Subgroups — C₁₄₉×#17388 #49196337

Order 38144.

976 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2975×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2972×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1472×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1468×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	#1461×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1458×C₁₄₉	C₂	1	2	yes	maximal, complemented
8	#542×C₁₄₉	—	2	4	no	—
9	#542×C₁₄₉	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
11	C₂×#126×C₁₄₉	C₄	1	2	yes	—
12	C₂×#124×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×#124×C₁₄₉	C₄	1	2	yes	—
14	C₂×#123×C₁₄₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
17	C₂×#121×C₁₄₉	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
21	#436×C₁₄₉	—	2	4	no	—
22	C₈×D₄×C₁₄₉	—	2	4	no	—
23	#431×C₁₄₉	C₂²	1	2	yes	—
24	#431×C₁₄₉	C₂²	1	2	yes	—
25	#407×C₁₄₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	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	2	yes	—
32	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
36	C₂×M₁₆×C₁₄₉	—	2	4	no	—
37	C₂²×C₈×C₁₄₉	—	2	4	no	—
38	C₄⋊Q₈×C₁₄₉	—	2	4	no	—
39	#126×C₁₄₉	—	2	8	no	—
40	#124×C₁₄₉	—	2	4	no	—
41	#124×C₁₄₉	—	2	8	no	—
42	#123×C₁₄₉	—	2	4	no	—
43	#123×C₁₄₉	—	2	4	no	—
44	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
45	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
46	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
47	#121×C₁₄₉	—	2	4	no	—
48	C₄×Q₈×C₁₄₉	—	2	2	no	—
49	C₄×Q₈×C₁₄₉	—	2	2	no	—
50	C₄×D₄×C₁₄₉	D₄	1	4	yes	—
51	C₄×D₄×C₁₄₉	D₄	1	4	yes	—
52	#117×C₁₄₉	—	2	2	no	—
53	#117×C₁₄₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₄₉	—	2	2	no	—
72	C₄⋊C₈×C₁₄₉	—	2	2	no	—
73	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
74	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
75	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
77	C₄×C₈×C₁₄₉	—	2	2	no	—
78	C₄×C₈×C₁₄₉	—	2	2	no	—
79	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
80	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
81	C₂×Q₈×C₁₄₉	—	2	2	no	—
82	C₂×Q₈×C₁₄₉	—	2	4	no	—
83	C₂×Q₈×C₁₄₉	—	2	4	no	—
84	C₂×Q₈×C₁₄₉	—	8	2	no	—
85	C₂×D₄×C₁₄₉	—	2	4	no	—
86	C₂×D₄×C₁₄₉	—	2	4	no	—
87	C₂×D₄×C₁₄₉	—	8	2	no	—
88	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₁₄₉	—	2	2	no	—
90	C₂²×C₄×C₁₄₉	—	2	4	no	—
91	C₂²×C₄×C₁₄₉	—	8	2	no	—
92	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
103	M₁₆×C₁₄₉	—	8	4	no	—
104	C₂×C₈×C₁₄₉	—	2	4	no	—
105	C₂×C₈×C₁₄₉	—	2	4	no	—
106	C₂×C₈×C₁₄₉	—	8	4	no	—
107	C₄⋊C₄×C₁₄₉	—	2	2	no	—
108	C₄⋊C₄×C₁₄₉	—	2	2	no	—
109	C₄⋊C₄×C₁₄₉	—	2	4	no	—
110	C₄⋊C₄×C₁₄₉	—	2	4	no	—
111	C₄⋊C₄×C₁₄₉	—	2	1	no	—
112	C₄⋊C₄×C₁₄₉	—	2	1	no	—
113	C₄⋊C₄×C₁₄₉	—	2	2	no	—
114	C₄⋊C₄×C₁₄₉	—	2	2	no	—
115	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
116	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	8	yes	—
124	C₄²×C₁₄₉	—	2	2	no	—
