Subgroups — C₁₃₇×#17836 #46867222

Order 35072.

616 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2990×C₁₃₇	C₂	1	2	yes	maximal
2	C₈×#41×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1574×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1573×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1568×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1567×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1564×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#335×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
10	#446×C₁₃₇	—	2	2	no	—
11	C₈×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
12	C₈×Q₈×C₁₃₇	C₄	1	1	yes	characteristic
13	#435×C₁₃₇	—	2	4	no	—
14	C₈×D₄×C₁₃₇	—	2	2	no	—
15	C₈×D₄×C₁₃₇	C₄	1	2	yes	—
16	C₈×D₄×C₁₃₇	C₄	1	1	yes	characteristic
17	C₈×D₄×C₁₃₇	C₄	1	2	yes	—
18	C₈×D₄×C₁₃₇	C₄	1	1	yes	characteristic
19	#432×C₁₃₇	C₂²	1	4	yes	—
20	#431×C₁₃₇	C₂²	1	2	yes	—
21	#431×C₁₃₇	C₂²	1	2	yes	—
22	#431×C₁₃₇	C₂²	1	1	yes	characteristic
23	#423×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	#335×C₁₃₇	C₂²	1	1	yes	characteristic
28	#335×C₁₃₇	C₂²	1	2	yes	—
29	#335×C₁₃₇	C₂²	1	4	yes	—
30	#335×C₁₃₇	C₂²	1	1	yes	characteristic
31	#335×C₁₃₇	C₂²	1	2	yes	—
32	#334×C₁₃₇	C₂²	1	2	yes	—
33	#334×C₁₃₇	C₂²	1	4	yes	—
34	C₂×#41×C₁₃₇	Q₈	1	1	yes	characteristic
35	C₂×M₁₆×C₁₃₇	—	2	2	no	—
36	C₂²×C₈×C₁₃₇	—	2	4	no	—
37	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
41	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
43	C₄×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
46	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
47	#117×C₁₃₇	Q₈	1	1	yes	characteristic
48	#117×C₁₃₇	Q₈	1	2	yes	—
49	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₄⋊C₈×C₁₃₇	—	2	4	no	—
52	C₄⋊C₈×C₁₃₇	—	2	2	no	—
53	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₄⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	C₄⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
58	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
59	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
60	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
61	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
62	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
65	#97×C₁₃₇	—	2	4	no	—
66	C₄×C₈×C₁₃₇	—	2	2	no	—
67	C₄×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
73	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
74	#41×C₁₃₇	—	2	4	no	—
75	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂×D₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
77	C₂×D₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
84	M₁₆×C₁₃₇	—	8	2	no	—
85	C₂×C₈×C₁₃₇	—	2	4	no	—
86	C₂×C₈×C₁₃₇	—	2	2	no	—
87	C₂×C₈×C₁₃₇	—	2	2	no	—
88	C₂×C₈×C₁₃₇	—	2	2	no	—
89	C₂×C₈×C₁₃₇	—	2	4	no	—
90	C₂×C₈×C₁₃₇	—	4	2	no	—
91	C₂×C₈×C₁₃₇	—	4	1	no	—
92	C₂×C₈×C₁₃₇	—	8	4	no	—
93	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
99	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
100	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
102	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
104	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
106	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
110	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
111	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
113	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
115	Q₈×C₁₃₇	—	2	2	no	—
116	D₄×C₁₃₇	—	2	4	no	—
117	D₄×C₁₃₇	#108	1	4	yes	—
118	C₂×C₄×C₁₃₇	—	2	4	no	—
119	C₂×C₄×C₁₃₇	—	2	2	no	—
120	C₂×C₄×C₁₃₇	—	2	1	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	1	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	1	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	1	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
137	C₈×C₁₃₇	—	2	2	no	—
138	C₈×C₁₃₇	—	2	1	no	—
139	C₈×C₁₃₇	—	2	1	no	—
140	C₈×C₁₃₇	—	2	2	no	—
141	C₈×C₁₃₇	—	2	1	no	—
142	C₈×C₁₃₇	—	4	2	no	—
143	C₈×C₁₃₇	—	4	4	no	—
144	C₈×C₁₃₇	—	4	2	no	—
145	C₈×C₁₃₇	#131	1	2	yes	—
146	C₂²×C₁₃₇	—	2	2	no	—
147	C₂²×C₁₃₇	—	2	2	no	—
148	C₂²×C₁₃₇	—	2	1	no	—
149	C₂²×C₁₃₇	—	2	1	no	—
150	C₂²×C₁₃₇	—	2	1	no	—
151	C₂²×C₁₃₇	C₂×#108	1	4	yes	—
152	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
153	C₄×C₁₃₇	—	2	2	no	—
154	C₄×C₁₃₇	—	2	1	no	—
155	C₄×C₁₃₇	—	2	2	no	—
156	C₄×C₁₃₇	—	2	1	no	—
157	C₄×C₁₃₇	—	2	1	no	—
158	C₄×C₁₃₇	—	2	2	no	—
159	C₄×C₁₃₇	C₂×#108	1	2	yes	—
160	C₄×C₁₃₇	C₂×#131	1	1	yes	characteristic
161	C₄×C₁₃₇	#568	1	1	yes	characteristic
162	C₄×C₁₃₇	#576	1	1	yes	characteristic
163	C₄×C₁₃₇	#578	1	1	yes	characteristic
164	C₂×C₁₃₇	—	2	4	no	—
165	C₂×C₁₃₇	—	4	1	no	—
166	C₂×C₁₃₇	#2906	1	1	yes	characteristic
167	C₂×C₁₃₇	#2913	1	1	yes	characteristic
168	C₂×C₁₃₇	C₂²×#108	1	1	yes	characteristic
169	#17836	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₁₃₇	#17836	1	1	yes	characteristic, direct product factor, Sylow
171	#2990	C₂×C₁₃₇	1	2	yes	—
172	C₈×#41	C₂×C₁₃₇	1	1	yes	characteristic
173	#1574	C₂×C₁₃₇	1	2	yes	complemented
174	#1573	C₂×C₁₃₇	1	4	yes	complemented
175	#1568	C₂×C₁₃₇	1	2	yes	complemented
176	#1567	C₂×C₁₃₇	1	1	yes	characteristic, complemented
