Subgroups — C₁₄₉×#18401 #49197350

Order 38144.

1262 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3497×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3205×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#2548×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1598×C₁₄₉	C₂	1	8	yes	maximal, complemented
5	#1502×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1461×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×2₋¹⁺⁴×C₁₄₉	—	2	1	no	—
8	#550×C₁₄₉	—	2	2	no	—
9	D₄×Q₈×C₁₄₉	—	2	2	no	—
10	#548×C₁₄₉	—	2	4	no	—
11	#537×C₁₄₉	—	2	1	no	—
12	#537×C₁₄₉	C₂²	1	4	yes	—
13	#532×C₁₄₉	—	2	2	no	—
14	#532×C₁₄₉	C₂²	1	2	yes	—
15	C₂×#127×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₄₉	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
18	#493×C₁₄₉	—	2	2	no	—
19	#486×C₁₄₉	—	2	2	no	—
20	#459×C₁₄₉	—	2	4	no	—
21	#447×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	#327×C₁₄₉	C₂²	1	8	yes	—
28	#324×C₁₄₉	C₂²	1	4	yes	—
29	2₋¹⁺⁴×C₁₄₉	—	4	4	no	—
30	2₋¹⁺⁴×C₁₄₉	—	4	4	no	—
31	C₂×#41×C₁₄₉	—	2	4	no	—
32	C₂×#41×C₁₄₉	—	2	4	no	—
33	C₂×#41×C₁₄₉	—	2	2	no	—
34	C₂²×Q₈×C₁₄₉	—	2	4	no	—
35	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₄₉	—	2	1	no	—
37	C₂²×D₄×C₁₄₉	—	2	1	no	—
38	C₂²×D₄×C₁₄₉	C₂³	1	2	yes	—
39	C₂×D₈×C₁₄₉	—	2	8	no	—
40	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
41	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
42	#127×C₁₄₉	—	2	2	no	—
43	#127×C₁₄₉	—	2	2	no	—
44	#127×C₁₄₉	—	2	2	no	—
45	#127×C₁₄₉	D₄	1	2	yes	—
46	#124×C₁₄₉	—	2	4	no	—
47	#124×C₁₄₉	—	2	2	no	—
48	#124×C₁₄₉	—	4	4	no	—
49	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
50	C₂²⋊Q₈×C₁₄₉	—	2	8	no	—
51	#121×C₁₄₉	—	2	4	no	—
52	#121×C₁₄₉	—	2	8	no	—
53	#121×C₁₄₉	—	2	2	no	—
54	#121×C₁₄₉	—	2	4	no	—
55	#121×C₁₄₉	C₂³	1	4	yes	—
56	C₄×Q₈×C₁₄₉	—	2	2	no	—
57	C₄×Q₈×C₁₄₉	—	2	2	no	—
58	C₄×D₄×C₁₄₉	—	2	4	no	—
59	C₄×D₄×C₁₄₉	—	2	4	no	—
60	C₄×D₄×C₁₄₉	—	2	2	no	—
61	C₄×D₄×C₁₄₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
67	C₂×C₄²×C₁₄₉	—	2	1	no	—
68	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
69	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₁₄₉	—	2	2	no	—
71	#102×C₁₄₉	—	2	8	no	—
72	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
73	C₄×C₈×C₁₄₉	—	2	2	no	—
74	#95×C₁₄₉	C₂³	1	2	yes	—
75	C₂⁴×C₁₄₉	—	2	2	no	—
76	#41×C₁₄₉	—	4	8	no	—
77	#41×C₁₄₉	—	4	16	no	—
78	#41×C₁₄₉	—	4	8	no	—
79	#41×C₁₄₉	—	4	4	no	—
80	#41×C₁₄₉	—	4	4	no	—
81	C₂×Q₈×C₁₄₉	—	2	4	no	—
82	C₂×Q₈×C₁₄₉	—	2	2	no	—
