Subgroups — C₁₄₉×#17520 #49196469

Order 38144.

1074 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3483×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2991×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#131×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1492×C₁₄₉	C₂	1	3	yes	maximal, complemented
5	#1489×C₁₄₉	C₂	1	3	yes	maximal, complemented
6	#1484×C₁₄₉	C₂	1	3	yes	maximal, complemented
7	#1476×C₁₄₉	C₂	1	3	yes	maximal, complemented
8	C₂×#131×C₁₄₉	—	2	1	no	—
9	Q₈²×C₁₄₉	C₄	1	1	yes	characteristic
10	#555×C₁₄₉	—	2	3	no	—
11	#555×C₁₄₉	C₄	1	3	yes	—
12	#550×C₁₄₉	—	2	1	no	—
13	#550×C₁₄₉	C₄	1	3	yes	—
14	#550×C₁₄₉	C₄	1	1	yes	characteristic
15	#532×C₁₄₉	—	2	3	no	—
16	#532×C₁₄₉	C₂²	1	3	yes	—
17	C₄×#41×C₁₄₉	—	2	1	no	—
18	C₄×#41×C₁₄₉	C₂²	1	3	yes	—
19	C₄×#41×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₈×Q₈×C₁₄₉	—	2	1	no	—
21	#436×C₁₄₉	—	2	3	no	—
22	#431×C₁₄₉	C₂²	1	3	yes	—
23	#423×C₁₄₉	C₂²	1	3	yes	—
24	#405×C₁₄₉	—	2	3	no	—
25	C₄×M₁₆×C₁₄₉	C₂²	1	3	yes	—
26	C₂×C₄×C₈×C₁₄₉	C₂²	1	3	yes	—
27	Q₈⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic
28	Q₈⋊C₈×C₁₄₉	C₂²	1	3	yes	—
29	D₄⋊C₈×C₁₄₉	C₂²	1	3	yes	—
30	D₄⋊C₈×C₁₄₉	C₂²	1	3	yes	—
31	D₄⋊C₈×C₁₄₉	C₂²	1	6	yes	—
32	C₂×#41×C₁₄₉	—	2	1	no	—
33	C₂×#41×C₁₄₉	—	2	3	no	—
34	C₂×#41×C₁₄₉	C₂×C₄	1	3	yes	—
35	C₂×#41×C₁₄₉	D₄	1	1	yes	characteristic
36	#131×C₁₄₉	—	2	8	no	—
37	C₂×M₁₆×C₁₄₉	—	2	3	no	—
38	C₂×M₁₆×C₁₄₉	—	2	3	no	—
39	C₂²×C₈×C₁₄₉	—	2	3	no	—
40	C₄⋊Q₈×C₁₄₉	—	2	3	no	—
41	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	3	yes	—
42	#127×C₁₄₉	—	2	3	no	—
43	#127×C₁₄₉	C₂×C₄	1	3	yes	—
44	#124×C₁₄₉	—	2	6	no	—
45	#124×C₁₄₉	—	2	3	no	—
46	#121×C₁₄₉	—	2	3	no	—
47	#121×C₁₄₉	—	2	3	no	—
48	#121×C₁₄₉	—	2	3	no	—
49	#121×C₁₄₉	—	2	6	no	—
50	#121×C₁₄₉	C₂×C₄	1	6	yes	—
51	C₄×Q₈×C₁₄₉	—	2	1	no	—
52	C₄×Q₈×C₁₄₉	C₂×C₄	1	3	yes	—
53	C₄×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₁₄₉	—	2	3	no	—
57	C₄×D₄×C₁₄₉	—	2	3	no	—
58	C₄×D₄×C₁₄₉	—	2	3	no	—
59	C₄×D₄×C₁₄₉	—	2	3	no	—
60	C₄×D₄×C₁₄₉	C₂×C₄	1	3	yes	—
61	C₄×D₄×C₁₄₉	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₁₄₉	D₄	1	3	yes	—
63	C₄×D₄×C₁₄₉	C₂³	1	3	yes	—
64	#117×C₁₄₉	—	2	3	no	—
65	#117×C₁₄₉	—	2	3	no	—
66	#117×C₁₄₉	C₂×C₄	1	3	yes	—
67	#117×C₁₄₉	D₄	1	3	yes	—
68	C₂×C₄²×C₁₄₉	—	2	3	no	—
69	C₂×C₄²×C₁₄₉	C₂³	1	3	yes	—
70	C₄⋊C₈×C₁₄₉	—	2	3	no	—
71	C₄⋊C₈×C₁₄₉	C₂³	1	3	yes	—
72	C₄⋊C₈×C₁₄₉	C₂³	1	1	yes	characteristic
73	C₂²⋊C₈×C₁₄₉	—	2	3	no	—
74	#97×C₁₄₉	—	2	3	no	—
