Subgroups — C₁₄₉×#10855 #49189804

Order 38144.

802 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#2285×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₁₄₉	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
6	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
7	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
9	#423×C₁₄₉	—	2	1	no	—
10	#423×C₁₄₉	—	2	1	no	—
11	#423×C₁₄₉	—	2	2	no	—
12	C₂×C₄⋊C₈×C₁₄₉	C₄	1	4	yes	complemented
13	C₄×M₁₆×C₁₄₉	—	2	1	no	—
14	C₄×M₁₆×C₁₄₉	—	2	1	no	—
15	C₄×M₁₆×C₁₄₉	C₄	1	2	yes	complemented
16	C₄×M₁₆×C₁₄₉	C₄	1	2	yes	complemented
17	C₂×#97×C₁₄₉	—	2	1	no	—
18	C₂×C₄×C₈×C₁₄₉	—	2	1	no	—
19	#384×C₁₄₉	—	2	1	no	—
20	#382×C₁₄₉	—	2	1	no	—
21	#380×C₁₄₉	C₄	1	4	yes	—
22	C₄×C₄⋊C₄×C₁₄₉	—	2	2	no	—
23	#344×C₁₄₉	—	2	8	no	—
24	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₁₄₉	—	2	2	no	—
27	C₂×M₁₆×C₁₄₉	—	2	2	no	—
28	C₂×M₁₆×C₁₄₉	—	2	2	no	—
29	C₂×M₁₆×C₁₄₉	—	2	2	no	—
30	C₂×M₁₆×C₁₄₉	—	2	2	no	—
31	C₂×M₁₆×C₁₄₉	—	2	4	no	—
32	C₂×M₁₆×C₁₄₉	—	2	4	no	—
33	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	—
34	C₂×M₁₆×C₁₄₉	D₄	1	4	yes	—
35	C₂×M₁₆×C₁₄₉	Q₈	1	4	yes	—
36	C₂²×C₈×C₁₄₉	—	2	2	no	—
37	C₂²×C₈×C₁₄₉	C₂×C₄	1	4	yes	—
38	#117×C₁₄₉	—	2	4	no	—
39	#117×C₁₄₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₄₉	—	2	2	no	—
44	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
50	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₄₉	Q₈	1	2	yes	—
53	C₄⋊C₈×C₁₄₉	—	2	4	no	—
54	C₄⋊C₈×C₁₄₉	—	2	4	no	—
55	#97×C₁₄₉	—	2	2	no	—
56	#97×C₁₄₉	—	2	2	no	—
57	C₄×C₈×C₁₄₉	—	2	2	no	—
58	C₄×C₈×C₁₄₉	—	2	2	no	—
59	#95×C₁₄₉	—	2	4	no	—
60	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₄₉	—	2	4	no	—
62	C₂²×C₄×C₁₄₉	—	4	4	no	—
63	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
64	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
78	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
79	M₁₆×C₁₄₉	—	2	4	no	—
80	M₁₆×C₁₄₉	—	2	4	no	—
81	M₁₆×C₁₄₉	—	2	4	no	—
82	M₁₆×C₁₄₉	—	4	4	no	—
83	M₁₆×C₁₄₉	—	4	2	no	—
84	M₁₆×C₁₄₉	—	4	2	no	—
85	M₁₆×C₁₄₉	C₄⋊C₄	1	8	yes	complemented
86	C₂×C₈×C₁₄₉	—	2	4	no	—
87	C₂×C₈×C₁₄₉	—	2	4	no	—
88	C₂×C₈×C₁₄₉	—	2	4	no	—
89	C₂×C₈×C₁₄₉	—	2	4	no	—
90	C₂×C₈×C₁₄₉	—	2	8	no	—
91	C₄⋊C₄×C₁₄₉	—	4	8	no	—
92	C₄⋊C₄×C₁₄₉	—	4	4	no	—
93	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
94	C₄²×C₁₄₉	—	4	2	no	—
95	C₄²×C₁₄₉	—	4	2	no	—
96	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
101	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
102	C₄²×C₁₄₉	C₄⋊C₄	1	2	yes	—
103	C₄²×C₁₄₉	C₄⋊C₄	1	2	yes	—
104	C₄²×C₁₄₉	C₄⋊C₄	1	2	yes	—
105	C₄²×C₁₄₉	C₄⋊C₄	1	2	yes	—
106	C₂³×C₁₄₉	—	4	2	no	—
107	C₂³×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
108	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂³×C₁₄₉	C₄×D₄	1	2	yes	—
111	C₂³×C₁₄₉	C₄×Q₈	1	2	yes	—
112	C₂×C₄×C₁₄₉	—	2	4	no	—
113	C₂×C₄×C₁₄₉	—	2	4	no	—
114	C₂×C₄×C₁₄₉	—	2	4	no	—
115	C₂×C₄×C₁₄₉	—	4	2	no	—
116	C₂×C₄×C₁₄₉	—	4	2	no	—
117	C₂×C₄×C₁₄₉	—	4	2	no	—
118	C₂×C₄×C₁₄₉	—	4	8	no	—
119	C₂×C₄×C₁₄₉	—	4	4	no	—
120	C₂×C₄×C₁₄₉	#95	1	2	yes	—
121	C₂×C₄×C₁₄₉	#95	1	2	yes	—
122	C₂×C₄×C₁₄₉	#95	1	2	yes	—
123	C₂×C₄×C₁₄₉	#95	1	2	yes	—
124	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₄₉	#117	1	2	yes	—
130	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₁₄₉	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₁₄₉	#121	1	2	yes	—
133	C₂×C₄×C₁₄₉	#121	1	2	yes	—
134	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
