Subgroups — C₁₄₉×#19163 #49198112

Order 38144.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3152×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3100×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#474×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×M₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1689×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1685×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1669×C₁₄₉	C₂	1	2	yes	maximal, complemented
8	#1665×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	#1565×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1547×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1546×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₄₉	—	2	1	no	—
13	C₂×#137×C₁₄₉	—	2	1	no	—
14	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
15	#532×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
18	#497×C₁₄₉	—	2	2	no	—
19	#494×C₁₄₉	C₂²	1	2	yes	complemented
20	#492×C₁₄₉	C₂²	1	2	yes	complemented
21	#480×C₁₄₉	—	2	1	no	—
22	#474×C₁₄₉	—	2	1	no	—
23	#474×C₁₄₉	—	2	1	no	—
24	#474×C₁₄₉	C₂²	1	2	yes	—
25	#474×C₁₄₉	C₂²	1	1	yes	characteristic
26	#474×C₁₄₉	C₂²	1	2	yes	—
27	#474×C₁₄₉	C₂²	1	1	yes	characteristic
28	#459×C₁₄₉	C₂²	1	1	yes	characteristic
29	#459×C₁₄₉	C₂²	1	1	yes	characteristic
30	#447×C₁₄₉	—	2	1	no	—
31	C₄×D₈×C₁₄₉	—	2	1	no	—
32	C₄×D₈×C₁₄₉	—	2	1	no	—
33	#436×C₁₄₉	C₂²	1	2	yes	—
34	#435×C₁₄₉	—	2	2	no	—
35	C₈×D₄×C₁₄₉	C₂²	1	2	yes	—
36	#431×C₁₄₉	C₂²	1	1	yes	characteristic
37	C₂×#107×C₁₄₉	—	2	1	no	—
38	#423×C₁₄₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₁₄₉	—	2	1	no	—
41	#407×C₁₄₉	—	2	1	no	—
42	C₄×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
43	#335×C₁₄₉	C₂²	1	2	yes	complemented
44	#334×C₁₄₉	C₂²	1	2	yes	complemented
45	#332×C₁₄₉	C₂²	1	2	yes	complemented
46	#332×C₁₄₉	C₂²	1	2	yes	complemented
47	#332×C₁₄₉	C₂²	1	2	yes	complemented
48	#331×C₁₄₉	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₄₉	—	2	1	no	—
50	C₂²×Q₈×C₁₄₉	—	2	1	no	—
51	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₄₉	—	2	1	no	—
53	#137×C₁₄₉	—	4	4	no	—
54	#137×C₁₄₉	—	4	4	no	—
55	C₂×Q₁₆×C₁₄₉	—	2	2	no	—
56	C₂×Q₁₆×C₁₄₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₄₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₄₉	—	2	2	no	—
59	C₂×D₈×C₁₄₉	—	2	1	no	—
60	C₂×D₈×C₁₄₉	—	2	1	no	—
61	C₂×M₁₆×C₁₄₉	—	2	1	no	—
62	C₂×M₁₆×C₁₄₉	—	2	2	no	—
63	C₂×M₁₆×C₁₄₉	—	4	4	no	—
64	C₂×M₁₆×C₁₄₉	D₄	1	1	yes	characteristic
65	C₂×M₁₆×C₁₄₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₄₉	—	2	1	no	—
