Subgroups — C₁₄₉×#17638 #49196587

Order 38144.

1144 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3444×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1526×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1525×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#1524×C₁₄₉	C₂	1	8	yes	maximal, complemented
6	C₂²×M₁₆×C₁₄₉	—	2	2	no	—
7	#533×C₁₄₉	C₄	1	2	yes	—
8	#533×C₁₄₉	C₂²	1	1	yes	characteristic
9	#532×C₁₄₉	C₄	1	2	yes	—
10	#532×C₁₄₉	C₂²	1	1	yes	characteristic
11	#529×C₁₄₉	—	2	2	no	—
12	#529×C₁₄₉	—	2	2	no	—
13	#529×C₁₄₉	C₂²	1	4	yes	—
14	#525×C₁₄₉	—	2	2	no	—
15	#525×C₁₄₉	C₄	1	2	yes	—
16	C₄×#41×C₁₄₉	—	2	2	no	—
17	C₄×#41×C₁₄₉	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
19	C₄×M₁₆×C₁₄₉	—	2	2	no	—
20	C₄×M₁₆×C₁₄₉	—	2	2	no	—
21	C₄×M₁₆×C₁₄₉	C₂²	1	4	yes	—
22	C₄×M₁₆×C₁₄₉	C₂²	1	4	yes	—
23	C₂×#97×C₁₄₉	C₂²	1	4	yes	—
24	C₂×C₄×C₈×C₁₄₉	—	2	2	no	—
25	#330×C₁₄₉	C₂²	1	8	yes	complemented
26	#329×C₁₄₉	C₂²	1	8	yes	complemented
27	C₂×#41×C₁₄₉	—	2	2	no	—
28	C₂×#41×C₁₄₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
31	C₂×M₁₆×C₁₄₉	—	2	16	no	—
32	C₂×M₁₆×C₁₄₉	—	2	4	no	—
33	C₂×M₁₆×C₁₄₉	—	2	4	no	—
34	C₂²×C₈×C₁₄₉	—	2	4	no	—
35	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
36	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
37	#127×C₁₄₉	C₂×C₄	1	1	yes	characteristic
38	#126×C₁₄₉	—	2	4	no	—
39	#125×C₁₄₉	—	2	2	no	—
40	#125×C₁₄₉	C₂³	1	2	yes	—
41	#124×C₁₄₉	—	2	2	no	—
42	#124×C₁₄₉	C₂³	1	2	yes	—
43	#123×C₁₄₉	—	2	2	no	—
44	#123×C₁₄₉	—	2	4	no	—
45	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
46	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
47	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
48	#121×C₁₄₉	—	2	2	no	—
49	#121×C₁₄₉	—	2	2	no	—
50	#121×C₁₄₉	C₂×C₄	1	4	yes	—
51	#120×C₁₄₉	—	2	2	no	—
52	C₄×Q₈×C₁₄₉	—	2	2	no	—
53	C₄×Q₈×C₁₄₉	—	2	2	no	—
54	C₄×Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
55	C₄×D₄×C₁₄₉	—	2	4	no	—
56	C₄×D₄×C₁₄₉	—	2	4	no	—
57	C₄×D₄×C₁₄₉	—	2	4	no	—
58	C₄×D₄×C₁₄₉	—	2	2	no	—
59	C₄×D₄×C₁₄₉	—	2	2	no	—
60	C₄×D₄×C₁₄₉	C₂×C₄	1	4	yes	—
61	#117×C₁₄₉	—	2	2	no	—
62	#117×C₁₄₉	—	2	2	no	—
63	#117×C₁₄₉	—	2	4	no	—
64	#117×C₁₄₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₄₉	—	2	2	no	—
66	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
69	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
73	#97×C₁₄₉	—	2	4	no	—
74	#97×C₁₄₉	C₂³	1	8	yes	—
75	C₄×C₈×C₁₄₉	—	2	4	no	—
76	C₄×C₈×C₁₄₉	—	2	4	no	—
77	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
78	#41×C₁₄₉	—	4	4	no	—
79	#41×C₁₄₉	—	4	8	no	—
80	C₂×Q₈×C₁₄₉	—	2	2	no	—
81	C₂×Q₈×C₁₄₉	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₁₄₉	—	2	2	no	—
83	C₂×D₄×C₁₄₉	—	2	4	no	—
84	C₂×D₄×C₁₄₉	—	2	2	no	—
85	C₂×D₄×C₁₄₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₄₉	—	2	8	no	—
87	C₂²×C₄×C₁₄₉	—	2	2	no	—
88	C₂²×C₄×C₁₄₉	—	2	4	no	—
89	C₂²×C₄×C₁₄₉	—	4	2	no	—
90	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
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	2	yes	—
95	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
100	M₁₆×C₁₄₉	—	2	16	no	—
101	M₁₆×C₁₄₉	—	2	16	no	—
102	C₂×C₈×C₁₄₉	—	2	16	no	—
103	C₂×C₈×C₁₄₉	—	2	8	no	—
104	C₄⋊C₄×C₁₄₉	—	2	2	no	—
105	C₄⋊C₄×C₁₄₉	—	2	2	no	—
106	C₄⋊C₄×C₁₄₉	—	2	4	no	—
107	C₄⋊C₄×C₁₄₉	—	2	4	no	—
108	C₄⋊C₄×C₁₄₉	—	2	4	no	—
109	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
