Subgroups — C₂×#1667×C₁₃₇ #46868485

Order 35072.

958 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#459×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1667×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#335×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#331×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₂²×D₈×C₁₃₇	—	2	2	no	—
8	C₂²×D₈×C₁₃₇	—	2	1	no	—
9	C₂²×D₈×C₁₃₇	—	2	1	no	—
10	C₂³×C₈×C₁₃₇	—	2	1	no	—
11	C₂×#127×C₁₃₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	#493×C₁₃₇	—	2	2	no	—
14	#493×C₁₃₇	C₂²	1	4	yes	complemented
15	#459×C₁₃₇	—	2	4	no	—
16	#459×C₁₃₇	C₂²	1	8	yes	complemented
17	C₈×D₄×C₁₃₇	—	2	2	no	—
18	C₈×D₄×C₁₃₇	C₂²	1	4	yes	complemented
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₇	—	2	2	no	—
22	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	#335×C₁₃₇	C₂²	1	4	yes	complemented
25	#331×C₁₃₇	C₂²	1	8	yes	complemented
26	C₂²×D₄×C₁₃₇	—	2	2	no	—
27	C₂²×D₄×C₁₃₇	—	2	2	no	—
28	C₂²×D₄×C₁₃₇	—	2	2	no	—
29	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₇	—	2	1	no	—
31	C₂×D₈×C₁₃₇	—	2	8	no	—
32	C₂×D₈×C₁₃₇	—	2	4	no	—
33	C₂×D₈×C₁₃₇	—	2	4	no	—
34	C₂×D₈×C₁₃₇	—	4	4	no	—
35	C₂×D₈×C₁₃₇	—	4	8	no	—
36	C₂×D₈×C₁₃₇	—	4	4	no	—
37	C₂²×C₈×C₁₃₇	—	2	1	no	—
38	C₂²×C₈×C₁₃₇	—	2	2	no	—
39	C₂²×C₈×C₁₃₇	—	2	4	no	—
40	C₂²×C₈×C₁₃₇	—	4	4	no	—
41	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
43	#127×C₁₃₇	—	2	2	no	—
44	#127×C₁₃₇	—	2	2	no	—
45	#127×C₁₃₇	—	2	2	no	—
46	#127×C₁₃₇	C₂³	1	4	yes	—
47	C₄×D₄×C₁₃₇	—	2	1	no	—
48	C₄×D₄×C₁₃₇	—	2	1	no	—
49	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
50	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
53	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₁₃₇	—	2	1	no	—
55	C₄⋊C₈×C₁₃₇	—	2	2	no	—
56	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
57	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
58	#102×C₁₃₇	—	2	8	no	—
59	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
60	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
61	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
62	C₂⁴×C₁₃₇	—	2	1	no	—
63	C₂⁴×C₁₃₇	—	4	2	no	—
64	C₂×D₄×C₁₃₇	—	2	1	no	—
65	C₂×D₄×C₁₃₇	—	2	2	no	—
66	C₂×D₄×C₁₃₇	—	2	4	no	—
67	C₂×D₄×C₁₃₇	—	2	4	no	—
68	C₂×D₄×C₁₃₇	—	2	4	no	—
69	C₂×D₄×C₁₃₇	—	4	2	no	—
70	C₂×D₄×C₁₃₇	—	4	2	no	—
71	C₂×D₄×C₁₃₇	—	4	2	no	—
72	C₂×D₄×C₁₃₇	—	4	4	no	—
73	C₂×D₄×C₁₃₇	—	4	4	no	—
74	C₂×D₄×C₁₃₇	—	4	4	no	—
75	C₂×D₄×C₁₃₇	—	4	4	no	—
76	C₂×D₄×C₁₃₇	—	8	4	no	—
77	C₂×D₄×C₁₃₇	D₈	1	4	yes	complemented
78	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₇	—	2	1	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	4	2	no	—
83	C₂²×C₄×C₁₃₇	—	4	2	no	—
84	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
87	D₈×C₁₃₇	—	4	8	no	—
88	D₈×C₁₃₇	—	4	16	no	—
89	D₈×C₁₃₇	—	4	8	no	—
90	C₂×C₈×C₁₃₇	—	2	2	no	—