67	C₂²×C₈×C₁₄₉	—	2	2	no	—
68	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
69	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
70	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
71	C₄⋊Q₈×C₁₄₉	C₂³	1	2	yes	—
72	C₄⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
73	#127×C₁₄₉	C₂³	1	1	yes	characteristic
74	#124×C₁₄₉	—	2	1	no	—
75	#121×C₁₄₉	—	2	1	no	—
76	#121×C₁₄₉	—	2	1	no	—
77	C₄×D₄×C₁₄₉	—	2	1	no	—
78	C₄×D₄×C₁₄₉	—	2	1	no	—
79	C₄×D₄×C₁₄₉	—	2	1	no	—
80	C₄×D₄×C₁₄₉	—	2	1	no	—
81	C₄×D₄×C₁₄₉	D₄	1	1	yes	characteristic
82	C₄×D₄×C₁₄₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
89	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
90	#107×C₁₄₉	—	2	2	no	—
91	#107×C₁₄₉	—	2	2	no	—
92	#107×C₁₄₉	—	2	1	no	—
93	#107×C₁₄₉	—	2	1	no	—
94	C₄⋊C₈×C₁₄₉	—	2	1	no	—
95	C₄⋊C₈×C₁₄₉	—	2	1	no	—
96	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
97	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
98	C₄⋊C₈×C₁₄₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₁₄₉	C₂³	1	1	yes	characteristic
100	#102×C₁₄₉	—	2	2	no	—
101	#102×C₁₄₉	—	2	2	no	—
102	#102×C₁₄₉	—	2	1	no	—
103	#102×C₁₄₉	—	2	1	no	—
104	#102×C₁₄₉	—	2	1	no	—
105	#102×C₁₄₉	—	2	1	no	—
106	C₂²⋊C₈×C₁₄₉	—	2	1	no	—
107	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
108	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
109	#97×C₁₄₉	D₄	1	2	yes	—
110	C₄×C₈×C₁₄₉	—	2	1	no	—
111	C₄×C₈×C₁₄₉	C₂³	1	2	yes	—
112	C₂⁴×C₁₄₉	—	2	1	no	—
113	#41×C₁₄₉	—	4	2	no	—
114	#41×C₁₄₉	—	4	2	no	—
115	C₂×Q₈×C₁₄₉	—	2	1	no	—
116	C₂×Q₈×C₁₄₉	—	2	2	no	—
117	C₂×Q₈×C₁₄₉	—	4	1	no	—
118	C₂×Q₈×C₁₄₉	—	4	2	no	—
119	C₂×Q₈×C₁₄₉	—	4	2	no	—
120	C₂×D₄×C₁₄₉	—	2	2	no	—
121	C₂×D₄×C₁₄₉	—	2	1	no	—
122	C₂×D₄×C₁₄₉	—	2	1	no	—
123	C₂×D₄×C₁₄₉	—	2	1	no	—
124	C₂×D₄×C₁₄₉	—	2	1	no	—
125	C₂×D₄×C₁₄₉	—	4	1	no	—
126	C₂×D₄×C₁₄₉	—	4	1	no	—
127	C₂×D₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₄₉	—	2	1	no	—
130	C₂²×C₄×C₁₄₉	—	2	1	no	—
131	C₂²×C₄×C₁₄₉	—	2	1	no	—
132	C₂²×C₄×C₁₄₉	—	2	1	no	—
133	C₂²×C₄×C₁₄₉	—	2	1	no	—
134	C₂²×C₄×C₁₄₉	—	4	2	no	—
135	C₂²×C₄×C₁₄₉	—	4	2	no	—
136	C₂²×C₄×C₁₄₉	—	4	1	no	—
137	C₂²×C₄×C₁₄₉	—	4	1	no	—
138	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
141	Q₁₆×C₁₄₉	—	4	4	no	—
142	Q₁₆×C₁₄₉	—	4	4	no	—
143	SD₁₆×C₁₄₉	—	4	4	no	—
144	SD₁₆×C₁₄₉	—	4	4	no	—
145	D₈×C₁₄₉	—	4	2	no	—
146	D₈×C₁₄₉	—	4	2	no	—
147	M₁₆×C₁₄₉	—	2	2	no	—
148	M₁₆×C₁₄₉	—	4	2	no	—
149	M₁₆×C₁₄₉	—	4	4	no	—
150	M₁₆×C₁₄₉	D₈	1	4	yes	complemented
151	C₂×C₈×C₁₄₉	—	2	1	no	—
152	C₂×C₈×C₁₄₉	—	2	1	no	—
153	C₂×C₈×C₁₄₉	—	2	2	no	—
154	C₂×C₈×C₁₄₉	—	2	2	no	—
155	C₂×C₈×C₁₄₉	—	4	2	no	—
