Subgroups — C₂×#41×C₉⋊D₉ #72268829

Order 5184.

10235 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13047442	C₂	1	3	yes	maximal, complemented
2	C₂×#13047416	C₂	1	3	yes	maximal, complemented
3	C₂×#13047456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉²×#41	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₉⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₉⋊D₉	C₂	1	16	yes	maximal, direct product factor
7	C₂²×C₄×C₉⋊D₉	C₂	1	3	yes	maximal, complemented
8	C₂×D₄×C₉⋊D₉	C₂	1	3	yes	maximal, complemented
9	C₂×#41×C₃⋊D₉	—	3	4	no	maximal
10	C₂³×C₉⋊D₉	C₂²	1	3	yes	—
11	C₉²×#41	C₂²	1	8	yes	complemented
12	C₂×Q₈×C₉²	C₂²	1	1	yes	characteristic, complemented
13	C₂×D₄×C₉²	C₂²	1	3	yes	complemented
14	C₂²×C₄×C₉²	C₂²	1	3	yes	complemented
15	C₂×#10619673	C₂²	1	6	yes	complemented
16	C₂²×C₉⋊Dic₉	C₂²	1	3	yes	complemented
17	#13047456	C₂²	1	8	yes	complemented
18	Q₈×C₉⋊D₉	C₂²	1	8	yes	complemented
19	#13047442	C₂²	1	24	yes	complemented
20	D₄×C₉⋊D₉	C₂²	1	24	yes	complemented
21	#13047416	C₂²	1	24	yes	complemented
22	C₂×C₄⋊(C₉⋊D₉)	C₂²	1	3	yes	complemented
23	C₂×C₄×C₉⋊D₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₉⋊D₉	C₂²	1	3	yes	—
25	C₂×C₄×C₉⋊D₉	C₂²	1	24	yes	complemented
26	C₂×C₄×C₉⋊D₉	C₂²	1	3	yes	complemented
27	C₂×C₄×C₉⋊D₉	C₂²	1	3	yes	complemented
28	C₂×#10619651	C₂²	1	3	yes	complemented
29	C₂×C₃×C₉×#41	D₃	1	4	yes	—
30	#41×C₃⋊D₉	—	3	64	no	—
31	C₂×#88746	—	3	4	no	—
32	C₂×Q₈×C₃⋊D₉	—	3	4	no	—
33	C₂×#88742	—	3	12	no	—
34	C₂×D₄×C₃⋊D₉	—	3	12	no	—
35	C₂×#88736	—	3	12	no	—
36	C₂²×C₄×C₃⋊D₉	—	3	12	no	—
37	C₂³×C₉²	C₂³	1	3	yes	—
38	C₂²×C₉⋊D₉	—	2	12	no	—
39	C₂²×C₉⋊D₉	C₂³	1	3	yes	—
40	C₂²×C₉⋊D₉	C₂³	1	12	yes	—
41	C₂²×C₉⋊D₉	C₂³	1	1	yes	characteristic
42	Q₈×C₉²	C₂³	1	4	yes	complemented
43	D₄×C₉²	C₂³	1	12	yes	complemented
44	C₂×C₄×C₉²	C₂³	1	3	yes	—
45	C₂×C₄×C₉²	C₂³	1	1	yes	characteristic
46	C₂×C₄×C₉²	C₂³	1	12	yes	complemented
47	#10619673	C₂³	1	24	yes	complemented
48	C₂×C₉⋊Dic₉	C₂³	1	3	yes	—
49	C₂×C₉⋊Dic₉	C₂³	1	1	yes	characteristic
