Subgroups — C₄×#342×C₁₄₉ #49189657

Order 38144.

1482 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂²⋊C₄×C₁₄₉	C₂	1	2	yes	maximal
2	C₂×C₄×C₂²⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#342×C₁₄₉	C₂	1	4	yes	maximal
4	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
5	C₂²×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
6	C₂²×C₂²⋊C₄×C₁₄₉	C₂²	1	4	yes	—
7	C₂²×C₄²×C₁₄₉	—	2	2	no	—
8	C₂²×C₄²×C₁₄₉	C₄	1	2	yes	complemented
9	C₄×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
10	C₄×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
11	C₄×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
12	C₄×C₂²⋊C₄×C₁₄₉	C₄	1	8	yes	complemented
13	C₂×#95×C₁₄₉	—	2	2	no	—
14	C₂×#95×C₁₄₉	C₄	1	2	yes	complemented
15	#342×C₁₄₉	C₄	1	16	yes	direct product factor
16	C₂⁵×C₁₄₉	C₂³	1	1	yes	characteristic
17	C₂³×C₄×C₁₄₉	—	2	4	no	—
18	C₂³×C₄×C₁₄₉	—	4	4	no	—
19	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₄₉	C₂×C₄	1	4	yes	—
21	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₄₉	C₂×C₄	1	4	yes	—
23	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
24	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
25	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
26	C₂³×C₄×C₁₄₉	Q₈	1	2	yes	—
27	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
30	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
31	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	8	yes	—
32	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	8	yes	—
33	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	16	yes	—
34	C₂×C₄²×C₁₄₉	—	2	2	no	—
35	C₂×C₄²×C₁₄₉	—	2	8	no	—
36	C₂×C₄²×C₁₄₉	—	2	2	no	—
37	C₂×C₄²×C₁₄₉	—	4	8	no	—
38	C₂×C₄²×C₁₄₉	—	4	4	no	—
39	#95×C₁₄₉	—	2	8	no	—
40	#95×C₁₄₉	—	2	4	no	—
41	C₂⁴×C₁₄₉	—	4	2	no	—
42	C₂⁴×C₁₄₉	—	4	2	no	—
43	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
44	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
45	C₂⁴×C₁₄₉	C₂²×C₄	1	4	yes	—
46	C₂⁴×C₁₄₉	C₂×D₄	1	2	yes	—
47	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
48	C₂⁴×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
49	C₂⁴×C₁₄₉	#41	1	4	yes	—
50	C₂²×C₄×C₁₄₉	—	2	4	no	—
51	C₂²×C₄×C₁₄₉	—	2	8	no	—
52	C₂²×C₄×C₁₄₉	—	2	4	no	—
53	C₂²×C₄×C₁₄₉	—	2	8	no	—
54	C₂²×C₄×C₁₄₉	—	2	4	no	—
55	C₂²×C₄×C₁₄₉	—	2	16	no	—
56	C₂²×C₄×C₁₄₉	—	4	8	no	—
57	C₂²×C₄×C₁₄₉	—	4	4	no	—
58	C₂²×C₄×C₁₄₉	—	4	4	no	—
59	C₂²×C₄×C₁₄₉	—	4	2	no	—
60	C₂²×C₄×C₁₄₉	—	4	4	no	—
61	C₂²×C₄×C₁₄₉	—	4	8	no	—
62	C₂²×C₄×C₁₄₉	—	4	8	no	—
63	C₂²×C₄×C₁₄₉	—	4	4	no	—
64	C₂²×C₄×C₁₄₉	—	4	4	no	—
65	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
66	C₂²×C₄×C₁₄₉	C₄²	1	2	yes	—
67	C₂²×C₄×C₁₄₉	C₄²	1	8	yes	complemented
68	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
71	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
72	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
77	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
