Subgroups — C₁₃₇×#26323 #46875709

Order 35072.

758 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2548×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2355×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2092×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2073×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1984×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1982×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1948×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1926×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1925×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₄×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₇	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	#394×C₁₃₇	—	2	2	no	—
25	#391×C₁₃₇	—	2	1	no	—
26	#390×C₁₃₇	—	2	1	no	—
27	#390×C₁₃₇	C₂²	1	2	yes	—
28	#390×C₁₃₇	C₂²	1	2	yes	—
29	#387×C₁₃₇	—	2	2	no	—
30	#384×C₁₃₇	C₂²	1	1	yes	characteristic
31	#382×C₁₃₇	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	#340×C₁₃₇	C₂²	1	1	yes	characteristic
37	#340×C₁₃₇	C₂²	1	1	yes	characteristic
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₇	—	2	1	no	—
43	C₂²×D₄×C₁₃₇	—	2	1	no	—
44	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	#127×C₁₃₇	—	2	2	no	—
49	#127×C₁₃₇	—	2	2	no	—
50	#124×C₁₃₇	—	4	4	no	—
51	C₄×Q₈×C₁₃₇	—	2	2	no	—
52	C₄×Q₈×C₁₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₄²×C₁₃₇	—	2	1	no	—
67	C₂×C₄²×C₁₃₇	—	2	1	no	—
68	C₂×C₄²×C₁₃₇	—	2	2	no	—
69	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	#107×C₁₃₇	—	2	2	no	—
72	#107×C₁₃₇	—	2	2	no	—
73	#106×C₁₃₇	—	4	2	no	—
74	C₄⋊C₈×C₁₃₇	—	2	2	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	#102×C₁₃₇	—	2	4	no	—
77	#102×C₁₃₇	—	4	2	no	—
78	#102×C₁₃₇	—	4	2	no	—
79	C₄×C₈×C₁₃₇	—	2	2	no	—
80	#95×C₁₃₇	—	2	2	no	—
81	#95×C₁₃₇	—	2	1	no	—
82	#95×C₁₃₇	—	2	2	no	—
83	#95×C₁₃₇	—	2	1	no	—
84	#95×C₁₃₇	—	2	2	no	—
85	C₂⁴×C₁₃₇	—	2	2	no	—
86	C₂×Q₈×C₁₃₇	—	2	2	no	—
87	C₂×Q₈×C₁₃₇	—	2	2	no	—
88	C₂×Q₈×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	4	2	no	—
96	C₂×D₄×C₁₃₇	—	4	2	no	—
97	C₂×D₄×C₁₃₇	—	4	2	no	—
98	C₂×D₄×C₁₃₇	—	4	2	no	—
99	C₂×D₄×C₁₃₇	—	8	1	no	—
100	C₂×D₄×C₁₃₇	—	8	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	2	1	no	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	2	1	no	—
105	C₂²×C₄×C₁₃₇	—	2	1	no	—
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	#41	1	2	yes	—
120	C₄⋊C₄×C₁₃₇	—	2	2	no	—
121	C₄⋊C₄×C₁₃₇	—	2	4	no	—
122	C₄⋊C₄×C₁₃₇	—	2	1	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	1	no	—
125	C₄⋊C₄×C₁₃₇	—	2	1	no	—
126	C₄⋊C₄×C₁₃₇	—	2	1	no	—
127	C₄⋊C₄×C₁₃₇	—	2	1	no	—
128	C₄⋊C₄×C₁₃₇	—	2	2	no	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	4	2	no	—
132	C₄⋊C₄×C₁₃₇	—	8	1	no	—
133	C₄⋊C₄×C₁₃₇	#41	1	2	yes	—
134	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
135	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
136	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
137	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
138	C₄²×C₁₃₇	—	2	2	no	—
139	C₄²×C₁₃₇	—	2	2	no	—
140	C₄²×C₁₃₇	—	4	2	no	—
141	C₄²×C₁₃₇	—	4	2	no	—
142	C₄²×C₁₃₇	—	8	2	no	—
143	C₄²×C₁₃₇	#41	1	2	yes	—
144	C₄²×C₁₃₇	#41	1	2	yes	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	—	4	2	no	—
147	C₂³×C₁₃₇	—	4	2	no	—
148	C₂³×C₁₃₇	—	4	2	no	—
149	C₂³×C₁₃₇	—	4	2	no	—
150	C₂³×C₁₃₇	—	4	2	no	—
151	C₂³×C₁₃₇	—	4	2	no	—
