Subgroups — C₁₄₉×#18748 #49197697

Order 38144.

1020 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3206×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3103×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#3036×C₁₄₉	C₂	1	1	yes	maximal, characteristic
5	#1643×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	#1622×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	#1548×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1487×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1478×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₁₄₉	—	2	1	no	—
11	#554×C₁₄₉	—	2	2	no	—
12	#554×C₁₄₉	—	2	2	no	—
13	#554×C₁₄₉	—	2	2	no	—
14	#554×C₁₄₉	C₂²	1	4	yes	—
15	#532×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₁₄₉	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₄₉	—	2	1	no	—
24	#492×C₁₄₉	C₂²	1	2	yes	complemented
25	#487×C₁₄₉	C₂²	1	2	yes	complemented
26	#481×C₁₄₉	—	2	1	no	—
27	#475×C₁₄₉	C₂²	1	2	yes	complemented
28	#463×C₁₄₉	—	2	2	no	—
29	#461×C₁₄₉	—	2	2	no	—
30	#461×C₁₄₉	C₂²	1	2	yes	—
31	#460×C₁₄₉	C₂²	1	2	yes	complemented
32	#459×C₁₄₉	C₂²	1	2	yes	—
33	#448×C₁₄₉	—	2	2	no	—
34	#448×C₁₄₉	—	2	1	no	—
35	C₄×SD₁₆×C₁₄₉	—	2	2	no	—
36	#431×C₁₄₉	C₂²	1	1	yes	characteristic
37	#431×C₁₄₉	C₂²	1	1	yes	characteristic
38	#423×C₁₄₉	C₂²	1	1	yes	characteristic
39	#417×C₁₄₉	—	2	1	no	—
40	#333×C₁₄₉	C₂²	1	4	yes	complemented
41	Q₈⋊C₈×C₁₄₉	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₄₉	C₂²	1	4	yes	—
43	C₂×#41×C₁₄₉	—	2	1	no	—
44	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₄₉	D₄	1	2	yes	—
46	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₄₉	—	2	2	no	—
48	C₂³×C₄×C₁₄₉	—	2	1	no	—
49	AGL(1,ℤ/8)×C₁₄₉	—	4	4	no	—
50	C₂×SD₁₆×C₁₄₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₄₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₄₉	—	2	4	no	—
53	C₂×D₈×C₁₄₉	—	2	2	no	—
54	C₂×M₁₆×C₁₄₉	—	2	1	no	—
55	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
56	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
57	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
58	C₄⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₄₉	C₂³	1	2	yes	—
60	#127×C₁₄₉	C₂³	1	1	yes	characteristic
61	#125×C₁₄₉	—	2	4	no	—
62	#125×C₁₄₉	—	2	4	no	—
63	#124×C₁₄₉	—	2	1	no	—
64	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
65	C₂²⋊Q₈×C₁₄₉	—	2	8	no	—
66	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
67	C₂²⋊Q₈×C₁₄₉	—	2	8	no	—
68	#121×C₁₄₉	—	2	1	no	—
69	#121×C₁₄₉	—	2	1	no	—