75	C₄×C₈×C₁₄₉	—	2	3	no	—
76	C₄×C₈×C₁₄₉	—	2	3	no	—
77	C₄×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₄₉	C₂³	1	3	yes	—
79	#41×C₁₄₉	—	2	4	no	—
80	#41×C₁₄₉	—	2	6	no	—
81	#41×C₁₄₉	—	4	3	no	—
82	#41×C₁₄₉	—	4	4	no	—
83	#41×C₁₄₉	—	8	3	no	—
84	#41×C₁₄₉	—	8	3	no	—
85	C₂×Q₈×C₁₄₉	—	2	3	no	—
86	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
88	C₂×D₄×C₁₄₉	—	2	3	no	—
89	C₂×D₄×C₁₄₉	—	2	6	no	—
90	C₂×D₄×C₁₄₉	—	2	3	no	—
91	C₂×D₄×C₁₄₉	—	2	3	no	—
92	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
93	C₂×D₄×C₁₄₉	C₂²×C₄	1	3	yes	—
94	C₂²×C₄×C₁₄₉	—	2	3	no	—
95	C₂²×C₄×C₁₄₉	—	2	3	no	—
96	C₂²×C₄×C₁₄₉	—	2	3	no	—
97	C₂²×C₄×C₁₄₉	C₂²×C₄	1	3	yes	—
98	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
100	M₁₆×C₁₄₉	—	2	12	no	—
101	M₁₆×C₁₄₉	—	8	3	no	—
102	C₂×C₈×C₁₄₉	—	2	12	no	—
103	C₂×C₈×C₁₄₉	—	2	1	no	—
104	C₂×C₈×C₁₄₉	—	2	3	no	—
105	C₂×C₈×C₁₄₉	—	2	1	no	—
106	C₂×C₈×C₁₄₉	—	2	3	no	—
107	C₄⋊C₄×C₁₄₉	—	2	3	no	—
108	C₄⋊C₄×C₁₄₉	—	2	3	no	—
109	C₄⋊C₄×C₁₄₉	—	2	1	no	—
110	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
111	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
112	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	3	yes	—
114	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
115	C₂²⋊C₄×C₁₄₉	—	2	6	no	—
116	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
117	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
118	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	6	yes	—
119	C₄²×C₁₄₉	—	2	3	no	—
120	C₄²×C₁₄₉	—	2	3	no	—
121	C₄²×C₁₄₉	—	2	1	no	—
122	C₄²×C₁₄₉	C₂²×C₄	1	3	yes	—
123	C₄²×C₁₄₉	C₂×D₄	1	3	yes	—
124	C₄²×C₁₄₉	C₂×D₄	1	3	yes	—
125	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
126	C₂³×C₁₄₉	—	2	3	no	—
127	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
128	Q₈×C₁₄₉	—	2	1	no	—
129	Q₈×C₁₄₉	—	8	3	no	—
130	Q₈×C₁₄₉	#104	1	4	yes	—
131	Q₈×C₁₄₉	#131	1	2	yes	complemented
132	D₄×C₁₄₉	—	2	3	no	—
133	D₄×C₁₄₉	—	2	3	no	—
134	D₄×C₁₄₉	—	2	6	no	—
135	D₄×C₁₄₉	—	4	6	no	—
136	D₄×C₁₄₉	—	4	6	no	—
137	D₄×C₁₄₉	—	8	3	no	—
138	D₄×C₁₄₉	—	8	6	no	—
139	C₂×C₄×C₁₄₉	—	2	1	no	—
140	C₂×C₄×C₁₄₉	—	2	3	no	—
141	C₂×C₄×C₁₄₉	—	2	3	no	—
142	C₂×C₄×C₁₄₉	—	2	3	no	—
143	C₂×C₄×C₁₄₉	—	2	3	no	—
144	C₂×C₄×C₁₄₉	—	2	6	no	—
145	C₂×C₄×C₁₄₉	—	2	1	no	—
146	C₂×C₄×C₁₄₉	—	2	3	no	—
147	C₂×C₄×C₁₄₉	—	4	6	no	—
148	C₂×C₄×C₁₄₉	—	4	3	no	—
149	C₂×C₄×C₁₄₉	—	4	3	no	—
150	C₂×C₄×C₁₄₉	—	4	6	no	—
151	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
