Subgroups — C₁₄₉×#11076 #49190025

Order 38144.

1266 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₁₄₉	C₂	1	2	yes	maximal
3	C₂×#390×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	C₄⋊#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₄₉	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
11	C₂²×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
12	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₄₉	—	2	4	no	—
14	C₂×C₄⋊C₈×C₁₄₉	—	2	2	no	—
15	C₂×#102×C₁₄₉	—	2	4	no	—
16	C₂×#102×C₁₄₉	—	2	4	no	—
17	C₂×#102×C₁₄₉	—	2	4	no	—
18	#390×C₁₄₉	—	2	2	no	—
19	#390×C₁₄₉	C₄	1	4	yes	complemented
20	C₂×#95×C₁₄₉	—	2	1	no	—
21	C₂×#95×C₁₄₉	—	2	1	no	—
22	#340×C₁₄₉	—	2	4	no	—
23	C₂⁵×C₁₄₉	—	2	1	no	—
24	C₂²×D₄×C₁₄₉	—	2	2	no	—
25	C₂²×D₄×C₁₄₉	—	2	2	no	—
26	C₂²×D₄×C₁₄₉	—	2	1	no	—
27	C₂²×D₄×C₁₄₉	—	2	2	no	—
28	C₂²×D₄×C₁₄₉	—	2	2	no	—
29	C₂²×D₄×C₁₄₉	—	2	1	no	—
30	C₂²×D₄×C₁₄₉	—	2	1	no	—
31	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
33	C₂²×D₄×C₁₄₉	Q₈	1	2	yes	—
34	C₂³×C₄×C₁₄₉	—	2	2	no	—
35	C₂³×C₄×C₁₄₉	—	2	1	no	—
36	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₄₉	—	2	2	no	—
40	C₂²×C₈×C₁₄₉	—	2	2	no	—
41	C₂²×C₈×C₁₄₉	—	2	2	no	—
42	C₂²×C₈×C₁₄₉	—	2	2	no	—
43	C₂²×C₈×C₁₄₉	—	2	2	no	—
44	C₂²×C₈×C₁₄₉	—	2	2	no	—
45	C₂²×C₈×C₁₄₉	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₄₉	D₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₄₉	—	4	4	no	—
59	C₂×C₂²⋊C₄×C₁₄₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₄₉	—	4	2	no	—
61	C₂×C₄²×C₁₄₉	—	2	2	no	—
62	C₂×C₄²×C₁₄₉	—	2	2	no	—
63	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
65	C₄⋊C₈×C₁₄₉	—	2	8	no	—
66	#102×C₁₄₉	—	2	16	no	—
67	#95×C₁₄₉	—	4	2	no	—
68	#95×C₁₄₉	—	4	2	no	—
69	C₂⁴×C₁₄₉	—	2	2	no	—
70	C₂⁴×C₁₄₉	—	2	2	no	—
71	C₂⁴×C₁₄₉	—	2	2	no	—
72	C₂⁴×C₁₄₉	—	4	2	no	—
73	C₂⁴×C₁₄₉	—	4	2	no	—
74	C₂⁴×C₁₄₉	—	4	1	no	—
75	C₂⁴×C₁₄₉	—	4	1	no	—
76	C₂⁴×C₁₄₉	—	4	2	no	—
77	C₂⁴×C₁₄₉	—	4	2	no	—
78	C₂⁴×C₁₄₉	—	4	1	no	—
79	C₂⁴×C₁₄₉	—	4	1	no	—
80	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₁₄₉	—	2	2	no	—
82	C₂×D₄×C₁₄₉	—	2	4	no	—
83	C₂×D₄×C₁₄₉	—	2	4	no	—
84	C₂×D₄×C₁₄₉	—	2	4	no	—
85	C₂×D₄×C₁₄₉	—	2	2	no	—
86	C₂×D₄×C₁₄₉	—	2	4	no	—
87	C₂×D₄×C₁₄₉	—	2	4	no	—
88	C₂×D₄×C₁₄₉	—	2	2	no	—
89	C₂×D₄×C₁₄₉	—	2	4	no	—
90	C₂×D₄×C₁₄₉	—	4	1	no	—
91	C₂×D₄×C₁₄₉	—	4	2	no	—
92	C₂×D₄×C₁₄₉	—	4	2	no	—
93	C₂×D₄×C₁₄₉	—	4	1	no	—
94	C₂×D₄×C₁₄₉	—	4	2	no	—
