Subgroups — C₁₄₉×#17452 #49196401

Order 38144.

1248 conjugacy classes of subgroups.

The subgroup lattice has 638 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	#2920×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#432×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1491×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#1490×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1488×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	#1477×C₁₄₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₄₉	C₄	1	1	yes	characteristic
9	C₄×#41×C₁₄₉	—	2	1	no	—
10	C₄×#41×C₁₄₉	—	2	1	no	—
11	C₄×#41×C₁₄₉	—	2	1	no	—
12	C₄×#41×C₁₄₉	—	2	1	no	—
13	C₄×#41×C₁₄₉	C₄	1	2	yes	—
14	C₄×#41×C₁₄₉	C₄	1	2	yes	—
15	C₄×#41×C₁₄₉	C₂²	1	2	yes	—
16	C₄×#41×C₁₄₉	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₄₉	—	2	1	no	—
24	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic
25	C₂²×C₄²×C₁₄₉	—	2	1	no	—
26	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
27	#432×C₁₄₉	—	2	1	no	—
28	#432×C₁₄₉	—	2	1	no	—
29	#432×C₁₄₉	—	2	1	no	—
30	#432×C₁₄₉	—	2	1	no	—
31	#432×C₁₄₉	C₂²	1	2	yes	—
32	#432×C₁₄₉	C₂²	1	2	yes	complemented
33	#431×C₁₄₉	C₂²	1	2	yes	complemented
34	#431×C₁₄₉	C₂²	1	2	yes	complemented
35	#423×C₁₄₉	—	2	1	no	—
36	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	2	yes	complemented
37	#407×C₁₄₉	—	2	1	no	—
38	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
39	C₄×M₁₆×C₁₄₉	C₂²	1	2	yes	—
40	C₂×#97×C₁₄₉	—	2	1	no	—
41	Q₈⋊C₈×C₁₄₉	C₂²	1	8	yes	complemented
42	D₄⋊C₈×C₁₄₉	C₂²	1	8	yes	complemented
43	C₂×#41×C₁₄₉	—	2	8	no	—
44	C₂×#41×C₁₄₉	—	2	1	no	—
45	C₂×#41×C₁₄₉	—	2	1	no	—
46	C₂×#41×C₁₄₉	C₂×C₄	1	2	yes	—
47	C₂×#41×C₁₄₉	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₄₉	—	2	1	no	—
50	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₄₉	—	2	1	no	—
52	C₂³×C₄×C₁₄₉	—	2	1	no	—
53	C₂³×C₄×C₁₄₉	—	2	1	no	—
54	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
57	C₂×M₁₆×C₁₄₉	—	2	2	no	—
58	C₂²×C₈×C₁₄₉	—	2	2	no	—
59	C₄×Q₈×C₁₄₉	—	2	1	no	—
60	C₄×Q₈×C₁₄₉	—	2	1	no	—
61	C₄×Q₈×C₁₄₉	—	2	1	no	—
62	C₄×Q₈×C₁₄₉	—	2	1	no	—
63	C₄×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
65	C₄×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
66	C₄×Q₈×C₁₄₉	C₂³	1	2	yes	—
67	C₄×D₄×C₁₄₉	—	2	2	no	—
68	C₄×D₄×C₁₄₉	—	2	2	no	—
69	C₄×D₄×C₁₄₉	—	2	2	no	—
70	C₄×D₄×C₁₄₉	—	2	2	no	—
71	C₄×D₄×C₁₄₉	—	2	2	no	—
72	C₄×D₄×C₁₄₉	—	2	2	no	—
73	C₄×D₄×C₁₄₉	—	2	2	no	—
74	C₄×D₄×C₁₄₉	—	2	2	no	—
75	C₄×D₄×C₁₄₉	—	2	1	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	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
81	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₁₄₉	C₂³	1	2	yes	—
83	#117×C₁₄₉	—	2	1	no	—
84	#117×C₁₄₉	—	2	1	no	—
85	#117×C₁₄₉	—	2	2	no	—
86	#117×C₁₄₉	—	2	2	no	—
87	#117×C₁₄₉	—	2	2	no	—
88	#117×C₁₄₉	—	2	2	no	—
89	#117×C₁₄₉	C₂×C₄	1	2	yes	—
90	#117×C₁₄₉	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
98	C₂×C₄²×C₁₄₉	—	2	1	no	—
