Subgroups — C₁₃₇×#34816 #46884202

Order 35072.

1918 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2514×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#2513×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2512×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2511×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2510×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#2481×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#2401×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₄×#126×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	#2297×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#2297×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#2297×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₃₇	C₂²	1	4	yes	—
18	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
25	#401×C₁₃₇	C₂²	1	4	yes	—
26	#400×C₁₃₇	C₂²	1	4	yes	—
27	#400×C₁₃₇	C₂²	1	4	yes	—
28	#400×C₁₃₇	C₂²	1	4	yes	—
29	#397×C₁₃₇	C₂²	1	4	yes	—
30	#397×C₁₃₇	C₂²	1	4	yes	—
31	#397×C₁₃₇	C₂²	1	4	yes	—
32	#396×C₁₃₇	C₂²	1	4	yes	—
33	#391×C₁₃₇	C₂²	1	1	yes	characteristic
34	#391×C₁₃₇	C₂²	1	2	yes	—
35	#391×C₁₃₇	C₂²	1	2	yes	—
36	#391×C₁₃₇	C₂²	1	1	yes	characteristic
37	#390×C₁₃₇	C₂²	1	1	yes	characteristic
38	#390×C₁₃₇	C₂²	1	2	yes	—
39	#390×C₁₃₇	C₂²	1	2	yes	—
40	#390×C₁₃₇	C₂²	1	1	yes	characteristic
41	#389×C₁₃₇	C₂²	1	2	yes	—
42	#389×C₁₃₇	C₂²	1	2	yes	—
43	#388×C₁₃₇	C₂²	1	4	yes	—
44	#388×C₁₃₇	C₂²	1	4	yes	—
45	#388×C₁₃₇	C₂²	1	4	yes	—
46	#387×C₁₃₇	C₂²	1	4	yes	—
47	#387×C₁₃₇	C₂²	1	4	yes	—
48	#387×C₁₃₇	C₂²	1	4	yes	—
49	#386×C₁₃₇	C₂²	1	2	yes	—
50	#386×C₁₃₇	C₂²	1	4	yes	—
51	#386×C₁₃₇	C₂²	1	4	yes	—
52	#386×C₁₃₇	C₂²	1	2	yes	—
53	#385×C₁₃₇	C₂²	1	2	yes	—
54	#385×C₁₃₇	C₂²	1	2	yes	—
55	#384×C₁₃₇	C₂²	1	2	yes	—
56	#383×C₁₃₇	C₂²	1	4	yes	—
57	#382×C₁₃₇	C₂²	1	2	yes	—
58	#380×C₁₃₇	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
66	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
72	#376×C₁₃₇	C₂²	1	2	yes	—
73	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
74	C₄³×C₁₃₇	C₂²	1	2	yes	—
75	C₂×#41×C₁₃₇	—	2	4	no	—
76	C₂×#41×C₁₃₇	—	2	4	no	—
77	C₂×#41×C₁₃₇	—	2	4	no	—
78	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
87	#126×C₁₃₇	—	2	16	no	—
88	#117×C₁₃₇	—	2	4	no	—
89	#117×C₁₃₇	—	2	4	no	—
90	#117×C₁₃₇	—	2	4	no	—
91	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
92	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃₇	—	2	4	no	—
114	C₂×C₄²×C₁₃₇	—	2	4	no	—
115	C₂×C₄²×C₁₃₇	—	2	4	no	—
116	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
129	#95×C₁₃₇	C₂³	1	2	yes	—
130	#95×C₁₃₇	C₂³	1	2	yes	—
131	#95×C₁₃₇	C₂³	1	2	yes	—
132	#95×C₁₃₇	C₂³	1	2	yes	—
133	#95×C₁₃₇	C₂³	1	4	yes	—
134	#95×C₁₃₇	C₂³	1	4	yes	—
135	#95×C₁₃₇	C₂³	1	4	yes	—
136	#95×C₁₃₇	C₂³	1	4	yes	—
137	#95×C₁₃₇	C₂³	1	4	yes	—
138	#95×C₁₃₇	C₂³	1	4	yes	—
139	#95×C₁₃₇	C₂³	1	4	yes	—
140	#95×C₁₃₇	C₂³	1	4	yes	—
141	#95×C₁₃₇	C₂³	1	4	yes	—
142	#95×C₁₃₇	C₂³	1	4	yes	—
143	#95×C₁₃₇	C₂³	1	4	yes	—
144	#95×C₁₃₇	C₂³	1	4	yes	—
