Subgroups — C₁₃₇×#21137 #46870523

Order 35072.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#135×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2922×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#131×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1929×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1922×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1876×C₁₃₇	C₂	1	2	yes	maximal
7	#1866×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₄×#108×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#104×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#104×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1744×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₁₃₇	C₂²	1	2	yes	—
14	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
17	C₄×Q₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
18	C₄×SD₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
19	C₄×SD₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
20	C₄×SD₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
21	C₄×SD₁₆×C₁₃₇	C₄	1	1	yes	characteristic, complemented
22	C₄×D₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
23	C₄×D₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
24	#433×C₁₃₇	—	2	2	no	—
25	#431×C₁₃₇	—	2	1	no	—
26	#431×C₁₃₇	—	2	1	no	—
27	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
28	#427×C₁₃₇	C₂²	1	1	yes	characteristic
29	#424×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
31	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
32	#416×C₁₃₇	C₂²	1	1	yes	characteristic
33	#416×C₁₃₇	C₂²	1	1	yes	characteristic
34	#408×C₁₃₇	C₂²	1	2	yes	—
35	#405×C₁₃₇	—	2	2	no	—
36	#405×C₁₃₇	C₂²	1	2	yes	—
37	C₄×M₁₆×C₁₃₇	—	2	1	no	—
38	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
41	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
43	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
44	#341×C₁₃₇	C₂²	1	2	yes	—
45	#339×C₁₃₇	C₂²	1	2	yes	—
46	#339×C₁₃₇	C₂²	1	2	yes	—
47	#336×C₁₃₇	C₂²	1	2	yes	—
48	#336×C₁₃₇	C₂²	1	2	yes	—
49	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
51	#135×C₁₃₇	—	2	4	no	—
52	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
55	C₂×D₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	#131×C₁₃₇	—	2	4	no	—
57	#131×C₁₃₇	—	2	4	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃₇	—	2	2	no	—
62	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
65	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃₇	—	2	1	no	—
70	C₄×D₄×C₁₃₇	—	2	1	no	—
71	C₄×D₄×C₁₃₇	—	2	1	no	—
72	C₄×D₄×C₁₃₇	—	2	1	no	—
73	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
75	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
77	#117×C₁₃₇	—	2	1	no	—
78	#117×C₁₃₇	—	2	1	no	—
79	#117×C₁₃₇	C₂³	1	1	yes	characteristic
80	#117×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃₇	—	2	1	no	—
82	C₂×C₄²×C₁₃₇	—	2	1	no	—
83	C₂×C₄²×C₁₃₇	—	2	1	no	—
84	C₂×C₄²×C₁₃₇	—	2	1	no	—
85	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
87	#108×C₁₃₇	—	2	4	no	—
88	#107×C₁₃₇	C₂×C₄	1	1	yes	characteristic
89	#107×C₁₃₇	C₂×C₄	1	1	yes	characteristic
90	#106×C₁₃₇	C₂×C₄	1	1	yes	characteristic
