Subgroups — C₁₄₉×#13964 #49192913

Order 38144.

1342 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#383×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#376×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1441×C₁₄₉	C₂	1	4	yes	maximal
5	#1436×C₁₄₉	C₂	1	4	yes	maximal
6	C₄⋊#95×C₁₄₉	C₂	1	2	yes	maximal
7	#1434×C₁₄₉	C₂	1	2	yes	maximal
8	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	4	yes	—
9	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₄₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
14	#383×C₁₄₉	—	2	4	no	—
15	C₄×C₄⋊C₄×C₁₄₉	C₄	1	8	yes	complemented
16	#376×C₁₄₉	—	2	4	no	—
17	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
18	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
19	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
20	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
21	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
23	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
24	C₂×#95×C₁₄₉	C₂²	1	4	yes	—
25	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
26	C₂³×C₄×C₁₄₉	C₂³	1	4	yes	—
27	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₄₉	C₂³	1	4	yes	—
29	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
34	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
35	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
36	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
37	C₂×C₄⋊C₄×C₁₄₉	—	4	4	no	—
38	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	8	yes	—
39	C₂×C₄²×C₁₄₉	—	2	4	no	—
40	C₂×C₄²×C₁₄₉	—	2	8	no	—
41	C₂×C₄²×C₁₄₉	—	4	2	no	—
42	C₂×C₄²×C₁₄₉	—	4	2	no	—
43	C₂×C₄²×C₁₄₉	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₄₉	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₄₉	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₄₉	D₄	1	4	yes	—
47	C₂×C₄²×C₁₄₉	Q₈	1	4	yes	—
48	#95×C₁₄₉	—	2	4	no	—
49	#95×C₁₄₉	—	2	4	no	—
50	#95×C₁₄₉	—	2	4	no	—
51	#95×C₁₄₉	—	2	4	no	—
52	#95×C₁₄₉	—	2	4	no	—
53	#95×C₁₄₉	—	2	8	no	—
54	#95×C₁₄₉	—	2	8	no	—
55	#95×C₁₄₉	—	4	4	no	—
56	#95×C₁₄₉	C₂×C₄	1	8	yes	—
57	C₂⁴×C₁₄₉	C₂⁴	1	1	yes	characteristic
58	C₂²×C₄×C₁₄₉	—	2	4	no	—
59	C₂²×C₄×C₁₄₉	—	2	2	no	—
60	C₂²×C₄×C₁₄₉	—	2	2	no	—
61	C₂²×C₄×C₁₄₉	—	2	4	no	—
62	C₂²×C₄×C₁₄₉	—	2	2	no	—
63	C₂²×C₄×C₁₄₉	—	2	4	no	—
64	C₂²×C₄×C₁₄₉	—	2	2	no	—
65	C₂²×C₄×C₁₄₉	—	2	4	no	—
66	C₂²×C₄×C₁₄₉	—	2	4	no	—
67	C₂²×C₄×C₁₄₉	—	2	4	no	—
68	C₂²×C₄×C₁₄₉	—	2	4	no	—
69	C₂²×C₄×C₁₄₉	—	2	2	no	—
70	C₂²×C₄×C₁₄₉	—	2	2	no	—
71	C₂²×C₄×C₁₄₉	—	2	4	no	—
72	C₂²×C₄×C₁₄₉	—	2	4	no	—
73	C₂²×C₄×C₁₄₉	—	2	4	no	—
