Subgroups — C₁₄₉×#17418 #49196367

Order 38144.

1002 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2924×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1471×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1469×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1465×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1464×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1459×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1458×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	#555×C₁₄₉	—	2	2	no	—
10	#555×C₁₄₉	—	2	2	no	—
11	#555×C₁₄₉	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×#124×C₁₄₉	C₄	1	2	yes	—
14	C₂×#124×C₁₄₉	C₂²	1	2	yes	—
15	C₂×#121×C₁₄₉	C₄	1	2	yes	—
16	C₂×#121×C₁₄₉	C₄	1	1	yes	characteristic
17	C₂×#121×C₁₄₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic
21	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
22	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
23	#433×C₁₄₉	—	2	4	no	—
24	#432×C₁₄₉	C₂²	1	4	yes	—
25	#431×C₁₄₉	C₂²	1	4	yes	—
26	#424×C₁₄₉	—	2	2	no	—
27	#407×C₁₄₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
29	#405×C₁₄₉	—	2	2	no	—
30	#324×C₁₄₉	C₂²	1	1	yes	characteristic
31	#324×C₁₄₉	C₂²	1	2	yes	—
32	#324×C₁₄₉	C₂²	1	1	yes	characteristic
33	#323×C₁₄₉	C₂²	1	4	yes	—
34	#323×C₁₄₉	C₂²	1	2	yes	—
35	#323×C₁₄₉	C₂²	1	4	yes	—
36	#323×C₁₄₉	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₄₉	—	2	2	no	—
46	C₂²×C₈×C₁₄₉	—	2	2	no	—
47	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
48	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
49	#124×C₁₄₉	—	2	4	no	—
50	#124×C₁₄₉	—	2	4	no	—
51	#124×C₁₄₉	—	2	4	no	—
52	#124×C₁₄₉	—	2	4	no	—
53	#121×C₁₄₉	—	2	2	no	—
54	#121×C₁₄₉	—	2	2	no	—
55	#121×C₁₄₉	—	2	2	no	—
56	#121×C₁₄₉	—	2	2	no	—
57	#121×C₁₄₉	—	2	4	no	—
58	#121×C₁₄₉	—	2	4	no	—
59	C₄×D₄×C₁₄₉	—	2	2	no	—
60	C₄×D₄×C₁₄₉	—	2	2	no	—
61	C₄×D₄×C₁₄₉	—	2	2	no	—
62	C₄×D₄×C₁₄₉	—	2	1	no	—
63	C₄×D₄×C₁₄₉	—	2	1	no	—
64	#117×C₁₄₉	—	2	2	no	—
65	#117×C₁₄₉	—	2	1	no	—
66	#117×C₁₄₉	—	2	1	no	—
67	#117×C₁₄₉	—	2	4	no	—
68	#117×C₁₄₉	—	2	4	no	—
69	#117×C₁₄₉	D₄	1	2	yes	—
70	#117×C₁₄₉	D₄	1	2	yes	—
71	#117×C₁₄₉	D₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₄₉	—	2	4	no	—
88	C₄⋊C₈×C₁₄₉	—	2	4	no	—
89	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
90	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
91	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
93	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
94	#97×C₁₄₉	—	2	4	no	—
95	C₄×C₈×C₁₄₉	—	2	4	no	—
96	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
98	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₄₉	—	2	4	no	—
100	C₂×Q₈×C₁₄₉	—	8	2	no	—
101	C₂×D₄×C₁₄₉	—	2	2	no	—
102	C₂×D₄×C₁₄₉	—	2	4	no	—
103	C₂×D₄×C₁₄₉	—	2	1	no	—
104	C₂×D₄×C₁₄₉	—	2	1	no	—
105	C₂×D₄×C₁₄₉	—	2	4	no	—
106	C₂×D₄×C₁₄₉	—	2	2	no	—
107	C₂×D₄×C₁₄₉	—	4	1	no	—
108	C₂×D₄×C₁₄₉	—	4	2	no	—
109	C₂×D₄×C₁₄₉	—	8	2	no	—
110	C₂×D₄×C₁₄₉	—	8	2	no	—
111	C₂²×C₄×C₁₄₉	—	2	2	no	—
