Subgroups — C₁₃₉×#7684 #48002280

Order 35584.

702 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#1728×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1270×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₁₃₉	—	2	1	no	—
6	C₂×#127×C₁₃₉	C₄	1	1	yes	characteristic
7	C₂×#121×C₁₃₉	—	2	1	no	—
8	C₂×#121×C₁₃₉	—	2	1	no	—
9	C₂×#121×C₁₃₉	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
12	C₂×C₄×C₈×C₁₃₉	—	2	1	no	—
13	#390×C₁₃₉	—	2	1	no	—
14	#390×C₁₃₉	—	2	1	no	—
15	#390×C₁₃₉	C₂²	1	2	yes	—
16	#384×C₁₃₉	C₄	1	1	yes	characteristic
17	#336×C₁₃₉	—	2	1	no	—
18	#336×C₁₃₉	C₂²	1	2	yes	—
19	#336×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×D₄×C₁₃₉	—	2	2	no	—
21	C₂²×D₄×C₁₃₉	—	2	1	no	—
22	C₂²×D₄×C₁₃₉	—	2	1	no	—
23	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₁₃₉	—	2	4	no	—
28	C₂×M₁₆×C₁₃₉	—	4	2	no	—
29	C₂×M₁₆×C₁₃₉	—	4	2	no	—
30	C₂²×C₈×C₁₃₉	—	2	2	no	—
31	C₂²×C₈×C₁₃₉	—	2	2	no	—
32	#127×C₁₃₉	—	4	2	no	—
33	#121×C₁₃₉	—	4	4	no	—
34	#121×C₁₃₉	—	4	2	no	—
35	#121×C₁₃₉	—	4	2	no	—
36	#121×C₁₃₉	—	4	4	no	—
37	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄²×C₁₃₉	—	4	2	no	—
44	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
49	C₄×C₈×C₁₃₉	—	4	2	no	—
50	C₂⁴×C₁₃₉	—	2	2	no	—
51	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×D₄×C₁₃₉	—	2	4	no	—
53	C₂×D₄×C₁₃₉	—	4	2	no	—
54	C₂×D₄×C₁₃₉	—	4	2	no	—
55	C₂×D₄×C₁₃₉	—	4	2	no	—
56	C₂×D₄×C₁₃₉	—	4	2	no	—
57	C₂×D₄×C₁₃₉	—	4	4	no	—
58	C₂×D₄×C₁₃₉	—	4	4	no	—
59	C₂×D₄×C₁₃₉	—	4	4	no	—
60	C₂×D₄×C₁₃₉	—	4	2	no	—
61	C₂×D₄×C₁₃₉	—	4	2	no	—
62	C₂×D₄×C₁₃₉	—	4	2	no	—
63	C₂×D₄×C₁₃₉	—	4	2	no	—
64	C₂²×C₄×C₁₃₉	—	2	2	no	—
65	C₂²×C₄×C₁₃₉	—	2	2	no	—
66	C₂²×C₄×C₁₃₉	—	2	2	no	—
67	C₂²×C₄×C₁₃₉	—	2	2	no	—
68	C₂²×C₄×C₁₃₉	—	2	2	no	—
69	C₂²×C₄×C₁₃₉	—	2	2	no	—
70	C₂²×C₄×C₁₃₉	—	2	2	no	—
71	C₂²×C₄×C₁₃₉	—	4	1	no	—
72	C₂²×C₄×C₁₃₉	—	4	1	no	—
73	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₉	D₈	1	2	yes	—
77	C₂²×C₄×C₁₃₉	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
81	M₁₆×C₁₃₉	—	4	8	no	—
82	C₂×C₈×C₁₃₉	—	2	4	no	—
83	C₂×C₈×C₁₃₉	—	2	4	no	—
84	C₂×C₈×C₁₃₉	—	4	2	no	—
85	C₂×C₈×C₁₃₉	—	4	2	no	—
86	C₂×C₈×C₁₃₉	—	4	2	no	—
87	C₂×C₈×C₁₃₉	—	4	2	no	—
88	C₄⋊C₄×C₁₃₉	—	4	2	no	—
89	C₄⋊C₄×C₁₃₉	—	4	2	no	—
90	C₄⋊C₄×C₁₃₉	—	4	2	no	—
91	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
92	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
93	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
94	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
95	C₄²×C₁₃₉	—	2	2	no	—
96	C₄²×C₁₃₉	—	2	2	no	—
97	C₄²×C₁₃₉	—	4	1	no	—
98	C₄²×C₁₃₉	—	4	1	no	—
99	C₂³×C₁₃₉	—	2	1	no	—
100	C₂³×C₁₃₉	—	2	1	no	—
101	C₂³×C₁₃₉	—	2	1	no	—
102	C₂³×C₁₃₉	—	2	1	no	—
103	C₂³×C₁₃₉	—	2	1	no	—
104	C₂³×C₁₃₉	—	2	1	no	—
105	C₂³×C₁₃₉	—	4	2	no	—
106	C₂³×C₁₃₉	—	4	2	no	—
107	C₂³×C₁₃₉	—	4	2	no	—
108	C₂³×C₁₃₉	—	4	2	no	—
109	C₂³×C₁₃₉	—	4	2	no	—
110	C₂³×C₁₃₉	—	4	2	no	—
111	C₂³×C₁₃₉	—	4	2	no	—
112	C₂³×C₁₃₉	#102	1	2	yes	—
113	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	D₄×C₁₃₉	—	8	4	no	—
115	D₄×C₁₃₉	—	8	4	no	—
116	D₄×C₁₃₉	—	8	8	no	—
117	D₄×C₁₃₉	—	8	4	no	—