91	C₂×C₈×C₁₃₇	—	2	2	no	—
92	C₂×C₈×C₁₃₇	—	2	4	no	—
93	C₂×C₈×C₁₃₇	—	4	2	no	—
94	C₂×C₈×C₁₃₇	—	4	4	no	—
95	C₂×C₈×C₁₃₇	—	4	8	no	—
96	C₂×C₈×C₁₃₇	D₈	1	4	yes	complemented
97	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
99	C₄⋊C₄×C₁₃₇	—	2	1	no	—
100	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
101	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
102	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₃₇	#41	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
107	C₂³×C₁₃₇	—	2	2	no	—
108	C₂³×C₁₃₇	—	2	4	no	—
109	C₂³×C₁₃₇	—	4	2	no	—
110	C₂³×C₁₃₇	—	4	2	no	—
111	C₂³×C₁₃₇	—	4	4	no	—
112	C₂³×C₁₃₇	—	8	4	no	—
113	C₂³×C₁₃₇	—	8	4	no	—
114	C₂³×C₁₃₇	—	8	4	no	—
115	C₂³×C₁₃₇	#121	1	1	yes	characteristic
116	D₄×C₁₃₇	—	2	2	no	—
117	D₄×C₁₃₇	—	2	4	no	—
118	D₄×C₁₃₇	—	4	4	no	—
119	D₄×C₁₃₇	—	4	4	no	—
120	D₄×C₁₃₇	—	4	4	no	—
121	D₄×C₁₃₇	—	4	4	no	—
122	D₄×C₁₃₇	—	8	4	no	—
123	D₄×C₁₃₇	—	8	4	no	—
124	D₄×C₁₃₇	—	8	4	no	—
125	D₄×C₁₃₇	—	8	4	no	—
126	D₄×C₁₃₇	C₂×D₈	1	4	yes	complemented
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	4	2	no	—
130	C₂×C₄×C₁₃₇	—	4	2	no	—
131	C₂×C₄×C₁₃₇	—	4	2	no	—
132	C₂×C₄×C₁₃₇	—	4	4	no	—
133	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
137	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
138	C₂×C₄×C₁₃₇	#135	1	2	yes	—
139	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
140	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
143	C₈×C₁₃₇	—	2	2	no	—
144	C₈×C₁₃₇	—	4	2	no	—
145	C₈×C₁₃₇	—	4	4	no	—
146	C₈×C₁₃₇	C₂×D₈	1	4	yes	complemented
147	C₂²×C₁₃₇	—	2	4	no	—
148	C₂²×C₁₃₇	—	4	8	no	—
149	C₂²×C₁₃₇	—	4	2	no	—
150	C₂²×C₁₃₇	—	4	2	no	—
151	C₂²×C₁₃₇	—	8	4	no	—
152	C₂²×C₁₃₇	—	8	4	no	—
153	C₂²×C₁₃₇	—	8	4	no	—
154	C₂²×C₁₃₇	—	16	8	no	—
155	C₂²×C₁₃₇	#459	1	2	yes	—
156	C₂²×C₁₃₇	#466	1	2	yes	—
157	C₂²×C₁₃₇	#472	1	2	yes	—
158	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
159	C₄×C₁₃₇	—	2	1	no	—
160	C₄×C₁₃₇	—	2	1	no	—
161	C₄×C₁₃₇	—	4	2	no	—
162	C₄×C₁₃₇	#459	1	2	yes	—
163	C₄×C₁₃₇	#466	1	2	yes	—
164	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
165	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
166	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
167	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₁₃₇	—	4	4	no	—
169	C₂×C₁₃₇	—	16	4	no	—
170	C₂×C₁₃₇	#1667	1	4	yes	direct product factor
171	C₂×C₁₃₇	C₂×#459	1	1	yes	characteristic
172	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
173	C₂×C₁₃₇	C₂×#472	1	1	yes	characteristic
174	C₂×#1667	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₃₇	C₂×#1667	1	1	yes	characteristic, direct product factor, Sylow
176	C₂×#493	C₂×C₁₃₇	1	1	yes	characteristic, complemented
177	C₂×#459	C₂×C₁₃₇	1	2	yes	complemented
178	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
179	#1667	C₂×C₁₃₇	1	8	yes	direct product factor