95	C₂×D₄×C₁₄₉	—	4	1	no	—
96	C₂×D₄×C₁₄₉	—	4	2	no	—
97	C₂×D₄×C₁₄₉	—	4	1	no	—
98	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₄₉	—	2	2	no	—
100	C₂²×C₄×C₁₄₉	—	2	2	no	—
101	C₂²×C₄×C₁₄₉	—	2	2	no	—
102	C₂²×C₄×C₁₄₉	—	2	1	no	—
103	C₂²×C₄×C₁₄₉	—	2	2	no	—
104	C₂²×C₄×C₁₄₉	—	2	1	no	—
105	C₂²×C₄×C₁₄₉	—	2	2	no	—
106	C₂²×C₄×C₁₄₉	—	2	4	no	—
107	C₂²×C₄×C₁₄₉	—	4	2	no	—
108	C₂²×C₄×C₁₄₉	—	4	2	no	—
109	C₂²×C₄×C₁₄₉	—	4	2	no	—
110	C₂²×C₄×C₁₄₉	—	4	2	no	—
111	C₂²×C₄×C₁₄₉	—	4	1	no	—
112	C₂²×C₄×C₁₄₉	—	4	1	no	—
113	C₂²×C₄×C₁₄₉	—	4	2	no	—
114	C₂²×C₄×C₁₄₉	—	4	2	no	—
115	C₂²×C₄×C₁₄₉	—	4	2	no	—
116	C₂²×C₄×C₁₄₉	—	4	2	no	—
117	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₁₄₉	D₈	1	2	yes	—
120	C₂²×C₄×C₁₄₉	SD₁₆	1	2	yes	—
121	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
131	C₂×C₈×C₁₄₉	—	2	4	no	—
132	C₂×C₈×C₁₄₉	—	2	4	no	—
133	C₂×C₈×C₁₄₉	—	2	4	no	—
134	C₂×C₈×C₁₄₉	—	4	2	no	—
135	C₂×C₈×C₁₄₉	—	4	2	no	—
136	C₂×C₈×C₁₄₉	—	4	2	no	—
137	C₂×C₈×C₁₄₉	—	4	2	no	—
138	C₄⋊C₄×C₁₄₉	—	2	4	no	—
139	C₄⋊C₄×C₁₄₉	—	2	4	no	—
140	C₄⋊C₄×C₁₄₉	—	2	4	no	—
141	C₄⋊C₄×C₁₄₉	—	4	2	no	—
142	C₄⋊C₄×C₁₄₉	—	4	1	no	—
143	C₄⋊C₄×C₁₄₉	—	4	2	no	—
144	C₄⋊C₄×C₁₄₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
146	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
147	C₄²×C₁₄₉	—	2	4	no	—
148	C₄²×C₁₄₉	—	2	2	no	—
149	C₄²×C₁₄₉	—	2	2	no	—
150	C₂³×C₁₄₉	—	2	4	no	—
151	C₂³×C₁₄₉	—	4	2	no	—
152	C₂³×C₁₄₉	—	4	2	no	—
153	C₂³×C₁₄₉	—	4	4	no	—
154	C₂³×C₁₄₉	—	4	4	no	—
155	C₂³×C₁₄₉	—	4	2	no	—
156	C₂³×C₁₄₉	—	4	2	no	—
157	C₂³×C₁₄₉	—	4	2	no	—
158	C₂³×C₁₄₉	—	4	2	no	—
159	C₂³×C₁₄₉	—	4	2	no	—
160	C₂³×C₁₄₉	—	4	2	no	—
161	C₂³×C₁₄₉	—	4	4	no	—
162	C₂³×C₁₄₉	—	4	2	no	—
163	C₂³×C₁₄₉	—	4	2	no	—
164	C₂³×C₁₄₉	—	4	4	no	—
165	C₂³×C₁₄₉	—	8	2	no	—
166	C₂³×C₁₄₉	—	8	2	no	—
167	C₂³×C₁₄₉	—	8	2	no	—
168	C₂³×C₁₄₉	—	8	2	no	—
169	C₂³×C₁₄₉	—	8	2	no	—
170	C₂³×C₁₄₉	—	8	2	no	—
171	C₂³×C₁₄₉	—	8	2	no	—
172	C₂³×C₁₄₉	—	8	2	no	—
173	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×C₁₄₉	#121	1	1	yes	characteristic
175	C₂³×C₁₄₉	#121	1	2	yes	—
176	C₂³×C₁₄₉	#121	1	2	yes	—
177	C₂³×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂³×C₁₄₉	C₂×D₈	1	1	yes	characteristic
179	C₂³×C₁₄₉	C₂×SD₁₆	1	1	yes	characteristic
180	C₂³×C₁₄₉	#135	1	2	yes	—
181	C₂³×C₁₄₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂³×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