70	C₄×Q₈×C₁₄₉	—	2	1	no	—
71	C₄×Q₈×C₁₄₉	—	2	1	no	—
72	C₄×Q₈×C₁₄₉	D₄	1	2	yes	—
73	C₄×Q₈×C₁₄₉	C₂³	1	2	yes	—
74	C₄×D₄×C₁₄₉	—	2	4	no	—
75	C₄×D₄×C₁₄₉	—	2	4	no	—
76	C₄×D₄×C₁₄₉	—	2	1	no	—
77	C₄×D₄×C₁₄₉	—	2	1	no	—
78	C₄×D₄×C₁₄₉	—	2	1	no	—
79	C₄×D₄×C₁₄₉	—	2	1	no	—
80	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
81	C₄×D₄×C₁₄₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
93	C₂×C₄²×C₁₄₉	—	2	1	no	—
94	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
95	#106×C₁₄₉	—	2	2	no	—
96	C₄⋊C₈×C₁₄₉	—	2	1	no	—
97	C₄⋊C₈×C₁₄₉	—	2	1	no	—
98	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
100	#103×C₁₄₉	—	2	2	no	—
101	#103×C₁₄₉	—	2	4	no	—
102	#103×C₁₄₉	—	2	2	no	—
103	#102×C₁₄₉	—	2	2	no	—
104	#102×C₁₄₉	—	2	2	no	—
105	C₂²⋊C₈×C₁₄₉	—	2	1	no	—
106	C₂²⋊C₈×C₁₄₉	—	2	1	no	—
107	C₄×C₈×C₁₄₉	—	2	1	no	—
108	C₄×C₈×C₁₄₉	C₂³	1	2	yes	—
109	C₂⁴×C₁₄₉	—	2	1	no	—
110	#41×C₁₄₉	—	4	2	no	—
111	#41×C₁₄₉	—	4	2	no	—
112	C₂×Q₈×C₁₄₉	—	2	1	no	—
113	C₂×Q₈×C₁₄₉	—	2	2	no	—
114	C₂×Q₈×C₁₄₉	—	2	1	no	—
115	C₂×Q₈×C₁₄₉	—	4	2	no	—
116	C₂×Q₈×C₁₄₉	—	8	2	no	—
117	C₂×Q₈×C₁₄₉	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₄₉	C₂×D₄	1	4	yes	—
119	C₂×D₄×C₁₄₉	—	2	1	no	—
120	C₂×D₄×C₁₄₉	—	2	2	no	—
121	C₂×D₄×C₁₄₉	—	2	1	no	—
122	C₂×D₄×C₁₄₉	—	2	1	no	—
123	C₂×D₄×C₁₄₉	—	2	1	no	—
124	C₂×D₄×C₁₄₉	—	4	1	no	—
125	C₂×D₄×C₁₄₉	SD₁₆	1	4	yes	complemented
126	C₂×D₄×C₁₄₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₄₉	—	2	1	no	—
128	C₂²×C₄×C₁₄₉	—	2	1	no	—
129	C₂²×C₄×C₁₄₉	—	2	1	no	—
130	C₂²×C₄×C₁₄₉	—	2	2	no	—
131	C₂²×C₄×C₁₄₉	—	2	8	no	—
132	C₂²×C₄×C₁₄₉	—	2	2	no	—
133	C₂²×C₄×C₁₄₉	—	2	2	no	—
134	C₂²×C₄×C₁₄₉	—	4	4	no	—
135	C₂²×C₄×C₁₄₉	—	4	1	no	—
136	C₂²×C₄×C₁₄₉	—	8	4	no	—
137	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
140	SD₁₆×C₁₄₉	—	4	4	no	—
141	SD₁₆×C₁₄₉	—	4	4	no	—
142	SD₁₆×C₁₄₉	—	8	4	no	—
143	D₈×C₁₄₉	—	4	4	no	—
144	M₁₆×C₁₄₉	—	4	2	no	—
145	C₂×C₈×C₁₄₉	—	2	2	no	—
146	C₂×C₈×C₁₄₉	—	2	2	no	—
147	C₂×C₈×C₁₄₉	—	2	2	no	—
148	C₄⋊C₄×C₁₄₉	—	2	8	no	—
149	C₄⋊C₄×C₁₄₉	—	2	8	no	—
150	C₄⋊C₄×C₁₄₉	—	2	1	no	—
151	C₄⋊C₄×C₁₄₉	—	2	2	no	—
152	C₄⋊C₄×C₁₄₉	—	2	2	no	—
153	C₄⋊C₄×C₁₄₉	—	2	2	no	—
154	C₄⋊C₄×C₁₄₉	—	2	1	no	—
155	C₄⋊C₄×C₁₄₉	—	2	2	no	—
156	C₄⋊C₄×C₁₄₉	—	2	2	no	—
157	C₄⋊C₄×C₁₄₉	—	2	2	no	—
158	C₄⋊C₄×C₁₄₉	—	2	1	no	—
159	C₄⋊C₄×C₁₄₉	—	2	1	no	—
160	C₄⋊C₄×C₁₄₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₄₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
167	C₄²×C₁₄₉	—	2	2	no	—
168	C₄²×C₁₄₉	—	2	2	no	—
