Subgroups — C₂×#1467×C₁₄₉ #49196309

Order 38144.

1218 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₄₉	C₂	1	2	yes	maximal
3	#1467×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
4	C₂×#324×C₁₄₉	C₂	1	4	yes	maximal
5	C₂³×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₄₉	—	2	2	no	—
7	C₂×C₄×Q₈×C₁₄₉	—	2	2	no	—
8	C₂×C₄×Q₈×C₁₄₉	—	2	4	no	—
9	C₂×C₄×Q₈×C₁₄₉	C₄	1	4	yes	—
10	C₂×C₄×Q₈×C₁₄₉	C₂²	1	4	yes	—
11	C₂²×C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₄₉	C₄	1	2	yes	—
14	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
15	#432×C₁₄₉	—	2	4	no	—
16	#432×C₁₄₉	C₂²	1	8	yes	—
17	C₂×C₄⋊C₈×C₁₄₉	—	2	2	no	—
18	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	yes	—
19	C₂×#97×C₁₄₉	—	2	2	no	—
20	#324×C₁₄₉	C₂²	1	16	yes	—
21	C₂²×Q₈×C₁₄₉	—	2	2	no	—
22	C₂²×Q₈×C₁₄₉	—	2	2	no	—
23	C₂²×Q₈×C₁₄₉	—	2	8	no	—
24	C₂²×Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₄₉	—	2	4	no	—
31	C₄×Q₈×C₁₄₉	—	2	8	no	—
32	C₄×Q₈×C₁₄₉	—	2	8	no	—
33	C₄×Q₈×C₁₄₉	—	2	8	no	—
34	C₄×Q₈×C₁₄₉	—	2	8	no	—
35	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
42	C₂×C₄²×C₁₄₉	—	2	4	no	—
43	C₂×C₄²×C₁₄₉	—	2	2	no	—
44	C₂×C₄²×C₁₄₉	—	2	2	no	—
45	C₂×C₄²×C₁₄₉	C₂×C₄	1	8	yes	—
46	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
48	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
49	C₂×C₄²×C₁₄₉	D₄	1	4	yes	—
50	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
51	C₄⋊C₈×C₁₄₉	—	2	8	no	—
52	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
53	C₂²⋊C₈×C₁₄₉	C₂³	1	8	yes	—
54	#97×C₁₄₉	—	2	8	no	—
55	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×Q₈×C₁₄₉	—	2	16	no	—
57	C₂×Q₈×C₁₄₉	—	2	16	no	—
58	C₂×Q₈×C₁₄₉	—	2	8	no	—
59	C₂×Q₈×C₁₄₉	—	2	16	no	—
60	C₂²×C₄×C₁₄₉	—	2	2	no	—
61	C₂²×C₄×C₁₄₉	—	2	2	no	—
62	C₂²×C₄×C₁₄₉	—	2	4	no	—
63	C₂²×C₄×C₁₄₉	—	2	4	no	—
64	C₂²×C₄×C₁₄₉	—	2	4	no	—
65	C₂²×C₄×C₁₄₉	—	2	2	no	—
66	C₂²×C₄×C₁₄₉	—	2	2	no	—
67	C₂²×C₄×C₁₄₉	—	4	2	no	—
68	C₂²×C₄×C₁₄₉	—	4	4	no	—
69	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₄₉	M₁₆	1	8	yes	—
75	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₄₉	—	2	8	no	—
84	C₂×C₈×C₁₄₉	—	4	8	no	—
85	C₄⋊C₄×C₁₄₉	—	2	8	no	—
86	C₄⋊C₄×C₁₄₉	—	2	8	no	—
87	C₄⋊C₄×C₁₄₉	—	2	8	no	—
88	C₄²×C₁₄₉	—	2	8	no	—
89	C₄²×C₁₄₉	—	2	8	no	—
90	C₄²×C₁₄₉	C₂²⋊C₄	1	4	yes	—
91	C₄²×C₁₄₉	C₂²⋊C₄	1	4	yes	—
92	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
93	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
94	C₂³×C₁₄₉	—	2	2	no	—
95	C₂³×C₁₄₉	—	2	2	no	—
96	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×C₁₄₉	C₂×M₁₆	1	4	yes	—
99	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
100	Q₈×C₁₄₉	—	2	32	no	—
101	C₂×C₄×C₁₄₉	—	2	4	no	—
102	C₂×C₄×C₁₄₉	—	2	4	no	—
103	C₂×C₄×C₁₄₉	—	2	4	no	—
104	C₂×C₄×C₁₄₉	—	2	4	no	—
105	C₂×C₄×C₁₄₉	—	2	4	no	—
106	C₂×C₄×C₁₄₉	—	2	8	no	—
107	C₂×C₄×C₁₄₉	—	2	8	no	—
108	C₂×C₄×C₁₄₉	—	2	4	no	—
109	C₂×C₄×C₁₄₉	—	2	2	no	—
110	C₂×C₄×C₁₄₉	—	2	4	no	—
111	C₂×C₄×C₁₄₉	—	2	4	no	—
112	C₂×C₄×C₁₄₉	—	2	4	no	—
113	C₂×C₄×C₁₄₉	—	4	1	no	—
114	C₂×C₄×C₁₄₉	—	4	2	no	—
115	C₂×C₄×C₁₄₉	—	4	1	no	—
116	C₂×C₄×C₁₄₉	—	4	4	no	—
117	C₂×C₄×C₁₄₉	—	4	4	no	—
118	C₂×C₄×C₁₄₉	—	4	4	no	—
119	C₂×C₄×C₁₄₉	#101	1	4	yes	—
120	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
121	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
