Subgroups — C₁₄₉×#17411 #49196360

Order 38144.

1424 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2880×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1471×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1468×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1465×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1462×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1459×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#323×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₄₉	C₄	1	1	yes	characteristic
11	C₂×#131×C₁₄₉	—	2	2	no	—
12	#546×C₁₄₉	—	2	2	no	—
13	#546×C₁₄₉	—	2	4	no	—
14	#546×C₁₄₉	—	2	2	no	—
15	C₂×#124×C₁₄₉	C₄	1	1	yes	characteristic
16	C₂×#123×C₁₄₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
18	C₂×#121×C₁₄₉	C₄	1	2	yes	—
19	C₂×#121×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#120×C₁₄₉	C₄	1	2	yes	—
21	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
24	#408×C₁₄₉	—	2	2	no	—
25	#408×C₁₄₉	—	2	4	no	—
26	#407×C₁₄₉	C₂²	1	4	yes	complemented
27	#407×C₁₄₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	complemented
30	#324×C₁₄₉	C₂²	1	2	yes	complemented
31	#324×C₁₄₉	C₂²	1	2	yes	complemented
32	#323×C₁₄₉	C₂²	1	1	yes	characteristic
33	#323×C₁₄₉	C₂²	1	2	yes	—
34	#323×C₁₄₉	C₂²	1	1	yes	characteristic
35	#323×C₁₄₉	C₂²	1	4	yes	complemented
36	#323×C₁₄₉	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₄₉	C₂×C₄	1	2	yes	—
38	C₂×#41×C₁₄₉	—	4	4	no	—
39	C₂×#41×C₁₄₉	D₄	1	2	yes	—
40	C₂×#41×C₁₄₉	D₄	1	4	yes	—
41	C₂×#41×C₁₄₉	D₄	1	2	yes	—
42	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₄₉	—	2	2	no	—
44	C₂²×D₄×C₁₄₉	—	2	1	no	—
45	C₂²×D₄×C₁₄₉	—	2	1	no	—
46	C₂²×D₄×C₁₄₉	—	4	4	no	—
47	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
57	#131×C₁₄₉	—	4	8	no	—
58	C₂×M₁₆×C₁₄₉	—	2	4	no	—
59	C₂×M₁₆×C₁₄₉	—	2	2	no	—
60	C₂²×C₈×C₁₄₉	—	2	4	no	—
61	C₂²×C₈×C₁₄₉	—	2	2	no	—
62	#124×C₁₄₉	—	2	2	no	—
63	#124×C₁₄₉	—	2	2	no	—
64	#123×C₁₄₉	—	2	4	no	—
65	#123×C₁₄₉	—	2	4	no	—
66	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
67	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
68	#121×C₁₄₉	—	2	4	no	—
69	#121×C₁₄₉	—	2	4	no	—
70	#121×C₁₄₉	—	2	2	no	—
71	#121×C₁₄₉	—	2	2	no	—
72	#120×C₁₄₉	—	2	4	no	—
73	#120×C₁₄₉	—	2	4	no	—
74	C₄×D₄×C₁₄₉	—	2	2	no	—
75	C₄×D₄×C₁₄₉	—	2	1	no	—
76	C₄×D₄×C₁₄₉	—	2	1	no	—
77	C₄×D₄×C₁₄₉	—	2	2	no	—
78	C₄×D₄×C₁₄₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
93	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
94	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
95	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
96	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
98	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
99	C₂⁴×C₁₄₉	—	2	2	no	—
100	C₂⁴×C₁₄₉	—	2	2	no	—
101	C₂⁴×C₁₄₉	—	2	4	no	—
102	C₂⁴×C₁₄₉	—	4	2	no	—
103	C₂⁴×C₁₄₉	—	4	4	no	—
104	C₂⁴×C₁₄₉	—	8	2	no	—
105	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