183	C₂³×C₁₄₉	#137	1	1	yes	characteristic
184	D₄×C₁₄₉	—	2	8	no	—
185	D₄×C₁₄₉	—	4	4	no	—
186	D₄×C₁₄₉	—	4	2	no	—
187	D₄×C₁₄₉	—	4	2	no	—
188	D₄×C₁₄₉	—	4	2	no	—
189	D₄×C₁₄₉	—	4	2	no	—
190	C₂×C₄×C₁₄₉	—	2	2	no	—
191	C₂×C₄×C₁₄₉	—	2	2	no	—
192	C₂×C₄×C₁₄₉	—	2	4	no	—
193	C₂×C₄×C₁₄₉	—	2	4	no	—
194	C₂×C₄×C₁₄₉	—	2	2	no	—
195	C₂×C₄×C₁₄₉	—	2	2	no	—
196	C₂×C₄×C₁₄₉	—	2	2	no	—
197	C₂×C₄×C₁₄₉	—	4	2	no	—
198	C₂×C₄×C₁₄₉	—	4	2	no	—
199	C₂×C₄×C₁₄₉	—	4	2	no	—
200	C₂×C₄×C₁₄₉	—	4	4	no	—
201	C₂×C₄×C₁₄₉	—	4	2	no	—
202	C₂×C₄×C₁₄₉	—	4	2	no	—
203	C₂×C₄×C₁₄₉	—	4	4	no	—
204	C₂×C₄×C₁₄₉	—	4	4	no	—
205	C₂×C₄×C₁₄₉	—	8	2	no	—
206	C₂×C₄×C₁₄₉	—	8	2	no	—
207	C₂×C₄×C₁₄₉	—	8	2	no	—
208	C₂×C₄×C₁₄₉	—	8	2	no	—
209	C₂×C₄×C₁₄₉	—	8	2	no	—
210	C₂×C₄×C₁₄₉	—	8	2	no	—
211	C₂×C₄×C₁₄₉	#102	1	4	yes	complemented
212	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
214	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₁₄₉	#120	1	2	yes	—
217	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₄₉	#121	1	2	yes	—
219	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
221	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
222	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₄₉	#123	1	2	yes	—
224	C₂×C₄×C₁₄₉	#123	1	2	yes	—
225	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₄₉	#124	1	2	yes	—
227	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
228	C₂×C₄×C₁₄₉	#126	1	2	yes	—
229	C₂×C₄×C₁₄₉	#127	1	1	yes	characteristic
230	C₈×C₁₄₉	—	4	4	no	—
231	C₂²×C₁₄₉	—	4	4	no	—
232	C₂²×C₁₄₉	—	4	4	no	—
233	C₂²×C₁₄₉	—	4	4	no	—
234	C₂²×C₁₄₉	—	8	4	no	—
235	C₂²×C₁₄₉	—	8	4	no	—
236	C₂²×C₁₄₉	—	8	4	no	—
237	C₂²×C₁₄₉	—	8	4	no	—
238	C₂²×C₁₄₉	—	8	2	no	—
239	C₂²×C₁₄₉	—	8	2	no	—
240	C₂²×C₁₄₉	—	8	2	no	—
241	C₂²×C₁₄₉	—	8	2	no	—
242	C₂²×C₁₄₉	#380	1	1	yes	characteristic
243	C₂²×C₁₄₉	#386	1	1	yes	characteristic
244	C₂²×C₁₄₉	#390	1	1	yes	characteristic
245	C₂²×C₁₄₉	#394	1	2	yes	—
246	C₂²×C₁₄₉	#396	1	2	yes	—
247	C₂²×C₁₄₉	C₂×#102	1	1	yes	characteristic
248	C₂²×C₁₄₉	#416	1	1	yes	characteristic
249	C₂²×C₁₄₉	#417	1	1	yes	characteristic
250	C₂²×C₁₄₉	#418	1	1	yes	characteristic
251	C₂²×C₁₄₉	#459	1	1	yes	characteristic
252	C₂²×C₁₄₉	#459	1	2	yes	—
253	C₂²×C₁₄₉	#460	1	2	yes	—
254	C₂²×C₁₄₉	#461	1	1	yes	characteristic
255	C₂²×C₁₄₉	#463	1	2	yes	—
256	C₂²×C₁₄₉	#463	1	2	yes	—
257	C₂²×C₁₄₉	#464	1	2	yes	—
258	C₂²×C₁₄₉	#465	1	2	yes	—