74	C₂²×C₄×C₁₄₉	—	2	4	no	—
75	C₂²×C₄×C₁₄₉	—	2	4	no	—
76	C₂²×C₄×C₁₄₉	—	2	4	no	—
77	C₂²×C₄×C₁₄₉	—	2	4	no	—
78	C₂²×C₄×C₁₄₉	—	2	4	no	—
79	C₂²×C₄×C₁₄₉	—	2	4	no	—
80	C₂²×C₄×C₁₄₉	—	2	4	no	—
81	C₂²×C₄×C₁₄₉	—	2	4	no	—
82	C₂²×C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₄₉	#41	1	8	yes	—
94	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
95	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
96	C₄⋊C₄×C₁₄₉	—	2	16	no	—
97	C₄⋊C₄×C₁₄₉	—	4	16	no	—
98	C₄²×C₁₄₉	—	2	16	no	—
99	C₄²×C₁₄₉	—	4	4	no	—
100	C₄²×C₁₄₉	—	4	4	no	—
101	C₄²×C₁₄₉	C₄⋊C₄	1	16	yes	complemented
102	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
103	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
104	C₂³×C₁₄₉	C₂²×Q₈	1	1	yes	characteristic
105	C₂³×C₁₄₉	C₂×#41	1	2	yes	—
106	C₂³×C₁₄₉	C₂×#41	1	2	yes	—
107	C₂³×C₁₄₉	C₂×#41	1	4	yes	—
108	C₂³×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
109	C₂³×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
110	C₂×C₄×C₁₄₉	—	2	4	no	—
111	C₂×C₄×C₁₄₉	—	2	4	no	—
112	C₂×C₄×C₁₄₉	—	2	4	no	—
113	C₂×C₄×C₁₄₉	—	2	2	no	—
114	C₂×C₄×C₁₄₉	—	2	4	no	—
115	C₂×C₄×C₁₄₉	—	2	2	no	—
116	C₂×C₄×C₁₄₉	—	2	4	no	—
117	C₂×C₄×C₁₄₉	—	2	4	no	—
118	C₂×C₄×C₁₄₉	—	2	2	no	—
119	C₂×C₄×C₁₄₉	—	2	2	no	—
120	C₂×C₄×C₁₄₉	—	2	4	no	—
121	C₂×C₄×C₁₄₉	—	2	4	no	—
122	C₂×C₄×C₁₄₉	—	2	4	no	—
123	C₂×C₄×C₁₄₉	—	2	8	no	—
124	C₂×C₄×C₁₄₉	—	2	8	no	—
125	C₂×C₄×C₁₄₉	—	2	4	no	—
126	C₂×C₄×C₁₄₉	—	2	4	no	—
127	C₂×C₄×C₁₄₉	—	2	4	no	—
128	C₂×C₄×C₁₄₉	—	2	8	no	—
129	C₂×C₄×C₁₄₉	—	2	8	no	—
130	C₂×C₄×C₁₄₉	—	2	8	no	—
131	C₂×C₄×C₁₄₉	—	4	4	no	—
132	C₂×C₄×C₁₄₉	—	4	4	no	—
133	C₂×C₄×C₁₄₉	—	4	4	no	—
134	C₂×C₄×C₁₄₉	—	4	4	no	—
135	C₂×C₄×C₁₄₉	—	4	4	no	—
136	C₂×C₄×C₁₄₉	—	4	4	no	—
137	C₂×C₄×C₁₄₉	—	4	4	no	—
138	C₂×C₄×C₁₄₉	—	4	4	no	—
139	C₂×C₄×C₁₄₉	—	4	4	no	—
140	C₂×C₄×C₁₄₉	—	4	4	no	—
141	C₂×C₄×C₁₄₉	—	4	4	no	—
142	C₂×C₄×C₁₄₉	—	4	4	no	—
143	C₂×C₄×C₁₄₉	—	4	4	no	—
144	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	4	yes	—
146	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	4	yes	—
147	C₂×C₄×C₁₄₉	#117	1	8	yes	—
148	C₂²×C₁₄₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×C₁₄₉	C₂×#117	1	2	yes	—
150	C₂²×C₁₄₉	C₄×#41	1	2	yes	—
151	C₂²×C₁₄₉	#518	1	1	yes	characteristic
152	C₂²×C₁₄₉	#519	1	1	yes	characteristic
153	C₂²×C₁₄₉	#525	1	2	yes	—
154	C₂²×C₁₄₉	#532	1	2	yes	—
155	C₂²×C₁₄₉	#533	1	1	yes	characteristic
156	C₂²×C₁₄₉	#533	1	2	yes	—
157	C₂²×C₁₄₉	#533	1	1	yes	characteristic
158	C₂²×C₁₄₉	#537	1	2	yes	—
159	C₂²×C₁₄₉	#544	1	2	yes	—
160	C₂²×C₁₄₉	#551	1	4	yes	—
161	C₂²×C₁₄₉	#552	1	4	yes	—
