Subgroups — C₁₄₉×#10734 #49189683

Order 38144.

1326 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#341×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₄₉	—	2	2	no	—
7	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
8	C₂²×M₁₆×C₁₄₉	—	2	8	no	—
9	C₂²×M₁₆×C₁₄₉	C₄	1	4	yes	—
10	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₄₉	—	2	1	no	—
13	C₂³×C₈×C₁₄₉	C₂²	1	2	yes	—
14	#407×C₁₄₉	—	2	2	no	—
15	#407×C₁₄₉	C₄	1	4	yes	—
16	C₂×C₂²⋊C₈×C₁₄₉	—	2	2	no	—
17	C₂×C₂²⋊C₈×C₁₄₉	—	2	2	no	—
18	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
19	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
20	C₂×C₂²⋊C₈×C₁₄₉	C₄	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₄₉	C₄	1	2	yes	—
22	#341×C₁₄₉	—	2	8	no	—
23	C₂⁵×C₁₄₉	Q₈	1	1	yes	characteristic
24	C₂³×C₄×C₁₄₉	—	2	4	no	—
25	C₂³×C₄×C₁₄₉	—	2	4	no	—
26	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₄₉	Q₈	1	1	yes	characteristic
35	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₄₉	—	2	16	no	—
37	C₂×M₁₆×C₁₄₉	—	2	8	no	—
38	C₂×M₁₆×C₁₄₉	—	2	4	no	—
39	C₂×M₁₆×C₁₄₉	—	2	2	no	—
40	C₂×M₁₆×C₁₄₉	—	2	4	no	—
41	C₂×M₁₆×C₁₄₉	—	2	16	no	—
42	C₂×M₁₆×C₁₄₉	—	2	2	no	—
43	C₂×M₁₆×C₁₄₉	—	2	4	no	—
44	C₂×M₁₆×C₁₄₉	—	2	4	no	—
45	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	—
46	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₁₄₉	D₄	1	8	yes	—
48	C₂²×C₈×C₁₄₉	—	2	8	no	—
49	C₂²×C₈×C₁₄₉	—	2	4	no	—
50	C₂²×C₈×C₁₄₉	—	2	2	no	—
51	C₂²×C₈×C₁₄₉	—	2	2	no	—
52	C₂²×C₈×C₁₄₉	—	2	2	no	—
53	C₂²×C₈×C₁₄₉	—	2	4	no	—
54	C₂²×C₈×C₁₄₉	—	2	2	no	—
55	C₂²×C₈×C₁₄₉	—	2	4	no	—
56	C₂²×C₈×C₁₄₉	C₂×C₄	1	4	yes	—
57	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
58	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
59	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
60	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
61	C₂⁴×C₁₄₉	—	2	4	no	—
62	C₂⁴×C₁₄₉	—	2	4	no	—
63	C₂⁴×C₁₄₉	—	4	2	no	—
64	C₂⁴×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
65	C₂⁴×C₁₄₉	C₄⋊C₄	1	2	yes	—
66	C₂⁴×C₁₄₉	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
68	C₂⁴×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₄₉	—	2	4	no	—
70	C₂²×C₄×C₁₄₉	—	2	4	no	—
71	C₂²×C₄×C₁₄₉	—	2	4	no	—
72	C₂²×C₄×C₁₄₉	—	2	4	no	—
73	C₂²×C₄×C₁₄₉	—	2	4	no	—
74	C₂²×C₄×C₁₄₉	—	2	8	no	—
75	C₂²×C₄×C₁₄₉	—	2	2	no	—
76	C₂²×C₄×C₁₄₉	—	2	4	no	—
77	C₂²×C₄×C₁₄₉	—	2	2	no	—
78	C₂²×C₄×C₁₄₉	—	2	8	no	—
79	C₂²×C₄×C₁₄₉	—	2	4	no	—
80	C₂²×C₄×C₁₄₉	—	2	2	no	—
81	C₂²×C₄×C₁₄₉	—	2	2	no	—
82	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
83	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
84	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