259	C₂²×C₁₄₉	#466	1	2	yes	—
260	C₂²×C₁₄₉	#468	1	2	yes	—
261	C₂²×C₁₄₉	#469	1	2	yes	—
262	C₂²×C₁₄₉	#474	1	1	yes	characteristic
263	C₂²×C₁₄₉	#476	1	1	yes	characteristic
264	C₂²×C₁₄₉	#478	1	2	yes	—
265	C₄×C₁₄₉	—	2	4	no	—
266	C₄×C₁₄₉	—	4	2	no	—
267	C₄×C₁₄₉	—	8	4	no	—
268	C₄×C₁₄₉	—	8	2	no	—
269	C₄×C₁₄₉	#385	1	2	yes	—
270	C₄×C₁₄₉	#388	1	2	yes	—
271	C₄×C₁₄₉	#392	1	1	yes	characteristic
272	C₄×C₁₄₉	#393	1	1	yes	characteristic
273	C₄×C₁₄₉	#397	1	1	yes	characteristic
274	C₄×C₁₄₉	#399	1	1	yes	characteristic
275	C₂×C₁₄₉	—	8	4	no	—
276	C₂×C₁₄₉	#1439	1	1	yes	characteristic
277	C₂×C₁₄₉	#1802	1	1	yes	characteristic
278	C₂×C₁₄₉	#1804	1	1	yes	characteristic
279	C₂×C₁₄₉	#1893	1	1	yes	characteristic
280	C₂×C₁₄₉	#1895	1	1	yes	characteristic
281	C₂×C₁₄₉	#1982	1	1	yes	characteristic
282	C₂×C₁₄₉	#1983	1	1	yes	characteristic
283	C₂×C₁₄₉	#2054	1	2	yes	—
284	C₂×C₁₄₉	#2055	1	2	yes	—
285	C₂×C₁₄₉	#2065	1	2	yes	—
286	C₂×C₁₄₉	#2067	1	2	yes	—
287	#11076	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₁₄₉	#11076	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×C₄⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic, complemented
290	C₂²×#102	C₂×C₁₄₉	1	2	yes	—
291	C₂×#390	C₂×C₁₄₉	1	1	yes	characteristic
292	C₂×#340	C₂×C₁₄₉	1	2	yes	complemented
293	C₄⋊#95	C₂×C₁₄₉	1	1	yes	characteristic, complemented
294	C₂³×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
295	C₂³×C₈	C₂²×C₁₄₉	1	2	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
298	C₂²×C₂²⋊C₄	—	2	1	no	—
299	C₂²×C₂²⋊C₄	—	2	1	no	—
300	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
301	C₂×C₄⋊C₈	—	2	4	no	—
302	C₂×C₄⋊C₈	—	2	2	no	—
303	C₂×#102	—	2	4	no	—
304	C₂×#102	—	2	4	no	—
305	C₂×#102	—	2	4	no	—
306	#390	—	2	2	no	—
307	#390	C₄×C₁₄₉	1	4	yes	complemented
308	C₂×#95	—	2	1	no	—
309	C₂×#95	—	2	1	no	—
310	#340	—	2	4	no	—
311	C₂⁵	—	2	1	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
320	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
321	C₂²×D₄	Q₈×C₁₄₉	1	2	yes	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
325	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	D₄×C₁₄₉	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
343	C₂×C₄⋊C₄	D₄×C₁₄₉	1	4	yes	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	—	4	4	no	—
347	C₂×C₂²⋊C₄	—	4	2	no	—
348	C₂×C₂²⋊C₄	—	4	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