145	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
147	#41×C₁₃₇	—	4	16	no	—
148	C₂×Q₈×C₁₃₇	—	2	2	no	—
149	C₂×Q₈×C₁₃₇	—	2	2	no	—
150	C₂×Q₈×C₁₃₇	—	2	2	no	—
151	C₂×D₄×C₁₃₇	—	2	4	no	—
152	C₂×D₄×C₁₃₇	—	2	4	no	—
153	C₂×D₄×C₁₃₇	—	2	4	no	—
154	C₂×D₄×C₁₃₇	—	2	2	no	—
155	C₂×D₄×C₁₃₇	—	2	2	no	—
156	C₂×D₄×C₁₃₇	—	2	2	no	—
157	C₂²×C₄×C₁₃₇	—	2	2	no	—
158	C₂²×C₄×C₁₃₇	—	2	4	no	—
159	C₂²×C₄×C₁₃₇	—	2	4	no	—
160	C₂²×C₄×C₁₃₇	—	2	4	no	—
161	C₂²×C₄×C₁₃₇	—	2	2	no	—
162	C₂²×C₄×C₁₃₇	—	2	4	no	—
163	C₂²×C₄×C₁₃₇	—	2	4	no	—
164	C₂²×C₄×C₁₃₇	—	2	4	no	—
165	C₂²×C₄×C₁₃₇	—	2	4	no	—
166	C₂²×C₄×C₁₃₇	—	2	4	no	—
167	C₂²×C₄×C₁₃₇	—	4	2	no	—
168	C₂²×C₄×C₁₃₇	—	4	2	no	—
169	C₂²×C₄×C₁₃₇	—	4	2	no	—
170	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
171	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
172	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
173	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₁₃₇	—	2	4	no	—
187	C₄⋊C₄×C₁₃₇	—	2	4	no	—
188	C₄⋊C₄×C₁₃₇	—	2	4	no	—
189	C₄⋊C₄×C₁₃₇	—	2	2	no	—
190	C₄⋊C₄×C₁₃₇	—	2	2	no	—
191	C₄⋊C₄×C₁₃₇	—	2	4	no	—
192	C₄⋊C₄×C₁₃₇	—	2	4	no	—
193	C₄⋊C₄×C₁₃₇	—	2	8	no	—
194	C₄⋊C₄×C₁₃₇	—	2	8	no	—
195	C₄⋊C₄×C₁₃₇	—	4	4	no	—
196	C₄⋊C₄×C₁₃₇	—	4	4	no	—
197	C₄⋊C₄×C₁₃₇	#41	1	8	yes	complemented
198	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
199	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
200	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
201	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
202	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
203	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
204	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
205	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
207	C₄²×C₁₃₇	—	2	2	no	—
208	C₄²×C₁₃₇	—	2	2	no	—
209	C₄²×C₁₃₇	—	2	4	no	—
210	C₄²×C₁₃₇	—	2	4	no	—
211	C₄²×C₁₃₇	—	2	4	no	—
212	C₄²×C₁₃₇	—	2	4	no	—
213	C₄²×C₁₃₇	—	2	2	no	—
214	C₄²×C₁₃₇	—	2	2	no	—
215	C₄²×C₁₃₇	—	2	4	no	—
216	C₄²×C₁₃₇	—	2	4	no	—
217	C₄²×C₁₃₇	—	2	4	no	—
218	C₄²×C₁₃₇	—	2	8	no	—
219	C₄²×C₁₃₇	—	4	4	no	—
220	C₂³×C₁₃₇	—	2	2	no	—
221	C₂³×C₁₃₇	—	2	2	no	—
222	C₂³×C₁₃₇	—	2	4	no	—
223	C₂³×C₁₃₇	—	2	2	no	—
224	C₂³×C₁₃₇	—	2	2	no	—
225	C₂³×C₁₃₇	—	2	2	no	—
226	C₂³×C₁₃₇	—	2	4	no	—
227	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
228	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
229	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
230	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
231	Q₈×C₁₃₇	—	4	4	no	—
232	D₄×C₁₃₇	—	4	8	no	—
233	D₄×C₁₃₇	—	4	4	no	—
234	C₂×C₄×C₁₃₇	—	2	8	no	—
235	C₂×C₄×C₁₃₇	—	2	2	no	—
236	C₂×C₄×C₁₃₇	—	2	2	no	—
237	C₂×C₄×C₁₃₇	—	2	2	no	—
238	C₂×C₄×C₁₃₇	—	2	2	no	—
239	C₂×C₄×C₁₃₇	—	2	2	no	—
240	C₂×C₄×C₁₃₇	—	2	2	no	—
241	C₂×C₄×C₁₃₇	—	2	2	no	—
242	C₂×C₄×C₁₃₇	—	2	2	no	—
243	C₂×C₄×C₁₃₇	—	2	2	no	—
244	C₂×C₄×C₁₃₇	—	2	2	no	—
245	C₂×C₄×C₁₃₇	—	2	4	no	—
246	C₂×C₄×C₁₃₇	—	2	2	no	—
247	C₂×C₄×C₁₃₇	—	2	4	no	—
248	C₂×C₄×C₁₃₇	—	2	4	no	—
249	C₂×C₄×C₁₃₇	—	2	4	no	—
250	C₂×C₄×C₁₃₇	—	2	4	no	—
