Subgroups — C₁₄₉×#16244 #49195193

Order 38144.

1034 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1445×C₁₄₉	C₂	1	2	yes	maximal
2	#1445×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#1442×C₁₄₉	C₂	1	2	yes	maximal
4	#1442×C₁₄₉	C₂	1	4	yes	maximal
5	#1436×C₁₄₉	C₂	1	4	yes	maximal
6	#1436×C₁₄₉	C₂	1	2	yes	maximal
7	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₄₉	C₂²	1	2	yes	—
11	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
12	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
13	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
14	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
15	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
16	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
17	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
18	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
19	C₂×#95×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#95×C₁₄₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₄₉	C₂³	1	4	yes	—
22	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
23	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
24	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
25	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
26	C₂³×C₄×C₁₄₉	C₂³	1	4	yes	—
27	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
28	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₄₉	—	4	1	no	—
30	C₂×C₄⋊C₄×C₁₄₉	—	4	1	no	—
31	C₂×C₄⋊C₄×C₁₄₉	—	4	2	no	—
32	C₂×C₄⋊C₄×C₁₄₉	—	4	2	no	—
33	C₂×C₄⋊C₄×C₁₄₉	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₄₉	Q₈	1	4	yes	—
35	C₂×C₄²×C₁₄₉	—	4	4	no	—
36	C₂×C₄²×C₁₄₉	—	4	2	no	—
37	#95×C₁₄₉	—	2	8	no	—
38	#95×C₁₄₉	—	2	8	no	—
39	#95×C₁₄₉	—	2	8	no	—
40	#95×C₁₄₉	—	2	8	no	—
41	#95×C₁₄₉	—	2	4	no	—
42	#95×C₁₄₉	—	4	2	no	—
43	#95×C₁₄₉	—	4	4	no	—
44	#95×C₁₄₉	—	4	1	no	—
45	#95×C₁₄₉	—	4	1	no	—
46	#95×C₁₄₉	—	4	2	no	—
47	C₂⁴×C₁₄₉	C₂⁴	1	1	yes	characteristic
48	C₂²×C₄×C₁₄₉	—	2	4	no	—
49	C₂²×C₄×C₁₄₉	—	2	4	no	—
50	C₂²×C₄×C₁₄₉	—	2	4	no	—
51	C₂²×C₄×C₁₄₉	—	2	4	no	—
52	C₂²×C₄×C₁₄₉	—	2	4	no	—
53	C₂²×C₄×C₁₄₉	—	2	4	no	—
54	C₂²×C₄×C₁₄₉	—	2	4	no	—
55	C₂²×C₄×C₁₄₉	—	2	4	no	—
56	C₂²×C₄×C₁₄₉	—	2	4	no	—
57	C₂²×C₄×C₁₄₉	—	2	4	no	—
58	C₂²×C₄×C₁₄₉	—	2	2	no	—
59	C₂²×C₄×C₁₄₉	—	2	2	no	—
60	C₂²×C₄×C₁₄₉	—	2	2	no	—
61	C₂²×C₄×C₁₄₉	—	2	2	no	—
62	C₂²×C₄×C₁₄₉	—	2	1	no	—
63	C₂²×C₄×C₁₄₉	—	2	1	no	—
64	C₂²×C₄×C₁₄₉	—	2	2	no	—
65	C₂²×C₄×C₁₄₉	—	2	4	no	—
66	C₂²×C₄×C₁₄₉	—	2	4	no	—
67	C₂²×C₄×C₁₄₉	—	2	2	no	—
68	C₂²×C₄×C₁₄₉	—	2	4	no	—
69	C₂²×C₄×C₁₄₉	—	2	4	no	—
70	C₂²×C₄×C₁₄₉	—	2	4	no	—
71	C₂²×C₄×C₁₄₉	—	2	4	no	—
72	C₂²×C₄×C₁₄₉	—	2	4	no	—
73	C₂²×C₄×C₁₄₉	—	2	4	no	—
74	C₂²×C₄×C₁₄₉	—	2	4	no	—
75	C₂²×C₄×C₁₄₉	—	2	4	no	—
76	C₂²×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₄₉	C₂×Q₈	1	4	yes	—
78	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
79	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
80	C₂²×C₄×C₁₄₉	#41	1	8	yes	—
81	C₄⋊C₄×C₁₄₉	—	4	4	no	—
82	C₄⋊C₄×C₁₄₉	—	4	8	no	—
83	C₄⋊C₄×C₁₄₉	—	4	8	no	—
84	C₄²×C₁₄₉	—	4	8	no	—
85	C₂³×C₁₄₉	C₂²×Q₈	1	1	yes	characteristic
86	C₂³×C₁₄₉	C₂×#41	1	2	yes	—
87	C₂³×C₁₄₉	C₂×#41	1	2	yes	—
88	C₂³×C₁₄₉	C₂×#41	1	4	yes	—
89	C₂³×C₁₄₉	H(5,𝔽₂)	1	1	yes	characteristic