106	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
107	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
108	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
109	#41×C₁₄₉	—	2	8	no	—
110	#41×C₁₄₉	—	4	8	no	—
111	#41×C₁₄₉	—	4	4	no	—
112	C₂×Q₈×C₁₄₉	—	4	2	no	—
113	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	2	yes	—
114	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	2	yes	—
115	C₂×D₄×C₁₄₉	—	2	4	no	—
116	C₂×D₄×C₁₄₉	—	2	2	no	—
117	C₂×D₄×C₁₄₉	—	2	2	no	—
118	C₂×D₄×C₁₄₉	—	2	2	no	—
119	C₂×D₄×C₁₄₉	—	2	2	no	—
120	C₂×D₄×C₁₄₉	—	2	4	no	—
121	C₂×D₄×C₁₄₉	—	2	1	no	—
122	C₂×D₄×C₁₄₉	—	2	1	no	—
123	C₂×D₄×C₁₄₉	—	4	1	no	—
124	C₂×D₄×C₁₄₉	—	4	2	no	—
125	C₂×D₄×C₁₄₉	—	4	4	no	—
126	C₂×D₄×C₁₄₉	—	4	8	no	—
127	C₂×D₄×C₁₄₉	—	4	4	no	—
128	C₂×D₄×C₁₄₉	—	4	4	no	—
129	C₂×D₄×C₁₄₉	—	4	4	no	—
130	C₂×D₄×C₁₄₉	—	8	2	no	—
131	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
132	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
134	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
135	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₄₉	—	2	2	no	—
137	C₂²×C₄×C₁₄₉	—	2	2	no	—
138	C₂²×C₄×C₁₄₉	—	2	1	no	—
139	C₂²×C₄×C₁₄₉	—	2	1	no	—
140	C₂²×C₄×C₁₄₉	—	4	2	no	—
141	C₂²×C₄×C₁₄₉	—	4	4	no	—
142	C₂²×C₄×C₁₄₉	—	4	2	no	—
143	C₂²×C₄×C₁₄₉	—	8	2	no	—
144	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₁₄₉	—	4	8	no	—
156	M₁₆×C₁₄₉	—	4	4	no	—
157	C₂×C₈×C₁₄₉	—	2	2	no	—
158	C₂×C₈×C₁₄₉	—	2	4	no	—
159	C₂×C₈×C₁₄₉	—	2	2	no	—
160	C₂×C₈×C₁₄₉	—	4	8	no	—
161	C₂×C₈×C₁₄₉	—	4	4	no	—
162	C₄⋊C₄×C₁₄₉	—	2	1	no	—
163	C₄⋊C₄×C₁₄₉	—	2	1	no	—
164	C₄⋊C₄×C₁₄₉	—	2	4	no	—
165	C₄⋊C₄×C₁₄₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
174	C₄²×C₁₄₉	—	2	1	no	—
175	C₄²×C₁₄₉	—	2	1	no	—
176	C₂³×C₁₄₉	—	2	1	no	—
177	C₂³×C₁₄₉	—	2	2	no	—
178	C₂³×C₁₄₉	—	2	1	no	—
179	C₂³×C₁₄₉	—	2	2	no	—
180	C₂³×C₁₄₉	—	2	4	no	—
181	C₂³×C₁₄₉	—	2	1	no	—
182	C₂³×C₁₄₉	—	2	1	no	—
183	C₂³×C₁₄₉	—	2	2	no	—
184	C₂³×C₁₄₉	—	2	2	no	—
185	C₂³×C₁₄₉	—	2	2	no	—
186	C₂³×C₁₄₉	—	4	2	no	—
187	C₂³×C₁₄₉	—	4	1	no	—
188	C₂³×C₁₄₉	—	4	1	no	—
189	C₂³×C₁₄₉	—	4	4	no	—
190	C₂³×C₁₄₉	—	4	4	no	—
191	C₂³×C₁₄₉	—	4	1	no	—
192	C₂³×C₁₄₉	—	4	1	no	—
193	C₂³×C₁₄₉	—	4	4	no	—
194	C₂³×C₁₄₉	—	4	2	no	—
195	C₂³×C₁₄₉	—	4	2	no	—
196	C₂³×C₁₄₉	—	4	4	no	—
197	C₂³×C₁₄₉	—	8	2	no	—
198	C₂³×C₁₄₉	—	8	2	no	—
199	C₂³×C₁₄₉	—	8	8	no	—
200	C₂³×C₁₄₉	—	8	8	no	—
201	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂³×C₁₄₉	#131	1	2	yes	complemented
205	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
206	Q₈×C₁₄₉	—	2	4	no	—
207	Q₈×C₁₄₉	—	4	2	no	—
208	D₄×C₁₄₉	—	2	4	no	—
209	D₄×C₁₄₉	—	2	8	no	—
210	D₄×C₁₄₉	—	2	2	no	—
211	D₄×C₁₄₉	—	4	4	no	—
212	D₄×C₁₄₉	—	4	2	no	—
213	D₄×C₁₄₉	—	4	4	no	—
214	D₄×C₁₄₉	—	4	4	no	—
215	D₄×C₁₄₉	—	4	4	no	—
216	D₄×C₁₄₉	—	4	2	no	—
217	D₄×C₁₄₉	—	8	4	no	—
218	D₄×C₁₄₉	#99	1	4	yes	—
219	C₂×C₄×C₁₄₉	—	2	8	no	—
220	C₂×C₄×C₁₄₉	—	2	4	no	—
221	C₂×C₄×C₁₄₉	—	2	2	no	—
222	C₂×C₄×C₁₄₉	—	2	1	no	—
