Subgroups — C₁₄₉×#17492 #49196441

Order 38144.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2920×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#423×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1495×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1487×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1486×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1483×C₁₄₉	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
9	#529×C₁₄₉	—	2	1	no	—
10	#529×C₁₄₉	—	2	1	no	—
11	#529×C₁₄₉	—	2	1	no	—
12	#529×C₁₄₉	—	2	1	no	—
13	#529×C₁₄₉	C₄	1	2	yes	—
14	#529×C₁₄₉	C₄	1	2	yes	—
15	#529×C₁₄₉	C₂²	1	2	yes	—
16	#529×C₁₄₉	C₂²	1	2	yes	—
17	C₂×#126×C₁₄₉	—	2	1	no	—
18	C₂×#125×C₁₄₉	C₄	1	1	yes	characteristic
19	C₂×#124×C₁₄₉	C₄	1	1	yes	characteristic
20	C₂×#123×C₁₄₉	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
22	C₂×#121×C₁₄₉	C₄	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₁₄₉	—	2	1	no	—
27	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
28	#432×C₁₄₉	—	2	1	no	—
29	#432×C₁₄₉	—	2	1	no	—
30	#431×C₁₄₉	C₂²	1	2	yes	—
31	#431×C₁₄₉	C₂²	1	2	yes	complemented
32	#423×C₁₄₉	—	2	1	no	—
33	#423×C₁₄₉	—	2	1	no	—
34	#423×C₁₄₉	—	2	1	no	—
35	#423×C₁₄₉	C₂²	1	2	yes	—
36	#423×C₁₄₉	C₂²	1	2	yes	complemented
37	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
38	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	2	yes	complemented
39	#407×C₁₄₉	—	2	1	no	—
40	C₄×M₁₆×C₁₄₉	C₂²	1	2	yes	complemented
41	Q₈⋊C₈×C₁₄₉	C₂²	1	8	yes	complemented
42	D₄⋊C₈×C₁₄₉	C₂²	1	8	yes	complemented
43	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₄₉	—	2	1	no	—
45	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₄₉	—	2	1	no	—
47	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
50	C₂×M₁₆×C₁₄₉	—	2	2	no	—
51	C₂×M₁₆×C₁₄₉	—	2	2	no	—
52	C₂×M₁₆×C₁₄₉	—	2	2	no	—
53	C₂×M₁₆×C₁₄₉	—	4	4	no	—
54	C₂²×C₈×C₁₄₉	—	2	2	no	—
55	#126×C₁₄₉	—	2	2	no	—
56	#126×C₁₄₉	—	2	2	no	—
57	#126×C₁₄₉	—	2	2	no	—
58	#126×C₁₄₉	—	2	2	no	—
59	#125×C₁₄₉	—	2	1	no	—
60	#125×C₁₄₉	—	2	1	no	—
61	#125×C₁₄₉	C₂×C₄	1	2	yes	—
62	#125×C₁₄₉	C₂×C₄	1	2	yes	—
63	#124×C₁₄₉	—	2	1	no	—
64	#124×C₁₄₉	—	2	1	no	—
65	#124×C₁₄₉	C₂×C₄	1	2	yes	—
66	#124×C₁₄₉	C₂×C₄	1	2	yes	—
67	#123×C₁₄₉	—	2	2	no	—
68	#123×C₁₄₉	—	2	2	no	—
69	#123×C₁₄₉	—	2	2	no	—
70	#123×C₁₄₉	—	2	2	no	—
71	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
72	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
73	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
74	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
75	#121×C₁₄₉	—	2	1	no	—
76	#121×C₁₄₉	—	2	1	no	—
77	#121×C₁₄₉	C₂×C₄	1	2	yes	—
78	#121×C₁₄₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₁₄₉	—	2	1	no	—
80	C₄×Q₈×C₁₄₉	—	2	1	no	—
81	C₄×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
82	C₄×Q₈×C₁₄₉	C₂³	1	2	yes	—
83	C₄×D₄×C₁₄₉	—	2	2	no	—
