Subgroups — C₁₄₉×#10310 #49189259

Order 38144.

670 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#487×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1990×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1957×C₁₄₉	C₂	1	1	yes	maximal, characteristic
7	#1273×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₄₉	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₄₉	C₂²	1	1	yes	characteristic
12	#492×C₁₄₉	—	2	2	no	—
13	#492×C₁₄₉	—	2	2	no	—
14	#487×C₁₄₉	—	2	2	no	—
15	#487×C₁₄₉	—	2	2	no	—
16	#486×C₁₄₉	—	2	2	no	—
17	#486×C₁₄₉	—	2	2	no	—
18	C₂×#103×C₁₄₉	—	2	2	no	—
19	C₂×#102×C₁₄₉	—	2	2	no	—
20	C₂×#102×C₁₄₉	—	2	2	no	—
21	C₂×C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
24	#384×C₁₄₉	C₂²	1	1	yes	characteristic
25	#340×C₁₄₉	—	2	2	no	—
26	#340×C₁₄₉	—	2	2	no	—
27	C₂²×Q₈×C₁₄₉	—	2	1	no	—
28	C₂²×Q₈×C₁₄₉	—	2	1	no	—
29	C₂²×D₄×C₁₄₉	—	2	1	no	—
30	C₂²×D₄×C₁₄₉	—	2	1	no	—
31	C₂²×D₄×C₁₄₉	—	2	1	no	—
32	C₂×SD₁₆×C₁₄₉	—	2	8	no	—
33	C₂×SD₁₆×C₁₄₉	—	4	4	no	—
34	C₂×SD₁₆×C₁₄₉	—	4	4	no	—
35	C₂²×C₈×C₁₄₉	D₄	1	2	yes	—
36	C₂²×C₈×C₁₄₉	D₄	1	2	yes	—
37	C₂²×C₈×C₁₄₉	D₄	1	2	yes	—
38	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
39	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
40	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
41	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
42	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
43	C₄⋊Q₈×C₁₄₉	—	2	1	no	—
44	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
45	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
46	#127×C₁₄₉	—	2	1	no	—
47	#127×C₁₄₉	—	2	1	no	—
48	#127×C₁₄₉	—	2	1	no	—
49	#127×C₁₄₉	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
57	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
58	#103×C₁₄₉	—	2	8	no	—
59	#102×C₁₄₉	—	2	8	no	—
60	#102×C₁₄₉	—	4	4	no	—
61	C₄×C₈×C₁₄₉	—	2	1	no	—
62	C₄×C₈×C₁₄₉	—	2	1	no	—
63	C₄×C₈×C₁₄₉	—	2	1	no	—
64	C₄×C₈×C₁₄₉	—	2	1	no	—
65	C₄×C₈×C₁₄₉	—	2	1	no	—
66	C₄×C₈×C₁₄₉	—	2	1	no	—
67	C₂⁴×C₁₄₉	—	4	1	no	—
68	C₂×Q₈×C₁₄₉	—	2	2	no	—
69	C₂×Q₈×C₁₄₉	—	2	2	no	—
70	C₂×Q₈×C₁₄₉	—	4	1	no	—
71	C₂×Q₈×C₁₄₉	—	4	1	no	—
72	C₂×Q₈×C₁₄₉	—	4	2	no	—
73	C₂×Q₈×C₁₄₉	—	4	2	no	—
74	C₂×Q₈×C₁₄₉	—	4	2	no	—
75	C₂×Q₈×C₁₄₉	—	4	2	no	—
76	C₂×D₄×C₁₄₉	—	2	2	no	—
77	C₂×D₄×C₁₄₉	—	2	2	no	—
78	C₂×D₄×C₁₄₉	—	2	2	no	—
79	C₂×D₄×C₁₄₉	—	4	1	no	—
80	C₂×D₄×C₁₄₉	—	4	1	no	—
81	C₂×D₄×C₁₄₉	—	4	1	no	—
82	C₂×D₄×C₁₄₉	—	4	2	no	—
83	C₂×D₄×C₁₄₉	—	4	2	no	—
