Subgroups — C₁₄₉×#11075 #49190024

Order 38144.

1110 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₁₄₉	C₂	1	2	yes	maximal
2	#2297×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#339×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#1728×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₄₉	—	2	1	no	—
10	C₂²×C₄²×C₁₄₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
12	C₂×#104×C₁₄₉	—	2	4	no	—
13	C₂×#104×C₁₄₉	—	2	4	no	—
14	C₂×#104×C₁₄₉	—	2	4	no	—
15	#391×C₁₄₉	C₄	1	2	yes	complemented
16	#390×C₁₄₉	C₄	1	2	yes	complemented
17	#386×C₁₄₉	—	2	1	no	—
18	#386×C₁₄₉	—	2	1	no	—
19	C₄×C₄⋊C₄×C₁₄₉	—	2	4	no	—
20	C₄×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
21	C₂×#95×C₁₄₉	—	2	1	no	—
22	#339×C₁₄₉	—	2	4	no	—
23	#336×C₁₄₉	—	2	2	no	—
24	C₂×#41×C₁₄₉	—	2	1	no	—
25	C₂×#41×C₁₄₉	—	2	1	no	—
26	C₂×#41×C₁₄₉	—	2	2	no	—
27	C₂×#41×C₁₄₉	—	2	2	no	—
28	C₂×#41×C₁₄₉	—	2	2	no	—
29	C₂×#41×C₁₄₉	—	2	2	no	—
30	C₂×#41×C₁₄₉	D₄	1	2	yes	—
31	C₂×#41×C₁₄₉	Q₈	1	2	yes	—
32	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₄₉	—	2	1	no	—
34	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₄₉	—	2	2	no	—
36	C₂³×C₄×C₁₄₉	—	2	1	no	—
37	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₄₉	—	2	2	no	—
41	C₂×M₁₆×C₁₄₉	—	2	2	no	—
42	C₂×M₁₆×C₁₄₉	—	2	2	no	—
43	C₂×M₁₆×C₁₄₉	—	2	2	no	—
44	C₂×M₁₆×C₁₄₉	—	2	2	no	—
45	C₂×M₁₆×C₁₄₉	D₄	1	4	yes	—
46	C₂²×C₈×C₁₄₉	—	2	2	no	—
47	#117×C₁₄₉	—	2	2	no	—
48	#117×C₁₄₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
55	C₂×C₄²×C₁₄₉	—	2	2	no	—
56	C₂×C₄²×C₁₄₉	—	2	2	no	—
57	C₂×C₄²×C₁₄₉	—	2	2	no	—
58	C₂×C₄²×C₁₄₉	—	2	2	no	—
59	C₂×C₄²×C₁₄₉	—	2	2	no	—
60	C₂×C₄²×C₁₄₉	—	2	2	no	—
61	C₂×C₄²×C₁₄₉	—	2	2	no	—
62	C₂×C₄²×C₁₄₉	—	2	1	no	—
63	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₄₉	D₄	1	4	yes	—
65	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
66	#104×C₁₄₉	—	2	16	no	—
67	#95×C₁₄₉	—	2	4	no	—
68	#95×C₁₄₉	—	2	2	no	—
69	#95×C₁₄₉	—	2	2	no	—
70	C₂⁴×C₁₄₉	—	2	1	no	—
71	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
72	#41×C₁₄₉	—	2	4	no	—
73	#41×C₁₄₉	—	2	4	no	—
74	#41×C₁₄₉	—	2	4	no	—
75	#41×C₁₄₉	—	2	4	no	—
76	#41×C₁₄₉	—	4	2	no	—
77	#41×C₁₄₉	—	4	2	no	—
78	#41×C₁₄₉	—	4	2	no	—
79	#41×C₁₄₉	—	4	2	no	—
80	C₂×Q₈×C₁₄₉	—	2	1	no	—
81	C₂×Q₈×C₁₄₉	—	2	2	no	—
82	C₂×Q₈×C₁₄₉	—	2	2	no	—
83	C₂×Q₈×C₁₄₉	C₄⋊C₄	1	2	yes	complemented