110	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
112	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
115	C₄²×C₁₄₉	—	2	4	no	—
116	C₄²×C₁₄₉	—	2	2	no	—
117	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
124	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
125	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
127	C₂³×C₁₄₉	—	2	4	no	—
128	C₂³×C₁₄₉	—	2	2	no	—
129	C₂³×C₁₄₉	—	4	1	no	—
130	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
132	Q₈×C₁₄₉	—	4	2	no	—
133	Q₈×C₁₄₉	—	4	4	no	—
134	D₄×C₁₄₉	—	4	2	no	—
135	D₄×C₁₄₉	—	4	4	no	—
136	D₄×C₁₄₉	—	4	8	no	—
137	D₄×C₁₄₉	—	4	4	no	—
138	C₂×C₄×C₁₄₉	—	2	4	no	—
139	C₂×C₄×C₁₄₉	—	2	4	no	—
140	C₂×C₄×C₁₄₉	—	2	2	no	—
141	C₂×C₄×C₁₄₉	—	2	4	no	—
142	C₂×C₄×C₁₄₉	—	2	4	no	—
143	C₂×C₄×C₁₄₉	—	2	4	no	—
144	C₂×C₄×C₁₄₉	—	2	4	no	—
145	C₂×C₄×C₁₄₉	—	2	2	no	—
146	C₂×C₄×C₁₄₉	—	2	4	no	—
147	C₂×C₄×C₁₄₉	—	4	1	no	—
148	C₂×C₄×C₁₄₉	—	4	2	no	—
149	C₂×C₄×C₁₄₉	—	4	4	no	—
150	C₂×C₄×C₁₄₉	—	4	8	no	—
151	C₂×C₄×C₁₄₉	#104	1	8	yes	—
152	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
159	C₈×C₁₄₉	—	2	16	no	—
160	C₂²×C₁₄₉	—	2	2	no	—
161	C₂²×C₁₄₉	—	2	2	no	—
162	C₂²×C₁₄₉	—	2	1	no	—
163	C₂²×C₁₄₉	—	2	2	no	—
164	C₂²×C₁₄₉	—	4	4	no	—
165	C₂²×C₁₄₉	—	4	2	no	—
166	C₂²×C₁₄₉	—	4	4	no	—
167	C₂²×C₁₄₉	C₂×#104	1	4	yes	—
168	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
169	C₄×C₁₄₉	—	2	2	no	—
170	C₄×C₁₄₉	—	2	1	no	—
171	C₄×C₁₄₉	—	2	2	no	—
172	C₄×C₁₄₉	—	2	2	no	—
173	C₄×C₁₄₉	—	4	2	no	—
174	C₄×C₁₄₉	—	4	4	no	—
175	C₄×C₁₄₉	#413	1	2	yes	—
176	C₄×C₁₄₉	C₂×#104	1	4	yes	—
177	C₄×C₁₄₉	C₂×#104	1	4	yes	—
178	C₂×C₁₄₉	—	2	4	no	—
179	C₂×C₁₄₉	—	4	1	no	—
180	C₂×C₁₄₉	—	8	2	no	—
181	C₂×C₁₄₉	C₂×#413	1	1	yes	characteristic
182	C₂×C₁₄₉	C₂²×#104	1	2	yes	—
183	#17638	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₄₉	#17638	1	1	yes	characteristic, direct product factor, Sylow
185	#3444	C₂×C₁₄₉	1	1	yes	characteristic
186	C₂×C₄×M₁₆	C₂×C₁₄₉	1	2	yes	complemented
187	#1526	C₂×C₁₄₉	1	2	yes	complemented
188	#1525	C₂×C₁₄₉	1	2	yes	complemented
189	#1524	C₂×C₁₄₉	1	8	yes	complemented
190	C₂²×M₁₆	—	2	2	no	—
191	#533	C₄×C₁₄₉	1	2	yes	—
192	#533	C₂²×C₁₄₉	1	1	yes	characteristic
193	#532	C₄×C₁₄₉	1	2	yes	—
194	#532	C₂²×C₁₄₉	1	1	yes	characteristic
195	#529	—	2	2	no	—
196	#529	—	2	2	no	—
197	#529	C₂²×C₁₄₉	1	4	yes	—
198	#525	—	2	2	no	—
199	#525	C₄×C₁₄₉	1	2	yes	—
200	C₄×#41	—	2	2	no	—
201	C₄×#41	C₄×C₁₄₉	1	2	yes	—
202	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
203	C₄×M₁₆	—	2	2	no	—
204	C₄×M₁₆	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₁₄₉	1	4	yes	—
206	C₄×M₁₆	C₂²×C₁₄₉	1	4	yes	—
207	C₂×#97	C₂²×C₁₄₉	1	4	yes	—
208	C₂×C₄×C₈	—	2	2	no	—
209	#330	C₂²×C₁₄₉	1	8	yes	complemented
210	#329	C₂²×C₁₄₉	1	8	yes	complemented
211	C₂×#41	—	2	2	no	—
212	C₂×#41	C₂×C₄×C₁₄₉	1	2	yes	—
213	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
215	C₂×M₁₆	—	2	16	no	—
216	C₂×M₁₆	—	2	4	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂²×C₈	—	2	4	no	—
219	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
220	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
221	#127	C₂×C₄×C₁₄₉	1	1	yes	characteristic
222	#126	—	2	4	no	—
223	#125	—	2	2	no	—
224	#125	C₂³×C₁₄₉	1	2	yes	—
225	#124	—	2	2	no	—
226	#124	C₂³×C₁₄₉	1	2	yes	—
227	#123	—	2	2	no	—
228	#123	—	2	4	no	—
229	C₂²⋊Q₈	—	2	2	no	—
230	C₂²⋊Q₈	—	2	2	no	—
231	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
