Subgroups — #31818372

Order 17792.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581608	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581596	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581312	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581282	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581270	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581244	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581203	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581179	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581097	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581085	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581063	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581023	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580953	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	1	yes	characteristic
17	C₂×#14555785	—	2	1	no	—
18	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#14555770	C₂²	1	1	yes	characteristic
20	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
22	#17984842	C₂²	1	1	yes	characteristic, complemented
23	#17984824	—	2	1	no	—
24	#17984824	—	2	1	no	—
25	#17984824	—	2	1	no	—
26	#17984821	—	2	1	no	—
27	#17984818	C₂²	1	1	yes	characteristic
28	#17984815	—	2	1	no	—
29	#17984813	C₂²	1	1	yes	characteristic
30	#17984813	C₂²	1	1	yes	characteristic
31	#17984813	C₂²	1	1	yes	characteristic, complemented
32	#17984812	—	2	1	no	—
33	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
34	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
38	#17984774	C₂²	1	1	yes	characteristic, complemented
39	#17984774	C₂²	1	1	yes	characteristic, complemented
40	#17984773	C₂²	1	1	yes	characteristic, complemented
41	#17984766	C₂²	1	1	yes	characteristic, complemented
42	#17984766	C₂²	1	1	yes	characteristic, complemented
43	#17984764	C₂²	1	1	yes	characteristic
44	#17984764	C₂²	1	1	yes	characteristic
45	#17984763	C₂²	1	1	yes	characteristic
46	#17984763	C₂²	1	1	yes	characteristic
47	#17984763	C₂²	1	1	yes	characteristic, complemented
48	#17984762	C₂²	1	1	yes	characteristic
49	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#17984753	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
54	#124×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₂³×D₁₃₉	—	2	1	no	—
60	#14555786	—	2	2	no	—
61	#14555786	—	4	1	no	—
62	#14555785	—	4	4	no	—
63	C₂×Dic₂₇₈	—	2	1	no	—
64	C₂×D₅₅₆	—	2	1	no	—
65	C₂×D₅₅₆	D₄	1	1	yes	characteristic
66	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
68	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
71	D₄×D₁₃₉	—	2	2	no	—
72	D₄×D₁₃₉	—	4	1	no	—
73	C₂×C₄×D₁₃₉	—	2	1	no	—
74	C₂×C₄×D₁₃₉	—	2	1	no	—
75	C₂×C₄×D₁₃₉	—	2	1	no	—
76	C₂×C₄×D₁₃₉	—	2	1	no	—
77	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
79	#14555770	—	2	2	no	—
80	#14555768	—	4	1	no	—
81	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₈×D₁₃₉	—	4	1	no	—
84	C₄⋊Dic₁₃₉	—	2	1	no	—
85	C₄⋊Dic₁₃₉	D₄	1	1	yes	characteristic