251	C₂×C₄×C₁₃₇	—	2	2	no	—
252	C₂×C₄×C₁₃₇	—	2	2	no	—
253	C₂×C₄×C₁₃₇	—	2	2	no	—
254	C₂×C₄×C₁₃₇	—	2	2	no	—
255	C₂×C₄×C₁₃₇	—	2	2	no	—
256	C₂×C₄×C₁₃₇	—	2	4	no	—
257	C₂×C₄×C₁₃₇	—	2	4	no	—
258	C₂×C₄×C₁₃₇	—	2	2	no	—
259	C₂×C₄×C₁₃₇	—	2	2	no	—
260	C₂×C₄×C₁₃₇	—	2	2	no	—
261	C₂×C₄×C₁₃₇	—	2	4	no	—
262	C₂×C₄×C₁₃₇	—	2	2	no	—
263	C₂×C₄×C₁₃₇	—	4	8	no	—
264	C₂×C₄×C₁₃₇	—	4	8	no	—
265	C₂×C₄×C₁₃₇	—	4	4	no	—
266	C₂×C₄×C₁₃₇	—	4	8	no	—
267	C₂×C₄×C₁₃₇	#126	1	16	yes	complemented
268	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
269	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
270	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
271	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
272	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
277	C₂²×C₁₃₇	—	2	2	no	—
278	C₂²×C₁₃₇	—	2	2	no	—
279	C₂²×C₁₃₇	—	2	4	no	—
280	C₂²×C₁₃₇	—	2	4	no	—
281	C₂²×C₁₃₇	—	4	2	no	—
282	C₂²×C₁₃₇	—	4	2	no	—
283	C₂²×C₁₃₇	—	4	2	no	—
284	C₂²×C₁₃₇	—	4	4	no	—
285	C₂²×C₁₃₇	—	4	4	no	—
286	C₂²×C₁₃₇	C₂×#126	1	4	yes	—
287	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
288	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
289	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
290	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
291	C₂²×C₁₃₇	#585	1	2	yes	—
292	C₄×C₁₃₇	—	2	4	no	—
293	C₄×C₁₃₇	—	2	4	no	—
294	C₄×C₁₃₇	—	2	4	no	—
295	C₄×C₁₃₇	—	4	2	no	—
296	C₄×C₁₃₇	—	4	2	no	—
297	C₄×C₁₃₇	—	4	2	no	—
298	C₄×C₁₃₇	—	4	2	no	—
299	C₄×C₁₃₇	—	4	2	no	—
300	C₄×C₁₃₇	—	4	2	no	—
301	C₄×C₁₃₇	—	4	4	no	—
302	C₄×C₁₃₇	—	4	4	no	—
303	C₄×C₁₃₇	C₂×#126	1	4	yes	—
304	C₄×C₁₃₇	C₂×#126	1	4	yes	—
305	C₂×C₁₃₇	—	2	4	no	—
306	C₂×C₁₃₇	—	8	2	no	—
307	C₂×C₁₃₇	C₂²×#126	1	1	yes	characteristic
308	C₂×C₁₃₇	#3444	1	1	yes	characteristic
309	C₂×C₁₃₇	#3455	1	1	yes	characteristic
310	C₂×C₁₃₇	#3475	1	2	yes	—
311	C₂×C₁₃₇	#3480	1	2	yes	—
312	#34816	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃₇	#34816	1	1	yes	characteristic, direct product factor, Sylow
314	#2514	C₂×C₁₃₇	1	2	yes	complemented
315	#2513	C₂×C₁₃₇	1	2	yes	complemented
316	#2512	C₂×C₁₃₇	1	2	yes	complemented
317	#2511	C₂×C₁₃₇	1	2	yes	complemented
318	#2510	C₂×C₁₃₇	1	4	yes	complemented
319	#2481	C₂×C₁₃₇	1	4	yes	complemented
320	#2401	C₂×C₁₃₇	1	4	yes	complemented
321	C₄×#126	C₂×C₁₃₇	1	4	yes	complemented
322	#2297	C₂×C₁₃₇	1	1	yes	characteristic
323	#2297	C₂×C₁₃₇	1	1	yes	characteristic
324	#2297	C₂×C₁₃₇	1	1	yes	characteristic
325	#2296	C₂×C₁₃₇	1	1	yes	characteristic, complemented
326	#2285	C₂×C₁₃₇	1	1	yes	characteristic, complemented
327	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
328	C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
329	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
330	C₂×#126	C₂²×C₁₃₇	1	4	yes	—
331	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
332	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
335	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
338	#401	C₂²×C₁₃₇	1	4	yes	—
339	#400	C₂²×C₁₃₇	1	4	yes	—