137	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
138	C₂×C₄×C₁₄₉	#125	1	2	yes	—
139	C₂×C₄×C₁₄₉	#127	1	1	yes	characteristic
140	C₂×C₄×C₁₄₉	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
142	C₈×C₁₄₉	—	2	8	no	—
143	C₈×C₁₄₉	—	4	4	no	—
144	C₂²×C₁₄₉	—	2	2	no	—
145	C₂²×C₁₄₉	—	2	2	no	—
146	C₂²×C₁₄₉	—	2	2	no	—
147	C₂²×C₁₄₉	—	4	2	no	—
148	C₂²×C₁₄₉	—	4	2	no	—
149	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
150	C₂²×C₁₄₉	C₄×C₄⋊C₄	1	2	yes	—
151	C₂²×C₁₄₉	#389	1	2	yes	—
152	C₂²×C₁₄₉	#390	1	1	yes	characteristic
153	C₂²×C₁₄₉	#391	1	1	yes	characteristic
154	C₄×C₁₄₉	—	2	2	no	—
155	C₄×C₁₄₉	—	2	2	no	—
156	C₄×C₁₄₉	—	2	2	no	—
157	C₄×C₁₄₉	—	8	4	no	—
158	C₄×C₁₄₉	#344	1	4	yes	complemented
159	C₄×C₁₄₉	#380	1	2	yes	—
160	C₄×C₁₄₉	#382	1	1	yes	characteristic
161	C₄×C₁₄₉	#384	1	1	yes	characteristic
162	C₄×C₁₄₉	#389	1	2	yes	—
163	C₄×C₁₄₉	#390	1	1	yes	characteristic
164	C₄×C₁₄₉	#391	1	1	yes	characteristic
165	C₂×C₁₄₉	—	2	1	no	—
166	C₂×C₁₄₉	—	2	2	no	—
167	C₂×C₁₄₉	—	2	2	no	—
168	C₂×C₁₄₉	—	2	1	no	—
169	C₂×C₁₄₉	C₄⋊#95	1	1	yes	characteristic
170	C₂×C₁₄₉	C₂×#344	1	2	yes	—
171	#10855	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₁₄₉	#10855	1	1	yes	characteristic, direct product factor, Sylow
173	C₂×#423	C₂×C₁₄₉	1	1	yes	characteristic
174	C₂×C₄×M₁₆	C₂×C₁₄₉	1	1	yes	characteristic
175	#2285	C₂×C₁₄₉	1	1	yes	characteristic
176	C₂×#344	C₂×C₁₄₉	1	4	yes	—
177	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
178	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
179	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
180	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
181	#423	—	2	1	no	—
182	#423	—	2	1	no	—
183	#423	—	2	2	no	—
184	C₂×C₄⋊C₈	C₄×C₁₄₉	1	4	yes	complemented
185	C₄×M₁₆	—	2	1	no	—
186	C₄×M₁₆	—	2	1	no	—
187	C₄×M₁₆	C₄×C₁₄₉	1	2	yes	complemented
188	C₄×M₁₆	C₄×C₁₄₉	1	2	yes	complemented
189	C₂×#97	—	2	1	no	—
190	C₂×C₄×C₈	—	2	1	no	—
191	#384	—	2	1	no	—
192	#382	—	2	1	no	—
193	#380	C₄×C₁₄₉	1	4	yes	—
194	C₄×C₄⋊C₄	—	2	2	no	—
195	#344	—	2	8	no	—
196	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
197	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	4	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	4	no	—
205	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	—
206	C₂×M₁₆	D₄×C₁₄₉	1	4	yes	—
207	C₂×M₁₆	Q₈×C₁₄₉	1	4	yes	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	C₂×C₄×C₁₄₉	1	4	yes	—
210	#117	—	2	4	no	—
211	#117	—	2	4	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
219	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
222	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
224	C₂×C₄²	Q₈×C₁₄₉	1	2	yes	—
225	C₄⋊C₈	—	2	4	no	—
226	C₄⋊C₈	—	2	4	no	—
227	#97	—	2	2	no	—
228	#97	—	2	2	no	—
229	C₄×C₈	—	2	2	no	—
230	C₄×C₈	—	2	2	no	—
231	#95	—	2	4	no	—
232	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
236	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
237	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
238	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
239	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
240	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
247	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
248	C₂²×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
249	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
250	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
251	M₁₆	—	2	4	no	—
