Subgroups — C₂²×#328×C₁₄₉ #49196477

Order 38144.

1846 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#328×C₁₄₉	C₂	1	12	yes	maximal, direct product factor
5	C₂³×Q₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
6	C₂⁴×C₄×C₁₄₉	—	2	1	no	—
7	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₄₉	—	2	1	no	—
9	C₂×C₂²⋊Q₈×C₁₄₉	—	2	3	no	—
10	C₂×C₂²⋊Q₈×C₁₄₉	—	2	3	no	—
11	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	6	yes	complemented
12	C₂×C₂²⋊Q₈×C₁₄₉	C₂²	1	6	yes	—
13	C₂²×C₄⋊C₄×C₁₄₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
16	C₂×C₂²⋊C₈×C₁₄₉	—	2	3	no	—
17	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	6	yes	—
18	C₂×#95×C₁₄₉	—	2	3	no	—
19	C₂×#95×C₁₄₉	C₂²	1	6	yes	—
20	#328×C₁₄₉	C₂²	1	16	yes	direct product factor
21	C₂⁵×C₁₄₉	D₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₄₉	—	2	3	no	—
23	C₂²×Q₈×C₁₄₉	—	4	4	no	—
24	C₂²×Q₈×C₁₄₉	C₂×C₄	1	6	yes	complemented
25	C₂³×C₄×C₁₄₉	—	2	8	no	—
26	C₂³×C₄×C₁₄₉	—	2	1	no	—
27	C₂³×C₄×C₁₄₉	—	2	1	no	—
28	C₂³×C₄×C₁₄₉	—	2	6	no	—
29	C₂³×C₄×C₁₄₉	—	4	4	no	—
30	C₂³×C₄×C₁₄₉	—	4	4	no	—
31	C₂³×C₄×C₁₄₉	—	4	4	no	—
32	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₄₉	C₂×C₄	1	3	yes	—
34	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₄₉	D₄	1	3	yes	—
36	C₂³×C₄×C₁₄₉	D₄	1	3	yes	—
37	C₂³×C₄×C₁₄₉	C₂³	1	3	yes	—
38	C₂²×C₈×C₁₄₉	—	2	6	no	—
39	C₂²×C₈×C₁₄₉	—	4	4	no	—
40	C₂²⋊Q₈×C₁₄₉	—	2	12	no	—
41	C₂²⋊Q₈×C₁₄₉	—	2	6	no	—
42	C₂²⋊Q₈×C₁₄₉	—	2	6	no	—
43	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	12	yes	complemented
44	C₂²⋊Q₈×C₁₄₉	C₂³	1	4	yes	—
45	C₂×C₄⋊C₄×C₁₄₉	—	2	6	no	—
46	C₂×C₄⋊C₄×C₁₄₉	—	2	3	no	—
47	C₂×C₄⋊C₄×C₁₄₉	—	2	6	no	—
48	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	6	yes	complemented
49	C₂×C₂²⋊C₄×C₁₄₉	—	2	6	no	—
50	C₂×C₂²⋊C₄×C₁₄₉	—	2	6	no	—
51	C₂²⋊C₈×C₁₄₉	—	2	6	no	—
52	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
53	#95×C₁₄₉	—	2	6	no	—
54	#95×C₁₄₉	C₂³	1	4	yes	—
55	C₂⁴×C₁₄₉	—	2	4	no	—
56	C₂⁴×C₁₄₉	—	2	4	no	—
57	C₂⁴×C₁₄₉	C₂²⋊C₄	1	3	yes	—
58	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂⁴×C₁₄₉	SD₁₆	1	4	yes	—
60	C₂⁴×C₁₄₉	Q₁₆	1	4	yes	—
61	C₂⁴×C₁₄₉	C₂×D₄	1	3	yes	—
62	C₂×Q₈×C₁₄₉	—	2	6	no	—
63	C₂×Q₈×C₁₄₉	—	4	12	no	—
64	C₂×Q₈×C₁₄₉	—	4	12	no	—
65	C₂×Q₈×C₁₄₉	C₂²×C₄	1	4	yes	complemented
66	C₂²×C₄×C₁₄₉	—	2	4	no	—
67	C₂²×C₄×C₁₄₉	—	2	4	no	—
68	C₂²×C₄×C₁₄₉	—	2	24	no	—
69	C₂²×C₄×C₁₄₉	—	2	6	no	—
70	C₂²×C₄×C₁₄₉	—	2	6	no	—
71	C₂²×C₄×C₁₄₉	—	2	4	no	—
72	C₂²×C₄×C₁₄₉	—	4	6	no	—
73	C₂²×C₄×C₁₄₉	—	4	6	no	—
