Subgroups — C₁₄₉×#18403 #49197352

Order 38144.

998 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3502×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3208×C₁₄₉	C₂	1	2	yes	maximal
3	#2548×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1599×C₁₄₉	C₂	1	8	yes	maximal, complemented
5	#1503×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1461×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈²×C₁₄₉	—	2	2	no	—
8	#557×C₁₄₉	—	2	2	no	—
9	#557×C₁₄₉	—	2	4	no	—
10	#544×C₁₄₉	—	2	1	no	—
11	#544×C₁₄₉	C₂²	1	4	yes	—
12	#533×C₁₄₉	—	2	2	no	—
13	#533×C₁₄₉	C₂²	1	2	yes	—
14	C₂×#127×C₁₄₉	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₄₉	—	2	1	no	—
16	#519×C₁₄₉	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
18	#492×C₁₄₉	—	2	2	no	—
19	#486×C₁₄₉	—	2	2	no	—
20	#460×C₁₄₉	—	2	4	no	—
21	#450×C₁₄₉	C₂²	1	8	yes	—
22	#431×C₁₄₉	C₂²	1	2	yes	—
23	#394×C₁₄₉	C₂²	1	4	yes	—
24	#390×C₁₄₉	—	2	1	no	—
25	#390×C₁₄₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
27	#328×C₁₄₉	C₂²	1	8	yes	—
28	#324×C₁₄₉	C₂²	1	4	yes	—
29	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₄₉	—	2	1	no	—
31	C₂²×D₄×C₁₄₉	—	2	1	no	—
32	C₂²×D₄×C₁₄₉	C₂³	1	2	yes	—
33	C₂×SD₁₆×C₁₄₉	—	2	8	no	—
34	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
35	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
36	C₄⋊Q₈×C₁₄₉	—	2	4	no	—
37	C₄⋊Q₈×C₁₄₉	—	2	8	no	—
38	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
39	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
40	#127×C₁₄₉	—	2	2	no	—
41	#127×C₁₄₉	—	2	2	no	—
42	#125×C₁₄₉	—	2	4	no	—
43	#125×C₁₄₉	—	2	4	no	—
44	#125×C₁₄₉	—	2	8	no	—
45	#125×C₁₄₉	—	2	2	no	—
46	#124×C₁₄₉	—	4	4	no	—
47	C₂²⋊Q₈×C₁₄₉	—	2	2	no	—
48	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
49	C₂²⋊Q₈×C₁₄₉	C₂³	1	4	yes	—
50	C₄×Q₈×C₁₄₉	—	2	4	no	—
51	C₄×Q₈×C₁₄₉	—	2	4	no	—
52	C₄×Q₈×C₁₄₉	—	2	4	no	—
53	C₄×Q₈×C₁₄₉	—	2	4	no	—
54	C₄×Q₈×C₁₄₉	—	2	2	no	—
55	C₄×Q₈×C₁₄₉	—	2	2	no	—
56	C₄×Q₈×C₁₄₉	—	2	2	no	—
57	C₄×Q₈×C₁₄₉	D₄	1	4	yes	—
58	#117×C₁₄₉	—	2	4	no	—
59	#117×C₁₄₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
65	C₂×C₄²×C₁₄₉	—	2	1	no	—
66	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₁₄₉	—	2	2	no	—
69	#102×C₁₄₉	—	2	8	no	—
70	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
71	C₄×C₈×C₁₄₉	—	2	2	no	—
72	#95×C₁₄₉	C₂³	1	2	yes	—
73	C₂⁴×C₁₄₉	—	2	2	no	—
74	C₂×Q₈×C₁₄₉	—	2	4	no	—
75	C₂×Q₈×C₁₄₉	—	2	2	no	—
76	C₂×Q₈×C₁₄₉	—	2	2	no	—
77	C₂×Q₈×C₁₄₉	—	2	2	no	—
78	C₂×Q₈×C₁₄₉	SD₁₆	1	4	yes	complemented