84	C₄×D₄×C₁₄₉	—	2	2	no	—
85	C₄×D₄×C₁₄₉	—	2	2	no	—
86	C₄×D₄×C₁₄₉	—	2	2	no	—
87	C₄×D₄×C₁₄₉	—	2	1	no	—
88	C₄×D₄×C₁₄₉	—	2	1	no	—
89	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
90	C₄×D₄×C₁₄₉	C₂³	1	2	yes	—
91	#117×C₁₄₉	—	2	2	no	—
92	#117×C₁₄₉	—	2	2	no	—
93	#117×C₁₄₉	—	2	2	no	—
94	#117×C₁₄₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
106	C₂×C₄²×C₁₄₉	—	2	1	no	—
107	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₁₄₉	—	2	2	no	—
120	C₄⋊C₈×C₁₄₉	—	2	2	no	—
121	C₄⋊C₈×C₁₄₉	—	2	2	no	—
122	C₄⋊C₈×C₁₄₉	—	2	2	no	—
123	C₄⋊C₈×C₁₄₉	—	2	2	no	—
124	C₄⋊C₈×C₁₄₉	C₂³	1	4	yes	—
125	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
126	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
127	#97×C₁₄₉	—	2	2	no	—
128	C₄×C₈×C₁₄₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₄₉	—	2	1	no	—
130	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₄₉	—	2	1	no	—
132	C₂×Q₈×C₁₄₉	—	4	2	no	—
133	C₂×Q₈×C₁₄₉	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₄₉	—	2	2	no	—
135	C₂×D₄×C₁₄₉	—	2	2	no	—
136	C₂×D₄×C₁₄₉	—	2	1	no	—
137	C₂×D₄×C₁₄₉	—	4	2	no	—
138	C₂×D₄×C₁₄₉	—	4	4	no	—
139	C₂×D₄×C₁₄₉	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₄₉	—	2	2	no	—
141	C₂²×C₄×C₁₄₉	—	2	2	no	—
142	C₂²×C₄×C₁₄₉	—	2	1	no	—
143	C₂²×C₄×C₁₄₉	—	2	1	no	—
144	C₂²×C₄×C₁₄₉	—	2	1	no	—
145	C₂²×C₄×C₁₄₉	—	2	2	no	—
146	C₂²×C₄×C₁₄₉	—	2	2	no	—
147	C₂²×C₄×C₁₄₉	—	4	2	no	—
148	C₂²×C₄×C₁₄₉	—	4	2	no	—
149	C₂²×C₄×C₁₄₉	—	4	2	no	—
150	C₂²×C₄×C₁₄₉	—	4	2	no	—
151	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
169	M₁₆×C₁₄₉	—	4	4	no	—
170	M₁₆×C₁₄₉	—	4	4	no	—
171	M₁₆×C₁₄₉	—	4	4	no	—
172	C₂×C₈×C₁₄₉	—	2	4	no	—
173	C₂×C₈×C₁₄₉	—	2	4	no	—
174	C₂×C₈×C₁₄₉	—	4	4	no	—
175	C₄⋊C₄×C₁₄₉	—	2	2	no	—
176	C₄⋊C₄×C₁₄₉	—	2	2	no	—
177	C₄⋊C₄×C₁₄₉	—	2	2	no	—
178	C₄⋊C₄×C₁₄₉	—	2	2	no	—
179	C₄⋊C₄×C₁₄₉	—	2	2	no	—
180	C₄⋊C₄×C₁₄₉	—	2	2	no	—
181	C₄⋊C₄×C₁₄₉	—	2	2	no	—
182	C₄⋊C₄×C₁₄₉	—	2	1	no	—
183	C₄⋊C₄×C₁₄₉	—	2	1	no	—
184	C₄⋊C₄×C₁₄₉	—	2	2	no	—
185	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
186	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
187	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
197	C₄²×C₁₄₉	—	2	2	no	—
198	C₄²×C₁₄₉	—	2	2	no	—
199	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
215	C₂³×C₁₄₉	—	2	2	no	—
216	C₂³×C₁₄₉	—	2	2	no	—
217	C₂³×C₁₄₉	—	2	2	no	—
218	C₂³×C₁₄₉	—	4	1	no	—
219	C₂³×C₁₄₉	—	4	2	no	—
220	C₂³×C₁₄₉	—	4	2	no	—
221	C₂³×C₁₄₉	—	4	2	no	—
222	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	Q₈×C₁₄₉	—	2	4	no	—
226	Q₈×C₁₄₉	—	4	2	no	—
227	D₄×C₁₄₉	—	2	4	no	—
228	D₄×C₁₄₉	—	4	2	no	—
229	D₄×C₁₄₉	—	4	4	no	—
230	D₄×C₁₄₉	—	4	4	no	—
231	C₂×C₄×C₁₄₉	—	2	2	no	—
232	C₂×C₄×C₁₄₉	—	2	2	no	—
233	C₂×C₄×C₁₄₉	—	2	2	no	—
234	C₂×C₄×C₁₄₉	—	2	2	no	—
235	C₂×C₄×C₁₄₉	—	2	2	no	—
236	C₂×C₄×C₁₄₉	—	2	2	no	—
237	C₂×C₄×C₁₄₉	—	2	1	no	—
238	C₂×C₄×C₁₄₉	—	2	1	no	—
