Subgroups — C₂×#1527×C₁₄₉ #49196588

Order 38144.

1394 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1527×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#329×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
7	C₂³×D₄×C₁₄₉	C₄	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
9	C₂×#124×C₁₄₉	—	2	1	no	—
10	C₂×#124×C₁₄₉	—	2	2	no	—
11	C₂×#124×C₁₄₉	—	2	1	no	—
12	C₂×#124×C₁₄₉	—	2	2	no	—
13	C₂×#124×C₁₄₉	C₄	1	4	yes	—
14	C₂×#124×C₁₄₉	C₄	1	2	yes	—
15	C₂×#124×C₁₄₉	C₂²	1	2	yes	—
16	C₂×#124×C₁₄₉	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
19	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
20	#432×C₁₄₉	—	2	2	no	—
21	#432×C₁₄₉	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
24	C₄×M₁₆×C₁₄₉	—	2	2	no	—
25	C₄×M₁₆×C₁₄₉	C₂²	1	4	yes	complemented
26	C₂×#97×C₁₄₉	C₂²	1	2	yes	complemented
27	C₂×#97×C₁₄₉	C₂²	1	2	yes	complemented
28	C₂×C₄×C₈×C₁₄₉	—	2	1	no	—
29	#329×C₁₄₉	C₂²	1	16	yes	complemented
30	C₂⁵×C₁₄₉	—	2	1	no	—
31	C₂²×Q₈×C₁₄₉	—	2	2	no	—
32	C₂²×Q₈×C₁₄₉	—	2	1	no	—
33	C₂²×Q₈×C₁₄₉	—	4	4	no	—
34	C₂²×Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
35	C₂²×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₄₉	—	2	2	no	—
37	C₂²×D₄×C₁₄₉	—	2	1	no	—
38	C₂²×D₄×C₁₄₉	—	4	4	no	—
39	C₂²×D₄×C₁₄₉	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₄₉	—	2	1	no	—
42	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
45	C₂×M₁₆×C₁₄₉	—	2	8	no	—
46	C₂×M₁₆×C₁₄₉	—	2	4	no	—
47	C₂²×C₈×C₁₄₉	—	2	2	no	—
48	C₂²×C₈×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	#124×C₁₄₉	—	2	2	no	—
54	#124×C₁₄₉	—	2	2	no	—
55	#124×C₁₄₉	—	2	4	no	—
56	#124×C₁₄₉	C₂×C₄	1	4	yes	—
57	#124×C₁₄₉	C₂×C₄	1	8	yes	—
58	#124×C₁₄₉	C₂³	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
67	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
73	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
75	C₄⋊C₈×C₁₄₉	—	2	4	no	—
76	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
77	#97×C₁₄₉	—	2	2	no	—
78	#97×C₁₄₉	—	2	2	no	—
79	#97×C₁₄₉	C₂³	1	4	yes	complemented
80	#97×C₁₄₉	C₂³	1	4	yes	complemented
81	C₄×C₈×C₁₄₉	—	2	4	no	—
82	C₂⁴×C₁₄₉	—	2	4	no	—
83	C₂⁴×C₁₄₉	—	2	2	no	—
84	C₂⁴×C₁₄₉	—	4	4	no	—
85	C₂⁴×C₁₄₉	—	4	4	no	—
86	C₂⁴×C₁₄₉	—	4	4	no	—
87	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×Q₈×C₁₄₉	—	2	2	no	—
89	C₂×Q₈×C₁₄₉	—	2	4	no	—
90	C₂×Q₈×C₁₄₉	—	4	8	no	—
91	C₂×Q₈×C₁₄₉	—	4	8	no	—
92	C₂×Q₈×C₁₄₉	—	4	4	no	—
93	C₂×Q₈×C₁₄₉	—	4	4	no	—
94	C₂×Q₈×C₁₄₉	C₂²×C₄	1	4	yes	—
95	C₂×D₄×C₁₄₉	—	2	2	no	—
96	C₂×D₄×C₁₄₉	—	2	4	no	—
97	C₂×D₄×C₁₄₉	—	4	8	no	—
98	C₂×D₄×C₁₄₉	—	4	4	no	—
99	C₂×D₄×C₁₄₉	—	4	8	no	—
100	C₂×D₄×C₁₄₉	—	4	4	no	—
101	C₂×D₄×C₁₄₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₄₉	—	2	4	no	—
103	C₂²×C₄×C₁₄₉	—	2	4	no	—
104	C₂²×C₄×C₁₄₉	—	2	4	no	—
105	C₂²×C₄×C₁₄₉	—	2	2	no	—
106	C₂²×C₄×C₁₄₉	—	4	2	no	—
107	C₂²×C₄×C₁₄₉	—	4	4	no	—
108	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
120	M₁₆×C₁₄₉	—	2	16	no	—
121	C₂×C₈×C₁₄₉	—	2	8	no	—
122	C₂×C₈×C₁₄₉	—	2	4	no	—
123	C₂×C₈×C₁₄₉	—	2	4	no	—
124	C₂×C₈×C₁₄₉	—	4	4	no	—
125	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
127	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
131	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
137	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
140	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
141	C₂³×C₁₄₉	—	2	2	no	—
142	C₂³×C₁₄₉	—	2	2	no	—
143	C₂³×C₁₄₉	—	2	4	no	—
144	C₂³×C₁₄₉	—	4	8	no	—
145	C₂³×C₁₄₉	—	4	8	no	—
146	C₂³×C₁₄₉	—	4	4	no	—
147	C₂³×C₁₄₉	—	4	8	no	—
148	C₂³×C₁₄₉	—	4	4	no	—
149	C₂³×C₁₄₉	—	4	4	no	—