99	C₂×C₄²×C₁₄₉	—	2	1	no	—
100	C₂×C₄²×C₁₄₉	—	2	1	no	—
101	C₂×C₄²×C₁₄₉	—	2	2	no	—
102	C₂×C₄²×C₁₄₉	—	2	2	no	—
103	C₂×C₄²×C₁₄₉	—	2	2	no	—
104	C₂×C₄²×C₁₄₉	—	2	2	no	—
105	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₁₄₉	—	2	2	no	—
118	C₄⋊C₈×C₁₄₉	—	2	2	no	—
119	C₄⋊C₈×C₁₄₉	—	2	2	no	—
120	C₄⋊C₈×C₁₄₉	C₂³	1	4	yes	—
121	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
122	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
123	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
124	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
125	#97×C₁₄₉	—	2	2	no	—
126	#97×C₁₄₉	—	2	2	no	—
127	#97×C₁₄₉	—	2	2	no	—
128	C₄×C₈×C₁₄₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₄₉	—	2	1	no	—
130	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
131	#41×C₁₄₉	—	2	8	no	—
132	#41×C₁₄₉	—	2	8	no	—
133	#41×C₁₄₉	—	2	4	no	—
134	#41×C₁₄₉	—	2	4	no	—
135	#41×C₁₄₉	—	2	4	no	—
136	#41×C₁₄₉	M₁₆	1	8	yes	complemented
137	C₂×Q₈×C₁₄₉	—	2	4	no	—
138	C₂×Q₈×C₁₄₉	—	2	1	no	—
139	C₂×Q₈×C₁₄₉	C₂²×C₄	1	2	yes	—
140	C₂×D₄×C₁₄₉	—	2	8	no	—
141	C₂×D₄×C₁₄₉	—	2	2	no	—
142	C₂×D₄×C₁₄₉	—	2	2	no	—
143	C₂×D₄×C₁₄₉	—	2	4	no	—
144	C₂×D₄×C₁₄₉	—	2	1	no	—
145	C₂×D₄×C₁₄₉	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₄₉	—	2	8	no	—
147	C₂²×C₄×C₁₄₉	—	2	1	no	—
148	C₂²×C₄×C₁₄₉	—	2	2	no	—
149	C₂²×C₄×C₁₄₉	—	2	2	no	—
150	C₂²×C₄×C₁₄₉	—	2	4	no	—
151	C₂²×C₄×C₁₄₉	—	2	1	no	—
152	C₂²×C₄×C₁₄₉	—	2	1	no	—
153	C₂²×C₄×C₁₄₉	—	2	2	no	—
154	C₂²×C₄×C₁₄₉	—	2	2	no	—
155	C₂²×C₄×C₁₄₉	—	2	2	no	—
156	C₂²×C₄×C₁₄₉	—	2	2	no	—
157	C₂²×C₄×C₁₄₉	—	4	2	no	—
158	C₂²×C₄×C₁₄₉	—	4	2	no	—
159	C₂²×C₄×C₁₄₉	—	4	4	no	—
160	C₂²×C₄×C₁₄₉	—	4	4	no	—
161	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
179	M₁₆×C₁₄₉	—	4	4	no	—
180	C₂×C₈×C₁₄₉	—	2	4	no	—
181	C₂×C₈×C₁₄₉	—	2	4	no	—
182	C₂×C₈×C₁₄₉	—	4	4	no	—
183	C₄⋊C₄×C₁₄₉	—	2	2	no	—
184	C₄⋊C₄×C₁₄₉	—	2	2	no	—
185	C₄⋊C₄×C₁₄₉	—	2	2	no	—
186	C₄⋊C₄×C₁₄₉	—	2	1	no	—
187	C₄⋊C₄×C₁₄₉	—	2	1	no	—
188	C₄⋊C₄×C₁₄₉	—	2	2	no	—
189	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
191	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
197	C₄²×C₁₄₉	—	2	2	no	—
198	C₄²×C₁₄₉	—	2	2	no	—
199	C₄²×C₁₄₉	—	2	2	no	—
200	C₄²×C₁₄₉	—	2	2	no	—
201	C₄²×C₁₄₉	—	2	2	no	—
202	C₄²×C₁₄₉	—	2	2	no	—
203	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
219	C₂³×C₁₄₉	—	2	4	no	—
220	C₂³×C₁₄₉	—	2	2	no	—
221	C₂³×C₁₄₉	—	2	2	no	—
222	C₂³×C₁₄₉	—	2	2	no	—
223	C₂³×C₁₄₉	—	4	1	no	—
224	C₂³×C₁₄₉	—	4	2	no	—
225	C₂³×C₁₄₉	—	4	2	no	—
226	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	Q₈×C₁₄₉	—	2	4	no	—
230	Q₈×C₁₄₉	—	2	2	no	—
231	Q₈×C₁₄₉	C₂×M₁₆	1	4	yes	—
232	D₄×C₁₄₉	—	2	8	no	—
233	D₄×C₁₄₉	—	2	4	no	—
234	D₄×C₁₄₉	—	2	8	no	—
235	D₄×C₁₄₉	—	2	2	no	—
236	D₄×C₁₄₉	C₂×M₁₆	1	4	yes	—
237	C₂×C₄×C₁₄₉	—	2	4	no	—
238	C₂×C₄×C₁₄₉	—	2	8	no	—
239	C₂×C₄×C₁₄₉	—	2	2	no	—
240	C₂×C₄×C₁₄₉	—	2	2	no	—
241	C₂×C₄×C₁₄₉	—	2	2	no	—
242	C₂×C₄×C₁₄₉	—	2	2	no	—
243	C₂×C₄×C₁₄₉	—	2	2	no	—
244	C₂×C₄×C₁₄₉	—	2	2	no	—
245	C₂×C₄×C₁₄₉	—	2	2	no	—