340	#400	C₂²×C₁₃₇	1	4	yes	—
341	#400	C₂²×C₁₃₇	1	4	yes	—
342	#397	C₂²×C₁₃₇	1	4	yes	—
343	#397	C₂²×C₁₃₇	1	4	yes	—
344	#397	C₂²×C₁₃₇	1	4	yes	—
345	#396	C₂²×C₁₃₇	1	4	yes	—
346	#391	C₂²×C₁₃₇	1	1	yes	characteristic
347	#391	C₂²×C₁₃₇	1	2	yes	—
348	#391	C₂²×C₁₃₇	1	2	yes	—
349	#391	C₂²×C₁₃₇	1	1	yes	characteristic
350	#390	C₂²×C₁₃₇	1	1	yes	characteristic
351	#390	C₂²×C₁₃₇	1	2	yes	—
352	#390	C₂²×C₁₃₇	1	2	yes	—
353	#390	C₂²×C₁₃₇	1	1	yes	characteristic
354	#389	C₂²×C₁₃₇	1	2	yes	—
355	#389	C₂²×C₁₃₇	1	2	yes	—
356	#388	C₂²×C₁₃₇	1	4	yes	—
357	#388	C₂²×C₁₃₇	1	4	yes	—
358	#388	C₂²×C₁₃₇	1	4	yes	—
359	#387	C₂²×C₁₃₇	1	4	yes	—
360	#387	C₂²×C₁₃₇	1	4	yes	—
361	#387	C₂²×C₁₃₇	1	4	yes	—
362	#386	C₂²×C₁₃₇	1	2	yes	—
363	#386	C₂²×C₁₃₇	1	4	yes	—
364	#386	C₂²×C₁₃₇	1	4	yes	—
365	#386	C₂²×C₁₃₇	1	2	yes	—
366	#385	C₂²×C₁₃₇	1	2	yes	—
367	#385	C₂²×C₁₃₇	1	2	yes	—
368	#384	C₂²×C₁₃₇	1	2	yes	—
369	#383	C₂²×C₁₃₇	1	4	yes	—
370	#382	C₂²×C₁₃₇	1	2	yes	—
371	#380	C₂²×C₁₃₇	1	4	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
384	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
385	#376	C₂²×C₁₃₇	1	2	yes	—
386	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
387	C₄³	C₂²×C₁₃₇	1	2	yes	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	—	2	4	no	—
390	C₂×#41	—	2	4	no	—
391	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
393	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
400	#126	—	2	16	no	—
401	#117	—	2	4	no	—
402	#117	—	2	4	no	—
403	#117	—	2	4	no	—
404	C₂×C₄⋊C₄	—	2	8	no	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	—	2	4	no	—
428	C₂×C₄²	—	2	4	no	—
429	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
433	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
437	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
438	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
442	#95	C₂³×C₁₃₇	1	2	yes	—
443	#95	C₂³×C₁₃₇	1	2	yes	—
444	#95	C₂³×C₁₃₇	1	2	yes	—
445	#95	C₂³×C₁₃₇	1	2	yes	—
446	#95	C₂³×C₁₃₇	1	4	yes	—
447	#95	C₂³×C₁₃₇	1	4	yes	—
448	#95	C₂³×C₁₃₇	1	4	yes	—
449	#95	C₂³×C₁₃₇	1	4	yes	—
450	#95	C₂³×C₁₃₇	1	4	yes	—
451	#95	C₂³×C₁₃₇	1	4	yes	—
452	#95	C₂³×C₁₃₇	1	4	yes	—
453	#95	C₂³×C₁₃₇	1	4	yes	—
454	#95	C₂³×C₁₃₇	1	4	yes	—
455	#95	C₂³×C₁₃₇	1	4	yes	—
456	#95	C₂³×C₁₃₇	1	4	yes	—
457	#95	C₂³×C₁₃₇	1	4	yes	—
458	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
459	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
460	#41	—	4	16	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
484	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
485	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	4	4	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	#41×C₁₃₇	1	8	yes	complemented
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₂²⋊C₄	—	4	4	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	8	no	—
532	C₄²	—	4	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
541	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
542	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
