4	no	—
198	C₃×SD₁₆	—	2	2	no	—
199	C₃×SD₁₆	—	2	2	no	—
200	C₃×SD₁₆	—	2	4	no	—
201	C₃×D₈	—	2	2	no	—
202	C₃×M₁₆	—	2	2	no	—
203	C₂×C₃×C₈	—	2	2	no	—
204	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
205	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	1	no	—
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	2	2	no	—
210	C₃×C₄⋊C₄	—	2	2	no	—
211	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₃×C₂²⋊C₄	—	2	2	no	—
215	C₃×C₂²⋊C₄	—	2	2	no	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
218	C₃×C₄²	—	2	2	no	—
219	C₃×C₄²	C₂³×C₃	1	2	yes	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	4	1	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	1	no	—
226	C₂²×C₉	—	4	1	no	—
227	C₂²×C₉	—	4	1	no	—
228	C₂²×C₉	#121	1	2	yes	—
229	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	4	1	no	—
234	C₄×C₉	—	4	2	no	—
235	C₄×C₉	—	4	2	no	—
236	C₄×C₉	#121	1	2	yes	—
237	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
238	C₄×C₉	C₂×#41	1	1	yes	characteristic
239	C₂×#41	C₂²×C₉	1	1	yes	characteristic
240	C₂×#41	C₂²×C₉	1	1	yes	characteristic
241	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
242	#137	—	2	4	no	—
243	#135	—	2	4	no	—
244	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
245	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
246	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
247	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
248	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
249	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
250	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
251	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
252	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
253	#124	C₂²×C₉	1	2	yes	—
254	#123	—	2	2	no	—
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	—	2	1	no	—
257	C₄×Q₈	C₂²×C₉	1	2	yes	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂²×C₉	1	2	yes	—
260	#117	—	2	1	no	—
261	#117	C₂²×C₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
264	C₄⋊C₈	C₂²×C₉	1	2	yes	—
265	C₄⋊C₈	C₂²×C₉	1	2	yes	—
266	#103	C₂²×C₉	1	2	yes	—
267	#103	C₂²×C₉	1	2	yes	—
268	#103	C₂²×C₉	1	2	yes	—
269	#102	C₂²×C₉	1	2	yes	—
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
273	C₃×Q₈	—	2	1	no	—
274	C₃×Q₈	—	2	2	no	—
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	2	1	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	1	no	—
282	C₃×D₄	—	2	1	no	—
283	C₃×D₄	—	2	1	no	—
284	C₃×D₄	—	4	2	no	—
285	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	4	2	no	—
292	C₂×C₃×C₄	—	4	2	no	—
293	C₂×C₃×C₄	—	8	2	no	—
294	C₂×C₃×C₄	—	8	1	no	—
295	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₃×C₄	C₃×#41	1	2	yes	—
300	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
301	C₃×C₈	—	2	1	no	—
302	C₃×C₈	—	2	1	no	—
303	C₃×C₈	—	2	2	no	—
304	C₂×C₉	—	2	2	no	—
305	C₂×C₉	—	4	2	no	—
306	C₂×C₉	—	8	1	no	—
307	C₂×C₉	C₂×#121	1	1	yes	characteristic
308	C₂×C₉	#577	1	1	yes	characteristic
309	C₂×C₉	#578	1	1	yes	characteristic
310	#41	—	2	2	no	—
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	D₄×C₉	1	4	yes	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	C₂³×C₉	1	2	yes	—
318	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
319	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
323	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	4	no	—
332	SD₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	4	no	—
335	D₈	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂³×C₉	1	2	yes	—
339	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
340	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
346	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
347	C₄⋊C₄	C₂³×C₉	1	2	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	D₄×C₉	1	2	yes	—
352	C₄²	—	2	2	no	—
353	C₄²	C₂³×C₉	1	2	yes	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	—	4	1	no	—
360	C₂²×C₃	—	4	1	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	C₃×#121	1	2	yes	—
363	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	C₃×#121	1	2	yes	—
371	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
372	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
373	C₉	#3046	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	2	1	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	C₂×D₄×C₉	1	2	yes	—
384	D₄	—	2	4	no	—
385	D₄	—	2	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	C₂×D₄×C₉	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
400	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
401	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
402	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
403	C₂×C₄	C₉×#41	1	2	yes	—
404	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	2	2	no	—
408	C₂×C₃	—	2	2	no	—
409	C₂×C₃	—	4	2	no	—
410	C₂×C₃	—	8	1	no	—
411	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
412	C₂×C₃	C₃×#577	1	1	yes	characteristic
413	C₂×C₃	C₃×#578	1	1	yes	characteristic
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	C₉×#121	1	2	yes	—
423	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	C₉×#121	1	2	yes	—
431	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
432	C₄	C₂×C₉×#41	1	1	yes	characteristic
433	C₃	C₃×#3046	1	1	yes	characteristic
434	C₂	—	2	2	no	—
435	C₂	—	4	2	no	—
436	C₂	—	8	1	no	—
437	C₂	C₂×C₉×#121	1	1	yes	characteristic
438	C₂	C₉×#577	1	1	yes	characteristic
439	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₂×C₃×#135	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
3. C₉×#536	C₂	semidirect
4. C₉×#520	C₂	semidirect
5. C₉×#464	C₂	semidirect
6. C₉×#463	C₂	semidirect
7. C₉×#462	C₂	semidirect
8. C₉×#461	C₂	semidirect
9. C₉×#424	C₂	semidirect
10. C₉×#417	C₂	semidirect
11. C₂×C₉×#103	C₂	semidirect
99. #3046	C₉	direct (N × H)
165. C₂×#137	C₂×C₉	semidirect
167. #536	C₂×C₉	semidirect
168. #520	C₂×C₉	semidirect
169. #464	C₂×C₉	semidirect
170. #463	C₂×C₉	semidirect
171. #462	C₂×C₉	semidirect
172. #461	C₂×C₉	semidirect
173. #424	C₂×C₉	semidirect
174. #417	C₂×C₉	semidirect
175. C₂×#103	C₂×C₉	semidirect
373. C₉	#3046	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×#137	2
C₂×C₉×#135	2
C₉×#536	2
C₉×#520	2
C₉×#464	2
C₉×#463	2
C₉×#462	2
C₉×#461	2
C₉×#424	2
C₉×#417	2
C₂×C₉×#103	2
C₃×#3046	3

Subgroups — C9×#3046 #11767767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3046 #11767767