122	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
123	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂×C₄×C₁₄₉	C₂×M₁₆	1	8	yes	—
125	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
126	C₈×C₁₄₉	—	4	8	no	—
127	C₂²×C₁₄₉	—	2	1	no	—
128	C₂²×C₁₄₉	—	2	1	no	—
129	C₂²×C₁₄₉	—	2	1	no	—
130	C₂²×C₁₄₉	—	2	1	no	—
131	C₂²×C₁₄₉	—	2	8	no	—
132	C₂²×C₁₄₉	#407	1	2	yes	—
133	C₂²×C₁₄₉	#407	1	2	yes	—
134	C₂²×C₁₄₉	#410	1	2	yes	—
135	C₂²×C₁₄₉	C₂×#101	1	2	yes	—
136	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₁₄₉	C₂²×M₁₆	1	2	yes	—
138	C₄×C₁₄₉	—	2	4	no	—
139	C₄×C₁₄₉	—	2	8	no	—
140	C₄×C₁₄₉	—	2	2	no	—
141	C₄×C₁₄₉	—	2	2	no	—
142	C₄×C₁₄₉	—	2	2	no	—
143	C₄×C₁₄₉	—	4	4	no	—
144	C₄×C₁₄₉	C₂×#101	1	4	yes	—
145	C₂×C₁₄₉	—	2	2	no	—
146	C₂×C₁₄₉	—	2	2	no	—
147	C₂×C₁₄₉	#1467	1	4	yes	direct product factor
148	C₂×C₁₄₉	C₂×#407	1	1	yes	characteristic
149	C₂×C₁₄₉	C₂×#410	1	1	yes	characteristic
150	C₂×C₁₄₉	C₂²×#101	1	1	yes	characteristic
151	C₂×#1467	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₁₄₉	C₂×#1467	1	1	yes	characteristic, direct product factor, Sylow
153	C₂²×C₄×Q₈	C₂×C₁₄₉	1	1	yes	characteristic
154	C₂×#432	C₂×C₁₄₉	1	2	yes	—
155	#1467	C₂×C₁₄₉	1	8	yes	direct product factor
156	C₂×#324	C₂×C₁₄₉	1	4	yes	—
157	C₂³×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
158	C₂×C₄×Q₈	—	2	2	no	—
159	C₂×C₄×Q₈	—	2	2	no	—
160	C₂×C₄×Q₈	—	2	4	no	—
161	C₂×C₄×Q₈	C₄×C₁₄₉	1	4	yes	—
162	C₂×C₄×Q₈	C₂²×C₁₄₉	1	4	yes	—
163	C₂²×C₄⋊C₄	C₄×C₁₄₉	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
165	C₂²×C₄²	C₄×C₁₄₉	1	2	yes	—
166	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
167	#432	—	2	4	no	—
168	#432	C₂²×C₁₄₉	1	8	yes	—
169	C₂×C₄⋊C₈	—	2	2	no	—
170	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	—
171	C₂×#97	—	2	2	no	—
172	#324	C₂²×C₁₄₉	1	16	yes	—
173	C₂²×Q₈	—	2	2	no	—
174	C₂²×Q₈	—	2	2	no	—
175	C₂²×Q₈	—	2	8	no	—
176	C₂²×Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
177	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
178	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
179	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
180	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
181	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
182	C₂²×C₈	—	2	4	no	—
183	C₄×Q₈	—	2	8	no	—
184	C₄×Q₈	—	2	8	no	—
185	C₄×Q₈	—	2	8	no	—
186	C₄×Q₈	—	2	8	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	2	4	no	—
190	C₂×C₄⋊C₄	—	2	4	no	—
191	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	—
192	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	—
193	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	4	yes	—
194	C₂×C₄²	—	2	2	no	—
195	C₂×C₄²	—	2	4	no	—
196	C₂×C₄²	—	2	2	no	—
197	C₂×C₄²	C₂×C₄×C₁₄₉	1	8	yes	—
198	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
199	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
200	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
201	C₂×C₄²	D₄×C₁₄₉	1	4	yes	—
202	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
203	C₄⋊C₈	—	2	8	no	—
204	C₂²⋊C₈	—	2	4	no	—
205	C₂²⋊C₈	C₂³×C₁₄₉	1	8	yes	—
206	#97	—	2	8	no	—
207	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
208	C₂×Q₈	—	2	16	no	—
209	C₂×Q₈	—	2	16	no	—
210	C₂×Q₈	—	2	8	no	—
