Subgroups — C₂×#1504×C₁₄₉ #49196487

Order 38144.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1504×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#328×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂×#327×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₄₉	C₄	1	1	yes	characteristic, complemented
8	C₂⁴×C₄×C₁₄₉	—	2	1	no	—
9	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
11	#525×C₁₄₉	—	2	2	no	—
12	#525×C₁₄₉	—	2	2	no	—
13	#525×C₁₄₉	C₄	1	4	yes	complemented
14	#525×C₁₄₉	C₂²	1	4	yes	—
15	C₂×#123×C₁₄₉	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
17	C₂×C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
18	C₂×#121×C₁₄₉	C₄	1	1	yes	characteristic, complemented
19	C₂×#121×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#120×C₁₄₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
23	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic, complemented
24	#407×C₁₄₉	—	2	2	no	—
25	#407×C₁₄₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
27	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
28	C₂×#95×C₁₄₉	—	2	2	no	—
29	C₂×#95×C₁₄₉	—	2	1	no	—
30	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
31	C₂×#95×C₁₄₉	C₂²	1	4	yes	complemented
32	#328×C₁₄₉	C₂²	1	8	yes	complemented
33	#327×C₁₄₉	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₄₉	D₄	1	1	yes	characteristic
35	C₂×#41×C₁₄₉	—	2	2	no	—
36	C₂×#41×C₁₄₉	—	4	4	no	—
37	C₂×#41×C₁₄₉	C₂×C₄	1	4	yes	complemented
38	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂²×D₄×C₁₄₉	—	2	1	no	—
40	C₂²×D₄×C₁₄₉	—	2	1	no	—
41	C₂²×D₄×C₁₄₉	—	2	1	no	—
42	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂³×C₄×C₁₄₉	—	2	8	no	—
44	C₂³×C₄×C₁₄₉	—	2	2	no	—
45	C₂³×C₄×C₁₄₉	—	2	4	no	—
46	C₂³×C₄×C₁₄₉	—	2	1	no	—
47	C₂³×C₄×C₁₄₉	—	4	4	no	—
48	C₂³×C₄×C₁₄₉	—	4	4	no	—
49	C₂³×C₄×C₁₄₉	—	4	4	no	—
50	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
56	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
58	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₄₉	—	2	4	no	—
61	C₂×M₁₆×C₁₄₉	—	4	4	no	—
62	C₂²×C₈×C₁₄₉	—	2	2	no	—
63	#123×C₁₄₉	—	2	4	no	—
64	#123×C₁₄₉	—	2	4	no	—
65	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
66	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
67	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
68	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	4	yes	complemented
69	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	2	yes	complemented
70	C₂²⋊Q₈×C₁₄₉	C₂³	1	2	yes	—
71	#121×C₁₄₉	—	2	2	no	—
72	#121×C₁₄₉	—	2	1	no	—
73	#121×C₁₄₉	—	2	1	no	—
74	#121×C₁₄₉	C₂×C₄	1	4	yes	complemented
75	#121×C₁₄₉	C₂×C₄	1	2	yes	complemented
76	#121×C₁₄₉	C₂³	1	2	yes	—
77	#120×C₁₄₉	—	2	4	no	—
78	#120×C₁₄₉	—	2	4	no	—
79	C₄×D₄×C₁₄₉	—	2	4	no	—
80	C₄×D₄×C₁₄₉	—	2	4	no	—
81	C₄×D₄×C₁₄₉	—	2	4	no	—
82	C₄×D₄×C₁₄₉	—	2	4	no	—
83	#117×C₁₄₉	—	2	2	no	—
84	#117×C₁₄₉	C₂×C₄	1	4	yes	complemented