84	C₂×D₄×C₁₄₉	—	2	2	no	—
85	C₂×D₄×C₁₄₉	—	2	2	no	—
86	C₂×D₄×C₁₄₉	—	2	1	no	—
87	C₂×D₄×C₁₄₉	—	2	2	no	—
88	C₂×D₄×C₁₄₉	—	2	2	no	—
89	C₂×D₄×C₁₄₉	—	4	1	no	—
90	C₂×D₄×C₁₄₉	—	4	1	no	—
91	C₂×D₄×C₁₄₉	—	4	1	no	—
92	C₂×D₄×C₁₄₉	—	4	1	no	—
93	C₂×D₄×C₁₄₉	C₄⋊C₄	1	2	yes	complemented
94	C₂²×C₄×C₁₄₉	—	2	1	no	—
95	C₂²×C₄×C₁₄₉	—	2	1	no	—
96	C₂²×C₄×C₁₄₉	—	2	4	no	—
97	C₂²×C₄×C₁₄₉	—	2	8	no	—
98	C₂²×C₄×C₁₄₉	—	2	1	no	—
99	C₂²×C₄×C₁₄₉	—	2	1	no	—
100	C₂²×C₄×C₁₄₉	—	2	4	no	—
101	C₂²×C₄×C₁₄₉	—	2	1	no	—
102	C₂²×C₄×C₁₄₉	—	2	2	no	—
103	C₂²×C₄×C₁₄₉	—	2	2	no	—
104	C₂²×C₄×C₁₄₉	—	2	2	no	—
105	C₂²×C₄×C₁₄₉	—	4	2	no	—
106	C₂²×C₄×C₁₄₉	—	4	4	no	—
107	C₂²×C₄×C₁₄₉	—	4	2	no	—
108	C₂²×C₄×C₁₄₉	—	4	2	no	—
109	C₂²×C₄×C₁₄₉	—	4	2	no	—
110	C₂²×C₄×C₁₄₉	—	4	2	no	—
111	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
122	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
123	M₁₆×C₁₄₉	—	2	4	no	—
124	M₁₆×C₁₄₉	—	2	4	no	—
125	M₁₆×C₁₄₉	—	4	2	no	—
126	M₁₆×C₁₄₉	—	4	2	no	—
127	C₂×C₈×C₁₄₉	—	2	4	no	—
128	C₂×C₈×C₁₄₉	—	4	2	no	—
129	C₂×C₈×C₁₄₉	—	4	2	no	—
130	C₄⋊C₄×C₁₄₉	—	2	16	no	—
131	C₄⋊C₄×C₁₄₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₄₉	—	4	4	no	—
133	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₄₉	—	4	4	no	—
136	C₄²×C₁₄₉	—	2	4	no	—
137	C₄²×C₁₄₉	—	2	4	no	—
138	C₄²×C₁₄₉	—	2	4	no	—
139	C₄²×C₁₄₉	—	2	4	no	—
140	C₄²×C₁₄₉	—	4	2	no	—
141	C₄²×C₁₄₉	—	4	2	no	—
142	C₄²×C₁₄₉	—	4	2	no	—
143	C₂³×C₁₄₉	—	2	2	no	—
144	C₂³×C₁₄₉	—	2	2	no	—
145	C₂³×C₁₄₉	—	2	2	no	—
146	C₂³×C₁₄₉	—	4	1	no	—
147	C₂³×C₁₄₉	—	4	1	no	—
148	C₂³×C₁₄₉	—	4	2	no	—
149	C₂³×C₁₄₉	—	4	2	no	—
150	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₁₄₉	#120	1	1	yes	characteristic
152	C₂³×C₁₄₉	#121	1	1	yes	characteristic
153	C₂³×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₁₄₉	#123	1	1	yes	characteristic
155	C₂³×C₁₄₉	#124	1	1	yes	characteristic
156	C₂³×C₁₄₉	#127	1	1	yes	characteristic
157	Q₈×C₁₄₉	—	2	4	no	—
158	Q₈×C₁₄₉	—	4	2	no	—
159	D₄×C₁₄₉	—	2	4	no	—
160	D₄×C₁₄₉	—	4	2	no	—
161	D₄×C₁₄₉	—	4	2	no	—
162	D₄×C₁₄₉	—	4	2	no	—
163	D₄×C₁₄₉	—	4	2	no	—
164	D₄×C₁₄₉	—	4	2	no	—
165	C₂×C₄×C₁₄₉	—	2	4	no	—
166	C₂×C₄×C₁₄₉	—	2	4	no	—
167	C₂×C₄×C₁₄₉	—	2	2	no	—
168	C₂×C₄×C₁₄₉	—	2	2	no	—
169	C₂×C₄×C₁₄₉	—	2	8	no	—
170	C₂×C₄×C₁₄₉	—	2	2	no	—
171	C₂×C₄×C₁₄₉	—	2	2	no	—
172	C₂×C₄×C₁₄₉	—	2	2	no	—
173	C₂×C₄×C₁₄₉	—	2	2	no	—