50	C₂×C₉⋊Dic₉	C₂³	1	12	yes	complemented
51	C₄⋊(C₉⋊D₉)	C₂³	1	12	yes	complemented
52	C₄×C₉⋊D₉	C₂³	1	4	yes	—
53	C₄×C₉⋊D₉	C₂³	1	12	yes	—
54	C₄×C₉⋊D₉	C₂³	1	12	yes	complemented
55	C₄×C₉⋊D₉	C₂³	1	12	yes	complemented
56	#10619651	C₂³	1	12	yes	complemented
57	C₂×#41×C₃⋊D₃	—	9	1	no	—
58	C₂×#41×D₉	—	9	12	no	—
59	C₂³×C₃⋊D₉	—	3	12	no	—
60	C₃×C₉×#41	C₂×D₃	1	32	yes	—
61	C₂×C₃×Q₈×C₉	C₂×D₃	1	4	yes	—
62	C₂×C₃×D₄×C₉	C₂×D₃	1	12	yes	—
63	C₂²×C₃×C₄×C₉	C₂×D₃	1	12	yes	—
64	C₂×#6233	—	3	24	no	—
65	C₂²×C₃⋊Dic₉	—	3	12	no	—
66	#88746	—	3	32	no	—
67	Q₈×C₃⋊D₉	—	3	32	no	—
68	#88742	—	3	96	no	—
69	D₄×C₃⋊D₉	—	3	96	no	—
70	#88736	—	3	96	no	—
71	C₂×C₄⋊(C₃⋊D₉)	—	3	12	no	—
72	C₂×C₄×C₃⋊D₉	—	3	4	no	—
73	C₂×C₄×C₃⋊D₉	—	3	12	no	—
74	C₂×C₄×C₃⋊D₉	—	3	12	no	—
75	C₂×C₄×C₃⋊D₉	—	3	12	no	—
76	C₂×C₄×C₃⋊D₉	—	3	96	no	—
77	C₂×#6226	—	3	12	no	—
78	C₂²×C₉²	—	2	6	no	—
79	C₂²×C₉²	C₂⁴	1	6	yes	—
80	C₂²×C₉²	C₂⁴	1	1	yes	characteristic
81	C₂×C₉⋊D₉	—	2	6	no	—
82	C₂×C₉⋊D₉	—	2	24	no	—
83	C₂×C₉⋊D₉	#41	1	4	yes	direct product factor
84	C₂×C₉⋊D₉	C₂⁴	1	6	yes	—
85	C₂×C₉⋊D₉	C₂⁴	1	2	yes	—
86	C₄×C₉²	C₂⁴	1	6	yes	—
87	C₄×C₉²	C₂⁴	1	2	yes	—
88	C₉⋊Dic₉	C₂⁴	1	6	yes	—
89	C₉⋊Dic₉	C₂⁴	1	2	yes	—
90	C₂×C₃²×#41	C₃⋊D₃	1	1	yes	characteristic
91	#41×C₃⋊D₃	—	9	16	no	—
92	C₂×#3832	—	9	1	no	—
93	C₂×Q₈×C₃⋊D₃	—	9	1	no	—
94	C₂×#3830	—	9	3	no	—
95	C₂×D₄×C₃⋊D₃	—	9	3	no	—
96	C₂×#3828	—	9	3	no	—
97	C₂²×C₄×C₃⋊D₃	—	9	3	no	—
98	C₂×C₉×#41	D₉	1	12	yes	complemented
99	#41×D₉	—	9	192	no	—
100	C₂×#3701	—	9	12	no	—
101	C₂×Q₈×D₉	—	9	12	no	—
102	C₂×#3699	—	9	36	no	—
103	C₂×D₄×D₉	—	9	36	no	—
104	C₂×#3697	—	9	36	no	—
105	C₂²×C₄×D₉	—	9	36	no	—
106	C₂³×C₃×C₉	C₂²×D₃	1	12	yes	—
107	C₂²×C₃⋊D₉	—	3	4	no	—
108	C₂²×C₃⋊D₉	—	3	12	no	—
109	C₂²×C₃⋊D₉	—	3	48	no	—
110	C₂²×C₃⋊D₉	—	6	48	no	—
111	C₃×Q₈×C₉	C₂²×D₃	1	16	yes	—
112	C₃×D₄×C₉	C₂²×D₃	1	48	yes	—
113	C₂×C₃×C₄×C₉	C₂²×D₃	1	12	yes	—
114	C₂×C₃×C₄×C₉	C₂²×D₃	1	4	yes	—
115	C₂×C₃×C₄×C₉	C₂²×D₃	1	48	yes	—
116	#6233	—	3	96	no	—
117	C₂×C₃⋊Dic₉	—	3	12	no	—
118	C₂×C₃⋊Dic₉	—	3	4	no	—
