Subgroups — C₁₃₇×#32955 #46882341

Order 35072.

1364 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#475×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#474×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1864×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1863×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1854×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1803×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1802×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1797×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1788×C₁₃₇	C₂	1	2	yes	maximal
12	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
15	C₄×#41×C₁₃₇	—	2	4	no	—
16	C₄×#41×C₁₃₇	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₇	—	2	1	no	—
24	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃₇	—	2	1	no	—
26	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
27	#475×C₁₃₇	—	2	4	no	—
28	#474×C₁₃₇	—	2	4	no	—
29	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
35	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
36	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
38	#391×C₁₃₇	—	2	1	no	—
39	#389×C₁₃₇	—	2	1	no	—
40	#389×C₁₃₇	C₂²	1	2	yes	—
41	#384×C₁₃₇	C₂²	1	1	yes	characteristic
42	#380×C₁₃₇	—	2	1	no	—
43	#380×C₁₃₇	C₂²	1	2	yes	—
44	#340×C₁₃₇	C₂²	1	2	yes	—
45	#340×C₁₃₇	C₂²	1	2	yes	—
46	#336×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	—	2	2	no	—
48	C₂×#41×C₁₃₇	—	2	2	no	—
49	C₂×#41×C₁₃₇	—	2	2	no	—
50	C₂×#41×C₁₃₇	—	2	2	no	—
51	C₂×#41×C₁₃₇	—	2	2	no	—
52	C₂×#41×C₁₃₇	Q₈	1	4	yes	complemented
53	C₂²×Q₈×C₁₃₇	—	2	1	no	—
54	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃₇	—	2	1	no	—
56	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃₇	—	2	1	no	—
58	C₂³×C₄×C₁₃₇	—	2	1	no	—
59	C₂³×C₄×C₁₃₇	—	2	1	no	—
60	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
66	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
67	C₂²⋊Q₈×C₁₃₇	—	4	4	no	—
68	C₄×Q₈×C₁₃₇	—	2	2	no	—
69	C₄×Q₈×C₁₃₇	—	2	2	no	—
70	C₄×Q₈×C₁₃₇	—	2	2	no	—
71	C₄×Q₈×C₁₃₇	D₄	1	4	yes	—
72	C₄×D₄×C₁₃₇	—	2	8	no	—
73	C₄×D₄×C₁₃₇	—	2	8	no	—
74	C₄×D₄×C₁₃₇	—	2	2	no	—
75	C₄×D₄×C₁₃₇	—	2	2	no	—
76	C₄×D₄×C₁₃₇	—	2	2	no	—
77	C₄×D₄×C₁₃₇	D₄	1	4	yes	—
78	#117×C₁₃₇	—	2	8	no	—
79	#117×C₁₃₇	—	2	2	no	—
80	#117×C₁₃₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
95	C₂×C₄²×C₁₃₇	—	2	8	no	—
96	C₂×C₄²×C₁₃₇	—	2	1	no	—
97	C₂×C₄²×C₁₃₇	—	2	1	no	—
98	C₂×C₄²×C₁₃₇	—	2	1	no	—
99	C₂×C₄²×C₁₃₇	—	2	2	no	—
100	C₂×C₄²×C₁₃₇	—	2	2	no	—
101	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
105	#107×C₁₃₇	—	2	4	no	—
106	#106×C₁₃₇	—	2	4	no	—
107	C₄⋊C₈×C₁₃₇	—	2	2	no	—
108	C₄⋊C₈×C₁₃₇	—	2	2	no	—
109	#103×C₁₃₇	—	2	4	no	—
110	#103×C₁₃₇	—	2	4	no	—
111	#102×C₁₃₇	—	2	4	no	—
112	#102×C₁₃₇	—	2	4	no	—
113	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
114	#95×C₁₃₇	—	2	2	no	—
115	#95×C₁₃₇	—	2	2	no	—
116	C₂⁴×C₁₃₇	—	2	1	no	—
117	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	#41×C₁₃₇	—	2	8	no	—
119	#41×C₁₃₇	—	2	8	no	—
120	#41×C₁₃₇	—	2	8	no	—