74	C₂²×C₄×C₁₄₉	—	4	6	no	—
75	C₂²×C₄×C₁₄₉	—	4	6	no	—
76	C₂²×C₄×C₁₄₉	—	4	32	no	—
77	C₂²×C₄×C₁₄₉	—	4	12	no	—
78	C₂²×C₄×C₁₄₉	—	4	4	no	—
79	C₂²×C₄×C₁₄₉	—	4	4	no	—
80	C₂²×C₄×C₁₄₉	—	4	12	no	—
81	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
82	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	3	yes	—
83	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	6	yes	—
84	C₂²×C₄×C₁₄₉	C₂²×C₄	1	3	yes	—
85	C₂²×C₄×C₁₄₉	C₂²×C₄	1	3	yes	—
86	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
87	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
88	C₂²×C₄×C₁₄₉	C₂×D₄	1	3	yes	—
89	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₁₄₉	—	2	4	no	—
91	C₂×C₈×C₁₄₉	—	4	12	no	—
92	C₄⋊C₄×C₁₄₉	—	2	12	no	—
93	C₄⋊C₄×C₁₄₉	—	2	6	no	—
94	C₄⋊C₄×C₁₄₉	—	2	4	no	—
95	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	4	yes	complemented
96	C₂²⋊C₄×C₁₄₉	—	2	12	no	—
97	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
98	C₂³×C₁₄₉	—	2	16	no	—
99	C₂³×C₁₄₉	—	2	16	no	—
100	C₂³×C₁₄₉	—	2	6	no	—
101	C₂³×C₁₄₉	—	2	6	no	—
102	C₂³×C₁₄₉	—	2	6	no	—
103	C₂³×C₁₄₉	—	2	6	no	—
104	C₂³×C₁₄₉	#99	1	4	yes	—
105	C₂³×C₁₄₉	#103	1	12	yes	—
106	C₂³×C₁₄₉	#103	1	4	yes	—
107	C₂³×C₁₄₉	#104	1	4	yes	—
108	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
109	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
110	C₂³×C₁₄₉	C₂×SD₁₆	1	6	yes	—
111	C₂³×C₁₄₉	C₂×Q₁₆	1	6	yes	—
112	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
113	Q₈×C₁₄₉	—	4	4	no	—
114	Q₈×C₁₄₉	—	4	12	no	—
115	C₂×C₄×C₁₄₉	—	2	6	no	—
116	C₂×C₄×C₁₄₉	—	2	6	no	—
117	C₂×C₄×C₁₄₉	—	2	6	no	—
118	C₂×C₄×C₁₄₉	—	2	6	no	—
119	C₂×C₄×C₁₄₉	—	2	8	no	—
120	C₂×C₄×C₁₄₉	—	2	4	no	—
121	C₂×C₄×C₁₄₉	—	2	4	no	—
122	C₂×C₄×C₁₄₉	—	4	6	no	—
123	C₂×C₄×C₁₄₉	—	4	3	no	—
124	C₂×C₄×C₁₄₉	—	4	3	no	—
125	C₂×C₄×C₁₄₉	—	4	3	no	—
126	C₂×C₄×C₁₄₉	—	4	1	no	—
127	C₂×C₄×C₁₄₉	—	4	4	no	—
128	C₂×C₄×C₁₄₉	—	4	48	no	—
129	C₂×C₄×C₁₄₉	—	4	4	no	—
130	C₂×C₄×C₁₄₉	—	4	12	no	—
131	C₂×C₄×C₁₄₉	—	4	12	no	—
132	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
133	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	3	yes	—
134	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
136	C₈×C₁₄₉	—	4	4	no	—
137	C₂²×C₁₄₉	—	2	1	no	—
138	C₂²×C₁₄₉	—	2	3	no	—
139	C₂²×C₁₄₉	—	2	1	no	—
140	C₂²×C₁₄₉	—	2	3	no	—
141	C₂²×C₁₄₉	—	2	12	no	—
142	C₂²×C₁₄₉	—	2	24	no	—
143	C₂²×C₁₄₉	—	2	12	no	—
144	C₂²×C₁₄₉	#328	1	16	yes	direct product factor
145	C₂²×C₁₄₉	C₂×#99	1	6	yes	—
146	C₂²×C₁₄₉	C₂×#103	1	6	yes	—
147	C₂²×C₁₄₉	C₂×#103	1	6	yes	—