83	C₂×Q₈×C₁₄₉	—	2	2	no	—
84	C₂×Q₈×C₁₄₉	—	2	2	no	—
85	C₂×Q₈×C₁₄₉	—	4	16	no	—
86	C₂×Q₈×C₁₄₉	D₈	1	4	yes	complemented
87	C₂×D₄×C₁₄₉	—	2	4	no	—
88	C₂×D₄×C₁₄₉	—	2	4	no	—
89	C₂×D₄×C₁₄₉	—	2	4	no	—
90	C₂×D₄×C₁₄₉	—	2	2	no	—
91	C₂×D₄×C₁₄₉	—	2	2	no	—
92	C₂×D₄×C₁₄₉	—	2	4	no	—
93	C₂×D₄×C₁₄₉	—	4	4	no	—
94	C₂×D₄×C₁₄₉	—	4	1	no	—
95	C₂×D₄×C₁₄₉	—	4	2	no	—
96	C₂×D₄×C₁₄₉	—	4	1	no	—
97	C₂×D₄×C₁₄₉	—	4	2	no	—
98	C₂×D₄×C₁₄₉	—	4	2	no	—
99	C₂×D₄×C₁₄₉	—	8	2	no	—
100	C₂×D₄×C₁₄₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₄₉	—	2	8	no	—
102	C₂²×C₄×C₁₄₉	—	2	4	no	—
103	C₂²×C₄×C₁₄₉	—	2	2	no	—
104	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
109	D₈×C₁₄₉	—	8	8	no	—
110	C₂×C₈×C₁₄₉	—	2	4	no	—
111	C₄⋊C₄×C₁₄₉	—	2	4	no	—
112	C₄⋊C₄×C₁₄₉	—	2	2	no	—
113	C₄⋊C₄×C₁₄₉	—	2	2	no	—
114	C₄⋊C₄×C₁₄₉	—	2	4	no	—
115	C₄⋊C₄×C₁₄₉	—	4	2	no	—
116	C₄⋊C₄×C₁₄₉	C₂×D₄	1	4	yes	—
117	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
118	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
121	C₂²⋊C₄×C₁₄₉	—	8	4	no	—
122	C₄²×C₁₄₉	—	2	2	no	—
123	C₄²×C₁₄₉	—	2	2	no	—
124	C₄²×C₁₄₉	—	4	2	no	—
125	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
127	C₂³×C₁₄₉	—	2	4	no	—
128	C₂³×C₁₄₉	—	4	4	no	—
129	C₂³×C₁₄₉	—	4	4	no	—
130	C₂³×C₁₄₉	—	4	2	no	—
131	C₂³×C₁₄₉	—	4	2	no	—
132	C₂³×C₁₄₉	—	4	2	no	—
133	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₄₉	—	2	8	no	—
135	Q₈×C₁₄₉	—	4	8	no	—
136	Q₈×C₁₄₉	—	4	4	no	—
137	D₄×C₁₄₉	—	4	4	no	—
138	D₄×C₁₄₉	—	4	8	no	—
139	D₄×C₁₄₉	—	4	8	no	—
140	D₄×C₁₄₉	—	4	4	no	—
141	D₄×C₁₄₉	—	4	4	no	—
142	D₄×C₁₄₉	—	4	4	no	—
143	D₄×C₁₄₉	—	4	4	no	—
144	D₄×C₁₄₉	—	8	2	no	—
145	D₄×C₁₄₉	—	8	4	no	—
146	D₄×C₁₄₉	—	8	4	no	—
147	D₄×C₁₄₉	—	8	2	no	—
148	C₂×C₄×C₁₄₉	—	2	2	no	—
149	C₂×C₄×C₁₄₉	—	2	2	no	—
150	C₂×C₄×C₁₄₉	—	2	2	no	—
151	C₂×C₄×C₁₄₉	—	2	2	no	—
152	C₂×C₄×C₁₄₉	—	2	4	no	—
153	C₂×C₄×C₁₄₉	—	4	1	no	—
154	C₂×C₄×C₁₄₉	—	4	16	no	—
155	C₂×C₄×C₁₄₉	—	4	8	no	—
156	C₂×C₄×C₁₄₉	—	4	2	no	—
157	C₂×C₄×C₁₄₉	—	4	2	no	—
158	C₂×C₄×C₁₄₉	—	4	2	no	—
159	C₂×C₄×C₁₄₉	—	4	2	no	—
160	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₄₉	#120	1	2	yes	—
162	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₄₉	C₂×D₈	1	4	yes	—
164	C₂×C₄×C₁₄₉	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
167	C₈×C₁₄₉	—	4	4	no	—
168	C₂²×C₁₄₉	—	2	1	no	—
169	C₂²×C₁₄₉	—	2	1	no	—
170	C₂²×C₁₄₉	—	4	4	no	—
171	C₂²×C₁₄₉	—	4	4	no	—
172	C₂²×C₁₄₉	—	4	4	no	—
173	C₂²×C₁₄₉	—	8	4	no	—
174	C₂²×C₁₄₉	—	8	4	no	—
175	C₂²×C₁₄₉	—	8	2	no	—
