Subgroups — C₁₃₇×#22692 #46872078

Order 35072.

862 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#443×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2951×C₁₃₇	C₂	1	2	yes	maximal
3	#2913×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1952×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1859×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1845×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1816×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1772×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×#131×C₁₃₇	C₂²	1	2	yes	—
11	#520×C₁₃₇	C₂²	1	4	yes	—
12	#443×C₁₃₇	C₄	1	8	yes	complemented
13	#440×C₁₃₇	—	2	4	no	—
14	C₄×Q₁₆×C₁₃₇	—	2	2	no	—
15	C₄×D₈×C₁₃₇	—	2	2	no	—
16	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
18	#428×C₁₃₇	—	2	4	no	—
19	#428×C₁₃₇	C₂²	1	4	yes	—
20	#427×C₁₃₇	—	2	2	no	—
21	#427×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₃₇	—	2	2	no	—
23	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
26	#417×C₁₃₇	C₂²	1	4	yes	—
27	#405×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	#384×C₁₃₇	C₂²	1	2	yes	—
30	#343×C₁₃₇	C₂²	1	4	yes	—
31	#339×C₁₃₇	C₂²	1	2	yes	—
32	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
33	#135×C₁₃₇	C₂×C₄	1	4	yes	—
34	#135×C₁₃₇	Q₈	1	4	yes	—
35	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂×SD₁₆×C₁₃₇	D₄	1	2	yes	—
37	C₂×D₈×C₁₃₇	D₄	1	1	yes	characteristic
38	#131×C₁₃₇	—	2	4	no	—
39	#131×C₁₃₇	C₂×C₄	1	8	yes	complemented
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
42	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₄×Q₈×C₁₃₇	—	2	4	no	—
47	C₄×D₄×C₁₃₇	—	2	4	no	—
48	C₄×D₄×C₁₃₇	—	4	4	no	—
49	#117×C₁₃₇	—	2	4	no	—
50	#117×C₁₃₇	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
54	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
55	#108×C₁₃₇	—	2	2	no	—
56	#108×C₁₃₇	C₂×C₄	1	4	yes	complemented
57	#107×C₁₃₇	—	2	2	no	—
58	#107×C₁₃₇	—	2	2	no	—
59	#107×C₁₃₇	—	2	2	no	—
60	#107×C₁₃₇	—	2	2	no	—
61	#107×C₁₃₇	—	2	4	no	—
62	#107×C₁₃₇	D₄	1	1	yes	characteristic
63	#107×C₁₃₇	D₄	1	1	yes	characteristic
64	#106×C₁₃₇	—	2	4	no	—
65	#106×C₁₃₇	D₄	1	2	yes	—
66	#104×C₁₃₇	C₂×C₄	1	8	yes	complemented
67	#103×C₁₃₇	—	2	4	no	—
68	#102×C₁₃₇	—	2	4	no	—
69	#97×C₁₃₇	—	2	2	no	—
70	C₄×C₈×C₁₃₇	—	2	2	no	—
71	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
72	#41×C₁₃₇	—	2	2	no	—
73	#41×C₁₃₇	—	2	2	no	—
74	#41×C₁₃₇	C₂²×C₄	1	4	yes	—
75	#41×C₁₃₇	C₂×Q₈	1	4	yes	—
76	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
77	C₂×D₄×C₁₃₇	—	2	2	no	—
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	4	no	—
82	C₂²×C₄×C₁₃₇	—	4	4	no	—
83	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
84	Q₁₆×C₁₃₇	C₄⋊C₄	1	4	yes	complemented
85	SD₁₆×C₁₃₇	C₄⋊C₄	1	8	yes	complemented
86	D₈×C₁₃₇	C₄⋊C₄	1	4	yes	complemented
87	M₁₆×C₁₃₇	—	2	2	no	—
88	M₁₆×C₁₃₇	—	2	8	no	—
89	M₁₆×C₁₃₇	—	2	2	no	—
90	M₁₆×C₁₃₇	—	2	2	no	—
91	M₁₆×C₁₃₇	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₁₃₇	—	2	2	no	—
93	C₂×C₈×C₁₃₇	—	2	8	no	—
94	C₂×C₈×C₁₃₇	—	2	2	no	—
95	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
102	C₂×C₈×C₁₃₇	#41	1	2	yes	—
103	C₄⋊C₄×C₁₃₇	—	2	4	no	—
104	C₄⋊C₄×C₁₃₇	—	2	4	no	—
105	C₄⋊C₄×C₁₃₇	—	4	4	no	—
106	C₄⋊C₄×C₁₃₇	—	8	4	no	—
107	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
110	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
111	C₄²×C₁₃₇	—	2	2	no	—
112	C₄²×C₁₃₇	—	2	1	no	—
113	C₄²×C₁₃₇	—	4	4	no	—
114	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
115	C₂³×C₁₃₇	—	2	2	no	—
116	C₂³×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
117	Q₈×C₁₃₇	—	2	2	no	—
118	Q₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
119	D₄×C₁₃₇	—	2	4	no	—
120	D₄×C₁₃₇	—	2	4	no	—
121	D₄×C₁₃₇	—	2	2	no	—