352	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
353	C₄⋊C₈	—	2	8	no	—
354	#102	—	2	16	no	—
355	#95	—	4	2	no	—
356	#95	—	4	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	1	no	—
363	C₂⁴	—	4	1	no	—
364	C₂⁴	—	4	2	no	—
365	C₂⁴	—	4	2	no	—
366	C₂⁴	—	4	1	no	—
367	C₂⁴	—	4	1	no	—
368	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
406	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
407	C₂²×C₄	D₈×C₁₄₉	1	2	yes	—
408	C₂²×C₄	SD₁₆×C₁₄₉	1	2	yes	—
409	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
415	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
417	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
418	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	—	4	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₂²⋊C₄	—	4	8	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	—	8	2	no	—
460	C₂³	—	8	2	no	—
461	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
462	C₂³	#121×C₁₄₉	1	1	yes	characteristic
463	C₂³	#121×C₁₄₉	1	2	yes	—
464	C₂³	#121×C₁₄₉	1	2	yes	—
465	C₂³	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
466	C₂³	C₂×D₈×C₁₄₉	1	1	yes	characteristic
467	C₂³	C₂×SD₁₆×C₁₄₉	1	1	yes	characteristic
468	C₂³	#135×C₁₄₉	1	2	yes	—
469	C₂³	AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
470	C₂³	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
471	C₂³	#137×C₁₄₉	1	1	yes	characteristic
472	D₄	—	2	8	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	#102×C₁₄₉	1	4	yes	complemented
500	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
501	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
502	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
503	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
504	C₂×C₄	#120×C₁₄₉	1	2	yes	—
505	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
506	C₂×C₄	#121×C₁₄₉	1	2	yes	—
507	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
508	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
509	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
510	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
511	C₂×C₄	#123×C₁₄₉	1	2	yes	—
512	C₂×C₄	#123×C₁₄₉	1	2	yes	—
513	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
514	C₂×C₄	#124×C₁₄₉	1	2	yes	—
515	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
516	C₂×C₄	#126×C₁₄₉	1	2	yes	—
517	C₂×C₄	#127×C₁₄₉	1	1	yes	characteristic