112	C₂²×C₄×C₁₄₉	—	2	2	no	—
113	C₂²×C₄×C₁₄₉	—	2	1	no	—
114	C₂²×C₄×C₁₄₉	—	2	1	no	—
115	C₂²×C₄×C₁₄₉	—	2	4	no	—
116	C₂²×C₄×C₁₄₉	—	4	2	no	—
117	C₂²×C₄×C₁₄₉	—	4	2	no	—
118	C₂²×C₄×C₁₄₉	—	4	2	no	—
119	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₁₄₉	—	4	4	no	—
130	C₂×C₈×C₁₄₉	—	2	2	no	—
131	C₂×C₈×C₁₄₉	—	2	4	no	—
132	C₂×C₈×C₁₄₉	—	2	2	no	—
133	C₂×C₈×C₁₄₉	—	4	4	no	—
134	C₄⋊C₄×C₁₄₉	—	2	4	no	—
135	C₄⋊C₄×C₁₄₉	—	2	1	no	—
136	C₄⋊C₄×C₁₄₉	—	2	1	no	—
137	C₄⋊C₄×C₁₄₉	—	2	2	no	—
138	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
139	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
142	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
143	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
151	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
152	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
153	C₄²×C₁₄₉	—	2	2	no	—
154	C₄²×C₁₄₉	—	2	2	no	—
155	C₄²×C₁₄₉	—	2	1	no	—
156	C₄²×C₁₄₉	—	2	1	no	—
157	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
158	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
159	C₂³×C₁₄₉	—	2	1	no	—
160	C₂³×C₁₄₉	—	2	1	no	—
161	C₂³×C₁₄₉	—	2	2	no	—
162	C₂³×C₁₄₉	—	2	1	no	—
163	C₂³×C₁₄₉	—	2	2	no	—
164	C₂³×C₁₄₉	—	2	1	no	—
165	C₂³×C₁₄₉	—	2	2	no	—
166	C₂³×C₁₄₉	—	2	1	no	—
167	C₂³×C₁₄₉	—	4	1	no	—
168	C₂³×C₁₄₉	—	4	1	no	—
169	C₂³×C₁₄₉	—	4	1	no	—
170	C₂³×C₁₄₉	—	4	2	no	—
171	C₂³×C₁₄₉	—	4	1	no	—
172	C₂³×C₁₄₉	—	4	2	no	—
173	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
175	Q₈×C₁₄₉	—	8	4	no	—
176	D₄×C₁₄₉	—	4	4	no	—
177	D₄×C₁₄₉	—	4	2	no	—
178	D₄×C₁₄₉	—	4	2	no	—
179	D₄×C₁₄₉	—	8	4	no	—
180	D₄×C₁₄₉	—	8	4	no	—
181	C₂×C₄×C₁₄₉	—	2	1	no	—
182	C₂×C₄×C₁₄₉	—	2	2	no	—
183	C₂×C₄×C₁₄₉	—	2	1	no	—
184	C₂×C₄×C₁₄₉	—	2	2	no	—
185	C₂×C₄×C₁₄₉	—	2	4	no	—
186	C₂×C₄×C₁₄₉	—	2	2	no	—
187	C₂×C₄×C₁₄₉	—	2	1	no	—
188	C₂×C₄×C₁₄₉	—	2	1	no	—
189	C₂×C₄×C₁₄₉	—	2	2	no	—
190	C₂×C₄×C₁₄₉	—	4	2	no	—
191	C₂×C₄×C₁₄₉	—	4	1	no	—
192	C₂×C₄×C₁₄₉	—	4	2	no	—
193	C₂×C₄×C₁₄₉	—	4	4	no	—
194	C₂×C₄×C₁₄₉	—	4	4	no	—
195	C₂×C₄×C₁₄₉	—	4	2	no	—
196	C₂×C₄×C₁₄₉	—	4	2	no	—
197	C₂×C₄×C₁₄₉	—	4	1	no	—
198	C₂×C₄×C₁₄₉	—	4	2	no	—
199	C₂×C₄×C₁₄₉	—	4	1	no	—
200	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
204	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₄₉	#131	1	2	yes	—
206	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
207	C₈×C₁₄₉	—	4	2	no	—
208	C₈×C₁₄₉	—	4	2	no	—
209	C₈×C₁₄₉	—	4	4	no	—
210	C₂²×C₁₄₉	—	2	1	no	—
211	C₂²×C₁₄₉	—	2	1	no	—
212	C₂²×C₁₄₉	—	2	2	no	—
213	C₂²×C₁₄₉	—	2	2	no	—
214	C₂²×C₁₄₉	—	2	2	no	—
215	C₂²×C₁₄₉	—	4	2	no	—
216	C₂²×C₁₄₉	—	4	1	no	—
217	C₂²×C₁₄₉	—	4	1	no	—
218	C₂²×C₁₄₉	—	4	2	no	—
219	C₂²×C₁₄₉	—	4	1	no	—
220	C₂²×C₁₄₉	—	4	2	no	—
221	C₂²×C₁₄₉	—	8	1	no	—
222	C₂²×C₁₄₉	—	8	1	no	—
223	C₂²×C₁₄₉	—	8	2	no	—
224	C₂²×C₁₄₉	—	8	1	no	—
225	C₂²×C₁₄₉	—	8	2	no	—
226	C₂²×C₁₄₉	—	8	1	no	—
227	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₄₉	C₂×#131	1	1	yes	characteristic
229	C₂²×C₁₄₉	#568	1	1	yes	characteristic
230	C₄×C₁₄₉	—	2	2	no	—
231	C₄×C₁₄₉	—	2	2	no	—
