Subgroups — C₁₃₇×#22823 #46872209

Order 35072.

736 conjugacy classes of subgroups.

The subgroup lattice has 494 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	#1985×C₁₃₇	C₂	1	2	yes	maximal
3	#1917×C₁₃₇	C₂	1	2	yes	maximal
4	#1916×C₁₃₇	C₂	1	2	yes	maximal
5	#1842×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1831×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1831×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1771×C₁₃₇	C₂	1	2	yes	maximal
9	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
36	#336×C₁₃₇	C₂²	1	2	yes	—
37	#336×C₁₃₇	C₂²	1	2	yes	—
38	#336×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	#336×C₁₃₇	C₂²	1	2	yes	—
42	#336×C₁₃₇	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₄×Q₈×C₁₃₇	—	2	4	no	—
49	C₄×Q₈×C₁₃₇	—	2	4	no	—
50	C₄×Q₈×C₁₃₇	—	2	2	no	—
51	C₄×Q₈×C₁₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₁₃₇	—	2	4	no	—
81	C₄⋊C₈×C₁₃₇	—	2	2	no	—
82	C₄⋊C₈×C₁₃₇	—	2	2	no	—
83	C₄⋊C₈×C₁₃₇	—	2	2	no	—
84	C₄⋊C₈×C₁₃₇	—	4	2	no	—
85	C₄⋊C₈×C₁₃₇	Q₈	1	4	yes	complemented
86	#97×C₁₃₇	—	2	4	no	—
87	#97×C₁₃₇	—	4	2	no	—
88	C₄×C₈×C₁₃₇	—	4	2	no	—
89	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
90	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
91	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
92	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
93	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
94	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	2	no	—
129	C₄⋊C₄×C₁₃₇	—	2	2	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	M₁₆	1	4	yes	—
134	C₄²×C₁₃₇	—	2	2	no	—
135	C₄²×C₁₃₇	—	2	2	no	—
136	C₄²×C₁₃₇	—	2	2	no	—
137	C₄²×C₁₃₇	—	2	2	no	—
138	C₄²×C₁₃₇	—	2	2	no	—
139	C₄²×C₁₃₇	—	2	2	no	—
140	C₄²×C₁₃₇	—	2	2	no	—
141	C₄²×C₁₃₇	—	2	2	no	—
142	C₄²×C₁₃₇	—	2	1	no	—
143	C₄²×C₁₃₇	—	2	1	no	—
144	C₄²×C₁₃₇	—	2	1	no	—
145	C₄²×C₁₃₇	—	2	1	no	—
146	C₄²×C₁₃₇	—	2	1	no	—
147	C₄²×C₁₃₇	—	2	1	no	—
148	C₄²×C₁₃₇	—	2	1	no	—
149	C₄²×C₁₃₇	—	2	1	no	—
150	C₄²×C₁₃₇	—	2	1	no	—
151	C₄²×C₁₃₇	—	2	1	no	—
152	C₄²×C₁₃₇	—	4	1	no	—
153	C₄²×C₁₃₇	—	4	1	no	—
154	C₄²×C₁₃₇	—	4	1	no	—
155	C₄²×C₁₃₇	M₁₆	1	4	yes	—
156	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
157	C₄²×C₁₃₇	#41	1	2	yes	—
158	C₄²×C₁₃₇	#41	1	2	yes	—
159	C₄²×C₁₃₇	#41	1	2	yes	—
160	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₁₃₇	—	2	8	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	2	1	no	—
165	C₂×C₄×C₁₃₇	—	2	1	no	—
166	C₂×C₄×C₁₃₇	—	2	1	no	—
167	C₂×C₄×C₁₃₇	—	2	1	no	—
168	C₂×C₄×C₁₃₇	—	2	1	no	—
169	C₂×C₄×C₁₃₇	—	2	1	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	1	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	1	no	—
174	C₂×C₄×C₁₃₇	—	2	1	no	—
175	C₂×C₄×C₁₃₇	—	2	1	no	—
176	C₂×C₄×C₁₃₇	—	2	1	no	—
177	C₂×C₄×C₁₃₇	—	2	1	no	—
178	C₂×C₄×C₁₃₇	—	2	1	no	—
179	C₂×C₄×C₁₃₇	—	2	1	no	—
180	C₂×C₄×C₁₃₇	—	2	1	no	—
181	C₂×C₄×C₁₃₇	—	2	1	no	—
182	C₂×C₄×C₁₃₇	—	2	1	no	—
183	C₂×C₄×C₁₃₇	—	2	1	no	—
184	C₂×C₄×C₁₃₇	—	2	1	no	—
185	C₂×C₄×C₁₃₇	—	2	1	no	—
186	C₂×C₄×C₁₃₇	—	2	1	no	—
187	C₂×C₄×C₁₃₇	—	2	1	no	—
188	C₂×C₄×C₁₃₇	—	2	1	no	—
189	C₂×C₄×C₁₃₇	—	2	1	no	—
190	C₂×C₄×C₁₃₇	—	2	1	no	—
191	C₂×C₄×C₁₃₇	—	2	1	no	—
192	C₂×C₄×C₁₃₇	—	2	1	no	—
193	C₂×C₄×C₁₃₇	#117	1	2	yes	—
194	C₂×C₄×C₁₃₇	#117	1	2	yes	—
195	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
197	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
200	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
202	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
203	C₂×C₄×C₁₃₇	#131	1	2	yes	—
204	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₃₇	—	2	4	no	—
211	C₈×C₁₃₇	—	4	2	no	—
212	C₈×C₁₃₇	—	4	2	no	—
213	C₈×C₁₃₇	—	4	2	no	—
214	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
215	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
216	C₂²×C₁₃₇	#520	1	1	yes	characteristic
217	C₂²×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
218	C₂²×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
219	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
220	C₂²×C₁₃₇	#568	1	1	yes	characteristic
221	C₄×C₁₃₇	—	2	2	no	—
222	C₄×C₁₃₇	—	2	2	no	—
223	C₄×C₁₃₇	—	2	2	no	—
224	C₄×C₁₃₇	—	2	2	no	—
225	C₄×C₁₃₇	—	2	2	no	—
226	C₄×C₁₃₇	—	2	2	no	—
227	C₄×C₁₃₇	—	2	2	no	—
228	C₄×C₁₃₇	—	2	2	no	—
229	C₄×C₁₃₇	—	4	1	no	—
230	C₄×C₁₃₇	—	4	1	no	—
231	C₄×C₁₃₇	—	4	1	no	—
232	C₄×C₁₃₇	—	4	1	no	—
233	C₄×C₁₃₇	—	4	1	no	—
