Subgroups — C₁₄₉×#17391 #49196340

Order 38144.

876 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2983×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2982×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1473×C₁₄₉	C₂	1	4	yes	maximal
5	#1470×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	#1461×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1458×C₁₄₉	C₂	1	2	yes	maximal
8	#541×C₁₄₉	—	2	4	no	—
9	#541×C₁₄₉	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
11	C₂×#126×C₁₄₉	C₄	1	2	yes	—
12	C₂×#126×C₁₄₉	C₂²	1	2	yes	—
13	C₂×#125×C₁₄₉	C₄	1	1	yes	characteristic
14	C₂×#125×C₁₄₉	C₄	1	2	yes	—
15	C₂×#125×C₁₄₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
21	#446×C₁₄₉	—	2	4	no	—
22	C₈×Q₈×C₁₄₉	—	2	4	no	—
23	#432×C₁₄₉	C₂²	1	4	yes	—
24	#431×C₁₄₉	C₂²	1	2	yes	—
25	#431×C₁₄₉	C₂²	1	4	yes	—
26	#431×C₁₄₉	C₂²	1	2	yes	—
27	#324×C₁₄₉	C₂²	1	4	yes	—
28	#324×C₁₄₉	C₂²	1	8	yes	—
29	#323×C₁₄₉	C₂²	1	4	yes	—
30	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
33	C₄⋊Q₈×C₁₄₉	—	2	4	no	—
34	#126×C₁₄₉	—	2	8	no	—
35	#126×C₁₄₉	—	2	4	no	—
36	#126×C₁₄₉	—	2	4	no	—
37	#125×C₁₄₉	—	2	4	no	—
38	#125×C₁₄₉	—	2	8	no	—
39	#125×C₁₄₉	—	2	4	no	—
40	#125×C₁₄₉	—	2	4	no	—
41	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
42	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
43	C₄×Q₈×C₁₄₉	—	2	2	no	—
44	C₄×Q₈×C₁₄₉	—	2	2	no	—
45	C₄×Q₈×C₁₄₉	D₄	1	4	yes	—
46	C₄×Q₈×C₁₄₉	D₄	1	4	yes	—
47	#117×C₁₄₉	—	2	2	no	—
48	#117×C₁₄₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₄₉	—	2	2	no	—
70	C₄⋊C₈×C₁₄₉	—	2	4	no	—
71	C₄⋊C₈×C₁₄₉	—	2	2	no	—
72	C₄⋊C₈×C₁₄₉	—	2	4	no	—
73	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
74	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
75	#97×C₁₄₉	—	2	4	no	—
76	C₄×C₈×C₁₄₉	—	2	2	no	—
77	C₄×C₈×C₁₄₉	—	2	4	no	—
78	C₄×C₈×C₁₄₉	—	2	2	no	—
79	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₁₄₉	—	2	2	no	—
81	C₂×Q₈×C₁₄₉	—	2	4	no	—
82	C₂×Q₈×C₁₄₉	—	2	4	no	—
83	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₄₉	—	2	2	no	—
85	C₂²×C₄×C₁₄₉	—	2	4	no	—
86	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₄₉	—	2	4	no	—
97	C₂×C₈×C₁₄₉	—	2	4	no	—
98	C₄⋊C₄×C₁₄₉	—	2	2	no	—
99	C₄⋊C₄×C₁₄₉	—	2	2	no	—
100	C₄⋊C₄×C₁₄₉	—	2	4	no	—
101	C₄⋊C₄×C₁₄₉	—	2	4	no	—
102	C₄⋊C₄×C₁₄₉	—	2	4	no	—
103	C₄⋊C₄×C₁₄₉	—	2	4	no	—
104	C₄⋊C₄×C₁₄₉	—	2	4	no	—
105	C₄⋊C₄×C₁₄₉	—	2	4	no	—
106	C₄⋊C₄×C₁₄₉	—	2	1	no	—
107	C₄⋊C₄×C₁₄₉	—	2	1	no	—
108	C₄⋊C₄×C₁₄₉	—	2	2	no	—
109	C₄⋊C₄×C₁₄₉	—	2	2	no	—
110	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
111	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	8	yes	—
112	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
113	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
117	C₄²×C₁₄₉	—	2	2	no	—
118	C₄²×C₁₄₉	—	2	4	no	—
119	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
120	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
121	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
122	C₄²×C₁₄₉	C₂×D₄	1	4	yes	—
123	C₂³×C₁₄₉	—	2	1	no	—
124	C₂³×C₁₄₉	—	2	2	no	—
125	C₂³×C₁₄₉	—	4	1	no	—
126	C₂³×C₁₄₉	—	4	1	no	—
127	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
128	Q₈×C₁₄₉	—	2	8	no	—
129	Q₈×C₁₄₉	—	4	4	no	—
130	C₂×C₄×C₁₄₉	—	2	4	no	—
131	C₂×C₄×C₁₄₉	—	2	1	no	—
132	C₂×C₄×C₁₄₉	—	2	2	no	—
133	C₂×C₄×C₁₄₉	—	2	1	no	—
134	C₂×C₄×C₁₄₉	—	2	2	no	—
135	C₂×C₄×C₁₄₉	—	2	1	no	—
136	C₂×C₄×C₁₄₉	—	2	2	no	—
137	C₂×C₄×C₁₄₉	—	2	4	no	—
138	C₂×C₄×C₁₄₉	—	4	1	no	—
139	C₂×C₄×C₁₄₉	—	4	2	no	—
140	C₂×C₄×C₁₄₉	—	4	1	no	—
141	C₂×C₄×C₁₄₉	—	4	4	no	—
142	C₂×C₄×C₁₄₉	—	4	1	no	—
143	C₂×C₄×C₁₄₉	—	4	2	no	—
144	C₂×C₄×C₁₄₉	—	4	1	no	—
145	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
147	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
148	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₁₄₉	#131	1	4	yes	—
150	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₁₄₉	—	4	4	no	—
153	C₈×C₁₄₉	—	4	4	no	—
154	C₂²×C₁₄₉	—	2	1	no	—
155	C₂²×C₁₄₉	—	2	1	no	—
156	C₂²×C₁₄₉	—	4	1	no	—
