Subgroups — C₁₄₉×#17363 #49196312

Order 38144.

1250 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1467×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1466×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#1464×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	#1459×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₁₄₉	C₄	1	1	yes	characteristic
8	C₄×#41×C₁₄₉	—	2	2	no	—
9	C₄×#41×C₁₄₉	—	2	2	no	—
10	C₄×#41×C₁₄₉	—	2	2	no	—
11	C₄×#41×C₁₄₉	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₄₉	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic
19	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₄₉	C₄	1	2	yes	—
21	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
22	#432×C₁₄₉	—	2	2	no	—
23	#432×C₁₄₉	—	2	2	no	—
24	#432×C₁₄₉	C₂²	1	4	yes	—
25	#432×C₁₄₉	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₁₄₉	—	2	2	no	—
27	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	yes	—
28	C₂×#97×C₁₄₉	—	2	2	no	—
29	#324×C₁₄₉	C₂²	1	8	yes	—
30	#323×C₁₄₉	C₂²	1	8	yes	—
31	C₂×#41×C₁₄₉	—	2	8	no	—
32	C₂×#41×C₁₄₉	—	2	2	no	—
33	C₂×#41×C₁₄₉	—	2	2	no	—
34	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₄₉	—	2	4	no	—
44	C₄×Q₈×C₁₄₉	—	2	2	no	—
45	C₄×Q₈×C₁₄₉	—	2	2	no	—
46	C₄×Q₈×C₁₄₉	—	2	2	no	—
47	C₄×Q₈×C₁₄₉	—	2	2	no	—
48	C₄×D₄×C₁₄₉	—	2	4	no	—
49	C₄×D₄×C₁₄₉	—	2	4	no	—
50	C₄×D₄×C₁₄₉	—	2	4	no	—
51	C₄×D₄×C₁₄₉	—	2	4	no	—
52	C₄×D₄×C₁₄₉	—	2	2	no	—
53	C₄×D₄×C₁₄₉	—	2	2	no	—
54	C₄×D₄×C₁₄₉	—	2	2	no	—
55	C₄×D₄×C₁₄₉	—	2	2	no	—
56	#117×C₁₄₉	—	2	2	no	—
57	#117×C₁₄₉	—	2	2	no	—
58	#117×C₁₄₉	—	2	4	no	—
59	#117×C₁₄₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₄₉	—	2	2	no	—
68	C₂×C₄²×C₁₄₉	—	2	2	no	—
69	C₂×C₄²×C₁₄₉	—	2	2	no	—
70	C₂×C₄²×C₁₄₉	—	2	2	no	—
71	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
79	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
80	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₁₄₉	—	2	4	no	—
83	C₄⋊C₈×C₁₄₉	—	2	4	no	—
84	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
85	C₂²⋊C₈×C₁₄₉	C₂³	1	8	yes	—
86	#97×C₁₄₉	—	2	4	no	—
87	#97×C₁₄₉	—	2	4	no	—
88	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
89	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
90	#41×C₁₄₉	—	2	16	no	—
91	#41×C₁₄₉	—	2	16	no	—
92	C₂×Q₈×C₁₄₉	—	2	2	no	—
93	C₂×Q₈×C₁₄₉	—	2	4	no	—
94	C₂×D₄×C₁₄₉	—	2	4	no	—
95	C₂×D₄×C₁₄₉	—	2	4	no	—
96	C₂×D₄×C₁₄₉	—	2	4	no	—
97	C₂×D₄×C₁₄₉	—	2	2	no	—
98	C₂×D₄×C₁₄₉	M₁₆	1	8	yes	—
99	C₂²×C₄×C₁₄₉	—	2	4	no	—
100	C₂²×C₄×C₁₄₉	—	2	4	no	—
101	C₂²×C₄×C₁₄₉	—	2	2	no	—
102	C₂²×C₄×C₁₄₉	—	2	2	no	—
103	C₂²×C₄×C₁₄₉	—	2	4	no	—
104	C₂²×C₄×C₁₄₉	—	2	2	no	—
105	C₂²×C₄×C₁₄₉	—	2	2	no	—
106	C₂²×C₄×C₁₄₉	—	2	2	no	—
107	C₂²×C₄×C₁₄₉	—	2	2	no	—
108	C₂²×C₄×C₁₄₉	—	4	2	no	—
109	C₂²×C₄×C₁₄₉	—	4	2	no	—
110	C₂²×C₄×C₁₄₉	—	4	4	no	—
111	C₂²×C₄×C₁₄₉	—	4	4	no	—
112	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₁₄₉	—	2	8	no	—
128	C₂×C₈×C₁₄₉	—	4	8	no	—
129	C₄⋊C₄×C₁₄₉	—	2	4	no	—
130	C₄⋊C₄×C₁₄₉	—	2	2	no	—
131	C₄⋊C₄×C₁₄₉	—	2	2	no	—
132	C₄⋊C₄×C₁₄₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
136	C₄²×C₁₄₉	—	2	2	no	—
137	C₄²×C₁₄₉	—	2	2	no	—
138	C₄²×C₁₄₉	—	2	2	no	—
139	C₄²×C₁₄₉	—	2	2	no	—
140	C₄²×C₁₄₉	—	2	2	no	—
141	C₄²×C₁₄₉	—	2	2	no	—
142	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
145	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
148	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
149	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
150	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
151	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