122	D₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	2	no	—
127	C₂×C₄×C₁₃₇	—	2	4	no	—
128	C₂×C₄×C₁₃₇	—	2	4	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	4	4	no	—
132	C₂×C₄×C₁₃₇	—	8	4	no	—
133	C₂×C₄×C₁₃₇	—	16	4	no	—
134	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
140	C₈×C₁₃₇	—	2	4	no	—
141	C₈×C₁₃₇	—	4	2	no	—
142	C₈×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₈×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₈×C₁₃₇	C₄×D₄	1	2	yes	—
145	C₈×C₁₃₇	C₄×D₄	1	2	yes	—
146	C₂²×C₁₃₇	—	2	1	no	—
147	C₂²×C₁₃₇	—	2	1	no	—
148	C₂²×C₁₃₇	—	2	4	no	—
149	C₂²×C₁₃₇	—	4	2	no	—
150	C₂²×C₁₃₇	—	4	2	no	—
151	C₂²×C₁₃₇	#520	1	1	yes	characteristic
152	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
153	C₂²×C₁₃₇	#554	1	1	yes	characteristic
154	C₄×C₁₃₇	—	2	4	no	—
155	C₄×C₁₃₇	—	2	4	no	—
156	C₄×C₁₃₇	—	4	2	no	—
157	C₄×C₁₃₇	—	4	2	no	—
158	C₄×C₁₃₇	—	8	4	no	—
159	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
161	C₄×C₁₃₇	#547	1	1	yes	characteristic
162	C₄×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
163	C₂×C₁₃₇	—	2	1	no	—
164	C₂×C₁₃₇	—	2	1	no	—
165	C₂×C₁₃₇	—	4	4	no	—
166	C₂×C₁₃₇	D₄×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₁₃₇	#3292	1	1	yes	characteristic
168	C₂×C₁₃₇	#3293	1	1	yes	characteristic
169	#22692	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₁₃₇	#22692	1	1	yes	characteristic, direct product factor, Sylow
171	C₂×#443	C₂×C₁₃₇	1	1	yes	characteristic
172	#2951	C₂×C₁₃₇	1	2	yes	—
173	#2913	C₂×C₁₃₇	1	2	yes	complemented
174	#1952	C₂×C₁₃₇	1	2	yes	complemented
175	#1859	C₂×C₁₃₇	1	4	yes	complemented
176	#1845	C₂×C₁₃₇	1	1	yes	characteristic, complemented
177	#1816	C₂×C₁₃₇	1	2	yes	complemented
178	#1772	C₂×C₁₃₇	1	1	yes	characteristic, complemented
179	C₂×#135	C₂²×C₁₃₇	1	1	yes	characteristic
180	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
181	#520	C₂²×C₁₃₇	1	4	yes	—
182	#443	C₄×C₁₃₇	1	8	yes	complemented
183	#440	—	2	4	no	—
184	C₄×Q₁₆	—	2	2	no	—
185	C₄×D₈	—	2	2	no	—
186	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
187	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
188	#428	—	2	4	no	—
189	#428	C₂²×C₁₃₇	1	4	yes	—
190	#427	—	2	2	no	—
191	#427	C₂²×C₁₃₇	1	1	yes	characteristic
192	C₂×#107	—	2	2	no	—
193	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
194	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
195	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
196	#417	C₂²×C₁₃₇	1	4	yes	—
197	#405	C₂²×C₁₃₇	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	#384	C₂²×C₁₃₇	1	2	yes	—
200	#343	C₂²×C₁₃₇	1	4	yes	—
201	#339	C₂²×C₁₃₇	1	2	yes	—
202	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
203	#135	C₂×C₄×C₁₃₇	1	4	yes	—
204	#135	Q₈×C₁₃₇	1	4	yes	—
205	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
206	C₂×SD₁₆	D₄×C₁₃₇	1	2	yes	—
207	C₂×D₈	D₄×C₁₃₇	1	1	yes	characteristic
208	#131	—	2	4	no	—
209	#131	C₂×C₄×C₁₃₇	1	8	yes	complemented
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
212	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
216	C₄×Q₈	—	2	4	no	—
217	C₄×D₄	—	2	4	no	—
218	C₄×D₄	—	4	4	no	—
219	#117	—	2	4	no	—
220	#117	C₂³×C₁₃₇	1	2	yes	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	4	2	no	—
223	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
224	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
225	#108	—	2	2	no	—
226	#108	C₂×C₄×C₁₃₇	1	4	yes	complemented
227	#107	—	2	2	no	—
228	#107	—	2	2	no	—
229	#107	—	2	2	no	—
230	#107	—	2	2	no	—
231	#107	—	2	4	no	—
232	#107	D₄×C₁₃₇	1	1	yes	characteristic
233	#107	D₄×C₁₃₇	1	1	yes	characteristic
234	#106	—	2	4	no	—
235	#106	D₄×C₁₃₇	1	2	yes	—
236	#104	C₂×C₄×C₁₃₇	1	8	yes	complemented
237	#103	—	2	4	no	—
238	#102	—	2	4	no	—