234	C₄×C₁₃₇	#446	1	4	yes	—
235	C₄×C₁₃₇	#554	1	1	yes	characteristic
236	C₄×C₁₃₇	#556	1	1	yes	characteristic
237	C₄×C₁₃₇	#557	1	1	yes	characteristic
238	C₄×C₁₃₇	#559	1	1	yes	characteristic
239	C₂×C₁₃₇	#2355	1	1	yes	characteristic
240	C₂×C₁₃₇	#2920	1	1	yes	characteristic
241	C₂×C₁₃₇	#2925	1	1	yes	characteristic
242	C₂×C₁₃₇	C₂×#446	1	1	yes	characteristic
243	C₂×C₁₃₇	Q₈×M₁₆	1	1	yes	characteristic
244	C₂×C₁₃₇	#2989	1	1	yes	characteristic
245	C₂×C₁₃₇	#2990	1	1	yes	characteristic
246	#22823	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₃₇	#22823	1	1	yes	characteristic, direct product factor, Sylow
248	C₄²×Q₈	C₂×C₁₃₇	1	1	yes	characteristic
249	#1985	C₂×C₁₃₇	1	2	yes	—
250	#1917	C₂×C₁₃₇	1	2	yes	—
251	#1916	C₂×C₁₃₇	1	2	yes	—
252	#1842	C₂×C₁₃₇	1	1	yes	characteristic
253	#1831	C₂×C₁₃₇	1	1	yes	characteristic
254	#1831	C₂×C₁₃₇	1	1	yes	characteristic
255	#1771	C₂×C₁₃₇	1	2	yes	—
256	#1767	C₂×C₁₃₇	1	1	yes	characteristic
257	#1767	C₂×C₁₃₇	1	1	yes	characteristic
258	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
268	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
269	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
271	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
283	#336	C₂²×C₁₃₇	1	2	yes	—
284	#336	C₂²×C₁₃₇	1	2	yes	—
285	#336	C₂²×C₁₃₇	1	2	yes	—
286	#336	C₂²×C₁₃₇	1	2	yes	—
287	#336	C₂²×C₁₃₇	1	2	yes	—
288	#336	C₂²×C₁₃₇	1	2	yes	—
289	#336	C₂²×C₁₃₇	1	2	yes	—
290	C₂²×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₄⋊C₈	—	2	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	4	2	no	—
332	C₄⋊C₈	Q₈×C₁₃₇	1	4	yes	complemented
333	#97	—	2	4	no	—
334	#97	—	4	2	no	—
335	C₄×C₈	—	4	2	no	—
336	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
337	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
338	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
339	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
340	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
341	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	M₁₆×C₁₃₇	1	4	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	M₁₆×C₁₃₇	1	4	yes	—
403	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
404	C₄²	#41×C₁₃₇	1	2	yes	—
405	C₄²	#41×C₁₃₇	1	2	yes	—
406	C₄²	#41×C₁₃₇	1	2	yes	—
407	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
408	Q₈	—	2	8	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	#117×C₁₃₇	1	2	yes	—
441	C₂×C₄	#117×C₁₃₇	1	2	yes	—
442	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
443	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
444	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
445	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
446	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
447	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
448	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
449	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
450	C₂×C₄	#131×C₁₃₇	1	2	yes	—
451	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
456	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
462	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
463	C₂²	#520×C₁₃₇	1	1	yes	characteristic
464	C₂²	C₂²×M₁₆×C₁₃₇	1	1	yes	characteristic
465	C₂²	C₂²×M₁₆×C₁₃₇	1	1	yes	characteristic
466	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
467	C₂²	#568×C₁₃₇	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	#446×C₁₃₇	1	4	yes	—
482	C₄	#554×C₁₃₇	1	1	yes	characteristic
483	C₄	#556×C₁₃₇	1	1	yes	characteristic
484	C₄	#557×C₁₃₇	1	1	yes	characteristic
485	C₄	#559×C₁₃₇	1	1	yes	characteristic
486	C₂	#2355×C₁₃₇	1	1	yes	characteristic
487	C₂	#2920×C₁₃₇	1	1	yes	characteristic
488	C₂	#2925×C₁₃₇	1	1	yes	characteristic
489	C₂	C₂×#446×C₁₃₇	1	1	yes	characteristic
490	C₂	Q₈×M₁₆×C₁₃₇	1	1	yes	characteristic
491	C₂	#2989×C₁₃₇	1	1	yes	characteristic
492	C₂	#2990×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
85. C₄⋊C₈×C₁₃₇	Q₈	semidirect
246. #22823	C₁₃₇	direct (N × H)
247. C₁₃₇	#22823	direct (N × H)
332. C₄⋊C₈	Q₈×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
#1985×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1842×C₁₃₇	2
#1831×C₁₃₇	2
#1771×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#22823	137

Subgroups — C137×#22823 #46872209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22823 #46872209