Subgroups — #31818149

Order 17792.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555775	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#22581616	C₂	1	1	yes	maximal, characteristic
5	#22581331	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581193	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581192	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581162	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581161	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581111	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581110	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581107	C₂	1	1	yes	maximal, characteristic, complemented
13	#22581045	C₂	1	1	yes	maximal, characteristic, complemented
14	(C₂²⋊D₁₃₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
15	#451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic
20	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic
21	C₂×#14555775	—	2	4	no	—
22	C₂×#14555775	C₂²	1	1	yes	characteristic
23	C₂×#14555775	C₂²	1	1	yes	characteristic
24	C₂×#14555775	C₂²	1	1	yes	characteristic
25	C₂×#14555775	C₂²	1	1	yes	characteristic
26	C₂×#14555775	C₂²	1	1	yes	characteristic
27	Q₁₆×D₁₃₉	—	2	4	no	—
28	C₂²×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
30	#17984841	—	2	1	no	—
31	#17984840	—	2	1	no	—
32	#17984840	C₂²	1	1	yes	characteristic
33	#17984840	C₂²	1	1	yes	characteristic
34	#17984822	C₂²	1	1	yes	characteristic
35	#17984821	—	2	1	no	—
36	#17984821	C₂²	1	1	yes	characteristic
37	#17984820	—	2	1	no	—
38	#17984819	—	2	1	no	—
39	#17984818	—	2	1	no	—
40	#17984818	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₃₉	C₂²	1	1	yes	characteristic
42	#17984807	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
44	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
45	(C₂²⋊D₁₃₉)⋊C₄	—	2	1	no	—
46	#17984775	C₂²	1	1	yes	characteristic
47	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
48	#17984767	C₂²	1	1	yes	characteristic
49	#17984767	C₂²	1	1	yes	characteristic
50	#17984766	C₂²	1	1	yes	characteristic
51	#17984765	C₂²	1	1	yes	characteristic
52	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
53	C₈×Dic₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
58	#103×C₁₃₉	C₂²	1	1	yes	characteristic
59	#103×C₁₃₉	C₂²	1	1	yes	characteristic
60	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₂×Dic₂₇₈	—	2	1	no	—
62	C₂×Dic₂₇₈	—	2	1	no	—
63	C₂×Dic₂₇₈	—	2	2	no	—
64	C₂×Dic₂₇₈	—	2	1	no	—
65	C₂×Dic₂₇₈	—	4	1	no	—
66	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
67	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
69	Q₈×D₁₃₉	—	2	2	no	—
70	Q₈×D₁₃₉	—	2	2	no	—
71	Q₈×D₁₃₉	—	4	1	no	—
72	Q₈×D₁₃₉	—	4	1	no	—
73	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
74	C₂²×Dic₁₃₉	—	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	Dic₅₅₆	—	2	2	no	—
79	Dic₅₅₆	—	4	1	no	—
80	#14555775	—	2	2	no	—
81	#14555775	—	2	2	no	—
82	#14555775	—	2	2	no	—
83	#14555775	—	2	2	no	—
