Subgroups — C₁₄₉×#17428 #49196377

Order 38144.

916 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2984×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1473×C₁₄₉	C₂	1	4	yes	maximal, complemented
4	#1469×C₁₄₉	C₂	1	2	yes	maximal
5	#1467×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1464×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1461×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1458×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	#556×C₁₄₉	—	2	2	no	—
10	#556×C₁₄₉	—	2	4	no	—
11	#556×C₁₄₉	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×#126×C₁₄₉	C₄	1	2	yes	—
14	C₂×#126×C₁₄₉	C₂²	1	2	yes	—
15	C₂×#124×C₁₄₉	C₄	1	1	yes	characteristic
16	C₂×#124×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	2	yes	—
18	C₂×C₄×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
22	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
23	#446×C₁₄₉	—	2	4	no	—
24	#446×C₁₄₉	—	2	2	no	—
25	C₈×Q₈×C₁₄₉	—	2	2	no	—
26	#432×C₁₄₉	C₂²	1	4	yes	—
27	#432×C₁₄₉	C₂²	1	2	yes	—
28	#431×C₁₄₉	C₂²	1	4	yes	—
29	#431×C₁₄₉	C₂²	1	2	yes	—
30	#324×C₁₄₉	C₂²	1	1	yes	characteristic
31	#324×C₁₄₉	C₂²	1	2	yes	—
32	#324×C₁₄₉	C₂²	1	1	yes	characteristic
33	#324×C₁₄₉	C₂²	1	2	yes	—
34	#324×C₁₄₉	C₂²	1	2	yes	—
35	#323×C₁₄₉	C₂²	1	4	yes	—
36	#323×C₁₄₉	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
42	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
43	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
44	#126×C₁₄₉	—	2	4	no	—
45	#126×C₁₄₉	—	2	4	no	—
46	#126×C₁₄₉	—	2	4	no	—
47	#126×C₁₄₉	—	2	4	no	—
48	#124×C₁₄₉	—	2	2	no	—
49	#124×C₁₄₉	—	2	2	no	—
50	#124×C₁₄₉	—	2	2	no	—
51	#124×C₁₄₉	—	2	2	no	—
52	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
53	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
54	C₄×Q₈×C₁₄₉	—	2	2	no	—
55	C₄×Q₈×C₁₄₉	—	2	1	no	—
56	C₄×Q₈×C₁₄₉	—	2	1	no	—
57	C₄×Q₈×C₁₄₉	—	2	2	no	—
58	C₄×Q₈×C₁₄₉	—	2	2	no	—
59	C₄×Q₈×C₁₄₉	D₄	1	2	yes	—
60	C₄×Q₈×C₁₄₉	D₄	1	4	yes	—
61	C₄×Q₈×C₁₄₉	D₄	1	2	yes	—
62	C₄×D₄×C₁₄₉	—	2	2	no	—
63	C₄×D₄×C₁₄₉	—	2	1	no	—
64	C₄×D₄×C₁₄₉	—	2	1	no	—
65	#117×C₁₄₉	—	2	4	no	—
66	#117×C₁₄₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
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	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₁₄₉	—	2	4	no	—
86	C₄⋊C₈×C₁₄₉	—	2	2	no	—
87	C₄⋊C₈×C₁₄₉	—	2	4	no	—
88	C₄⋊C₈×C₁₄₉	—	2	2	no	—
89	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
90	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
91	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
92	#97×C₁₄₉	—	2	4	no	—
93	#97×C₁₄₉	—	2	2	no	—
94	C₄×C₈×C₁₄₉	—	2	4	no	—
95	C₄×C₈×C₁₄₉	—	2	2	no	—
96	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
97	C₂×Q₈×C₁₄₉	—	2	2	no	—
98	C₂×Q₈×C₁₄₉	—	2	1	no	—
99	C₂×Q₈×C₁₄₉	—	2	1	no	—
100	C₂×Q₈×C₁₄₉	—	2	2	no	—
101	C₂×Q₈×C₁₄₉	—	4	1	no	—
102	C₂×Q₈×C₁₄₉	—	4	2	no	—
103	C₂×Q₈×C₁₄₉	—	4	2	no	—
104	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	2	yes	—
105	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	2	yes	—
106	C₂×D₄×C₁₄₉	—	2	1	no	—
107	C₂×D₄×C₁₄₉	—	2	1	no	—
108	C₂×D₄×C₁₄₉	—	4	2	no	—
109	C₂²×C₄×C₁₄₉	—	2	2	no	—
110	C₂²×C₄×C₁₄₉	—	2	2	no	—
111	C₂²×C₄×C₁₄₉	—	2	4	no	—
112	C₂²×C₄×C₁₄₉	—	4	2	no	—
113	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₄₉	—	2	2	no	—
124	C₂×C₈×C₁₄₉	—	2	4	no	—
125	C₂×C₈×C₁₄₉	—	2	2	no	—
126	C₄⋊C₄×C₁₄₉	—	2	4	no	—
127	C₄⋊C₄×C₁₄₉	—	2	2	no	—
128	C₄⋊C₄×C₁₄₉	—	2	2	no	—
129	C₄⋊C₄×C₁₄₉	—	2	2	no	—
130	C₄⋊C₄×C₁₄₉	—	2	4	no	—
131	C₄⋊C₄×C₁₄₉	—	2	2	no	—