174	C₂×C₄×C₁₄₉	—	4	8	no	—
175	C₂×C₄×C₁₄₉	—	4	4	no	—
176	C₂×C₄×C₁₄₉	—	4	8	no	—
177	C₂×C₄×C₁₄₉	—	4	2	no	—
178	C₂×C₄×C₁₄₉	—	4	2	no	—
179	C₂×C₄×C₁₄₉	—	4	1	no	—
180	C₂×C₄×C₁₄₉	—	4	1	no	—
181	C₂×C₄×C₁₄₉	—	4	4	no	—
182	C₂×C₄×C₁₄₉	—	4	4	no	—
183	C₂×C₄×C₁₄₉	—	4	4	no	—
184	C₂×C₄×C₁₄₉	—	4	2	no	—
185	C₂×C₄×C₁₄₉	—	4	2	no	—
186	C₂×C₄×C₁₄₉	—	4	2	no	—
187	C₂×C₄×C₁₄₉	#104	1	4	yes	complemented
188	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₄₉	#120	1	2	yes	—
193	C₂×C₄×C₁₄₉	#121	1	2	yes	—
194	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₄₉	#121	1	2	yes	—
196	C₂×C₄×C₁₄₉	#121	1	2	yes	—
197	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₄₉	#123	1	2	yes	—
201	C₂×C₄×C₁₄₉	#123	1	2	yes	—
202	C₂×C₄×C₁₄₉	#124	1	2	yes	—
203	C₂×C₄×C₁₄₉	#126	1	2	yes	—
204	C₈×C₁₄₉	—	4	4	no	—
205	C₂²×C₁₄₉	—	2	2	no	—
206	C₂²×C₁₄₉	—	2	2	no	—
207	C₂²×C₁₄₉	—	2	1	no	—
208	C₂²×C₁₄₉	—	2	1	no	—
209	C₂²×C₁₄₉	—	2	1	no	—
210	C₂²×C₁₄₉	—	2	1	no	—
211	C₂²×C₁₄₉	—	2	2	no	—
212	C₂²×C₁₄₉	—	2	2	no	—
213	C₂²×C₁₄₉	—	4	4	no	—
214	C₂²×C₁₄₉	—	4	2	no	—
215	C₂²×C₁₄₉	—	8	1	no	—
216	C₂²×C₁₄₉	—	8	1	no	—
217	C₂²×C₁₄₉	—	8	2	no	—
218	C₂²×C₁₄₉	#380	1	1	yes	characteristic
219	C₂²×C₁₄₉	#386	1	1	yes	characteristic
220	C₂²×C₁₄₉	#390	1	1	yes	characteristic
221	C₂²×C₁₄₉	#392	1	1	yes	characteristic
222	C₂²×C₁₄₉	#393	1	1	yes	characteristic
223	C₂²×C₁₄₉	#397	1	1	yes	characteristic
224	C₂²×C₁₄₉	#399	1	1	yes	characteristic
225	C₂²×C₁₄₉	C₂×#104	1	2	yes	—
226	C₂²×C₁₄₉	#421	1	2	yes	—
227	C₄×C₁₄₉	—	2	4	no	—
228	C₄×C₁₄₉	—	4	8	no	—
229	C₄×C₁₄₉	—	4	2	no	—
230	C₄×C₁₄₉	—	4	2	no	—
231	C₄×C₁₄₉	—	8	2	no	—
232	C₄×C₁₄₉	#385	1	2	yes	—
233	C₄×C₁₄₉	#388	1	2	yes	—
234	C₄×C₁₄₉	#394	1	2	yes	—
235	C₄×C₁₄₉	#396	1	2	yes	—
236	C₂×C₁₄₉	—	2	1	no	—
237	C₂×C₁₄₉	—	2	1	no	—
238	C₂×C₁₄₉	—	2	1	no	—
239	C₂×C₁₄₉	—	2	1	no	—
240	C₂×C₁₄₉	—	8	2	no	—
241	C₂×C₁₄₉	#1439	1	1	yes	characteristic
242	C₂×C₁₄₉	#1806	1	2	yes	—
243	C₂×C₁₄₉	#1896	1	1	yes	characteristic
244	C₂×C₁₄₉	#1897	1	1	yes	characteristic
245	C₂×C₁₄₉	#1980	1	2	yes	—
246	#11075	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₄₉	#11075	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×#104	C₂×C₁₄₉	1	2	yes	—
249	#2297	C₂×C₁₄₉	1	1	yes	characteristic
250	C₂×C₄×C₄⋊C₄	C₂×C₁₄₉	1	1	yes	characteristic, complemented
251	C₂×#339	C₂×C₁₄₉	1	2	yes	complemented