152	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₃₇	—	4	4	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	D₄×C₁₃₇	—	4	2	no	—
156	D₄×C₁₃₇	—	4	2	no	—
157	D₄×C₁₃₇	—	4	2	no	—
158	D₄×C₁₃₇	—	8	4	no	—
159	D₄×C₁₃₇	—	8	4	no	—
160	C₂×C₄×C₁₃₇	—	2	1	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	2	2	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	4	1	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	4	1	no	—
174	C₂×C₄×C₁₃₇	—	4	1	no	—
175	C₂×C₄×C₁₃₇	—	4	2	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	4	1	no	—
178	C₂×C₄×C₁₃₇	—	4	1	no	—
179	C₂×C₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	4	1	no	—
181	C₂×C₄×C₁₃₇	—	4	1	no	—
182	C₂×C₄×C₁₃₇	—	4	1	no	—
183	C₂×C₄×C₁₃₇	#123	1	2	yes	—
184	C₂×C₄×C₁₃₇	#123	1	2	yes	—
185	C₂×C₄×C₁₃₇	#135	1	2	yes	—
186	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₁₃₇	—	2	2	no	—
194	C₈×C₁₃₇	—	4	1	no	—
195	C₈×C₁₃₇	—	4	2	no	—
196	C₂²×C₁₃₇	—	8	2	no	—
197	C₂²×C₁₃₇	—	8	2	no	—
198	C₂²×C₁₃₇	—	8	2	no	—
199	C₂²×C₁₃₇	—	8	2	no	—
200	C₂²×C₁₃₇	—	8	2	no	—
201	C₂²×C₁₃₇	—	8	2	no	—
202	C₂²×C₁₃₇	—	8	2	no	—
203	C₂²×C₁₃₇	C₂×#123	1	1	yes	characteristic
204	C₂²×C₁₃₇	#548	1	1	yes	characteristic
205	C₂²×C₁₃₇	#550	1	1	yes	characteristic
206	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
207	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂²×C₁₃₇	#576	1	1	yes	characteristic
209	C₂²×C₁₃₇	#577	1	1	yes	characteristic
210	C₄×C₁₃₇	—	2	2	no	—
211	C₄×C₁₃₇	—	4	2	no	—
212	C₄×C₁₃₇	—	4	2	no	—
213	C₄×C₁₃₇	—	4	2	no	—
214	C₄×C₁₃₇	—	8	1	no	—
215	C₄×C₁₃₇	—	8	2	no	—
216	C₄×C₁₃₇	—	8	1	no	—
217	C₄×C₁₃₇	—	8	1	no	—
218	C₄×C₁₃₇	#482	1	4	yes	—
219	C₄×C₁₃₇	#529	1	1	yes	characteristic
220	C₄×C₁₃₇	#542	1	1	yes	characteristic
221	C₄×C₁₃₇	#556	1	1	yes	characteristic
222	C₄×C₁₃₇	#559	1	1	yes	characteristic
223	C₂×C₁₃₇	—	16	2	no	—
224	C₂×C₁₃₇	#2448	1	1	yes	characteristic
225	C₂×C₁₃₇	C₂×#482	1	1	yes	characteristic
226	C₂×C₁₃₇	#3096	1	1	yes	characteristic
227	C₂×C₁₃₇	#3365	1	1	yes	characteristic
228	C₂×C₁₃₇	#3366	1	1	yes	characteristic
229	C₂×C₁₃₇	#3396	1	1	yes	characteristic
230	C₂×C₁₃₇	#3397	1	1	yes	characteristic
231	#26323	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃₇	#26323	1	1	yes	characteristic, direct product factor, Sylow
233	#2548	C₂×C₁₃₇	1	1	yes	characteristic
234	#2355	C₂×C₁₃₇	1	1	yes	characteristic, complemented
235	#2092	C₂×C₁₃₇	1	2	yes	complemented
236	#2073	C₂×C₁₃₇	1	2	yes	complemented
237	#1984	C₂×C₁₃₇	1	1	yes	characteristic, complemented
238	#1982	C₂×C₁₃₇	1	1	yes	characteristic
239	#1957	C₂×C₁₃₇	1	1	yes	characteristic
240	#1948	C₂×C₁₃₇	1	1	yes	characteristic, complemented
241	#1926	C₂×C₁₃₇	1	2	yes	complemented
242	#1925	C₂×C₁₃₇	1	2	yes	complemented
243	C₄×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
244	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
245	C₂×#124	—	2	1	no	—
246	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
249	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
251	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
252	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
253	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
254	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
256	#394	—	2	2	no	—
257	#391	—	2	1	no	—
258	#390	—	2	1	no	—
259	#390	C₂²×C₁₃₇	1	2	yes	—
260	#390	C₂²×C₁₃₇	1	2	yes	—
261	#387	—	2	2	no	—
262	#384	C₂²×C₁₃₇	1	1	yes	characteristic