118	C₂×C₄×C₁₃₉	—	2	1	no	—
119	C₂×C₄×C₁₃₉	—	2	1	no	—
120	C₂×C₄×C₁₃₉	—	2	1	no	—
121	C₂×C₄×C₁₃₉	—	2	1	no	—
122	C₂×C₄×C₁₃₉	—	2	1	no	—
123	C₂×C₄×C₁₃₉	—	2	1	no	—
124	C₂×C₄×C₁₃₉	—	2	1	no	—
125	C₂×C₄×C₁₃₉	—	2	1	no	—
126	C₂×C₄×C₁₃₉	—	2	1	no	—
127	C₂×C₄×C₁₃₉	—	2	1	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	4	4	no	—
131	C₂×C₄×C₁₃₉	—	4	4	no	—
132	C₂×C₄×C₁₃₉	—	4	2	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	#99	1	2	yes	—
136	C₂×C₄×C₁₃₉	#100	1	2	yes	—
137	C₂×C₄×C₁₃₉	#102	1	2	yes	—
138	C₂×C₄×C₁₃₉	#104	1	2	yes	—
139	C₂×C₄×C₁₃₉	#104	1	2	yes	—
140	C₂×C₄×C₁₃₉	#131	1	2	yes	—
141	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
143	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
144	C₈×C₁₃₉	—	4	4	no	—
145	C₈×C₁₃₉	—	4	4	no	—
146	C₂²×C₁₃₉	—	2	2	no	—
147	C₂²×C₁₃₉	—	2	2	no	—
148	C₂²×C₁₃₉	—	2	2	no	—
149	C₂²×C₁₃₉	—	4	1	no	—
150	C₂²×C₁₃₉	—	4	1	no	—
151	C₂²×C₁₃₉	—	4	1	no	—
152	C₂²×C₁₃₉	—	4	1	no	—
153	C₂²×C₁₃₉	—	8	2	no	—
154	C₂²×C₁₃₉	—	8	2	no	—
155	C₂²×C₁₃₉	—	8	2	no	—
156	C₂²×C₁₃₉	—	8	2	no	—
157	C₂²×C₁₃₉	—	8	2	no	—
158	C₂²×C₁₃₉	—	8	2	no	—
159	C₂²×C₁₃₉	—	8	2	no	—
160	C₂²×C₁₃₉	#408	1	1	yes	characteristic
161	C₂²×C₁₃₉	C₂×#99	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#100	1	1	yes	characteristic
163	C₂²×C₁₃₉	C₂×#102	1	1	yes	characteristic
164	C₂²×C₁₃₉	#418	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₂×#104	1	1	yes	characteristic
166	C₂²×C₁₃₉	C₂×#104	1	1	yes	characteristic
167	C₄×C₁₃₉	—	2	2	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	2	1	no	—
170	C₄×C₁₃₉	—	2	1	no	—
171	C₄×C₁₃₉	—	2	2	no	—
172	C₄×C₁₃₉	—	2	2	no	—
173	C₄×C₁₃₉	—	8	2	no	—
174	C₄×C₁₃₉	#327	1	4	yes	—
175	C₂×C₁₃₉	—	4	2	no	—
176	C₂×C₁₃₉	—	16	2	no	—
177	C₂×C₁₃₉	#1471	1	1	yes	characteristic
178	C₂×C₁₃₉	#1484	1	1	yes	characteristic
179	C₂×C₁₃₉	#1492	1	1	yes	characteristic
180	C₂×C₁₃₉	C₂×#327	1	1	yes	characteristic
181	C₂×C₁₃₉	#1507	1	1	yes	characteristic
182	C₂×C₁₃₉	#1525	1	1	yes	characteristic
183	C₂×C₁₃₉	#1545	1	1	yes	characteristic
184	#7684	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₉	#7684	1	1	yes	characteristic, direct product factor, Sylow
186	#2856	C₂×C₁₃₉	1	1	yes	characteristic
187	C₄×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
188	#1728	C₂×C₁₃₉	1	1	yes	characteristic, complemented
189	#1270	C₂×C₁₃₉	1	4	yes	complemented
190	C₂²×M₁₆	—	2	1	no	—
191	C₂×#127	C₄×C₁₃₉	1	1	yes	characteristic
192	C₂×#121	—	2	1	no	—
193	C₂×#121	—	2	1	no	—
194	C₂×#121	C₄×C₁₃₉	1	2	yes	—
195	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
196	C₂×C₂²⋊C₈	—	2	1	no	—
197	C₂×C₄×C₈	—	2	1	no	—
198	#390	—	2	1	no	—
199	#390	—	2	1	no	—
200	#390	C₂²×C₁₃₉	1	2	yes	—
201	#384	C₄×C₁₃₉	1	1	yes	characteristic
202	#336	—	2	1	no	—
203	#336	C₂²×C₁₃₉	1	2	yes	—
204	#336	C₂²×C₁₃₉	1	2	yes	—
205	C₂²×D₄	—	2	2	no	—
206	C₂²×D₄	—	2	1	no	—
207	C₂²×D₄	—	2	1	no	—
208	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
209	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
210	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	—	4	2	no	—
214	C₂×M₁₆	—	4	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	#127	—	4	2	no	—