246	C₂×C₄×C₁₄₉	—	2	2	no	—
247	C₂×C₄×C₁₄₉	—	2	2	no	—
248	C₂×C₄×C₁₄₉	—	2	2	no	—
249	C₂×C₄×C₁₄₉	—	2	8	no	—
250	C₂×C₄×C₁₄₉	—	2	2	no	—
251	C₂×C₄×C₁₄₉	—	2	2	no	—
252	C₂×C₄×C₁₄₉	—	2	2	no	—
253	C₂×C₄×C₁₄₉	—	4	1	no	—
254	C₂×C₄×C₁₄₉	—	4	1	no	—
255	C₂×C₄×C₁₄₉	—	4	1	no	—
256	C₂×C₄×C₁₄₉	—	4	1	no	—
257	C₂×C₄×C₁₄₉	—	4	1	no	—
258	C₂×C₄×C₁₄₉	—	4	1	no	—
259	C₂×C₄×C₁₄₉	—	4	1	no	—
260	C₂×C₄×C₁₄₉	—	4	4	no	—
261	C₂×C₄×C₁₄₉	—	4	4	no	—
262	C₂×C₄×C₁₄₉	—	4	4	no	—
263	C₂×C₄×C₁₄₉	—	4	2	no	—
264	C₂×C₄×C₁₄₉	—	4	2	no	—
265	C₂×C₄×C₁₄₉	—	4	4	no	—
266	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₁₄₉	C₂×M₁₆	1	4	yes	—
276	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₁₄₉	—	4	4	no	—
280	C₈×C₁₄₉	—	4	4	no	—
281	C₂²×C₁₄₉	—	2	1	no	—
282	C₂²×C₁₄₉	—	2	1	no	—
283	C₂²×C₁₄₉	—	2	1	no	—
284	C₂²×C₁₄₉	—	2	1	no	—
285	C₂²×C₁₄₉	—	2	1	no	—
286	C₂²×C₁₄₉	—	2	4	no	—
287	C₂²×C₁₄₉	—	2	1	no	—
288	C₂²×C₁₄₉	—	2	1	no	—
289	C₂²×C₁₄₉	—	4	4	no	—
290	C₂²×C₁₄₉	—	4	8	no	—
291	C₂²×C₁₄₉	—	4	2	no	—
292	C₂²×C₁₄₉	—	4	2	no	—
293	C₂²×C₁₄₉	#407	1	2	yes	—
294	C₂²×C₁₄₉	#421	1	2	yes	—
295	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₄×C₁₄₉	—	2	1	no	—
297	C₄×C₁₄₉	—	2	4	no	—
298	C₄×C₁₄₉	—	2	1	no	—
299	C₄×C₁₄₉	—	2	1	no	—
300	C₄×C₁₄₉	—	2	1	no	—
301	C₄×C₁₄₉	—	2	1	no	—
302	C₄×C₁₄₉	—	2	1	no	—
303	C₄×C₁₄₉	—	2	1	no	—
304	C₄×C₁₄₉	—	2	1	no	—
305	C₄×C₁₄₉	—	2	1	no	—
306	C₄×C₁₄₉	—	4	2	no	—
307	C₄×C₁₄₉	—	4	2	no	—
308	C₄×C₁₄₉	#407	1	2	yes	—
309	C₄×C₁₄₉	C₂²×M₁₆	1	2	yes	—
310	C₄×C₁₄₉	#575	1	2	yes	—
311	C₂×C₁₄₉	—	2	2	no	—
312	C₂×C₁₄₉	—	2	2	no	—
313	C₂×C₁₄₉	—	4	1	no	—
314	C₂×C₁₄₉	—	4	4	no	—
315	C₂×C₁₄₉	C₂×#407	1	1	yes	characteristic
316	C₂×C₁₄₉	#2896	1	1	yes	characteristic
317	C₂×C₁₄₉	C₂×#421	1	1	yes	characteristic
318	#17452	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₁₄₉	#17452	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×C₄×#41	C₂×C₁₄₉	1	1	yes	characteristic
321	#2920	C₂×C₁₄₉	1	1	yes	characteristic, complemented
322	C₂×#432	C₂×C₁₄₉	1	1	yes	characteristic, complemented
323	#1491	C₂×C₁₄₉	1	2	yes	complemented
324	#1490	C₂×C₁₄₉	1	2	yes	complemented
325	#1488	C₂×C₁₄₉	1	4	yes	complemented
326	#1477	C₂×C₁₄₉	1	4	yes	complemented
327	C₂²×#41	C₄×C₁₄₉	1	1	yes	characteristic
328	C₄×#41	—	2	1	no	—
329	C₄×#41	—	2	1	no	—
330	C₄×#41	—	2	1	no	—
331	C₄×#41	—	2	1	no	—
332	C₄×#41	C₄×C₁₄₉	1	2	yes	—
333	C₄×#41	C₄×C₁₄₉	1	2	yes	—
334	C₄×#41	C₂²×C₁₄₉	1	2	yes	—
335	C₄×#41	C₂²×C₁₄₉	1	2	yes	—
336	C₂×C₄×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
338	C₂×C₄×D₄	—	2	1	no	—
339	C₂×C₄×D₄	—	2	1	no	—
340	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
342	C₂×#117	—	2	1	no	—
343	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic
344	C₂²×C₄²	—	2	1	no	—
345	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
346	#432	—	2	1	no	—
347	#432	—	2	1	no	—
348	#432	—	2	1	no	—
349	#432	—	2	1	no	—
350	#432	C₂²×C₁₄₉	1	2	yes	—
351	#432	C₂²×C₁₄₉	1	2	yes	complemented