169	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
173	C₂³×C₁₄₉	—	2	2	no	—
174	C₂³×C₁₄₉	—	2	4	no	—
175	C₂³×C₁₄₉	—	4	2	no	—
176	C₂³×C₁₄₉	—	4	2	no	—
177	C₂³×C₁₄₉	—	4	1	no	—
178	C₂³×C₁₄₉	#120	1	1	yes	characteristic
179	Q₈×C₁₄₉	—	2	2	no	—
180	Q₈×C₁₄₉	—	2	2	no	—
181	Q₈×C₁₄₉	—	4	4	no	—
182	Q₈×C₁₄₉	—	4	2	no	—
183	Q₈×C₁₄₉	—	4	1	no	—
184	Q₈×C₁₄₉	—	4	1	no	—
185	Q₈×C₁₄₉	—	8	2	no	—
186	D₄×C₁₄₉	—	2	2	no	—
187	D₄×C₁₄₉	—	2	4	no	—
188	D₄×C₁₄₉	—	4	2	no	—
189	D₄×C₁₄₉	—	4	1	no	—
190	D₄×C₁₄₉	—	4	1	no	—
191	D₄×C₁₄₉	—	4	2	no	—
192	D₄×C₁₄₉	—	8	2	no	—
193	D₄×C₁₄₉	C₂×SD₁₆	1	4	yes	—
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	—	2	2	no	—
198	C₂×C₄×C₁₄₉	—	2	4	no	—
199	C₂×C₄×C₁₄₉	—	4	1	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	2	no	—
205	C₂×C₄×C₁₄₉	—	4	4	no	—
206	C₂×C₄×C₁₄₉	—	4	1	no	—
207	C₂×C₄×C₁₄₉	—	8	8	no	—
208	C₂×C₄×C₁₄₉	—	8	2	no	—
209	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₁₄₉	#137	1	2	yes	—
214	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₁₄₉	—	4	2	no	—
218	C₈×C₁₄₉	—	4	2	no	—
219	C₈×C₁₄₉	—	4	2	no	—
220	C₂²×C₁₄₉	—	2	1	no	—
221	C₂²×C₁₄₉	—	2	1	no	—
222	C₂²×C₁₄₉	—	2	4	no	—
223	C₂²×C₁₄₉	—	4	8	no	—
224	C₂²×C₁₄₉	—	4	2	no	—
225	C₂²×C₁₄₉	—	4	2	no	—
226	C₂²×C₁₄₉	—	8	1	no	—
227	C₂²×C₁₄₉	—	8	1	no	—
228	C₂²×C₁₄₉	—	8	1	no	—
229	C₂²×C₁₄₉	#448	1	2	yes	—
230	C₂²×C₁₄₉	C₂×#120	1	1	yes	characteristic
231	C₄×C₁₄₉	—	2	1	no	—
232	C₄×C₁₄₉	—	2	1	no	—
233	C₄×C₁₄₉	—	2	1	no	—
234	C₄×C₁₄₉	—	4	2	no	—
235	C₄×C₁₄₉	—	4	2	no	—
236	C₄×C₁₄₉	—	4	2	no	—
237	C₄×C₁₄₉	—	4	4	no	—
238	C₄×C₁₄₉	—	8	1	no	—
239	C₄×C₁₄₉	#448	1	2	yes	—
240	C₄×C₁₄₉	C₂²×SD₁₆	1	1	yes	characteristic
241	C₄×C₁₄₉	C₂×#137	1	1	yes	characteristic
242	C₄×C₁₄₉	#575	1	2	yes	—
243	C₂×C₁₄₉	—	2	2	no	—
244	C₂×C₁₄₉	—	4	4	no	—
245	C₂×C₁₄₉	—	16	1	no	—
246	C₂×C₁₄₉	C₂×#448	1	1	yes	characteristic
247	C₂×C₁₄₉	#3005	1	1	yes	characteristic
248	C₂×C₁₄₉	#3019	1	1	yes	characteristic
249	#18748	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₁₄₉	#18748	1	1	yes	characteristic, direct product factor, Sylow
251	C₂×#554	C₂×C₁₄₉	1	1	yes	characteristic, complemented
252	#3206	C₂×C₁₄₉	1	1	yes	characteristic, complemented
253	#3103	C₂×C₁₄₉	1	1	yes	characteristic, complemented
254	#3036	C₂×C₁₄₉	1	1	yes	characteristic
255	#1643	C₂×C₁₄₉	1	4	yes	complemented
256	#1622	C₂×C₁₄₉	1	4	yes	complemented
257	#1548	C₂×C₁₄₉	1	1	yes	characteristic, complemented
258	#1487	C₂×C₁₄₉	1	1	yes	characteristic, complemented
259	#1478	C₂×C₁₄₉	1	1	yes	characteristic, complemented