148	C₂²×C₁₄₉	C₂×#104	1	6	yes	—
149	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₁₄₉	C₂²×SD₁₆	1	1	yes	characteristic
151	C₂²×C₁₄₉	C₂²×Q₁₆	1	1	yes	characteristic
152	C₄×C₁₄₉	—	2	1	no	—
153	C₄×C₁₄₉	—	2	3	no	—
154	C₄×C₁₄₉	—	2	3	no	—
155	C₄×C₁₄₉	—	2	1	no	—
156	C₄×C₁₄₉	—	4	8	no	—
157	C₄×C₁₄₉	—	4	4	no	—
158	C₄×C₁₄₉	—	4	4	no	—
159	C₂×C₁₄₉	—	2	1	no	—
160	C₂×C₁₄₉	—	2	1	no	—
161	C₂×C₁₄₉	—	2	6	no	—
162	C₂×C₁₄₉	C₂×#328	1	12	yes	direct product factor
163	C₂×C₁₄₉	C₂²×#99	1	1	yes	characteristic
164	C₂×C₁₄₉	C₂²×#103	1	1	yes	characteristic
165	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
166	C₂²×#328	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₁₄₉	C₂²×#328	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²×C₂²⋊Q₈	C₂×C₁₄₉	1	1	yes	characteristic
169	C₂²×C₂²⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic
170	C₂²×#95	C₂×C₁₄₉	1	1	yes	characteristic
171	C₂×#328	C₂×C₁₄₉	1	12	yes	direct product factor
172	C₂³×Q₈	C₄×C₁₄₉	1	1	yes	characteristic, complemented
173	C₂⁴×C₄	—	2	1	no	—
174	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
175	C₂³×C₈	—	2	1	no	—
176	C₂×C₂²⋊Q₈	—	2	3	no	—
177	C₂×C₂²⋊Q₈	—	2	3	no	—
178	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	6	yes	complemented
179	C₂×C₂²⋊Q₈	C₂²×C₁₄₉	1	6	yes	—
180	C₂²×C₄⋊C₄	—	2	1	no	—
181	C₂²×C₄⋊C₄	C₄×C₁₄₉	1	1	yes	characteristic, complemented
182	C₂²×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₂²⋊C₈	—	2	3	no	—
184	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	6	yes	—
185	C₂×#95	—	2	3	no	—
186	C₂×#95	C₂²×C₁₄₉	1	6	yes	—
187	#328	C₂²×C₁₄₉	1	16	yes	direct product factor
188	C₂⁵	D₄×C₁₄₉	1	1	yes	characteristic
189	C₂²×Q₈	—	2	3	no	—
190	C₂²×Q₈	—	4	4	no	—
191	C₂²×Q₈	C₂×C₄×C₁₄₉	1	6	yes	complemented
192	C₂³×C₄	—	2	8	no	—
193	C₂³×C₄	—	2	1	no	—
194	C₂³×C₄	—	2	1	no	—
195	C₂³×C₄	—	2	6	no	—
196	C₂³×C₄	—	4	4	no	—
197	C₂³×C₄	—	4	4	no	—
198	C₂³×C₄	—	4	4	no	—
199	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
200	C₂³×C₄	C₂×C₄×C₁₄₉	1	3	yes	—
201	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
202	C₂³×C₄	D₄×C₁₄₉	1	3	yes	—
203	C₂³×C₄	D₄×C₁₄₉	1	3	yes	—
204	C₂³×C₄	C₂³×C₁₄₉	1	3	yes	—
205	C₂²×C₈	—	2	6	no	—
206	C₂²×C₈	—	4	4	no	—
207	C₂²⋊Q₈	—	2	12	no	—
208	C₂²⋊Q₈	—	2	6	no	—
209	C₂²⋊Q₈	—	2	6	no	—
210	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	12	yes	complemented
211	C₂²⋊Q₈	C₂³×C₁₄₉	1	4	yes	—
212	C₂×C₄⋊C₄	—	2	6	no	—
213	C₂×C₄⋊C₄	—	2	3	no	—