352	#431	C₂²×C₁₄₉	1	2	yes	complemented
353	#431	C₂²×C₁₄₉	1	2	yes	complemented
354	#423	—	2	1	no	—
355	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	2	yes	complemented
356	#407	—	2	1	no	—
357	C₂×C₂²⋊C₈	—	2	1	no	—
358	C₄×M₁₆	C₂²×C₁₄₉	1	2	yes	—
359	C₂×#97	—	2	1	no	—
360	Q₈⋊C₈	C₂²×C₁₄₉	1	8	yes	complemented
361	D₄⋊C₈	C₂²×C₁₄₉	1	8	yes	complemented
362	C₂×#41	—	2	8	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂×C₄×C₁₄₉	1	2	yes	—
366	C₂×#41	C₂×C₄×C₁₄₉	1	2	yes	—
367	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
374	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
375	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
376	C₂×M₁₆	—	2	2	no	—
377	C₂²×C₈	—	2	2	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
383	C₄×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
384	C₄×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
385	C₄×Q₈	C₂³×C₁₄₉	1	2	yes	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
399	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
400	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
401	C₄×D₄	C₂³×C₁₄₉	1	2	yes	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	2	no	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	C₂×C₄×C₁₄₉	1	2	yes	—
409	#117	C₂×C₄×C₁₄₉	1	2	yes	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	2	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	—	2	2	no	—
424	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
425	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
426	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
427	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
430	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
432	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
436	C₄⋊C₈	—	2	2	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	C₂³×C₁₄₉	1	4	yes	—
440	C₂²⋊C₈	—	2	2	no	—
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	#97	—	2	2	no	—
445	#97	—	2	2	no	—
446	#97	—	2	2	no	—
447	C₄×C₈	C₂³×C₁₄₉	1	4	yes	—
448	C₂⁴	—	2	1	no	—
449	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
450	#41	—	2	8	no	—
451	#41	—	2	8	no	—
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	M₁₆×C₁₄₉	1	8	yes	complemented
456	C₂×Q₈	—	2	4	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	C₂²×C₄×C₁₄₉	1	2	yes	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	C₂²×C₄×C₁₄₉	1	2	yes	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
481	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
482	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
483	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
484	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
490	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
498	M₁₆	—	4	4	no	—
499	C₂×C₈	—	2	4	no	—
500	C₂×C₈	—	2	4	no	—
501	C₂×C₈	—	4	4	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
523	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