91	#106×C₁₃₇	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₈×C₁₃₇	—	2	2	no	—
93	C₄⋊C₈×C₁₃₇	—	2	2	no	—
94	#104×C₁₃₇	—	2	4	no	—
95	#104×C₁₃₇	—	2	4	no	—
96	#103×C₁₃₇	C₂×C₄	1	1	yes	characteristic
97	#103×C₁₃₇	C₂×C₄	1	1	yes	characteristic
98	#103×C₁₃₇	C₂×C₄	1	1	yes	characteristic
99	#103×C₁₃₇	C₂×C₄	1	1	yes	characteristic
100	#102×C₁₃₇	C₂×C₄	1	1	yes	characteristic
101	#102×C₁₃₇	C₂×C₄	1	1	yes	characteristic
102	#102×C₁₃₇	C₂×C₄	1	1	yes	characteristic
103	#102×C₁₃₇	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
105	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
106	#97×C₁₃₇	—	2	2	no	—
107	#97×C₁₃₇	—	2	1	no	—
108	#97×C₁₃₇	—	2	1	no	—
109	C₄×C₈×C₁₃₇	—	2	2	no	—
110	C₄×C₈×C₁₃₇	—	2	1	no	—
111	C₄×C₈×C₁₃₇	—	2	1	no	—
112	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
113	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
114	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
117	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
118	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
119	#41×C₁₃₇	—	2	2	no	—
120	#41×C₁₃₇	—	2	2	no	—
121	#41×C₁₃₇	—	2	2	no	—
122	#41×C₁₃₇	#41	1	4	yes	—
123	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₃₇	—	2	1	no	—
126	C₂×D₄×C₁₃₇	—	2	1	no	—
127	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₇	—	2	1	no	—
130	C₂²×C₄×C₁₃₇	—	2	2	no	—
131	C₂²×C₄×C₁₃₇	—	2	1	no	—
132	C₂²×C₄×C₁₃₇	—	2	1	no	—
133	C₂²×C₄×C₁₃₇	—	2	1	no	—
134	C₂²×C₄×C₁₃₇	—	2	1	no	—
135	C₂²×C₄×C₁₃₇	—	2	1	no	—
136	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₁₃₇	—	2	2	no	—
140	SD₁₆×C₁₃₇	—	2	2	no	—
141	SD₁₆×C₁₃₇	—	2	2	no	—
142	D₈×C₁₃₇	—	2	2	no	—
143	M₁₆×C₁₃₇	—	2	8	no	—
144	M₁₆×C₁₃₇	—	2	2	no	—
145	M₁₆×C₁₃₇	—	2	2	no	—
146	M₁₆×C₁₃₇	—	2	2	no	—
147	M₁₆×C₁₃₇	#41	1	4	yes	—
148	C₂×C₈×C₁₃₇	—	2	8	no	—
149	C₂×C₈×C₁₃₇	—	2	2	no	—
150	C₂×C₈×C₁₃₇	—	2	2	no	—
151	C₂×C₈×C₁₃₇	—	2	2	no	—
152	C₂×C₈×C₁₃₇	—	2	2	no	—
153	C₂×C₈×C₁₃₇	—	2	2	no	—
154	C₂×C₈×C₁₃₇	—	2	2	no	—
155	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₃₇	—	2	1	no	—
162	C₄⋊C₄×C₁₃₇	—	2	1	no	—
163	C₄⋊C₄×C₁₃₇	—	2	1	no	—
164	C₄⋊C₄×C₁₃₇	—	2	1	no	—
165	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
170	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
171	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
172	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
173	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
174	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
175	C₄²×C₁₃₇	—	2	4	no	—
176	C₄²×C₁₃₇	—	2	1	no	—
177	C₄²×C₁₃₇	—	2	1	no	—
178	C₄²×C₁₃₇	—	2	1	no	—
179	C₄²×C₁₃₇	—	2	1	no	—
180	C₄²×C₁₃₇	—	2	1	no	—
181	C₄²×C₁₃₇	—	2	1	no	—
182	C₄²×C₁₃₇	—	2	2	no	—
183	C₄²×C₁₃₇	—	2	2	no	—
184	C₄²×C₁₃₇	—	4	2	no	—
185	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₁₃₇	—	2	1	no	—
190	C₂³×C₁₃₇	—	2	1	no	—
191	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
192	Q₈×C₁₃₇	—	2	1	no	—
193	Q₈×C₁₃₇	—	2	1	no	—
194	Q₈×C₁₃₇	—	2	1	no	—
195	Q₈×C₁₃₇	#117	1	2	yes	—
196	D₄×C₁₃₇	—	2	4	no	—
197	D₄×C₁₃₇	—	2	1	no	—
198	D₄×C₁₃₇	—	2	1	no	—
199	D₄×C₁₃₇	—	2	1	no	—
200	D₄×C₁₃₇	—	4	2	no	—
201	D₄×C₁₃₇	#117	1	2	yes	—
202	C₂×C₄×C₁₃₇	—	2	1	no	—
203	C₂×C₄×C₁₃₇	—	2	4	no	—
204	C₂×C₄×C₁₃₇	—	2	2	no	—
205	C₂×C₄×C₁₃₇	—	2	2	no	—