232	#121	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	C₂×C₄×C₁₄₉	1	4	yes	—
235	#120	—	2	2	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
239	C₄×D₄	—	2	4	no	—
240	C₄×D₄	—	2	4	no	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	C₂×C₄×C₁₄₉	1	4	yes	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	4	no	—
248	#117	C₂×C₄×C₁₄₉	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
252	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
253	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
254	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
255	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
256	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
257	#97	—	2	4	no	—
258	#97	C₂³×C₁₄₉	1	8	yes	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	—	2	4	no	—
261	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
262	#41	—	4	4	no	—
263	#41	—	4	8	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	C₂²×C₄×C₁₄₉	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₂²×C₄×C₁₄₉	1	2	yes	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
284	M₁₆	—	2	16	no	—
285	M₁₆	—	2	16	no	—
286	C₂×C₈	—	2	16	no	—
287	C₂×C₈	—	2	8	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	2	no	—
301	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
302	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
303	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
304	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
305	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
306	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
307	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
308	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
309	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
310	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
311	C₂³	—	2	4	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
315	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	4	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	#104×C₁₄₉	1	8	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
341	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
343	C₈	—	2	16	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	4	no	—
351	C₂²	C₂×#104×C₁₄₉	1	4	yes	—
352	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	4	no	—
359	C₄	#413×C₁₄₉	1	2	yes	—
360	C₄	C₂×#104×C₁₄₉	1	4	yes	—
361	C₄	C₂×#104×C₁₄₉	1	4	yes	—
362	C₂	—	2	4	no	—
363	C₂	—	4	1	no	—
364	C₂	—	8	2	no	—
365	C₂	C₂×#413×C₁₄₉	1	1	yes	characteristic
366	C₂	C₂²×#104×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₄₉	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	#3444×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₁₄₉	C₂	semidirect
3. #1526×C₁₄₉	C₂	semidirect
4. #1525×C₁₄₉	C₂	semidirect
5. #1524×C₁₄₉	C₂	semidirect
25. #330×C₁₄₉	C₂²	semidirect
26. #329×C₁₄₉	C₂²	semidirect
183. #17638	C₁₄₉	direct (N × H)
184. C₁₄₉	#17638	direct (N × H)
186. C₂×C₄×M₁₆	C₂×C₁₄₉	semidirect
187. #1526	C₂×C₁₄₉	semidirect
188. #1525	C₂×C₁₄₉	semidirect
189. #1524	C₂×C₁₄₉	semidirect
209. #330	C₂²×C₁₄₉	semidirect
210. #329	C₂²×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3444×C₁₄₉	2
C₂×C₄×M₁₆×C₁₄₉	2
#1526×C₁₄₉	2
#1525×C₁₄₉	2
#1524×C₁₄₉	2
#17638	149

Subgroups — C149×#17638 #49196587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17638 #49196587