132	C₄⋊C₄×C₁₄₉	—	2	2	no	—
133	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
134	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
137	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
138	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
144	C₄²×C₁₄₉	—	2	2	no	—
145	C₄²×C₁₄₉	—	2	2	no	—
146	C₄²×C₁₄₉	—	2	1	no	—
147	C₄²×C₁₄₉	—	2	1	no	—
148	C₄²×C₁₄₉	—	2	1	no	—
149	C₄²×C₁₄₉	—	2	1	no	—
150	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
151	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
152	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
153	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
154	C₂³×C₁₄₉	—	2	2	no	—
155	C₂³×C₁₄₉	—	2	2	no	—
156	C₂³×C₁₄₉	—	2	2	no	—
157	C₂³×C₁₄₉	—	4	2	no	—
158	C₂³×C₁₄₉	—	4	2	no	—
159	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
160	Q₈×C₁₄₉	—	2	4	no	—
161	Q₈×C₁₄₉	—	4	2	no	—
162	Q₈×C₁₄₉	—	4	4	no	—
163	Q₈×C₁₄₉	—	4	2	no	—
164	Q₈×C₁₄₉	—	4	2	no	—
165	D₄×C₁₄₉	—	4	2	no	—
166	D₄×C₁₄₉	—	4	2	no	—
167	C₂×C₄×C₁₄₉	—	2	1	no	—
168	C₂×C₄×C₁₄₉	—	2	2	no	—
169	C₂×C₄×C₁₄₉	—	2	1	no	—
170	C₂×C₄×C₁₄₉	—	2	1	no	—
171	C₂×C₄×C₁₄₉	—	2	2	no	—
172	C₂×C₄×C₁₄₉	—	2	1	no	—
173	C₂×C₄×C₁₄₉	—	2	2	no	—
174	C₂×C₄×C₁₄₉	—	2	1	no	—
175	C₂×C₄×C₁₄₉	—	2	1	no	—
176	C₂×C₄×C₁₄₉	—	2	1	no	—
177	C₂×C₄×C₁₄₉	—	2	2	no	—
178	C₂×C₄×C₁₄₉	—	2	1	no	—
179	C₂×C₄×C₁₄₉	—	2	1	no	—
180	C₂×C₄×C₁₄₉	—	4	2	no	—
181	C₂×C₄×C₁₄₉	—	4	1	no	—
182	C₂×C₄×C₁₄₉	—	4	4	no	—
183	C₂×C₄×C₁₄₉	—	4	4	no	—
184	C₂×C₄×C₁₄₉	—	4	1	no	—
185	C₂×C₄×C₁₄₉	—	4	1	no	—
186	C₂×C₄×C₁₄₉	—	4	2	no	—
187	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₄₉	#131	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
195	C₈×C₁₄₉	—	4	2	no	—
196	C₈×C₁₄₉	—	4	4	no	—
197	C₈×C₁₄₉	—	4	2	no	—
198	C₂²×C₁₄₉	—	2	1	no	—
199	C₂²×C₁₄₉	—	2	1	no	—
200	C₂²×C₁₄₉	—	4	2	no	—
201	C₂²×C₁₄₉	—	4	2	no	—
202	C₂²×C₁₄₉	—	4	2	no	—
203	C₂²×C₁₄₉	—	8	2	no	—
204	C₂²×C₁₄₉	—	8	2	no	—
205	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×C₁₄₉	C₂×#131	1	1	yes	characteristic
207	C₂²×C₁₄₉	#568	1	1	yes	characteristic
208	C₄×C₁₄₉	—	2	2	no	—
209	C₄×C₁₄₉	—	2	2	no	—
210	C₄×C₁₄₉	—	2	2	no	—
211	C₄×C₁₄₉	—	2	2	no	—
212	C₄×C₁₄₉	—	2	2	no	—
213	C₄×C₁₄₉	—	2	1	no	—
214	C₄×C₁₄₉	—	2	4	no	—
215	C₄×C₁₄₉	—	4	1	no	—
216	C₄×C₁₄₉	—	4	1	no	—
217	C₄×C₁₄₉	—	4	1	no	—
218	C₄×C₁₄₉	—	4	2	no	—
219	C₄×C₁₄₉	#413	1	2	yes	—
220	C₂×C₁₄₉	—	2	1	no	—
221	C₂×C₁₄₉	—	2	1	no	—
222	C₂×C₁₄₉	—	8	2	no	—
223	C₂×C₁₄₉	#2880	1	1	yes	characteristic
224	C₂×C₁₄₉	#2884	1	1	yes	characteristic
225	C₂×C₁₄₉	C₂×#413	1	1	yes	characteristic
226	#17428	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₄₉	#17428	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×#556	C₂×C₁₄₉	1	1	yes	characteristic
229	#2984	C₂×C₁₄₉	1	2	yes	complemented
230	#1473	C₂×C₁₄₉	1	4	yes	complemented
231	#1469	C₂×C₁₄₉	1	2	yes	—
232	#1467	C₂×C₁₄₉	1	1	yes	characteristic, complemented
233	#1464	C₂×C₁₄₉	1	2	yes	complemented
234	#1461	C₂×C₁₄₉	1	1	yes	characteristic, complemented
235	#1458	C₂×C₁₄₉	1	2	yes	complemented
236	#556	—	2	2	no	—
237	#556	—	2	4	no	—
238	#556	—	2	2	no	—
239	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
240	C₂×#126	C₄×C₁₄₉	1	2	yes	—
241	C₂×#126	C₂²×C₁₄₉	1	2	yes	—
242	C₂×#124	C₄×C₁₄₉	1	1	yes	characteristic
243	C₂×#124	C₂²×C₁₄₉	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	2	yes	—
245	C₂×C₄×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
250	#446	—	2	4	no	—
251	#446	—	2	2	no	—
252	C₈×Q₈	—	2	2	no	—
253	#432	C₂²×C₁₄₉	1	4	yes	—