90	C₂³×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
91	C₂³×C₁₄₉	H(5,𝔽₂)	1	1	yes	characteristic
92	C₂³×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
93	C₂×C₄×C₁₄₉	—	2	8	no	—
94	C₂×C₄×C₁₄₉	—	2	4	no	—
95	C₂×C₄×C₁₄₉	—	2	4	no	—
96	C₂×C₄×C₁₄₉	—	2	4	no	—
97	C₂×C₄×C₁₄₉	—	2	8	no	—
98	C₂×C₄×C₁₄₉	—	2	2	no	—
99	C₂×C₄×C₁₄₉	—	2	4	no	—
100	C₂×C₄×C₁₄₉	—	2	8	no	—
101	C₂×C₄×C₁₄₉	—	2	8	no	—
102	C₂×C₄×C₁₄₉	—	2	8	no	—
103	C₂×C₄×C₁₄₉	—	2	8	no	—
104	C₂×C₄×C₁₄₉	—	4	4	no	—
105	C₂×C₄×C₁₄₉	—	4	4	no	—
106	C₂×C₄×C₁₄₉	—	4	4	no	—
107	C₂×C₄×C₁₄₉	—	4	4	no	—
108	C₂×C₄×C₁₄₉	—	4	2	no	—
109	C₂×C₄×C₁₄₉	—	4	2	no	—
110	C₂×C₄×C₁₄₉	—	4	4	no	—
111	C₂×C₄×C₁₄₉	—	4	4	no	—
112	C₂×C₄×C₁₄₉	—	4	2	no	—
113	C₂×C₄×C₁₄₉	—	4	2	no	—
114	C₂×C₄×C₁₄₉	—	4	2	no	—
115	C₂×C₄×C₁₄₉	—	4	2	no	—
116	C₂×C₄×C₁₄₉	—	4	4	no	—
117	C₂×C₄×C₁₄₉	—	4	2	no	—
118	C₂×C₄×C₁₄₉	—	4	2	no	—
119	C₂×C₄×C₁₄₉	—	4	4	no	—
120	C₂×C₄×C₁₄₉	—	4	4	no	—
121	C₂×C₄×C₁₄₉	—	4	4	no	—
122	C₂×C₄×C₁₄₉	—	4	4	no	—
123	C₂×C₄×C₁₄₉	—	4	4	no	—
124	C₂×C₄×C₁₄₉	—	4	4	no	—
125	C₂×C₄×C₁₄₉	—	4	4	no	—
126	C₂²×C₁₄₉	#529	1	4	yes	—
127	C₂²×C₁₄₉	#533	1	2	yes	—
128	C₂²×C₁₄₉	#538	1	2	yes	—
129	C₂²×C₁₄₉	#539	1	4	yes	—
130	C₂²×C₁₄₉	#539	1	2	yes	—
131	C₂²×C₁₄₉	#543	1	1	yes	characteristic
132	C₂²×C₁₄₉	#551	1	2	yes	—
133	C₂²×C₁₄₉	#552	1	4	yes	—
134	C₂²×C₁₄₉	#553	1	4	yes	—
135	C₂²×C₁₄₉	#554	1	2	yes	—
136	C₂²×C₁₄₉	#555	1	1	yes	characteristic
137	C₂²×C₁₄₉	#557	1	2	yes	—
138	C₂²×C₁₄₉	#559	1	2	yes	—
139	C₂²×C₁₄₉	#559	1	1	yes	characteristic
140	C₂²×C₁₄₉	H(3,𝔽₄)	1	1	yes	characteristic
141	C₂²×C₁₄₉	#563	1	1	yes	characteristic
142	C₄×C₁₄₉	—	4	2	no	—
143	C₄×C₁₄₉	—	4	4	no	—
144	C₄×C₁₄₉	—	4	4	no	—
145	C₄×C₁₄₉	—	4	8	no	—
146	C₄×C₁₄₉	—	4	4	no	—
147	C₄×C₁₄₉	—	8	4	no	—
148	C₂×C₁₄₉	#2517	1	2	yes	—
149	C₂×C₁₄₉	#2590	1	4	yes	—
150	C₂×C₁₄₉	#2593	1	2	yes	—
151	C₂×C₁₄₉	#2607	1	1	yes	characteristic
152	C₂×C₁₄₉	#2771	1	2	yes	—
153	C₂×C₁₄₉	#2782	1	2	yes	—
154	C₂×C₁₄₉	#2804	1	1	yes	characteristic
155	C₂×C₁₄₉	#2809	1	1	yes	characteristic
156	#16244	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₁₄₉	#16244	1	1	yes	characteristic, direct product factor, Sylow
158	#1445	C₂×C₁₄₉	1	2	yes	—
159	#1445	C₂×C₁₄₉	1	1	yes	characteristic
160	#1442	C₂×C₁₄₉	1	2	yes	—
161	#1442	C₂×C₁₄₉	1	4	yes	—
162	#1436	C₂×C₁₄₉	1	4	yes	—
163	#1436	C₂×C₁₄₉	1	2	yes	—
164	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₁₄₉	1	2	yes	—
168	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
169	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
170	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
171	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
172	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
173	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
174	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
175	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
176	C₂×#95	C₂²×C₁₄₉	1	1	yes	characteristic
177	C₂×#95	C₂²×C₁₄₉	1	1	yes	characteristic
178	C₂³×C₄	C₂³×C₁₄₉	1	4	yes	—
179	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
180	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
181	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
182	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