156	C₂×C₈×C₁₄₉	—	4	4	no	—
157	C₂×C₈×C₁₄₉	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₄₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₄₉	—	2	1	no	—
160	C₄⋊C₄×C₁₄₉	—	2	2	no	—
161	C₄⋊C₄×C₁₄₉	—	2	1	no	—
162	C₄⋊C₄×C₁₄₉	—	2	2	no	—
163	C₄⋊C₄×C₁₄₉	—	2	1	no	—
164	C₄⋊C₄×C₁₄₉	—	4	1	no	—
165	C₄⋊C₄×C₁₄₉	—	4	1	no	—
166	C₄⋊C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
169	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
170	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
171	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
172	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
173	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
174	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₄₉	#41	1	1	yes	characteristic
177	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
178	C₂³×C₁₄₉	—	2	1	no	—
179	C₂³×C₁₄₉	—	2	1	no	—
180	C₂³×C₁₄₉	—	4	2	no	—
181	C₂³×C₁₄₉	—	4	2	no	—
182	C₂³×C₁₄₉	—	4	1	no	—
183	C₂³×C₁₄₉	—	8	1	no	—
184	C₂³×C₁₄₉	#121	1	1	yes	characteristic
185	Q₈×C₁₄₉	—	4	2	no	—
186	Q₈×C₁₄₉	—	4	1	no	—
187	Q₈×C₁₄₉	—	4	2	no	—
188	Q₈×C₁₄₉	—	4	1	no	—
189	Q₈×C₁₄₉	—	8	2	no	—
190	D₄×C₁₄₉	—	2	1	no	—
191	D₄×C₁₄₉	—	2	1	no	—
192	D₄×C₁₄₉	—	2	1	no	—
193	D₄×C₁₄₉	—	4	2	no	—
194	D₄×C₁₄₉	—	4	1	no	—
195	D₄×C₁₄₉	—	4	1	no	—
196	D₄×C₁₄₉	—	4	1	no	—
197	D₄×C₁₄₉	—	4	1	no	—
198	D₄×C₁₄₉	—	8	1	no	—
199	D₄×C₁₄₉	—	8	2	no	—
200	D₄×C₁₄₉	#137	1	2	yes	complemented
201	C₂×C₄×C₁₄₉	—	2	1	no	—
202	C₂×C₄×C₁₄₉	—	2	1	no	—
203	C₂×C₄×C₁₄₉	—	2	1	no	—
204	C₂×C₄×C₁₄₉	—	2	1	no	—
205	C₂×C₄×C₁₄₉	—	4	1	no	—
206	C₂×C₄×C₁₄₉	—	4	2	no	—
207	C₂×C₄×C₁₄₉	—	4	1	no	—
208	C₂×C₄×C₁₄₉	—	4	1	no	—
209	C₂×C₄×C₁₄₉	—	4	1	no	—
210	C₂×C₄×C₁₄₉	—	4	1	no	—
211	C₂×C₄×C₁₄₉	—	4	2	no	—
212	C₂×C₄×C₁₄₉	—	4	2	no	—
213	C₂×C₄×C₁₄₉	—	4	1	no	—
214	C₂×C₄×C₁₄₉	—	4	2	no	—
215	C₂×C₄×C₁₄₉	—	8	2	no	—
216	C₂×C₄×C₁₄₉	—	8	2	no	—
217	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₄₉	C₂×D₈	1	2	yes	—
221	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
222	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₄₉	C₂×#41	1	1	yes	characteristic
225	C₈×C₁₄₉	—	2	2	no	—
226	C₈×C₁₄₉	—	4	2	no	—
227	C₈×C₁₄₉	—	4	1	no	—
228	C₈×C₁₄₉	—	4	2	no	—
229	C₈×C₁₄₉	—	4	1	no	—
230	C₈×C₁₄₉	C₂×D₈	1	4	yes	—
231	C₂²×C₁₄₉	—	2	1	no	—
232	C₂²×C₁₄₉	—	2	1	no	—
233	C₂²×C₁₄₉	—	2	2	no	—
234	C₂²×C₁₄₉	—	4	1	no	—
235	C₂²×C₁₄₉	—	4	1	no	—
236	C₂²×C₁₄₉	—	4	1	no	—
237	C₂²×C₁₄₉	—	4	1	no	—
238	C₂²×C₁₄₉	—	4	1	no	—
239	C₂²×C₁₄₉	—	8	4	no	—
240	C₂²×C₁₄₉	—	8	1	no	—
241	C₂²×C₁₄₉	—	8	1	no	—
242	C₂²×C₁₄₉	—	8	1	no	—
243	C₂²×C₁₄₉	#459	1	2	yes	—