252	#1728	C₂×C₁₄₉	1	1	yes	characteristic, complemented
253	C₂²×#41	C₂²×C₁₄₉	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
255	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	—	2	1	no	—
257	C₂²×C₄²	C₂²×C₁₄₉	1	2	yes	—
258	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
259	C₂×#104	—	2	4	no	—
260	C₂×#104	—	2	4	no	—
261	C₂×#104	—	2	4	no	—
262	#391	C₄×C₁₄₉	1	2	yes	complemented
263	#390	C₄×C₁₄₉	1	2	yes	complemented
264	#386	—	2	1	no	—
265	#386	—	2	1	no	—
266	C₄×C₄⋊C₄	—	2	4	no	—
267	C₄×C₂²⋊C₄	—	2	2	no	—
268	C₂×#95	—	2	1	no	—
269	#339	—	2	4	no	—
270	#336	—	2	2	no	—
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	2	1	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	D₄×C₁₄₉	1	2	yes	—
278	C₂×#41	Q₈×C₁₄₉	1	2	yes	—
279	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	D₄×C₁₄₉	1	4	yes	—
293	C₂²×C₈	—	2	2	no	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	8	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
311	C₂×C₄²	D₄×C₁₄₉	1	4	yes	—
312	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
313	#104	—	2	16	no	—
314	#95	—	2	4	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	4	2	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₄⋊C₄×C₁₄₉	1	2	yes	complemented
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₄⋊C₄×C₁₄₉	1	2	yes	complemented
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
359	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
366	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
367	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
368	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
369	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	—	4	2	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₄⋊C₄	—	2	16	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	4	2	no	—
388	C₄²	—	4	2	no	—
389	C₄²	—	4	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
398	C₂³	#120×C₁₄₉	1	1	yes	characteristic
399	C₂³	#121×C₁₄₉	1	1	yes	characteristic
400	C₂³	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
401	C₂³	#123×C₁₄₉	1	1	yes	characteristic
402	C₂³	#124×C₁₄₉	1	1	yes	characteristic
403	C₂³	#127×C₁₄₉	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	#104×C₁₄₉	1	4	yes	complemented
435	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
436	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