121	#41×C₁₃₇	—	2	8	no	—
122	C₂×Q₈×C₁₃₇	—	2	1	no	—
123	C₂×Q₈×C₁₃₇	—	2	1	no	—
124	C₂×Q₈×C₁₃₇	—	2	1	no	—
125	C₂×Q₈×C₁₃₇	—	4	2	no	—
126	C₂×Q₈×C₁₃₇	—	4	2	no	—
127	C₂×Q₈×C₁₃₇	—	4	2	no	—
128	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₃₇	C₂×Q₈	1	2	yes	—
130	C₂×Q₈×C₁₃₇	#41	1	2	yes	—
131	C₂×D₄×C₁₃₇	—	2	4	no	—
132	C₂×D₄×C₁₃₇	—	2	4	no	—
133	C₂×D₄×C₁₃₇	—	2	4	no	—
134	C₂×D₄×C₁₃₇	—	2	1	no	—
135	C₂×D₄×C₁₃₇	—	2	1	no	—
136	C₂×D₄×C₁₃₇	—	2	1	no	—
137	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₃₇	C₂×Q₈	1	2	yes	—
139	C₂×D₄×C₁₃₇	#41	1	2	yes	—
140	C₂²×C₄×C₁₃₇	—	2	4	no	—
141	C₂²×C₄×C₁₃₇	—	2	4	no	—
142	C₂²×C₄×C₁₃₇	—	2	1	no	—
143	C₂²×C₄×C₁₃₇	—	2	4	no	—
144	C₂²×C₄×C₁₃₇	—	2	1	no	—
145	C₂²×C₄×C₁₃₇	—	2	1	no	—
146	C₂²×C₄×C₁₃₇	—	2	1	no	—
147	C₂²×C₄×C₁₃₇	—	2	1	no	—
148	C₂²×C₄×C₁₃₇	—	2	4	no	—
149	C₂²×C₄×C₁₃₇	—	2	1	no	—
150	C₂²×C₄×C₁₃₇	—	2	1	no	—
151	C₂²×C₄×C₁₃₇	—	2	2	no	—
152	C₂²×C₄×C₁₃₇	—	2	2	no	—
153	C₂²×C₄×C₁₃₇	—	2	4	no	—
154	C₂²×C₄×C₁₃₇	—	2	2	no	—
155	C₂²×C₄×C₁₃₇	—	2	2	no	—
156	C₂²×C₄×C₁₃₇	—	2	2	no	—
157	C₂²×C₄×C₁₃₇	—	2	2	no	—
158	C₂²×C₄×C₁₃₇	—	2	2	no	—
159	C₂²×C₄×C₁₃₇	—	4	1	no	—
160	C₂²×C₄×C₁₃₇	—	4	2	no	—
161	C₂²×C₄×C₁₃₇	—	4	2	no	—
162	C₂²×C₄×C₁₃₇	—	4	2	no	—
163	C₂²×C₄×C₁₃₇	—	4	2	no	—
164	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
170	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
171	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₃₇	—	2	2	no	—
173	C₂×C₈×C₁₃₇	—	2	2	no	—
174	C₂×C₈×C₁₃₇	—	2	2	no	—
175	C₂×C₈×C₁₃₇	—	2	2	no	—
176	C₂×C₈×C₁₃₇	—	2	2	no	—
177	C₂×C₈×C₁₃₇	—	2	2	no	—
178	C₄⋊C₄×C₁₃₇	—	2	4	no	—
179	C₄⋊C₄×C₁₃₇	—	2	4	no	—
180	C₄⋊C₄×C₁₃₇	—	2	1	no	—
181	C₄⋊C₄×C₁₃₇	—	2	1	no	—
182	C₄⋊C₄×C₁₃₇	—	2	2	no	—
183	C₄⋊C₄×C₁₃₇	—	2	2	no	—
184	C₄⋊C₄×C₁₃₇	—	2	2	no	—
185	C₄⋊C₄×C₁₃₇	—	2	2	no	—
186	C₄⋊C₄×C₁₃₇	—	4	2	no	—
187	C₄⋊C₄×C₁₃₇	—	4	4	no	—
188	C₄⋊C₄×C₁₃₇	—	4	2	no	—
189	C₄⋊C₄×C₁₃₇	—	4	2	no	—
190	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
193	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
194	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
195	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
196	C₄²×C₁₃₇	—	2	4	no	—
197	C₄²×C₁₃₇	—	2	4	no	—
198	C₄²×C₁₃₇	—	2	2	no	—
199	C₄²×C₁₃₇	—	2	4	no	—
200	C₄²×C₁₃₇	—	2	2	no	—
201	C₄²×C₁₃₇	—	2	1	no	—
202	C₄²×C₁₃₇	—	2	1	no	—
203	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
205	C₂³×C₁₃₇	—	2	1	no	—
206	C₂³×C₁₃₇	—	2	2	no	—
207	C₂³×C₁₃₇	—	2	2	no	—
208	C₂³×C₁₃₇	—	2	1	no	—
209	C₂³×C₁₃₇	—	2	2	no	—
210	C₂³×C₁₃₇	—	2	1	no	—
211	C₂³×C₁₃₇	—	2	1	no	—
212	C₂³×C₁₃₇	—	2	1	no	—
213	C₂³×C₁₃₇	—	2	1	no	—
214	C₂³×C₁₃₇	—	4	1	no	—
215	C₂³×C₁₃₇	—	4	1	no	—
216	C₂³×C₁₃₇	—	4	1	no	—
217	C₂³×C₁₃₇	—	4	1	no	—
218	C₂³×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
219	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₃₇	—	2	2	no	—
221	Q₈×C₁₃₇	—	2	2	no	—
222	Q₈×C₁₃₇	—	2	2	no	—
223	Q₈×C₁₃₇	—	8	4	no	—
224	Q₈×C₁₃₇	C₂²⋊Q₈	1	4	yes	complemented
225	D₄×C₁₃₇	—	2	16	no	—
226	D₄×C₁₃₇	—	2	2	no	—
227	D₄×C₁₃₇	—	2	2	no	—
228	D₄×C₁₃₇	—	2	2	no	—