119	C₂×C₃⋊Dic₉	—	3	48	no	—
120	C₄⋊(C₃⋊D₉)	—	3	48	no	—
121	C₄×C₃⋊D₉	—	3	16	no	—
122	C₄×C₃⋊D₉	—	3	48	no	—
123	C₄×C₃⋊D₉	—	3	48	no	—
124	C₄×C₃⋊D₉	—	3	48	no	—
125	#6226	—	3	48	no	—
126	C₂×D₃×#41	—	27	4	no	—
127	C₂×C₉²	—	2	6	no	—
128	C₂×C₉²	C₂×#41	1	2	yes	complemented
129	C₂×C₉²	C₂⁵	1	1	yes	characteristic
130	C₉⋊D₉	—	2	6	no	—
131	C₉⋊D₉	C₂×#41	1	4	yes	direct product factor
132	C₂³×C₃⋊D₃	—	9	3	no	—
133	C₃²×#41	C₂×C₃⋊D₃	1	8	yes	—
134	C₂×C₃²×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
135	C₂×C₃²×D₄	C₂×C₃⋊D₃	1	3	yes	—
136	C₂²×C₃²×C₄	C₂×C₃⋊D₃	1	3	yes	—
137	C₂×#638	—	9	6	no	—
138	C₂²×C₃⋊Dic₃	—	9	3	no	—
139	#3832	—	9	8	no	—
140	Q₈×C₃⋊D₃	—	9	8	no	—
141	#3830	—	9	24	no	—
142	D₄×C₃⋊D₃	—	9	24	no	—
143	#3828	—	9	24	no	—
144	C₂×C₄⋊(C₃⋊D₃)	—	9	3	no	—
145	C₂×C₄×C₃⋊D₃	—	9	1	no	—
146	C₂×C₄×C₃⋊D₃	—	9	3	no	—
147	C₂×C₄×C₃⋊D₃	—	9	3	no	—
148	C₂×C₄×C₃⋊D₃	—	9	3	no	—
149	C₂×C₄×C₃⋊D₃	—	9	24	no	—
150	C₂×#634	—	9	3	no	—
151	C₂³×D₉	—	9	36	no	—
152	C₉×#41	C₂×D₉	1	96	yes	complemented
153	C₂×Q₈×C₉	C₂×D₉	1	12	yes	complemented
154	C₂×D₄×C₉	C₂×D₉	1	36	yes	complemented
155	C₂²×C₄×C₉	C₂×D₉	1	36	yes	complemented
156	C₂×#611	—	9	72	no	—
157	C₂²×Dic₉	—	9	36	no	—
158	#3701	—	9	96	no	—
159	Q₈×D₉	—	9	96	no	—
160	#3699	—	9	288	no	—
161	D₄×D₉	—	9	288	no	—
162	#3697	—	9	288	no	—
163	C₂×D₃₆	—	9	36	no	—
164	C₂×C₄×D₉	—	9	12	no	—
165	C₂×C₄×D₉	—	9	36	no	—
166	C₂×C₄×D₉	—	9	36	no	—
167	C₂×C₄×D₉	—	9	36	no	—
168	C₂×C₄×D₉	—	9	288	no	—
169	C₂×Dic₁₈	—	9	36	no	—
170	C₂²×C₃×C₉	—	2	24	no	—
171	C₂²×C₃×C₉	C₂³×D₃	1	24	yes	—
172	C₂²×C₃×C₉	C₂³×D₃	1	4	yes	—
173	C₂×C₃⋊D₉	—	3	16	no	—
174	C₂×C₃⋊D₉	—	3	8	no	—
175	C₂×C₃⋊D₉	—	3	24	no	—
176	C₂×C₃⋊D₉	—	6	96	no	—
177	C₂×C₃⋊D₉	—	6	24	no	—
178	C₃×C₄×C₉	C₂³×D₃	1	24	yes	—
179	C₃×C₄×C₉	C₂³×D₃	1	8	yes	—
180	C₃⋊Dic₉	—	3	24	no	—
181	C₃⋊Dic₉	—	3	8	no	—
182	C₂×C₃×#41	C₃⋊D₉	1	4	yes	—
183	D₃×#41	—	27	64	no	—
184	C₂×#239	—	27	4	no	—
185	C₂×D₃×Q₈	—	27	4	no	—
186	C₂×#237	—	27	12	no	—
187	C₂×D₃×D₄	—	27	12	no	—
188	C₂×#235	—	27	12	no	—