254	#432	C₂²×C₁₄₉	1	2	yes	—
255	#431	C₂²×C₁₄₉	1	4	yes	—
256	#431	C₂²×C₁₄₉	1	2	yes	—
257	#324	C₂²×C₁₄₉	1	1	yes	characteristic
258	#324	C₂²×C₁₄₉	1	2	yes	—
259	#324	C₂²×C₁₄₉	1	1	yes	characteristic
260	#324	C₂²×C₁₄₉	1	2	yes	—
261	#324	C₂²×C₁₄₉	1	2	yes	—
262	#323	C₂²×C₁₄₉	1	4	yes	—
263	#323	C₂²×C₁₄₉	1	4	yes	—
264	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
265	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
266	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
267	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
268	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	#126	—	2	4	no	—
272	#126	—	2	4	no	—
273	#126	—	2	4	no	—
274	#126	—	2	4	no	—
275	#124	—	2	2	no	—
276	#124	—	2	2	no	—
277	#124	—	2	2	no	—
278	#124	—	2	2	no	—
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	D₄×C₁₄₉	1	2	yes	—
287	C₄×Q₈	D₄×C₁₄₉	1	4	yes	—
288	C₄×Q₈	D₄×C₁₄₉	1	2	yes	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	#117	—	2	4	no	—
293	#117	—	2	4	no	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
307	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
308	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
312	C₄⋊C₈	—	2	4	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	4	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
317	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
318	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
319	#97	—	2	4	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	4	no	—
322	C₄×C₈	—	2	2	no	—
323	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	2	yes	—
332	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	2	yes	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
361	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
362	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
363	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
364	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
378	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
379	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
380	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
415	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
420	C₂×C₄	#131×C₁₄₉	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
422	C₈	—	4	2	no	—
423	C₈	—	4	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
433	C₂²	C₂×#131×C₁₄₉	1	1	yes	characteristic
434	C₂²	#568×C₁₄₉	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	2	no	—
446	C₄	#413×C₁₄₉	1	2	yes	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	#2880×C₁₄₉	1	1	yes	characteristic
451	C₂	#2884×C₁₄₉	1	1	yes	characteristic
452	C₂	C₂×#413×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	C₂²×D₄×C₁₄₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×Q₈×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2984×C₁₄₉	C₂	semidirect
3. #1473×C₁₄₉	C₂	semidirect
5. #1467×C₁₄₉	C₂	semidirect
6. #1464×C₁₄₉	C₂	semidirect
7. #1461×C₁₄₉	C₂	semidirect
8. #1458×C₁₄₉	C₂	semidirect
226. #17428	C₁₄₉	direct (N × H)
227. C₁₄₉	#17428	direct (N × H)
229. #2984	C₂×C₁₄₉	semidirect
230. #1473	C₂×C₁₄₉	semidirect
232. #1467	C₂×C₁₄₉	semidirect
233. #1464	C₂×C₁₄₉	semidirect
234. #1461	C₂×C₁₄₉	semidirect
235. #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×#556×C₁₄₉	2
#2984×C₁₄₉	2
#1473×C₁₄₉	2
#1469×C₁₄₉	2
#1467×C₁₄₉	2
#1464×C₁₄₉	2
#1461×C₁₄₉	2
#1458×C₁₄₉	2
#17428	149

Subgroups — C149×#17428 #49196377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17428 #49196377