239	C₂×C₄×C₁₄₉	—	2	1	no	—
240	C₂×C₄×C₁₄₉	—	2	1	no	—
241	C₂×C₄×C₁₄₉	—	2	2	no	—
242	C₂×C₄×C₁₄₉	—	2	2	no	—
243	C₂×C₄×C₁₄₉	—	2	2	no	—
244	C₂×C₄×C₁₄₉	—	2	2	no	—
245	C₂×C₄×C₁₄₉	—	2	2	no	—
246	C₂×C₄×C₁₄₉	—	4	1	no	—
247	C₂×C₄×C₁₄₉	—	4	1	no	—
248	C₂×C₄×C₁₄₉	—	4	1	no	—
249	C₂×C₄×C₁₄₉	—	4	1	no	—
250	C₂×C₄×C₁₄₉	—	4	1	no	—
251	C₂×C₄×C₁₄₉	—	4	1	no	—
252	C₂×C₄×C₁₄₉	—	4	1	no	—
253	C₂×C₄×C₁₄₉	—	4	2	no	—
254	C₂×C₄×C₁₄₉	—	4	2	no	—
255	C₂×C₄×C₁₄₉	—	4	2	no	—
256	C₂×C₄×C₁₄₉	—	4	2	no	—
257	C₂×C₄×C₁₄₉	—	4	2	no	—
258	C₂×C₄×C₁₄₉	—	4	4	no	—
259	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₁₄₉	#137	1	2	yes	—
270	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₁₄₉	—	4	4	no	—
274	C₈×C₁₄₉	—	4	4	no	—
275	C₂²×C₁₄₉	—	2	1	no	—
276	C₂²×C₁₄₉	—	2	1	no	—
277	C₂²×C₁₄₉	—	2	1	no	—
278	C₂²×C₁₄₉	—	2	1	no	—
279	C₂²×C₁₄₉	—	2	1	no	—
280	C₂²×C₁₄₉	—	2	1	no	—
281	C₂²×C₁₄₉	—	2	1	no	—
282	C₂²×C₁₄₉	—	4	4	no	—
283	C₂²×C₁₄₉	—	4	2	no	—
284	C₂²×C₁₄₉	—	4	2	no	—
285	C₂²×C₁₄₉	—	4	2	no	—
286	C₂²×C₁₄₉	—	8	4	no	—
287	C₂²×C₁₄₉	#417	1	2	yes	—
288	C₂²×C₁₄₉	#421	1	2	yes	—
289	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₄×C₁₄₉	—	2	1	no	—
291	C₄×C₁₄₉	—	2	1	no	—
292	C₄×C₁₄₉	—	2	1	no	—
293	C₄×C₁₄₉	—	2	1	no	—
294	C₄×C₁₄₉	—	2	1	no	—
295	C₄×C₁₄₉	—	2	1	no	—
296	C₄×C₁₄₉	—	2	1	no	—
297	C₄×C₁₄₉	—	2	1	no	—
298	C₄×C₁₄₉	—	2	1	no	—
299	C₄×C₁₄₉	—	4	2	no	—
300	C₄×C₁₄₉	—	4	2	no	—
301	C₄×C₁₄₉	—	4	2	no	—
302	C₄×C₁₄₉	#417	1	2	yes	—
303	C₄×C₁₄₉	#568	1	2	yes	—
304	C₄×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₄×C₁₄₉	C₂×#137	1	1	yes	characteristic
306	C₂×C₁₄₉	—	2	2	no	—
307	C₂×C₁₄₉	—	2	2	no	—
308	C₂×C₁₄₉	—	4	1	no	—
309	C₂×C₁₄₉	—	8	2	no	—
310	C₂×C₁₄₉	#2879	1	1	yes	characteristic
311	C₂×C₁₄₉	C₂×#417	1	1	yes	characteristic
312	C₂×C₁₄₉	C₂×#421	1	1	yes	characteristic
313	#17492	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₁₄₉	#17492	1	1	yes	characteristic, direct product factor, Sylow
315	C₂×#529	C₂×C₁₄₉	1	1	yes	characteristic
316	#2920	C₂×C₁₄₉	1	1	yes	characteristic, complemented
317	C₂×#423	C₂×C₁₄₉	1	1	yes	characteristic, complemented
318	#1495	C₂×C₁₄₉	1	4	yes	complemented
319	#1487	C₂×C₁₄₉	1	2	yes	complemented
320	#1486	C₂×C₁₄₉	1	2	yes	complemented
321	#1483	C₂×C₁₄₉	1	4	yes	complemented
322	C₂²×M₁₆	—	2	1	no	—
323	#529	—	2	1	no	—
324	#529	—	2	1	no	—
325	#529	—	2	1	no	—
326	#529	—	2	1	no	—
327	#529	C₄×C₁₄₉	1	2	yes	—
328	#529	C₄×C₁₄₉	1	2	yes	—
329	#529	C₂²×C₁₄₉	1	2	yes	—
330	#529	C₂²×C₁₄₉	1	2	yes	—
331	C₂×#126	—	2	1	no	—
332	C₂×#125	C₄×C₁₄₉	1	1	yes	characteristic
333	C₂×#124	C₄×C₁₄₉	1	1	yes	characteristic
334	C₂×#123	—	2	1	no	—
335	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
336	C₂×#121	C₄×C₁₄₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
338	C₂×C₄×D₄	—	2	1	no	—
339	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
340	C₂×#117	—	2	1	no	—