183	C₂³×C₄	C₂³×C₁₄₉	1	4	yes	—
184	C₂×C₄⋊C₄	—	2	8	no	—
185	C₂×C₄⋊C₄	—	2	4	no	—
186	C₂×C₄⋊C₄	—	4	1	no	—
187	C₂×C₄⋊C₄	—	4	1	no	—
188	C₂×C₄⋊C₄	—	4	2	no	—
189	C₂×C₄⋊C₄	—	4	2	no	—
190	C₂×C₄⋊C₄	—	4	2	no	—
191	C₂×C₄⋊C₄	Q₈×C₁₄₉	1	4	yes	—
192	C₂×C₄²	—	4	4	no	—
193	C₂×C₄²	—	4	2	no	—
194	#95	—	2	8	no	—
195	#95	—	2	8	no	—
196	#95	—	2	8	no	—
197	#95	—	2	8	no	—
198	#95	—	2	4	no	—
199	#95	—	4	2	no	—
200	#95	—	4	4	no	—
201	#95	—	4	1	no	—
202	#95	—	4	1	no	—
203	#95	—	4	2	no	—
204	C₂⁴	C₂⁴×C₁₄₉	1	1	yes	characteristic
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	4	no	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	2	4	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	1	no	—
220	C₂²×C₄	—	2	1	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	4	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
234	C₂²×C₄	C₂×Q₈×C₁₄₉	1	4	yes	—
235	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
236	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
237	C₂²×C₄	#41×C₁₄₉	1	8	yes	—
238	C₄⋊C₄	—	4	4	no	—
239	C₄⋊C₄	—	4	8	no	—
240	C₄⋊C₄	—	4	8	no	—
241	C₄²	—	4	8	no	—
242	C₂³	C₂²×Q₈×C₁₄₉	1	1	yes	characteristic
243	C₂³	C₂×#41×C₁₄₉	1	2	yes	—
244	C₂³	C₂×#41×C₁₄₉	1	2	yes	—
245	C₂³	C₂×#41×C₁₄₉	1	4	yes	—
246	C₂³	H(5,𝔽₂)×C₁₄₉	1	1	yes	characteristic
247	C₂³	H(5,𝔽₂)×C₁₄₉	1	2	yes	—
248	C₂³	H(5,𝔽₂)×C₁₄₉	1	1	yes	characteristic
249	C₂³	2₋¹⁺⁴×C₁₄₉	1	2	yes	—
250	C₂×C₄	—	2	8	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	2	8	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	8	no	—
258	C₂×C₄	—	2	8	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	8	no	—
261	C₂×C₄	—	4	4	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	4	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	4	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂²	#529×C₁₄₉	1	4	yes	—
284	C₂²	#533×C₁₄₉	1	2	yes	—
285	C₂²	#538×C₁₄₉	1	2	yes	—
286	C₂²	#539×C₁₄₉	1	4	yes	—
287	C₂²	#539×C₁₄₉	1	2	yes	—
288	C₂²	#543×C₁₄₉	1	1	yes	characteristic
289	C₂²	#551×C₁₄₉	1	2	yes	—
290	C₂²	#552×C₁₄₉	1	4	yes	—
291	C₂²	#553×C₁₄₉	1	4	yes	—
292	C₂²	#554×C₁₄₉	1	2	yes	—
293	C₂²	#555×C₁₄₉	1	1	yes	characteristic
294	C₂²	#557×C₁₄₉	1	2	yes	—
295	C₂²	#559×C₁₄₉	1	2	yes	—
296	C₂²	#559×C₁₄₉	1	1	yes	characteristic
297	C₂²	H(3,𝔽₄)×C₁₄₉	1	1	yes	characteristic
298	C₂²	#563×C₁₄₉	1	1	yes	characteristic
299	C₄	—	4	4	no	—
300	C₄	—	4	4	no	—
301	C₄	—	4	8	no	—
302	C₄	—	4	4	no	—
303	C₄	—	4	2	no	—
304	C₄	—	8	4	no	—
305	C₂	#2517×C₁₄₉	1	2	yes	—
306	C₂	#2590×C₁₄₉	1	4	yes	—
307	C₂	#2593×C₁₄₉	1	2	yes	—
308	C₂	#2607×C₁₄₉	1	1	yes	characteristic
309	C₂	#2771×C₁₄₉	1	2	yes	—
310	C₂	#2782×C₁₄₉	1	2	yes	—
311	C₂	#2804×C₁₄₉	1	1	yes	characteristic
312	C₂	#2809×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₄₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₄₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
156. #16244	C₁₄₉	direct (N × H)
157. C₁₄₉	#16244	direct (N × H)

Maximal subgroups

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

subgroup	index
#1445×C₁₄₉	2
#1442×C₁₄₉	2
#1436×C₁₄₉	2
#16244	149

Subgroups — C149×#16244 #49195193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#16244 #49195193