Subgroups — C₁₄₉×#17550 #49196499

Order 38144.

1030 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	#3522×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2984×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2276×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1509×C₁₄₉	C₂	1	3	yes	maximal, complemented
5	#1505×C₁₄₉	C₂	1	3	yes	maximal, complemented
6	#1502×C₁₄₉	C₂	1	3	yes	maximal, complemented
7	#1500×C₁₄₉	C₂	1	3	yes	maximal, complemented
8	#559×C₁₄₉	C₄	1	3	yes	complemented
9	Q₈²×C₁₄₉	C₄	1	1	yes	characteristic, complemented
10	#554×C₁₄₉	C₄	1	3	yes	complemented
11	#550×C₁₄₉	C₄	1	1	yes	characteristic, complemented
12	#548×C₁₄₉	—	2	1	no	—
13	#547×C₁₄₉	—	2	3	no	—
14	#542×C₁₄₉	—	2	3	no	—
15	#532×C₁₄₉	C₂²	1	3	yes	—
16	#529×C₁₄₉	C₂²	1	3	yes	—
17	#520×C₁₄₉	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₄₉	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
20	#446×C₁₄₉	—	2	3	no	—
21	C₈×Q₈×C₁₄₉	—	2	1	no	—
22	#432×C₁₄₉	C₂²	1	3	yes	—
23	#431×C₁₄₉	C₂²	1	3	yes	—
24	C₄×C₄⋊C₄×C₁₄₉	—	2	3	no	—
25	C₄×C₄⋊C₄×C₁₄₉	C₂²	1	3	yes	—
26	#376×C₁₄₉	C₂²	1	3	yes	—
27	#328×C₁₄₉	C₂²	1	1	yes	characteristic
28	#328×C₁₄₉	C₂²	1	3	yes	—
29	#327×C₁₄₉	C₂²	1	3	yes	—
30	#327×C₁₄₉	C₂²	1	3	yes	—
31	#327×C₁₄₉	C₂²	1	6	yes	—
32	C₂×#41×C₁₄₉	—	2	1	no	—
33	C₂×#41×C₁₄₉	—	2	3	no	—
34	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
35	C₄⋊Q₈×C₁₄₉	—	2	3	no	—
36	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	3	yes	—
37	#127×C₁₄₉	C₂×C₄	1	3	yes	—
38	#126×C₁₄₉	—	2	3	no	—
39	#125×C₁₄₉	C₂×C₄	1	3	yes	—
40	#124×C₁₄₉	—	2	3	no	—
41	#124×C₁₄₉	—	2	3	no	—
42	#124×C₁₄₉	C₂×C₄	1	3	yes	—
43	#123×C₁₄₉	—	2	3	no	—
44	#123×C₁₄₉	—	2	6	no	—
45	C₂²⋊Q₈×C₁₄₉	—	2	3	no	—
46	C₂²⋊Q₈×C₁₄₉	—	2	6	no	—
47	C₂²⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
48	#121×C₁₄₉	—	2	3	no	—
49	#121×C₁₄₉	—	2	3	no	—
50	#121×C₁₄₉	C₂³	1	3	yes	—
51	C₄×Q₈×C₁₄₉	—	2	8	no	—
52	C₄×Q₈×C₁₄₉	—	2	1	no	—
53	C₄×Q₈×C₁₄₉	C₂×C₄	1	3	yes	—
54	C₄×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₄₉	C₂×C₄	1	3	yes	—
56	C₄×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₄₉	D₄	1	3	yes	—
58	C₄×D₄×C₁₄₉	—	2	3	no	—
59	C₄×D₄×C₁₄₉	—	2	3	no	—
60	C₄×D₄×C₁₄₉	—	2	3	no	—
61	C₄×D₄×C₁₄₉	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₁₄₉	C₂×C₄	1	6	yes	—
63	#117×C₁₄₉	—	2	3	no	—
64	C₂×C₄⋊C₄×C₁₄₉	—	2	3	no	—
65	C₂×C₄⋊C₄×C₁₄₉	—	2	3	no	—
66	C₂×C₄⋊C₄×C₁₄₉	D₄	1	3	yes	—
67	C₂×C₄²×C₁₄₉	—	2	3	no	—
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	—	2	3	no	—
72	C₂²⋊C₈×C₁₄₉	C₂³	1	1	yes	characteristic
73	C₂²⋊C₈×C₁₄₉	C₂³	1	3	yes	—
74	#97×C₁₄₉	—	2	3	no	—
75	C₄×C₈×C₁₄₉	—	2	3	no	—
76	#95×C₁₄₉	—	2	3	no	—
77	#95×C₁₄₉	C₂³	1	1	yes	characteristic
78	#95×C₁₄₉	C₂³	1	3	yes	—
79	#41×C₁₄₉	—	4	4	no	—
80	#41×C₁₄₉	—	8	3	no	—
81	#41×C₁₄₉	—	8	3	no	—
82	C₂×Q₈×C₁₄₉	—	2	4	no	—
83	C₂×Q₈×C₁₄₉	—	2	3	no	—
84	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	3	yes	—
85	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
87	C₂×D₄×C₁₄₉	—	2	3	no	—