150	C₂³×C₁₄₉	—	8	16	no	—
151	C₂³×C₁₄₉	#104	1	4	yes	—
152	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	Q₈×C₁₄₉	—	4	4	no	—
155	Q₈×C₁₄₉	—	4	4	no	—
156	Q₈×C₁₄₉	—	4	8	no	—
157	D₄×C₁₄₉	—	4	4	no	—
158	D₄×C₁₄₉	—	4	4	no	—
159	D₄×C₁₄₉	—	4	8	no	—
160	C₂×C₄×C₁₄₉	—	2	2	no	—
161	C₂×C₄×C₁₄₉	—	2	2	no	—
162	C₂×C₄×C₁₄₉	—	2	4	no	—
163	C₂×C₄×C₁₄₉	—	2	4	no	—
164	C₂×C₄×C₁₄₉	—	2	2	no	—
165	C₂×C₄×C₁₄₉	—	2	2	no	—
166	C₂×C₄×C₁₄₉	—	2	2	no	—
167	C₂×C₄×C₁₄₉	—	2	4	no	—
168	C₂×C₄×C₁₄₉	—	2	4	no	—
169	C₂×C₄×C₁₄₉	—	2	4	no	—
170	C₂×C₄×C₁₄₉	—	4	2	no	—
171	C₂×C₄×C₁₄₉	—	4	2	no	—
172	C₂×C₄×C₁₄₉	—	4	8	no	—
173	C₂×C₄×C₁₄₉	—	4	4	no	—
174	C₂×C₄×C₁₄₉	#100	1	4	yes	—
175	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₄₉	—	2	8	no	—
185	C₈×C₁₄₉	—	4	4	no	—
186	C₂²×C₁₄₉	—	2	2	no	—
187	C₂²×C₁₄₉	—	2	2	no	—
188	C₂²×C₁₄₉	—	2	8	no	—
189	C₂²×C₁₄₉	—	4	4	no	—
190	C₂²×C₁₄₉	—	4	4	no	—
191	C₂²×C₁₄₉	—	4	4	no	—
192	C₂²×C₁₄₉	—	8	16	no	—
193	C₂²×C₁₄₉	—	8	8	no	—
194	C₂²×C₁₄₉	C₂×#100	1	2	yes	—
195	C₂²×C₁₄₉	C₂×#104	1	4	yes	—
196	C₂²×C₁₄₉	C₂×#104	1	2	yes	—
197	C₂²×C₁₄₉	#421	1	2	yes	—
198	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₄×C₁₄₉	—	2	1	no	—
200	C₄×C₁₄₉	—	2	1	no	—
201	C₄×C₁₄₉	—	2	1	no	—
202	C₄×C₁₄₉	—	2	1	no	—
203	C₄×C₁₄₉	—	2	2	no	—
204	C₄×C₁₄₉	—	2	1	no	—
205	C₄×C₁₄₉	—	2	1	no	—
206	C₄×C₁₄₉	—	2	2	no	—
207	C₄×C₁₄₉	—	4	4	no	—
208	C₄×C₁₄₉	C₂×#100	1	4	yes	—
209	C₂×C₁₄₉	—	2	4	no	—
210	C₂×C₁₄₉	—	8	4	no	—
211	C₂×C₁₄₉	#1527	1	4	yes	direct product factor
212	C₂×C₁₄₉	C₂²×#100	1	1	yes	characteristic
213	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
214	C₂×C₁₄₉	C₂×#421	1	1	yes	characteristic
215	C₂×#1527	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₄₉	C₂×#1527	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×#124	C₂×C₁₄₉	1	1	yes	characteristic
218	C₂×#432	C₂×C₁₄₉	1	1	yes	characteristic, complemented
219	C₂×C₄×M₁₆	C₂×C₁₄₉	1	1	yes	characteristic, complemented
220	#1527	C₂×C₁₄₉	1	8	yes	direct product factor
221	C₂×#329	C₂×C₁₄₉	1	4	yes	complemented
222	C₂³×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
223	C₂³×D₄	C₄×C₁₄₉	1	1	yes	characteristic
224	C₂²×M₁₆	—	2	1	no	—
225	C₂×#124	—	2	1	no	—
226	C₂×#124	—	2	2	no	—
227	C₂×#124	—	2	1	no	—
228	C₂×#124	—	2	2	no	—
229	C₂×#124	C₄×C₁₄₉	1	2	yes	—
230	C₂×#124	C₄×C₁₄₉	1	4	yes	—
231	C₂×#124	C₂²×C₁₄₉	1	2	yes	—
232	C₂×#124	C₂²×C₁₄₉	1	4	yes	—
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
236	#432	—	2	2	no	—
237	#432	C₂²×C₁₄₉	1	4	yes	complemented
238	C₂×C₄⋊C₈	—	2	1	no	—
239	C₂×C₂²⋊C₈	—	2	1	no	—
240	C₄×M₁₆	—	2	2	no	—
241	C₄×M₁₆	C₂²×C₁₄₉	1	4	yes	complemented
242	C₂×#97	C₂²×C₁₄₉	1	2	yes	complemented
243	C₂×#97	C₂²×C₁₄₉	1	2	yes	complemented
244	C₂×C₄×C₈	—	2	1	no	—
245	#329	C₂²×C₁₄₉	1	16	yes	complemented
246	C₂⁵	—	2	1	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×Q₈	—	4	4	no	—
250	C₂²×Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
251	C₂²×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	4	4	no	—
255	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
256	C₂²×D₄	C₂×C₄×C₁₄₉	1	4	yes	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
260	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
261	C₂×M₁₆	—	2	8	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	2	no	—
265	#124	—	2	4	no	—
266	#124	—	2	4	no	—
267	#124	—	2	4	no	—
268	#124	—	2	4	no	—
269	#124	—	2	2	no	—
270	#124	—	2	2	no	—
271	#124	—	2	4	no	—
272	#124	C₂×C₄×C₁₄₉	1	4	yes	—
273	#124	C₂×C₄×C₁₄₉	1	8	yes	—
274	#124	C₂³×C₁₄₉	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
285	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