218	#121	—	4	4	no	—
219	#121	—	4	2	no	—
220	#121	—	4	2	no	—
221	#121	—	4	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	4	2	no	—
229	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
233	C₂²⋊C₈	—	2	4	no	—
234	C₄×C₈	—	4	2	no	—
235	C₂⁴	—	2	2	no	—
236	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	4	2	no	—
239	C₂×D₄	—	4	2	no	—
240	C₂×D₄	—	4	2	no	—
241	C₂×D₄	—	4	2	no	—
242	C₂×D₄	—	4	4	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	—	4	4	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	2	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
261	C₂²×C₄	D₈×C₁₃₉	1	2	yes	—
262	C₂²×C₄	SD₁₆×C₁₃₉	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
266	M₁₆	—	4	8	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	4	2	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₄⋊C₄	—	4	2	no	—
275	C₄⋊C₄	—	4	2	no	—
276	C₂²⋊C₄	—	4	4	no	—
277	C₂²⋊C₄	—	4	2	no	—
278	C₂²⋊C₄	—	4	2	no	—
279	C₂²⋊C₄	—	4	4	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	4	1	no	—
283	C₄²	—	4	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	4	2	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	2	no	—
297	C₂³	#102×C₁₃₉	1	2	yes	—
298	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
299	D₄	—	8	4	no	—
300	D₄	—	8	4	no	—
301	D₄	—	8	8	no	—
302	D₄	—	8	4	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	#99×C₁₃₉	1	2	yes	—
321	C₂×C₄	#100×C₁₃₉	1	2	yes	—
322	C₂×C₄	#102×C₁₃₉	1	2	yes	—
323	C₂×C₄	#104×C₁₃₉	1	2	yes	—
324	C₂×C₄	#104×C₁₃₉	1	2	yes	—
325	C₂×C₄	#131×C₁₃₉	1	2	yes	—
326	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
327	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
329	C₈	—	4	4	no	—
330	C₈	—	4	4	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	2	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	#408×C₁₃₉	1	1	yes	characteristic
346	C₂²	C₂×#99×C₁₃₉	1	1	yes	characteristic
347	C₂²	C₂×#100×C₁₃₉	1	1	yes	characteristic
348	C₂²	C₂×#102×C₁₃₉	1	1	yes	characteristic
349	C₂²	#418×C₁₃₉	1	1	yes	characteristic
350	C₂²	C₂×#104×C₁₃₉	1	1	yes	characteristic
351	C₂²	C₂×#104×C₁₃₉	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	8	2	no	—
359	C₄	#327×C₁₃₉	1	4	yes	—
360	C₂	—	4	2	no	—
361	C₂	—	16	2	no	—
362	C₂	#1471×C₁₃₉	1	1	yes	characteristic
363	C₂	#1484×C₁₃₉	1	1	yes	characteristic
364	C₂	#1492×C₁₃₉	1	1	yes	characteristic
365	C₂	C₂×#327×C₁₃₉	1	1	yes	characteristic
366	C₂	#1507×C₁₃₉	1	1	yes	characteristic
367	C₂	#1525×C₁₃₉	1	1	yes	characteristic
368	C₂	#1545×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	#2856×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂²⋊C₈×C₁₃₉	C₂	semidirect
3. #1728×C₁₃₉	C₂	semidirect
4. #1270×C₁₃₉	C₂	semidirect
184. #7684	C₁₃₉	direct (N × H)
185. C₁₃₉	#7684	direct (N × H)
187. C₄×C₂²⋊C₈	C₂×C₁₃₉	semidirect
188. #1728	C₂×C₁₃₉	semidirect
189. #1270	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2856×C₁₃₉	2
C₄×C₂²⋊C₈×C₁₃₉	2
#1728×C₁₃₉	2
#1270×C₁₃₉	2
#7684	139

Subgroups — C139×#7684 #48002280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#7684 #48002280