152	C₂³×C₁₄₉	—	2	2	no	—
153	C₂³×C₁₄₉	—	2	2	no	—
154	C₂³×C₁₄₉	—	4	1	no	—
155	C₂³×C₁₄₉	—	4	1	no	—
156	C₂³×C₁₄₉	—	4	2	no	—
157	C₂³×C₁₄₉	—	4	2	no	—
158	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₄₉	C₂×M₁₆	1	4	yes	—
160	C₂³×C₁₄₉	C₂×M₁₆	1	4	yes	—
161	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
162	Q₈×C₁₄₉	—	2	8	no	—
163	D₄×C₁₄₉	—	2	8	no	—
164	D₄×C₁₄₉	—	2	16	no	—
165	C₂×C₄×C₁₄₉	—	2	8	no	—
166	C₂×C₄×C₁₄₉	—	2	8	no	—
167	C₂×C₄×C₁₄₉	—	2	2	no	—
168	C₂×C₄×C₁₄₉	—	2	2	no	—
169	C₂×C₄×C₁₄₉	—	2	2	no	—
170	C₂×C₄×C₁₄₉	—	2	2	no	—
171	C₂×C₄×C₁₄₉	—	2	4	no	—
172	C₂×C₄×C₁₄₉	—	2	4	no	—
173	C₂×C₄×C₁₄₉	—	2	4	no	—
174	C₂×C₄×C₁₄₉	—	2	2	no	—
175	C₂×C₄×C₁₄₉	—	2	2	no	—
176	C₂×C₄×C₁₄₉	—	2	4	no	—
177	C₂×C₄×C₁₄₉	—	2	2	no	—
178	C₂×C₄×C₁₄₉	—	2	2	no	—
179	C₂×C₄×C₁₄₉	—	4	2	no	—
180	C₂×C₄×C₁₄₉	—	4	1	no	—
181	C₂×C₄×C₁₄₉	—	4	2	no	—
182	C₂×C₄×C₁₄₉	—	4	1	no	—
183	C₂×C₄×C₁₄₉	—	4	4	no	—
184	C₂×C₄×C₁₄₉	—	4	4	no	—
185	C₂×C₄×C₁₄₉	—	4	4	no	—
186	C₂×C₄×C₁₄₉	—	4	4	no	—
187	C₂×C₄×C₁₄₉	—	4	2	no	—
188	C₂×C₄×C₁₄₉	—	4	2	no	—
189	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₄₉	C₂×M₁₆	1	4	yes	—
198	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
199	C₈×C₁₄₉	—	4	8	no	—
200	C₂²×C₁₄₉	—	2	1	no	—
201	C₂²×C₁₄₉	—	2	2	no	—
202	C₂²×C₁₄₉	—	2	1	no	—
203	C₂²×C₁₄₉	—	2	2	no	—
204	C₂²×C₁₄₉	—	2	4	no	—
205	C₂²×C₁₄₉	—	4	4	no	—
206	C₂²×C₁₄₉	—	4	4	no	—
207	C₂²×C₁₄₉	—	4	4	no	—
208	C₂²×C₁₄₉	—	4	2	no	—
209	C₂²×C₁₄₉	—	4	2	no	—
210	C₂²×C₁₄₉	#407	1	4	yes	—
211	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₄₉	C₂²×M₁₆	1	2	yes	—
213	C₄×C₁₄₉	—	2	1	no	—
214	C₄×C₁₄₉	—	2	1	no	—
215	C₄×C₁₄₉	—	2	2	no	—
216	C₄×C₁₄₉	—	2	4	no	—
217	C₄×C₁₄₉	—	2	2	no	—
218	C₄×C₁₄₉	—	2	1	no	—
219	C₄×C₁₄₉	—	2	1	no	—
220	C₄×C₁₄₉	—	2	2	no	—
221	C₄×C₁₄₉	—	4	2	no	—
222	C₄×C₁₄₉	—	4	2	no	—
223	C₄×C₁₄₉	#410	1	2	yes	—
224	C₄×C₁₄₉	#413	1	2	yes	—
225	C₂×C₁₄₉	—	2	2	no	—
226	C₂×C₁₄₉	—	2	4	no	—
227	C₂×C₁₄₉	—	4	4	no	—
228	C₂×C₁₄₉	C₂×#407	1	1	yes	characteristic
229	C₂×C₁₄₉	C₂×#410	1	1	yes	characteristic
230	C₂×C₁₄₉	C₂×#413	1	1	yes	characteristic
231	#17363	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₄₉	#17363	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×C₄×#41	C₂×C₁₄₉	1	1	yes	characteristic
234	C₂×#432	C₂×C₁₄₉	1	2	yes	complemented
235	#1467	C₂×C₁₄₉	1	2	yes	complemented
236	#1466	C₂×C₁₄₉	1	2	yes	complemented
237	#1464	C₂×C₁₄₉	1	4	yes	complemented
238	#1459	C₂×C₁₄₉	1	4	yes	complemented
239	C₂²×#41	C₄×C₁₄₉	1	1	yes	characteristic
240	C₄×#41	—	2	2	no	—
241	C₄×#41	—	2	2	no	—
242	C₄×#41	—	2	2	no	—
243	C₄×#41	—	2	2	no	—
244	C₂×C₄×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
246	C₂×C₄×D₄	C₄×C₁₄₉	1	2	yes	—
247	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₄₉	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
250	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
252	C₂²×C₄²	C₄×C₁₄₉	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
254	#432	—	2	2	no	—
255	#432	—	2	2	no	—
256	#432	C₂²×C₁₄₉	1	4	yes	—
257	#432	C₂²×C₁₄₉	1	4	yes	—
258	C₂×C₄⋊C₈	—	2	2	no	—
259	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	—
260	C₂×#97	—	2	2	no	—
261	#324	C₂²×C₁₄₉	1	8	yes	—
262	#323	C₂²×C₁₄₉	1	8	yes	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
267	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
268	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
269	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
270	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
271	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