84	C₂×D₄×C₁₄₉	—	4	2	no	—
85	C₂×D₄×C₁₄₉	—	4	2	no	—
86	C₂×D₄×C₁₄₉	—	4	2	no	—
87	C₂×D₄×C₁₄₉	—	4	2	no	—
88	C₂²×C₄×C₁₄₉	—	4	1	no	—
89	C₂²×C₄×C₁₄₉	—	4	1	no	—
90	C₂²×C₄×C₁₄₉	—	4	1	no	—
91	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
94	SD₁₆×C₁₄₉	—	4	16	no	—
95	C₂×C₈×C₁₄₉	—	2	2	no	—
96	C₂×C₈×C₁₄₉	—	2	2	no	—
97	C₂×C₈×C₁₄₉	—	2	2	no	—
98	C₂×C₈×C₁₄₉	—	2	2	no	—
99	C₂×C₈×C₁₄₉	—	2	2	no	—
100	C₂×C₈×C₁₄₉	—	2	2	no	—
101	C₂×C₈×C₁₄₉	—	2	2	no	—
102	C₂×C₈×C₁₄₉	—	2	2	no	—
103	C₂×C₈×C₁₄₉	SD₁₆	1	4	yes	—
104	C₄⋊C₄×C₁₄₉	—	2	2	no	—
105	C₄⋊C₄×C₁₄₉	—	2	2	no	—
106	C₄⋊C₄×C₁₄₉	—	2	2	no	—
107	C₄⋊C₄×C₁₄₉	—	2	2	no	—
108	C₄⋊C₄×C₁₄₉	—	4	1	no	—
109	C₄⋊C₄×C₁₄₉	—	4	1	no	—
110	C₄⋊C₄×C₁₄₉	—	4	1	no	—
111	C₄⋊C₄×C₁₄₉	—	4	1	no	—
112	C₄⋊C₄×C₁₄₉	—	4	2	no	—
113	C₄⋊C₄×C₁₄₉	—	4	2	no	—
114	C₄⋊C₄×C₁₄₉	—	4	2	no	—
115	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₄₉	#41	1	1	yes	characteristic
119	C₂³×C₁₄₉	—	4	2	no	—
120	C₂³×C₁₄₉	—	8	1	no	—
121	C₂³×C₁₄₉	—	8	1	no	—
122	C₂³×C₁₄₉	—	8	1	no	—
123	C₂³×C₁₄₉	—	8	1	no	—
124	C₂³×C₁₄₉	—	8	1	no	—
125	C₂³×C₁₄₉	—	8	1	no	—
126	C₂³×C₁₄₉	#127	1	1	yes	characteristic
127	Q₈×C₁₄₉	—	4	4	no	—
128	Q₈×C₁₄₉	—	4	4	no	—
129	Q₈×C₁₄₉	—	8	2	no	—
130	Q₈×C₁₄₉	—	8	2	no	—
131	D₄×C₁₄₉	—	4	4	no	—
132	D₄×C₁₄₉	—	4	4	no	—
133	D₄×C₁₄₉	—	4	4	no	—
134	D₄×C₁₄₉	—	8	2	no	—
135	D₄×C₁₄₉	—	8	2	no	—
136	D₄×C₁₄₉	—	8	2	no	—
137	C₂×C₄×C₁₄₉	—	4	2	no	—
138	C₂×C₄×C₁₄₉	—	4	2	no	—
139	C₂×C₄×C₁₄₉	—	8	1	no	—
140	C₂×C₄×C₁₄₉	—	8	1	no	—
141	C₂×C₄×C₁₄₉	—	8	1	no	—
142	C₂×C₄×C₁₄₉	—	8	1	no	—
143	C₂×C₄×C₁₄₉	—	8	1	no	—
144	C₂×C₄×C₁₄₉	—	8	1	no	—
145	C₂×C₄×C₁₄₉	—	8	1	no	—
146	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
148	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₁₄₉	#135	1	2	yes	—
154	C₂×C₄×C₁₄₉	#135	1	2	yes	—
155	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₁₄₉	#137	1	2	yes	—
158	C₈×C₁₄₉	—	2	4	no	—
159	C₈×C₁₄₉	—	4	2	no	—
160	C₈×C₁₄₉	—	4	2	no	—
161	C₂²×C₁₄₉	—	8	2	no	—
162	C₂²×C₁₄₉	—	8	2	no	—
163	C₂²×C₁₄₉	—	8	2	no	—
164	C₂²×C₁₄₉	—	16	1	no	—
165	C₂²×C₁₄₉	—	16	1	no	—
166	C₂²×C₁₄₉	—	16	1	no	—
167	C₂²×C₁₄₉	—	16	1	no	—
168	C₂²×C₁₄₉	#392	1	1	yes	characteristic
169	C₂²×C₁₄₉	#492	1	1	yes	characteristic
170	C₂²×C₁₄₉	#495	1	1	yes	characteristic
171	C₂²×C₁₄₉	#495	1	1	yes	characteristic
172	C₂²×C₁₄₉	#496	1	1	yes	characteristic
173	C₂²×C₁₄₉	#496	1	1	yes	characteristic
174	C₂²×C₁₄₉	#497	1	1	yes	characteristic
175	C₄×C₁₄₉	—	8	2	no	—
176	C₄×C₁₄₉	—	8	2	no	—