84	#14555775	D₄	1	4	yes	complemented
85	C₂×C₁₃₉⋊C₈	—	2	2	no	—
86	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
88	C₈×D₁₃₉	—	2	2	no	—
89	C₄⋊Dic₁₃₉	—	2	1	no	—
90	C₄⋊Dic₁₃₉	—	2	1	no	—
91	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
92	Dic₁₃₉⋊C₄	—	2	1	no	—
93	Dic₁₃₉⋊C₄	—	2	1	no	—
94	Dic₁₃₉⋊C₄	—	2	1	no	—
95	Dic₁₃₉⋊C₄	—	2	1	no	—
96	Dic₁₃₉⋊C₄	—	2	1	no	—
97	Dic₁₃₉⋊C₄	—	2	1	no	—
98	Dic₁₃₉⋊C₄	—	2	1	no	—
99	Dic₁₃₉⋊C₄	D₄	1	1	yes	characteristic
100	C₂²⋊Dic₁₃₉	—	2	1	no	—
101	C₂²⋊Dic₁₃₉	D₄	1	1	yes	characteristic
102	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
103	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
104	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
105	C₄×Dic₁₃₉	—	2	1	no	—
106	C₄×Dic₁₃₉	—	2	1	no	—
107	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₃₉	—	2	1	no	—
109	C₂×Q₈×C₁₃₉	—	2	2	no	—
110	C₂×Q₈×C₁₃₉	—	4	1	no	—
111	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	—	2	1	no	—
115	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	Q₁₆×C₁₃₉	—	2	2	no	—
117	Q₁₆×C₁₃₉	—	4	1	no	—
118	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₁₃₉	—	2	1	no	—
121	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
123	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
124	Dic₂₇₈	—	2	1	no	—
125	Dic₂₇₈	—	2	1	no	—
126	Dic₂₇₈	—	2	1	no	—
127	Dic₂₇₈	—	2	1	no	—
128	Dic₂₇₈	—	2	1	no	—
129	Dic₂₇₈	—	4	2	no	—
130	Dic₂₇₈	—	4	2	no	—
131	Dic₂₇₈	—	4	2	no	—
132	Dic₂₇₈	C₂×D₄	1	2	yes	—
133	C₂²⋊D₁₃₉	Q₁₆	1	4	yes	complemented
134	C₂×Dic₁₃₉	—	2	1	no	—
135	C₂×Dic₁₃₉	—	2	1	no	—
136	C₂×Dic₁₃₉	—	2	1	no	—
137	C₂×Dic₁₃₉	—	2	1	no	—
138	C₂×Dic₁₃₉	—	4	2	no	—
139	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₄×D₁₃₉	—	2	1	no	—
143	C₄×D₁₃₉	—	2	1	no	—
144	C₄×D₁₃₉	—	4	2	no	—
145	C₄×D₁₃₉	—	4	2	no	—
146	C₁₃₉⋊C₈	—	2	1	no	—
147	C₁₃₉⋊C₈	C₂×D₄	1	2	yes	—
148	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
149	Q₈×C₁₃₉	—	2	1	no	—
150	Q₈×C₁₃₉	—	2	1	no	—
151	Q₈×C₁₃₉	—	2	1	no	—
152	Q₈×C₁₃₉	—	2	1	no	—
153	Q₈×C₁₃₉	—	2	1	no	—
154	Q₈×C₁₃₉	—	4	2	no	—
155	Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	1	no	—
158	C₂×C₄×C₁₃₉	—	2	1	no	—
159	C₂×C₄×C₁₃₉	—	2	1	no	—
160	C₂×C₄×C₁₃₉	—	2	1	no	—
161	C₂×C₄×C₁₃₉	—	2	1	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	C₈×C₁₃₉	—	2	1	no	—
166	C₈×C₁₃₉	—	2	1	no	—
167	C₂²×C₁₃₉	—	2	1	no	—
168	C₂²×C₁₃₉	—	2	1	no	—
169	C₂²×C₁₃₉	C₂×Q₁₆	1	2	yes	complemented
170	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×D₁₃₉	—	2	1	no	—
172	C₂×D₁₃₉	—	2	1	no	—
173	C₂×D₁₃₉	C₂×Q₁₆	1	2	yes	complemented
174	C₄×C₁₃₉	—	2	1	no	—
175	C₄×C₁₃₉	—	2	2	no	—
176	C₄×C₁₃₉	—	4	1	no	—
177	C₄×C₁₃₉	—	4	1	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
180	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
181	Dic₁₃₉	—	2	1	no	—
182	Dic₁₃₉	—	2	2	no	—
183	Dic₁₃₉	—	2	1	no	—
184	Dic₁₃₉	—	4	1	no	—
185	Dic₁₃₉	—	4	1	no	—
186	Dic₁₃₉	—	4	1	no	—
187	Dic₁₃₉	C₂×Q₁₆	1	2	yes	complemented
188	C₂×C₁₃₉	—	2	2	no	—