223	C₂×C₄×C₁₄₉	—	2	1	no	—
224	C₂×C₄×C₁₄₉	—	2	2	no	—
225	C₂×C₄×C₁₄₉	—	2	1	no	—
226	C₂×C₄×C₁₄₉	—	2	1	no	—
227	C₂×C₄×C₁₄₉	—	2	1	no	—
228	C₂×C₄×C₁₄₉	—	4	1	no	—
229	C₂×C₄×C₁₄₉	—	4	2	no	—
230	C₂×C₄×C₁₄₉	—	4	2	no	—
231	C₂×C₄×C₁₄₉	—	4	4	no	—
232	C₂×C₄×C₁₄₉	—	4	2	no	—
233	C₂×C₄×C₁₄₉	—	4	2	no	—
234	C₂×C₄×C₁₄₉	—	4	1	no	—
235	C₂×C₄×C₁₄₉	—	4	1	no	—
236	C₂×C₄×C₁₄₉	—	4	2	no	—
237	C₂×C₄×C₁₄₉	—	8	2	no	—
238	C₂×C₄×C₁₄₉	—	8	2	no	—
239	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
243	C₈×C₁₄₉	—	4	2	no	—
244	C₈×C₁₄₉	—	4	4	no	—
245	C₈×C₁₄₉	—	4	2	no	—
246	C₂²×C₁₄₉	—	2	2	no	—
247	C₂²×C₁₄₉	—	2	1	no	—
248	C₂²×C₁₄₉	—	2	1	no	—
249	C₂²×C₁₄₉	—	2	2	no	—
250	C₂²×C₁₄₉	—	2	2	no	—
251	C₂²×C₁₄₉	—	2	2	no	—
252	C₂²×C₁₄₉	—	2	2	no	—
253	C₂²×C₁₄₉	—	2	2	no	—
254	C₂²×C₁₄₉	—	2	2	no	—
255	C₂²×C₁₄₉	—	2	2	no	—
256	C₂²×C₁₄₉	—	2	2	no	—
257	C₂²×C₁₄₉	—	4	4	no	—
258	C₂²×C₁₄₉	—	4	4	no	—
259	C₂²×C₁₄₉	—	4	2	no	—
260	C₂²×C₁₄₉	—	4	2	no	—
261	C₂²×C₁₄₉	—	4	1	no	—
262	C₂²×C₁₄₉	—	4	1	no	—
263	C₂²×C₁₄₉	—	4	2	no	—
264	C₂²×C₁₄₉	—	4	2	no	—
265	C₂²×C₁₄₉	—	4	2	no	—
266	C₂²×C₁₄₉	—	8	1	no	—
267	C₂²×C₁₄₉	—	8	1	no	—
268	C₂²×C₁₄₉	—	8	8	no	—
269	C₂²×C₁₄₉	—	8	2	no	—
270	C₂²×C₁₄₉	—	8	2	no	—
271	C₂²×C₁₄₉	—	8	8	no	—
272	C₂²×C₁₄₉	C₂×#99	1	4	yes	—
273	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₄₉	C₂×#131	1	1	yes	characteristic
275	C₂²×C₁₄₉	#568	1	1	yes	characteristic
276	C₄×C₁₄₉	—	2	2	no	—
277	C₄×C₁₄₉	—	2	1	no	—
278	C₄×C₁₄₉	—	2	4	no	—
279	C₄×C₁₄₉	—	4	1	no	—
280	C₄×C₁₄₉	—	4	1	no	—
281	C₄×C₁₄₉	—	4	1	no	—
282	C₄×C₁₄₉	—	4	2	no	—
283	C₄×C₁₄₉	C₂×#99	1	2	yes	—
284	C₂×C₁₄₉	—	2	1	no	—
285	C₂×C₁₄₉	—	2	1	no	—
286	C₂×C₁₄₉	—	2	4	no	—
287	C₂×C₁₄₉	—	4	2	no	—
288	C₂×C₁₄₉	—	4	2	no	—
289	C₂×C₁₄₉	—	4	2	no	—
290	C₂×C₁₄₉	—	8	2	no	—
291	C₂×C₁₄₉	#2880	1	1	yes	characteristic
292	C₂×C₁₄₉	C₂²×#99	1	1	yes	characteristic
293	C₂×C₁₄₉	#2888	1	1	yes	characteristic
294	#17411	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₁₄₉	#17411	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#546	C₂×C₁₄₉	1	1	yes	characteristic
297	#2880	C₂×C₁₄₉	1	2	yes	complemented
298	#1471	C₂×C₁₄₉	1	2	yes	complemented
299	#1468	C₂×C₁₄₉	1	4	yes	complemented
300	#1465	C₂×C₁₄₉	1	1	yes	characteristic, complemented
301	#1462	C₂×C₁₄₉	1	2	yes	complemented
302	#1459	C₂×C₁₄₉	1	1	yes	characteristic, complemented
303	C₂×#323	C₂×C₁₄₉	1	2	yes	complemented
304	C₂²×#41	C₂²×C₁₄₉	1	1	yes	characteristic
305	C₂³×D₄	C₄×C₁₄₉	1	1	yes	characteristic
306	C₂×#131	—	2	2	no	—
307	#546	—	2	2	no	—
308	#546	—	2	4	no	—
309	#546	—	2	2	no	—
310	C₂×#124	C₄×C₁₄₉	1	1	yes	characteristic
311	C₂×#123	C₂²×C₁₄₉	1	2	yes	—
312	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
313	C₂×#121	C₄×C₁₄₉	1	2	yes	—
314	C₂×#121	C₂²×C₁₄₉	1	1	yes	characteristic
315	C₂×#120	C₄×C₁₄₉	1	2	yes	—
316	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
319	#408	—	2	2	no	—
320	#408	—	2	4	no	—
321	#407	C₂²×C₁₄₉	1	4	yes	complemented
322	#407	C₂²×C₁₄₉	1	2	yes	complemented