206	C₂×C₄×C₁₃₇	—	2	4	no	—
207	C₂×C₄×C₁₃₇	—	2	1	no	—
208	C₂×C₄×C₁₃₇	—	2	1	no	—
209	C₂×C₄×C₁₃₇	—	2	1	no	—
210	C₂×C₄×C₁₃₇	—	2	1	no	—
211	C₂×C₄×C₁₃₇	—	2	1	no	—
212	C₂×C₄×C₁₃₇	—	4	2	no	—
213	C₂×C₄×C₁₃₇	—	4	2	no	—
214	C₂×C₄×C₁₃₇	—	4	2	no	—
215	C₂×C₄×C₁₃₇	—	4	2	no	—
216	C₂×C₄×C₁₃₇	—	4	2	no	—
217	C₂×C₄×C₁₃₇	—	4	2	no	—
218	C₂×C₄×C₁₃₇	—	4	2	no	—
219	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
227	C₈×C₁₃₇	—	2	1	no	—
228	C₈×C₁₃₇	—	2	1	no	—
229	C₈×C₁₃₇	—	2	1	no	—
230	C₈×C₁₃₇	—	2	1	no	—
231	C₈×C₁₃₇	—	2	2	no	—
232	C₈×C₁₃₇	—	2	4	no	—
233	C₈×C₁₃₇	—	2	2	no	—
234	C₈×C₁₃₇	—	4	2	no	—
235	C₂²×C₁₃₇	—	2	1	no	—
236	C₂²×C₁₃₇	—	2	1	no	—
237	C₂²×C₁₃₇	—	2	2	no	—
238	C₂²×C₁₃₇	—	4	1	no	—
239	C₂²×C₁₃₇	—	4	1	no	—
240	C₂²×C₁₃₇	—	4	1	no	—
241	C₂²×C₁₃₇	—	4	1	no	—
242	C₂²×C₁₃₇	—	4	1	no	—
243	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₁₃₇	#529	1	2	yes	—
245	C₄×C₁₃₇	—	2	1	no	—
246	C₄×C₁₃₇	—	2	1	no	—
247	C₄×C₁₃₇	—	2	2	no	—
248	C₄×C₁₃₇	—	4	4	no	—
249	C₄×C₁₃₇	—	4	1	no	—
250	C₄×C₁₃₇	—	4	1	no	—
251	C₄×C₁₃₇	—	4	1	no	—
252	C₄×C₁₃₇	—	4	1	no	—
253	C₄×C₁₃₇	—	4	1	no	—
254	C₄×C₁₃₇	#443	1	2	yes	—
255	C₄×C₁₃₇	#444	1	2	yes	—
256	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
257	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
258	C₄×C₁₃₇	#525	1	2	yes	—
259	C₂×C₁₃₇	—	2	2	no	—
260	C₂×C₁₃₇	—	4	2	no	—
261	C₂×C₁₃₇	—	8	1	no	—
262	C₂×C₁₃₇	#2290	1	1	yes	characteristic
263	C₂×C₁₃₇	C₂×#443	1	1	yes	characteristic
264	C₂×C₁₃₇	C₂×#444	1	1	yes	characteristic
265	#21137	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₁₃₇	#21137	1	1	yes	characteristic, direct product factor, Sylow
267	C₄×#135	C₂×C₁₃₇	1	1	yes	characteristic
268	#2922	C₂×C₁₃₇	1	1	yes	characteristic, complemented
269	C₄×#131	C₂×C₁₃₇	1	1	yes	characteristic, complemented
270	#1929	C₂×C₁₃₇	1	2	yes	complemented
271	#1922	C₂×C₁₃₇	1	2	yes	complemented
272	#1876	C₂×C₁₃₇	1	2	yes	—
273	#1866	C₂×C₁₃₇	1	2	yes	complemented
274	C₄×#108	C₂×C₁₃₇	1	1	yes	characteristic, complemented
275	C₄×#104	C₂×C₁₃₇	1	1	yes	characteristic, complemented
276	C₄×#104	C₂×C₁₃₇	1	1	yes	characteristic, complemented
277	#1744	C₂×C₁₃₇	1	1	yes	characteristic, complemented
278	C₂×#135	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
280	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₄×Q₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
283	C₄×Q₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
284	C₄×SD₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
285	C₄×SD₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
286	C₄×SD₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
287	C₄×SD₁₆	C₄×C₁₃₇	1	1	yes	characteristic, complemented
288	C₄×D₈	C₄×C₁₃₇	1	1	yes	characteristic, complemented
289	C₄×D₈	C₄×C₁₃₇	1	1	yes	characteristic, complemented
290	#433	—	2	2	no	—
291	#431	—	2	1	no	—
292	#431	—	2	1	no	—
293	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
294	#427	C₂²×C₁₃₇	1	1	yes	characteristic
295	#424	C₂²×C₁₃₇	1	2	yes	—
296	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
297	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
298	#416	C₂²×C₁₃₇	1	1	yes	characteristic
299	#416	C₂²×C₁₃₇	1	1	yes	characteristic
300	#408	C₂²×C₁₃₇	1	2	yes	—