287	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
291	C₄⋊C₈	—	2	4	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	#97	—	2	2	no	—
294	#97	—	2	2	no	—
295	#97	C₂³×C₁₄₉	1	4	yes	complemented
296	#97	C₂³×C₁₄₉	1	4	yes	complemented
297	C₄×C₈	—	2	4	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	—	4	8	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	C₂²×C₄×C₁₄₉	1	4	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	8	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	C₂²×C₄×C₁₄₉	1	4	yes	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
325	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
328	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
329	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
336	M₁₆	—	2	16	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
348	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
349	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
350	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
351	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
352	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
353	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
356	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	8	16	no	—
367	C₂³	#104×C₁₄₉	1	4	yes	—
368	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
369	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
370	Q₈	—	4	4	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	4	8	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	#100×C₁₄₉	1	4	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
395	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
396	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
397	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
400	C₈	—	2	8	no	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	8	16	no	—
409	C₂²	—	8	8	no	—
410	C₂²	C₂×#100×C₁₄₉	1	2	yes	—
411	C₂²	C₂×#104×C₁₄₉	1	4	yes	—
412	C₂²	C₂×#104×C₁₄₉	1	2	yes	—
413	C₂²	#421×C₁₄₉	1	2	yes	—
414	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	C₂×#100×C₁₄₉	1	4	yes	—
425	C₂	—	2	4	no	—
426	C₂	—	8	4	no	—
427	C₂	#1527×C₁₄₉	1	4	yes	direct product factor
428	C₂	C₂²×#100×C₁₄₉	1	1	yes	characteristic
429	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic
430	C₂	C₂×#421×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
prime radical	C₂³×D₄×C₁₄₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×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. C₂×C₄×M₁₆×C₁₄₉	C₂	semidirect
4. #1527×C₁₄₉	C₂	direct (N × H)
5. C₂×#329×C₁₄₉	C₂	semidirect
21. #432×C₁₄₉	C₂²	semidirect
25. C₄×M₁₆×C₁₄₉	C₂²	semidirect
26. C₂×#97×C₁₄₉	C₂²	semidirect
27. C₂×#97×C₁₄₉	C₂²	semidirect
29. #329×C₁₄₉	C₂²	semidirect
79. #97×C₁₄₉	C₂³	semidirect
80. #97×C₁₄₉	C₂³	semidirect
211. C₂×C₁₄₉	#1527	direct (N × H)
215. C₂×#1527	C₁₄₉	direct (N × H)
216. C₁₄₉	C₂×#1527	direct (N × H)
218. C₂×#432	C₂×C₁₄₉	semidirect
219. C₂×C₄×M₁₆	C₂×C₁₄₉	semidirect
220. #1527	C₂×C₁₄₉	direct (N × H)
221. C₂×#329	C₂×C₁₄₉	semidirect
237. #432	C₂²×C₁₄₉	semidirect
241. C₄×M₁₆	C₂²×C₁₄₉	semidirect
242. C₂×#97	C₂²×C₁₄₉	semidirect
243. C₂×#97	C₂²×C₁₄₉	semidirect
245. #329	C₂²×C₁₄₉	semidirect
295. #97	C₂³×C₁₄₉	semidirect
296. #97	C₂³×C₁₄₉	semidirect
427. C₂	#1527×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₁₄₉	2
C₂×#432×C₁₄₉	2
C₂×C₄×M₁₆×C₁₄₉	2
#1527×C₁₄₉	2
C₂×#329×C₁₄₉	2
C₂×#1527	149

Subgroups — C2×#1527×C149 #49196588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1527×C₁₄₉ #49196588