Subgroups — C₁₄₉×#10737 #49189686

Order 38144.

1334 conjugacy classes of subgroups.

The subgroup lattice has 408 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	#2280×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×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	complemented
10	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₄₉	—	2	1	no	—
13	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
14	#407×C₁₄₉	—	2	1	no	—
15	#407×C₁₄₉	—	2	1	no	—
16	#407×C₁₄₉	—	2	2	no	—
17	C₂×C₂²⋊C₈×C₁₄₉	C₄	1	4	yes	complemented
18	#381×C₁₄₉	C₄	1	2	yes	—
19	#380×C₁₄₉	—	2	2	no	—
20	#379×C₁₄₉	C₄	1	2	yes	—
21	C₄×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
22	#344×C₁₄₉	—	2	8	no	—
23	C₂⁵×C₁₄₉	C₂×C₄	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	2	yes	—
28	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₄₉	Q₈	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	2	no	—
44	C₂×M₁₆×C₁₄₉	—	2	4	no	—
45	C₂×M₁₆×C₁₄₉	—	2	4	no	—
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	C₂×C₄	1	4	yes	—
52	#117×C₁₄₉	—	2	4	no	—
53	#117×C₁₄₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₄₉	—	2	2	no	—
58	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
59	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
60	#95×C₁₄₉	—	2	4	no	—
61	C₂⁴×C₁₄₉	—	2	4	no	—
62	C₂⁴×C₁₄₉	—	4	4	no	—
63	C₂⁴×C₁₄₉	C₄²	1	2	yes	—
64	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂⁴×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
67	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₄₉	—	2	4	no	—
69	C₂²×C₄×C₁₄₉	—	2	4	no	—
70	C₂²×C₄×C₁₄₉	—	2	4	no	—
71	C₂²×C₄×C₁₄₉	—	2	8	no	—
72	C₂²×C₄×C₁₄₉	—	2	2	no	—
73	C₂²×C₄×C₁₄₉	—	2	2	no	—
74	C₂²×C₄×C₁₄₉	—	2	4	no	—
75	C₂²×C₄×C₁₄₉	—	2	8	no	—
76	C₂²×C₄×C₁₄₉	—	2	4	no	—
77	C₂²×C₄×C₁₄₉	—	2	4	no	—
78	C₂²×C₄×C₁₄₉	—	2	2	no	—
79	C₂²×C₄×C₁₄₉	—	2	2	no	—
80	C₂²×C₄×C₁₄₉	—	2	4	no	—
81	C₂²×C₄×C₁₄₉	—	2	4	no	—
82	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
83	C₂²×C₄×C₁₄₉	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
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	2	yes	—
93	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₄₉	C₂×Q₈	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	—	4	2	no	—
106	M₁₆×C₁₄₉	—	4	4	no	—
107	M₁₆×C₁₄₉	—	4	2	no	—
108	M₁₆×C₁₄₉	C₂²⋊C₄	1	8	yes	complemented
109	C₂×C₈×C₁₄₉	—	2	16	no	—
110	C₂×C₈×C₁₄₉	—	2	4	no	—
111	C₂×C₈×C₁₄₉	—	2	8	no	—
112	C₂×C₈×C₁₄₉	—	2	4	no	—
113	C₂×C₈×C₁₄₉	—	2	8	no	—
114	C₄⋊C₄×C₁₄₉	—	4	2	no	—
115	C₄⋊C₄×C₁₄₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
118	C₄²×C₁₄₉	—	4	4	no	—
119	C₂³×C₁₄₉	—	2	4	no	—
120	C₂³×C₁₄₉	—	2	2	no	—
121	C₂³×C₁₄₉	—	2	4	no	—
122	C₂³×C₁₄₉	—	2	4	no	—
123	C₂³×C₁₄₉	—	2	4	no	—
124	C₂³×C₁₄₉	—	2	2	no	—
125	C₂³×C₁₄₉	—	2	4	no	—
126	C₂³×C₁₄₉	—	4	2	no	—
127	C₂³×C₁₄₉	—	4	2	no	—
128	C₂³×C₁₄₉	—	4	2	no	—
129	C₂³×C₁₄₉	—	4	2	no	—
130	C₂³×C₁₄₉	—	4	16	no	—
131	C₂³×C₁₄₉	#95	1	2	yes	—
132	C₂³×C₁₄₉	#95	1	2	yes	—
133	C₂³×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
134	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₄₉	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₁₄₉	—	2	4	no	—
138	C₂×C₄×C₁₄₉	—	2	2	no	—
139	C₂×C₄×C₁₄₉	—	2	2	no	—
140	C₂×C₄×C₁₄₉	—	2	4	no	—