78	C₂²⋊C₄×C₁₄₉	—	2	16	no	—
79	C₂²⋊C₄×C₁₄₉	—	2	16	no	—
80	C₂²⋊C₄×C₁₄₉	C₄²	1	16	yes	complemented
81	C₄²×C₁₄₉	—	4	4	no	—
82	C₄²×C₁₄₉	—	4	16	no	—
83	C₄²×C₁₄₉	—	4	4	no	—
84	C₂³×C₁₄₉	—	2	2	no	—
85	C₂³×C₁₄₉	—	2	4	no	—
86	C₂³×C₁₄₉	—	2	2	no	—
87	C₂³×C₁₄₉	—	2	4	no	—
88	C₂³×C₁₄₉	—	4	2	no	—
89	C₂³×C₁₄₉	—	4	1	no	—
90	C₂³×C₁₄₉	—	4	1	no	—
91	C₂³×C₁₄₉	—	4	2	no	—
92	C₂³×C₁₄₉	—	4	8	no	—
93	C₂³×C₁₄₉	—	4	1	no	—
94	C₂³×C₁₄₉	—	4	1	no	—
95	C₂³×C₁₄₉	—	4	8	no	—
96	C₂³×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
97	C₂³×C₁₄₉	C₂×C₄²	1	2	yes	—
98	C₂³×C₁₄₉	C₂×C₄²	1	4	yes	—
99	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
100	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	2	yes	—
103	C₂³×C₁₄₉	#117	1	2	yes	—
104	C₂³×C₁₄₉	#117	1	4	yes	—
105	C₂³×C₁₄₉	C₄×D₄	1	8	yes	—
106	C₂³×C₁₄₉	C₄×D₄	1	4	yes	—
107	C₂³×C₁₄₉	C₄×Q₈	1	4	yes	—
108	C₂×C₄×C₁₄₉	—	2	2	no	—
109	C₂×C₄×C₁₄₉	—	2	4	no	—
110	C₂×C₄×C₁₄₉	—	2	8	no	—
111	C₂×C₄×C₁₄₉	—	2	4	no	—
112	C₂×C₄×C₁₄₉	—	2	4	no	—
113	C₂×C₄×C₁₄₉	—	2	8	no	—
114	C₂×C₄×C₁₄₉	—	2	8	no	—
115	C₂×C₄×C₁₄₉	—	2	16	no	—
116	C₂×C₄×C₁₄₉	—	4	2	no	—
117	C₂×C₄×C₁₄₉	—	4	4	no	—
118	C₂×C₄×C₁₄₉	—	4	4	no	—
119	C₂×C₄×C₁₄₉	—	4	2	no	—
120	C₂×C₄×C₁₄₉	—	4	8	no	—
121	C₂×C₄×C₁₄₉	—	4	8	no	—
122	C₂×C₄×C₁₄₉	—	4	32	no	—
123	C₂×C₄×C₁₄₉	—	4	8	no	—
124	C₂×C₄×C₁₄₉	—	4	4	no	—
125	C₂×C₄×C₁₄₉	—	4	4	no	—
126	C₂×C₄×C₁₄₉	—	4	8	no	—
127	C₂×C₄×C₁₄₉	#95	1	2	yes	—
128	C₂×C₄×C₁₄₉	#95	1	4	yes	—
129	C₂×C₄×C₁₄₉	#95	1	2	yes	—
130	C₂×C₄×C₁₄₉	#99	1	4	yes	—
131	C₂²×C₁₄₉	—	2	2	no	—
132	C₂²×C₁₄₉	—	2	1	no	—
133	C₂²×C₁₄₉	—	2	1	no	—
134	C₂²×C₁₄₉	—	2	2	no	—
135	C₂²×C₁₄₉	—	2	2	no	—
136	C₂²×C₁₄₉	—	2	1	no	—
137	C₂²×C₁₄₉	—	2	1	no	—
138	C₂²×C₁₄₉	—	2	2	no	—
139	C₂²×C₁₄₉	—	2	4	no	—
140	C₂²×C₁₄₉	—	2	4	no	—
141	C₂²×C₁₄₉	—	2	16	no	—
142	C₂²×C₁₄₉	—	4	4	no	—
143	C₂²×C₁₄₉	—	4	4	no	—
144	C₂²×C₁₄₉	—	4	4	no	—
145	C₂²×C₁₄₉	—	4	4	no	—
146	C₂²×C₁₄₉	C₄³	1	1	yes	characteristic
147	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
148	C₂²×C₁₄₉	#376	1	1	yes	characteristic
149	C₂²×C₁₄₉	C₄×C₂²⋊C₄	1	4	yes	—
150	C₂²×C₁₄₉	C₄×C₂²⋊C₄	1	2	yes	—
151	C₂²×C₁₄₉	C₄×C₄⋊C₄	1	2	yes	—
152	C₂²×C₁₄₉	C₄×C₄⋊C₄	1	4	yes	—
153	C₂²×C₁₄₉	C₂×#99	1	2	yes	—
154	C₂²×C₁₄₉	#410	1	2	yes	—
155	C₄×C₁₄₉	—	2	2	no	—
156	C₄×C₁₄₉	—	2	4	no	—
157	C₄×C₁₄₉	—	4	16	no	—
158	C₄×C₁₄₉	—	4	8	no	—
159	C₄×C₁₄₉	#342	1	4	yes	direct product factor
160	C₂×C₁₄₉	—	2	4	no	—
161	C₂×C₁₄₉	—	2	1	no	—
162	C₂×C₁₄₉	—	2	1	no	—
163	C₂×C₁₄₉	—	2	2	no	—
164	C₂×C₁₄₉	—	2	4	no	—
165	C₂×C₁₄₉	C₄×#95	1	1	yes	characteristic
166	C₂×C₁₄₉	C₂×#342	1	1	yes	characteristic
167	C₂×C₁₄₉	#1740	1	1	yes	characteristic
168	C₂×C₁₄₉	C₄×#99	1	4	yes	—
169	C₄×#342	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₁₄₉	C₄×#342	1	1	yes	characteristic, direct product factor, Sylow
171	C₂×C₄×C₂²⋊C₄	C₂×C₁₄₉	1	2	yes	—
172	C₂×C₄×C₂²⋊C₄	C₂×C₁₄₉	1	1	yes	characteristic
173	C₂×#342	C₂×C₁₄₉	1	4	yes	—
174	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