341	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
342	#432	—	2	1	no	—
343	#432	—	2	1	no	—
344	#431	C₂²×C₁₄₉	1	2	yes	—
345	#431	C₂²×C₁₄₉	1	2	yes	complemented
346	#423	—	2	1	no	—
347	#423	—	2	1	no	—
348	#423	—	2	1	no	—
349	#423	C₂²×C₁₄₉	1	2	yes	—
350	#423	C₂²×C₁₄₉	1	2	yes	complemented
351	C₂×C₄⋊C₈	—	2	1	no	—
352	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	2	yes	complemented
353	#407	—	2	1	no	—
354	C₄×M₁₆	C₂²×C₁₄₉	1	2	yes	complemented
355	Q₈⋊C₈	C₂²×C₁₄₉	1	8	yes	complemented
356	D₄⋊C₈	C₂²×C₁₄₉	1	8	yes	complemented
357	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
362	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
363	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	—	4	4	no	—
368	C₂²×C₈	—	2	2	no	—
369	#126	—	2	2	no	—
370	#126	—	2	2	no	—
371	#126	—	2	2	no	—
372	#126	—	2	2	no	—
373	#125	—	2	1	no	—
374	#125	—	2	1	no	—
375	#125	C₂×C₄×C₁₄₉	1	2	yes	—
376	#125	C₂×C₄×C₁₄₉	1	2	yes	—
377	#124	—	2	1	no	—
378	#124	—	2	1	no	—
379	#124	C₂×C₄×C₁₄₉	1	2	yes	—
380	#124	C₂×C₄×C₁₄₉	1	2	yes	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
388	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	C₂×C₄×C₁₄₉	1	2	yes	—
392	#121	C₂×C₄×C₁₄₉	1	2	yes	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
396	C₄×Q₈	C₂³×C₁₄₉	1	2	yes	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
404	C₄×D₄	C₂³×C₁₄₉	1	2	yes	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
422	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
423	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
424	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
425	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
426	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
427	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
433	C₄⋊C₈	—	2	2	no	—
434	C₄⋊C₈	—	2	2	no	—
435	C₄⋊C₈	—	2	2	no	—
436	C₄⋊C₈	—	2	2	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	C₂³×C₁₄₉	1	4	yes	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	#97	—	2	2	no	—
442	C₄×C₈	C₂³×C₁₄₉	1	4	yes	—
443	C₂⁴	—	2	1	no	—
444	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	C₂²×C₄×C₁₄₉	1	2	yes	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	C₂²×C₄×C₁₄₉	1	2	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
466	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
472	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
483	M₁₆	—	4	4	no	—
484	M₁₆	—	4	4	no	—
485	M₁₆	—	4	4	no	—
486	C₂×C₈	—	2	4	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	4	4	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
500	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
514	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
515	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
516	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
