Subgroups — C₄×#17984869 #31815213

Order 17792.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984869	C₂	1	1	yes	maximal, characteristic
2	C₄×#14555786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581064	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581062	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581056	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#14555772	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₁₁₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14555770	C₂	1	1	yes	maximal, characteristic, complemented
11	#22580992	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580956	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580953	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14555768	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃₉	—	2	1	no	—
19	#17984869	C₄	1	8	yes	direct product factor
20	C₂×#14555772	C₂²	1	1	yes	characteristic
21	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic
22	C₂×#14555770	C₂²	1	1	yes	characteristic
23	C₂×#14555768	C₂²	1	1	yes	characteristic
24	C₂×#14555768	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₅₅₆	—	2	1	no	—
27	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
28	C₄×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
29	D₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
30	#17984804	—	2	1	no	—
31	#17984804	C₂²	1	1	yes	characteristic
32	#17984804	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
34	(C₂²⋊D₁₃₉)⋊C₄	—	2	1	no	—
35	#17984800	—	2	1	no	—
36	#17984800	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
39	C₄²×D₁₃₉	—	2	1	no	—
40	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic
41	#17984776	C₂²	1	1	yes	characteristic, complemented
42	#17984775	C₂²	1	1	yes	characteristic, complemented
43	#17984773	C₂²	1	1	yes	characteristic, complemented
44	#17984766	C₂²	1	1	yes	characteristic, complemented
45	#17984764	C₂²	1	1	yes	characteristic
46	#17984764	C₂²	1	1	yes	characteristic, complemented
47	#17984763	C₂²	1	1	yes	characteristic
48	#17984762	C₂²	1	1	yes	characteristic
49	#17984762	C₂²	1	1	yes	characteristic, complemented
50	#17984752	C₂²	1	1	yes	characteristic, complemented
51	#17984752	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	#106×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	C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₃₉	—	2	1	no	—
61	#14555786	—	2	2	no	—
62	#14555786	C₂×C₄	1	4	yes	complemented
63	C₂×D₅₅₆	—	2	1	no	—
64	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
65	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
67	D₄×D₁₃₉	—	2	2	no	—
68	D₄×D₁₃₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₁₃₉	—	2	1	no	—
70	C₂×C₄×D₁₃₉	—	2	1	no	—
71	C₂×C₄×D₁₃₉	—	2	1	no	—
72	C₂×C₄×D₁₃₉	—	2	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	—	4	4	no	—
77	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
80	#14555772	C₂×C₄	1	4	yes	complemented
81	D₁₁₁₂	C₂×C₄	1	4	yes	complemented
82	#14555770	C₂×C₄	1	4	yes	complemented
83	#14555768	—	2	2	no	—
84	#14555768	C₂×C₄	1	4	yes	complemented
85	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₁₃₉	—	2	1	no	—
88	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
90	Dic₁₃₉⋊C₄	—	2	1	no	—
