Subgroups — C₁₃₇×#17825 #46867211

Order 35072.

572 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2989×C₁₃₇	C₂	1	2	yes	maximal
2	#2922×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1574×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1573×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1572×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1571×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1569×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1568×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1567×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
11	#446×C₁₃₇	—	2	2	no	—
12	#436×C₁₃₇	—	2	2	no	—
13	#435×C₁₃₇	—	2	2	no	—
14	#435×C₁₃₇	—	2	2	no	—
15	#433×C₁₃₇	C₄	1	4	yes	—
16	#432×C₁₃₇	C₂²	1	2	yes	—
17	#432×C₁₃₇	C₂²	1	2	yes	—
18	#431×C₁₃₇	C₂²	1	2	yes	—
19	#431×C₁₃₇	C₂²	1	2	yes	—
20	#431×C₁₃₇	C₂²	1	2	yes	—
21	#424×C₁₃₇	C₄	1	2	yes	—
22	#423×C₁₃₇	C₂²	1	2	yes	—
23	#423×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
25	#408×C₁₃₇	C₄	1	2	yes	—
26	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	#335×C₁₃₇	C₂²	1	2	yes	—
29	#335×C₁₃₇	C₂²	1	1	yes	characteristic
30	#335×C₁₃₇	C₂²	1	1	yes	characteristic
31	#335×C₁₃₇	C₂²	1	1	yes	characteristic
32	#335×C₁₃₇	C₂²	1	1	yes	characteristic
33	#335×C₁₃₇	C₂²	1	2	yes	—
34	#335×C₁₃₇	C₂²	1	2	yes	—
35	#334×C₁₃₇	C₂²	1	2	yes	—
36	#334×C₁₃₇	C₂²	1	2	yes	—
37	#334×C₁₃₇	C₂²	1	2	yes	—
38	C₂×#41×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₁₃₇	—	2	2	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₃₇	Q₈	1	1	yes	characteristic
46	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
47	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
48	C₄×D₄×C₁₃₇	Q₈	1	1	yes	characteristic
49	C₄×D₄×C₁₃₇	Q₈	1	2	yes	—
50	#117×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	#117×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
54	C₄⋊C₈×C₁₃₇	—	2	2	no	—
55	C₄⋊C₈×C₁₃₇	—	2	2	no	—
56	C₄⋊C₈×C₁₃₇	—	2	2	no	—
57	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
58	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
59	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
60	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
61	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
62	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
63	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
64	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
65	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
66	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
67	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
68	#97×C₁₃₇	—	2	2	no	—
69	#97×C₁₃₇	—	2	2	no	—
70	#97×C₁₃₇	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₃₇	—	2	2	no	—
72	C₄×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
76	#41×C₁₃₇	—	4	2	no	—
77	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂×D₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
86	M₁₆×C₁₃₇	—	4	2	no	—
87	M₁₆×C₁₃₇	—	8	2	no	—
88	M₁₆×C₁₃₇	—	8	2	no	—
89	C₂×C₈×C₁₃₇	—	2	2	no	—
90	C₂×C₈×C₁₃₇	—	2	2	no	—
91	C₂×C₈×C₁₃₇	—	2	2	no	—
92	C₂×C₈×C₁₃₇	—	2	2	no	—
93	C₂×C₈×C₁₃₇	—	4	2	no	—
94	C₂×C₈×C₁₃₇	—	8	2	no	—
95	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
98	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
100	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
102	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
103	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
104	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
105	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
111	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
112	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