88	C₂×D₄×C₁₄₉	—	2	3	no	—
89	C₂×D₄×C₁₄₉	—	2	3	no	—
90	C₂×D₄×C₁₄₉	C₂²×C₄	1	3	yes	—
91	C₂²×C₄×C₁₄₉	—	2	1	no	—
92	C₂²×C₄×C₁₄₉	—	2	3	no	—
93	C₂²×C₄×C₁₄₉	—	2	3	no	—
94	C₂²×C₄×C₁₄₉	—	2	6	no	—
95	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₄₉	—	2	1	no	—
99	C₂×C₈×C₁₄₉	—	2	3	no	—
100	C₄⋊C₄×C₁₄₉	—	2	12	no	—
101	C₄⋊C₄×C₁₄₉	—	2	3	no	—
102	C₄⋊C₄×C₁₄₉	—	2	3	no	—
103	C₄⋊C₄×C₁₄₉	—	2	3	no	—
104	C₄⋊C₄×C₁₄₉	—	2	3	no	—
105	C₄⋊C₄×C₁₄₉	—	2	1	no	—
106	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
107	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
108	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	6	yes	—
109	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
110	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	3	yes	—
111	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
112	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
113	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
114	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
115	C₂²⋊C₄×C₁₄₉	—	2	6	no	—
116	C₂²⋊C₄×C₁₄₉	—	2	3	no	—
117	C₄²×C₁₄₉	—	2	12	no	—
118	C₄²×C₁₄₉	—	2	3	no	—
119	C₄²×C₁₄₉	—	8	3	no	—
120	C₄²×C₁₄₉	C₂²×C₄	1	3	yes	—
121	C₄²×C₁₄₉	C₂²×C₄	1	3	yes	—
122	C₄²×C₁₄₉	C₂×D₄	1	3	yes	—
123	C₄²×C₁₄₉	C₂×D₄	1	3	yes	—
124	C₂³×C₁₄₉	—	2	3	no	—
125	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₁₄₉	—	2	6	no	—
127	Q₈×C₁₄₉	—	4	1	no	—
128	Q₈×C₁₄₉	—	8	3	no	—
129	Q₈×C₁₄₉	#104	1	4	yes	—
130	D₄×C₁₄₉	—	4	3	no	—
131	D₄×C₁₄₉	—	4	3	no	—
132	D₄×C₁₄₉	—	4	3	no	—
133	D₄×C₁₄₉	—	4	6	no	—
134	D₄×C₁₄₉	—	8	3	no	—
135	C₂×C₄×C₁₄₉	—	2	3	no	—
136	C₂×C₄×C₁₄₉	—	2	3	no	—
137	C₂×C₄×C₁₄₉	—	2	6	no	—
138	C₂×C₄×C₁₄₉	—	2	2	no	—
139	C₂×C₄×C₁₄₉	—	2	6	no	—
140	C₂×C₄×C₁₄₉	—	2	1	no	—
141	C₂×C₄×C₁₄₉	—	2	3	no	—
142	C₂×C₄×C₁₄₉	—	2	1	no	—
143	C₂×C₄×C₁₄₉	—	4	1	no	—
144	C₂×C₄×C₁₄₉	—	4	1	no	—
145	C₂×C₄×C₁₄₉	—	4	3	no	—
146	C₂×C₄×C₁₄₉	—	4	3	no	—
147	C₂×C₄×C₁₄₉	—	4	1	no	—
148	C₂×C₄×C₁₄₉	—	4	6	no	—
149	C₂×C₄×C₁₄₉	—	8	6	no	—
150	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
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	C₈×C₁₄₉	—	4	1	no	—
157	C₈×C₁₄₉	—	4	3	no	—
158	C₂²×C₁₄₉	—	2	1	no	—
159	C₂²×C₁₄₉	—	2	1	no	—
160	C₂²×C₁₄₉	—	4	3	no	—
161	C₂²×C₁₄₉	—	4	3	no	—
162	C₂²×C₁₄₉	—	4	3	no	—
163	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₄₉	#576	1	1	yes	characteristic
165	C₂²×C₁₄₉	#577	1	1	yes	characteristic
166	C₄×C₁₄₉	—	2	1	no	—
167	C₄×C₁₄₉	—	2	1	no	—
168	C₄×C₁₄₉	—	2	3	no	—
169	C₄×C₁₄₉	—	2	3	no	—
170	C₄×C₁₄₉	—	2	3	no	—
171	C₄×C₁₄₉	—	4	6	no	—
172	C₄×C₁₄₉	—	4	2	no	—
173	C₄×C₁₄₉	—	4	1	no	—
174	C₄×C₁₄₉	—	4	3	no	—
175	C₄×C₁₄₉	—	4	1	no	—
176	C₄×C₁₄₉	C₂×#104	1	6	yes	—
177	C₂×C₁₄₉	—	2	1	no	—
178	C₂×C₁₄₉	—	2	1	no	—
179	C₂×C₁₄₉	—	8	3	no	—
180	C₂×C₁₄₉	#2884	1	1	yes	characteristic
181	C₂×C₁₄₉	#2897	1	1	yes	characteristic
182	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
183	#17550	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₄₉	#17550	1	1	yes	characteristic, direct product factor, Sylow