152	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
153	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
154	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₄₉	—	2	2	no	—
158	C₈×C₁₄₉	—	2	6	no	—
159	C₈×C₁₄₉	—	4	3	no	—
160	C₈×C₁₄₉	—	4	1	no	—
161	C₂²×C₁₄₉	—	2	3	no	—
162	C₂²×C₁₄₉	—	2	3	no	—
163	C₂²×C₁₄₉	—	2	3	no	—
164	C₂²×C₁₄₉	—	4	3	no	—
165	C₂²×C₁₄₉	—	4	3	no	—
166	C₂²×C₁₄₉	—	4	3	no	—
167	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×C₁₄₉	—	2	3	no	—
169	C₄×C₁₄₉	—	2	2	no	—
170	C₄×C₁₄₉	—	2	3	no	—
171	C₄×C₁₄₉	—	2	1	no	—
172	C₄×C₁₄₉	—	4	3	no	—
173	C₄×C₁₄₉	—	4	1	no	—
174	C₄×C₁₄₉	C₂×#104	1	6	yes	—
175	C₄×C₁₄₉	C₂×#131	1	1	yes	characteristic
176	C₄×C₁₄₉	#568	1	1	yes	characteristic
177	C₄×C₁₄₉	#576	1	1	yes	characteristic
178	C₄×C₁₄₉	#577	1	1	yes	characteristic
179	C₂×C₁₄₉	—	4	3	no	—
180	C₂×C₁₄₉	—	8	3	no	—
181	C₂×C₁₄₉	#2880	1	1	yes	characteristic
182	C₂×C₁₄₉	#2897	1	1	yes	characteristic
183	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
184	#17520	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₄₉	#17520	1	1	yes	characteristic, direct product factor, Sylow
186	#3483	C₂×C₁₄₉	1	1	yes	characteristic
187	#2991	C₂×C₁₄₉	1	1	yes	characteristic, complemented
188	C₄×#131	C₂×C₁₄₉	1	1	yes	characteristic, complemented
189	#1492	C₂×C₁₄₉	1	3	yes	complemented
190	#1489	C₂×C₁₄₉	1	3	yes	complemented
191	#1484	C₂×C₁₄₉	1	3	yes	complemented
192	#1476	C₂×C₁₄₉	1	3	yes	complemented
193	C₂×#131	—	2	1	no	—
194	Q₈²	C₄×C₁₄₉	1	1	yes	characteristic
195	#555	—	2	3	no	—
196	#555	C₄×C₁₄₉	1	3	yes	—
197	#550	—	2	1	no	—
198	#550	C₄×C₁₄₉	1	3	yes	—
199	#550	C₄×C₁₄₉	1	1	yes	characteristic
200	#532	—	2	3	no	—
201	#532	C₂²×C₁₄₉	1	3	yes	—
202	C₄×#41	—	2	1	no	—
203	C₄×#41	C₂²×C₁₄₉	1	3	yes	—
204	C₄×#41	C₂²×C₁₄₉	1	1	yes	characteristic
205	C₈×Q₈	—	2	1	no	—
206	#436	—	2	3	no	—
207	#431	C₂²×C₁₄₉	1	3	yes	—
208	#423	C₂²×C₁₄₉	1	3	yes	—
209	#405	—	2	3	no	—
210	C₄×M₁₆	C₂²×C₁₄₉	1	3	yes	—
211	C₂×C₄×C₈	C₂²×C₁₄₉	1	3	yes	—
212	Q₈⋊C₈	C₂²×C₁₄₉	1	1	yes	characteristic
213	Q₈⋊C₈	C₂²×C₁₄₉	1	3	yes	—
214	D₄⋊C₈	C₂²×C₁₄₉	1	3	yes	—
215	D₄⋊C₈	C₂²×C₁₄₉	1	3	yes	—
216	D₄⋊C₈	C₂²×C₁₄₉	1	6	yes	—
217	C₂×#41	—	2	1	no	—
218	C₂×#41	—	2	3	no	—
219	C₂×#41	C₂×C₄×C₁₄₉	1	3	yes	—
220	C₂×#41	D₄×C₁₄₉	1	1	yes	characteristic
221	#131	—	2	8	no	—
222	C₂×M₁₆	—	2	3	no	—
223	C₂×M₁₆	—	2	3	no	—
224	C₂²×C₈	—	2	3	no	—
225	C₄⋊Q₈	—	2	3	no	—
226	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	3	yes	—
227	#127	—	2	3	no	—