301	#405	—	2	2	no	—
302	#405	C₂²×C₁₃₇	1	2	yes	—
303	C₄×M₁₆	—	2	1	no	—
304	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
305	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
306	C₂×C₄×C₈	—	2	1	no	—
307	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
309	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
310	#341	C₂²×C₁₃₇	1	2	yes	—
311	#339	C₂²×C₁₃₇	1	2	yes	—
312	#339	C₂²×C₁₃₇	1	2	yes	—
313	#336	C₂²×C₁₃₇	1	2	yes	—
314	#336	C₂²×C₁₃₇	1	2	yes	—
315	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
316	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
317	#135	—	2	4	no	—
318	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
319	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
321	C₂×D₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
322	#131	—	2	4	no	—
323	#131	—	2	4	no	—
324	C₂×M₁₆	—	2	2	no	—
325	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
331	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
332	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
333	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
334	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
340	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
341	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
342	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂³×C₁₃₇	1	1	yes	characteristic
346	#117	C₂³×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
353	#108	—	2	4	no	—
354	#107	C₂×C₄×C₁₃₇	1	1	yes	characteristic
355	#107	C₂×C₄×C₁₃₇	1	1	yes	characteristic
356	#106	C₂×C₄×C₁₃₇	1	1	yes	characteristic
357	#106	C₂×C₄×C₁₃₇	1	1	yes	characteristic
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	#104	—	2	4	no	—
361	#104	—	2	4	no	—
362	#103	C₂×C₄×C₁₃₇	1	1	yes	characteristic
363	#103	C₂×C₄×C₁₃₇	1	1	yes	characteristic
364	#103	C₂×C₄×C₁₃₇	1	1	yes	characteristic
365	#103	C₂×C₄×C₁₃₇	1	1	yes	characteristic
366	#102	C₂×C₄×C₁₃₇	1	1	yes	characteristic
367	#102	C₂×C₄×C₁₃₇	1	1	yes	characteristic
368	#102	C₂×C₄×C₁₃₇	1	1	yes	characteristic
369	#102	C₂×C₄×C₁₃₇	1	1	yes	characteristic
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	#97	—	2	2	no	—
373	#97	—	2	1	no	—
374	#97	—	2	1	no	—
375	C₄×C₈	—	2	2	no	—
376	C₄×C₈	—	2	1	no	—
377	C₄×C₈	—	2	1	no	—
378	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
379	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
380	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
381	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
382	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
383	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
384	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	#41×C₁₃₇	1	4	yes	—
389	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
390	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
394	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
403	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
405	Q₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	SD₁₆	—	2	2	no	—
408	D₈	—	2	2	no	—
409	M₁₆	—	2	8	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	#41×C₁₃₇	1	4	yes	—
414	C₂×C₈	—	2	8	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