79	C₂×Q₈×C₁₄₉	C₂×D₄	1	4	yes	—
80	C₂×D₄×C₁₄₉	—	2	4	no	—
81	C₂×D₄×C₁₄₉	—	4	4	no	—
82	C₂×D₄×C₁₄₉	—	4	1	no	—
83	C₂×D₄×C₁₄₉	—	4	2	no	—
84	C₂×D₄×C₁₄₉	—	4	1	no	—
85	C₂×D₄×C₁₄₉	—	4	2	no	—
86	C₂×D₄×C₁₄₉	—	4	2	no	—
87	C₂×D₄×C₁₄₉	—	8	2	no	—
88	C₂²×C₄×C₁₄₉	—	2	2	no	—
89	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
94	SD₁₆×C₁₄₉	—	8	8	no	—
95	C₂×C₈×C₁₄₉	—	2	4	no	—
96	C₄⋊C₄×C₁₄₉	—	2	4	no	—
97	C₄⋊C₄×C₁₄₉	—	2	4	no	—
98	C₄⋊C₄×C₁₄₉	—	2	4	no	—
99	C₄⋊C₄×C₁₄₉	—	2	8	no	—
100	C₄⋊C₄×C₁₄₉	—	2	2	no	—
101	C₄⋊C₄×C₁₄₉	—	2	2	no	—
102	C₄⋊C₄×C₁₄₉	—	2	2	no	—
103	C₄⋊C₄×C₁₄₉	—	2	2	no	—
104	C₄⋊C₄×C₁₄₉	—	2	4	no	—
105	C₄⋊C₄×C₁₄₉	—	2	4	no	—
106	C₄⋊C₄×C₁₄₉	—	2	4	no	—
107	C₄⋊C₄×C₁₄₉	—	4	2	no	—
108	C₄⋊C₄×C₁₄₉	C₂×D₄	1	4	yes	—
109	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
111	C₂²⋊C₄×C₁₄₉	—	8	4	no	—
112	C₄²×C₁₄₉	—	2	8	no	—
113	C₄²×C₁₄₉	—	2	2	no	—
114	C₄²×C₁₄₉	—	2	2	no	—
115	C₄²×C₁₄₉	—	2	4	no	—
116	C₄²×C₁₄₉	—	4	2	no	—
117	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
118	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
119	C₂³×C₁₄₉	—	4	4	no	—
120	C₂³×C₁₄₉	—	4	4	no	—
121	C₂³×C₁₄₉	—	4	2	no	—
122	C₂³×C₁₄₉	—	4	2	no	—
123	C₂³×C₁₄₉	—	4	2	no	—
124	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₁₄₉	—	2	8	no	—
126	Q₈×C₁₄₉	—	4	4	no	—
127	Q₈×C₁₄₉	—	4	4	no	—
128	Q₈×C₁₄₉	—	8	4	no	—
129	D₄×C₁₄₉	—	4	8	no	—
130	D₄×C₁₄₉	—	8	2	no	—
131	D₄×C₁₄₉	—	8	4	no	—
132	D₄×C₁₄₉	—	8	2	no	—
133	C₂×C₄×C₁₄₉	—	2	2	no	—
134	C₂×C₄×C₁₄₉	—	2	2	no	—
135	C₂×C₄×C₁₄₉	—	2	2	no	—
136	C₂×C₄×C₁₄₉	—	2	4	no	—
137	C₂×C₄×C₁₄₉	—	2	4	no	—
138	C₂×C₄×C₁₄₉	—	2	2	no	—
139	C₂×C₄×C₁₄₉	—	4	1	no	—
140	C₂×C₄×C₁₄₉	—	4	2	no	—
141	C₂×C₄×C₁₄₉	—	4	2	no	—
142	C₂×C₄×C₁₄₉	—	4	2	no	—
143	C₂×C₄×C₁₄₉	—	4	2	no	—
144	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
145	C₂×C₄×C₁₄₉	#120	1	2	yes	—
146	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	4	yes	—
148	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₁₄₉	#137	1	2	yes	—
150	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
151	C₈×C₁₄₉	—	4	4	no	—
152	C₂²×C₁₄₉	—	2	1	no	—
153	C₂²×C₁₄₉	—	2	1	no	—
154	C₂²×C₁₄₉	—	8	4	no	—
155	C₂²×C₁₄₉	—	8	4	no	—
156	C₂²×C₁₄₉	—	8	2	no	—
157	C₂²×C₁₄₉	—	8	2	no	—
158	C₂²×C₁₄₉	—	8	2	no	—
159	C₂²×C₁₄₉	C₂×#120	1	1	yes	characteristic
160	C₂²×C₁₄₉	C₂²×SD₁₆	1	1	yes	characteristic
161	C₂²×C₁₄₉	C₂×#137	1	1	yes	characteristic
162	C₄×C₁₄₉	—	2	4	no	—
163	C₄×C₁₄₉	—	2	1	no	—
164	C₄×C₁₄₉	—	2	2	no	—
165	C₄×C₁₄₉	—	4	4	no	—
166	C₄×C₁₄₉	—	4	2	no	—
167	C₄×C₁₄₉	—	4	4	no	—