229	D₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	complemented
230	C₂×C₄×C₁₃₇	—	2	16	no	—
231	C₂×C₄×C₁₃₇	—	2	1	no	—
232	C₂×C₄×C₁₃₇	—	2	1	no	—
233	C₂×C₄×C₁₃₇	—	2	2	no	—
234	C₂×C₄×C₁₃₇	—	2	2	no	—
235	C₂×C₄×C₁₃₇	—	2	1	no	—
236	C₂×C₄×C₁₃₇	—	2	2	no	—
237	C₂×C₄×C₁₃₇	—	2	1	no	—
238	C₂×C₄×C₁₃₇	—	2	1	no	—
239	C₂×C₄×C₁₃₇	—	2	1	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	1	no	—
245	C₂×C₄×C₁₃₇	—	2	2	no	—
246	C₂×C₄×C₁₃₇	—	2	2	no	—
247	C₂×C₄×C₁₃₇	—	2	1	no	—
248	C₂×C₄×C₁₃₇	—	2	1	no	—
249	C₂×C₄×C₁₃₇	—	4	4	no	—
250	C₂×C₄×C₁₃₇	—	4	8	no	—
251	C₂×C₄×C₁₃₇	—	4	1	no	—
252	C₂×C₄×C₁₃₇	—	4	1	no	—
253	C₂×C₄×C₁₃₇	—	4	1	no	—
254	C₂×C₄×C₁₃₇	—	4	1	no	—
255	C₂×C₄×C₁₃₇	—	4	4	no	—
256	C₂×C₄×C₁₃₇	—	4	8	no	—
257	C₂×C₄×C₁₃₇	—	4	2	no	—
258	C₂×C₄×C₁₃₇	—	4	2	no	—
259	C₂×C₄×C₁₃₇	—	4	2	no	—
260	C₂×C₄×C₁₃₇	—	4	2	no	—
261	C₂×C₄×C₁₃₇	—	4	2	no	—
262	C₂×C₄×C₁₃₇	—	4	2	no	—
263	C₂×C₄×C₁₃₇	#120	1	2	yes	—
264	C₂×C₄×C₁₃₇	#120	1	2	yes	—
265	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
266	C₂×C₄×C₁₃₇	#135	1	2	yes	—
267	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄×C₁₃₇	#137	1	2	yes	—
269	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
272	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
275	C₈×C₁₃₇	—	4	2	no	—
276	C₈×C₁₃₇	—	4	2	no	—
277	C₂²×C₁₃₇	—	2	2	no	—
278	C₂²×C₁₃₇	—	2	2	no	—
279	C₂²×C₁₃₇	—	2	2	no	—
280	C₂²×C₁₃₇	—	2	4	no	—
281	C₂²×C₁₃₇	—	4	2	no	—
282	C₂²×C₁₃₇	—	4	2	no	—
283	C₂²×C₁₃₇	—	4	1	no	—
284	C₂²×C₁₃₇	—	4	2	no	—
285	C₂²×C₁₃₇	—	4	1	no	—
286	C₂²×C₁₃₇	—	4	2	no	—
287	C₂²×C₁₃₇	—	4	1	no	—
288	C₂²×C₁₃₇	—	4	2	no	—
289	C₂²×C₁₃₇	—	4	1	no	—
290	C₂²×C₁₃₇	—	4	2	no	—
291	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
292	C₂²×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₂²×C₁₃₇	#525	1	1	yes	characteristic
294	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
295	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
297	C₂²×C₁₃₇	#575	1	1	yes	characteristic
298	C₄×C₁₃₇	—	2	2	no	—
299	C₄×C₁₃₇	—	2	4	no	—
300	C₄×C₁₃₇	—	2	2	no	—
301	C₄×C₁₃₇	—	2	2	no	—
302	C₄×C₁₃₇	—	4	1	no	—
303	C₄×C₁₃₇	—	4	2	no	—
304	C₄×C₁₃₇	—	4	2	no	—
305	C₄×C₁₃₇	—	8	2	no	—
306	C₄×C₁₃₇	—	8	2	no	—
307	C₄×C₁₃₇	#449	1	4	yes	—
308	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
309	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
310	C₄×C₁₃₇	#525	1	1	yes	characteristic
311	C₄×C₁₃₇	#525	1	1	yes	characteristic
312	C₂×C₁₃₇	—	4	2	no	—
313	C₂×C₁₃₇	—	4	4	no	—
314	C₂×C₁₃₇	#2848	1	1	yes	characteristic
315	C₂×C₁₃₇	C₂×#449	1	1	yes	characteristic
316	C₂×C₁₃₇	#3007	1	1	yes	characteristic
317	C₂×C₁₃₇	#3076	1	1	yes	characteristic
318	C₂×C₁₃₇	#3079	1	1	yes	characteristic
319	C₂×C₁₃₇	#3107	1	1	yes	characteristic
320	C₂×C₁₃₇	#3115	1	1	yes	characteristic
321	#32955	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₁₃₇	#32955	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×C₄×#41	C₂×C₁₃₇	1	1	yes	characteristic
324	C₂×#475	C₂×C₁₃₇	1	1	yes	characteristic, complemented
325	C₂×#474	C₂×C₁₃₇	1	1	yes	characteristic, complemented