244	C₂²×C₁₄₉	C₂×#121	1	1	yes	characteristic
245	C₄×C₁₄₉	—	2	1	no	—
246	C₄×C₁₄₉	—	2	1	no	—
247	C₄×C₁₄₉	—	2	1	no	—
248	C₄×C₁₄₉	—	4	1	no	—
249	C₄×C₁₄₉	—	4	1	no	—
250	C₄×C₁₄₉	—	8	1	no	—
251	C₄×C₁₄₉	—	8	2	no	—
252	C₄×C₁₄₉	#459	1	2	yes	—
253	C₄×C₁₄₉	C₂²×D₈	1	1	yes	characteristic
254	C₄×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₄×C₁₄₉	C₂×#137	1	1	yes	characteristic
256	C₄×C₁₄₉	#575	1	1	yes	characteristic
257	C₂×C₁₄₉	—	2	2	no	—
258	C₂×C₁₄₉	—	4	2	no	—
259	C₂×C₁₄₉	—	8	1	no	—
260	C₂×C₁₄₉	—	16	1	no	—
261	C₂×C₁₄₉	C₂×#459	1	1	yes	characteristic
262	C₂×C₁₄₉	#3056	1	1	yes	characteristic
263	C₂×C₁₄₉	#3069	1	1	yes	characteristic
264	#19163	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₁₄₉	#19163	1	1	yes	characteristic, direct product factor, Sylow
266	#3152	C₂×C₁₄₉	1	1	yes	characteristic, complemented
267	#3100	C₂×C₁₄₉	1	1	yes	characteristic
268	C₂×#474	C₂×C₁₄₉	1	1	yes	characteristic, complemented
269	D₄×M₁₆	C₂×C₁₄₉	1	1	yes	characteristic, complemented
270	#1689	C₂×C₁₄₉	1	2	yes	complemented
271	#1685	C₂×C₁₄₉	1	2	yes	complemented
272	#1669	C₂×C₁₄₉	1	2	yes	complemented
273	#1665	C₂×C₁₄₉	1	2	yes	complemented
274	#1565	C₂×C₁₄₉	1	1	yes	characteristic, complemented
275	#1547	C₂×C₁₄₉	1	1	yes	characteristic, complemented
276	#1546	C₂×C₁₄₉	1	1	yes	characteristic, complemented
277	C₂×#137	—	2	1	no	—
278	C₂×#137	—	2	1	no	—
279	C₂²×M₁₆	—	2	1	no	—
280	#532	C₂²×C₁₄₉	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
283	#497	—	2	2	no	—
284	#494	C₂²×C₁₄₉	1	2	yes	complemented
285	#492	C₂²×C₁₄₉	1	2	yes	complemented
286	#480	—	2	1	no	—
287	#474	—	2	1	no	—
288	#474	—	2	1	no	—
289	#474	C₂²×C₁₄₉	1	1	yes	characteristic
290	#474	C₂²×C₁₄₉	1	1	yes	characteristic
291	#474	C₂²×C₁₄₉	1	2	yes	—
292	#474	C₂²×C₁₄₉	1	2	yes	—
293	#459	C₂²×C₁₄₉	1	1	yes	characteristic
294	#459	C₂²×C₁₄₉	1	1	yes	characteristic
295	#447	—	2	1	no	—
296	C₄×D₈	—	2	1	no	—
297	C₄×D₈	—	2	1	no	—
298	#436	C₂²×C₁₄₉	1	2	yes	—
299	#435	—	2	2	no	—
300	C₈×D₄	C₂²×C₁₄₉	1	2	yes	—
301	#431	C₂²×C₁₄₉	1	1	yes	characteristic
302	C₂×#107	—	2	1	no	—
303	#423	C₂²×C₁₄₉	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	1	yes	characteristic
305	C₂×#102	—	2	1	no	—
306	#407	—	2	1	no	—
307	C₄×M₁₆	C₂²×C₁₄₉	1	1	yes	characteristic
308	#335	C₂²×C₁₄₉	1	2	yes	complemented
309	#334	C₂²×C₁₄₉	1	2	yes	complemented
310	#332	C₂²×C₁₄₉	1	2	yes	complemented
311	#332	C₂²×C₁₄₉	1	2	yes	complemented
312	#332	C₂²×C₁₄₉	1	2	yes	complemented
313	#331	C₂²×C₁₄₉	1	2	yes	complemented
314	C₂×#41	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	#137	—	4	4	no	—
