Subgroups — C₁₄₉×#11073 #49190022

Order 38144.

1026 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2905×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#418×C₁₄₉	C₂	1	2	yes	maximal
3	#2309×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1740×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×H(3,ℤ/4)×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
9	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
11	#424×C₁₄₉	—	2	4	no	—
12	#423×C₁₄₉	—	2	2	no	—
13	#418×C₁₄₉	—	2	4	no	—
14	#418×C₁₄₉	—	2	4	no	—
15	C₂×#102×C₁₄₉	—	2	4	no	—
16	#390×C₁₄₉	—	2	2	no	—
17	#390×C₁₄₉	C₄	1	4	yes	complemented
18	#379×C₁₄₉	—	2	2	no	—
19	#342×C₁₄₉	—	2	2	no	—
20	H(3,ℤ/4)×C₁₄₉	—	2	4	no	—
21	C₂⁵×C₁₄₉	—	2	1	no	—
22	C₂²×D₄×C₁₄₉	—	2	2	no	—
23	C₂²×D₄×C₁₄₉	—	2	2	no	—
24	C₂²×D₄×C₁₄₉	—	2	1	no	—
25	C₂²×D₄×C₁₄₉	—	2	2	no	—
26	C₂²×D₄×C₁₄₉	—	2	2	no	—
27	C₂²×D₄×C₁₄₉	—	2	1	no	—
28	C₂²×D₄×C₁₄₉	—	2	1	no	—
29	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
31	C₂²×D₄×C₁₄₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₄₉	—	2	2	no	—
34	C₂×M₁₆×C₁₄₉	—	2	2	no	—
35	C₂×M₁₆×C₁₄₉	—	2	2	no	—
36	C₂×M₁₆×C₁₄₉	—	2	2	no	—
37	C₂×M₁₆×C₁₄₉	—	2	2	no	—
38	C₂×M₁₆×C₁₄₉	—	2	2	no	—
39	C₂²×C₈×C₁₄₉	D₄	1	4	yes	—
40	#117×C₁₄₉	—	2	2	no	—
41	#117×C₁₄₉	—	2	2	no	—
42	#117×C₁₄₉	—	2	2	no	—
43	#117×C₁₄₉	—	2	2	no	—
44	#117×C₁₄₉	—	2	2	no	—
45	#117×C₁₄₉	—	2	2	no	—
46	#117×C₁₄₉	—	2	2	no	—
47	#117×C₁₄₉	D₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₄₉	D₄	1	2	yes	—
55	C₂×C₄²×C₁₄₉	—	2	2	no	—
56	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
58	C₄⋊C₈×C₁₄₉	—	2	8	no	—
59	#102×C₁₄₉	—	2	16	no	—
60	C₂⁴×C₁₄₉	—	2	2	no	—
61	C₂⁴×C₁₄₉	—	2	2	no	—
62	C₂⁴×C₁₄₉	—	2	2	no	—
63	C₂⁴×C₁₄₉	—	4	2	no	—
64	C₂⁴×C₁₄₉	—	4	2	no	—
65	C₂⁴×C₁₄₉	—	8	4	no	—
66	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₁₄₉	—	2	2	no	—
68	C₂×D₄×C₁₄₉	—	2	4	no	—
69	C₂×D₄×C₁₄₉	—	2	4	no	—
70	C₂×D₄×C₁₄₉	—	2	4	no	—
71	C₂×D₄×C₁₄₉	—	2	2	no	—
72	C₂×D₄×C₁₄₉	—	2	4	no	—
73	C₂×D₄×C₁₄₉	—	2	4	no	—
74	C₂×D₄×C₁₄₉	—	2	2	no	—
75	C₂×D₄×C₁₄₉	—	2	4	no	—
76	C₂×D₄×C₁₄₉	—	4	1	no	—
77	C₂×D₄×C₁₄₉	—	4	2	no	—
78	C₂×D₄×C₁₄₉	—	4	2	no	—
79	C₂×D₄×C₁₄₉	—	4	1	no	—
80	C₂×D₄×C₁₄₉	—	4	2	no	—
81	C₂×D₄×C₁₄₉	—	4	1	no	—
82	C₂×D₄×C₁₄₉	—	4	2	no	—
83	C₂×D₄×C₁₄₉	—	4	1	no	—
84	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₄₉	—	2	2	no	—
86	C₂²×C₄×C₁₄₉	—	4	2	no	—
87	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
98	M₁₆×C₁₄₉	—	4	2	no	—
99	M₁₆×C₁₄₉	—	4	2	no	—
100	M₁₆×C₁₄₉	—	4	2	no	—
101	M₁₆×C₁₄₉	—	4	2	no	—
102	C₂×C₈×C₁₄₉	—	2	4	no	—
103	C₂×C₈×C₁₄₉	—	2	4	no	—
104	C₂×C₈×C₁₄₉	—	2	4	no	—
105	C₄⋊C₄×C₁₄₉	—	2	4	no	—
106	C₄⋊C₄×C₁₄₉	—	2	4	no	—
107	C₄⋊C₄×C₁₄₉	—	4	1	no	—
108	C₄⋊C₄×C₁₄₉	—	4	2	no	—
109	C₄⋊C₄×C₁₄₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₄₉	—	8	8	no	—
115	C₄²×C₁₄₉	—	2	2	no	—
116	C₄²×C₁₄₉	—	2	2	no	—
117	C₄²×C₁₄₉	—	2	4	no	—
118	C₄²×C₁₄₉	—	2	4	no	—
119	C₄²×C₁₄₉	—	4	2	no	—
120	C₂³×C₁₄₉	—	2	4	no	—
121	C₂³×C₁₄₉	—	4	2	no	—
122	C₂³×C₁₄₉	—	4	8	no	—
123	C₂³×C₁₄₉	—	4	2	no	—
124	C₂³×C₁₄₉	—	4	2	no	—
125	C₂³×C₁₄₉	—	4	4	no	—
126	C₂³×C₁₄₉	—	4	4	no	—
127	C₂³×C₁₄₉	—	8	8	no	—
128	C₂³×C₁₄₉	—	8	4	no	—
129	C₂³×C₁₄₉	—	8	4	no	—
130	C₂³×C₁₄₉	—	8	8	no	—