524	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
525	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
528	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
529	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
530	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
536	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
537	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
538	C₂³	—	2	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
546	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
547	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
548	Q₈	—	2	4	no	—
549	Q₈	—	2	2	no	—
550	Q₈	C₂×M₁₆×C₁₄₉	1	4	yes	—
551	D₄	—	2	8	no	—
552	D₄	—	2	4	no	—
553	D₄	—	2	8	no	—
554	D₄	—	2	2	no	—
555	D₄	C₂×M₁₆×C₁₄₉	1	4	yes	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
586	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
587	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
588	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
590	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
594	C₂×C₄	C₂×M₁₆×C₁₄₉	1	4	yes	—
595	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
598	C₈	—	4	4	no	—
599	C₈	—	4	4	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	8	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	#407×C₁₄₉	1	2	yes	—
613	C₂²	#421×C₁₄₉	1	2	yes	—
614	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	4	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	#407×C₁₄₉	1	2	yes	—
628	C₄	C₂²×M₁₆×C₁₄₉	1	2	yes	—
629	C₄	#575×C₁₄₉	1	2	yes	—
630	C₂	—	2	2	no	—
631	C₂	—	2	2	no	—
632	C₂	—	4	1	no	—
633	C₂	—	4	4	no	—
634	C₂	C₂×#407×C₁₄₉	1	1	yes	characteristic
635	C₂	#2896×C₁₄₉	1	1	yes	characteristic
636	C₂	C₂×#421×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₄₉	C₄
LCS	G ▷ C₂×C₄ ▷ 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. #2920×C₁₄₉	C₂	semidirect
3. C₂×#432×C₁₄₉	C₂	semidirect
4. #1491×C₁₄₉	C₂	semidirect
5. #1490×C₁₄₉	C₂	semidirect
6. #1488×C₁₄₉	C₂	semidirect
7. #1477×C₁₄₉	C₂	semidirect
32. #432×C₁₄₉	C₂²	semidirect
33. #431×C₁₄₉	C₂²	semidirect
34. #431×C₁₄₉	C₂²	semidirect
36. C₂×C₄⋊C₈×C₁₄₉	C₂²	semidirect
41. Q₈⋊C₈×C₁₄₉	C₂²	semidirect
42. D₄⋊C₈×C₁₄₉	C₂²	semidirect
136. #41×C₁₄₉	M₁₆	semidirect
318. #17452	C₁₄₉	direct (N × H)
319. C₁₄₉	#17452	direct (N × H)
321. #2920	C₂×C₁₄₉	semidirect
322. C₂×#432	C₂×C₁₄₉	semidirect
323. #1491	C₂×C₁₄₉	semidirect
324. #1490	C₂×C₁₄₉	semidirect
325. #1488	C₂×C₁₄₉	semidirect
326. #1477	C₂×C₁₄₉	semidirect
351. #432	C₂²×C₁₄₉	semidirect
352. #431	C₂²×C₁₄₉	semidirect
353. #431	C₂²×C₁₄₉	semidirect
355. C₂×C₄⋊C₈	C₂²×C₁₄₉	semidirect
360. Q₈⋊C₈	C₂²×C₁₄₉	semidirect
361. D₄⋊C₈	C₂²×C₁₄₉	semidirect
455. #41	M₁₆×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
#2920×C₁₄₉	2
C₂×#432×C₁₄₉	2
#1491×C₁₄₉	2
#1490×C₁₄₉	2
#1488×C₁₄₉	2
#1477×C₁₄₉	2
#17452	149

Subgroups — C149×#17452 #49196401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17452 #49196401