Subgroups — C₁₄₉×#17350 #49196299

Order 38144.

1418 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2972×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1460×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1459×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1458×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂×#323×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₄₉	C₄	1	1	yes	characteristic
8	#518×C₁₄₉	—	2	8	no	—
9	C₂×C₄×D₄×C₁₄₉	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic
16	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₄₉	C₄	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
19	C₈×D₄×C₁₄₉	—	2	8	no	—
20	#431×C₁₄₉	C₂²	1	4	yes	complemented
21	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	8	yes	complemented
22	#324×C₁₄₉	C₂²	1	4	yes	complemented
23	#323×C₁₄₉	C₂²	1	4	yes	—
24	#323×C₁₄₉	C₂²	1	8	yes	complemented
25	C₂⁵×C₁₄₉	C₂×C₄	1	2	yes	—
26	C₂²×D₄×C₁₄₉	—	2	4	no	—
27	C₂²×D₄×C₁₄₉	—	2	4	no	—
28	C₂²×D₄×C₁₄₉	C₈	1	8	yes	complemented
29	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₄₉	—	2	8	no	—
38	C₄×D₄×C₁₄₉	—	2	4	no	—
39	C₄×D₄×C₁₄₉	—	2	8	no	—
40	C₄×D₄×C₁₄₉	—	2	4	no	—
41	C₄×D₄×C₁₄₉	—	2	8	no	—
42	C₄×D₄×C₁₄₉	—	2	4	no	—
43	C₄×D₄×C₁₄₉	D₄	1	8	yes	—
44	#117×C₁₄₉	—	2	4	no	—
45	#117×C₁₄₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₁₄₉	—	2	4	no	—
63	C₂²⋊C₈×C₁₄₉	—	2	8	no	—
64	C₂²⋊C₈×C₁₄₉	C₂³	1	8	yes	—
65	C₄×C₈×C₁₄₉	—	2	4	no	—
66	C₂⁴×C₁₄₉	—	2	4	no	—
67	C₂⁴×C₁₄₉	—	2	4	no	—
68	C₂⁴×C₁₄₉	—	8	2	no	—
69	C₂⁴×C₁₄₉	—	8	2	no	—
70	C₂⁴×C₁₄₉	C₂×C₈	1	8	yes	complemented
71	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
74	C₂×D₄×C₁₄₉	—	2	4	no	—
75	C₂×D₄×C₁₄₉	—	2	4	no	—
76	C₂×D₄×C₁₄₉	—	2	32	no	—
77	C₂×D₄×C₁₄₉	—	2	2	no	—
78	C₂×D₄×C₁₄₉	—	2	2	no	—
79	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
80	C₂×D₄×C₁₄₉	C₂×C₈	1	4	yes	—
81	C₂×D₄×C₁₄₉	C₂×C₈	1	8	yes	complemented
82	C₂×D₄×C₁₄₉	C₂×C₈	1	4	yes	complemented
83	C₂×D₄×C₁₄₉	M₁₆	1	4	yes	—
84	C₂²×C₄×C₁₄₉	—	2	2	no	—
85	C₂²×C₄×C₁₄₉	—	2	2	no	—
86	C₂²×C₄×C₁₄₉	—	2	4	no	—
87	C₂²×C₄×C₁₄₉	—	2	4	no	—
88	C₂²×C₄×C₁₄₉	—	2	4	no	—
89	C₂²×C₄×C₁₄₉	—	8	2	no	—
90	C₂²×C₄×C₁₄₉	—	8	2	no	—
91	C₂²×C₄×C₁₄₉	—	8	2	no	—
92	C₂²×C₄×C₁₄₉	—	8	2	no	—
93	C₂²×C₄×C₁₄₉	C₂×C₈	1	4	yes	complemented
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	2	yes	—
97	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₄₉	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₄₉	—	2	8	no	—
104	C₂×C₈×C₁₄₉	—	8	8	no	—
105	C₄⋊C₄×C₁₄₉	—	2	2	no	—
106	C₄⋊C₄×C₁₄₉	—	2	2	no	—
107	C₄⋊C₄×C₁₄₉	—	2	2	no	—
108	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
109	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
112	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