85	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
88	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
94	C₂×C₄²×C₁₄₉	—	2	1	no	—
95	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
96	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
97	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
98	#95×C₁₄₉	—	2	2	no	—
99	#95×C₁₄₉	—	2	4	no	—
100	#95×C₁₄₉	C₂³	1	4	yes	—
101	C₂⁴×C₁₄₉	—	2	4	no	—
102	C₂⁴×C₁₄₉	—	2	4	no	—
103	C₂⁴×C₁₄₉	—	2	2	no	—
104	C₂⁴×C₁₄₉	—	2	2	no	—
105	C₂⁴×C₁₄₉	—	2	1	no	—
106	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
107	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×C₁₄₉	C₂×D₄	1	2	yes	—
110	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
111	#41×C₁₄₉	—	4	8	no	—
112	#41×C₁₄₉	—	4	8	no	—
113	C₂×Q₈×C₁₄₉	—	2	1	no	—
114	C₂×Q₈×C₁₄₉	—	4	2	no	—
115	C₂×Q₈×C₁₄₉	C₂²×C₄	1	2	yes	complemented
116	C₂×D₄×C₁₄₉	—	2	2	no	—
117	C₂×D₄×C₁₄₉	—	2	4	no	—
118	C₂×D₄×C₁₄₉	—	2	4	no	—
119	C₂×D₄×C₁₄₉	—	2	2	no	—
120	C₂×D₄×C₁₄₉	—	2	1	no	—
121	C₂×D₄×C₁₄₉	—	4	2	no	—
122	C₂×D₄×C₁₄₉	—	4	4	no	—
123	C₂×D₄×C₁₄₉	—	4	4	no	—
124	C₂×D₄×C₁₄₉	—	4	2	no	—
125	C₂×D₄×C₁₄₉	—	4	2	no	—
126	C₂×D₄×C₁₄₉	C₂²×C₄	1	2	yes	complemented
127	C₂²×C₄×C₁₄₉	—	2	4	no	—
128	C₂²×C₄×C₁₄₉	—	2	4	no	—
129	C₂²×C₄×C₁₄₉	—	2	8	no	—
130	C₂²×C₄×C₁₄₉	—	2	16	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	—	2	4	no	—
135	C₂²×C₄×C₁₄₉	—	2	4	no	—
136	C₂²×C₄×C₁₄₉	—	4	2	no	—
137	C₂²×C₄×C₁₄₉	—	4	4	no	—
138	C₂²×C₄×C₁₄₉	—	4	2	no	—
139	C₂²×C₄×C₁₄₉	—	4	4	no	—
140	C₂²×C₄×C₁₄₉	—	4	2	no	—
141	C₂²×C₄×C₁₄₉	—	4	4	no	—
142	C₂²×C₄×C₁₄₉	—	4	2	no	—
143	C₂²×C₄×C₁₄₉	—	4	4	no	—
144	C₂²×C₄×C₁₄₉	—	4	4	no	—
145	C₂²×C₄×C₁₄₉	—	4	32	no	—
146	C₂²×C₄×C₁₄₉	—	4	4	no	—
147	C₂²×C₄×C₁₄₉	—	4	8	no	—
148	C₂²×C₄×C₁₄₉	—	4	8	no	—
149	C₂²×C₄×C₁₄₉	—	4	4	no	—
150	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
151	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
152	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
155	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
156	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
157	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
168	M₁₆×C₁₄₉	—	4	8	no	—
169	C₂×C₈×C₁₄₉	—	2	4	no	—
170	C₂×C₈×C₁₄₉	—	4	4	no	—
171	C₄⋊C₄×C₁₄₉	—	2	4	no	—
172	C₄⋊C₄×C₁₄₉	—	2	2	no	—
173	C₄⋊C₄×C₁₄₉	—	2	1	no	—
174	C₄⋊C₄×C₁₄₉	—	2	1	no	—
175	C₄⋊C₄×C₁₄₉	—	2	2	no	—
176	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	complemented
177	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	complemented
178	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
179	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
185	C₄²×C₁₄₉	—	2	4	no	—
186	C₂³×C₁₄₉	—	2	16	no	—
187	C₂³×C₁₄₉	—	2	16	no	—
188	C₂³×C₁₄₉	—	2	2	no	—
189	C₂³×C₁₄₉	—	2	2	no	—
190	C₂³×C₁₄₉	—	2	4	no	—
191	C₂³×C₁₄₉	—	2	2	no	—
192	C₂³×C₁₄₉	—	2	4	no	—
193	C₂³×C₁₄₉	—	2	2	no	—
194	C₂³×C₁₄₉	—	2	4	no	—
195	C₂³×C₁₄₉	—	2	2	no	—
196	C₂³×C₁₄₉	—	2	2	no	—
197	C₂³×C₁₄₉	—	2	4	no	—
