Subgroups — C₂×C₉×#942 #13153641

Order 1728.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#216	C₂	1	2	yes	maximal, complemented
4	C₉×#942	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₉×#215	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#942	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#137	—	3	1	no	maximal
9	C₂×C₃×Q₈×C₉	—	2	1	no	—
10	C₂×C₃×Q₈×C₉	—	2	2	no	—
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₃×Q₈×C₉	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₄×C₉	—	2	1	no	—
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×#67	—	2	1	no	—
16	C₉×#235	—	2	2	no	—
17	C₉×#235	C₂²	1	4	yes	—
18	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	—	2	1	no	—
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
21	C₉×#216	C₂²	1	8	yes	complemented
22	C₉×#215	C₂²	1	8	yes	complemented
23	C₉×#208	C₂²	1	4	yes	complemented
24	C₂×C₉×C₃⋊C₈	C₂²	1	2	yes	—
25	C₂²×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#216	C₂×C₃	1	2	yes	—
28	C₃×#942	C₂×C₃	1	8	yes	—
29	C₂×C₃×#215	C₂×C₃	1	2	yes	—
30	C₂×C₃×#208	C₂×C₃	1	1	yes	characteristic
31	C₂×C₉×#41	—	3	1	no	—
32	C₂²×Q₈×C₉	—	2	1	no	—
33	C₂²×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
34	C₉×#137	—	3	8	no	—
35	C₂×C₉×Q₁₆	—	3	2	no	—
36	C₂×C₉×SD₁₆	—	3	2	no	—
37	C₂×C₉×M₁₆	—	3	1	no	—
38	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₃×Q₈×C₉	—	2	2	no	—
41	C₃×Q₈×C₉	—	2	4	no	—
42	C₃×Q₈×C₉	C₂³	1	4	yes	—
43	C₂×C₃×C₄×C₉	—	2	2	no	—
44	C₂×C₃×C₄×C₉	—	2	4	no	—
45	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₉×#67	—	2	4	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₉×D₁₂	—	2	1	no	—
52	C₉×D₁₂	C₂³	1	2	yes	—
53	C₄×D₃×C₉	—	2	4	no	—
54	C₉×Dic₆	—	2	1	no	—
55	C₉×Dic₆	C₂³	1	2	yes	—
56	C₉×C₃⋊C₈	C₂³	1	4	yes	—
57	C₂×C₃×#137	—	3	1	no	—
58	C₂×#942	C₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	—	2	1	no	—
60	C₂×C₃²×Q₈	—	2	2	no	—
61	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
62	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
63	C₂²×C₃²×C₄	—	2	1	no	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×#67	—	2	1	no	—
66	C₃×#235	—	2	2	no	—
67	C₃×#235	C₂²×C₃	1	4	yes	—
68	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	—	2	1	no	—
70	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
71	C₃×#216	C₂²×C₃	1	8	yes	—
72	C₃×#215	C₂²×C₃	1	8	yes	—
73	C₃×#208	C₂²×C₃	1	4	yes	—
74	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	2	yes	—
75	C₉×#41	—	3	4	no	—
76	C₉×#41	—	6	2	no	—
77	C₂×Q₈×C₉	—	2	2	no	—
78	C₂×Q₈×C₉	—	2	4	no	—
79	C₂×Q₈×C₉	—	2	2	no	—
80	C₂×Q₈×C₉	—	2	4	no	—
81	C₂×Q₈×C₉	—	2	2	no	—
82	C₂×Q₈×C₉	—	2	1	no	—
83	C₂×Q₈×C₉	—	3	1	no	—
84	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
85	C₂×Q₈×C₉	C₂×D₃	1	4	yes	complemented
86	C₂×D₄×C₉	—	3	1	no	—
87	C₂×D₄×C₉	—	6	1	no	—
88	C₂²×C₄×C₉	—	2	2	no	—
89	C₂²×C₄×C₉	—	2	1	no	—
90	C₂²×C₄×C₉	—	2	1	no	—
91	C₂²×C₄×C₉	—	6	1	no	—
92	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
93	C₉×Q₁₆	—	3	8	no	—
94	C₉×SD₁₆	—	3	8	no	—
95	C₉×M₁₆	—	3	4	no	—
96	C₂×C₈×C₉	—	3	2	no	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
99	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
100	C₂×D₃×C₉	—	2	2	no	—
101	C₂×D₃×C₉	—	4	2	no	—
102	C₃×C₄×C₉	—	2	4	no	—
103	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