91	C₂²⋊Dic₁₃₉	—	2	1	no	—
92	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
93	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
94	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
95	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
96	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
97	C₄×Dic₁₃₉	—	2	1	no	—
98	C₄×Dic₁₃₉	—	2	1	no	—
99	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
100	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
101	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	SD₁₆×C₁₃₉	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₉	—	2	1	no	—
109	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
112	C₄²×C₁₃₉	—	2	1	no	—
113	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×D₁₃₉	—	2	1	no	—
115	C₂²×D₁₃₉	—	2	1	no	—
116	C₂²×D₁₃₉	—	2	4	no	—
117	C₂²×D₁₃₉	—	4	2	no	—
118	C₂²×D₁₃₉	—	4	2	no	—
119	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
120	D₅₅₆	—	2	4	no	—
121	D₅₅₆	—	2	1	no	—
122	D₅₅₆	—	2	1	no	—
123	D₅₅₆	C₂²×C₄	1	2	yes	—
124	D₅₅₆	C₂²×C₄	1	2	yes	complemented
125	C₂²⋊D₁₃₉	—	2	4	no	—
126	C₂×Dic₁₃₉	—	2	1	no	—
127	C₂×Dic₁₃₉	—	2	1	no	—
128	C₂×Dic₁₃₉	—	4	2	no	—
129	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
132	C₄×D₁₃₉	—	2	2	no	—
133	C₄×D₁₃₉	—	2	4	no	—
134	C₄×D₁₃₉	—	4	1	no	—
135	C₄×D₁₃₉	—	4	2	no	—
136	C₄×D₁₃₉	—	4	2	no	—
137	C₄×D₁₃₉	—	4	2	no	—
138	C₄×D₁₃₉	—	4	2	no	—
139	C₄×D₁₃₉	—	4	2	no	—
140	C₄×D₁₃₉	C₂²×C₄	1	2	yes	—
141	C₄×D₁₃₉	#41	1	2	yes	—
142	C₁₃₉⋊C₈	—	2	1	no	—
143	C₁₃₉⋊C₈	C₂²×C₄	1	2	yes	complemented
144	C₂³×C₁₃₉	—	2	1	no	—
145	Q₈×C₁₃₉	—	2	1	no	—
146	Q₈×C₁₃₉	C₂²×C₄	1	2	yes	complemented
147	D₄×C₁₃₉	—	2	1	no	—
148	D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
149	C₂×C₄×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	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₁₃₉	—	2	2	no	—
159	C₂²×C₁₃₉	—	4	1	no	—
160	C₂²×C₁₃₉	—	4	1	no	—
161	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₁₃₉	—	2	1	no	—
163	C₂×D₁₃₉	—	2	1	no	—
164	C₂×D₁₃₉	—	2	2	no	—
165	C₂×D₁₃₉	—	2	2	no	—
166	C₂×D₁₃₉	—	4	8	no	—
167	C₂×D₁₃₉	—	4	1	no	—
168	C₂×D₁₃₉	—	4	1	no	—
169	C₂×D₁₃₉	—	4	1	no	—
170	C₂×D₁₃₉	—	4	1	no	—
171	C₂×D₁₃₉	C₄×D₄	1	2	yes	—
172	C₄×C₁₃₉	—	2	2	no	—
173	C₄×C₁₃₉	—	2	1	no	—
174	C₄×C₁₃₉	—	4	1	no	—
175	C₄×C₁₃₉	—	4	1	no	—
176	C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	complemented
177	C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
178	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
179	Dic₁₃₉	—	2	1	no	—
180	Dic₁₃₉	—	2	1	no	—
181	Dic₁₃₉	—	4	1	no	—
182	Dic₁₃₉	—	4	1	no	—
183	Dic₁₃₉	C₄×D₄	1	2	yes	—
184	C₂×C₁₃₉	—	4	2	no	—
185	C₂×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₁₃₉	#575	1	1	yes	characteristic
188	D₁₃₉	—	2	2	no	—
189	D₁₃₉	—	4	2	no	—
190	D₁₃₉	—	4	2	no	—
191	C₁₃₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
192	C₄×AGL(1,ℤ/8)	—	139	1	no	maximal, Sylow
193	C₂×AGL(1,ℤ/8)	—	139	1	no	—
194	C₄×#41	—	139	1	no	—
195	C₂×C₄×D₄	—	139	1	no	—
196	#442	—	139	1	no	—
197	#442	—	139	1	no	—
198	#440	—	139	1	no	—
199	#440	—	139	1	no	—
200	C₄×SD₁₆	—	139	1	no	—
201	C₄×SD₁₆	D₁₃₉	1	1	yes	characteristic, complemented
202	C₄×D₈	—	139	1	no	—
203	C₄×D₈	—	139	1	no	—
204	#428	—	139	1	no	—
205	#418	—	139	1	no	—
206	#417	—	139	1	no	—
