Subgroups — C₂×#1479×C₁₄₉ #49196384

Order 38144.

1282 conjugacy classes of subgroups.

The subgroup lattice has 404 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×#431×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#431×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1479×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₄₉	—	2	1	no	—
8	C₂×C₄×Q₈×C₁₄₉	—	2	2	no	—
9	C₂×C₄×Q₈×C₁₄₉	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₄₉	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₄₉	C₄	1	2	yes	—
12	C₂×C₄×Q₈×C₁₄₉	C₄	1	4	yes	—
13	C₂×C₄×Q₈×C₁₄₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₄₉	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₁₄₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₁₄₉	—	2	1	no	—
18	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
19	#431×C₁₄₉	—	2	2	no	—
20	#431×C₁₄₉	—	2	2	no	—
21	#431×C₁₄₉	C₂²	1	4	yes	—
22	#431×C₁₄₉	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
27	C₂×C₄×C₈×C₁₄₉	—	2	1	no	—
28	C₂×C₄×C₈×C₁₄₉	C₂²	1	2	yes	—
29	Q₈⋊C₈×C₁₄₉	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₁₄₉	—	2	1	no	—
31	C₂²×Q₈×C₁₄₉	—	2	2	no	—
32	C₂²×Q₈×C₁₄₉	—	2	4	no	—
33	C₂²×Q₈×C₁₄₉	C₈	1	8	yes	complemented
34	C₂²×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₄₉	—	2	1	no	—
37	C₂³×C₄×C₁₄₉	—	2	1	no	—
38	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₄₉	—	2	2	no	—
42	C₂²×C₈×C₁₄₉	—	2	2	no	—
43	C₄×Q₈×C₁₄₉	—	2	4	no	—
44	C₄×Q₈×C₁₄₉	—	2	4	no	—
45	C₄×Q₈×C₁₄₉	—	2	4	no	—
46	C₄×Q₈×C₁₄₉	—	2	2	no	—
47	C₄×Q₈×C₁₄₉	—	2	4	no	—
48	C₄×Q₈×C₁₄₉	—	2	4	no	—
49	C₄×Q₈×C₁₄₉	—	2	2	no	—
50	C₄×Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
51	C₄×Q₈×C₁₄₉	C₂×C₄	1	8	yes	—
52	C₄×Q₈×C₁₄₉	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₄₉	—	2	2	no	—
62	C₂×C₄²×C₁₄₉	—	2	4	no	—
63	C₂×C₄²×C₁₄₉	—	2	4	no	—
64	C₂×C₄²×C₁₄₉	—	2	2	no	—
65	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
69	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₄₉	—	2	4	no	—
74	C₄⋊C₈×C₁₄₉	—	2	2	no	—
75	C₄⋊C₈×C₁₄₉	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
77	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
78	C₄×C₈×C₁₄₉	—	2	4	no	—
79	C₄×C₈×C₁₄₉	—	2	2	no	—
80	C₄×C₈×C₁₄₉	C₂³	1	4	yes	—
81	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₄₉	—	2	8	no	—
83	C₂×Q₈×C₁₄₉	—	2	16	no	—
84	C₂×Q₈×C₁₄₉	—	2	2	no	—
85	C₂×Q₈×C₁₄₉	—	2	4	no	—
86	C₂×Q₈×C₁₄₉	—	2	4	no	—
87	C₂×Q₈×C₁₄₉	—	2	8	no	—
88	C₂×Q₈×C₁₄₉	C₂×C₈	1	8	yes	—
89	C₂×Q₈×C₁₄₉	C₂×C₈	1	16	yes	complemented
90	C₂×Q₈×C₁₄₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₄₉	—	2	8	no	—
92	C₂²×C₄×C₁₄₉	—	2	2	no	—
93	C₂²×C₄×C₁₄₉	—	2	4	no	—
94	C₂²×C₄×C₁₄₉	—	2	4	no	—
95	C₂²×C₄×C₁₄₉	—	2	4	no	—
96	C₂²×C₄×C₁₄₉	—	2	2	no	—
97	C₂²×C₄×C₁₄₉	—	4	2	no	—
98	C₂²×C₄×C₁₄₉	—	4	4	no	—
99	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₄₉	C₂×C₈	1	4	yes	—
106	C₂²×C₄×C₁₄₉	M₁₆	1	4	yes	—
107	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₄₉	—	2	4	no	—
114	C₂×C₈×C₁₄₉	—	2	4	no	—
115	C₂×C₈×C₁₄₉	—	4	4	no	—
116	C₂×C₈×C₁₄₉	—	4	4	no	—
117	C₄⋊C₄×C₁₄₉	—	2	8	no	—
118	C₄⋊C₄×C₁₄₉	—	2	4	no	—
119	C₄⋊C₄×C₁₄₉	—	2	2	no	—
120	C₄⋊C₄×C₁₄₉	—	2	4	no	—
121	C₄⋊C₄×C₁₄₉	—	2	4	no	—
122	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
123	C₄²×C₁₄₉	—	2	8	no	—
124	C₄²×C₁₄₉	—	2	4	no	—
125	C₄²×C₁₄₉	—	2	4	no	—
126	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
132	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
134	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₁₄₉	—	2	2	no	—