543	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
544	Q₈	—	4	4	no	—
545	D₄	—	4	8	no	—
546	D₄	—	4	4	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	8	no	—
577	C₂×C₄	—	4	8	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	#126×C₁₃₇	1	16	yes	complemented
581	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
582	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
583	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
584	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
585	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
586	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
587	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
588	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
589	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	C₂×#126×C₁₃₇	1	4	yes	—
600	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
601	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
602	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
603	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
604	C₂²	#585×C₁₃₇	1	2	yes	—
605	C₄	—	2	4	no	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	4	no	—
615	C₄	—	4	4	no	—
616	C₄	C₂×#126×C₁₃₇	1	4	yes	—
617	C₄	C₂×#126×C₁₃₇	1	4	yes	—
618	C₂	—	2	4	no	—
619	C₂	—	8	2	no	—
620	C₂	C₂²×#126×C₁₃₇	1	1	yes	characteristic
621	C₂	#3444×C₁₃₇	1	1	yes	characteristic
622	C₂	#3455×C₁₃₇	1	1	yes	characteristic
623	C₂	#3475×C₁₃₇	1	2	yes	—
624	C₂	#3480×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
socle	C₂³×C₁₃₇	C₂⁵
prime radical	C₂²×#41×C₁₃₇	C₂²
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
1. #2514×C₁₃₇	C₂	semidirect
2. #2513×C₁₃₇	C₂	semidirect
3. #2512×C₁₃₇	C₂	semidirect
4. #2511×C₁₃₇	C₂	semidirect
5. #2510×C₁₃₇	C₂	semidirect
6. #2481×C₁₃₇	C₂	semidirect
7. #2401×C₁₃₇	C₂	semidirect
8. C₄×#126×C₁₃₇	C₂	semidirect
12. #2296×C₁₃₇	C₂	semidirect
13. #2285×C₁₃₇	C₂	semidirect
14. C₄×#117×C₁₃₇	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	semidirect
197. C₄⋊C₄×C₁₃₇	#41	semidirect
267. C₂×C₄×C₁₃₇	#126	semidirect
312. #34816	C₁₃₇	direct (N × H)
313. C₁₃₇	#34816	direct (N × H)
314. #2514	C₂×C₁₃₇	semidirect
315. #2513	C₂×C₁₃₇	semidirect
316. #2512	C₂×C₁₃₇	semidirect
317. #2511	C₂×C₁₃₇	semidirect
318. #2510	C₂×C₁₃₇	semidirect
319. #2481	C₂×C₁₃₇	semidirect
320. #2401	C₂×C₁₃₇	semidirect
321. C₄×#126	C₂×C₁₃₇	semidirect
325. #2296	C₂×C₁₃₇	semidirect
326. #2285	C₂×C₁₃₇	semidirect
327. C₄×#117	C₂×C₁₃₇	semidirect
328. C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	semidirect
510. C₄⋊C₄	#41×C₁₃₇	semidirect
580. C₂×C₄	#126×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2514×C₁₃₇	2
#2513×C₁₃₇	2
#2512×C₁₃₇	2
#2511×C₁₃₇	2
#2510×C₁₃₇	2
#2481×C₁₃₇	2
#2401×C₁₃₇	2
C₄×#126×C₁₃₇	2
#2297×C₁₃₇	2
#2296×C₁₃₇	2
#2285×C₁₃₇	2
C₄×#117×C₁₃₇	2
C₂×C₄×C₄⋊C₄×C₁₃₇	2
#34816	137

Subgroups — C137×#34816 #46884202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34816 #46884202