198	C₂³×C₁₄₉	—	2	2	no	—
199	C₂³×C₁₄₉	—	2	4	no	—
200	C₂³×C₁₄₉	—	2	2	no	—
201	C₂³×C₁₄₉	—	2	2	no	—
202	C₂³×C₁₄₉	—	4	2	no	—
203	C₂³×C₁₄₉	—	4	2	no	—
204	C₂³×C₁₄₉	—	4	2	no	—
205	C₂³×C₁₄₉	#99	1	4	yes	—
206	C₂³×C₁₄₉	#104	1	4	yes	—
207	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
212	C₂³×C₁₄₉	#137	1	2	yes	—
213	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₁₄₉	—	4	2	no	—
215	Q₈×C₁₄₉	—	4	2	no	—
216	D₄×C₁₄₉	—	4	2	no	—
217	D₄×C₁₄₉	—	4	2	no	—
218	D₄×C₁₄₉	—	4	2	no	—
219	D₄×C₁₄₉	—	4	2	no	—
220	D₄×C₁₄₉	—	4	8	no	—
221	D₄×C₁₄₉	—	4	4	no	—
222	D₄×C₁₄₉	—	4	8	no	—
223	C₂×C₄×C₁₄₉	—	2	2	no	—
224	C₂×C₄×C₁₄₉	—	2	4	no	—
225	C₂×C₄×C₁₄₉	—	2	2	no	—
226	C₂×C₄×C₁₄₉	—	2	4	no	—
227	C₂×C₄×C₁₄₉	—	2	2	no	—
228	C₂×C₄×C₁₄₉	—	2	4	no	—
229	C₂×C₄×C₁₄₉	—	2	2	no	—
230	C₂×C₄×C₁₄₉	—	2	4	no	—
231	C₂×C₄×C₁₄₉	—	2	8	no	—
232	C₂×C₄×C₁₄₉	—	2	2	no	—
233	C₂×C₄×C₁₄₉	—	2	2	no	—
234	C₂×C₄×C₁₄₉	—	2	2	no	—
235	C₂×C₄×C₁₄₉	—	4	2	no	—
236	C₂×C₄×C₁₄₉	—	4	2	no	—
237	C₂×C₄×C₁₄₉	—	4	2	no	—
238	C₂×C₄×C₁₄₉	—	4	1	no	—
239	C₂×C₄×C₁₄₉	—	4	2	no	—
240	C₂×C₄×C₁₄₉	—	4	2	no	—
241	C₂×C₄×C₁₄₉	—	4	1	no	—
242	C₂×C₄×C₁₄₉	—	4	2	no	—
243	C₂×C₄×C₁₄₉	—	4	1	no	—
244	C₂×C₄×C₁₄₉	—	4	1	no	—
245	C₂×C₄×C₁₄₉	—	4	8	no	—
246	C₂×C₄×C₁₄₉	—	4	32	no	—
247	C₂×C₄×C₁₄₉	—	4	4	no	—
248	C₂×C₄×C₁₄₉	—	4	16	no	—
249	C₂×C₄×C₁₄₉	—	4	4	no	—
250	C₂×C₄×C₁₄₉	—	4	2	no	—
251	C₂×C₄×C₁₄₉	—	4	2	no	—
252	C₂×C₄×C₁₄₉	—	4	2	no	—
253	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₄₉	—	4	4	no	—
260	C₂²×C₁₄₉	—	2	8	no	—
261	C₂²×C₁₄₉	—	2	8	no	—
262	C₂²×C₁₄₉	—	2	16	no	—
263	C₂²×C₁₄₉	—	2	1	no	—
264	C₂²×C₁₄₉	—	2	1	no	—
265	C₂²×C₁₄₉	—	2	2	no	—
266	C₂²×C₁₄₉	—	2	2	no	—
267	C₂²×C₁₄₉	—	2	2	no	—
268	C₂²×C₁₄₉	—	2	1	no	—
269	C₂²×C₁₄₉	—	2	2	no	—
270	C₂²×C₁₄₉	—	2	1	no	—
271	C₂²×C₁₄₉	—	2	4	no	—
272	C₂²×C₁₄₉	—	2	8	no	—
273	C₂²×C₁₄₉	—	2	8	no	—
274	C₂²×C₁₄₉	—	2	4	no	—
275	C₂²×C₁₄₉	—	4	2	no	—
276	C₂²×C₁₄₉	—	4	2	no	—
277	C₂²×C₁₄₉	—	4	2	no	—
278	C₂²×C₁₄₉	—	8	4	no	—
279	C₂²×C₁₄₉	C₂×#99	1	4	yes	—
280	C₂²×C₁₄₉	C₂×#99	1	2	yes	—
281	C₂²×C₁₄₉	#417	1	2	yes	—
282	C₂²×C₁₄₉	#417	1	2	yes	—
283	C₂²×C₁₄₉	C₂×#104	1	4	yes	—
284	C₂²×C₁₄₉	C₂×#104	1	2	yes	—
285	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₂²×C₁₄₉	C₂×#137	1	1	yes	characteristic
288	C₄×C₁₄₉	—	2	1	no	—
289	C₄×C₁₄₉	—	2	2	no	—
290	C₄×C₁₄₉	—	2	1	no	—
291	C₄×C₁₄₉	—	2	2	no	—
292	C₄×C₁₄₉	—	2	1	no	—
293	C₄×C₁₄₉	—	2	1	no	—
294	C₄×C₁₄₉	—	4	8	no	—
295	C₄×C₁₄₉	—	4	2	no	—
296	C₄×C₁₄₉	—	4	2	no	—
297	C₄×C₁₄₉	—	4	2	no	—
298	C₂×C₁₄₉	—	2	1	no	—
299	C₂×C₁₄₉	—	2	1	no	—
300	C₂×C₁₄₉	—	2	4	no	—
301	C₂×C₁₄₉	—	2	2	no	—
302	C₂×C₁₄₉	—	2	4	no	—
303	C₂×C₁₄₉	—	8	2	no	—
304	C₂×C₁₄₉	#1504	1	4	yes	direct product factor
305	C₂×C₁₄₉	C₂²×#99	1	1	yes	characteristic
306	C₂×C₁₄₉	C₂×#417	1	1	yes	characteristic
307	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
308	C₂×#1504	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₁₄₉	C₂×#1504	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×#525	C₂×C₁₄₉	1	1	yes	characteristic