114	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	8	yes	—
116	C₄²×C₁₄₉	—	2	4	no	—
117	C₄²×C₁₄₉	—	2	2	no	—
118	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
119	C₂³×C₁₄₉	—	2	1	no	—
120	C₂³×C₁₄₉	—	2	2	no	—
121	C₂³×C₁₄₉	—	2	1	no	—
122	C₂³×C₁₄₉	—	2	2	no	—
123	C₂³×C₁₄₉	—	2	16	no	—
124	C₂³×C₁₄₉	—	4	2	no	—
125	C₂³×C₁₄₉	—	4	2	no	—
126	C₂³×C₁₄₉	—	4	2	no	—
127	C₂³×C₁₄₉	—	4	2	no	—
128	C₂³×C₁₄₉	—	4	1	no	—
129	C₂³×C₁₄₉	—	4	1	no	—
130	C₂³×C₁₄₉	—	8	4	no	—
131	C₂³×C₁₄₉	—	8	4	no	—
132	C₂³×C₁₄₉	—	8	8	no	—
133	C₂³×C₁₄₉	—	8	8	no	—
134	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂³×C₁₄₉	C₂²×C₈	1	2	yes	—
136	C₂³×C₁₄₉	C₂²×C₈	1	4	yes	—
137	C₂³×C₁₄₉	C₂²×C₈	1	4	yes	—
138	C₂³×C₁₄₉	C₂×M₁₆	1	4	yes	—
139	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
140	D₄×C₁₄₉	—	2	16	no	—
141	D₄×C₁₄₉	—	2	8	no	—
142	D₄×C₁₄₉	C₂²⋊C₈	1	16	yes	—
143	C₂×C₄×C₁₄₉	—	2	1	no	—
144	C₂×C₄×C₁₄₉	—	2	1	no	—
145	C₂×C₄×C₁₄₉	—	2	8	no	—
146	C₂×C₄×C₁₄₉	—	2	1	no	—
147	C₂×C₄×C₁₄₉	—	2	2	no	—
148	C₂×C₄×C₁₄₉	—	2	1	no	—
149	C₂×C₄×C₁₄₉	—	4	8	no	—
150	C₂×C₄×C₁₄₉	—	4	2	no	—
151	C₂×C₄×C₁₄₉	—	4	1	no	—
152	C₂×C₄×C₁₄₉	—	4	1	no	—
153	C₂×C₄×C₁₄₉	—	4	1	no	—
154	C₂×C₄×C₁₄₉	—	4	2	no	—
155	C₂×C₄×C₁₄₉	—	4	1	no	—
156	C₂×C₄×C₁₄₉	—	8	4	no	—
157	C₂×C₄×C₁₄₉	—	8	4	no	—
158	C₂×C₄×C₁₄₉	—	8	4	no	—
159	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₄₉	C₂²×C₈	1	2	yes	—
163	C₂×C₄×C₁₄₉	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₁₄₉	C₂×M₁₆	1	2	yes	—
165	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
166	C₈×C₁₄₉	—	4	8	no	—
167	C₂²×C₁₄₉	—	2	1	no	—
168	C₂²×C₁₄₉	—	2	4	no	—
169	C₂²×C₁₄₉	—	2	1	no	—
170	C₂²×C₁₄₉	—	2	4	no	—
171	C₂²×C₁₄₉	—	2	2	no	—
172	C₂²×C₁₄₉	—	2	4	no	—
173	C₂²×C₁₄₉	—	4	4	no	—
174	C₂²×C₁₄₉	—	4	4	no	—
175	C₂²×C₁₄₉	—	4	2	no	—
176	C₂²×C₁₄₉	—	4	4	no	—
177	C₂²×C₁₄₉	—	4	4	no	—
178	C₂²×C₁₄₉	—	4	2	no	—
179	C₂²×C₁₄₉	—	4	2	no	—
180	C₂²×C₁₄₉	—	4	1	no	—
181	C₂²×C₁₄₉	—	4	2	no	—
182	C₂²×C₁₄₉	—	4	1	no	—
183	C₂²×C₁₄₉	—	8	16	no	—
184	C₂²×C₁₄₉	C₂×C₂²⋊C₈	1	8	yes	—
185	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₁₄₉	C₂³×C₈	1	1	yes	characteristic
187	C₂²×C₁₄₉	C₂²×M₁₆	1	1	yes	characteristic
188	C₄×C₁₄₉	—	2	2	no	—
189	C₄×C₁₄₉	—	2	2	no	—
190	C₄×C₁₄₉	—	2	4	no	—
191	C₄×C₁₄₉	—	2	2	no	—
192	C₄×C₁₄₉	—	4	1	no	—
193	C₄×C₁₄₉	—	4	2	no	—
194	C₄×C₁₄₉	—	4	1	no	—
195	C₄×C₁₄₉	C₂×C₂²⋊C₈	1	4	yes	—
196	C₂×C₁₄₉	—	2	1	no	—
197	C₂×C₁₄₉	—	2	1	no	—
198	C₂×C₁₄₉	—	2	8	no	—
199	C₂×C₁₄₉	—	4	4	no	—
200	C₂×C₁₄₉	—	4	2	no	—
201	C₂×C₁₄₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic
202	C₂×C₁₄₉	#2883	1	1	yes	characteristic
203	C₂×C₁₄₉	#2888	1	1	yes	characteristic
204	#17350	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₄₉	#17350	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#518	C₂×C₁₄₉	1	1	yes	characteristic