207	C₄×M₁₆	—	139	1	no	—
208	C₂×#41	—	139	1	no	—
209	C₂²×D₄	—	139	1	no	—
210	C₂³×C₄	—	278	1	no	—
211	AGL(1,ℤ/8)	—	139	8	no	—
212	C₂×SD₁₆	—	139	1	no	—
213	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
214	C₂×D₈	—	139	1	no	—
215	C₂×D₈	—	139	1	no	—
216	C₂×M₁₆	—	139	1	no	—
217	C₂×M₁₆	—	139	1	no	—
218	C₄×Q₈	—	139	1	no	—
219	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
220	C₄×D₄	—	278	1	no	—
221	C₄×D₄	—	278	1	no	—
222	C₄×D₄	—	278	1	no	—
223	C₄×D₄	—	278	1	no	—
224	C₄×D₄	—	139	1	no	—
225	C₄×D₄	—	139	1	no	—
226	C₄×D₄	—	139	1	no	—
227	C₄×D₄	—	139	1	no	—
228	C₄×D₄	—	139	1	no	—
229	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
230	#117	—	278	1	no	—
231	#117	—	139	1	no	—
232	C₂×C₄⋊C₄	—	139	1	no	—
233	C₂×C₂²⋊C₄	—	278	1	no	—
234	C₂×C₄²	—	278	1	no	—
235	C₂×C₄²	—	139	1	no	—
236	#107	—	139	1	no	—
237	#107	—	139	1	no	—
238	#106	—	139	1	no	—
239	#106	C₂×D₁₃₉	1	1	yes	characteristic, complemented
240	#103	—	139	1	no	—
241	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
242	#102	—	139	1	no	—
243	#102	—	139	1	no	—
244	#102	—	139	1	no	—
245	#102	—	139	1	no	—
246	#102	—	139	1	no	—
247	#102	C₂×D₁₃₉	1	1	yes	characteristic
248	#97	—	139	1	no	—
249	#97	—	139	1	no	—
250	C₄×C₈	—	139	1	no	—
251	C₄×C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
252	C₂⁴	—	278	1	no	—
253	#41	—	278	2	no	—
254	#41	—	139	4	no	—
255	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
256	C₂×D₄	—	278	1	no	—
257	C₂×D₄	—	278	2	no	—
258	C₂×D₄	—	278	1	no	—
259	C₂×D₄	—	139	4	no	—
260	C₂×D₄	—	139	1	no	—
261	C₂×D₄	—	139	1	no	—
262	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	278	1	no	—
265	C₂²×C₄	—	278	1	no	—
266	C₂²×C₄	—	278	1	no	—
267	C₂²×C₄	—	278	1	no	—
268	C₂²×C₄	—	278	1	no	—
269	C₂²×C₄	—	278	1	no	—
270	C₂²×C₄	—	278	1	no	—
271	C₂²×C₄	—	556	4	no	—
272	C₂²×C₄	—	139	1	no	—
273	C₂²×C₄	—	139	1	no	—
274	C₂²×C₄	—	139	1	no	—
275	SD₁₆	—	139	4	no	—
276	SD₁₆	C₄×D₁₃₉	1	4	yes	complemented
277	D₈	—	139	4	no	—
278	D₈	—	139	4	no	—
279	M₁₆	—	278	2	no	—
280	M₁₆	—	139	4	no	—
281	C₂×C₈	—	139	1	no	—
282	C₂×C₈	—	139	1	no	—
283	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	278	1	no	—
287	C₄⋊C₄	—	278	1	no	—
288	C₄⋊C₄	—	139	1	no	—
289	C₄⋊C₄	—	139	1	no	—
290	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	278	1	no	—
294	C₂²⋊C₄	—	278	1	no	—
295	C₂²⋊C₄	—	278	1	no	—
296	C₂²⋊C₄	—	278	1	no	—
297	C₂²⋊C₄	—	278	1	no	—
298	C₂²⋊C₄	—	278	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	278	1	no	—
301	C₄²	—	278	1	no	—
302	C₄²	—	139	1	no	—
303	C₄²	—	139	1	no	—
304	C₄²	—	139	1	no	—
305	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	278	4	no	—
308	C₂³	—	278	1	no	—
309	C₂³	—	278	1	no	—
310	C₂³	—	556	2	no	—
311	C₂³	—	556	2	no	—
312	C₂³	—	139	1	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₁₃₉	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	278	4	no	—
317	D₄	—	278	4	no	—
318	D₄	—	278	1	no	—
319	D₄	—	278	1	no	—
320	D₄	—	139	2	no	—
321	D₄	—	139	2	no	—
322	D₄	C₂×C₄×D₁₃₉	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	278	4	no	—
328	C₂×C₄	—	278	2	no	—
329	C₂×C₄	—	278	1	no	—
330	C₂×C₄	—	278	1	no	—
331	C₂×C₄	—	556	1	no	—
332	C₂×C₄	—	556	2	no	—
333	C₂×C₄	—	556	2	no	—
334	C₂×C₄	—	556	2	no	—
335	C₂×C₄	—	556	2	no	—
336	C₂×C₄	—	556	2	no	—
