Subgroups — C₁₃₇×#22828 #46872214

Order 35072.

764 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	C₄²×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1984×C₁₃₇	C₂	1	2	yes	maximal
3	#1916×C₁₃₇	C₂	1	4	yes	maximal
4	#1839×C₁₃₇	C₂	1	2	yes	maximal
5	#1831×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄⋊C₄×C₁₃₇	C₂	1	2	yes	maximal
7	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1744×C₁₃₇	C₂	1	2	yes	maximal
9	C₂×C₄×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃₇	C₂²	1	4	yes	—
16	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
18	C₄×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
19	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
22	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₄³×C₁₃₇	C₂²	1	2	yes	—
24	#336×C₁₃₇	C₂²	1	1	yes	characteristic
25	#336×C₁₃₇	C₂²	1	1	yes	characteristic
26	#336×C₁₃₇	C₂²	1	4	yes	—
27	#336×C₁₃₇	C₂²	1	2	yes	—
28	#336×C₁₃₇	C₂²	1	2	yes	—
29	#336×C₁₃₇	C₂²	1	4	yes	—
30	#336×C₁₃₇	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
35	C₄×Q₈×C₁₃₇	—	2	4	no	—
36	C₄×Q₈×C₁₃₇	—	2	2	no	—
37	C₄×Q₈×C₁₃₇	—	2	2	no	—
38	C₄×Q₈×C₁₃₇	C₈	1	8	yes	complemented
39	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₁₃₇	—	2	4	no	—
59	C₄⋊C₈×C₁₃₇	—	2	4	no	—
60	C₄×C₈×C₁₃₇	—	2	8	no	—
61	C₄×C₈×C₁₃₇	—	2	4	no	—
62	#95×C₁₃₇	C₂×C₄	1	2	yes	—
63	#95×C₁₃₇	C₂×C₄	1	2	yes	—
64	#95×C₁₃₇	C₂×C₄	1	2	yes	—
65	C₂×Q₈×C₁₃₇	—	2	2	no	—
66	C₂×Q₈×C₁₃₇	—	2	2	no	—
67	C₂×Q₈×C₁₃₇	C₂×C₈	1	4	yes	—
68	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₁₃₇	—	2	2	no	—
80	C₂×C₈×C₁₃₇	—	2	2	no	—
81	C₂×C₈×C₁₃₇	—	2	2	no	—
82	C₂×C₈×C₁₃₇	—	2	4	no	—
83	C₂×C₈×C₁₃₇	—	2	2	no	—
84	C₂×C₈×C₁₃₇	—	2	4	no	—
85	C₂×C₈×C₁₃₇	—	2	2	no	—
86	C₂×C₈×C₁₃₇	—	2	4	no	—
87	C₂×C₈×C₁₃₇	#41	1	4	yes	—
88	C₄⋊C₄×C₁₃₇	—	2	4	no	—
89	C₄⋊C₄×C₁₃₇	—	2	2	no	—
90	C₄⋊C₄×C₁₃₇	—	2	4	no	—
91	C₄⋊C₄×C₁₃₇	C₂×C₈	1	8	yes	—
92	C₄⋊C₄×C₁₃₇	C₂×C₈	1	4	yes	—
93	C₄⋊C₄×C₁₃₇	M₁₆	1	4	yes	—
94	C₄²×C₁₃₇	—	2	4	no	—
95	C₄²×C₁₃₇	—	2	2	no	—
96	C₄²×C₁₃₇	—	2	2	no	—
97	C₄²×C₁₃₇	—	2	4	no	—
98	C₄²×C₁₃₇	—	2	4	no	—
99	C₄²×C₁₃₇	—	2	2	no	—
100	C₄²×C₁₃₇	—	2	2	no	—
101	C₄²×C₁₃₇	—	2	2	no	—
102	C₄²×C₁₃₇	—	2	2	no	—
103	C₄²×C₁₃₇	—	4	1	no	—
104	C₄²×C₁₃₇	—	4	2	no	—
105	C₄²×C₁₃₇	C₂×C₈	1	8	yes	—
106	C₄²×C₁₃₇	C₂×C₈	1	4	yes	—
107	C₄²×C₁₃₇	#41	1	2	yes	—
108	C₄²×C₁₃₇	#41	1	2	yes	—
109	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
110	Q₈×C₁₃₇	—	2	8	no	—
111	C₂×C₄×C₁₃₇	—	2	2	no	—
112	C₂×C₄×C₁₃₇	—	2	2	no	—
113	C₂×C₄×C₁₃₇	—	2	1	no	—
114	C₂×C₄×C₁₃₇	—	2	2	no	—
115	C₂×C₄×C₁₃₇	—	2	1	no	—
116	C₂×C₄×C₁₃₇	—	2	1	no	—
117	C₂×C₄×C₁₃₇	—	2	1	no	—
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	1	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	—	2	1	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	1	no	—
127	C₂×C₄×C₁₃₇	—	2	1	no	—
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	1	no	—