311	C₂×#407	C₂×C₁₄₉	1	1	yes	characteristic, complemented
312	C₂²×#95	C₂×C₁₄₉	1	1	yes	characteristic, complemented
313	#1504	C₂×C₁₄₉	1	8	yes	direct product factor
314	C₂×#328	C₂×C₁₄₉	1	2	yes	complemented
315	C₂×#327	C₂×C₁₄₉	1	2	yes	complemented
316	C₂²×#41	C₄×C₁₄₉	1	1	yes	characteristic, complemented
317	C₂⁴×C₄	—	2	1	no	—
318	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
319	C₂²×M₁₆	—	2	1	no	—
320	#525	—	2	2	no	—
321	#525	—	2	2	no	—
322	#525	C₄×C₁₄₉	1	4	yes	complemented
323	#525	C₂²×C₁₄₉	1	4	yes	—
324	C₂×#123	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic, complemented
326	C₂×C₂²⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
327	C₂×#121	C₄×C₁₄₉	1	1	yes	characteristic, complemented
328	C₂×#121	C₂²×C₁₄₉	1	1	yes	characteristic
329	C₂×#120	—	2	1	no	—
330	C₂×C₄×D₄	—	2	1	no	—
331	C₂×C₄×D₄	—	2	1	no	—
332	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic, complemented
333	#407	—	2	2	no	—
334	#407	C₂²×C₁₄₉	1	4	yes	complemented
335	C₂×C₂²⋊C₈	—	2	1	no	—
336	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
337	C₂×#95	—	2	2	no	—
338	C₂×#95	—	2	1	no	—
339	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
340	C₂×#95	C₂²×C₁₄₉	1	4	yes	complemented
341	#328	C₂²×C₁₄₉	1	8	yes	complemented
342	#327	C₂²×C₁₄₉	1	8	yes	complemented
343	C₂⁵	D₄×C₁₄₉	1	1	yes	characteristic
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	4	4	no	—
346	C₂×#41	C₂×C₄×C₁₄₉	1	4	yes	complemented
347	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic, complemented
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic, complemented
352	C₂³×C₄	—	2	8	no	—
353	C₂³×C₄	—	2	2	no	—
354	C₂³×C₄	—	2	4	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	4	4	no	—
357	C₂³×C₄	—	4	4	no	—
358	C₂³×C₄	—	4	4	no	—
359	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
360	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
361	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
362	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
363	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
364	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
365	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
366	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
369	C₂×M₁₆	—	2	4	no	—
370	C₂×M₁₆	—	4	4	no	—
371	C₂²×C₈	—	2	2	no	—
372	#123	—	2	4	no	—
373	#123	—	2	4	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	4	yes	complemented
378	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	2	yes	complemented
379	C₂²⋊Q₈	C₂³×C₁₄₉	1	2	yes	—
380	#121	—	2	2	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	C₂×C₄×C₁₄₉	1	4	yes	complemented
384	#121	C₂×C₄×C₁₄₉	1	2	yes	complemented
385	#121	C₂³×C₁₄₉	1	2	yes	—
386	#120	—	2	4	no	—
387	#120	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	#117	—	2	2	no	—
393	#117	C₂×C₄×C₁₄₉	1	4	yes	complemented