176	C₂²×C₁₄₉	—	8	2	no	—
177	C₂²×C₁₄₉	—	8	2	no	—
178	C₂²×C₁₄₉	C₂×#120	1	1	yes	characteristic
179	C₂²×C₁₄₉	C₂²×D₈	1	1	yes	characteristic
180	C₂²×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₄×C₁₄₉	—	2	4	no	—
182	C₄×C₁₄₉	—	2	1	no	—
183	C₄×C₁₄₉	—	2	2	no	—
184	C₄×C₁₄₉	—	4	4	no	—
185	C₄×C₁₄₉	—	4	2	no	—
186	C₄×C₁₄₉	—	8	2	no	—
187	C₄×C₁₄₉	#447	1	4	yes	—
188	C₄×C₁₄₉	#454	1	2	yes	—
189	C₂×C₁₄₉	—	2	1	no	—
190	C₂×C₁₄₉	—	2	1	no	—
191	C₂×C₁₄₉	—	8	4	no	—
192	C₂×C₁₄₉	—	16	2	no	—
193	C₂×C₁₄₉	C₂×#447	1	1	yes	characteristic
194	C₂×C₁₄₉	C₂×#454	1	1	yes	characteristic
195	C₂×C₁₄₉	#3027	1	1	yes	characteristic
196	#18401	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₄₉	#18401	1	1	yes	characteristic, direct product factor, Sylow
198	#3497	C₂×C₁₄₉	1	1	yes	characteristic, complemented
199	#3205	C₂×C₁₄₉	1	2	yes	complemented
200	#2548	C₂×C₁₄₉	1	1	yes	characteristic, complemented
201	#1598	C₂×C₁₄₉	1	8	yes	complemented
202	#1502	C₂×C₁₄₉	1	2	yes	complemented
203	#1461	C₂×C₁₄₉	1	1	yes	characteristic, complemented
204	C₂×2₋¹⁺⁴	—	2	1	no	—
205	#550	—	2	2	no	—
206	D₄×Q₈	—	2	2	no	—
207	#548	—	2	4	no	—
208	#537	—	2	1	no	—
209	#537	C₂²×C₁₄₉	1	4	yes	—
210	#532	—	2	2	no	—
211	#532	C₂²×C₁₄₉	1	2	yes	—
212	C₂×#127	C₂²×C₁₄₉	1	1	yes	characteristic
213	C₂×#124	—	2	1	no	—
214	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
215	#493	—	2	2	no	—
216	#486	—	2	2	no	—
217	#459	—	2	4	no	—
218	#447	C₂²×C₁₄₉	1	8	yes	—
219	#431	C₂²×C₁₄₉	1	2	yes	—
220	#394	C₂²×C₁₄₉	1	4	yes	—
221	#390	—	2	1	no	—
222	#390	—	2	2	no	—
223	C₄×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
224	#327	C₂²×C₁₄₉	1	8	yes	—
225	#324	C₂²×C₁₄₉	1	4	yes	—
226	2₋¹⁺⁴	—	4	4	no	—
227	2₋¹⁺⁴	—	4	4	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	—	2	2	no	—
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂³×C₁₄₉	1	2	yes	—
236	C₂×D₈	—	2	8	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
239	#127	—	2	2	no	—
240	#127	—	2	2	no	—
241	#127	—	2	2	no	—
242	#127	D₄×C₁₄₉	1	2	yes	—
243	#124	—	2	4	no	—
244	#124	—	2	2	no	—
245	#124	—	4	4	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	#121	—	2	4	no	—
249	#121	—	2	8	no	—
250	#121	—	2	2	no	—
251	#121	—	2	4	no	—
252	#121	C₂³×C₁₄₉	1	4	yes	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	D₄×C₁₄₉	1	4	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	#102	—	2	8	no	—
269	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
270	C₄×C₈	—	2	2	no	—
271	#95	C₂³×C₁₄₉	1	2	yes	—