131	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₄₉	#121	1	2	yes	—
133	C₂³×C₁₄₉	#121	1	1	yes	characteristic
134	C₂³×C₁₄₉	#121	1	2	yes	—
135	C₂³×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
136	D₄×C₁₄₉	—	2	8	no	—
137	D₄×C₁₄₉	—	4	4	no	—
138	D₄×C₁₄₉	—	4	2	no	—
139	D₄×C₁₄₉	—	4	2	no	—
140	D₄×C₁₄₉	—	4	2	no	—
141	D₄×C₁₄₉	—	4	2	no	—
142	C₂×C₄×C₁₄₉	—	2	4	no	—
143	C₂×C₄×C₁₄₉	—	4	4	no	—
144	C₂×C₄×C₁₄₉	—	4	4	no	—
145	C₂×C₄×C₁₄₉	—	4	2	no	—
146	C₂×C₄×C₁₄₉	—	4	4	no	—
147	C₂×C₄×C₁₄₉	—	8	4	no	—
148	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
150	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₄₉	#120	1	2	yes	—
153	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
154	C₂×C₄×C₁₄₉	#121	1	2	yes	—
155	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₄₉	#123	1	2	yes	—
160	C₂×C₄×C₁₄₉	#123	1	2	yes	—
161	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
162	C₂×C₄×C₁₄₉	#124	1	2	yes	—
163	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
164	C₂×C₄×C₁₄₉	#126	1	2	yes	—
165	C₂×C₄×C₁₄₉	#127	1	1	yes	characteristic
166	C₈×C₁₄₉	—	4	4	no	—
167	C₂²×C₁₄₉	—	2	2	no	—
168	C₂²×C₁₄₉	—	2	4	no	—
169	C₂²×C₁₄₉	—	4	2	no	—
170	C₂²×C₁₄₉	—	4	1	no	—
171	C₂²×C₁₄₉	—	4	1	no	—
172	C₂²×C₁₄₉	—	4	8	no	—
173	C₂²×C₁₄₉	—	4	4	no	—
174	C₂²×C₁₄₉	—	8	4	no	—
175	C₂²×C₁₄₉	—	8	8	no	—
176	C₂²×C₁₄₉	—	8	8	no	—
177	C₂²×C₁₄₉	—	8	4	no	—
178	C₂²×C₁₄₉	#380	1	1	yes	characteristic
179	C₂²×C₁₄₉	#386	1	1	yes	characteristic
180	C₂²×C₁₄₉	#390	1	1	yes	characteristic
181	C₂²×C₁₄₉	#394	1	2	yes	—
182	C₂²×C₁₄₉	#396	1	2	yes	—
183	C₄×C₁₄₉	—	4	4	no	—
184	C₄×C₁₄₉	—	8	2	no	—
185	C₄×C₁₄₉	—	8	4	no	—
186	C₄×C₁₄₉	#385	1	2	yes	—
187	C₄×C₁₄₉	#388	1	2	yes	—
188	C₄×C₁₄₉	#392	1	1	yes	characteristic
189	C₄×C₁₄₉	#393	1	1	yes	characteristic
190	C₄×C₁₄₉	#397	1	1	yes	characteristic
191	C₄×C₁₄₉	#399	1	1	yes	characteristic
192	C₂×C₁₄₉	—	2	1	no	—
193	C₂×C₁₄₉	—	2	2	no	—
194	C₂×C₁₄₉	—	2	1	no	—
195	C₂×C₁₄₉	—	2	2	no	—
196	C₂×C₁₄₉	—	8	4	no	—
197	C₂×C₁₄₉	#1439	1	1	yes	characteristic
198	C₂×C₁₄₉	#1910	1	2	yes	—
199	#11073	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₄₉	#11073	1	1	yes	characteristic, direct product factor, Sylow
201	#2905	C₂×C₁₄₉	1	1	yes	characteristic, complemented
202	C₂×#418	C₂×C₁₄₉	1	2	yes	—
203	#2309	C₂×C₁₄₉	1	1	yes	characteristic
204	#1740	C₂×C₁₄₉	1	1	yes	characteristic, complemented
205	C₂×H(3,ℤ/4)	C₂×C₁₄₉	1	2	yes	complemented
206	C₂³×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
208	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
209	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
210	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
211	#424	—	2	4	no	—
212	#423	—	2	2	no	—
213	#418	—	2	4	no	—
214	#418	—	2	4	no	—
215	C₂×#102	—	2	4	no	—
216	#390	—	2	2	no	—
217	#390	C₄×C₁₄₉	1	4	yes	complemented
218	#379	—	2	2	no	—
219	#342	—	2	2	no	—
220	H(3,ℤ/4)	—	2	4	no	—
221	C₂⁵	—	2	1	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
230	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
231	C₂²×D₄	Q₈×C₁₄₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂²×C₈	D₄×C₁₄₉	1	4	yes	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	D₄×C₁₄₉	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	D₄×C₁₄₉	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