104	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
105	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
106	C₉×Dic₃	—	2	2	no	—
107	C₂×C₃×#41	—	3	1	no	—
108	C₂²×C₃×Q₈	—	2	1	no	—
109	C₂²×C₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
110	C₂²×C₃×Q₈	C₃×D₃	1	1	yes	characteristic
111	C₂×#235	C₂×C₉	1	1	yes	characteristic
112	C₃×#137	—	3	8	no	—
113	C₂×C₃×Q₁₆	—	3	2	no	—
114	C₂×C₃×SD₁₆	—	3	2	no	—
115	C₂×C₃×M₁₆	—	3	1	no	—
116	C₂×#216	C₂×C₉	1	2	yes	complemented
117	#942	C₂×C₉	1	8	yes	direct product factor
118	C₂×#215	C₂×C₉	1	2	yes	complemented
119	C₂×#208	C₂×C₉	1	1	yes	characteristic, complemented
120	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	2	1	no	—
122	C₃²×Q₈	—	2	2	no	—
123	C₃²×Q₈	—	2	4	no	—
124	C₃²×Q₈	C₂³×C₃	1	4	yes	—
125	C₂×C₃²×C₄	—	2	2	no	—
126	C₂×C₃²×C₄	—	2	4	no	—
127	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
129	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
131	C₃×#67	—	2	4	no	—
132	C₂×C₃×Dic₃	—	2	1	no	—
133	C₃×D₁₂	—	2	1	no	—
134	C₃×D₁₂	C₂³×C₃	1	2	yes	—
135	C₃×C₄×D₃	—	2	4	no	—
136	C₃×Dic₆	—	2	1	no	—
137	C₃×Dic₆	C₂³×C₃	1	2	yes	—
138	C₂³×C₉	—	2	1	no	—
139	C₂³×C₉	—	6	1	no	—
140	C₂³×C₉	#67	1	1	yes	characteristic
141	C₃×C₃⋊C₈	C₂³×C₃	1	4	yes	—
142	Q₈×C₉	—	2	4	no	—
143	Q₈×C₉	—	2	8	no	—
144	Q₈×C₉	—	2	2	no	—
145	Q₈×C₉	—	2	4	no	—
146	Q₈×C₉	—	2	4	no	—
147	Q₈×C₉	—	3	2	no	—
148	Q₈×C₉	—	6	1	no	—
149	Q₈×C₉	C₂²×D₃	1	4	yes	—
150	D₄×C₉	—	3	2	no	—
151	D₄×C₉	—	6	4	no	—
152	D₄×C₉	—	6	1	no	—
153	C₂×C₄×C₉	—	2	4	no	—
154	C₂×C₄×C₉	—	2	8	no	—
155	C₂×C₄×C₉	—	2	4	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	2	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	2	no	—
161	C₂×C₄×C₉	—	6	1	no	—
162	C₂×C₄×C₉	—	6	4	no	—
163	C₂×C₄×C₉	#67	1	2	yes	—
164	C₂×C₄×C₉	#67	1	1	yes	characteristic
165	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
166	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
167	C₈×C₉	—	3	4	no	—
168	C₂×#137	—	3	1	no	Sylow
169	C₂×C₃×C₉	—	2	2	no	—
170	C₂×C₃×C₉	#137	1	2	yes	complemented
171	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
172	D₃×C₉	—	4	2	no	—
173	C₃×#41	—	3	4	no	—
174	C₃×#41	—	6	2	no	—
175	C₂×C₃×Q₈	—	2	2	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	1	no	—
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	2	2	no	—
181	C₂×C₃×Q₈	—	2	2	no	—
182	C₂×C₃×Q₈	—	2	4	no	—
183	C₂×C₃×Q₈	—	3	1	no	—
184	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
185	C₂×C₃×Q₈	C₂²×C₉	1	4	yes	complemented
186	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
187	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
188	C₂×C₃×D₄	—	3	1	no	—
189	C₂×C₃×D₄	—	6	1	no	—
190	C₂²×C₃×C₄	—	2	2	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	—	6	1	no	—
195	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
197	C₂×#67	—	2	1	no	—
198	#235	—	2	2	no	—
199	#235	C₂²×C₉	1	4	yes	—
200	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
203	C₃×Q₁₆	—	3	8	no	—
204	C₃×SD₁₆	—	3	8	no	—
205	C₃×M₁₆	—	3	4	no	—
206	C₂×C₃×C₈	—	3	2	no	—
207	#216	C₂²×C₉	1	8	yes	complemented
208	#215	C₂²×C₉	1	8	yes	complemented
209	#208	C₂²×C₉	1	4	yes	complemented
210	C₂×C₃⋊C₈	C₂²×C₉	1	2	yes	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
213	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