319	#137	—	4	4	no	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×Q₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×D₈	—	2	1	no	—
325	C₂×D₈	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	4	4	no	—
329	C₂×M₁₆	D₄×C₁₄₉	1	1	yes	characteristic
330	C₂×M₁₆	D₄×C₁₄₉	1	1	yes	characteristic
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	C₂³×C₁₄₉	1	2	yes	—
337	C₄⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
338	#127	C₂³×C₁₄₉	1	1	yes	characteristic
339	#124	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	D₄×C₁₄₉	1	1	yes	characteristic
347	C₄×D₄	D₄×C₁₄₉	1	1	yes	characteristic
348	C₄×D₄	C₂³×C₁₄₉	1	1	yes	characteristic
349	C₄×D₄	C₂³×C₁₄₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
355	#107	—	2	2	no	—
356	#107	—	2	2	no	—
357	#107	—	2	1	no	—
358	#107	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
362	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
363	C₄⋊C₈	C₂³×C₁₄₉	1	1	yes	characteristic
364	C₄⋊C₈	C₂³×C₁₄₉	1	1	yes	characteristic
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	1	no	—
368	#102	—	2	1	no	—
369	#102	—	2	1	no	—
370	#102	—	2	1	no	—
371	C₂²⋊C₈	—	2	1	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	#97	D₄×C₁₄₉	1	2	yes	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	C₂³×C₁₄₉	1	2	yes	—
377	C₂⁴	—	2	1	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
393	C₂×D₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
405	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
406	Q₁₆	—	4	4	no	—
407	Q₁₆	—	4	4	no	—
408	SD₁₆	—	4	4	no	—
409	SD₁₆	—	4	4	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	4	2	no	—
414	M₁₆	—	4	4	no	—
415	M₁₆	D₈×C₁₄₉	1	4	yes	complemented
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	4	4	no	—
422	C₂×C₈	C₂×D₄×C₁₄₉	1	2	yes	—
423	C₂×C₈	C₂×D₄×C₁₄₉	1	2	yes	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
432	C₄⋊C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
441	C₄²	#41×C₁₄₉	1	1	yes	characteristic
442	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	8	1	no	—
449	C₂³	#121×C₁₄₉	1	1	yes	characteristic
450	Q₈	—	4	2	no	—
451	Q₈	—	4	1	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	1	no	—
454	Q₈	—	8	2	no	—
455	D₄	—	2	1	no	—
456	D₄	—	2	1	no	—
457	D₄	—	2	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	—	8	1	no	—
464	D₄	—	8	2	no	—
465	D₄	#137×C₁₄₉	1	2	yes	complemented
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
483	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
484	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