102	M₁₆×C₁₄₉	—	2	16	no	—
103	M₁₆×C₁₄₉	—	2	4	no	—
104	M₁₆×C₁₄₉	—	2	8	no	—
105	M₁₆×C₁₄₉	—	2	8	no	—
106	M₁₆×C₁₄₉	—	4	4	no	—
107	M₁₆×C₁₄₉	C₂²⋊C₄	1	8	yes	—
108	C₂×C₈×C₁₄₉	—	2	16	no	—
109	C₂×C₈×C₁₄₉	—	2	4	no	—
110	C₂×C₈×C₁₄₉	—	2	8	no	—
111	C₂×C₈×C₁₄₉	—	2	4	no	—
112	C₂×C₈×C₁₄₉	—	2	4	no	—
113	C₂×C₈×C₁₄₉	—	2	8	no	—
114	C₂×C₈×C₁₄₉	—	4	2	no	—
115	C₂×C₈×C₁₄₉	—	4	2	no	—
116	C₂×C₈×C₁₄₉	—	4	4	no	—
117	C₂×C₈×C₁₄₉	—	4	2	no	—
118	C₂×C₈×C₁₄₉	—	4	2	no	—
119	C₂³×C₁₄₉	—	2	2	no	—
120	C₂³×C₁₄₉	—	2	2	no	—
121	C₂³×C₁₄₉	—	2	2	no	—
122	C₂³×C₁₄₉	—	2	2	no	—
123	C₂³×C₁₄₉	—	2	4	no	—
124	C₂³×C₁₄₉	—	2	4	no	—
125	C₂³×C₁₄₉	—	2	4	no	—
126	C₂³×C₁₄₉	—	2	4	no	—
127	C₂³×C₁₄₉	—	2	2	no	—
128	C₂³×C₁₄₉	—	2	2	no	—
129	C₂³×C₁₄₉	—	2	2	no	—
130	C₂³×C₁₄₉	—	4	2	no	—
131	C₂³×C₁₄₉	—	4	2	no	—
132	C₂³×C₁₄₉	—	4	16	no	—
133	C₂³×C₁₄₉	#95	1	2	yes	—
134	C₂³×C₁₄₉	#95	1	2	yes	—
135	C₂³×C₁₄₉	#108	1	4	yes	—
136	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₄₉	C₂²⋊Q₈	1	4	yes	—
140	C₂×C₄×C₁₄₉	—	2	4	no	—
141	C₂×C₄×C₁₄₉	—	2	4	no	—
142	C₂×C₄×C₁₄₉	—	2	2	no	—
143	C₂×C₄×C₁₄₉	—	2	2	no	—
144	C₂×C₄×C₁₄₉	—	2	4	no	—
145	C₂×C₄×C₁₄₉	—	2	4	no	—
146	C₂×C₄×C₁₄₉	—	2	2	no	—
147	C₂×C₄×C₁₄₉	—	2	2	no	—
148	C₂×C₄×C₁₄₉	—	2	2	no	—
149	C₂×C₄×C₁₄₉	—	2	2	no	—
150	C₂×C₄×C₁₄₉	—	2	4	no	—
151	C₂×C₄×C₁₄₉	—	2	4	no	—
152	C₂×C₄×C₁₄₉	—	2	4	no	—
153	C₂×C₄×C₁₄₉	—	2	4	no	—
154	C₂×C₄×C₁₄₉	#95	1	2	yes	—
155	C₂×C₄×C₁₄₉	#95	1	2	yes	—
156	C₂×C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₄₉	#117	1	2	yes	—
162	C₂×C₄×C₁₄₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₄₉	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₁₄₉	#120	1	2	yes	—
165	C₂×C₄×C₁₄₉	#120	1	2	yes	—
166	C₂×C₄×C₁₄₉	#121	1	4	yes	—
167	C₂×C₄×C₁₄₉	#123	1	2	yes	—
168	C₂×C₄×C₁₄₉	#123	1	2	yes	—
169	C₈×C₁₄₉	—	2	8	no	—
170	C₈×C₁₄₉	—	4	4	no	—
171	C₈×C₁₄₉	—	4	4	no	—
172	C₂²×C₁₄₉	—	2	8	no	—
173	C₂²×C₁₄₉	—	2	8	no	—
174	C₂²×C₁₄₉	—	2	2	no	—
175	C₂²×C₁₄₉	—	2	1	no	—
176	C₂²×C₁₄₉	—	2	1	no	—
177	C₂²×C₁₄₉	—	2	2	no	—
178	C₂²×C₁₄₉	—	2	1	no	—
179	C₂²×C₁₄₉	—	2	1	no	—
180	C₂²×C₁₄₉	—	2	2	no	—
181	C₂²×C₁₄₉	—	2	2	no	—
182	C₂²×C₁₄₉	—	2	2	no	—
183	C₂²×C₁₄₉	—	4	8	no	—
184	C₂²×C₁₄₉	—	4	8	no	—
185	C₂²×C₁₄₉	—	4	4	no	—
186	C₂²×C₁₄₉	#341	1	4	yes	complemented
187	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
188	C₂²×C₁₄₉	#380	1	2	yes	—
189	C₂²×C₁₄₉	#385	1	2	yes	—
190	C₂²×C₁₄₉	#385	1	2	yes	—
191	C₂²×C₁₄₉	C₂×#108	1	2	yes	—
192	C₂²×C₁₄₉	#430	1	2	yes	—
193	C₄×C₁₄₉	—	2	2	no	—
194	C₄×C₁₄₉	—	2	2	no	—
195	C₄×C₁₄₉	C₄×C₂²⋊C₄	1	2	yes	—
196	C₄×C₁₄₉	#379	1	1	yes	characteristic
197	C₄×C₁₄₉	#381	1	1	yes	characteristic
198	C₄×C₁₄₉	#386	1	2	yes	—
199	C₄×C₁₄₉	#386	1	2	yes	—
200	C₂×C₁₄₉	—	2	4	no	—