214	C₂×C₃×D₃	—	2	2	no	—
215	C₂×C₃×D₃	—	4	2	no	—
216	C₃²×C₄	—	2	4	no	—
217	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
218	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
219	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
220	C₃×Dic₃	—	2	2	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	—	6	2	no	—
226	C₂²×C₉	—	12	2	no	—
227	C₂²×C₉	C₂×#67	1	2	yes	—
228	C₂²×C₉	C₂×#67	1	1	yes	characteristic
229	C₄×C₉	—	2	8	no	—
230	C₄×C₉	—	2	4	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	1	no	—
234	C₄×C₉	—	6	2	no	—
235	C₄×C₉	C₂×#67	1	2	yes	—
236	C₄×C₉	C₂×#67	1	1	yes	characteristic
237	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
238	C₂×#41	—	3	1	no	—
239	C₂²×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
240	#137	—	3	8	no	—
241	C₂×Q₁₆	—	3	2	no	—
242	C₂×SD₁₆	—	3	2	no	—
243	C₂×M₁₆	—	3	1	no	—
244	C₃×C₉	C₂×#137	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	6	1	no	—
247	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
248	C₂³×C₃	C₃×#67	1	1	yes	characteristic
249	C₂²×D₃	—	2	1	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	2	8	no	—
252	C₃×Q₈	—	2	2	no	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	2	4	no	—
257	C₃×Q₈	—	3	2	no	—
258	C₃×Q₈	—	6	1	no	—
259	C₃×Q₈	C₂³×C₉	1	4	yes	—
260	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
261	C₃×D₄	—	3	2	no	—
262	C₃×D₄	—	6	4	no	—
263	C₃×D₄	—	6	1	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	8	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	6	1	no	—
275	C₂×C₃×C₄	—	6	4	no	—
276	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
277	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
278	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
280	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
281	C₂×C₃×C₄	C₃×#67	1	2	yes	—
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
284	#67	—	2	4	no	—
285	C₂×Dic₃	—	2	1	no	—
286	D₁₂	—	2	1	no	—
287	D₁₂	C₂³×C₉	1	2	yes	—
288	C₄×D₃	—	2	4	no	—
289	Dic₆	—	2	1	no	—
290	Dic₆	C₂³×C₉	1	2	yes	—
291	C₃×C₈	—	3	4	no	—
292	C₃⋊C₈	C₂³×C₉	1	4	yes	—
293	C₂×C₃²	—	2	2	no	—
294	C₂×C₃²	C₃×#137	1	2	yes	—
295	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
296	C₃×D₃	—	4	2	no	—
297	C₂×C₉	—	2	4	no	—
298	C₂×C₉	—	2	2	no	—
299	C₂×C₉	—	2	2	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	—	12	2	no	—
302	C₂×C₉	#942	1	2	yes	direct product factor
303	C₂×C₉	C₂²×#67	1	1	yes	characteristic
304	#41	—	3	4	no	—
305	#41	—	6	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	3	1	no	—
309	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
310	C₂×Q₈	C₂×D₃×C₉	1	4	yes	complemented
311	C₂×D₄	—	3	1	no	—
312	C₂×D₄	—	6	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	6	1	no	—
315	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
316	Q₁₆	—	3	8	no	—
317	SD₁₆	—	3	8	no	—
318	M₁₆	—	3	4	no	—
319	C₂×C₈	—	3	2	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	6	2	no	—
326	C₂²×C₃	—	12	2	no	—
327	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
328	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
330	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
331	C₂×D₃	—	2	2	no	—
332	C₂×D₃	—	4	2	no	—
333	C₃×C₄	—	2	8	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	6	2	no	—