326	#2857	C₂×C₁₃₇	1	1	yes	characteristic, complemented
327	#1864	C₂×C₁₃₇	1	2	yes	complemented
328	#1863	C₂×C₁₃₇	1	2	yes	complemented
329	#1854	C₂×C₁₃₇	1	2	yes	complemented
330	#1803	C₂×C₁₃₇	1	1	yes	characteristic, complemented
331	#1802	C₂×C₁₃₇	1	1	yes	characteristic, complemented
332	#1797	C₂×C₁₃₇	1	1	yes	characteristic, complemented
333	#1788	C₂×C₁₃₇	1	2	yes	—
334	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
335	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
336	C₂×C₂²⋊Q₈	—	2	1	no	—
337	C₄×#41	—	2	4	no	—
338	C₄×#41	—	2	4	no	—
339	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄×D₄	—	2	1	no	—
342	C₂×C₄×D₄	—	2	1	no	—
343	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
345	C₂×#117	—	2	1	no	—
346	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
347	C₂²×C₄²	—	2	1	no	—
348	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
349	#475	—	2	4	no	—
350	#474	—	2	4	no	—
351	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
352	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
353	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
355	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
356	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
357	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
358	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
359	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
360	#391	—	2	1	no	—
361	#389	—	2	1	no	—
362	#389	C₂²×C₁₃₇	1	2	yes	—
363	#384	C₂²×C₁₃₇	1	1	yes	characteristic
364	#380	—	2	1	no	—
365	#380	C₂²×C₁₃₇	1	2	yes	—
366	#340	C₂²×C₁₃₇	1	2	yes	—
367	#340	C₂²×C₁₃₇	1	2	yes	—
368	#336	C₂²×C₁₃₇	1	2	yes	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	2	no	—
371	C₂×#41	—	2	2	no	—
372	C₂×#41	—	2	2	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	Q₈×C₁₃₇	1	4	yes	complemented
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
383	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
386	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₄⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	4	4	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	D₄×C₁₃₇	1	4	yes	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	8	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	D₄×C₁₃₇	1	4	yes	—
400	#117	—	2	8	no	—
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₄²	—	2	8	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
424	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
427	#107	—	2	4	no	—
428	#106	—	2	4	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	#103	—	2	4	no	—
432	#103	—	2	4	no	—
433	#102	—	2	4	no	—
434	#102	—	2	4	no	—
435	C₂²⋊C₈	—	2	4	no	—
436	#95	—	2	2	no	—
437	#95	—	2	2	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
440	#41	—	2	8	no	—
441	#41	—	2	8	no	—
442	#41	—	2	8	no	—
443	#41	—	2	8	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	4	2	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
451	C₂×Q₈	C₂×Q₈×C₁₃₇	1	2	yes	—
452	C₂×Q₈	#41×C₁₃₇	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