189	C₂×C₁₃₉	D₄²	1	1	yes	characteristic
190	C₂×C₁₃₉	C₂²×Q₁₆	1	1	yes	characteristic
191	C₂×C₁₃₉	#578	1	1	yes	characteristic
192	D₁₃₉	—	2	2	no	—
193	C₁₃₉	D₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
194	D₄×Q₁₆	—	139	1	no	maximal, Sylow
195	C₂²×Q₁₆	—	139	1	no	—
196	C₂²×Q₁₆	—	139	1	no	—
197	D₄×Q₈	—	139	1	no	—
198	D₄×Q₈	—	139	1	no	—
199	#494	—	139	1	no	—
200	#467	—	139	1	no	—
201	#467	—	139	1	no	—
202	#462	—	139	1	no	—
203	#462	—	139	1	no	—
204	#451	—	139	1	no	—
205	#451	—	139	1	no	—
206	#451	—	139	1	no	—
207	#451	D₁₃₉	1	1	yes	characteristic, complemented
208	C₄×Q₁₆	—	139	1	no	—
209	C₈×D₄	—	139	1	no	—
210	C₂²×Q₈	—	139	1	no	—
211	C₂²×Q₈	—	139	1	no	—
212	C₂²×Q₈	—	139	1	no	—
213	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
214	C₂×Q₁₆	—	278	4	no	—
215	C₂×Q₁₆	—	278	4	no	—
216	C₂×Q₁₆	—	139	1	no	—
217	C₂×Q₁₆	—	139	1	no	—
218	C₂×Q₁₆	—	139	1	no	—
219	C₂×Q₁₆	—	139	1	no	—
220	C₂×Q₁₆	—	139	1	no	—
221	C₂×Q₁₆	—	139	1	no	—
222	C₂×Q₁₆	—	139	1	no	—
223	C₂×Q₁₆	C₂×D₁₃₉	1	1	yes	characteristic
224	C₂×Q₁₆	C₂×D₁₃₉	1	1	yes	characteristic
225	C₂²×C₈	—	139	1	no	—
226	C₂²×C₈	—	139	1	no	—
227	C₄⋊Q₈	—	278	1	no	—
228	C₄⋊Q₈	—	278	1	no	—
229	C₄⋊Q₈	—	139	1	no	—
230	C₄⋊Q₈	—	139	1	no	—
231	C₂²⋊Q₈	—	278	1	no	—
232	C₂²⋊Q₈	—	278	1	no	—
233	C₂²⋊Q₈	—	278	1	no	—
234	C₂²⋊Q₈	—	278	1	no	—
235	C₂²⋊Q₈	—	139	1	no	—
236	C₂²⋊Q₈	—	139	1	no	—
237	C₂²⋊Q₈	—	139	1	no	—
238	C₂²⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic
239	C₄×Q₈	—	139	1	no	—
240	C₄×Q₈	—	139	1	no	—
241	C₄×D₄	—	278	1	no	—
242	C₄×D₄	—	278	1	no	—
243	C₄×D₄	—	139	1	no	—
244	#107	—	139	1	no	—
245	C₄⋊C₈	—	139	1	no	—
246	#103	—	139	1	no	—
247	#103	—	139	1	no	—
248	#103	—	139	1	no	—
249	#103	—	139	1	no	—
250	#103	C₂×D₁₃₉	1	1	yes	characteristic
251	#103	C₂×D₁₃₉	1	1	yes	characteristic
252	C₂²⋊C₈	—	139	1	no	—
253	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic
254	C₄×C₈	—	139	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	278	1	no	—
259	C₂×Q₈	—	278	1	no	—
260	C₂×Q₈	—	278	2	no	—
261	C₂×Q₈	—	278	1	no	—
262	C₂×Q₈	—	278	2	no	—
263	C₂×Q₈	—	278	2	no	—
264	C₂×Q₈	—	556	1	no	—
265	C₂×Q₈	—	556	1	no	—
266	C₂×Q₈	—	556	1	no	—
267	C₂×Q₈	—	139	1	no	—
268	C₂×Q₈	—	139	1	no	—
269	C₂×Q₈	—	139	1	no	—
270	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
271	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
272	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
273	C₂×D₄	—	139	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	278	1	no	—
276	C₂²×C₄	—	278	1	no	—
277	C₂²×C₄	—	278	1	no	—
278	C₂²×C₄	—	139	1	no	—
279	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	4	1	no	—
282	Q₁₆	—	278	2	no	—
283	Q₁₆	—	278	2	no	—
284	Q₁₆	—	278	2	no	—
285	Q₁₆	—	278	2	no	—
286	Q₁₆	—	278	2	no	—
287	Q₁₆	—	556	1	no	—
288	Q₁₆	—	139	4	no	—
289	C₂×C₈	—	278	2	no	—
290	C₂×C₈	—	278	2	no	—
291	C₂×C₈	—	139	1	no	—
292	C₂×C₈	—	139	1	no	—
293	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
294	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	278	1	no	—