260	C₂×AGL(1,ℤ/8)	—	2	1	no	—
261	#554	—	2	2	no	—
262	#554	—	2	2	no	—
263	#554	—	2	2	no	—
264	#554	C₂²×C₁₄₉	1	4	yes	—
265	#532	C₂²×C₁₄₉	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
267	C₂×#125	—	2	1	no	—
268	C₂×C₂²⋊Q₈	—	2	1	no	—
269	C₂×C₂²⋊Q₈	—	2	2	no	—
270	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
271	C₂×C₄×D₄	—	2	1	no	—
272	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	—	2	1	no	—
274	#492	C₂²×C₁₄₉	1	2	yes	complemented
275	#487	C₂²×C₁₄₉	1	2	yes	complemented
276	#481	—	2	1	no	—
277	#475	C₂²×C₁₄₉	1	2	yes	complemented
278	#463	—	2	2	no	—
279	#461	—	2	2	no	—
280	#461	C₂²×C₁₄₉	1	2	yes	—
281	#460	C₂²×C₁₄₉	1	2	yes	complemented
282	#459	C₂²×C₁₄₉	1	2	yes	—
283	#448	—	2	1	no	—
284	#448	—	2	2	no	—
285	C₄×SD₁₆	—	2	2	no	—
286	#431	C₂²×C₁₄₉	1	1	yes	characteristic
287	#431	C₂²×C₁₄₉	1	1	yes	characteristic
288	#423	C₂²×C₁₄₉	1	1	yes	characteristic
289	#417	—	2	1	no	—
290	#333	C₂²×C₁₄₉	1	4	yes	complemented
291	Q₈⋊C₈	C₂²×C₁₄₉	1	4	yes	complemented
292	D₄⋊C₈	C₂²×C₁₄₉	1	4	yes	—
293	C₂×#41	—	2	1	no	—
294	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
295	C₂²×Q₈	D₄×C₁₄₉	1	2	yes	—
296	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	—	4	4	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₁₄₉	1	2	yes	—
310	#127	C₂³×C₁₄₉	1	1	yes	characteristic
311	#125	—	2	4	no	—
312	#125	—	2	4	no	—
313	#124	—	2	1	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	D₄×C₁₄₉	1	2	yes	—
323	C₄×Q₈	C₂³×C₁₄₉	1	2	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
331	C₄×D₄	C₂³×C₁₄₉	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
345	#106	—	2	2	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
349	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
350	#103	—	2	2	no	—
351	#103	—	2	4	no	—
352	#103	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	C₂³×C₁₄₉	1	2	yes	—
359	C₂⁴	—	2	1	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	8	2	no	—
367	C₂×Q₈	C₂×D₄×C₁₄₉	1	2	yes	—
368	C₂×Q₈	C₂×D₄×C₁₄₉	1	4	yes	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	SD₁₆×C₁₄₉	1	4	yes	complemented
376	C₂×D₄	C₂×D₄×C₁₄₉	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	8	4	no	—
387	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
390	SD₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	8	4	no	—
393	D₈	—	4	4	no	—
394	M₁₆	—	4	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	C₂×D₄×C₁₄₉	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₄₉	1	2	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