168	C₄×C₁₄₉	—	8	2	no	—
169	C₄×C₁₄₉	#448	1	4	yes	—
170	C₄×C₁₄₉	#454	1	2	yes	—
171	C₂×C₁₄₉	—	2	1	no	—
172	C₂×C₁₄₉	—	2	1	no	—
173	C₂×C₁₄₉	—	16	2	no	—
174	C₂×C₁₄₉	C₂×#448	1	1	yes	characteristic
175	C₂×C₁₄₉	C₂×#454	1	1	yes	characteristic
176	C₂×C₁₄₉	#3027	1	1	yes	characteristic
177	#18403	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₄₉	#18403	1	1	yes	characteristic, direct product factor, Sylow
179	#3502	C₂×C₁₄₉	1	1	yes	characteristic, complemented
180	#3208	C₂×C₁₄₉	1	2	yes	—
181	#2548	C₂×C₁₄₉	1	1	yes	characteristic
182	#1599	C₂×C₁₄₉	1	8	yes	complemented
183	#1503	C₂×C₁₄₉	1	2	yes	complemented
184	#1461	C₂×C₁₄₉	1	1	yes	characteristic, complemented
185	Q₈²	—	2	2	no	—
186	#557	—	2	2	no	—
187	#557	—	2	4	no	—
188	#544	—	2	1	no	—
189	#544	C₂²×C₁₄₉	1	4	yes	—
190	#533	—	2	2	no	—
191	#533	C₂²×C₁₄₉	1	2	yes	—
192	C₂×#127	C₂²×C₁₄₉	1	1	yes	characteristic
193	C₂×#124	—	2	1	no	—
194	#519	—	2	1	no	—
195	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
196	#492	—	2	2	no	—
197	#486	—	2	2	no	—
198	#460	—	2	4	no	—
199	#450	C₂²×C₁₄₉	1	8	yes	—
200	#431	C₂²×C₁₄₉	1	2	yes	—
201	#394	C₂²×C₁₄₉	1	4	yes	—
202	#390	—	2	1	no	—
203	#390	—	2	2	no	—
204	C₄×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
205	#328	C₂²×C₁₄₉	1	8	yes	—
206	#324	C₂²×C₁₄₉	1	4	yes	—
207	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
208	C₂²×D₄	—	2	1	no	—
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	C₂³×C₁₄₉	1	2	yes	—
211	C₂×SD₁₆	—	2	8	no	—
212	C₄⋊Q₈	—	2	2	no	—
213	C₄⋊Q₈	—	2	2	no	—
214	C₄⋊Q₈	—	2	4	no	—
215	C₄⋊Q₈	—	2	8	no	—
216	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
217	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
218	#127	—	2	2	no	—
219	#127	—	2	2	no	—
220	#125	—	2	4	no	—
221	#125	—	2	4	no	—
222	#125	—	2	8	no	—
223	#125	—	2	2	no	—
224	#124	—	4	4	no	—
225	C₂²⋊Q₈	—	2	2	no	—
226	C₂²⋊Q₈	—	2	4	no	—
227	C₂²⋊Q₈	C₂³×C₁₄₉	1	4	yes	—
228	C₄×Q₈	—	2	4	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	—	2	4	no	—
231	C₄×Q₈	—	2	4	no	—
232	C₄×Q₈	—	2	2	no	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	D₄×C₁₄₉	1	4	yes	—
236	#117	—	2	4	no	—
237	#117	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
245	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
246	C₄⋊C₈	—	2	2	no	—
247	#102	—	2	8	no	—
248	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
249	C₄×C₈	—	2	2	no	—
250	#95	C₂³×C₁₄₉	1	2	yes	—
251	C₂⁴	—	2	2	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	SD₁₆×C₁₄₉	1	4	yes	complemented