422	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
423	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
424	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
426	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
433	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
434	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	4	2	no	—
451	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
452	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
453	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
454	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	#117×C₁₃₇	1	2	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	4	2	no	—
467	D₄	#117×C₁₃₇	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
486	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
487	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
488	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
489	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
492	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	2	2	no	—
498	C₈	—	2	4	no	—
499	C₈	—	2	2	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
510	C₂²	#529×C₁₃₇	1	2	yes	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	#443×C₁₃₇	1	2	yes	—
521	C₄	#444×C₁₃₇	1	2	yes	—
522	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
523	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
524	C₄	#525×C₁₃₇	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	1	no	—
528	C₂	#2290×C₁₃₇	1	1	yes	characteristic
529	C₂	C₂×#443×C₁₃₇	1	1	yes	characteristic
530	C₂	C₂×#444×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	C₂×#135×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃₇ ◁ C₂×C₄×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2922×C₁₃₇	C₂	semidirect
3. C₄×#131×C₁₃₇	C₂	semidirect
4. #1929×C₁₃₇	C₂	semidirect
5. #1922×C₁₃₇	C₂	semidirect
7. #1866×C₁₃₇	C₂	semidirect
8. C₄×#108×C₁₃₇	C₂	semidirect
9. C₄×#104×C₁₃₇	C₂	semidirect
10. C₄×#104×C₁₃₇	C₂	semidirect
11. #1744×C₁₃₇	C₂	semidirect
16. C₄×Q₁₆×C₁₃₇	C₄	semidirect
17. C₄×Q₁₆×C₁₃₇	C₄	semidirect
18. C₄×SD₁₆×C₁₃₇	C₄	semidirect
19. C₄×SD₁₆×C₁₃₇	C₄	semidirect
20. C₄×SD₁₆×C₁₃₇	C₄	semidirect
21. C₄×SD₁₆×C₁₃₇	C₄	semidirect
22. C₄×D₈×C₁₃₇	C₄	semidirect
23. C₄×D₈×C₁₃₇	C₄	semidirect
265. #21137	C₁₃₇	direct (N × H)
266. C₁₃₇	#21137	direct (N × H)
268. #2922	C₂×C₁₃₇	semidirect
269. C₄×#131	C₂×C₁₃₇	semidirect
270. #1929	C₂×C₁₃₇	semidirect
271. #1922	C₂×C₁₃₇	semidirect
273. #1866	C₂×C₁₃₇	semidirect
274. C₄×#108	C₂×C₁₃₇	semidirect
275. C₄×#104	C₂×C₁₃₇	semidirect
276. C₄×#104	C₂×C₁₃₇	semidirect
277. #1744	C₂×C₁₃₇	semidirect
282. C₄×Q₁₆	C₄×C₁₃₇	semidirect
283. C₄×Q₁₆	C₄×C₁₃₇	semidirect
284. C₄×SD₁₆	C₄×C₁₃₇	semidirect
285. C₄×SD₁₆	C₄×C₁₃₇	semidirect
286. C₄×SD₁₆	C₄×C₁₃₇	semidirect
287. C₄×SD₁₆	C₄×C₁₃₇	semidirect
288. C₄×D₈	C₄×C₁₃₇	semidirect
289. C₄×D₈	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#135×C₁₃₇	2
#2922×C₁₃₇	2
C₄×#131×C₁₃₇	2
#1929×C₁₃₇	2
#1922×C₁₃₇	2
#1876×C₁₃₇	2
#1866×C₁₃₇	2
C₄×#108×C₁₃₇	2
C₄×#104×C₁₃₇	2
#1744×C₁₃₇	2
#21137	137

Subgroups — C137×#21137 #46870523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21137 #46870523