228	#127	C₂×C₄×C₁₄₉	1	3	yes	—
229	#124	—	2	6	no	—
230	#124	—	2	3	no	—
231	#121	—	2	3	no	—
232	#121	—	2	3	no	—
233	#121	—	2	3	no	—
234	#121	—	2	6	no	—
235	#121	C₂×C₄×C₁₄₉	1	6	yes	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₂×C₄×C₁₄₉	1	3	yes	—
238	C₄×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
239	C₄×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
240	C₄×Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
241	C₄×D₄	—	2	3	no	—
242	C₄×D₄	—	2	3	no	—
243	C₄×D₄	—	2	3	no	—
244	C₄×D₄	—	2	3	no	—
245	C₄×D₄	C₂×C₄×C₁₄₉	1	3	yes	—
246	C₄×D₄	C₂×C₄×C₁₄₉	1	3	yes	—
247	C₄×D₄	D₄×C₁₄₉	1	3	yes	—
248	C₄×D₄	C₂³×C₁₄₉	1	3	yes	—
249	#117	—	2	3	no	—
250	#117	—	2	3	no	—
251	#117	C₂×C₄×C₁₄₉	1	3	yes	—
252	#117	D₄×C₁₄₉	1	3	yes	—
253	C₂×C₄²	—	2	3	no	—
254	C₂×C₄²	C₂³×C₁₄₉	1	3	yes	—
255	C₄⋊C₈	—	2	3	no	—
256	C₄⋊C₈	C₂³×C₁₄₉	1	3	yes	—
257	C₄⋊C₈	C₂³×C₁₄₉	1	1	yes	characteristic
258	C₂²⋊C₈	—	2	3	no	—
259	#97	—	2	3	no	—
260	C₄×C₈	—	2	3	no	—
261	C₄×C₈	—	2	3	no	—
262	C₄×C₈	C₂³×C₁₄₉	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₁₄₉	1	3	yes	—
264	#41	—	2	4	no	—
265	#41	—	2	6	no	—
266	#41	—	4	3	no	—
267	#41	—	4	4	no	—
268	#41	—	8	3	no	—
269	#41	—	8	3	no	—
270	C₂×Q₈	—	2	3	no	—
271	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
272	C₂×Q₈	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
273	C₂×D₄	—	2	3	no	—
274	C₂×D₄	—	2	6	no	—
275	C₂×D₄	—	2	3	no	—
276	C₂×D₄	—	2	3	no	—
277	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
278	C₂×D₄	C₂²×C₄×C₁₄₉	1	3	yes	—
279	C₂²×C₄	—	2	3	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	C₂²×C₄×C₁₄₉	1	3	yes	—
283	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
284	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
285	M₁₆	—	2	12	no	—
286	M₁₆	—	8	3	no	—
287	C₂×C₈	—	2	12	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	3	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	3	no	—
292	C₄⋊C₄	—	2	3	no	—
293	C₄⋊C₄	—	2	3	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
296	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
297	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
298	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	3	yes	—
299	C₂²⋊C₄	—	2	3	no	—
300	C₂²⋊C₄	—	2	6	no	—
301	C₂²⋊C₄	—	2	3	no	—
302	C₂²⋊C₄	—	2	3	no	—
303	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	6	yes	—
304	C₄²	—	2	3	no	—
305	C₄²	—	2	3	no	—
306	C₄²	—	2	1	no	—
307	C₄²	C₂²×C₄×C₁₄₉	1	3	yes	—