113	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
114	Q₈×C₁₃₇	—	4	1	no	—
115	D₄×C₁₃₇	—	4	1	no	—
116	D₄×C₁₃₇	—	4	2	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	4	no	—
119	C₂×C₄×C₁₃₇	—	2	2	no	—
120	C₂×C₄×C₁₃₇	—	2	1	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	1	no	—
123	C₂×C₄×C₁₃₇	—	4	1	no	—
124	C₂×C₄×C₁₃₇	—	4	2	no	—
125	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
134	C₈×C₁₃₇	—	2	2	no	—
135	C₈×C₁₃₇	—	2	2	no	—
136	C₈×C₁₃₇	—	2	4	no	—
137	C₈×C₁₃₇	—	4	2	no	—
138	C₈×C₁₃₇	—	4	2	no	—
139	C₈×C₁₃₇	—	4	2	no	—
140	C₈×C₁₃₇	—	4	2	no	—
141	C₂²×C₁₃₇	—	2	1	no	—
142	C₂²×C₁₃₇	—	2	2	no	—
143	C₂²×C₁₃₇	—	2	2	no	—
144	C₂²×C₁₃₇	—	2	1	no	—
145	C₂²×C₁₃₇	—	2	2	no	—
146	C₂²×C₁₃₇	—	2	1	no	—
147	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
148	C₄×C₁₃₇	—	2	1	no	—
149	C₄×C₁₃₇	—	2	2	no	—
150	C₄×C₁₃₇	—	2	2	no	—
151	C₄×C₁₃₇	—	2	1	no	—
152	C₄×C₁₃₇	—	2	1	no	—
153	C₄×C₁₃₇	—	2	1	no	—
154	C₄×C₁₃₇	—	2	2	no	—
155	C₄×C₁₃₇	#568	1	2	yes	—
156	C₄×C₁₃₇	#576	1	1	yes	characteristic
157	C₄×C₁₃₇	#578	1	1	yes	characteristic
158	C₂×C₁₃₇	—	4	1	no	—
159	C₂×C₁₃₇	—	4	2	no	—
160	C₂×C₁₃₇	#2905	1	1	yes	characteristic
161	C₂×C₁₃₇	#2913	1	1	yes	characteristic
162	C₂×C₁₃₇	#2916	1	1	yes	characteristic
163	#17825	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₁₃₇	#17825	1	1	yes	characteristic, direct product factor, Sylow
165	#2989	C₂×C₁₃₇	1	2	yes	—
166	#2922	C₂×C₁₃₇	1	1	yes	characteristic
167	#1574	C₂×C₁₃₇	1	2	yes	complemented
168	#1573	C₂×C₁₃₇	1	2	yes	complemented
169	#1572	C₂×C₁₃₇	1	2	yes	complemented
170	#1571	C₂×C₁₃₇	1	2	yes	complemented
171	#1569	C₂×C₁₃₇	1	2	yes	complemented
172	#1568	C₂×C₁₃₇	1	1	yes	characteristic, complemented
173	#1567	C₂×C₁₃₇	1	1	yes	characteristic, complemented
174	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
175	#446	—	2	2	no	—
176	#436	—	2	2	no	—
177	#435	—	2	2	no	—
178	#435	—	2	2	no	—
179	#433	C₄×C₁₃₇	1	4	yes	—
180	#432	C₂²×C₁₃₇	1	2	yes	—
181	#432	C₂²×C₁₃₇	1	2	yes	—
182	#431	C₂²×C₁₃₇	1	2	yes	—
183	#431	C₂²×C₁₃₇	1	2	yes	—
184	#431	C₂²×C₁₃₇	1	2	yes	—
185	#424	C₄×C₁₃₇	1	2	yes	—
186	#423	C₂²×C₁₃₇	1	2	yes	—
187	#423	C₂²×C₁₃₇	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
189	#408	C₄×C₁₃₇	1	2	yes	—
190	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
192	#335	C₂²×C₁₃₇	1	2	yes	—
193	#335	C₂²×C₁₃₇	1	1	yes	characteristic
194	#335	C₂²×C₁₃₇	1	1	yes	characteristic
195	#335	C₂²×C₁₃₇	1	1	yes	characteristic
196	#335	C₂²×C₁₃₇	1	1	yes	characteristic
197	#335	C₂²×C₁₃₇	1	2	yes	—
198	#335	C₂²×C₁₃₇	1	2	yes	—
199	#334	C₂²×C₁₃₇	1	2	yes	—
200	#334	C₂²×C₁₃₇	1	2	yes	—
201	#334	C₂²×C₁₃₇	1	2	yes	—
202	C₂×#41	C₂×C₄×C₁₃₇	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
208	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
209	C₄×Q₈	Q₈×C₁₃₇	1	1	yes	characteristic
210	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
211	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
212	C₄×D₄	Q₈×C₁₃₇	1	1	yes	characteristic
213	C₄×D₄	Q₈×C₁₃₇	1	2	yes	—
214	#117	C₂×C₄×C₁₃₇	1	1	yes	characteristic
215	#117	C₂×C₄×C₁₃₇	1	2	yes	—
216	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
222	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
223	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
224	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
225	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
226	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	—	2	2	no	—
229	C₂²⋊C₈	—	2	2	no	—
230	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
231	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
232	#97	—	2	2	no	—
233	#97	—	2	2	no	—
234	#97	C₂×C₄×C₁₃₇	1	2	yes	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