201	C₂×C₁₄₉	—	2	2	no	—
202	C₂×C₁₄₉	—	2	2	no	—
203	C₂×C₁₄₉	—	4	2	no	—
204	C₂×C₁₄₉	C₂²⋊#95	1	1	yes	characteristic
205	C₂×C₁₄₉	C₂×#341	1	1	yes	characteristic
206	C₂×C₁₄₉	#1738	1	1	yes	characteristic
207	C₂×C₁₄₉	#1855	1	4	yes	—
208	#10734	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₁₄₉	#10734	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³×M₁₆	C₂×C₁₄₉	1	1	yes	characteristic
211	C₂×#407	C₂×C₁₄₉	1	1	yes	characteristic
212	C₂²×C₂²⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic
213	C₂×#341	C₂×C₁₄₉	1	4	yes	complemented
214	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
215	C₂²×M₁₆	—	2	2	no	—
216	C₂²×M₁₆	—	2	1	no	—
217	C₂²×M₁₆	—	2	8	no	—
218	C₂²×M₁₆	C₄×C₁₄₉	1	4	yes	—
219	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
220	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
221	C₂³×C₈	—	2	1	no	—
222	C₂³×C₈	C₂²×C₁₄₉	1	2	yes	—
223	#407	—	2	2	no	—
224	#407	C₄×C₁₄₉	1	4	yes	—
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₂×C₂²⋊C₈	—	2	2	no	—
227	C₂×C₂²⋊C₈	—	2	1	no	—
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	C₂×C₂²⋊C₈	C₄×C₁₄₉	1	2	yes	—
230	C₂×C₂²⋊C₈	C₄×C₁₄₉	1	2	yes	—
231	#341	—	2	8	no	—
232	C₂⁵	Q₈×C₁₄₉	1	1	yes	characteristic
233	C₂³×C₄	—	2	4	no	—
234	C₂³×C₄	—	2	4	no	—
235	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
239	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
241	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
242	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
243	C₂³×C₄	Q₈×C₁₄₉	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	16	no	—
246	C₂×M₁₆	—	2	8	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	—	2	16	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	—
255	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	—
256	C₂×M₁₆	D₄×C₁₄₉	1	8	yes	—
257	C₂²×C₈	—	2	8	no	—
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	4	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	C₂×C₄×C₁₄₉	1	4	yes	—
266	C₂²⋊C₈	—	2	4	no	—
267	C₂²⋊C₈	—	2	4	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	—	2	4	no	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	4	2	no	—
273	C₂⁴	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
274	C₂⁴	C₄⋊C₄×C₁₄₉	1	2	yes	—
275	C₂⁴	C₄⋊C₄×C₁₄₉	1	2	yes	—
276	C₂⁴	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
277	C₂⁴	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
292	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
295	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
296	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
298	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