180	C₂×#335	C₂×C₁₃₇	1	1	yes	characteristic, complemented
181	C₂×#331	C₂×C₁₃₇	1	2	yes	complemented
182	C₂²×D₈	—	2	2	no	—
183	C₂²×D₈	—	2	1	no	—
184	C₂²×D₈	—	2	1	no	—
185	C₂³×C₈	—	2	1	no	—
186	C₂×#127	C₂²×C₁₃₇	1	2	yes	—
187	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
188	#493	—	2	2	no	—
189	#493	C₂²×C₁₃₇	1	4	yes	complemented
190	#459	—	2	4	no	—
191	#459	C₂²×C₁₃₇	1	8	yes	complemented
192	C₈×D₄	—	2	2	no	—
193	C₈×D₄	C₂²×C₁₃₇	1	4	yes	complemented
194	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
196	C₂×#102	—	2	2	no	—
197	C₂×C₂²⋊C₈	—	2	1	no	—
198	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	#335	C₂²×C₁₃₇	1	4	yes	complemented
200	#331	C₂²×C₁₃₇	1	8	yes	complemented
201	C₂²×D₄	—	2	2	no	—
202	C₂²×D₄	—	2	2	no	—
203	C₂²×D₄	—	2	2	no	—
204	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
205	C₂³×C₄	—	2	1	no	—
206	C₂×D₈	—	2	8	no	—
207	C₂×D₈	—	2	4	no	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	—	4	4	no	—
210	C₂×D₈	—	4	8	no	—
211	C₂×D₈	—	4	4	no	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	—	4	4	no	—
216	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
217	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
218	#127	—	2	2	no	—
219	#127	—	2	2	no	—
220	#127	—	2	2	no	—
221	#127	C₂³×C₁₃₇	1	4	yes	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
225	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
226	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
232	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
233	#102	—	2	8	no	—
234	C₂²⋊C₈	—	2	4	no	—
235	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
236	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
237	C₂⁴	—	2	1	no	—
238	C₂⁴	—	4	2	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	4	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂×D₄	—	4	4	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	—	8	4	no	—
252	C₂×D₄	D₈×C₁₃₇	1	4	yes	complemented
253	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
262	D₈	—	4	8	no	—
263	D₈	—	4	16	no	—
264	D₈	—	4	8	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	4	2	no	—
269	C₂×C₈	—	4	4	no	—
270	C₂×C₈	—	4	8	no	—
271	C₂×C₈	D₈×C₁₃₇	1	4	yes	complemented
272	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
273	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
276	C₂²⋊C₄	—	2	2	no	—
277	C₂²⋊C₄	—	2	2	no	—
278	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
279	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
280	C₄²	#41×C₁₃₇	1	1	yes	characteristic
281	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
282	C₂³	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	4	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	4	no	—
287	C₂³	—	8	4	no	—
288	C₂³	—	8	4	no	—
289	C₂³	—	8	4	no	—
290	C₂³	#121×C₁₃₇	1	1	yes	characteristic