175	C₂²×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
176	C₂²×C₂²⋊C₄	C₂²×C₁₄₉	1	4	yes	—
177	C₂²×C₄²	—	2	2	no	—
178	C₂²×C₄²	C₄×C₁₄₉	1	2	yes	complemented
179	C₄×C₂²⋊C₄	—	2	4	no	—
180	C₄×C₂²⋊C₄	—	2	2	no	—
181	C₄×C₂²⋊C₄	—	2	2	no	—
182	C₄×C₂²⋊C₄	C₄×C₁₄₉	1	8	yes	complemented
183	C₂×#95	—	2	2	no	—
184	C₂×#95	C₄×C₁₄₉	1	2	yes	complemented
185	#342	C₄×C₁₄₉	1	16	yes	direct product factor
186	C₂⁵	C₂³×C₁₄₉	1	1	yes	characteristic
187	C₂³×C₄	—	2	4	no	—
188	C₂³×C₄	—	4	4	no	—
189	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
190	C₂³×C₄	C₂×C₄×C₁₄₉	1	4	yes	—
191	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
192	C₂³×C₄	C₂×C₄×C₁₄₉	1	4	yes	—
193	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
194	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
195	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
196	C₂³×C₄	Q₈×C₁₄₉	1	2	yes	—
197	C₂×C₂²⋊C₄	—	2	4	no	—
198	C₂×C₂²⋊C₄	—	2	4	no	—
199	C₂×C₂²⋊C₄	—	2	8	no	—
200	C₂×C₂²⋊C₄	—	2	4	no	—
201	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	8	yes	—
202	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	16	yes	—
203	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	8	yes	—
204	C₂×C₄²	—	2	2	no	—
205	C₂×C₄²	—	2	2	no	—
206	C₂×C₄²	—	2	8	no	—
207	C₂×C₄²	—	4	8	no	—
208	C₂×C₄²	—	4	4	no	—
209	#95	—	2	8	no	—
210	#95	—	2	4	no	—
211	C₂⁴	—	4	2	no	—
212	C₂⁴	—	4	2	no	—
213	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
214	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
215	C₂⁴	C₂²×C₄×C₁₄₉	1	4	yes	—
216	C₂⁴	C₂×D₄×C₁₄₉	1	2	yes	—
217	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
218	C₂⁴	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
219	C₂⁴	#41×C₁₄₉	1	4	yes	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	2	8	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	8	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	16	no	—
226	C₂²×C₄	—	4	8	no	—
227	C₂²×C₄	—	4	4	no	—
228	C₂²×C₄	—	4	4	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	4	8	no	—
232	C₂²×C₄	—	4	8	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
236	C₂²×C₄	C₄²×C₁₄₉	1	2	yes	—
237	C₂²×C₄	C₄²×C₁₄₉	1	8	yes	complemented
238	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
239	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
240	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
241	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
242	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
243	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
244	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
245	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
246	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
247	C₂²⋊C₄	—	2	8	no	—
248	C₂²⋊C₄	—	2	16	no	—
249	C₂²⋊C₄	—	2	16	no	—
250	C₂²⋊C₄	C₄²×C₁₄₉	1	16	yes	complemented
251	C₄²	—	4	4	no	—
252	C₄²	—	4	16	no	—
253	C₄²	—	4	4	no	—