272	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
273	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
275	C₂²×C₈	—	2	4	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	2	4	no	—
291	#117	—	2	4	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
304	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
305	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
306	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
307	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
309	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
310	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
311	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
312	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
314	C₄⋊C₈	—	2	4	no	—
315	C₄⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	C₂³×C₁₄₉	1	8	yes	—
318	#97	—	2	4	no	—
319	#97	—	2	4	no	—
320	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
321	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
322	#41	—	2	16	no	—
323	#41	—	2	16	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	M₁₆×C₁₄₉	1	8	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
345	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
346	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
347	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
359	C₂×C₈	—	2	8	no	—
360	C₂×C₈	—	4	8	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
375	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
376	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
377	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
378	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
379	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
380	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
381	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
382	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
383	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
391	C₂³	C₂×M₁₆×C₁₄₉	1	4	yes	—
392	C₂³	C₂×M₁₆×C₁₄₉	1	4	yes	—
393	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
394	Q₈	—	2	8	no	—
395	D₄	—	2	8	no	—
396	D₄	—	2	16	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
425	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
428	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
429	C₂×C₄	C₂×M₁₆×C₁₄₉	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
431	C₈	—	4	8	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	#407×C₁₄₉	1	4	yes	—
443	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
444	C₂²	C₂²×M₁₆×C₁₄₉	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	#410×C₁₄₉	1	2	yes	—
456	C₄	#413×C₁₄₉	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	2	4	no	—
459	C₂	—	4	4	no	—
460	C₂	C₂×#407×C₁₄₉	1	1	yes	characteristic
461	C₂	C₂×#410×C₁₄₉	1	1	yes	characteristic
462	C₂	C₂×#413×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₄₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₁₄₉	C₂	semidirect
3. #1467×C₁₄₉	C₂	semidirect
4. #1466×C₁₄₉	C₂	semidirect
5. #1464×C₁₄₉	C₂	semidirect
6. #1459×C₁₄₉	C₂	semidirect
231. #17363	C₁₄₉	direct (N × H)
232. C₁₄₉	#17363	direct (N × H)
234. C₂×#432	C₂×C₁₄₉	semidirect
235. #1467	C₂×C₁₄₉	semidirect
236. #1466	C₂×C₁₄₉	semidirect
237. #1464	C₂×C₁₄₉	semidirect
238. #1459	C₂×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₄₉	2
C₂×#432×C₁₄₉	2
#1467×C₁₄₉	2
#1466×C₁₄₉	2
#1464×C₁₄₉	2
#1459×C₁₄₉	2
#17363	149

Subgroups — C149×#17363 #49196312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17363 #49196312