291	D₄	—	2	4	no	—
292	D₄	—	2	2	no	—
293	D₄	—	4	4	no	—
294	D₄	—	4	4	no	—
295	D₄	—	4	4	no	—
296	D₄	—	4	4	no	—
297	D₄	—	8	4	no	—
298	D₄	—	8	4	no	—
299	D₄	—	8	4	no	—
300	D₄	—	8	4	no	—
301	D₄	C₂×D₈×C₁₃₇	1	4	yes	complemented
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
309	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
312	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
313	C₂×C₄	#135×C₁₃₇	1	2	yes	—
314	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	—	4	2	no	—
320	C₈	—	4	4	no	—
321	C₈	C₂×D₈×C₁₃₇	1	4	yes	complemented
322	C₂²	—	2	4	no	—
323	C₂²	—	4	2	no	—
324	C₂²	—	4	8	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	8	4	no	—
327	C₂²	—	8	4	no	—
328	C₂²	—	8	4	no	—
329	C₂²	—	16	8	no	—
330	C₂²	#459×C₁₃₇	1	2	yes	—
331	C₂²	#466×C₁₃₇	1	2	yes	—
332	C₂²	#472×C₁₃₇	1	2	yes	—
333	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	4	2	no	—
337	C₄	#459×C₁₃₇	1	2	yes	—
338	C₄	#466×C₁₃₇	1	2	yes	—
339	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
340	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
341	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
342	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
343	C₂	—	4	4	no	—
344	C₂	—	16	4	no	—
345	C₂	#1667×C₁₃₇	1	4	yes	direct product factor
346	C₂	C₂×#459×C₁₃₇	1	1	yes	characteristic
347	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic
348	C₂	C₂×#472×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#493×C₁₃₇	C₂	semidirect
2. C₂×#459×C₁₃₇	C₂	semidirect
3. C₂×C₈×D₄×C₁₃₇	C₂	semidirect
4. #1667×C₁₃₇	C₂	direct (N × H)
5. C₂×#335×C₁₃₇	C₂	semidirect
6. C₂×#331×C₁₃₇	C₂	semidirect
14. #493×C₁₃₇	C₂²	semidirect
16. #459×C₁₃₇	C₂²	semidirect
18. C₈×D₄×C₁₃₇	C₂²	semidirect
24. #335×C₁₃₇	C₂²	semidirect
25. #331×C₁₃₇	C₂²	semidirect
77. C₂×D₄×C₁₃₇	D₈	semidirect
96. C₂×C₈×C₁₃₇	D₈	semidirect
126. D₄×C₁₃₇	C₂×D₈	semidirect
146. C₈×C₁₃₇	C₂×D₈	semidirect
170. C₂×C₁₃₇	#1667	direct (N × H)
174. C₂×#1667	C₁₃₇	direct (N × H)
175. C₁₃₇	C₂×#1667	direct (N × H)
176. C₂×#493	C₂×C₁₃₇	semidirect
177. C₂×#459	C₂×C₁₃₇	semidirect
178. C₂×C₈×D₄	C₂×C₁₃₇	semidirect
179. #1667	C₂×C₁₃₇	direct (N × H)
180. C₂×#335	C₂×C₁₃₇	semidirect
181. C₂×#331	C₂×C₁₃₇	semidirect
189. #493	C₂²×C₁₃₇	semidirect
191. #459	C₂²×C₁₃₇	semidirect
193. C₈×D₄	C₂²×C₁₃₇	semidirect
199. #335	C₂²×C₁₃₇	semidirect
200. #331	C₂²×C₁₃₇	semidirect
252. C₂×D₄	D₈×C₁₃₇	semidirect
271. C₂×C₈	D₈×C₁₃₇	semidirect
301. D₄	C₂×D₈×C₁₃₇	semidirect
321. C₈	C₂×D₈×C₁₃₇	semidirect
345. C₂	#1667×C₁₃₇	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×#493×C₁₃₇	2
C₂×#459×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
#1667×C₁₃₇	2
C₂×#335×C₁₃₇	2
C₂×#331×C₁₃₇	2
C₂×#1667	137

Subgroups — C2×#1667×C137 #46868485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1667×C₁₃₇ #46868485