252	M₁₆	—	2	4	no	—
253	M₁₆	—	2	4	no	—
254	M₁₆	—	4	4	no	—
255	M₁₆	—	4	2	no	—
256	M₁₆	—	4	2	no	—
257	M₁₆	C₄⋊C₄×C₁₄₉	1	8	yes	complemented
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	8	no	—
263	C₄⋊C₄	—	4	8	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₂²⋊C₄	—	2	8	no	—
266	C₄²	—	4	2	no	—
267	C₄²	—	4	2	no	—
268	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
269	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
270	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
271	C₄²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
272	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
273	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
274	C₄²	C₄⋊C₄×C₁₄₉	1	2	yes	—
275	C₄²	C₄⋊C₄×C₁₄₉	1	2	yes	—
276	C₄²	C₄⋊C₄×C₁₄₉	1	2	yes	—
277	C₄²	C₄⋊C₄×C₁₄₉	1	2	yes	—
278	C₂³	—	4	2	no	—
279	C₂³	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
280	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
281	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
282	C₂³	C₄×D₄×C₁₄₉	1	2	yes	—
283	C₂³	C₄×Q₈×C₁₄₉	1	2	yes	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	8	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	#95×C₁₄₉	1	2	yes	—
293	C₂×C₄	#95×C₁₄₉	1	2	yes	—
294	C₂×C₄	#95×C₁₄₉	1	2	yes	—
295	C₂×C₄	#95×C₁₄₉	1	2	yes	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
297	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
298	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
301	C₂×C₄	#117×C₁₄₉	1	2	yes	—
302	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₁₄₉	1	2	yes	—
304	C₂×C₄	#121×C₁₄₉	1	2	yes	—
305	C₂×C₄	#121×C₁₄₉	1	2	yes	—
306	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
307	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
308	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
309	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
310	C₂×C₄	#125×C₁₄₉	1	2	yes	—
311	C₂×C₄	#127×C₁₄₉	1	1	yes	characteristic
312	C₂×C₄	C₄⋊Q₈×C₁₄₉	1	2	yes	—
313	C₂×C₄	C₄⋊Q₈×C₁₄₉	1	1	yes	characteristic
314	C₈	—	2	8	no	—
315	C₈	—	4	4	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
322	C₂²	C₄×C₄⋊C₄×C₁₄₉	1	2	yes	—
323	C₂²	#389×C₁₄₉	1	2	yes	—
324	C₂²	#390×C₁₄₉	1	1	yes	characteristic
325	C₂²	#391×C₁₄₉	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	8	4	no	—
330	C₄	#344×C₁₄₉	1	4	yes	complemented
331	C₄	#380×C₁₄₉	1	2	yes	—
332	C₄	#382×C₁₄₉	1	1	yes	characteristic
333	C₄	#384×C₁₄₉	1	1	yes	characteristic
334	C₄	#389×C₁₄₉	1	2	yes	—
335	C₄	#390×C₁₄₉	1	1	yes	characteristic
336	C₄	#391×C₁₄₉	1	1	yes	characteristic
337	C₂	—	2	1	no	—
338	C₂	—	2	2	no	—
339	C₂	—	2	2	no	—
340	C₂	—	2	1	no	—
341	C₂	C₄⋊#95×C₁₄₉	1	1	yes	characteristic
342	C₂	C₂×#344×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	C₂×#95
prime radical	C₂⁴×C₁₄₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₄⋊C₈×C₁₄₉	C₄	semidirect
15. C₄×M₁₆×C₁₄₉	C₄	semidirect
16. C₄×M₁₆×C₁₄₉	C₄	semidirect
85. M₁₆×C₁₄₉	C₄⋊C₄	semidirect
158. C₄×C₁₄₉	#344	semidirect
171. #10855	C₁₄₉	direct (N × H)
172. C₁₄₉	#10855	direct (N × H)
184. C₂×C₄⋊C₈	C₄×C₁₄₉	semidirect
187. C₄×M₁₆	C₄×C₁₄₉	semidirect
188. C₄×M₁₆	C₄×C₁₄₉	semidirect
257. M₁₆	C₄⋊C₄×C₁₄₉	semidirect
330. C₄	#344×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#423×C₁₄₉	2
C₂×C₄×M₁₆×C₁₄₉	2
#2285×C₁₄₉	2
C₂×#344×C₁₄₉	2
#10855	149

Subgroups — C149×#10855 #49189804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10855 #49189804