239	#97	—	2	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
242	#41	—	2	2	no	—
243	#41	—	2	2	no	—
244	#41	C₂²×C₄×C₁₃₇	1	4	yes	—
245	#41	C₂×Q₈×C₁₃₇	1	4	yes	—
246	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
254	Q₁₆	C₄⋊C₄×C₁₃₇	1	4	yes	complemented
255	SD₁₆	C₄⋊C₄×C₁₃₇	1	8	yes	complemented
256	D₈	C₄⋊C₄×C₁₃₇	1	4	yes	complemented
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	8	no	—
259	M₁₆	—	2	2	no	—
260	M₁₆	—	2	2	no	—
261	M₁₆	C₂²×C₄×C₁₃₇	1	4	yes	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	8	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
266	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
267	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
268	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
269	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
270	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
271	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
272	C₂×C₈	#41×C₁₃₇	1	2	yes	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	8	4	no	—
277	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
278	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	4	4	no	—
284	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	Q₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
289	D₄	—	2	4	no	—
290	D₄	—	2	4	no	—
291	D₄	—	2	2	no	—
292	D₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	8	4	no	—
303	C₂×C₄	—	16	4	no	—
304	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
309	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
310	C₈	—	2	4	no	—
311	C₈	—	4	2	no	—
312	C₈	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
313	C₈	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
314	C₈	C₄×D₄×C₁₃₇	1	2	yes	—
315	C₈	C₄×D₄×C₁₃₇	1	2	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	#520×C₁₃₇	1	1	yes	characteristic
322	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
323	C₂²	#554×C₁₃₇	1	1	yes	characteristic
324	C₄	—	2	4	no	—
325	C₄	—	2	4	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	—	8	4	no	—
329	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
330	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
331	C₄	#547×C₁₃₇	1	1	yes	characteristic
332	C₄	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
333	C₂	—	2	1	no	—
334	C₂	—	2	1	no	—
335	C₂	—	4	4	no	—
336	C₂	D₄×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
337	C₂	#3292×C₁₃₇	1	1	yes	characteristic
338	C₂	#3293×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#135×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2913×C₁₃₇	C₂	semidirect
4. #1952×C₁₃₇	C₂	semidirect
5. #1859×C₁₃₇	C₂	semidirect
6. #1845×C₁₃₇	C₂	semidirect
7. #1816×C₁₃₇	C₂	semidirect
8. #1772×C₁₃₇	C₂	semidirect
12. #443×C₁₃₇	C₄	semidirect
39. #131×C₁₃₇	C₂×C₄	semidirect
56. #108×C₁₃₇	C₂×C₄	semidirect
66. #104×C₁₃₇	C₂×C₄	semidirect
71. C₄×C₈×C₁₃₇	C₂×C₄	semidirect
84. Q₁₆×C₁₃₇	C₄⋊C₄	semidirect
85. SD₁₆×C₁₃₇	C₄⋊C₄	semidirect
86. D₈×C₁₃₇	C₄⋊C₄	semidirect
169. #22692	C₁₃₇	direct (N × H)
170. C₁₃₇	#22692	direct (N × H)
173. #2913	C₂×C₁₃₇	semidirect
174. #1952	C₂×C₁₃₇	semidirect
175. #1859	C₂×C₁₃₇	semidirect
176. #1845	C₂×C₁₃₇	semidirect
177. #1816	C₂×C₁₃₇	semidirect
178. #1772	C₂×C₁₃₇	semidirect
182. #443	C₄×C₁₃₇	semidirect
209. #131	C₂×C₄×C₁₃₇	semidirect
226. #108	C₂×C₄×C₁₃₇	semidirect
236. #104	C₂×C₄×C₁₃₇	semidirect
241. C₄×C₈	C₂×C₄×C₁₃₇	semidirect
254. Q₁₆	C₄⋊C₄×C₁₃₇	semidirect
255. SD₁₆	C₄⋊C₄×C₁₃₇	semidirect
256. D₈	C₄⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#443×C₁₃₇	2
#2951×C₁₃₇	2
#2913×C₁₃₇	2
#1952×C₁₃₇	2
#1859×C₁₃₇	2
#1845×C₁₃₇	2
#1816×C₁₃₇	2
#1772×C₁₃₇	2
#22692	137

Subgroups — C137×#22692 #46872078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22692 #46872078