157	C₂²×C₁₄₉	—	4	1	no	—
158	C₂²×C₁₄₉	—	4	1	no	—
159	C₂²×C₁₄₉	—	8	2	no	—
160	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₁₄₉	C₂×#131	1	2	yes	—
162	C₄×C₁₄₉	—	2	4	no	—
163	C₄×C₁₄₉	—	2	1	no	—
164	C₄×C₁₄₉	—	2	1	no	—
165	C₄×C₁₄₉	—	2	2	no	—
166	C₄×C₁₄₉	—	2	4	no	—
167	C₄×C₁₄₉	—	4	1	no	—
168	C₄×C₁₄₉	—	4	2	no	—
169	C₄×C₁₄₉	—	4	1	no	—
170	C₄×C₁₄₉	—	4	2	no	—
171	C₄×C₁₄₉	—	4	1	no	—
172	C₄×C₁₄₉	#408	1	4	yes	—
173	C₂×C₁₄₉	—	2	2	no	—
174	C₂×C₁₄₉	—	8	1	no	—
175	C₂×C₁₄₉	C₂×#408	1	1	yes	characteristic
176	C₂×C₁₄₉	#2884	1	1	yes	characteristic
177	C₂×C₁₄₉	#2889	1	1	yes	characteristic
178	#17391	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₁₄₉	#17391	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×#541	C₂×C₁₄₉	1	1	yes	characteristic
181	#2983	C₂×C₁₄₉	1	1	yes	characteristic, complemented
182	#2982	C₂×C₁₄₉	1	1	yes	characteristic, complemented
183	#1473	C₂×C₁₄₉	1	4	yes	—
184	#1470	C₂×C₁₄₉	1	4	yes	complemented
185	#1461	C₂×C₁₄₉	1	2	yes	complemented
186	#1458	C₂×C₁₄₉	1	2	yes	—
187	#541	—	2	4	no	—
188	#541	—	2	4	no	—
189	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
190	C₂×#126	C₄×C₁₄₉	1	2	yes	—
191	C₂×#126	C₂²×C₁₄₉	1	2	yes	—
192	C₂×#125	C₄×C₁₄₉	1	1	yes	characteristic
193	C₂×#125	C₄×C₁₄₉	1	2	yes	—
194	C₂×#125	C₂²×C₁₄₉	1	2	yes	—
195	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
196	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
200	#446	—	2	4	no	—
201	C₈×Q₈	—	2	4	no	—
202	#432	C₂²×C₁₄₉	1	4	yes	—
203	#431	C₂²×C₁₄₉	1	2	yes	—
204	#431	C₂²×C₁₄₉	1	4	yes	—
205	#431	C₂²×C₁₄₉	1	2	yes	—
206	#324	C₂²×C₁₄₉	1	4	yes	—
207	#324	C₂²×C₁₄₉	1	8	yes	—
208	#323	C₂²×C₁₄₉	1	4	yes	—
209	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
210	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
211	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	4	no	—
213	#126	—	2	8	no	—
214	#126	—	2	4	no	—
215	#126	—	2	4	no	—
216	#125	—	2	4	no	—
217	#125	—	2	8	no	—
218	#125	—	2	4	no	—
219	#125	—	2	4	no	—
220	C₂²⋊Q₈	—	2	4	no	—
221	C₂²⋊Q₈	—	2	4	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	2	no	—
224	C₄×Q₈	D₄×C₁₄₉	1	4	yes	—
225	C₄×Q₈	D₄×C₁₄₉	1	4	yes	—
226	#117	—	2	2	no	—
227	#117	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
253	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	2	4	no	—
257	C₄×C₈	—	2	2	no	—
258	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
290	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	8	yes	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	4	no	—
298	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
299	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
300	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
301	C₄²	C₂×D₄×C₁₄₉	1	4	yes	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
328	C₂×C₄	#131×C₁₄₉	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
331	C₈	—	4	4	no	—
332	C₈	—	4	4	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	2	no	—
339	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
340	C₂²	C₂×#131×C₁₄₉	1	2	yes	—
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	1	no	—
351	C₄	#408×C₁₄₉	1	4	yes	—
352	C₂	—	2	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×#408×C₁₄₉	1	1	yes	characteristic
355	C₂	#2884×C₁₄₉	1	1	yes	characteristic
356	C₂	#2889×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	C₂⁴×C₁₄₉	C₂²×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. #2983×C₁₄₉	C₂	semidirect
3. #2982×C₁₄₉	C₂	semidirect
5. #1470×C₁₄₉	C₂	semidirect
6. #1461×C₁₄₉	C₂	semidirect
178. #17391	C₁₄₉	direct (N × H)
179. C₁₄₉	#17391	direct (N × H)
181. #2983	C₂×C₁₄₉	semidirect
182. #2982	C₂×C₁₄₉	semidirect
184. #1470	C₂×C₁₄₉	semidirect
185. #1461	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×#541×C₁₄₉	2
#2983×C₁₄₉	2
#2982×C₁₄₉	2
#1473×C₁₄₉	2
#1470×C₁₄₉	2
#1461×C₁₄₉	2
#1458×C₁₄₉	2
#17391	149

Subgroups — C149×#17391 #49196340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17391 #49196340