308	C₄²	C₂×D₄×C₁₄₉	1	3	yes	—
309	C₄²	C₂×D₄×C₁₄₉	1	3	yes	—
310	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
311	C₂³	—	2	3	no	—
312	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
313	Q₈	—	2	1	no	—
314	Q₈	—	8	3	no	—
315	Q₈	#104×C₁₄₉	1	4	yes	—
316	Q₈	#131×C₁₄₉	1	2	yes	complemented
317	D₄	—	2	6	no	—
318	D₄	—	2	3	no	—
319	D₄	—	2	3	no	—
320	D₄	—	4	6	no	—
321	D₄	—	4	6	no	—
322	D₄	—	8	3	no	—
323	D₄	—	8	6	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	6	no	—
326	C₂×C₄	—	2	3	no	—
327	C₂×C₄	—	2	3	no	—
328	C₂×C₄	—	2	3	no	—
329	C₂×C₄	—	2	3	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	3	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	4	6	no	—
334	C₂×C₄	—	4	3	no	—
335	C₂×C₄	—	4	3	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
339	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	—	2	6	no	—
344	C₈	—	4	3	no	—
345	C₈	—	4	1	no	—
346	C₂²	—	2	3	no	—
347	C₂²	—	2	3	no	—
348	C₂²	—	2	3	no	—
349	C₂²	—	4	3	no	—
350	C₂²	—	4	3	no	—
351	C₂²	—	4	3	no	—
352	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
353	C₄	—	2	3	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	3	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	3	no	—
358	C₄	—	4	1	no	—
359	C₄	C₂×#104×C₁₄₉	1	6	yes	—
360	C₄	C₂×#131×C₁₄₉	1	1	yes	characteristic
361	C₄	#568×C₁₄₉	1	1	yes	characteristic
362	C₄	#576×C₁₄₉	1	1	yes	characteristic
363	C₄	#577×C₁₄₉	1	1	yes	characteristic
364	C₂	—	4	3	no	—
365	C₂	—	8	3	no	—
366	C₂	#2880×C₁₄₉	1	1	yes	characteristic
367	C₂	#2897×C₁₄₉	1	1	yes	characteristic
368	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	#3483×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₄×#41×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2991×C₁₄₉	C₂	semidirect
3. C₄×#131×C₁₄₉	C₂	semidirect
4. #1492×C₁₄₉	C₂	semidirect
5. #1489×C₁₄₉	C₂	semidirect
6. #1484×C₁₄₉	C₂	semidirect
7. #1476×C₁₄₉	C₂	semidirect
131. Q₈×C₁₄₉	#131	semidirect
184. #17520	C₁₄₉	direct (N × H)
185. C₁₄₉	#17520	direct (N × H)
187. #2991	C₂×C₁₄₉	semidirect
188. C₄×#131	C₂×C₁₄₉	semidirect
189. #1492	C₂×C₁₄₉	semidirect
190. #1489	C₂×C₁₄₉	semidirect
191. #1484	C₂×C₁₄₉	semidirect
192. #1476	C₂×C₁₄₉	semidirect
316. Q₈	#131×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3483×C₁₄₉	2
#2991×C₁₄₉	2
C₄×#131×C₁₄₉	2
#1492×C₁₄₉	2
#1489×C₁₄₉	2
#1484×C₁₄₉	2
#1476×C₁₄₉	2
#17520	149

Subgroups — C149×#17520 #49196469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17520 #49196469