297	C₄⋊C₄	—	278	1	no	—
298	C₄⋊C₄	—	278	1	no	—
299	C₄⋊C₄	—	278	1	no	—
300	C₄⋊C₄	—	278	1	no	—
301	C₄⋊C₄	—	278	1	no	—
302	C₄⋊C₄	—	278	1	no	—
303	C₄⋊C₄	—	278	1	no	—
304	C₄⋊C₄	—	278	1	no	—
305	C₄⋊C₄	—	139	1	no	—
306	C₄⋊C₄	—	139	1	no	—
307	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	278	1	no	—
310	C₂²⋊C₄	—	278	1	no	—
311	C₂²⋊C₄	—	278	1	no	—
312	C₂²⋊C₄	—	139	1	no	—
313	C₂²⋊C₄	—	139	1	no	—
314	C₄²	—	278	1	no	—
315	C₄²	—	278	1	no	—
316	C₄²	—	139	1	no	—
317	C₂³	—	139	1	no	—
318	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	4	2	no	—
325	Q₈	—	278	1	no	—
326	Q₈	—	278	1	no	—
327	Q₈	—	278	1	no	—
328	Q₈	—	278	1	no	—
329	Q₈	—	278	1	no	—
330	Q₈	—	556	2	no	—
331	Q₈	—	556	2	no	—
332	Q₈	—	556	2	no	—
333	Q₈	—	139	2	no	—
334	Q₈	D₄×D₁₃₉	1	2	yes	—
335	D₄	—	139	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	278	1	no	—
344	C₂×C₄	—	278	1	no	—
345	C₂×C₄	—	278	1	no	—
346	C₂×C₄	—	278	1	no	—
347	C₂×C₄	—	278	1	no	—
348	C₂×C₄	—	278	1	no	—
349	C₂×C₄	—	556	2	no	—
350	C₂×C₄	—	556	2	no	—
351	C₂×C₄	—	556	2	no	—
352	C₂×C₄	—	139	1	no	—
353	C₂×C₄	—	139	1	no	—
354	C₂×C₄	—	139	1	no	—
355	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
356	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	278	1	no	—
360	C₈	—	139	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	278	1	no	—
364	C₂²	—	278	1	no	—
365	C₂²	—	139	2	no	—
366	C₂²	Q₁₆×D₁₃₉	1	2	yes	complemented
367	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	278	1	no	—
374	C₄	—	278	1	no	—
375	C₄	—	278	2	no	—
376	C₄	—	556	1	no	—
377	C₄	—	556	1	no	—
378	C₄	—	556	1	no	—
379	C₄	—	139	2	no	—
380	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
381	C₄	#17984887	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	278	2	no	—
384	C₂	#22581585	1	1	yes	characteristic
385	C₂	C₂×Q₁₆×D₁₃₉	1	1	yes	characteristic
386	C₂	#22581769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#451×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×C₂²⋊D₁₃₉	D₄
hypercenter	#451	D₁₃₉
hypocenter	C₁₃₉	D₄×Q₁₆
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #451

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555775	C₂	semidirect
2. C₂×Q₁₆×D₁₃₉	C₂	semidirect
5. #22581331	C₂	semidirect
6. #22581193	C₂	semidirect
7. #22581192	C₂	semidirect
8. #22581162	C₂	semidirect
9. #22581161	C₂	semidirect
10. #22581111	C₂	semidirect
11. #22581110	C₂	semidirect
12. #22581107	C₂	semidirect
13. #22581045	C₂	semidirect
15. #451×C₁₃₉	C₂	semidirect
84. #14555775	D₄	semidirect
133. C₂²⋊D₁₃₉	Q₁₆	semidirect
169. C₂²×C₁₃₉	C₂×Q₁₆	semidirect
173. C₂×D₁₃₉	C₂×Q₁₆	semidirect
187. Dic₁₃₉	C₂×Q₁₆	semidirect
193. C₁₃₉	D₄×Q₁₆	semidirect
207. #451	D₁₃₉	semidirect
366. C₂²	Q₁₆×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14555775	2
C₂×Q₁₆×D₁₃₉	2
Q₈×C₂²⋊D₁₃₉	2
#22581616	2
#22581331	2
#22581193	2
#22581192	2
#22581162	2
#22581161	2
#22581111	2
#22581110	2
#22581107	2
#22581045	2
(C₂²⋊D₁₃₉)⋊C₈	2
#451×C₁₃₉	2
D₄×Q₁₆	139