185	#3522	C₂×C₁₄₉	1	1	yes	characteristic
186	#2984	C₂×C₁₄₉	1	1	yes	characteristic, complemented
187	#2276	C₂×C₁₄₉	1	1	yes	characteristic, complemented
188	#1509	C₂×C₁₄₉	1	3	yes	complemented
189	#1505	C₂×C₁₄₉	1	3	yes	complemented
190	#1502	C₂×C₁₄₉	1	3	yes	complemented
191	#1500	C₂×C₁₄₉	1	3	yes	complemented
192	#559	C₄×C₁₄₉	1	3	yes	complemented
193	Q₈²	C₄×C₁₄₉	1	1	yes	characteristic, complemented
194	#554	C₄×C₁₄₉	1	3	yes	complemented
195	#550	C₄×C₁₄₉	1	1	yes	characteristic, complemented
196	#548	—	2	1	no	—
197	#547	—	2	3	no	—
198	#542	—	2	3	no	—
199	#532	C₂²×C₁₄₉	1	3	yes	—
200	#529	C₂²×C₁₄₉	1	3	yes	—
201	#520	—	2	1	no	—
202	C₂×C₄×Q₈	—	2	1	no	—
203	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
204	#446	—	2	3	no	—
205	C₈×Q₈	—	2	1	no	—
206	#432	C₂²×C₁₄₉	1	3	yes	—
207	#431	C₂²×C₁₄₉	1	3	yes	—
208	C₄×C₄⋊C₄	—	2	3	no	—
209	C₄×C₄⋊C₄	C₂²×C₁₄₉	1	3	yes	—
210	#376	C₂²×C₁₄₉	1	3	yes	—
211	#328	C₂²×C₁₄₉	1	1	yes	characteristic
212	#328	C₂²×C₁₄₉	1	3	yes	—
213	#327	C₂²×C₁₄₉	1	3	yes	—
214	#327	C₂²×C₁₄₉	1	3	yes	—
215	#327	C₂²×C₁₄₉	1	6	yes	—
216	C₂×#41	—	2	1	no	—
217	C₂×#41	—	2	3	no	—
218	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
219	C₄⋊Q₈	—	2	3	no	—
220	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	3	yes	—
221	#127	C₂×C₄×C₁₄₉	1	3	yes	—
222	#126	—	2	3	no	—
223	#125	C₂×C₄×C₁₄₉	1	3	yes	—
224	#124	—	2	3	no	—
225	#124	—	2	3	no	—
226	#124	C₂×C₄×C₁₄₉	1	3	yes	—
227	#123	—	2	3	no	—
228	#123	—	2	6	no	—
229	C₂²⋊Q₈	—	2	3	no	—
230	C₂²⋊Q₈	—	2	6	no	—
231	C₂²⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
232	#121	—	2	3	no	—
233	#121	—	2	3	no	—
234	#121	C₂³×C₁₄₉	1	3	yes	—
235	C₄×Q₈	—	2	8	no	—
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	C₂×C₄×C₁₄₉	1	3	yes	—
240	C₄×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
241	C₄×Q₈	D₄×C₁₄₉	1	3	yes	—
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	6	yes	—
247	#117	—	2	3	no	—
248	C₂×C₄⋊C₄	—	2	3	no	—
249	C₂×C₄⋊C₄	—	2	3	no	—
250	C₂×C₄⋊C₄	D₄×C₁₄₉	1	3	yes	—
251	C₂×C₄²	—	2	3	no	—
252	C₂×C₄²	—	2	3	no	—
253	C₂×C₄²	C₂³×C₁₄₉	1	3	yes	—
254	C₄⋊C₈	—	2	3	no	—
255	C₄⋊C₈	—	2	3	no	—
256	C₂²⋊C₈	C₂³×C₁₄₉	1	1	yes	characteristic
257	C₂²⋊C₈	C₂³×C₁₄₉	1	3	yes	—
258	#97	—	2	3	no	—
259	C₄×C₈	—	2	3	no	—
260	#95	—	2	3	no	—
261	#95	C₂³×C₁₄₉	1	1	yes	characteristic
262	#95	C₂³×C₁₄₉	1	3	yes	—
263	#41	—	4	4	no	—
264	#41	—	8	3	no	—
265	#41	—	8	3	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	3	no	—
268	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	3	yes	—
269	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
270	C₂×Q₈	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
271	C₂×D₄	—	2	3	no	—
272	C₂×D₄	—	2	3	no	—
273	C₂×D₄	—	2	3	no	—
274	C₂×D₄	C₂²×C₄×C₁₄₉	1	3	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
280	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
281	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	3	no	—
284	C₄⋊C₄	—	2	12	no	—
285	C₄⋊C₄	—	2	3	no	—
286	C₄⋊C₄	—	2	3	no	—
287	C₄⋊C₄	—	2	3	no	—