438	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
439	C₂×C₄	#120×C₁₄₉	1	2	yes	—
440	C₂×C₄	#121×C₁₄₉	1	2	yes	—
441	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
442	C₂×C₄	#121×C₁₄₉	1	2	yes	—
443	C₂×C₄	#121×C₁₄₉	1	2	yes	—
444	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
445	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
446	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
447	C₂×C₄	#123×C₁₄₉	1	2	yes	—
448	C₂×C₄	#123×C₁₄₉	1	2	yes	—
449	C₂×C₄	#124×C₁₄₉	1	2	yes	—
450	C₂×C₄	#126×C₁₄₉	1	2	yes	—
451	C₈	—	4	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	#380×C₁₄₉	1	1	yes	characteristic
466	C₂²	#386×C₁₄₉	1	1	yes	characteristic
467	C₂²	#390×C₁₄₉	1	1	yes	characteristic
468	C₂²	#392×C₁₄₉	1	1	yes	characteristic
469	C₂²	#393×C₁₄₉	1	1	yes	characteristic
470	C₂²	#397×C₁₄₉	1	1	yes	characteristic
471	C₂²	#399×C₁₄₉	1	1	yes	characteristic
472	C₂²	C₂×#104×C₁₄₉	1	2	yes	—
473	C₂²	#421×C₁₄₉	1	2	yes	—
474	C₄	—	2	4	no	—
475	C₄	—	4	8	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	2	no	—
479	C₄	#385×C₁₄₉	1	2	yes	—
480	C₄	#388×C₁₄₉	1	2	yes	—
481	C₄	#394×C₁₄₉	1	2	yes	—
482	C₄	#396×C₁₄₉	1	2	yes	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	2	no	—
488	C₂	#1439×C₁₄₉	1	1	yes	characteristic
489	C₂	#1806×C₁₄₉	1	2	yes	—
490	C₂	#1896×C₁₄₉	1	1	yes	characteristic
491	C₂	#1897×C₁₄₉	1	1	yes	characteristic
492	C₂	#1980×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₄₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊C₄×C₁₄₉	C₂	semidirect
4. C₂×#339×C₁₄₉	C₂	semidirect
5. #1728×C₁₄₉	C₂	semidirect
15. #391×C₁₄₉	C₄	semidirect
16. #390×C₁₄₉	C₄	semidirect
83. C₂×Q₈×C₁₄₉	C₄⋊C₄	semidirect
93. C₂×D₄×C₁₄₉	C₄⋊C₄	semidirect
187. C₂×C₄×C₁₄₉	#104	semidirect
246. #11075	C₁₄₉	direct (N × H)
247. C₁₄₉	#11075	direct (N × H)
250. C₂×C₄×C₄⋊C₄	C₂×C₁₄₉	semidirect
251. C₂×#339	C₂×C₁₄₉	semidirect
252. #1728	C₂×C₁₄₉	semidirect
262. #391	C₄×C₁₄₉	semidirect
263. #390	C₄×C₁₄₉	semidirect
330. C₂×Q₈	C₄⋊C₄×C₁₄₉	semidirect
340. C₂×D₄	C₄⋊C₄×C₁₄₉	semidirect
434. C₂×C₄	#104×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#104×C₁₄₉	2
#2297×C₁₄₉	2
C₂×C₄×C₄⋊C₄×C₁₄₉	2
C₂×#339×C₁₄₉	2
#1728×C₁₄₉	2
#11075	149

Subgroups — C149×#11075 #49190024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11075 #49190024