257	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
258	C₄⋊C₈	—	2	8	no	—
259	#102	—	2	16	no	—
260	C₂⁴	—	2	2	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	4	2	no	—
264	C₂⁴	—	4	2	no	—
265	C₂⁴	—	8	4	no	—
266	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
294	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
296	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
297	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	M₁₆	—	4	2	no	—
301	M₁₆	—	4	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	8	8	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	8	8	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	8	no	—
331	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
332	C₂³	#121×C₁₄₉	1	2	yes	—
333	C₂³	#121×C₁₄₉	1	1	yes	characteristic
334	C₂³	#121×C₁₄₉	1	2	yes	—
335	C₂³	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
336	D₄	—	2	8	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
349	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
352	C₂×C₄	#120×C₁₄₉	1	2	yes	—
353	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
354	C₂×C₄	#121×C₁₄₉	1	2	yes	—
355	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
356	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
358	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
359	C₂×C₄	#123×C₁₄₉	1	2	yes	—
360	C₂×C₄	#123×C₁₄₉	1	2	yes	—
361	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
362	C₂×C₄	#124×C₁₄₉	1	2	yes	—
363	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
364	C₂×C₄	#126×C₁₄₉	1	2	yes	—
365	C₂×C₄	#127×C₁₄₉	1	1	yes	characteristic
366	C₈	—	4	4	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	8	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	4	no	—
378	C₂²	#380×C₁₄₉	1	1	yes	characteristic
379	C₂²	#386×C₁₄₉	1	1	yes	characteristic
380	C₂²	#390×C₁₄₉	1	1	yes	characteristic
381	C₂²	#394×C₁₄₉	1	2	yes	—
382	C₂²	#396×C₁₄₉	1	2	yes	—
383	C₄	—	4	4	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	4	no	—
386	C₄	#385×C₁₄₉	1	2	yes	—
387	C₄	#388×C₁₄₉	1	2	yes	—
388	C₄	#392×C₁₄₉	1	1	yes	characteristic
389	C₄	#393×C₁₄₉	1	1	yes	characteristic
390	C₄	#397×C₁₄₉	1	1	yes	characteristic
391	C₄	#399×C₁₄₉	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	8	4	no	—
397	C₂	#1439×C₁₄₉	1	1	yes	characteristic
398	C₂	#1910×C₁₄₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₄₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
prime radical	C₂³×D₄×C₁₄₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂³×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2905×C₁₄₉	C₂	semidirect
4. #1740×C₁₄₉	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₄₉	C₂	semidirect
17. #390×C₁₄₉	C₄	semidirect
199. #11073	C₁₄₉	direct (N × H)
200. C₁₄₉	#11073	direct (N × H)
201. #2905	C₂×C₁₄₉	semidirect
204. #1740	C₂×C₁₄₉	semidirect
205. C₂×H(3,ℤ/4)	C₂×C₁₄₉	semidirect
217. #390	C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#2905×C₁₄₉	2
C₂×#418×C₁₄₉	2
#2309×C₁₄₉	2
#1740×C₁₄₉	2
C₂×H(3,ℤ/4)×C₁₄₉	2
#11073	149

Subgroups — C149×#11073 #49190022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11073 #49190022