257	C₂×Q₈	C₂×D₄×C₁₄₉	1	4	yes	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	4	4	no	—
260	C₂×D₄	—	4	1	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	8	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
272	SD₁₆	—	8	8	no	—
273	C₂×C₈	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	C₂×D₄×C₁₄₉	1	4	yes	—
287	C₂²⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	4	8	no	—
289	C₂²⋊C₄	—	8	4	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
296	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
297	C₂³	—	4	4	no	—
298	C₂³	—	4	4	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
303	Q₈	—	2	8	no	—
304	Q₈	—	4	4	no	—
305	Q₈	—	4	4	no	—
306	Q₈	—	8	4	no	—
307	D₄	—	4	8	no	—
308	D₄	—	8	2	no	—
309	D₄	—	8	4	no	—
310	D₄	—	8	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
323	C₂×C₄	#120×C₁₄₉	1	2	yes	—
324	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
325	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	4	yes	—
326	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	2	yes	—
327	C₂×C₄	#137×C₁₄₉	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
329	C₈	—	4	4	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	8	4	no	—
333	C₂²	—	8	4	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	8	2	no	—
337	C₂²	C₂×#120×C₁₄₉	1	1	yes	characteristic
338	C₂²	C₂²×SD₁₆×C₁₄₉	1	1	yes	characteristic
339	C₂²	C₂×#137×C₁₄₉	1	1	yes	characteristic
340	C₄	—	2	4	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	2	no	—
345	C₄	—	4	4	no	—
346	C₄	—	8	2	no	—
347	C₄	#448×C₁₄₉	1	4	yes	—
348	C₄	#454×C₁₄₉	1	2	yes	—
349	C₂	—	2	1	no	—
350	C₂	—	2	1	no	—
351	C₂	—	16	2	no	—
352	C₂	C₂×#448×C₁₄₉	1	1	yes	characteristic
353	C₂	C₂×#454×C₁₄₉	1	1	yes	characteristic
354	C₂	#3027×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂×#127×C₁₄₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3502×C₁₄₉	C₂	semidirect
4. #1599×C₁₄₉	C₂	semidirect
5. #1503×C₁₄₉	C₂	semidirect
6. #1461×C₁₄₉	C₂	semidirect
78. C₂×Q₈×C₁₄₉	SD₁₆	semidirect
177. #18403	C₁₄₉	direct (N × H)
178. C₁₄₉	#18403	direct (N × H)
179. #3502	C₂×C₁₄₉	semidirect
182. #1599	C₂×C₁₄₉	semidirect
183. #1503	C₂×C₁₄₉	semidirect
184. #1461	C₂×C₁₄₉	semidirect
256. C₂×Q₈	SD₁₆×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3502×C₁₄₉	2
#3208×C₁₄₉	2
#2548×C₁₄₉	2
#1599×C₁₄₉	2
#1503×C₁₄₉	2
#1461×C₁₄₉	2
#18403	149

Subgroups — C149×#18403 #49197352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#18403 #49197352