422	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	1	no	—
428	C₂³	#120×C₁₄₉	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	4	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	8	2	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	2	no	—
443	D₄	C₂×SD₁₆×C₁₄₉	1	4	yes	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
460	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
461	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
462	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	2	yes	—
463	C₂×C₄	#137×C₁₄₉	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	#448×C₁₄₉	1	2	yes	—
480	C₂²	C₂×#120×C₁₄₉	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	8	1	no	—
489	C₄	#448×C₁₄₉	1	2	yes	—
490	C₄	C₂²×SD₁₆×C₁₄₉	1	1	yes	characteristic
491	C₄	C₂×#137×C₁₄₉	1	1	yes	characteristic
492	C₄	#575×C₁₄₉	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	4	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₂×#448×C₁₄₉	1	1	yes	characteristic
497	C₂	#3005×C₁₄₉	1	1	yes	characteristic
498	C₂	#3019×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
prime radical	#3036×C₁₄₉	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₁₄₉	C₂	semidirect
2. #3206×C₁₄₉	C₂	semidirect
3. #3103×C₁₄₉	C₂	semidirect
5. #1643×C₁₄₉	C₂	semidirect
6. #1622×C₁₄₉	C₂	semidirect
7. #1548×C₁₄₉	C₂	semidirect
8. #1487×C₁₄₉	C₂	semidirect
9. #1478×C₁₄₉	C₂	semidirect
24. #492×C₁₄₉	C₂²	semidirect
25. #487×C₁₄₉	C₂²	semidirect
27. #475×C₁₄₉	C₂²	semidirect
31. #460×C₁₄₉	C₂²	semidirect
40. #333×C₁₄₉	C₂²	semidirect
41. Q₈⋊C₈×C₁₄₉	C₂²	semidirect
125. C₂×D₄×C₁₄₉	SD₁₆	semidirect
249. #18748	C₁₄₉	direct (N × H)
250. C₁₄₉	#18748	direct (N × H)
251. C₂×#554	C₂×C₁₄₉	semidirect
252. #3206	C₂×C₁₄₉	semidirect
253. #3103	C₂×C₁₄₉	semidirect
255. #1643	C₂×C₁₄₉	semidirect
256. #1622	C₂×C₁₄₉	semidirect
257. #1548	C₂×C₁₄₉	semidirect
258. #1487	C₂×C₁₄₉	semidirect
259. #1478	C₂×C₁₄₉	semidirect
274. #492	C₂²×C₁₄₉	semidirect
275. #487	C₂²×C₁₄₉	semidirect
277. #475	C₂²×C₁₄₉	semidirect
281. #460	C₂²×C₁₄₉	semidirect
290. #333	C₂²×C₁₄₉	semidirect
291. Q₈⋊C₈	C₂²×C₁₄₉	semidirect
375. C₂×D₄	SD₁₆×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₄₉	2
#3206×C₁₄₉	2
#3103×C₁₄₉	2
#3036×C₁₄₉	2
#1643×C₁₄₉	2
#1622×C₁₄₉	2
#1548×C₁₄₉	2
#1487×C₁₄₉	2
#1478×C₁₄₉	2
#18748	149

Subgroups — C149×#18748 #49197697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#18748 #49197697