86	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
89	Dic₁₃₉⋊C₄	—	2	1	no	—
90	Dic₁₃₉⋊C₄	—	2	1	no	—
91	Dic₁₃₉⋊C₄	—	2	1	no	—
92	C₂²⋊Dic₁₃₉	—	2	1	no	—
93	C₂²⋊Dic₁₃₉	—	2	1	no	—
94	C₂²⋊Dic₁₃₉	—	2	1	no	—
95	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
96	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
97	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
98	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	—	2	1	no	—
103	SD₁₆×C₁₃₉	—	4	1	no	—
104	D₈×C₁₃₉	—	4	1	no	—
105	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
111	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₁₃₉	—	2	1	no	—
113	C₂²×D₁₃₉	—	4	2	no	—
114	C₂²×D₁₃₉	—	4	2	no	—
115	C₂²×D₁₃₉	—	8	1	no	—
116	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
118	Dic₂₇₈	—	4	2	no	—
119	D₅₅₆	—	2	2	no	—
120	D₅₅₆	—	2	1	no	—
121	D₅₅₆	—	4	2	no	—
122	D₅₅₆	#41	1	2	yes	complemented
123	C₂²⋊D₁₃₉	—	4	2	no	—
124	C₂²⋊D₁₃₉	—	4	2	no	—
125	C₂²⋊D₁₃₉	—	4	2	no	—
126	C₂²⋊D₁₃₉	—	8	1	no	—
127	C₂×Dic₁₃₉	—	2	1	no	—
128	C₂×Dic₁₃₉	—	2	1	no	—
129	C₂×Dic₁₃₉	—	2	1	no	—
130	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
132	C₄×D₁₃₉	—	2	1	no	—
133	C₄×D₁₃₉	—	2	1	no	—
134	C₄×D₁₃₉	—	2	1	no	—
135	C₄×D₁₃₉	—	2	1	no	—
136	C₄×D₁₃₉	—	4	2	no	—
137	C₄×D₁₃₉	—	4	2	no	—
138	C₄×D₁₃₉	—	4	2	no	—
139	C₄×D₁₃₉	—	8	1	no	—
140	C₁₃₉⋊C₈	—	2	1	no	—
141	C₁₃₉⋊C₈	—	2	1	no	—
142	C₂³×C₁₃₉	—	2	1	no	—
143	C₂³×C₁₃₉	—	2	1	no	—
144	Q₈×C₁₃₉	—	2	1	no	—
145	Q₈×C₁₃₉	—	2	1	no	—
146	D₄×C₁₃₉	—	2	1	no	—
147	D₄×C₁₃₉	—	2	1	no	—
148	D₄×C₁₃₉	—	2	1	no	—
149	D₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
156	C₈×C₁₃₉	—	2	1	no	—
157	C₈×C₁₃₉	—	2	1	no	—
158	C₂²×C₁₃₉	—	4	1	no	—
159	C₂²×C₁₃₉	—	4	1	no	—
160	C₂²×C₁₃₉	—	4	1	no	—
161	C₂²×C₁₃₉	—	4	1	no	—
162	C₂²×C₁₃₉	—	4	1	no	—
163	C₂²×C₁₃₉	—	4	1	no	—
164	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₁₃₉	—	2	1	no	—
166	C₂×D₁₃₉	—	2	1	no	—
167	C₂×D₁₃₉	—	2	1	no	—
168	C₂×D₁₃₉	—	2	2	no	—
169	C₂×D₁₃₉	—	2	1	no	—
170	C₂×D₁₃₉	—	2	1	no	—
171	C₂×D₁₃₉	—	4	1	no	—
172	C₂×D₁₃₉	—	4	1	no	—
173	C₂×D₁₃₉	—	8	4	no	—
174	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₄×C₁₃₉	—	2	1	no	—
176	C₄×C₁₃₉	—	2	1	no	—
177	C₄×C₁₃₉	—	4	1	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
180	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
181	Dic₁₃₉	—	2	1	no	—
182	Dic₁₃₉	—	2	1	no	—
183	Dic₁₃₉	—	4	1	no	—
184	Dic₁₃₉	—	4	1	no	—
185	Dic₁₃₉	—	4	1	no	—
186	C₂×C₁₃₉	—	8	1	no	—
187	C₂×C₁₃₉	—	8	1	no	—
188	C₂×C₁₃₉	#546	1	1	yes	characteristic
189	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₁₃₉	#577	1	1	yes	characteristic
191	D₁₃₉	—	2	2	no	—
192	D₁₃₉	—	4	1	no	—
193	D₁₃₉	—	4	2	no	—
194	C₁₃₉	#3306	1	1	yes	characteristic, complemented, Sylow
195	#3306	—	139	1	no	maximal, Sylow
196	#547	—	139	1	no	—
197	#546	—	139	1	no	—
198	#489	—	139	1	no	—
199	#483	—	139	1	no	—
200	#481	—	139	1	no	—
201	#476	—	139	1	no	—
202	#469	—	139	1	no	—
203	#465	—	139	1	no	—
204	#463	D₁₃₉	1	1	yes	characteristic, complemented
205	#449	—	139	1	no	—