131	C₂×C₄×C₁₃₇	#117	1	2	yes	—
132	C₂×C₄×C₁₃₇	#117	1	2	yes	—
133	C₂×C₄×C₁₃₇	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₁₃₇	C₂²×C₈	1	4	yes	—
135	C₂×C₄×C₁₃₇	C₂²×C₈	1	2	yes	—
136	C₂×C₄×C₁₃₇	C₂²×C₈	1	4	yes	—
137	C₂×C₄×C₁₃₇	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
139	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₁₃₇	#131	1	2	yes	—
141	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
143	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
145	C₈×C₁₃₇	—	2	4	no	—
146	C₈×C₁₃₇	—	4	2	no	—
147	C₈×C₁₃₇	—	4	4	no	—
148	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
149	C₂²×C₁₃₇	C₄×#41	1	1	yes	characteristic
150	C₂²×C₁₃₇	#519	1	1	yes	characteristic
151	C₂²×C₁₃₇	C₂³×C₈	1	1	yes	characteristic
152	C₂²×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
153	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
154	C₂²×C₁₃₇	#568	1	1	yes	characteristic
155	C₄×C₁₃₇	—	2	4	no	—
156	C₄×C₁₃₇	—	2	2	no	—
157	C₄×C₁₃₇	—	2	4	no	—
158	C₄×C₁₃₇	—	2	2	no	—
159	C₄×C₁₃₇	—	2	4	no	—
160	C₄×C₁₃₇	—	2	2	no	—
161	C₄×C₁₃₇	—	2	2	no	—
162	C₄×C₁₃₇	—	4	2	no	—
163	C₄×C₁₃₇	—	4	1	no	—
164	C₄×C₁₃₇	#431	1	4	yes	—
165	C₄×C₁₃₇	#552	1	2	yes	—
166	C₄×C₁₃₇	#556	1	2	yes	—
167	C₂×C₁₃₇	#2356	1	1	yes	characteristic
168	C₂×C₁₃₇	C₂×#431	1	1	yes	characteristic
169	C₂×C₁₃₇	#2925	1	1	yes	characteristic
170	C₂×C₁₃₇	C₈×#41	1	1	yes	characteristic
171	C₂×C₁₃₇	#2970	1	1	yes	characteristic
172	C₂×C₁₃₇	#2982	1	1	yes	characteristic
173	C₂×C₁₃₇	#2984	1	1	yes	characteristic
174	#22828	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₃₇	#22828	1	1	yes	characteristic, direct product factor, Sylow
176	C₄²×Q₈	C₂×C₁₃₇	1	1	yes	characteristic
177	#1984	C₂×C₁₃₇	1	2	yes	—
178	#1916	C₂×C₁₃₇	1	4	yes	—
179	#1839	C₂×C₁₃₇	1	2	yes	—
180	#1831	C₂×C₁₃₇	1	1	yes	characteristic
181	C₈×C₄⋊C₄	C₂×C₁₃₇	1	2	yes	—
182	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
183	#1744	C₂×C₁₃₇	1	2	yes	—
184	C₂×C₄×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
185	C₂×C₄×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
186	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₁₃₇	1	4	yes	—
190	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
191	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
194	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
195	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
196	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₄³	C₂²×C₁₃₇	1	2	yes	—
199	#336	C₂²×C₁₃₇	1	2	yes	—
200	#336	C₂²×C₁₃₇	1	2	yes	—
201	#336	C₂²×C₁₃₇	1	1	yes	characteristic
202	#336	C₂²×C₁₃₇	1	4	yes	—
203	#336	C₂²×C₁₃₇	1	4	yes	—
204	#336	C₂²×C₁₃₇	1	4	yes	—
205	#336	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂²×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
209	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