299	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
300	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
301	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
302	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
310	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
311	M₁₆	—	2	16	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	8	no	—
314	M₁₆	—	2	8	no	—
315	M₁₆	—	4	4	no	—
316	M₁₆	C₂²⋊C₄×C₁₄₉	1	8	yes	—
317	C₂×C₈	—	2	16	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	8	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	16	no	—
342	C₂³	#95×C₁₄₉	1	2	yes	—
343	C₂³	#95×C₁₄₉	1	2	yes	—
344	C₂³	#108×C₁₄₉	1	4	yes	—
345	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
346	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
347	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
348	C₂³	C₂²⋊Q₈×C₁₄₉	1	4	yes	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	#95×C₁₄₉	1	2	yes	—
364	C₂×C₄	#95×C₁₄₉	1	2	yes	—
365	C₂×C₄	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
370	C₂×C₄	#117×C₁₄₉	1	2	yes	—
371	C₂×C₄	C₄×D₄×C₁₄₉	1	4	yes	—
372	C₂×C₄	C₄×D₄×C₁₄₉	1	4	yes	—
373	C₂×C₄	#120×C₁₄₉	1	2	yes	—
374	C₂×C₄	#120×C₁₄₉	1	2	yes	—
375	C₂×C₄	#121×C₁₄₉	1	4	yes	—
376	C₂×C₄	#123×C₁₄₉	1	2	yes	—
377	C₂×C₄	#123×C₁₄₉	1	2	yes	—
378	C₈	—	2	8	no	—
379	C₈	—	4	4	no	—
380	C₈	—	4	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	8	no	—
393	C₂²	—	4	8	no	—
394	C₂²	—	4	4	no	—
395	C₂²	#341×C₁₄₉	1	4	yes	complemented
396	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
397	C₂²	#380×C₁₄₉	1	2	yes	—
398	C₂²	#385×C₁₄₉	1	2	yes	—
399	C₂²	#385×C₁₄₉	1	2	yes	—
400	C₂²	C₂×#108×C₁₄₉	1	2	yes	—
401	C₂²	#430×C₁₄₉	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	C₄×C₂²⋊C₄×C₁₄₉	1	2	yes	—
405	C₄	#379×C₁₄₉	1	1	yes	characteristic
406	C₄	#381×C₁₄₉	1	1	yes	characteristic
407	C₄	#386×C₁₄₉	1	2	yes	—
408	C₄	#386×C₁₄₉	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	4	no	—
412	C₂	—	4	2	no	—
413	C₂	C₂²⋊#95×C₁₄₉	1	1	yes	characteristic
414	C₂	C₂×#341×C₁₄₉	1	1	yes	characteristic
415	C₂	#1738×C₁₄₉	1	1	yes	characteristic
416	C₂	#1855×C₁₄₉	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₄⋊C₄
prime radical	C₂⁵×C₁₄₉	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#341×C₁₄₉	C₂	semidirect
186. C₂²×C₁₄₉	#341	semidirect
208. #10734	C₁₄₉	direct (N × H)
209. C₁₄₉	#10734	direct (N × H)
213. C₂×#341	C₂×C₁₄₉	semidirect
395. C₂²	#341×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₄₉	2
C₂×#407×C₁₄₉	2
C₂²×C₂²⋊C₈×C₁₄₉	2
C₂×#341×C₁₄₉	2
#10734	149

Subgroups — C149×#10734 #49189683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10734 #49189683