288	C₄⋊C₄	—	2	3	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
291	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
292	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	6	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
294	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	3	yes	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	3	no	—
297	C₂²⋊C₄	—	2	3	no	—
298	C₂²⋊C₄	—	2	3	no	—
299	C₂²⋊C₄	—	2	6	no	—
300	C₂²⋊C₄	—	2	3	no	—
301	C₄²	—	2	12	no	—
302	C₄²	—	2	3	no	—
303	C₄²	—	8	3	no	—
304	C₄²	C₂²×C₄×C₁₄₉	1	3	yes	—
305	C₄²	C₂²×C₄×C₁₄₉	1	3	yes	—
306	C₄²	C₂×D₄×C₁₄₉	1	3	yes	—
307	C₄²	C₂×D₄×C₁₄₉	1	3	yes	—
308	C₂³	—	2	3	no	—
309	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
310	Q₈	—	2	6	no	—
311	Q₈	—	4	1	no	—
312	Q₈	—	8	3	no	—
313	Q₈	#104×C₁₄₉	1	4	yes	—
314	D₄	—	4	3	no	—
315	D₄	—	4	3	no	—
316	D₄	—	4	3	no	—
317	D₄	—	4	6	no	—
318	D₄	—	8	3	no	—
319	C₂×C₄	—	2	3	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	6	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	3	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	3	no	—
330	C₂×C₄	—	4	3	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	8	6	no	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
338	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
340	C₈	—	4	1	no	—
341	C₈	—	4	3	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	3	no	—
345	C₂²	—	4	3	no	—
346	C₂²	—	4	3	no	—
347	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
348	C₂²	#576×C₁₄₉	1	1	yes	characteristic
349	C₂²	#577×C₁₄₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	3	no	—
353	C₄	—	2	3	no	—
354	C₄	—	2	3	no	—
355	C₄	—	4	6	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	3	no	—
359	C₄	—	4	1	no	—
360	C₄	C₂×#104×C₁₄₉	1	6	yes	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	8	3	no	—
364	C₂	#2884×C₁₄₉	1	1	yes	characteristic
365	C₂	#2897×C₁₄₉	1	1	yes	characteristic
366	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	#3522×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×Q₈×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2984×C₁₄₉	C₂	semidirect
3. #2276×C₁₄₉	C₂	semidirect
4. #1509×C₁₄₉	C₂	semidirect
5. #1505×C₁₄₉	C₂	semidirect
6. #1502×C₁₄₉	C₂	semidirect
7. #1500×C₁₄₉	C₂	semidirect
8. #559×C₁₄₉	C₄	semidirect
9. Q₈²×C₁₄₉	C₄	semidirect
10. #554×C₁₄₉	C₄	semidirect
11. #550×C₁₄₉	C₄	semidirect
183. #17550	C₁₄₉	direct (N × H)
184. C₁₄₉	#17550	direct (N × H)
186. #2984	C₂×C₁₄₉	semidirect
187. #2276	C₂×C₁₄₉	semidirect
188. #1509	C₂×C₁₄₉	semidirect
189. #1505	C₂×C₁₄₉	semidirect
190. #1502	C₂×C₁₄₉	semidirect
191. #1500	C₂×C₁₄₉	semidirect
192. #559	C₄×C₁₄₉	semidirect
193. Q₈²	C₄×C₁₄₉	semidirect
194. #554	C₄×C₁₄₉	semidirect
195. #550	C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3522×C₁₄₉	2
#2984×C₁₄₉	2
#2276×C₁₄₉	2
#1509×C₁₄₉	2
#1505×C₁₄₉	2
#1502×C₁₄₉	2
#1500×C₁₄₉	2
#17550	149

Subgroups — C149×#17550 #49196499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17550 #49196499