177	C₄×C₁₄₉	—	16	1	no	—
178	C₄×C₁₄₉	#449	1	2	yes	—
179	C₄×C₁₄₉	#450	1	2	yes	—
180	C₄×C₁₄₉	#452	1	2	yes	—
181	C₄×C₁₄₉	#460	1	2	yes	—
182	C₄×C₁₄₉	#463	1	2	yes	—
183	C₄×C₁₄₉	#464	1	2	yes	—
184	C₂×C₁₄₉	—	16	2	no	—
185	C₂×C₁₄₉	#1708	1	1	yes	characteristic
186	C₂×C₁₄₉	#1714	1	1	yes	characteristic
187	C₂×C₁₄₉	#1717	1	1	yes	characteristic
188	C₂×C₁₄₉	#1719	1	1	yes	characteristic
189	C₂×C₁₄₉	#2012	1	1	yes	characteristic
190	C₂×C₁₄₉	#2014	1	1	yes	characteristic
191	C₂×C₁₄₉	#2015	1	1	yes	characteristic
192	#10310	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₄₉	#10310	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#492	C₂×C₁₄₉	1	1	yes	characteristic
195	C₂×#487	C₂×C₁₄₉	1	1	yes	characteristic, complemented
196	C₂×#486	C₂×C₁₄₉	1	1	yes	characteristic
197	#1990	C₂×C₁₄₉	1	1	yes	characteristic, complemented
198	#1990	C₂×C₁₄₉	1	1	yes	characteristic, complemented
199	#1957	C₂×C₁₄₉	1	1	yes	characteristic
200	#1273	C₂×C₁₄₉	1	1	yes	characteristic, complemented
201	C₂²×SD₁₆	—	2	2	no	—
202	C₂×C₄⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
204	C₂×#127	C₂²×C₁₄₉	1	1	yes	characteristic
205	#492	—	2	2	no	—
206	#492	—	2	2	no	—
207	#487	—	2	2	no	—
208	#487	—	2	2	no	—
209	#486	—	2	2	no	—
210	#486	—	2	2	no	—
211	C₂×#103	—	2	2	no	—
212	C₂×#102	—	2	2	no	—
213	C₂×#102	—	2	2	no	—
214	C₂×C₄×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
217	#384	C₂²×C₁₄₉	1	1	yes	characteristic
218	#340	—	2	2	no	—
219	#340	—	2	2	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂×SD₁₆	—	2	8	no	—
226	C₂×SD₁₆	—	4	4	no	—
227	C₂×SD₁₆	—	4	4	no	—
228	C₂²×C₈	D₄×C₁₄₉	1	2	yes	—
229	C₂²×C₈	D₄×C₁₄₉	1	2	yes	—
230	C₂²×C₈	D₄×C₁₄₉	1	2	yes	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
238	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
239	#127	—	2	1	no	—
240	#127	—	2	1	no	—
241	#127	—	2	1	no	—
242	#127	D₄×C₁₄₉	1	2	yes	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
251	#103	—	2	8	no	—
252	#102	—	2	8	no	—
253	#102	—	4	4	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₂⁴	—	4	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
287	SD₁₆	—	4	16	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	SD₁₆×C₁₄₉	1	4	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
311	C₄²	#41×C₁₄₉	1	1	yes	characteristic
312	C₂³	—	4	2	no	—
313	C₂³	—	8	1	no	—
314	C₂³	—	8	1	no	—
315	C₂³	—	8	1	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	1	no	—