232	C₄×C₁₄₉	—	2	2	no	—
233	C₄×C₁₄₉	—	2	2	no	—
234	C₄×C₁₄₉	—	2	1	no	—
235	C₄×C₁₄₉	—	2	4	no	—
236	C₄×C₁₄₉	—	4	1	no	—
237	C₄×C₁₄₉	—	4	2	no	—
238	C₄×C₁₄₉	—	4	1	no	—
239	C₄×C₁₄₉	#410	1	2	yes	—
240	C₂×C₁₄₉	—	2	1	no	—
241	C₂×C₁₄₉	—	2	1	no	—
242	C₂×C₁₄₉	—	4	2	no	—
243	C₂×C₁₄₉	—	8	2	no	—
244	C₂×C₁₄₉	—	8	1	no	—
245	C₂×C₁₄₉	#2880	1	1	yes	characteristic
246	C₂×C₁₄₉	C₂×#410	1	1	yes	characteristic
247	C₂×C₁₄₉	#2888	1	1	yes	characteristic
248	#17418	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₁₄₉	#17418	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#555	C₂×C₁₄₉	1	1	yes	characteristic
251	#2924	C₂×C₁₄₉	1	2	yes	complemented
252	#1471	C₂×C₁₄₉	1	2	yes	complemented
253	#1469	C₂×C₁₄₉	1	4	yes	complemented
254	#1465	C₂×C₁₄₉	1	1	yes	characteristic, complemented
255	#1464	C₂×C₁₄₉	1	2	yes	complemented
256	#1459	C₂×C₁₄₉	1	1	yes	characteristic, complemented
257	#1458	C₂×C₁₄₉	1	2	yes	complemented
258	#555	—	2	2	no	—
259	#555	—	2	2	no	—
260	#555	—	2	4	no	—
261	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
262	C₂×#124	C₄×C₁₄₉	1	2	yes	—
263	C₂×#124	C₂²×C₁₄₉	1	2	yes	—
264	C₂×#121	C₄×C₁₄₉	1	2	yes	—
265	C₂×#121	C₄×C₁₄₉	1	1	yes	characteristic
266	C₂×#121	C₂²×C₁₄₉	1	1	yes	characteristic
267	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
269	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic
270	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
271	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
272	#433	—	2	4	no	—
273	#432	C₂²×C₁₄₉	1	4	yes	—
274	#431	C₂²×C₁₄₉	1	4	yes	—
275	#424	—	2	2	no	—
276	#407	C₂²×C₁₄₉	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
278	#405	—	2	2	no	—
279	#324	C₂²×C₁₄₉	1	1	yes	characteristic
280	#324	C₂²×C₁₄₉	1	2	yes	—
281	#324	C₂²×C₁₄₉	1	1	yes	characteristic
282	#323	C₂²×C₁₄₉	1	4	yes	—
283	#323	C₂²×C₁₄₉	1	2	yes	—
284	#323	C₂²×C₁₄₉	1	4	yes	—
285	#323	C₂²×C₁₄₉	1	2	yes	—
286	C₂²×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
287	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
288	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
289	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
290	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
291	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
292	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
294	C₂×M₁₆	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	#124	—	2	4	no	—
299	#124	—	2	4	no	—
300	#124	—	2	4	no	—
301	#124	—	2	4	no	—
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	4	no	—
307	#121	—	2	4	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	#117	—	2	2	no	—
314	#117	—	2	1	no	—
315	#117	—	2	1	no	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	#117	D₄×C₁₄₉	1	2	yes	—
319	#117	D₄×C₁₄₉	1	2	yes	—
320	#117	D₄×C₁₄₉	1	4	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
333	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
334	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
336	C₄⋊C₈	—	2	4	no	—