518	C₈	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	4	no	—
525	C₂²	—	8	4	no	—
526	C₂²	—	8	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	#380×C₁₄₉	1	1	yes	characteristic
531	C₂²	#386×C₁₄₉	1	1	yes	characteristic
532	C₂²	#390×C₁₄₉	1	1	yes	characteristic
533	C₂²	#394×C₁₄₉	1	2	yes	—
534	C₂²	#396×C₁₄₉	1	2	yes	—
535	C₂²	C₂×#102×C₁₄₉	1	1	yes	characteristic
536	C₂²	#416×C₁₄₉	1	1	yes	characteristic
537	C₂²	#417×C₁₄₉	1	1	yes	characteristic
538	C₂²	#418×C₁₄₉	1	1	yes	characteristic
539	C₂²	#459×C₁₄₉	1	2	yes	—
540	C₂²	#459×C₁₄₉	1	1	yes	characteristic
541	C₂²	#460×C₁₄₉	1	2	yes	—
542	C₂²	#461×C₁₄₉	1	1	yes	characteristic
543	C₂²	#463×C₁₄₉	1	2	yes	—
544	C₂²	#463×C₁₄₉	1	2	yes	—
545	C₂²	#464×C₁₄₉	1	2	yes	—
546	C₂²	#465×C₁₄₉	1	2	yes	—
547	C₂²	#466×C₁₄₉	1	2	yes	—
548	C₂²	#468×C₁₄₉	1	2	yes	—
549	C₂²	#469×C₁₄₉	1	2	yes	—
550	C₂²	#474×C₁₄₉	1	1	yes	characteristic
551	C₂²	#476×C₁₄₉	1	1	yes	characteristic
552	C₂²	#478×C₁₄₉	1	2	yes	—
553	C₄	—	2	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	8	2	no	—
556	C₄	—	8	4	no	—
557	C₄	#385×C₁₄₉	1	2	yes	—
558	C₄	#388×C₁₄₉	1	2	yes	—
559	C₄	#392×C₁₄₉	1	1	yes	characteristic
560	C₄	#393×C₁₄₉	1	1	yes	characteristic
561	C₄	#397×C₁₄₉	1	1	yes	characteristic
562	C₄	#399×C₁₄₉	1	1	yes	characteristic
563	C₂	—	8	4	no	—
564	C₂	#1439×C₁₄₉	1	1	yes	characteristic
565	C₂	#1802×C₁₄₉	1	1	yes	characteristic
566	C₂	#1804×C₁₄₉	1	1	yes	characteristic
567	C₂	#1893×C₁₄₉	1	1	yes	characteristic
568	C₂	#1895×C₁₄₉	1	1	yes	characteristic
569	C₂	#1982×C₁₄₉	1	1	yes	characteristic
570	C₂	#1983×C₁₄₉	1	1	yes	characteristic
571	C₂	#2054×C₁₄₉	1	2	yes	—
572	C₂	#2055×C₁₄₉	1	2	yes	—
573	C₂	#2065×C₁₄₉	1	2	yes	—
574	C₂	#2067×C₁₄₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊C₈×C₁₄₉	C₂	semidirect
4. C₂×#340×C₁₄₉	C₂	semidirect
5. C₄⋊#95×C₁₄₉	C₂	semidirect
19. #390×C₁₄₉	C₄	semidirect
211. C₂×C₄×C₁₄₉	#102	semidirect
287. #11076	C₁₄₉	direct (N × H)
288. C₁₄₉	#11076	direct (N × H)
289. C₂²×C₄⋊C₈	C₂×C₁₄₉	semidirect
292. C₂×#340	C₂×C₁₄₉	semidirect
293. C₄⋊#95	C₂×C₁₄₉	semidirect
307. #390	C₄×C₁₄₉	semidirect
499. C₂×C₄	#102×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₁₄₉	2
C₂²×#102×C₁₄₉	2
C₂×#390×C₁₄₉	2
C₂×#340×C₁₄₉	2
C₄⋊#95×C₁₄₉	2
#11076	149

Subgroups — C149×#11076 #49190025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11076 #49190025