318	C₂³	—	8	1	no	—
319	C₂³	#127×C₁₄₉	1	1	yes	characteristic
320	Q₈	—	4	4	no	—
321	Q₈	—	4	4	no	—
322	Q₈	—	8	2	no	—
323	Q₈	—	8	2	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	8	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
340	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
341	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
342	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
343	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
344	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
345	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	2	yes	—
346	C₂×C₄	#135×C₁₄₉	1	2	yes	—
347	C₂×C₄	#135×C₁₄₉	1	2	yes	—
348	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
349	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
350	C₂×C₄	#137×C₁₄₉	1	2	yes	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	16	1	no	—
358	C₂²	—	16	1	no	—
359	C₂²	—	16	1	no	—
360	C₂²	—	16	1	no	—
361	C₂²	#392×C₁₄₉	1	1	yes	characteristic
362	C₂²	#492×C₁₄₉	1	1	yes	characteristic
363	C₂²	#495×C₁₄₉	1	1	yes	characteristic
364	C₂²	#495×C₁₄₉	1	1	yes	characteristic
365	C₂²	#496×C₁₄₉	1	1	yes	characteristic
366	C₂²	#496×C₁₄₉	1	1	yes	characteristic
367	C₂²	#497×C₁₄₉	1	1	yes	characteristic
368	C₄	—	8	2	no	—
369	C₄	—	8	2	no	—
370	C₄	—	16	1	no	—
371	C₄	#449×C₁₄₉	1	2	yes	—
372	C₄	#450×C₁₄₉	1	2	yes	—
373	C₄	#452×C₁₄₉	1	2	yes	—
374	C₄	#460×C₁₄₉	1	2	yes	—
375	C₄	#463×C₁₄₉	1	2	yes	—
376	C₄	#464×C₁₄₉	1	2	yes	—
377	C₂	—	16	2	no	—
378	C₂	#1708×C₁₄₉	1	1	yes	characteristic
379	C₂	#1714×C₁₄₉	1	1	yes	characteristic
380	C₂	#1717×C₁₄₉	1	1	yes	characteristic
381	C₂	#1719×C₁₄₉	1	1	yes	characteristic
382	C₂	#2012×C₁₄₉	1	1	yes	characteristic
383	C₂	#2014×C₁₄₉	1	1	yes	characteristic
384	C₂	#2015×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₄₉
prime radical	C₂×#127×C₁₄₉	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#487×C₁₄₉	C₂	semidirect
4. #1990×C₁₄₉	C₂	semidirect
5. #1990×C₁₄₉	C₂	semidirect
7. #1273×C₁₄₉	C₂	semidirect
192. #10310	C₁₄₉	direct (N × H)
193. C₁₄₉	#10310	direct (N × H)
195. C₂×#487	C₂×C₁₄₉	semidirect
197. #1990	C₂×C₁₄₉	semidirect
198. #1990	C₂×C₁₄₉	semidirect
200. #1273	C₂×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#492×C₁₄₉	2
C₂×#487×C₁₄₉	2
C₂×#486×C₁₄₉	2
#1990×C₁₄₉	2
#1957×C₁₄₉	2
#1273×C₁₄₉	2
#10310	149

Subgroups — C149×#10310 #49189259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10310 #49189259