337	C₂×C₄	—	556	2	no	—
338	C₂×C₄	—	139	1	no	—
339	C₂×C₄	—	139	1	no	—
340	C₂×C₄	—	139	1	no	—
341	C₂×C₄	—	139	2	no	—
342	C₂×C₄	—	139	2	no	—
343	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
344	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	278	1	no	—
348	C₈	—	139	2	no	—
349	C₈	C₂×C₄×D₁₃₉	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	278	1	no	—
354	C₂²	—	278	1	no	—
355	C₂²	—	278	2	no	—
356	C₂²	—	278	2	no	—
357	C₂²	—	556	8	no	—
358	C₂²	—	556	1	no	—
359	C₂²	—	556	1	no	—
360	C₂²	—	556	1	no	—
361	C₂²	—	556	1	no	—
362	C₂²	—	139	2	no	—
363	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	278	1	no	—
369	C₄	—	278	1	no	—
370	C₄	—	556	1	no	—
371	C₄	—	556	1	no	—
372	C₄	—	139	2	no	—
373	C₄	#17984869	1	2	yes	direct product factor
374	C₄	C₂²×C₄×D₁₃₉	1	1	yes	characteristic
375	C₄	#41×D₁₃₉	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	278	2	no	—
378	C₂	—	556	2	no	—
379	C₂	—	556	2	no	—
380	C₂	C₄×D₄×D₁₃₉	1	1	yes	characteristic
381	C₂	C₂×#17984869	1	1	yes	characteristic
382	C₂	#22581750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	C₄×SD₁₆×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×#17984869	C₂
cosocle	C₂×C₄×C₁₃₉	C₂⁴
hypercenter	C₄×SD₁₆	D₁₃₉
hypocenter	C₁₃₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#14555786	C₂	semidirect
3. C₄×D₄×D₁₃₉	C₂	semidirect
4. #22581064	C₂	semidirect
5. #22581062	C₂	semidirect
6. #22581056	C₂	semidirect
7. #22581054	C₂	semidirect
8. C₄×#14555772	C₂	semidirect
9. C₄×D₁₁₁₂	C₂	semidirect
10. C₄×#14555770	C₂	semidirect
11. #22580992	C₂	semidirect
12. #22580956	C₂	semidirect
13. #22580953	C₂	semidirect
14. C₄×#14555768	C₂	semidirect
15. C₄×SD₁₆×C₁₃₉	C₂	semidirect
19. #17984869	C₄	direct (N × H)
25. Q₈×Dic₁₃₉	C₂²	semidirect
28. C₄×D₅₅₆	C₂²	semidirect
32. #17984804	C₂²	semidirect
41. #17984776	C₂²	semidirect
42. #17984775	C₂²	semidirect
43. #17984773	C₂²	semidirect
44. #17984766	C₂²	semidirect
46. #17984764	C₂²	semidirect
49. #17984762	C₂²	semidirect
50. #17984752	C₂²	semidirect
51. #17984752	C₂²	semidirect
52. C₄×C₁₃₉⋊C₈	C₂²	semidirect
54. C₄×Q₈×C₁₃₉	C₂²	semidirect
56. #106×C₁₃₉	C₂²	semidirect
57. #103×C₁₃₉	C₂²	semidirect
59. C₄×C₈×C₁₃₉	C₂²	semidirect
62. #14555786	C₂×C₄	semidirect
68. D₄×D₁₃₉	C₂×C₄	semidirect
80. #14555772	C₂×C₄	semidirect
81. D₁₁₁₂	C₂×C₄	semidirect
82. #14555770	C₂×C₄	semidirect
84. #14555768	C₂×C₄	semidirect
105. SD₁₆×C₁₃₉	C₂×C₄	semidirect
124. D₅₅₆	C₂²×C₄	semidirect
143. C₁₃₉⋊C₈	C₂²×C₄	semidirect
146. Q₈×C₁₃₉	C₂²×C₄	semidirect
157. C₈×C₁₃₉	C₂²×C₄	semidirect
176. C₄×C₁₃₉	AGL(1,ℤ/8)	semidirect
191. C₁₃₉	C₄×AGL(1,ℤ/8)	semidirect
201. C₄×SD₁₆	D₁₃₉	semidirect
219. C₄×Q₈	C₂×D₁₃₉	semidirect
239. #106	C₂×D₁₃₉	semidirect
241. #103	C₂×D₁₃₉	semidirect
251. C₄×C₈	C₂×D₁₃₉	semidirect
276. SD₁₆	C₄×D₁₃₉	semidirect
314. Q₈	C₂×C₄×D₁₃₉	semidirect
349. C₈	C₂×C₄×D₁₃₉	semidirect
373. C₄	#17984869	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17984869	2
C₄×#14555786	2
C₄×D₄×D₁₃₉	2
#22581064	2
#22581062	2
#22581056	2
#22581054	2
C₄×#14555772	2
C₄×D₁₁₁₂	2
C₄×#14555770	2
#22580992	2
#22580956	2
#22580953	2
C₄×#14555768	2
C₄×SD₁₆×C₁₃₉	2
C₄×AGL(1,ℤ/8)	139

Subgroups — C4×#17984869 #31815213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17984869 #31815213