340	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
341	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
342	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
343	C₃×C₄	C₂×C₃×#67	1	2	yes	—
344	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
345	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
346	Dic₃	—	2	2	no	—
347	C₃²	C₂×C₃×#137	1	1	yes	characteristic
348	C₉	—	2	1	no	—
349	C₉	C₂×#942	1	1	yes	characteristic, direct product factor
350	C₂³	—	6	1	no	—
351	C₂³	C₉×#67	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	3	2	no	—
355	Q₈	—	6	1	no	—
356	Q₈	C₂²×D₃×C₉	1	4	yes	—
357	D₄	—	3	2	no	—
358	D₄	—	6	4	no	—
359	D₄	—	6	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	6	1	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	C₉×#67	1	1	yes	characteristic
365	C₂×C₄	C₉×#67	1	2	yes	—
366	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
368	C₈	—	3	4	no	—
369	C₂×C₃	—	2	4	no	—
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	12	2	no	—
375	C₂×C₃	C₉×#137	1	2	yes	complemented
376	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
377	C₂×C₃	C₃×#942	1	2	yes	—
378	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
379	D₃	—	4	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	6	2	no	—
382	C₂²	—	12	2	no	—
383	C₂²	C₂×C₉×#67	1	2	yes	—
384	C₂²	C₂×C₉×#67	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	6	2	no	—
387	C₄	C₂×C₉×#67	1	2	yes	—
388	C₄	C₂×C₉×#67	1	1	yes	characteristic
389	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
390	C₃	—	2	1	no	—
391	C₃	C₂×C₉×#137	1	1	yes	characteristic, complemented
392	C₃	C₂×C₃×#942	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	12	2	no	—
395	C₂	C₉×#942	1	2	yes	direct product factor
396	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂×#67
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃×Q₈×C₉	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#235	C₂×C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂²×Q₈×C₉	D₃
hypocenter	C₃	C₂×C₉×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ C₂²×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×C₉	C₂	semidirect
3. C₂×C₉×#216	C₂	semidirect
4. C₉×#942	C₂	direct (N × H)
5. C₂×C₉×#215	C₂	semidirect
6. C₂×C₉×#208	C₂	semidirect
12. C₂×C₃×Q₈×C₉	C₂²	semidirect
21. C₉×#216	C₂²	semidirect
22. C₉×#215	C₂²	semidirect
23. C₉×#208	C₂²	semidirect
33. C₂²×Q₈×C₉	D₃	semidirect
58. C₂×#942	C₉	direct (N × H)
85. C₂×Q₈×C₉	C₂×D₃	semidirect
109. C₂²×C₃×Q₈	C₂×C₉	semidirect
116. C₂×#216	C₂×C₉	semidirect
117. #942	C₂×C₉	direct (N × H)
118. C₂×#215	C₂×C₉	semidirect
119. C₂×#208	C₂×C₉	semidirect
170. C₂×C₃×C₉	#137	semidirect
185. C₂×C₃×Q₈	C₂²×C₉	semidirect
207. #216	C₂²×C₉	semidirect
208. #215	C₂²×C₉	semidirect
209. #208	C₂²×C₉	semidirect
239. C₂²×Q₈	D₃×C₉	semidirect
244. C₃×C₉	C₂×#137	semidirect
302. C₂×C₉	#942	direct (N × H)
310. C₂×Q₈	C₂×D₃×C₉	semidirect
349. C₉	C₂×#942	direct (N × H)
375. C₂×C₃	C₉×#137	semidirect
391. C₃	C₂×C₉×#137	semidirect
395. C₂	C₉×#942	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈×C₉	2
C₂×C₉×#235	2
C₂×C₉×#216	2
C₉×#942	2
C₂×C₉×#215	2
C₂×C₉×#208	2
C₂×C₃×#942	3
C₂×C₉×#137	3

Subgroups — C2×C9×#942 #13153641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#942 #13153641