162	C₂²×C₁₄₉	#553	1	4	yes	—
163	C₂²×C₁₄₉	#556	1	4	yes	—
164	C₄×C₁₄₉	—	2	4	no	—
165	C₄×C₁₄₉	—	2	8	no	—
166	C₄×C₁₄₉	—	2	4	no	—
167	C₄×C₁₄₉	—	2	4	no	—
168	C₄×C₁₄₉	—	4	8	no	—
169	C₄×C₁₄₉	—	4	4	no	—
170	C₄×C₁₄₉	—	8	4	no	—
171	C₂×C₁₄₉	#2285	1	1	yes	characteristic
172	C₂×C₁₄₉	#2296	1	1	yes	characteristic
173	C₂×C₁₄₉	#2316	1	1	yes	characteristic
174	C₂×C₁₄₉	#2353	1	2	yes	—
175	C₂×C₁₄₉	#2356	1	2	yes	—
176	C₂×C₁₄₉	#2601	1	4	yes	—
177	C₂×C₁₄₉	#2605	1	2	yes	—
178	C₂×C₁₄₉	#2606	1	2	yes	—
179	#13964	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₄₉	#13964	1	1	yes	characteristic, direct product factor, Sylow
181	C₂×#383	C₂×C₁₄₉	1	1	yes	characteristic
182	C₂×C₄×C₄⋊C₄	C₂×C₁₄₉	1	1	yes	characteristic
183	C₂×#376	C₂×C₁₄₉	1	1	yes	characteristic
184	#1441	C₂×C₁₄₉	1	4	yes	—
185	#1436	C₂×C₁₄₉	1	4	yes	—
186	C₄⋊#95	C₂×C₁₄₉	1	2	yes	—
187	#1434	C₂×C₁₄₉	1	2	yes	—
188	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	4	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
190	C₂²×C₄²	C₂²×C₁₄₉	1	2	yes	—
191	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
192	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
194	#383	—	2	4	no	—
195	C₄×C₄⋊C₄	C₄×C₁₄₉	1	8	yes	complemented
196	#376	—	2	4	no	—
197	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
198	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
199	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
200	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
201	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
202	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
203	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
204	C₂×#95	C₂²×C₁₄₉	1	4	yes	—
205	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₄₉	1	4	yes	—
207	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
208	C₂³×C₄	C₂³×C₁₄₉	1	4	yes	—
209	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	—	2	8	no	—
217	C₂×C₄⋊C₄	—	4	4	no	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	8	yes	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	2	8	no	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	—	4	2	no	—
223	C₂×C₄²	C₂×C₄×C₁₄₉	1	4	yes	—
224	C₂×C₄²	C₂×C₄×C₁₄₉	1	4	yes	—
225	C₂×C₄²	C₂×C₄×C₁₄₉	1	4	yes	—
226	C₂×C₄²	D₄×C₁₄₉	1	4	yes	—
227	C₂×C₄²	Q₈×C₁₄₉	1	4	yes	—
228	#95	—	2	4	no	—
229	#95	—	2	4	no	—
230	#95	—	2	4	no	—
231	#95	—	2	4	no	—
232	#95	—	2	4	no	—
233	#95	—	2	8	no	—
234	#95	—	2	8	no	—
235	#95	—	4	4	no	—
236	#95	C₂×C₄×C₁₄₉	1	8	yes	—
237	C₂⁴	C₂⁴×C₁₄₉	1	1	yes	characteristic