254	C₂³	—	2	2	no	—
255	C₂³	—	2	4	no	—
256	C₂³	—	2	2	no	—
257	C₂³	—	2	4	no	—
258	C₂³	—	4	2	no	—
259	C₂³	—	4	1	no	—
260	C₂³	—	4	1	no	—
261	C₂³	—	4	2	no	—
262	C₂³	—	4	8	no	—
263	C₂³	—	4	1	no	—
264	C₂³	—	4	1	no	—
265	C₂³	—	4	8	no	—
266	C₂³	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
267	C₂³	C₂×C₄²×C₁₄₉	1	2	yes	—
268	C₂³	C₂×C₄²×C₁₄₉	1	4	yes	—
269	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
270	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
271	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
272	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	2	yes	—
273	C₂³	#117×C₁₄₉	1	2	yes	—
274	C₂³	#117×C₁₄₉	1	4	yes	—
275	C₂³	C₄×D₄×C₁₄₉	1	8	yes	—
276	C₂³	C₄×D₄×C₁₄₉	1	4	yes	—
277	C₂³	C₄×Q₈×C₁₄₉	1	4	yes	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	8	no	—
291	C₂×C₄	—	4	8	no	—
292	C₂×C₄	—	4	32	no	—
293	C₂×C₄	—	4	8	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	8	no	—
297	C₂×C₄	#95×C₁₄₉	1	2	yes	—
298	C₂×C₄	#95×C₁₄₉	1	4	yes	—
299	C₂×C₄	#95×C₁₄₉	1	2	yes	—
300	C₂×C₄	#99×C₁₄₉	1	4	yes	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	2	4	no	—
311	C₂²	—	2	16	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	4	4	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	4	no	—
316	C₂²	C₄³×C₁₄₉	1	1	yes	characteristic
317	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
318	C₂²	#376×C₁₄₉	1	1	yes	characteristic
319	C₂²	C₄×C₂²⋊C₄×C₁₄₉	1	4	yes	—
320	C₂²	C₄×C₂²⋊C₄×C₁₄₉	1	2	yes	—
321	C₂²	C₄×C₄⋊C₄×C₁₄₉	1	2	yes	—
322	C₂²	C₄×C₄⋊C₄×C₁₄₉	1	4	yes	—
323	C₂²	C₂×#99×C₁₄₉	1	2	yes	—
324	C₂²	#410×C₁₄₉	1	2	yes	—
325	C₄	—	2	2	no	—
326	C₄	—	2	4	no	—
327	C₄	—	4	16	no	—
328	C₄	—	4	8	no	—
329	C₄	#342×C₁₄₉	1	4	yes	direct product factor
330	C₂	—	2	4	no	—
331	C₂	—	2	1	no	—
332	C₂	—	2	1	no	—
333	C₂	—	2	2	no	—
334	C₂	—	2	4	no	—
335	C₂	C₄×#95×C₁₄₉	1	1	yes	characteristic
336	C₂	C₂×#342×C₁₄₉	1	1	yes	characteristic
337	C₂	#1740×C₁₄₉	1	1	yes	characteristic
338	C₂	C₄×#99×C₁₄₉	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂²⋊C₄
commutator	C₂²	C₄³×C₁₄₉
Frattini, cosocle	C₂⁵	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₄₉	C₂³
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂²×C₄²×C₁₄₉	C₄	semidirect
12. C₄×C₂²⋊C₄×C₁₄₉	C₄	semidirect
14. C₂×#95×C₁₄₉	C₄	semidirect
15. #342×C₁₄₉	C₄	direct (N × H)
67. C₂²×C₄×C₁₄₉	C₄²	semidirect
80. C₂²⋊C₄×C₁₄₉	C₄²	semidirect
159. C₄×C₁₄₉	#342	direct (N × H)
169. C₄×#342	C₁₄₉	direct (N × H)
170. C₁₄₉	C₄×#342	direct (N × H)
178. C₂²×C₄²	C₄×C₁₄₉	semidirect
182. C₄×C₂²⋊C₄	C₄×C₁₄₉	semidirect
184. C₂×#95	C₄×C₁₄₉	semidirect
185. #342	C₄×C₁₄₉	direct (N × H)
237. C₂²×C₄	C₄²×C₁₄₉	semidirect
250. C₂²⋊C₄	C₄²×C₁₄₉	semidirect
329. C₄	#342×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₂²⋊C₄×C₁₄₉	2
C₂×#342×C₁₄₉	2
C₄×#342	149

Subgroups — C4×#342×C149 #49189657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#342×C₁₄₉ #49189657