189	C₂²×C₄×D₃	—	27	12	no	—
190	C₉²	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
191	C₂³×C₃²	C₂²×C₃⋊D₃	1	3	yes	—
192	C₂²×C₃⋊D₃	—	9	1	no	—
193	C₂²×C₃⋊D₃	—	9	3	no	—
194	C₂²×C₃⋊D₃	—	9	12	no	—
195	C₂²×C₃⋊D₃	—	18	12	no	—
196	C₃²×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
197	C₃²×D₄	C₂²×C₃⋊D₃	1	12	yes	—
198	C₂×C₃²×C₄	C₂²×C₃⋊D₃	1	3	yes	—
199	C₂×C₃²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
200	C₂×C₃²×C₄	C₂²×C₃⋊D₃	1	12	yes	—
201	#638	—	9	24	no	—
202	C₂×C₃⋊Dic₃	—	9	3	no	—
203	C₂×C₃⋊Dic₃	—	9	1	no	—
204	C₂×C₃⋊Dic₃	—	9	12	no	—
205	C₄⋊(C₃⋊D₃)	—	9	12	no	—
206	C₄×C₃⋊D₃	—	9	4	no	—
207	C₄×C₃⋊D₃	—	9	12	no	—
208	C₄×C₃⋊D₃	—	9	12	no	—
209	C₄×C₃⋊D₃	—	9	12	no	—
210	#634	—	9	12	no	—
211	C₂³×C₉	C₂²×D₉	1	36	yes	—
212	C₂²×D₉	—	9	12	no	—
213	C₂²×D₉	—	9	36	no	—
214	C₂²×D₉	—	9	144	no	—
215	C₂²×D₉	—	18	144	no	—
216	Q₈×C₉	C₂²×D₉	1	48	yes	complemented
217	D₄×C₉	C₂²×D₉	1	144	yes	complemented
218	C₂×C₄×C₉	C₂²×D₉	1	36	yes	—
219	C₂×C₄×C₉	C₂²×D₉	1	12	yes	—
220	C₂×C₄×C₉	C₂²×D₉	1	144	yes	complemented
221	#611	—	9	288	no	—
222	C₂×Dic₉	—	9	36	no	—
223	C₂×Dic₉	—	9	12	no	—
224	C₂×Dic₉	—	9	144	no	—
225	D₃₆	—	9	144	no	—
226	C₄×D₉	—	9	48	no	—
227	C₄×D₉	—	9	144	no	—
228	C₄×D₉	—	9	144	no	—
229	C₄×D₉	—	9	144	no	—
230	Dic₁₈	—	9	144	no	—
231	C₂²×#41	—	81	1	no	Sylow
232	C₂×C₃×C₉	—	2	24	no	—
233	C₂×C₃×C₉	D₃×#41	1	8	yes	—
234	C₂×C₃×C₉	C₂⁴×D₃	1	4	yes	—
235	C₃⋊D₉	—	3	16	no	—
236	C₃⋊D₉	—	6	24	no	—
237	C₂³×D₃	—	27	12	no	—
238	C₃×#41	C₂×C₃⋊D₉	1	32	yes	—
239	C₂×C₃×Q₈	C₂×C₃⋊D₉	1	4	yes	—
240	C₂×C₃×D₄	C₂×C₃⋊D₉	1	12	yes	—
241	C₂²×C₃×C₄	C₂×C₃⋊D₉	1	12	yes	—
242	C₂×#67	—	27	24	no	—
243	C₂²×Dic₃	—	27	12	no	—
244	#239	—	27	32	no	—
245	D₃×Q₈	—	27	32	no	—
246	#237	—	27	96	no	—
247	D₃×D₄	—	27	96	no	—
248	#235	—	27	96	no	—
249	C₂×D₁₂	—	27	12	no	—
250	C₂×C₄×D₃	—	27	4	no	—
251	C₂×C₄×D₃	—	27	12	no	—
252	C₂×C₄×D₃	—	27	12	no	—
253	C₂×C₄×D₃	—	27	12	no	—
254	C₂×C₄×D₃	—	27	96	no	—
255	C₂×Dic₆	—	27	12	no	—
256	C₂²×C₃²	—	2	6	no	—
257	C₂²×C₃²	C₂³×C₃⋊D₃	1	6	yes	—