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
271	C₂²×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
272	C₂²×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
273	C₂²×C₄	#41×C₁₄₉	1	8	yes	—
274	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
275	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	4	16	no	—
278	C₄²	—	2	16	no	—
279	C₄²	—	4	4	no	—
280	C₄²	—	4	4	no	—
281	C₄²	C₄⋊C₄×C₁₄₉	1	16	yes	complemented
282	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
283	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
284	C₂³	C₂²×Q₈×C₁₄₉	1	1	yes	characteristic
285	C₂³	C₂×#41×C₁₄₉	1	2	yes	—
286	C₂³	C₂×#41×C₁₄₉	1	2	yes	—
287	C₂³	C₂×#41×C₁₄₉	1	4	yes	—
288	C₂³	H(5,𝔽₂)×C₁₄₉	1	2	yes	—
289	C₂³	2₋¹⁺⁴×C₁₄₉	1	2	yes	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	4	yes	—
325	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	4	yes	—
326	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	4	yes	—
327	C₂×C₄	#117×C₁₄₉	1	8	yes	—
328	C₂²	C₂²×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
329	C₂²	C₂×#117×C₁₄₉	1	2	yes	—
330	C₂²	C₄×#41×C₁₄₉	1	2	yes	—
331	C₂²	#518×C₁₄₉	1	1	yes	characteristic
332	C₂²	#519×C₁₄₉	1	1	yes	characteristic
333	C₂²	#525×C₁₄₉	1	2	yes	—
334	C₂²	#532×C₁₄₉	1	2	yes	—
335	C₂²	#533×C₁₄₉	1	1	yes	characteristic
336	C₂²	#533×C₁₄₉	1	1	yes	characteristic
337	C₂²	#533×C₁₄₉	1	2	yes	—
338	C₂²	#537×C₁₄₉	1	2	yes	—
339	C₂²	#544×C₁₄₉	1	2	yes	—
340	C₂²	#551×C₁₄₉	1	4	yes	—
341	C₂²	#552×C₁₄₉	1	4	yes	—
342	C₂²	#553×C₁₄₉	1	4	yes	—
343	C₂²	#556×C₁₄₉	1	4	yes	—
344	C₄	—	2	4	no	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	8	no	—
348	C₄	—	4	8	no	—
349	C₄	—	4	4	no	—
350	C₄	—	8	4	no	—
351	C₂	#2285×C₁₄₉	1	1	yes	characteristic
352	C₂	#2296×C₁₄₉	1	1	yes	characteristic
353	C₂	#2316×C₁₄₉	1	1	yes	characteristic
354	C₂	#2353×C₁₄₉	1	2	yes	—
355	C₂	#2356×C₁₄₉	1	2	yes	—
356	C₂	#2601×C₁₄₉	1	4	yes	—
357	C₂	#2605×C₁₄₉	1	2	yes	—
358	C₂	#2606×C₁₄₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₄₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₄₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄×C₄⋊C₄×C₁₄₉	C₄	semidirect
101. C₄²×C₁₄₉	C₄⋊C₄	semidirect
179. #13964	C₁₄₉	direct (N × H)
180. C₁₄₉	#13964	direct (N × H)
195. C₄×C₄⋊C₄	C₄×C₁₄₉	semidirect
281. C₄²	C₄⋊C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#383×C₁₄₉	2
C₂×C₄×C₄⋊C₄×C₁₄₉	2
C₂×#376×C₁₄₉	2
#1441×C₁₄₉	2
#1436×C₁₄₉	2
C₄⋊#95×C₁₄₉	2
#1434×C₁₄₉	2
#13964	149

Subgroups — C149×#13964 #49192913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#13964 #49192913