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic, complemented
397	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic, complemented
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂²⋊C₈	—	2	4	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
407	#95	—	2	2	no	—
408	#95	—	2	4	no	—
409	#95	C₂³×C₁₄₉	1	4	yes	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
416	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
417	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
418	C₂⁴	C₂×D₄×C₁₄₉	1	2	yes	—
419	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
420	#41	—	4	8	no	—
421	#41	—	4	8	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	C₂²×C₄×C₁₄₉	1	2	yes	complemented
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	C₂²×C₄×C₁₄₉	1	2	yes	complemented
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	16	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	32	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	8	no	—
457	C₂²×C₄	—	4	8	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
460	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
461	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
462	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
463	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
464	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
465	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
466	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
468	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
477	M₁₆	—	4	8	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	4	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	complemented
486	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	complemented
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₄²	—	2	4	no	—
495	C₂³	—	2	16	no	—
496	C₂³	—	2	16	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	#99×C₁₄₉	1	4	yes	—
515	C₂³	#104×C₁₄₉	1	4	yes	—
516	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
517	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
518	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
519	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
520	C₂³	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
521	C₂³	#137×C₁₄₉	1	2	yes	—
522	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	32	no	—
556	C₂×C₄	—	4	16	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
563	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
566	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
568	C₈	—	4	4	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	16	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	4	no	—
588	C₂²	C₂×#99×C₁₄₉	1	4	yes	—
589	C₂²	C₂×#99×C₁₄₉	1	2	yes	—
590	C₂²	#417×C₁₄₉	1	2	yes	—
591	C₂²	#417×C₁₄₉	1	2	yes	—
592	C₂²	C₂×#104×C₁₄₉	1	4	yes	—
593	C₂²	C₂×#104×C₁₄₉	1	2	yes	—
594	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