125	C₄²×C₁₄₉	—	2	4	no	—
126	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
127	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
128	C₂³×C₁₄₉	—	2	4	no	—
129	C₂³×C₁₄₉	—	2	1	no	—
130	C₂³×C₁₄₉	—	2	2	no	—
131	C₂³×C₁₄₉	—	4	2	no	—
132	C₂³×C₁₄₉	—	4	2	no	—
133	C₂³×C₁₄₉	—	4	1	no	—
134	C₂³×C₁₄₉	—	4	1	no	—
135	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₁₄₉	—	4	4	no	—
138	Q₈×C₁₄₉	—	8	4	no	—
139	D₄×C₁₄₉	—	2	8	no	—
140	D₄×C₁₄₉	—	8	4	no	—
141	C₂×C₄×C₁₄₉	—	2	1	no	—
142	C₂×C₄×C₁₄₉	—	2	2	no	—
143	C₂×C₄×C₁₄₉	—	2	1	no	—
144	C₂×C₄×C₁₄₉	—	2	2	no	—
145	C₂×C₄×C₁₄₉	—	2	1	no	—
146	C₂×C₄×C₁₄₉	—	2	2	no	—
147	C₂×C₄×C₁₄₉	—	2	4	no	—
148	C₂×C₄×C₁₄₉	—	4	4	no	—
149	C₂×C₄×C₁₄₉	—	4	4	no	—
150	C₂×C₄×C₁₄₉	—	4	1	no	—
151	C₂×C₄×C₁₄₉	—	4	2	no	—
152	C₂×C₄×C₁₄₉	—	4	1	no	—
153	C₂×C₄×C₁₄₉	—	4	4	no	—
154	C₂×C₄×C₁₄₉	—	4	1	no	—
155	C₂×C₄×C₁₄₉	—	4	2	no	—
156	C₂×C₄×C₁₄₉	—	4	1	no	—
157	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₄₉	#131	1	4	yes	—
161	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₁₄₉	—	4	4	no	—
164	C₈×C₁₄₉	—	4	4	no	—
165	C₂²×C₁₄₉	—	2	1	no	—
166	C₂²×C₁₄₉	—	2	1	no	—
167	C₂²×C₁₄₉	—	2	4	no	—
168	C₂²×C₁₄₉	—	2	4	no	—
169	C₂²×C₁₄₉	—	2	4	no	—
170	C₂²×C₁₄₉	—	4	1	no	—
171	C₂²×C₁₄₉	—	4	1	no	—
172	C₂²×C₁₄₉	—	4	1	no	—
173	C₂²×C₁₄₉	—	8	4	no	—
174	C₂²×C₁₄₉	—	8	2	no	—
175	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₄₉	C₂×#131	1	2	yes	—
177	C₄×C₁₄₉	—	2	1	no	—
178	C₄×C₁₄₉	—	2	1	no	—
179	C₄×C₁₄₉	—	2	4	no	—
180	C₄×C₁₄₉	—	2	2	no	—
181	C₄×C₁₄₉	—	4	1	no	—
182	C₄×C₁₄₉	—	4	2	no	—
183	C₄×C₁₄₉	—	4	2	no	—
184	C₄×C₁₄₉	—	4	1	no	—
185	C₄×C₁₄₉	—	4	1	no	—
186	C₄×C₁₄₉	#408	1	4	yes	—
187	C₂×C₁₄₉	—	2	2	no	—
188	C₂×C₁₄₉	—	4	4	no	—
189	C₂×C₁₄₉	—	8	1	no	—
190	C₂×C₁₄₉	C₂×#408	1	1	yes	characteristic
191	C₂×C₁₄₉	#2883	1	1	yes	characteristic
192	C₂×C₁₄₉	#2889	1	1	yes	characteristic
193	#17388	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₁₄₉	#17388	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×#542	C₂×C₁₄₉	1	1	yes	characteristic
196	#2975	C₂×C₁₄₉	1	1	yes	characteristic, complemented
197	#2972	C₂×C₁₄₉	1	1	yes	characteristic, complemented
198	#1472	C₂×C₁₄₉	1	4	yes	complemented
199	#1468	C₂×C₁₄₉	1	4	yes	complemented
200	#1461	C₂×C₁₄₉	1	2	yes	complemented
201	#1458	C₂×C₁₄₉	1	2	yes	complemented
202	#542	—	2	4	no	—
203	#542	—	2	4	no	—
204	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
205	C₂×#126	C₄×C₁₄₉	1	2	yes	—
206	C₂×#124	C₄×C₁₄₉	1	1	yes	characteristic
207	C₂×#124	C₄×C₁₄₉	1	2	yes	—
208	C₂×#123	C₂²×C₁₄₉	1	2	yes	—
209	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	C₂²×C₁₄₉	1	2	yes	—
211	C₂×#121	C₄×C₁₄₉	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
214	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
215	#436	—	2	4	no	—
216	C₈×D₄	—	2	4	no	—
217	#431	C₂²×C₁₄₉	1	2	yes	—
218	#431	C₂²×C₁₄₉	1	2	yes	—
219	#407	C₂²×C₁₄₉	1	4	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	—
221	#324	C₂²×C₁₄₉	1	4	yes	—