211	C₂×Q₈	—	2	16	no	—
212	C₂²×C₄	—	2	2	no	—
213	C₂²×C₄	—	2	2	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	4	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	4	2	no	—
220	C₂²×C₄	—	4	4	no	—
221	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
222	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
223	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
224	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
225	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
226	C₂²×C₄	M₁₆×C₁₄₉	1	8	yes	—
227	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
228	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
229	C₂²×C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
230	C₂²×C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
231	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
233	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
234	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
235	C₂×C₈	—	2	8	no	—
236	C₂×C₈	—	4	8	no	—
237	C₄⋊C₄	—	2	8	no	—
238	C₄⋊C₄	—	2	8	no	—
239	C₄⋊C₄	—	2	8	no	—
240	C₄²	—	2	8	no	—
241	C₄²	—	2	8	no	—
242	C₄²	C₂²⋊C₄×C₁₄₉	1	4	yes	—
243	C₄²	C₂²⋊C₄×C₁₄₉	1	4	yes	—
244	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
245	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
246	C₂³	—	2	2	no	—
247	C₂³	—	2	2	no	—
248	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
249	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
250	C₂³	C₂×M₁₆×C₁₄₉	1	4	yes	—
251	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
252	Q₈	—	2	32	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	4	no	—
260	C₂×C₄	—	2	4	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	1	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	#101×C₁₄₉	1	4	yes	—
272	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
273	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
274	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
275	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
276	C₂×C₄	C₂×M₁₆×C₁₄₉	1	8	yes	—
277	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
278	C₈	—	4	8	no	—
279	C₂²	—	2	8	no	—
280	C₂²	—	2	1	no	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	#407×C₁₄₉	1	2	yes	—
285	C₂²	#407×C₁₄₉	1	2	yes	—
286	C₂²	#410×C₁₄₉	1	2	yes	—
287	C₂²	C₂×#101×C₁₄₉	1	2	yes	—
288	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
289	C₂²	C₂²×M₁₆×C₁₄₉	1	2	yes	—
290	C₄	—	2	4	no	—
291	C₄	—	2	8	no	—
292	C₄	—	2	2	no	—
293	C₄	—	2	2	no	—
294	C₄	—	2	2	no	—
295	C₄	—	4	4	no	—
296	C₄	C₂×#101×C₁₄₉	1	4	yes	—
297	C₂	—	2	2	no	—
298	C₂	—	2	2	no	—
299	C₂	#1467×C₁₄₉	1	4	yes	direct product factor
300	C₂	C₂×#407×C₁₄₉	1	1	yes	characteristic
301	C₂	C₂×#410×C₁₄₉	1	1	yes	characteristic
302	C₂	C₂²×#101×C₁₄₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #1467×C₁₄₉	C₂	direct (N × H)
147. C₂×C₁₄₉	#1467	direct (N × H)
151. C₂×#1467	C₁₄₉	direct (N × H)
152. C₁₄₉	C₂×#1467	direct (N × H)
155. #1467	C₂×C₁₄₉	direct (N × H)
299. C₂	#1467×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
C₂²×C₄×Q₈×C₁₄₉	2
C₂×#432×C₁₄₉	2
#1467×C₁₄₉	2
C₂×#324×C₁₄₉	2
C₂×#1467	149

Subgroups — C2×#1467×C149 #49196309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1467×C₁₄₉ #49196309