485	C₂×C₄	C₂×D₈×C₁₄₉	1	2	yes	—
486	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₁₄₉	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	4	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	1	no	—
495	C₈	C₂×D₈×C₁₄₉	1	4	yes	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	8	4	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	#459×C₁₄₉	1	2	yes	—
509	C₂²	C₂×#121×C₁₄₉	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₄	#459×C₁₄₉	1	2	yes	—
518	C₄	C₂²×D₈×C₁₄₉	1	1	yes	characteristic
519	C₄	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
520	C₄	C₂×#137×C₁₄₉	1	1	yes	characteristic
521	C₄	#575×C₁₄₉	1	1	yes	characteristic
522	C₂	—	2	2	no	—
523	C₂	—	4	2	no	—
524	C₂	—	8	1	no	—
525	C₂	—	16	1	no	—
526	C₂	C₂×#459×C₁₄₉	1	1	yes	characteristic
527	C₂	#3056×C₁₄₉	1	1	yes	characteristic
528	C₂	#3069×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
prime radical	#3100×C₁₄₉	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3152×C₁₄₉	C₂	semidirect
3. C₂×#474×C₁₄₉	C₂	semidirect
4. D₄×M₁₆×C₁₄₉	C₂	semidirect
5. #1689×C₁₄₉	C₂	semidirect
6. #1685×C₁₄₉	C₂	semidirect
7. #1669×C₁₄₉	C₂	semidirect
8. #1665×C₁₄₉	C₂	semidirect
9. #1565×C₁₄₉	C₂	semidirect
10. #1547×C₁₄₉	C₂	semidirect
11. #1546×C₁₄₉	C₂	semidirect
19. #494×C₁₄₉	C₂²	semidirect
20. #492×C₁₄₉	C₂²	semidirect
43. #335×C₁₄₉	C₂²	semidirect
44. #334×C₁₄₉	C₂²	semidirect
45. #332×C₁₄₉	C₂²	semidirect
46. #332×C₁₄₉	C₂²	semidirect
47. #332×C₁₄₉	C₂²	semidirect
48. #331×C₁₄₉	C₂²	semidirect
150. M₁₆×C₁₄₉	D₈	semidirect
200. D₄×C₁₄₉	#137	semidirect
264. #19163	C₁₄₉	direct (N × H)
265. C₁₄₉	#19163	direct (N × H)
266. #3152	C₂×C₁₄₉	semidirect
268. C₂×#474	C₂×C₁₄₉	semidirect
269. D₄×M₁₆	C₂×C₁₄₉	semidirect
270. #1689	C₂×C₁₄₉	semidirect
271. #1685	C₂×C₁₄₉	semidirect
272. #1669	C₂×C₁₄₉	semidirect
273. #1665	C₂×C₁₄₉	semidirect
274. #1565	C₂×C₁₄₉	semidirect
275. #1547	C₂×C₁₄₉	semidirect
276. #1546	C₂×C₁₄₉	semidirect
284. #494	C₂²×C₁₄₉	semidirect
285. #492	C₂²×C₁₄₉	semidirect
308. #335	C₂²×C₁₄₉	semidirect
309. #334	C₂²×C₁₄₉	semidirect
310. #332	C₂²×C₁₄₉	semidirect
311. #332	C₂²×C₁₄₉	semidirect
312. #332	C₂²×C₁₄₉	semidirect
313. #331	C₂²×C₁₄₉	semidirect
415. M₁₆	D₈×C₁₄₉	semidirect
465. D₄	#137×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3152×C₁₄₉	2
#3100×C₁₄₉	2
C₂×#474×C₁₄₉	2
D₄×M₁₆×C₁₄₉	2
#1689×C₁₄₉	2
#1685×C₁₄₉	2
#1669×C₁₄₉	2
#1665×C₁₄₉	2
#1565×C₁₄₉	2
#1547×C₁₄₉	2
#1546×C₁₄₉	2
#19163	149

Subgroups — C149×#19163 #49198112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#19163 #49198112