460	C₂×D₄	C₂×Q₈×C₁₃₇	1	2	yes	—
461	C₂×D₄	#41×C₁₃₇	1	2	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
491	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
492	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
526	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
541	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	8	4	no	—
546	Q₈	C₂²⋊Q₈×C₁₃₇	1	4	yes	complemented
547	D₄	—	2	16	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	complemented
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	#120×C₁₃₇	1	2	yes	—
586	C₂×C₄	#120×C₁₃₇	1	2	yes	—
587	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
588	C₂×C₄	#135×C₁₃₇	1	2	yes	—
589	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
590	C₂×C₄	#137×C₁₃₇	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
593	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
597	C₈	—	4	2	no	—
598	C₈	—	4	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
614	C₂²	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
615	C₂²	#525×C₁₃₇	1	1	yes	characteristic
616	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
617	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
618	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
619	C₂²	#575×C₁₃₇	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	2	no	—
628	C₄	—	8	2	no	—
629	C₄	#449×C₁₃₇	1	4	yes	—
630	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
631	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
632	C₄	#525×C₁₃₇	1	1	yes	characteristic
633	C₄	#525×C₁₃₇	1	1	yes	characteristic
634	C₂	—	4	2	no	—
635	C₂	—	4	4	no	—
636	C₂	#2848×C₁₃₇	1	1	yes	characteristic
637	C₂	C₂×#449×C₁₃₇	1	1	yes	characteristic
638	C₂	#3007×C₁₃₇	1	1	yes	characteristic
639	C₂	#3076×C₁₃₇	1	1	yes	characteristic
640	C₂	#3079×C₁₃₇	1	1	yes	characteristic
641	C₂	#3107×C₁₃₇	1	1	yes	characteristic
642	C₂	#3115×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#475×C₁₃₇	C₂	semidirect
3. C₂×#474×C₁₃₇	C₂	semidirect
4. #2857×C₁₃₇	C₂	semidirect
5. #1864×C₁₃₇	C₂	semidirect
6. #1863×C₁₃₇	C₂	semidirect
7. #1854×C₁₃₇	C₂	semidirect
8. #1803×C₁₃₇	C₂	semidirect
9. #1802×C₁₃₇	C₂	semidirect
10. #1797×C₁₃₇	C₂	semidirect
52. C₂×#41×C₁₃₇	Q₈	semidirect
224. Q₈×C₁₃₇	C₂²⋊Q₈	semidirect
229. D₄×C₁₃₇	C₂²⋊Q₈	semidirect
321. #32955	C₁₃₇	direct (N × H)
322. C₁₃₇	#32955	direct (N × H)
324. C₂×#475	C₂×C₁₃₇	semidirect
325. C₂×#474	C₂×C₁₃₇	semidirect
326. #2857	C₂×C₁₃₇	semidirect
327. #1864	C₂×C₁₃₇	semidirect
328. #1863	C₂×C₁₃₇	semidirect
329. #1854	C₂×C₁₃₇	semidirect
330. #1803	C₂×C₁₃₇	semidirect
331. #1802	C₂×C₁₃₇	semidirect
332. #1797	C₂×C₁₃₇	semidirect
374. C₂×#41	Q₈×C₁₃₇	semidirect
546. Q₈	C₂²⋊Q₈×C₁₃₇	semidirect
551. D₄	C₂²⋊Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₃₇	2
C₂×#475×C₁₃₇	2
C₂×#474×C₁₃₇	2
#2857×C₁₃₇	2
#1864×C₁₃₇	2
#1863×C₁₃₇	2
#1854×C₁₃₇	2
#1803×C₁₃₇	2
#1802×C₁₃₇	2
#1797×C₁₃₇	2
#1788×C₁₃₇	2
#32955	137

Subgroups — C137×#32955 #46882341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#32955 #46882341