137	C₂³×C₁₄₉	—	2	2	no	—
138	C₂³×C₁₄₉	C₂²⋊C₈	1	4	yes	—
139	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	Q₈×C₁₄₉	—	2	4	no	—
142	Q₈×C₁₄₉	—	2	8	no	—
143	Q₈×C₁₄₉	—	2	16	no	—
144	Q₈×C₁₄₉	C₂²×C₈	1	8	yes	—
145	C₂×C₄×C₁₄₉	—	2	4	no	—
146	C₂×C₄×C₁₄₉	—	2	8	no	—
147	C₂×C₄×C₁₄₉	—	2	16	no	—
148	C₂×C₄×C₁₄₉	—	2	2	no	—
149	C₂×C₄×C₁₄₉	—	2	2	no	—
150	C₂×C₄×C₁₄₉	—	2	2	no	—
151	C₂×C₄×C₁₄₉	—	2	4	no	—
152	C₂×C₄×C₁₄₉	—	2	4	no	—
153	C₂×C₄×C₁₄₉	—	2	4	no	—
154	C₂×C₄×C₁₄₉	—	4	2	no	—
155	C₂×C₄×C₁₄₉	—	4	2	no	—
156	C₂×C₄×C₁₄₉	—	4	8	no	—
157	C₂×C₄×C₁₄₉	—	4	4	no	—
158	C₂×C₄×C₁₄₉	C₂²⋊C₈	1	8	yes	—
159	C₂×C₄×C₁₄₉	C₂²⋊C₈	1	4	yes	—
160	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₄₉	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₁₄₉	C₂²×C₈	1	4	yes	—
168	C₂×C₄×C₁₄₉	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₁₄₉	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₁₄₉	#137	1	4	yes	—
171	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₄₉	—	4	4	no	—
175	C₈×C₁₄₉	—	4	4	no	—
176	C₂²×C₁₄₉	—	2	2	no	—
177	C₂²×C₁₄₉	—	2	2	no	—
178	C₂²×C₁₄₉	—	2	8	no	—
179	C₂²×C₁₄₉	C₂×C₂²⋊C₈	1	4	yes	—
180	C₂²×C₁₄₉	C₂×C₂²⋊C₈	1	2	yes	—
181	C₂²×C₁₄₉	#419	1	2	yes	—
182	C₂²×C₁₄₉	#421	1	2	yes	—
183	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₄×C₁₄₉	—	2	8	no	—
185	C₄×C₁₄₉	—	2	2	no	—
186	C₄×C₁₄₉	—	2	1	no	—
187	C₄×C₁₄₉	—	2	1	no	—
188	C₄×C₁₄₉	—	2	2	no	—
189	C₄×C₁₄₉	—	4	4	no	—
190	C₄×C₁₄₉	C₂×C₂²⋊C₈	1	2	yes	—
191	C₄×C₁₄₉	C₂×C₂²⋊C₈	1	4	yes	—
192	C₄×C₁₄₉	#419	1	2	yes	—
193	C₄×C₁₄₉	C₂³×C₈	1	1	yes	characteristic
194	C₄×C₁₄₉	C₂²×M₁₆	1	1	yes	characteristic
195	C₄×C₁₄₉	C₂×#137	1	2	yes	—
196	C₂×C₁₄₉	—	2	4	no	—
197	C₂×C₁₄₉	#1479	1	4	yes	direct product factor
198	C₂×C₁₄₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic
199	C₂×C₁₄₉	C₂×#419	1	1	yes	characteristic
200	C₂×C₁₄₉	C₂×#421	1	1	yes	characteristic
201	C₂×#1479	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₁₄₉	C₂×#1479	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×C₄×Q₈	C₂×C₁₄₉	1	1	yes	characteristic
204	C₂×#431	C₂×C₁₄₉	1	1	yes	characteristic
205	C₂×#431	C₂×C₁₄₉	1	1	yes	characteristic
206	#1479	C₂×C₁₄₉	1	8	yes	direct product factor
207	C₂×Q₈⋊C₈	C₂×C₁₄₉	1	4	yes	complemented
208	C₂³×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	—	2	2	no	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	—	2	2	no	—
213	C₂×C₄×Q₈	C₄×C₁₄₉	1	2	yes	—
214	C₂×C₄×Q₈	C₄×C₁₄₉	1	4	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₄₉	1	2	yes	—
216	C₂×C₄×Q₈	C₂²×C₁₄₉	1	4	yes	—
217	C₂²×C₄⋊C₄	—	2	1	no	—
218	C₂²×C₄⋊C₄	C₄×C₁₄₉	1	1	yes	characteristic
219	C₂²×C₄²	—	2	1	no	—
220	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
221	#431	—	2	2	no	—
222	#431	—	2	2	no	—
223	#431	C₂²×C₁₄₉	1	4	yes	—
224	#431	C₂²×C₁₄₉	1	4	yes	—
225	C₂×C₄⋊C₈	—	2	1	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	2	yes	—
227	C₂×C₂²⋊C₈	—	2	1	no	—
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	C₂×C₄×C₈	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₁₄₉	1	2	yes	—
231	Q₈⋊C₈	C₂²×C₁₄₉	1	16	yes	complemented
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	C₈×C₁₄₉	1	8	yes	complemented
236	C₂²×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
237	C₂²×Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
242	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
253	C₄×Q₈	C₂×C₄×C₁₄₉	1	8	yes	—
254	C₄×Q₈	C₂³×C₁₄₉	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