272	C₂⁴	—	2	2	no	—
273	#41	—	4	8	no	—
274	#41	—	4	16	no	—
275	#41	—	4	8	no	—
276	#41	—	4	4	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	16	no	—
283	C₂×Q₈	D₈×C₁₄₉	1	4	yes	complemented
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	C₂×D₄×C₁₄₉	1	4	yes	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
306	D₈	—	8	8	no	—
307	C₂×C₈	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₁₄₉	1	4	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₂²⋊C₄	—	8	4	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	2	no	—
322	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
323	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
331	Q₈	—	2	8	no	—
332	Q₈	—	4	8	no	—
333	Q₈	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	8	no	—
336	D₄	—	4	8	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	8	4	no	—
344	D₄	—	8	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
358	C₂×C₄	#120×C₁₄₉	1	2	yes	—
359	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
360	C₂×C₄	C₂×D₈×C₁₄₉	1	4	yes	—
361	C₂×C₄	C₂×D₈×C₁₄₉	1	2	yes	—
362	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
364	C₈	—	4	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	4	no	—
371	C₂²	—	8	4	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₂×#120×C₁₄₉	1	1	yes	characteristic
376	C₂²	C₂²×D₈×C₁₄₉	1	1	yes	characteristic
377	C₂²	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	#447×C₁₄₉	1	4	yes	—
385	C₄	#454×C₁₄₉	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	8	4	no	—
389	C₂	—	16	2	no	—
390	C₂	C₂×#447×C₁₄₉	1	1	yes	characteristic
391	C₂	C₂×#454×C₁₄₉	1	1	yes	characteristic
392	C₂	#3027×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
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. #3497×C₁₄₉	C₂	semidirect
2. #3205×C₁₄₉	C₂	semidirect
3. #2548×C₁₄₉	C₂	semidirect
4. #1598×C₁₄₉	C₂	semidirect
5. #1502×C₁₄₉	C₂	semidirect
6. #1461×C₁₄₉	C₂	semidirect
86. C₂×Q₈×C₁₄₉	D₈	semidirect
196. #18401	C₁₄₉	direct (N × H)
197. C₁₄₉	#18401	direct (N × H)
198. #3497	C₂×C₁₄₉	semidirect
199. #3205	C₂×C₁₄₉	semidirect
200. #2548	C₂×C₁₄₉	semidirect
201. #1598	C₂×C₁₄₉	semidirect
202. #1502	C₂×C₁₄₉	semidirect
203. #1461	C₂×C₁₄₉	semidirect
283. C₂×Q₈	D₈×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3497×C₁₄₉	2
#3205×C₁₄₉	2
#2548×C₁₄₉	2
#1598×C₁₄₉	2
#1502×C₁₄₉	2
#1461×C₁₄₉	2
#18401	149

Subgroups — C149×#18401 #49197350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#18401 #49197350