517	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
518	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
519	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
520	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
521	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
523	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
526	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
528	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
537	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
538	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
539	Q₈	—	2	4	no	—
540	Q₈	—	4	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
574	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
575	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
576	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
577	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
578	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
582	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
583	C₂×C₄	#137×C₁₄₉	1	2	yes	—
584	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
587	C₈	—	4	4	no	—
588	C₈	—	4	4	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	8	4	no	—
601	C₂²	#417×C₁₄₉	1	2	yes	—
602	C₂²	#421×C₁₄₉	1	2	yes	—
603	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	#417×C₁₄₉	1	2	yes	—
617	C₄	#568×C₁₄₉	1	2	yes	—
618	C₄	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
619	C₄	C₂×#137×C₁₄₉	1	1	yes	characteristic
620	C₂	—	2	2	no	—
621	C₂	—	2	2	no	—
622	C₂	—	4	1	no	—
623	C₂	—	8	2	no	—
624	C₂	#2879×C₁₄₉	1	1	yes	characteristic
625	C₂	C₂×#417×C₁₄₉	1	1	yes	characteristic
626	C₂	C₂×#421×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₁₄₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2920×C₁₄₉	C₂	semidirect
3. C₂×#423×C₁₄₉	C₂	semidirect
4. #1495×C₁₄₉	C₂	semidirect
5. #1487×C₁₄₉	C₂	semidirect
6. #1486×C₁₄₉	C₂	semidirect
7. #1483×C₁₄₉	C₂	semidirect
31. #431×C₁₄₉	C₂²	semidirect
36. #423×C₁₄₉	C₂²	semidirect
38. C₂×C₄⋊C₈×C₁₄₉	C₂²	semidirect
40. C₄×M₁₆×C₁₄₉	C₂²	semidirect
41. Q₈⋊C₈×C₁₄₉	C₂²	semidirect
42. D₄⋊C₈×C₁₄₉	C₂²	semidirect
313. #17492	C₁₄₉	direct (N × H)
314. C₁₄₉	#17492	direct (N × H)
316. #2920	C₂×C₁₄₉	semidirect
317. C₂×#423	C₂×C₁₄₉	semidirect
318. #1495	C₂×C₁₄₉	semidirect
319. #1487	C₂×C₁₄₉	semidirect
320. #1486	C₂×C₁₄₉	semidirect
321. #1483	C₂×C₁₄₉	semidirect
345. #431	C₂²×C₁₄₉	semidirect
350. #423	C₂²×C₁₄₉	semidirect
352. C₂×C₄⋊C₈	C₂²×C₁₄₉	semidirect
354. C₄×M₁₆	C₂²×C₁₄₉	semidirect
355. Q₈⋊C₈	C₂²×C₁₄₉	semidirect
356. D₄⋊C₈	C₂²×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₄₉	2
#2920×C₁₄₉	2
C₂×#423×C₁₄₉	2
#1495×C₁₄₉	2
#1487×C₁₄₉	2
#1486×C₁₄₉	2
#1483×C₁₄₉	2
#17492	149

Subgroups — C149×#17492 #49196441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17492 #49196441