258	C₂²×C₃²	C₂³×C₃⋊D₃	1	1	yes	characteristic
259	C₂×C₃⋊D₃	—	9	4	no	—
260	C₂×C₃⋊D₃	—	9	2	no	—
261	C₂×C₃⋊D₃	—	9	6	no	—
262	C₂×C₃⋊D₃	—	18	24	no	—
263	C₂×C₃⋊D₃	—	18	6	no	—
264	C₃²×C₄	C₂³×C₃⋊D₃	1	6	yes	—
265	C₃²×C₄	C₂³×C₃⋊D₃	1	2	yes	—
266	C₃⋊Dic₃	—	9	6	no	—
267	C₃⋊Dic₃	—	9	2	no	—
268	C₂²×C₉	—	2	72	no	—
269	C₂²×C₉	C₂³×D₉	1	72	yes	—
270	C₂²×C₉	C₂³×D₉	1	12	yes	—
271	C₂×D₉	—	9	24	no	—
272	C₂×D₉	—	9	48	no	—
273	C₂×D₉	—	9	72	no	—
274	C₂×D₉	—	18	288	no	—
275	C₂×D₉	—	18	72	no	—
276	C₄×C₉	C₂³×D₉	1	72	yes	—
277	C₄×C₉	C₂³×D₉	1	24	yes	—
278	Dic₉	—	9	72	no	—
279	Dic₉	—	9	24	no	—
280	C₂×#41	—	81	16	no	—
281	C₂×#41	—	81	1	no	—
282	C₂×#41	—	81	3	no	—
283	C₂×#41	—	81	3	no	—
284	C₂×#41	C₉⋊D₉	1	1	yes	characteristic, direct product factor
285	C₂²×Q₈	—	81	1	no	—
286	C₂²×D₄	—	81	3	no	—
287	C₂³×C₄	—	81	3	no	—
288	C₃×C₉	C₂×D₃×#41	1	4	yes	—
289	C₂³×C₃	C₂²×C₃⋊D₉	1	12	yes	—
290	C₂²×D₃	—	27	4	no	—
291	C₂²×D₃	—	27	12	no	—
292	C₂²×D₃	—	27	48	no	—
293	C₂²×D₃	—	54	48	no	—
294	C₃×Q₈	C₂²×C₃⋊D₉	1	16	yes	—
295	C₃×D₄	C₂²×C₃⋊D₉	1	48	yes	—
296	C₂×C₃×C₄	C₂²×C₃⋊D₉	1	12	yes	—
297	C₂×C₃×C₄	C₂²×C₃⋊D₉	1	4	yes	—
298	C₂×C₃×C₄	C₂²×C₃⋊D₉	1	48	yes	—
299	#67	—	27	96	no	—
300	C₂×Dic₃	—	27	12	no	—
301	C₂×Dic₃	—	27	4	no	—
302	C₂×Dic₃	—	27	48	no	—
303	D₁₂	—	27	48	no	—
304	C₄×D₃	—	27	16	no	—
305	C₄×D₃	—	27	48	no	—
306	C₄×D₃	—	27	48	no	—
307	C₄×D₃	—	27	48	no	—
308	Dic₆	—	27	48	no	—
309	C₂×C₃²	—	2	6	no	—
310	C₂×C₃²	#41×C₃⋊D₃	1	2	yes	—
311	C₂×C₃²	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
312	C₃⋊D₃	—	9	4	no	—
313	C₃⋊D₃	—	18	6	no	—
314	C₂×C₉	—	2	72	no	—
315	C₂×C₉	#41×D₉	1	24	yes	complemented
316	C₂×C₉	C₂⁴×D₉	1	12	yes	—
317	D₉	—	9	48	no	—
318	D₉	—	18	72	no	—
319	C₂⁴	—	81	3	no	—
320	#41	—	81	8	no	—
321	#41	—	81	24	no	—
322	#41	—	81	24	no	—
323	#41	C₂×C₉⋊D₉	1	8	yes	direct product factor
324	C₂×Q₈	—	81	8	no	—
325	C₂×Q₈	—	81	3	no	—
326	C₂×Q₈	C₂×C₉⋊D₉	1	1	yes	characteristic, complemented
327	C₂×D₄	—	81	6	no	—
328	C₂×D₄	—	81	24	no	—
329	C₂×D₄	—	81	3	no	—