210	C₄×Q₈	—	2	4	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	—	2	2	no	—
213	C₄×Q₈	C₈×C₁₃₇	1	8	yes	complemented
214	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
231	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
233	C₄⋊C₈	—	2	4	no	—
234	C₄⋊C₈	—	2	4	no	—
235	C₄×C₈	—	2	8	no	—
236	C₄×C₈	—	2	4	no	—
237	#95	C₂×C₄×C₁₃₇	1	2	yes	—
238	#95	C₂×C₄×C₁₃₇	1	2	yes	—
239	#95	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	C₂×C₈×C₁₃₇	1	4	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	#41×C₁₃₇	1	4	yes	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	C₂×C₈×C₁₃₇	1	8	yes	—
267	C₄⋊C₄	C₂×C₈×C₁₃₇	1	4	yes	—
268	C₄⋊C₄	M₁₆×C₁₃₇	1	4	yes	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	4	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	2	no	—
280	C₄²	C₂×C₈×C₁₃₇	1	8	yes	—
281	C₄²	C₂×C₈×C₁₃₇	1	4	yes	—
282	C₄²	#41×C₁₃₇	1	2	yes	—
283	C₄²	#41×C₁₃₇	1	2	yes	—
284	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
285	Q₈	—	2	8	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	#117×C₁₃₇	1	2	yes	—
307	C₂×C₄	#117×C₁₃₇	1	2	yes	—
308	C₂×C₄	C₂²×C₈×C₁₃₇	1	2	yes	—
309	C₂×C₄	C₂²×C₈×C₁₃₇	1	4	yes	—
310	C₂×C₄	C₂²×C₈×C₁₃₇	1	2	yes	—
311	C₂×C₄	C₂²×C₈×C₁₃₇	1	4	yes	—
312	C₂×C₄	C₂²×C₈×C₁₃₇	1	2	yes	—
313	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
314	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
315	C₂×C₄	#131×C₁₃₇	1	2	yes	—
316	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
318	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
320	C₈	—	2	4	no	—
321	C₈	—	4	2	no	—
322	C₈	—	4	4	no	—
323	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
324	C₂²	C₄×#41×C₁₃₇	1	1	yes	characteristic
325	C₂²	#519×C₁₃₇	1	1	yes	characteristic
326	C₂²	C₂³×C₈×C₁₃₇	1	1	yes	characteristic
327	C₂²	C₂²×M₁₆×C₁₃₇	1	1	yes	characteristic
328	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
329	C₂²	#568×C₁₃₇	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	1	no	—
339	C₄	#431×C₁₃₇	1	4	yes	—
340	C₄	#552×C₁₃₇	1	2	yes	—
341	C₄	#556×C₁₃₇	1	2	yes	—
342	C₂	#2356×C₁₃₇	1	1	yes	characteristic
343	C₂	C₂×#431×C₁₃₇	1	1	yes	characteristic
344	C₂	#2925×C₁₃₇	1	1	yes	characteristic
345	C₂	C₈×#41×C₁₃₇	1	1	yes	characteristic
346	C₂	#2970×C₁₃₇	1	1	yes	characteristic
347	C₂	#2982×C₁₃₇	1	1	yes	characteristic
348	C₂	#2984×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle, prime radical	C₂³×C₁₃₇	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
38. C₄×Q₈×C₁₃₇	C₈	semidirect
174. #22828	C₁₃₇	direct (N × H)
175. C₁₃₇	#22828	direct (N × H)
213. C₄×Q₈	C₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₁₃₇	2
#1984×C₁₃₇	2
#1916×C₁₃₇	2
#1839×C₁₃₇	2
#1831×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1744×C₁₃₇	2
#22828	137

Subgroups — C137×#22828 #46872214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22828 #46872214