207	#2972	C₂×C₁₄₉	1	2	yes	complemented
208	#1460	C₂×C₁₄₉	1	2	yes	complemented
209	#1459	C₂×C₁₄₉	1	4	yes	complemented
210	#1458	C₂×C₁₄₉	1	2	yes	complemented
211	C₂×#323	C₂×C₁₄₉	1	4	yes	complemented
212	C₂³×D₄	C₄×C₁₄₉	1	1	yes	characteristic
213	#518	—	2	8	no	—
214	C₂×C₄×D₄	C₄×C₁₄₉	1	2	yes	—
215	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
216	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₄₉	1	2	yes	—
218	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
220	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
222	C₂²×C₂²⋊C₄	C₄×C₁₄₉	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
224	C₈×D₄	—	2	8	no	—
225	#431	C₂²×C₁₄₉	1	4	yes	complemented
226	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	8	yes	complemented
227	#324	C₂²×C₁₄₉	1	4	yes	complemented
228	#323	C₂²×C₁₄₉	1	4	yes	—
229	#323	C₂²×C₁₄₉	1	8	yes	complemented
230	C₂⁵	C₂×C₄×C₁₄₉	1	2	yes	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	—	2	4	no	—
233	C₂²×D₄	C₈×C₁₄₉	1	8	yes	complemented
234	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
235	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
236	C₂²×D₄	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	C₂×C₄×C₁₄₉	1	2	yes	—
240	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
241	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
242	C₂²×C₈	—	2	8	no	—
243	C₄×D₄	—	2	4	no	—
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	2	8	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	D₄×C₁₄₉	1	8	yes	—
249	#117	—	2	4	no	—
250	#117	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	—	2	8	no	—
256	C₂×C₂²⋊C₄	—	2	8	no	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
264	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
265	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	4	no	—
268	C₂²⋊C₈	—	2	8	no	—
269	C₂²⋊C₈	C₂³×C₁₄₉	1	8	yes	—
270	C₄×C₈	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	8	2	no	—
274	C₂⁴	—	8	2	no	—
275	C₂⁴	C₂×C₈×C₁₄₉	1	8	yes	complemented
276	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
277	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
278	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	32	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
285	C₂×D₄	C₂×C₈×C₁₄₉	1	4	yes	—
286	C₂×D₄	C₂×C₈×C₁₄₉	1	8	yes	complemented
287	C₂×D₄	C₂×C₈×C₁₄₉	1	4	yes	complemented
288	C₂×D₄	M₁₆×C₁₄₉	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	8	2	no	—
295	C₂²×C₄	—	8	2	no	—
296	C₂²×C₄	—	8	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	C₂×C₈×C₁₄₉	1	4	yes	complemented
299	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
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	8	yes	—