222	#324	C₂²×C₁₄₉	1	8	yes	—
223	#323	C₂²×C₁₄₉	1	4	yes	—
224	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
225	C₂²×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
226	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
227	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
228	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
230	C₂×M₁₆	—	2	4	no	—
231	C₂²×C₈	—	2	4	no	—
232	C₄⋊Q₈	—	2	4	no	—
233	#126	—	2	8	no	—
234	#124	—	2	4	no	—
235	#124	—	2	8	no	—
236	#123	—	2	4	no	—
237	#123	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	#121	—	2	4	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×D₄	D₄×C₁₄₉	1	4	yes	—
245	C₄×D₄	D₄×C₁₄₉	1	4	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	4	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
270	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
274	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	8	2	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	8	2	no	—
282	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	8	2	no	—
286	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
297	M₁₆	—	8	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	8	4	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	8	yes	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	4	no	—
320	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
321	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
330	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
331	Q₈	—	4	4	no	—
332	Q₈	—	8	4	no	—
333	D₄	—	2	8	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
354	C₂×C₄	#131×C₁₄₉	1	4	yes	—
355	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
357	C₈	—	4	4	no	—
358	C₈	—	4	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	8	2	no	—
369	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
370	C₂²	C₂×#131×C₁₄₉	1	2	yes	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	#408×C₁₄₉	1	4	yes	—
381	C₂	—	2	2	no	—
382	C₂	—	4	4	no	—
383	C₂	—	8	1	no	—
384	C₂	C₂×#408×C₁₄₉	1	1	yes	characteristic
385	C₂	#2883×C₁₄₉	1	1	yes	characteristic
386	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	C₂×#121×C₁₄₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×D₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2975×C₁₄₉	C₂	semidirect
3. #2972×C₁₄₉	C₂	semidirect
4. #1472×C₁₄₉	C₂	semidirect
5. #1468×C₁₄₉	C₂	semidirect
6. #1461×C₁₄₉	C₂	semidirect
7. #1458×C₁₄₉	C₂	semidirect
193. #17388	C₁₄₉	direct (N × H)
194. C₁₄₉	#17388	direct (N × H)
196. #2975	C₂×C₁₄₉	semidirect
197. #2972	C₂×C₁₄₉	semidirect
198. #1472	C₂×C₁₄₉	semidirect
199. #1468	C₂×C₁₄₉	semidirect
200. #1461	C₂×C₁₄₉	semidirect
201. #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×#542×C₁₄₉	2
#2975×C₁₄₉	2
#2972×C₁₄₉	2
#1472×C₁₄₉	2
#1468×C₁₄₉	2
#1461×C₁₄₉	2
#1458×C₁₄₉	2
#17388	149

Subgroups — C149×#17388 #49196337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17388 #49196337