330	C₂×D₄	C₂×C₉⋊D₉	1	3	yes	complemented
331	C₂²×C₄	—	81	3	no	—
332	C₂²×C₄	—	81	3	no	—
333	C₂²×C₄	—	81	3	no	—
334	C₂²×C₄	—	81	1	no	—
335	C₂²×C₄	—	81	3	no	—
336	C₂²×C₄	—	81	24	no	—
337	C₂²×C₄	C₂×C₉⋊D₉	1	3	yes	complemented
338	C₂²×C₃	—	2	24	no	—
339	C₂²×C₃	C₂³×C₃⋊D₉	1	24	yes	—
340	C₂²×C₃	C₂³×C₃⋊D₉	1	4	yes	—
341	C₂×D₃	—	27	8	no	—
342	C₂×D₃	—	27	16	no	—
343	C₂×D₃	—	27	24	no	—
344	C₂×D₃	—	54	96	no	—
345	C₂×D₃	—	54	24	no	—
346	C₃×C₄	C₂³×C₃⋊D₉	1	24	yes	—
347	C₃×C₄	C₂³×C₃⋊D₉	1	8	yes	—
348	Dic₃	—	27	24	no	—
349	Dic₃	—	27	8	no	—
350	C₃²	C₂×#41×C₃⋊D₃	1	1	yes	characteristic
351	C₉	C₂×#41×D₉	1	12	yes	complemented
352	C₂³	—	81	1	no	—
353	C₂³	—	81	12	no	—
354	C₂³	—	81	3	no	—
355	C₂³	—	162	12	no	—
356	C₂³	C₂²×C₉⋊D₉	1	3	yes	—
357	Q₈	—	81	12	no	—
358	Q₈	C₂²×C₉⋊D₉	1	4	yes	complemented
359	D₄	—	81	24	no	—
360	D₄	—	81	12	no	—
361	D₄	C₂²×C₉⋊D₉	1	12	yes	complemented
362	C₂×C₄	—	81	1	no	—
363	C₂×C₄	—	81	3	no	—
364	C₂×C₄	—	81	12	no	—
365	C₂×C₄	—	81	4	no	—
366	C₂×C₄	—	81	12	no	—
367	C₂×C₄	—	81	12	no	—
368	C₂×C₄	—	81	12	no	—
369	C₂×C₄	C₂²×C₉⋊D₉	1	3	yes	—
370	C₂×C₄	C₂²×C₉⋊D₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₉⋊D₉	1	12	yes	complemented
372	C₂×C₃	—	2	24	no	—
373	C₂×C₃	#41×C₃⋊D₉	1	8	yes	—
374	C₂×C₃	C₂⁴×C₃⋊D₉	1	4	yes	—
375	D₃	—	27	16	no	—
376	D₃	—	54	24	no	—
377	C₂²	—	2	6	no	—
378	C₂²	—	81	2	no	—
379	C₂²	—	81	4	no	—
380	C₂²	—	81	6	no	—
381	C₂²	—	162	24	no	—
382	C₂²	—	162	6	no	—
383	C₂²	C₂³×C₉⋊D₉	1	6	yes	—
384	C₂²	C₂³×C₉⋊D₉	1	1	yes	characteristic
385	C₄	—	81	2	no	—
386	C₄	—	81	6	no	—
387	C₄	C₂³×C₉⋊D₉	1	2	yes	—
388	C₄	C₂³×C₉⋊D₉	1	6	yes	—
389	C₃	C₂×#41×C₃⋊D₉	1	4	yes	—
390	C₂	—	2	6	no	—
391	C₂	—	81	4	no	—
392	C₂	—	162	6	no	—
393	C₂	C₂⁴×C₉⋊D₉	1	1	yes	characteristic
394	C₂	#41×C₉⋊D₉	1	2	yes	direct product factor

	subgroup	G/H
center	C₂×C₄	C₂²×C₉⋊D₉
commutator, cosocle	C₂×C₉²	C₂⁵
Frattini	C₂×C₃²	C₂⁴×C₃⋊D₃
Fitting	C₂×C₉²×#41	C₂
socle	C₂²×C₃²	C₂³×C₃⋊D₃
hypercenter	C₂×#41	C₉⋊D₉
hypocenter	C₉²	C₂²×#41
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#13047442	C₂	semidirect