269	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
272	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	C₂³×C₁₄₉	1	4	yes	—
278	C₂²⋊C₈	—	2	4	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₄×C₈	—	2	4	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	C₂³×C₁₄₉	1	4	yes	—
283	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	16	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	8	no	—
290	C₂×Q₈	C₂×C₈×C₁₄₉	1	8	yes	—
291	C₂×Q₈	C₂×C₈×C₁₄₉	1	16	yes	complemented
292	C₂×Q₈	C₂²×C₄×C₁₄₉	1	4	yes	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
303	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
306	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₈×C₁₄₉	1	4	yes	—
308	C₂²×C₄	M₁₆×C₁₄₉	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	4	no	—
318	C₂×C₈	—	4	4	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
325	C₄²	—	2	8	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
329	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
331	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
332	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
334	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
336	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
337	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₂²⋊C₈×C₁₄₉	1	4	yes	—
341	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
342	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
343	Q₈	—	2	8	no	—
344	Q₈	—	2	16	no	—
345	Q₈	—	2	4	no	—
346	Q₈	C₂²×C₈×C₁₄₉	1	8	yes	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	16	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	C₂²⋊C₈×C₁₄₉	1	8	yes	—
361	C₂×C₄	C₂²⋊C₈×C₁₄₉	1	4	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₈×C₁₄₉	1	2	yes	—
369	C₂×C₄	C₂²×C₈×C₁₄₉	1	4	yes	—
370	C₂×C₄	C₂×M₁₆×C₁₄₉	1	4	yes	—
371	C₂×C₄	C₂×M₁₆×C₁₄₉	1	2	yes	—
372	C₂×C₄	#137×C₁₄₉	1	4	yes	—
373	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	C₂×C₂²⋊C₈×C₁₄₉	1	4	yes	—
382	C₂²	C₂×C₂²⋊C₈×C₁₄₉	1	2	yes	—
383	C₂²	#419×C₁₄₉	1	2	yes	—
384	C₂²	#421×C₁₄₉	1	2	yes	—
385	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
386	C₄	—	2	8	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	C₂×C₂²⋊C₈×C₁₄₉	1	2	yes	—
393	C₄	C₂×C₂²⋊C₈×C₁₄₉	1	4	yes	—
394	C₄	#419×C₁₄₉	1	2	yes	—
395	C₄	C₂³×C₈×C₁₄₉	1	1	yes	characteristic
396	C₄	C₂²×M₁₆×C₁₄₉	1	1	yes	characteristic
397	C₄	C₂×#137×C₁₄₉	1	2	yes	—
398	C₂	—	2	4	no	—
399	C₂	#1479×C₁₄₉	1	4	yes	direct product factor
400	C₂	C₂²×C₂²⋊C₈×C₁₄₉	1	1	yes	characteristic
401	C₂	C₂×#419×C₁₄₉	1	1	yes	characteristic
402	C₂	C₂×#421×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂×D₄
commutator	C₄	C₂³×C₈×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₄₉	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1479×C₁₄₉	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₁₄₉	C₂	semidirect
29. Q₈⋊C₈×C₁₄₉	C₂²	semidirect
33. C₂²×Q₈×C₁₄₉	C₈	semidirect
89. C₂×Q₈×C₁₄₉	C₂×C₈	semidirect
197. C₂×C₁₄₉	#1479	direct (N × H)
201. C₂×#1479	C₁₄₉	direct (N × H)
202. C₁₄₉	C₂×#1479	direct (N × H)
206. #1479	C₂×C₁₄₉	direct (N × H)
207. C₂×Q₈⋊C₈	C₂×C₁₄₉	semidirect
231. Q₈⋊C₈	C₂²×C₁₄₉	semidirect
235. C₂²×Q₈	C₈×C₁₄₉	semidirect
291. C₂×Q₈	C₂×C₈×C₁₄₉	semidirect
399. C₂	#1479×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×#431×C₁₄₉	2
#1479×C₁₄₉	2
C₂×Q₈⋊C₈×C₁₄₉	2
C₂×#1479	149

Subgroups — C2×#1479×C149 #49196384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1479×C₁₄₉ #49196384