206	#447	—	139	1	no	—
207	#442	—	139	1	no	—
208	#435	—	139	1	no	—
209	#417	—	139	1	no	—
210	C₂×#102	—	139	1	no	—
211	C₂×#41	—	278	1	no	—
212	C₂×#41	—	139	1	no	—
213	C₂²×D₄	—	139	1	no	—
214	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
215	C₂×D₈	—	139	1	no	—
216	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic
217	C₂×M₁₆	—	139	1	no	—
218	C₂²×C₈	—	139	1	no	—
219	C₄⋊Q₈	—	139	1	no	—
220	#124	C₂×D₁₃₉	1	1	yes	characteristic
221	#123	—	278	1	no	—
222	#123	—	278	1	no	—
223	#123	—	278	1	no	—
224	C₂²⋊Q₈	—	278	1	no	—
225	C₂²⋊Q₈	—	139	1	no	—
226	#121	—	278	1	no	—
227	#121	—	139	1	no	—
228	#121	—	139	1	no	—
229	#121	—	139	1	no	—
230	#120	—	278	1	no	—
231	C₄×D₄	—	139	1	no	—
232	C₄×D₄	—	139	1	no	—
233	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
234	C₂×C₄⋊C₄	—	139	1	no	—
235	C₂×C₄⋊C₄	—	139	1	no	—
236	C₂×C₂²⋊C₄	—	278	1	no	—
237	#106	—	139	1	no	—
238	#106	—	139	1	no	—
239	#106	—	139	1	no	—
240	C₄⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
241	#103	—	139	1	no	—
242	#103	—	139	1	no	—
243	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
244	#102	—	139	1	no	—
245	#102	—	139	1	no	—
246	#102	—	139	1	no	—
247	#102	—	139	1	no	—
248	#102	—	139	1	no	—
249	#102	—	139	1	no	—
250	#102	C₂×D₁₃₉	1	1	yes	characteristic
251	C₂²⋊C₈	—	139	1	no	—
252	C₂²⋊C₈	—	139	1	no	—
253	#97	—	139	1	no	—
254	C₂⁴	—	278	1	no	—
255	#41	—	278	2	no	—
256	#41	—	556	4	no	—
257	#41	—	556	1	no	—
258	C₂×Q₈	—	278	1	no	—
259	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
260	C₂×D₄	—	278	1	no	—
261	C₂×D₄	—	278	2	no	—
262	C₂×D₄	—	278	1	no	—
263	C₂×D₄	—	278	1	no	—
264	C₂×D₄	—	278	1	no	—
265	C₂×D₄	—	278	1	no	—
266	C₂×D₄	—	556	1	no	—
267	C₂×D₄	—	139	1	no	—
268	C₂×D₄	—	139	1	no	—
269	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
270	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	278	1	no	—
273	C₂²×C₄	—	278	1	no	—
274	C₂²×C₄	—	278	1	no	—
275	C₂²×C₄	—	278	1	no	—
276	C₂²×C₄	—	139	1	no	—
277	C₂²×C₄	—	139	1	no	—
278	SD₁₆	—	4	1	no	—
279	D₈	—	4	1	no	—
280	D₈	—	278	2	no	—
281	M₁₆	—	556	1	no	—
282	C₂×C₈	—	556	1	no	—
283	C₂×C₈	—	139	1	no	—
284	C₂×C₈	—	139	1	no	—
285	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
286	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
287	C₄⋊C₄	—	278	1	no	—
288	C₄⋊C₄	—	278	1	no	—
289	C₄⋊C₄	—	278	1	no	—
290	C₄⋊C₄	—	278	1	no	—
291	C₄⋊C₄	—	139	1	no	—
292	C₄⋊C₄	—	139	1	no	—
293	C₄⋊C₄	—	139	1	no	—
294	C₄⋊C₄	—	139	1	no	—
295	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	278	1	no	—
300	C₂²⋊C₄	—	278	1	no	—
301	C₂²⋊C₄	—	278	1	no	—
302	C₂²⋊C₄	—	278	1	no	—
303	C₂²⋊C₄	—	278	1	no	—
304	C₂²⋊C₄	—	139	1	no	—
305	C₂²⋊C₄	—	139	1	no	—
306	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	278	1	no	—
310	C₂³	—	556	2	no	—
311	C₂³	—	556	2	no	—
312	C₂³	—	1112	1	no	—
313	C₂³	—	139	1	no	—
314	C₂³	—	139	1	no	—
315	Q₈	—	2	1	no	—
316	Q₈	—	2	1	no	—
317	Q₈	—	556	2	no	—
318	D₄	—	2	1	no	—
319	D₄	—	2	1	no	—
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	278	2	no	—