237	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
238	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
239	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
240	#41	—	4	2	no	—
241	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
242	C₂×D₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
243	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
250	M₁₆	—	4	2	no	—
251	M₁₆	—	8	2	no	—
252	M₁₆	—	8	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	8	2	no	—
259	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
261	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
262	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
263	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
264	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
265	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
266	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
267	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
268	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
269	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
270	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
271	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
272	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
273	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
274	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
275	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
276	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
277	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
278	Q₈	—	4	1	no	—
279	D₄	—	4	1	no	—
280	D₄	—	4	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	4	1	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
290	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
291	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
293	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
294	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
295	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
296	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
297	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	—	2	4	no	—
301	C₈	—	4	2	no	—
302	C₈	—	4	2	no	—
303	C₈	—	4	2	no	—
304	C₈	—	4	2	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	1	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	1	no	—
311	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
312	C₄	—	2	1	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	2	1	no	—
318	C₄	—	2	2	no	—
319	C₄	#568×C₁₃₇	1	2	yes	—
320	C₄	#576×C₁₃₇	1	1	yes	characteristic
321	C₄	#578×C₁₃₇	1	1	yes	characteristic
322	C₂	—	4	1	no	—
323	C₂	—	4	2	no	—
324	C₂	#2905×C₁₃₇	1	1	yes	characteristic
325	C₂	#2913×C₁₃₇	1	1	yes	characteristic
326	C₂	#2916×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₁₃₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₄×#41×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1574×C₁₃₇	C₂	semidirect
4. #1573×C₁₃₇	C₂	semidirect
5. #1572×C₁₃₇	C₂	semidirect
6. #1571×C₁₃₇	C₂	semidirect
7. #1569×C₁₃₇	C₂	semidirect
8. #1568×C₁₃₇	C₂	semidirect
9. #1567×C₁₃₇	C₂	semidirect
163. #17825	C₁₃₇	direct (N × H)
164. C₁₃₇	#17825	direct (N × H)
167. #1574	C₂×C₁₃₇	semidirect
168. #1573	C₂×C₁₃₇	semidirect
169. #1572	C₂×C₁₃₇	semidirect
170. #1571	C₂×C₁₃₇	semidirect
171. #1569	C₂×C₁₃₇	semidirect
172. #1568	C₂×C₁₃₇	semidirect
173. #1567	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2989×C₁₃₇	2
#2922×C₁₃₇	2
#1574×C₁₃₇	2
#1573×C₁₃₇	2
#1572×C₁₃₇	2
#1571×C₁₃₇	2
#1569×C₁₃₇	2
#1568×C₁₃₇	2
#1567×C₁₃₇	2
#17825	137

Subgroups — C137×#17825 #46867211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17825 #46867211