307	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
308	C₂×C₈	—	2	8	no	—
309	C₂×C₈	—	8	8	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	8	yes	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	16	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	8	4	no	—
336	C₂³	—	8	4	no	—
337	C₂³	—	8	8	no	—
338	C₂³	—	8	8	no	—
339	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
340	C₂³	C₂²×C₈×C₁₄₉	1	2	yes	—
341	C₂³	C₂²×C₈×C₁₄₉	1	4	yes	—
342	C₂³	C₂²×C₈×C₁₄₉	1	4	yes	—
343	C₂³	C₂×M₁₆×C₁₄₉	1	4	yes	—
344	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
345	D₄	—	2	16	no	—
346	D₄	—	2	8	no	—
347	D₄	C₂²⋊C₈×C₁₄₉	1	16	yes	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
367	C₂×C₄	C₂²×C₈×C₁₄₉	1	2	yes	—
368	C₂×C₄	C₂²×C₈×C₁₄₉	1	2	yes	—
369	C₂×C₄	C₂×M₁₆×C₁₄₉	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
371	C₈	—	4	8	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	8	16	no	—
389	C₂²	C₂×C₂²⋊C₈×C₁₄₉	1	8	yes	—
390	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
391	C₂²	C₂³×C₈×C₁₄₉	1	1	yes	characteristic
392	C₂²	C₂²×M₁₆×C₁₄₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	C₂×C₂²⋊C₈×C₁₄₉	1	4	yes	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	8	no	—
404	C₂	—	4	2	no	—
405	C₂	—	4	4	no	—
406	C₂	C₂²×C₂²⋊C₈×C₁₄₉	1	1	yes	characteristic
407	C₂	#2883×C₁₄₉	1	1	yes	characteristic
408	C₂	#2888×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂³×D₄×C₁₄₉	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×D₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2972×C₁₄₉	C₂	semidirect
3. #1460×C₁₄₉	C₂	semidirect
4. #1459×C₁₄₉	C₂	semidirect
5. #1458×C₁₄₉	C₂	semidirect
6. C₂×#323×C₁₄₉	C₂	semidirect
20. #431×C₁₄₉	C₂²	semidirect
21. C₂×C₂²⋊C₈×C₁₄₉	C₂²	semidirect
22. #324×C₁₄₉	C₂²	semidirect
24. #323×C₁₄₉	C₂²	semidirect
28. C₂²×D₄×C₁₄₉	C₈	semidirect
70. C₂⁴×C₁₄₉	C₂×C₈	semidirect
81. C₂×D₄×C₁₄₉	C₂×C₈	semidirect
82. C₂×D₄×C₁₄₉	C₂×C₈	semidirect
93. C₂²×C₄×C₁₄₉	C₂×C₈	semidirect
204. #17350	C₁₄₉	direct (N × H)
205. C₁₄₉	#17350	direct (N × H)
207. #2972	C₂×C₁₄₉	semidirect
208. #1460	C₂×C₁₄₉	semidirect
209. #1459	C₂×C₁₄₉	semidirect
210. #1458	C₂×C₁₄₉	semidirect
211. C₂×#323	C₂×C₁₄₉	semidirect
225. #431	C₂²×C₁₄₉	semidirect
226. C₂×C₂²⋊C₈	C₂²×C₁₄₉	semidirect
227. #324	C₂²×C₁₄₉	semidirect
229. #323	C₂²×C₁₄₉	semidirect
233. C₂²×D₄	C₈×C₁₄₉	semidirect
275. C₂⁴	C₂×C₈×C₁₄₉	semidirect
286. C₂×D₄	C₂×C₈×C₁₄₉	semidirect
287. C₂×D₄	C₂×C₈×C₁₄₉	semidirect
298. C₂²×C₄	C₂×C₈×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₁₄₉	2
#2972×C₁₄₉	2
#1460×C₁₄₉	2
#1459×C₁₄₉	2
#1458×C₁₄₉	2
C₂×#323×C₁₄₉	2
#17350	149

Subgroups — C149×#17350 #49196299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17350 #49196299