323	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	complemented
324	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	complemented
325	#324	C₂²×C₁₄₉	1	2	yes	complemented
326	#324	C₂²×C₁₄₉	1	2	yes	complemented
327	#323	C₂²×C₁₄₉	1	1	yes	characteristic
328	#323	C₂²×C₁₄₉	1	2	yes	—
329	#323	C₂²×C₁₄₉	1	1	yes	characteristic
330	#323	C₂²×C₁₄₉	1	4	yes	complemented
331	#323	C₂²×C₁₄₉	1	4	yes	complemented
332	C₂⁵	C₂×C₄×C₁₄₉	1	2	yes	—
333	C₂×#41	—	4	4	no	—
334	C₂×#41	D₄×C₁₄₉	1	2	yes	—
335	C₂×#41	D₄×C₁₄₉	1	4	yes	—
336	C₂×#41	D₄×C₁₄₉	1	2	yes	—
337	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	4	4	no	—
342	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
343	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
344	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
345	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
346	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
347	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
348	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
349	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
352	#131	—	4	8	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂²×C₈	—	2	4	no	—
356	C₂²×C₈	—	2	2	no	—
357	#124	—	2	2	no	—
358	#124	—	2	2	no	—
359	#123	—	2	4	no	—
360	#123	—	2	4	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	#121	—	2	4	no	—
364	#121	—	2	4	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#120	—	2	4	no	—
368	#120	—	2	4	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
386	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
387	C₂²⋊C₈	—	2	4	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	2	4	no	—
390	C₂²⋊C₈	—	2	2	no	—
391	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
392	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
393	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	4	no	—
399	C₂⁴	—	8	2	no	—
400	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
401	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
402	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
403	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
404	#41	—	2	8	no	—
405	#41	—	4	8	no	—
406	#41	—	4	4	no	—
407	C₂×Q₈	—	4	2	no	—
408	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	2	yes	—
409	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
427	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
428	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
429	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
430	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	8	2	no	—
439	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
443	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
448	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
450	M₁₆	—	4	8	no	—
451	M₁₆	—	4	4	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	4	8	no	—