214	C₂×C₄⋊C₄	—	2	6	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	6	yes	complemented
216	C₂×C₂²⋊C₄	—	2	6	no	—
217	C₂×C₂²⋊C₄	—	2	6	no	—
218	C₂²⋊C₈	—	2	6	no	—
219	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
220	#95	—	2	6	no	—
221	#95	C₂³×C₁₄₉	1	4	yes	—
222	C₂⁴	—	2	4	no	—
223	C₂⁴	—	2	4	no	—
224	C₂⁴	C₂²⋊C₄×C₁₄₉	1	3	yes	—
225	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
226	C₂⁴	SD₁₆×C₁₄₉	1	4	yes	—
227	C₂⁴	Q₁₆×C₁₄₉	1	4	yes	—
228	C₂⁴	C₂×D₄×C₁₄₉	1	3	yes	—
229	C₂×Q₈	—	2	6	no	—
230	C₂×Q₈	—	4	12	no	—
231	C₂×Q₈	—	4	12	no	—
232	C₂×Q₈	C₂²×C₄×C₁₄₉	1	4	yes	complemented
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	24	no	—
236	C₂²×C₄	—	2	6	no	—
237	C₂²×C₄	—	2	6	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	4	6	no	—
240	C₂²×C₄	—	4	6	no	—
241	C₂²×C₄	—	4	6	no	—
242	C₂²×C₄	—	4	6	no	—
243	C₂²×C₄	—	4	12	no	—
244	C₂²×C₄	—	4	32	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	—	4	4	no	—
247	C₂²×C₄	—	4	12	no	—
248	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
249	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	3	yes	—
250	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	6	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₄₉	1	3	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₄₉	1	3	yes	—
253	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
254	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
255	C₂²×C₄	C₂×D₄×C₁₄₉	1	3	yes	—
256	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	4	12	no	—
259	C₄⋊C₄	—	2	12	no	—
260	C₄⋊C₄	—	2	6	no	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	4	yes	complemented
263	C₂²⋊C₄	—	2	12	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₂³	—	2	6	no	—
266	C₂³	—	2	6	no	—
267	C₂³	—	2	6	no	—
268	C₂³	—	2	6	no	—
269	C₂³	—	2	16	no	—
270	C₂³	—	2	16	no	—
271	C₂³	#99×C₁₄₉	1	4	yes	—
272	C₂³	#103×C₁₄₉	1	12	yes	—
273	C₂³	#103×C₁₄₉	1	4	yes	—
274	C₂³	#104×C₁₄₉	1	4	yes	—
275	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
276	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
277	C₂³	C₂×SD₁₆×C₁₄₉	1	6	yes	—
278	C₂³	C₂×Q₁₆×C₁₄₉	1	6	yes	—
279	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
280	Q₈	—	4	4	no	—
281	Q₈	—	4	12	no	—
282	C₂×C₄	—	2	6	no	—
283	C₂×C₄	—	2	6	no	—
284	C₂×C₄	—	2	6	no	—
285	C₂×C₄	—	2	6	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	4	6	no	—
290	C₂×C₄	—	4	3	no	—
291	C₂×C₄	—	4	3	no	—
292	C₂×C₄	—	4	3	no	—
293	C₂×C₄	—	4	1	no	—
294	C₂×C₄	—	4	48	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	12	no	—