141	C₂×C₄×C₁₄₉	—	2	2	no	—
142	C₂×C₄×C₁₄₉	—	2	2	no	—
143	C₂×C₄×C₁₄₉	—	2	4	no	—
144	C₂×C₄×C₁₄₉	—	2	4	no	—
145	C₂×C₄×C₁₄₉	—	2	2	no	—
146	C₂×C₄×C₁₄₉	—	2	2	no	—
147	C₂×C₄×C₁₄₉	—	2	4	no	—
148	C₂×C₄×C₁₄₉	—	2	4	no	—
149	C₂×C₄×C₁₄₉	—	2	4	no	—
150	C₂×C₄×C₁₄₉	—	2	4	no	—
151	C₂×C₄×C₁₄₉	—	4	8	no	—
152	C₂×C₄×C₁₄₉	—	4	4	no	—
153	C₂×C₄×C₁₄₉	#95	1	2	yes	—
154	C₂×C₄×C₁₄₉	#95	1	2	yes	—
155	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₄₉	#117	1	2	yes	—
161	C₂×C₄×C₁₄₉	C₄×D₄	1	4	yes	—
162	C₂×C₄×C₁₄₉	#120	1	2	yes	—
163	C₂×C₄×C₁₄₉	#120	1	2	yes	—
164	C₂×C₄×C₁₄₉	#121	1	4	yes	—
165	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₄₉	#123	1	2	yes	—
167	C₂×C₄×C₁₄₉	#123	1	2	yes	—
168	C₈×C₁₄₉	—	2	8	no	—
169	C₈×C₁₄₉	—	4	4	no	—
170	C₂²×C₁₄₉	—	2	8	no	—
171	C₂²×C₁₄₉	—	2	2	no	—
172	C₂²×C₁₄₉	—	2	2	no	—
173	C₂²×C₁₄₉	—	2	2	no	—
174	C₂²×C₁₄₉	—	2	2	no	—
175	C₂²×C₁₄₉	—	2	2	no	—
176	C₂²×C₁₄₉	—	2	2	no	—
177	C₂²×C₁₄₉	—	2	2	no	—
178	C₂²×C₁₄₉	—	2	2	no	—
179	C₂²×C₁₄₉	—	4	4	no	—
180	C₂²×C₁₄₉	—	4	8	no	—
181	C₂²×C₁₄₉	—	4	8	no	—
182	C₂²×C₁₄₉	—	4	4	no	—
183	C₂²×C₁₄₉	#344	1	4	yes	complemented
184	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
185	C₂²×C₁₄₉	C₄×C₂²⋊C₄	1	2	yes	—
186	C₂²×C₁₄₉	#385	1	2	yes	—
187	C₂²×C₁₄₉	#386	1	2	yes	—
188	C₄×C₁₄₉	—	2	2	no	—
189	C₄×C₁₄₉	—	2	2	no	—
190	C₄×C₁₄₉	—	8	4	no	—
191	C₄×C₁₄₉	#379	1	1	yes	characteristic
192	C₄×C₁₄₉	#380	1	2	yes	—
193	C₄×C₁₄₉	#381	1	1	yes	characteristic
194	C₄×C₁₄₉	#385	1	2	yes	—
195	C₄×C₁₄₉	#386	1	2	yes	—
196	C₂×C₁₄₉	—	2	2	no	—
197	C₂×C₁₄₉	—	2	4	no	—
198	C₂×C₁₄₉	—	2	2	no	—
199	C₂×C₁₄₉	—	2	2	no	—
200	C₂×C₁₄₉	—	4	2	no	—
201	C₂×C₁₄₉	C₂²⋊#95	1	1	yes	characteristic
202	C₂×C₁₄₉	C₂×#344	1	2	yes	—
203	#10737	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₄₉	#10737	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³×M₁₆	C₂×C₁₄₉	1	1	yes	characteristic
206	C₂×#407	C₂×C₁₄₉	1	1	yes	characteristic
207	#2280	C₂×C₁₄₉	1	1	yes	characteristic
208	C₂×#344	C₂×C₁₄₉	1	4	yes	complemented
209	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
210	C₂²×M₁₆	—	2	2	no	—
211	C₂²×M₁₆	—	2	1	no	—
212	C₂²×M₁₆	—	2	8	no	—
213	C₂²×M₁₆	C₄×C₁₄₉	1	4	yes	complemented
214	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
215	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
216	C₂³×C₈	—	2	1	no	—
217	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
218	#407	—	2	1	no	—
219	#407	—	2	1	no	—
220	#407	—	2	2	no	—
221	C₂×C₂²⋊C₈	C₄×C₁₄₉	1	4	yes	complemented
222	#381	C₄×C₁₄₉	1	2	yes	—
223	#380	—	2	2	no	—
224	#379	C₄×C₁₄₉	1	2	yes	—
225	C₄×C₂²⋊C₄	—	2	2	no	—
226	#344	—	2	8	no	—
227	C₂⁵	C₂×C₄×C₁₄₉	1	1	yes	characteristic
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	2	4	no	—
230	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
232	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
233	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
236	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
237	C₂³×C₄	Q₈×C₁₄₉	1	1	yes	characteristic
238	C₂³×C₄	Q₈×C₁₄₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
240	C₂×M₁₆	—	2	16	no	—
241	C₂×M₁₆	—	2	8	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	16	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	—