323	D₄	—	278	1	no	—
324	D₄	—	556	2	no	—
325	D₄	—	556	2	no	—
326	D₄	—	556	2	no	—
327	D₄	—	556	2	no	—
328	D₄	—	1112	1	no	—
329	D₄	—	139	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	278	1	no	—
334	C₂×C₄	—	278	1	no	—
335	C₂×C₄	—	278	1	no	—
336	C₂×C₄	—	278	1	no	—
337	C₂×C₄	—	278	1	no	—
338	C₂×C₄	—	278	1	no	—
339	C₂×C₄	—	278	1	no	—
340	C₂×C₄	—	556	2	no	—
341	C₂×C₄	—	556	2	no	—
342	C₂×C₄	—	556	2	no	—
343	C₂×C₄	—	1112	1	no	—
344	C₂×C₄	—	139	1	no	—
345	C₂×C₄	—	139	1	no	—
346	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
347	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
348	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	278	1	no	—
352	C₈	—	278	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	278	1	no	—
360	C₂²	—	278	1	no	—
361	C₂²	—	278	1	no	—
362	C₂²	—	278	1	no	—
363	C₂²	—	278	2	no	—
364	C₂²	—	278	1	no	—
365	C₂²	—	556	1	no	—
366	C₂²	—	556	1	no	—
367	C₂²	—	1112	4	no	—
368	C₂²	—	139	2	no	—
369	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	278	1	no	—
375	C₄	—	278	1	no	—
376	C₄	—	556	1	no	—
377	C₄	—	556	1	no	—
378	C₄	—	556	1	no	—
379	C₄	#41×D₁₃₉	1	1	yes	characteristic
380	C₄	#17984887	1	1	yes	characteristic
381	C₂	—	8	1	no	—
382	C₂	—	8	1	no	—
383	C₂	—	278	2	no	—
384	C₂	—	556	1	no	—
385	C₂	—	556	2	no	—
386	C₂	#22581600	1	1	yes	characteristic
387	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
388	C₂	#22581760	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#463×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#463	D₁₃₉
hypocenter	C₁₃₉	#3306
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. #22581608	C₂	semidirect
2. #22581596	C₂	semidirect
3. #22581312	C₂	semidirect
4. #22581282	C₂	semidirect
5. #22581270	C₂	semidirect
6. #22581244	C₂	semidirect
7. #22581203	C₂	semidirect
8. #22581179	C₂	semidirect
9. #22581097	C₂	semidirect
10. #22581085	C₂	semidirect
11. #22581063	C₂	semidirect
12. #22581023	C₂	semidirect
13. #22580953	C₂	semidirect
14. #102×D₁₃₉	C₂	semidirect
15. #463×C₁₃₉	C₂	semidirect
20. C₂×#14555768	C₂²	semidirect
22. #17984842	C₂²	semidirect
31. #17984813	C₂²	semidirect
36. C₄⋊C₄×D₁₃₉	C₂²	semidirect
38. #17984774	C₂²	semidirect
39. #17984774	C₂²	semidirect
40. #17984773	C₂²	semidirect
41. #17984766	C₂²	semidirect
42. #17984766	C₂²	semidirect
47. #17984763	C₂²	semidirect
50. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
51. #17984753	C₂²	semidirect
52. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
55. C₄×D₄×C₁₃₉	C₂²	semidirect
56. C₄⋊C₈×C₁₃₉	C₂²	semidirect
57. #103×C₁₃₉	C₂²	semidirect
122. D₅₅₆	#41	semidirect
194. C₁₃₉	#3306	semidirect
204. #463	D₁₃₉	semidirect
214. C₂×SD₁₆	C₂×D₁₃₉	semidirect
233. C₄×D₄	C₂×D₁₃₉	semidirect
240. C₄⋊C₈	C₂×D₁₃₉	semidirect
243. #103	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#22581608	2
#22581596	2
#22581312	2
#22581282	2
#22581270	2
#22581244	2
#22581203	2
#22581179	2
#22581097	2
#22581085	2
#22581063	2
#22581023	2
#22580953	2
#102×D₁₃₉	2
#463×C₁₃₉	2
#3306	139