595	C₂²	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
596	C₂²	C₂×#137×C₁₄₉	1	1	yes	characteristic
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	4	8	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	4	no	—
609	C₂	—	2	2	no	—
610	C₂	—	2	4	no	—
611	C₂	—	2	1	no	—
612	C₂	—	8	2	no	—
613	C₂	#1504×C₁₄₉	1	4	yes	direct product factor
614	C₂	C₂²×#99×C₁₄₉	1	1	yes	characteristic
615	C₂	C₂×#417×C₁₄₉	1	1	yes	characteristic
616	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂×#525×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₄₉	C₂	semidirect
3. C₂²×#95×C₁₄₉	C₂	semidirect
4. #1504×C₁₄₉	C₂	direct (N × H)
5. C₂×#328×C₁₄₉	C₂	semidirect
6. C₂×#327×C₁₄₉	C₂	semidirect
7. C₂²×#41×C₁₄₉	C₄	semidirect
13. #525×C₁₄₉	C₄	semidirect
16. C₂×C₂²⋊Q₈×C₁₄₉	C₄	semidirect
18. C₂×#121×C₁₄₉	C₄	semidirect
23. C₂×#117×C₁₄₉	C₄	semidirect
25. #407×C₁₄₉	C₂²	semidirect
31. C₂×#95×C₁₄₉	C₂²	semidirect
32. #328×C₁₄₉	C₂²	semidirect
33. #327×C₁₄₉	C₂²	semidirect
37. C₂×#41×C₁₄₉	C₂×C₄	semidirect
38. C₂²×Q₈×C₁₄₉	C₂×C₄	semidirect
42. C₂²×D₄×C₁₄₉	C₂×C₄	semidirect
68. C₂²⋊Q₈×C₁₄₉	C₂×C₄	semidirect
69. C₂²⋊Q₈×C₁₄₉	C₂×C₄	semidirect
74. #121×C₁₄₉	C₂×C₄	semidirect
75. #121×C₁₄₉	C₂×C₄	semidirect
84. #117×C₁₄₉	C₂×C₄	semidirect
87. C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
88. C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
115. C₂×Q₈×C₁₄₉	C₂²×C₄	semidirect
126. C₂×D₄×C₁₄₉	C₂²×C₄	semidirect
176. C₄⋊C₄×C₁₄₉	C₂²×C₄	semidirect
177. C₄⋊C₄×C₁₄₉	C₂²×C₄	semidirect
304. C₂×C₁₄₉	#1504	direct (N × H)
308. C₂×#1504	C₁₄₉	direct (N × H)
309. C₁₄₉	C₂×#1504	direct (N × H)
311. C₂×#407	C₂×C₁₄₉	semidirect
312. C₂²×#95	C₂×C₁₄₉	semidirect
313. #1504	C₂×C₁₄₉	direct (N × H)
314. C₂×#328	C₂×C₁₄₉	semidirect
315. C₂×#327	C₂×C₁₄₉	semidirect
316. C₂²×#41	C₄×C₁₄₉	semidirect
322. #525	C₄×C₁₄₉	semidirect
325. C₂×C₂²⋊Q₈	C₄×C₁₄₉	semidirect
327. C₂×#121	C₄×C₁₄₉	semidirect
332. C₂×#117	C₄×C₁₄₉	semidirect
334. #407	C₂²×C₁₄₉	semidirect
340. C₂×#95	C₂²×C₁₄₉	semidirect
341. #328	C₂²×C₁₄₉	semidirect
342. #327	C₂²×C₁₄₉	semidirect
346. C₂×#41	C₂×C₄×C₁₄₉	semidirect
347. C₂²×Q₈	C₂×C₄×C₁₄₉	semidirect
351. C₂²×D₄	C₂×C₄×C₁₄₉	semidirect
377. C₂²⋊Q₈	C₂×C₄×C₁₄₉	semidirect
378. C₂²⋊Q₈	C₂×C₄×C₁₄₉	semidirect
383. #121	C₂×C₄×C₁₄₉	semidirect
384. #121	C₂×C₄×C₁₄₉	semidirect
393. #117	C₂×C₄×C₁₄₉	semidirect
396. C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	semidirect
397. C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	semidirect
424. C₂×Q₈	C₂²×C₄×C₁₄₉	semidirect
435. C₂×D₄	C₂²×C₄×C₁₄₉	semidirect
485. C₄⋊C₄	C₂²×C₄×C₁₄₉	semidirect
486. C₄⋊C₄	C₂²×C₄×C₁₄₉	semidirect
613. C₂	#1504×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₄₉	2
C₂×#407×C₁₄₉	2
C₂²×#95×C₁₄₉	2
#1504×C₁₄₉	2
C₂×#328×C₁₄₉	2
C₂×#327×C₁₄₉	2
C₂×#1504	149

Subgroups — C2×#1504×C149 #49196487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1504×C₁₄₉ #49196487