263	#382	C₂²×C₁₃₇	1	2	yes	—
264	C₄×C₄⋊C₄	—	2	1	no	—
265	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
268	#340	C₂²×C₁₃₇	1	1	yes	characteristic
269	#340	C₂²×C₁₃₇	1	2	yes	—
270	#340	C₂²×C₁₃₇	1	1	yes	characteristic
271	#336	C₂²×C₁₃₇	1	2	yes	—
272	#336	C₂²×C₁₃₇	1	2	yes	—
273	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
280	#127	—	2	2	no	—
281	#127	—	2	2	no	—
282	#124	—	4	4	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#107	—	2	2	no	—
305	#106	—	4	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#102	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	4	2	no	—
310	#102	—	4	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	2	no	—
315	#95	—	2	1	no	—
316	#95	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	8	1	no	—
332	C₂×D₄	—	8	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	#41×C₁₃₇	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	8	1	no	—
365	C₄⋊C₄	#41×C₁₃₇	1	2	yes	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	8	2	no	—
375	C₄²	#41×C₁₃₇	1	2	yes	—
376	C₄²	#41×C₁₃₇	1	2	yes	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
385	Q₈	—	4	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	4	no	—
391	D₄	—	8	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	#123×C₁₃₇	1	2	yes	—
416	C₂×C₄	#123×C₁₃₇	1	2	yes	—
417	C₂×C₄	#135×C₁₃₇	1	2	yes	—
418	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
419	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
423	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
424	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₂×#123×C₁₃₇	1	1	yes	characteristic
436	C₂²	#548×C₁₃₇	1	1	yes	characteristic
437	C₂²	#550×C₁₃₇	1	1	yes	characteristic
438	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
439	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
440	C₂²	#576×C₁₃₇	1	1	yes	characteristic
441	C₂²	#577×C₁₃₇	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	#482×C₁₃₇	1	4	yes	—
451	C₄	#529×C₁₃₇	1	1	yes	characteristic
452	C₄	#542×C₁₃₇	1	1	yes	characteristic
453	C₄	#556×C₁₃₇	1	1	yes	characteristic
454	C₄	#559×C₁₃₇	1	1	yes	characteristic
455	C₂	—	16	2	no	—
456	C₂	#2448×C₁₃₇	1	1	yes	characteristic
457	C₂	C₂×#482×C₁₃₇	1	1	yes	characteristic
458	C₂	#3096×C₁₃₇	1	1	yes	characteristic
459	C₂	#3365×C₁₃₇	1	1	yes	characteristic
460	C₂	#3366×C₁₃₇	1	1	yes	characteristic
461	C₂	#3396×C₁₃₇	1	1	yes	characteristic
462	C₂	#3397×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×Q₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2355×C₁₃₇	C₂	semidirect
3. #2092×C₁₃₇	C₂	semidirect
4. #2073×C₁₃₇	C₂	semidirect
5. #1984×C₁₃₇	C₂	semidirect
8. #1948×C₁₃₇	C₂	semidirect
9. #1926×C₁₃₇	C₂	semidirect
10. #1925×C₁₃₇	C₂	semidirect
11. C₄×#107×C₁₃₇	C₂	semidirect
231. #26323	C₁₃₇	direct (N × H)
232. C₁₃₇	#26323	direct (N × H)
234. #2355	C₂×C₁₃₇	semidirect
235. #2092	C₂×C₁₃₇	semidirect
236. #2073	C₂×C₁₃₇	semidirect
237. #1984	C₂×C₁₃₇	semidirect
240. #1948	C₂×C₁₃₇	semidirect
241. #1926	C₂×C₁₃₇	semidirect
242. #1925	C₂×C₁₃₇	semidirect
243. C₄×#107	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2548×C₁₃₇	2
#2355×C₁₃₇	2
#2092×C₁₃₇	2
#2073×C₁₃₇	2
#1984×C₁₃₇	2
#1982×C₁₃₇	2
#1957×C₁₃₇	2
#1948×C₁₃₇	2
#1926×C₁₃₇	2
#1925×C₁₃₇	2
C₄×#107×C₁₃₇	2
#26323	137

Subgroups — C137×#26323 #46875709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26323 #46875709