337	C₄⋊C₈	—	2	4	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
341	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
342	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
343	#97	—	2	4	no	—
344	C₄×C₈	—	2	4	no	—
345	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
346	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
347	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	8	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	8	2	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
374	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
378	M₁₆	—	4	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
388	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
389	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
390	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
391	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
401	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
407	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
423	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
424	Q₈	—	8	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	4	no	—
429	D₄	—	8	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
450	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
451	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
452	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
453	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
454	C₂×C₄	#131×C₁₄₉	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	4	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	1	no	—
476	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
477	C₂²	C₂×#131×C₁₄₉	1	1	yes	characteristic
478	C₂²	#568×C₁₄₉	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	4	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	1	no	—
488	C₄	#410×C₁₄₉	1	2	yes	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	4	2	no	—
492	C₂	—	8	2	no	—
493	C₂	—	8	1	no	—
494	C₂	#2880×C₁₄₉	1	1	yes	characteristic
495	C₂	C₂×#410×C₁₄₉	1	1	yes	characteristic
496	C₂	#2888×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂×#555×C₁₄₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×#117×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2924×C₁₄₉	C₂	semidirect
3. #1471×C₁₄₉	C₂	semidirect
4. #1469×C₁₄₉	C₂	semidirect
5. #1465×C₁₄₉	C₂	semidirect
6. #1464×C₁₄₉	C₂	semidirect
7. #1459×C₁₄₉	C₂	semidirect
8. #1458×C₁₄₉	C₂	semidirect
248. #17418	C₁₄₉	direct (N × H)
249. C₁₄₉	#17418	direct (N × H)
251. #2924	C₂×C₁₄₉	semidirect
252. #1471	C₂×C₁₄₉	semidirect
253. #1469	C₂×C₁₄₉	semidirect
254. #1465	C₂×C₁₄₉	semidirect
255. #1464	C₂×C₁₄₉	semidirect
256. #1459	C₂×C₁₄₉	semidirect
257. #1458	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×#555×C₁₄₉	2
#2924×C₁₄₉	2
#1471×C₁₄₉	2
#1469×C₁₄₉	2
#1465×C₁₄₉	2
#1464×C₁₄₉	2
#1459×C₁₄₉	2
#1458×C₁₄₉	2
#17418	149

Subgroups — C149×#17418 #49196367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17418 #49196367