2. C₂×#13047416	C₂	semidirect
3. C₂×#13047456	C₂	semidirect
4. C₂×C₉²×#41	C₂	semidirect
5. C₂×Q₈×C₉⋊D₉	C₂	semidirect
6. #41×C₉⋊D₉	C₂	direct (N × H)
7. C₂²×C₄×C₉⋊D₉	C₂	semidirect
8. C₂×D₄×C₉⋊D₉	C₂	semidirect
11. C₉²×#41	C₂²	semidirect
12. C₂×Q₈×C₉²	C₂²	semidirect
13. C₂×D₄×C₉²	C₂²	semidirect
14. C₂²×C₄×C₉²	C₂²	semidirect
15. C₂×#10619673	C₂²	semidirect
16. C₂²×C₉⋊Dic₉	C₂²	semidirect
17. #13047456	C₂²	semidirect
18. Q₈×C₉⋊D₉	C₂²	semidirect
19. #13047442	C₂²	semidirect
20. D₄×C₉⋊D₉	C₂²	semidirect
21. #13047416	C₂²	semidirect
22. C₂×C₄⋊(C₉⋊D₉)	C₂²	semidirect
25. C₂×C₄×C₉⋊D₉	C₂²	semidirect
26. C₂×C₄×C₉⋊D₉	C₂²	semidirect
27. C₂×C₄×C₉⋊D₉	C₂²	semidirect
28. C₂×#10619651	C₂²	semidirect
42. Q₈×C₉²	C₂³	semidirect
43. D₄×C₉²	C₂³	semidirect
46. C₂×C₄×C₉²	C₂³	semidirect
47. #10619673	C₂³	semidirect
50. C₂×C₉⋊Dic₉	C₂³	semidirect
51. C₄⋊(C₉⋊D₉)	C₂³	semidirect
54. C₄×C₉⋊D₉	C₂³	semidirect
55. C₄×C₉⋊D₉	C₂³	semidirect
56. #10619651	C₂³	semidirect
83. C₂×C₉⋊D₉	#41	direct (N × H)
98. C₂×C₉×#41	D₉	semidirect
128. C₂×C₉²	C₂×#41	semidirect
131. C₉⋊D₉	C₂×#41	direct (N × H)
152. C₉×#41	C₂×D₉	semidirect
153. C₂×Q₈×C₉	C₂×D₉	semidirect
154. C₂×D₄×C₉	C₂×D₉	semidirect
155. C₂²×C₄×C₉	C₂×D₉	semidirect
190. C₉²	C₂²×#41	semidirect
216. Q₈×C₉	C₂²×D₉	semidirect
217. D₄×C₉	C₂²×D₉	semidirect
220. C₂×C₄×C₉	C₂²×D₉	semidirect
284. C₂×#41	C₉⋊D₉	direct (N × H)
315. C₂×C₉	#41×D₉	semidirect
323. #41	C₂×C₉⋊D₉	direct (N × H)
326. C₂×Q₈	C₂×C₉⋊D₉	semidirect
330. C₂×D₄	C₂×C₉⋊D₉	semidirect
337. C₂²×C₄	C₂×C₉⋊D₉	semidirect
351. C₉	C₂×#41×D₉	semidirect
358. Q₈	C₂²×C₉⋊D₉	semidirect
361. D₄	C₂²×C₉⋊D₉	semidirect
371. C₂×C₄	C₂²×C₉⋊D₉	semidirect
394. C₂	#41×C₉⋊D₉	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×#13047442	2
C₂×#13047416	2
C₂×#13047456	2
C₂×C₉²×#41	2
C₂×Q₈×C₉⋊D₉	2
#41×C₉⋊D₉	2
C₂²×C₄×C₉⋊D₉	2
C₂×D₄×C₉⋊D₉	2
C₂×#41×C₃⋊D₉	3

Subgroups — C2×#41×C9⋊D9 #72268829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×C₉⋊D₉ #72268829