297	C₂×C₄	—	4	12	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
300	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	3	yes	—
301	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
302	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
303	C₈	—	4	4	no	—
304	C₂²	—	2	12	no	—
305	C₂²	—	2	24	no	—
306	C₂²	—	2	12	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	2	3	no	—
309	C₂²	—	2	1	no	—
310	C₂²	—	2	3	no	—
311	C₂²	#328×C₁₄₉	1	16	yes	direct product factor
312	C₂²	C₂×#99×C₁₄₉	1	6	yes	—
313	C₂²	C₂×#103×C₁₄₉	1	6	yes	—
314	C₂²	C₂×#103×C₁₄₉	1	6	yes	—
315	C₂²	C₂×#104×C₁₄₉	1	6	yes	—
316	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
317	C₂²	C₂²×SD₁₆×C₁₄₉	1	1	yes	characteristic
318	C₂²	C₂²×Q₁₆×C₁₄₉	1	1	yes	characteristic
319	C₄	—	2	1	no	—
320	C₄	—	2	3	no	—
321	C₄	—	2	3	no	—
322	C₄	—	2	1	no	—
323	C₄	—	4	8	no	—
324	C₄	—	4	4	no	—
325	C₄	—	4	4	no	—
326	C₂	—	2	1	no	—
327	C₂	—	2	6	no	—
328	C₂	—	2	1	no	—
329	C₂	C₂×#328×C₁₄₉	1	12	yes	direct product factor
330	C₂	C₂²×#99×C₁₄₉	1	1	yes	characteristic
331	C₂	C₂²×#103×C₁₄₉	1	1	yes	characteristic
332	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₄₉	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂⁵×C₁₄₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#328×C₁₄₉	C₂	direct (N × H)
5. C₂³×Q₈×C₁₄₉	C₄	semidirect
11. C₂×C₂²⋊Q₈×C₁₄₉	C₄	semidirect
14. C₂²×C₄⋊C₄×C₁₄₉	C₄	semidirect
20. #328×C₁₄₉	C₂²	direct (N × H)
24. C₂²×Q₈×C₁₄₉	C₂×C₄	semidirect
43. C₂²⋊Q₈×C₁₄₉	C₂×C₄	semidirect
48. C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
65. C₂×Q₈×C₁₄₉	C₂²×C₄	semidirect
95. C₄⋊C₄×C₁₄₉	C₂²×C₄	semidirect
144. C₂²×C₁₄₉	#328	direct (N × H)
162. C₂×C₁₄₉	C₂×#328	direct (N × H)
166. C₂²×#328	C₁₄₉	direct (N × H)
167. C₁₄₉	C₂²×#328	direct (N × H)
171. C₂×#328	C₂×C₁₄₉	direct (N × H)
172. C₂³×Q₈	C₄×C₁₄₉	semidirect
178. C₂×C₂²⋊Q₈	C₄×C₁₄₉	semidirect
181. C₂²×C₄⋊C₄	C₄×C₁₄₉	semidirect
187. #328	C₂²×C₁₄₉	direct (N × H)
191. C₂²×Q₈	C₂×C₄×C₁₄₉	semidirect
210. C₂²⋊Q₈	C₂×C₄×C₁₄₉	semidirect
215. C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	semidirect
232. C₂×Q₈	C₂²×C₄×C₁₄₉	semidirect
262. C₄⋊C₄	C₂²×C₄×C₁₄₉	semidirect
311. C₂²	#328×C₁₄₉	direct (N × H)
329. C₂	C₂×#328×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
C₂²×C₂²⋊Q₈×C₁₄₉	2
C₂²×C₂²⋊C₈×C₁₄₉	2
C₂²×#95×C₁₄₉	2
C₂×#328×C₁₄₉	2
C₂²×#328	149

Subgroups — C22×#328×C149 #49196477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#328×C₁₄₉ #49196477