456	C₂×C₈	—	4	4	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	8	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	8	no	—
495	C₂³	—	8	8	no	—
496	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
497	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
498	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
499	C₂³	#131×C₁₄₉	1	2	yes	complemented
500	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
501	Q₈	—	2	4	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	2	8	no	—
505	D₄	—	2	2	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	4	no	—
513	D₄	#99×C₁₄₉	1	4	yes	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
535	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
536	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
538	C₈	—	4	2	no	—
539	C₈	—	4	4	no	—
540	C₈	—	4	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	8	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	8	no	—
567	C₂²	C₂×#99×C₁₄₉	1	4	yes	—
568	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
569	C₂²	C₂×#131×C₁₄₉	1	1	yes	characteristic
570	C₂²	#568×C₁₄₉	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	4	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	C₂×#99×C₁₄₉	1	2	yes	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	4	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	2	no	—
586	C₂	#2880×C₁₄₉	1	1	yes	characteristic
587	C₂	C₂²×#99×C₁₄₉	1	1	yes	characteristic
588	C₂	#2888×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂×#546×C₁₄₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂²×#41×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2880×C₁₄₉	C₂	semidirect
3. #1471×C₁₄₉	C₂	semidirect
4. #1468×C₁₄₉	C₂	semidirect
5. #1465×C₁₄₉	C₂	semidirect
6. #1462×C₁₄₉	C₂	semidirect
7. #1459×C₁₄₉	C₂	semidirect
8. C₂×#323×C₁₄₉	C₂	semidirect
26. #407×C₁₄₉	C₂²	semidirect
27. #407×C₁₄₉	C₂²	semidirect
28. C₂×C₂²⋊C₈×C₁₄₉	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₁₄₉	C₂²	semidirect
30. #324×C₁₄₉	C₂²	semidirect
31. #324×C₁₄₉	C₂²	semidirect
35. #323×C₁₄₉	C₂²	semidirect
36. #323×C₁₄₉	C₂²	semidirect
204. C₂³×C₁₄₉	#131	semidirect
294. #17411	C₁₄₉	direct (N × H)
295. C₁₄₉	#17411	direct (N × H)
297. #2880	C₂×C₁₄₉	semidirect
298. #1471	C₂×C₁₄₉	semidirect
299. #1468	C₂×C₁₄₉	semidirect
300. #1465	C₂×C₁₄₉	semidirect
301. #1462	C₂×C₁₄₉	semidirect
302. #1459	C₂×C₁₄₉	semidirect
303. C₂×#323	C₂×C₁₄₉	semidirect
321. #407	C₂²×C₁₄₉	semidirect
322. #407	C₂²×C₁₄₉	semidirect
323. C₂×C₂²⋊C₈	C₂²×C₁₄₉	semidirect
324. C₂×C₂²⋊C₈	C₂²×C₁₄₉	semidirect
325. #324	C₂²×C₁₄₉	semidirect
326. #324	C₂²×C₁₄₉	semidirect
330. #323	C₂²×C₁₄₉	semidirect
331. #323	C₂²×C₁₄₉	semidirect
499. C₂³	#131×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₁₄₉	2
#2880×C₁₄₉	2
#1471×C₁₄₉	2
#1468×C₁₄₉	2
#1465×C₁₄₉	2
#1462×C₁₄₉	2
#1459×C₁₄₉	2
C₂×#323×C₁₄₉	2
#17411	149

Subgroups — C149×#17411 #49196360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17411 #49196360