251	C₂×M₁₆	D₄×C₁₄₉	1	8	yes	—
252	C₂²×C₈	—	2	8	no	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	C₂×C₄×C₁₄₉	1	4	yes	—
256	#117	—	2	4	no	—
257	#117	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	#95	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	4	4	no	—
267	C₂⁴	C₄²×C₁₄₉	1	2	yes	—
268	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
269	C₂⁴	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
270	C₂⁴	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
271	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
288	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
292	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
295	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
296	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
297	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
306	M₁₆	—	2	16	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	8	no	—
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	C₂²⋊C₄×C₁₄₉	1	8	yes	complemented
313	C₂×C₈	—	2	16	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	8	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₄²	—	4	4	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	16	no	—
335	C₂³	#95×C₁₄₉	1	2	yes	—
336	C₂³	#95×C₁₄₉	1	2	yes	—
337	C₂³	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
338	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
339	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
340	C₂³	C₄×D₄×C₁₄₉	1	4	yes	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	#95×C₁₄₉	1	2	yes	—
358	C₂×C₄	#95×C₁₄₉	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
364	C₂×C₄	#117×C₁₄₉	1	2	yes	—
365	C₂×C₄	C₄×D₄×C₁₄₉	1	4	yes	—
366	C₂×C₄	#120×C₁₄₉	1	2	yes	—
367	C₂×C₄	#120×C₁₄₉	1	2	yes	—
368	C₂×C₄	#121×C₁₄₉	1	4	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	4	yes	—
370	C₂×C₄	#123×C₁₄₉	1	2	yes	—
371	C₂×C₄	#123×C₁₄₉	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	#344×C₁₄₉	1	4	yes	complemented
388	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
389	C₂²	C₄×C₂²⋊C₄×C₁₄₉	1	2	yes	—
390	C₂²	#385×C₁₄₉	1	2	yes	—
391	C₂²	#386×C₁₄₉	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	8	4	no	—
395	C₄	#379×C₁₄₉	1	1	yes	characteristic
396	C₄	#380×C₁₄₉	1	2	yes	—
397	C₄	#381×C₁₄₉	1	1	yes	characteristic
398	C₄	#385×C₁₄₉	1	2	yes	—
399	C₄	#386×C₁₄₉	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	—	2	4	no	—
403	C₂	—	2	2	no	—
404	C₂	—	4	2	no	—
405	C₂	C₂²⋊#95×C₁₄₉	1	1	yes	characteristic
406	C₂	C₂×#344×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	C₂×#95
prime radical	C₂⁵×C₁₄₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#344×C₁₄₉	C₂	semidirect
9. C₂²×M₁₆×C₁₄₉	C₄	semidirect
17. C₂×C₂²⋊C₈×C₁₄₉	C₄	semidirect
108. M₁₆×C₁₄₉	C₂²⋊C₄	semidirect
183. C₂²×C₁₄₉	#344	semidirect
203. #10737	C₁₄₉	direct (N × H)
204. C₁₄₉	#10737	direct (N × H)
208. C₂×#344	C₂×C₁₄₉	semidirect
213. C₂²×M₁₆	C₄×C₁₄₉	semidirect
221. C₂×C₂²⋊C₈	C₄×C₁₄₉	semidirect
312. M₁₆	C₂²⋊C₄×C₁₄₉	semidirect
387. C₂²	#344×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
#2280×C₁₄₉	2
C₂×#344×C₁₄₉	2
#10737	149

Subgroups — C149×#10737 #49189686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10737 #49189686