177	#1564	C₂×C₁₃₇	1	1	yes	characteristic, complemented
178	C₂×#335	C₂×C₁₃₇	1	2	yes	complemented
179	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
180	#446	—	2	2	no	—
181	C₈×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
182	C₈×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
183	#435	—	2	4	no	—
184	C₈×D₄	—	2	2	no	—
185	C₈×D₄	C₄×C₁₃₇	1	2	yes	—
186	C₈×D₄	C₄×C₁₃₇	1	1	yes	characteristic
187	C₈×D₄	C₄×C₁₃₇	1	2	yes	—
188	C₈×D₄	C₄×C₁₃₇	1	1	yes	characteristic
189	#432	C₂²×C₁₃₇	1	4	yes	—
190	#431	C₂²×C₁₃₇	1	2	yes	—
191	#431	C₂²×C₁₃₇	1	2	yes	—
192	#431	C₂²×C₁₃₇	1	1	yes	characteristic
193	#423	C₂²×C₁₃₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
195	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
197	#335	C₂²×C₁₃₇	1	1	yes	characteristic
198	#335	C₂²×C₁₃₇	1	2	yes	—
199	#335	C₂²×C₁₃₇	1	4	yes	—
200	#335	C₂²×C₁₃₇	1	1	yes	characteristic
201	#335	C₂²×C₁₃₇	1	2	yes	—
202	#334	C₂²×C₁₃₇	1	2	yes	—
203	#334	C₂²×C₁₃₇	1	4	yes	—
204	C₂×#41	Q₈×C₁₃₇	1	1	yes	characteristic
205	C₂×M₁₆	—	2	2	no	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
211	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
212	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
213	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
214	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
215	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
216	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
217	#117	Q₈×C₁₃₇	1	1	yes	characteristic
218	#117	Q₈×C₁₃₇	1	2	yes	—
219	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
220	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
221	C₄⋊C₈	—	2	4	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
225	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
226	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
227	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
228	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
229	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₂²⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
233	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
234	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
235	#97	—	2	4	no	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
238	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
239	C₄×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
243	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
244	#41	—	2	4	no	—
245	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
246	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
247	C₂×D₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
250	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
253	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
254	M₁₆	—	8	2	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	1	no	—
262	C₂×C₈	—	8	4	no	—
263	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
265	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
269	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
270	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
271	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
272	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
273	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
274	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
275	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
276	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
277	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
278	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
279	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
280	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
281	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
282	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
283	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
284	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
285	Q₈	—	2	2	no	—
286	D₄	—	2	4	no	—
287	D₄	#108×C₁₃₇	1	4	yes	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
300	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
303	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
306	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
307	C₈	—	2	2	no	—
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	—	2	2	no	—
311	C₈	—	2	1	no	—
312	C₈	—	4	2	no	—
313	C₈	—	4	4	no	—
314	C₈	—	4	2	no	—
315	C₈	#131×C₁₃₇	1	2	yes	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	C₂×#108×C₁₃₇	1	4	yes	—
322	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	2	no	—
329	C₄	C₂×#108×C₁₃₇	1	2	yes	—
330	C₄	C₂×#131×C₁₃₇	1	1	yes	characteristic
331	C₄	#568×C₁₃₇	1	1	yes	characteristic
332	C₄	#576×C₁₃₇	1	1	yes	characteristic
333	C₄	#578×C₁₃₇	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	1	no	—
336	C₂	#2906×C₁₃₇	1	1	yes	characteristic
337	C₂	#2913×C₁₃₇	1	1	yes	characteristic
338	C₂	C₂²×#108×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₁₃₇	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₄×#41×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1574×C₁₃₇	C₂	semidirect
4. #1573×C₁₃₇	C₂	semidirect
5. #1568×C₁₃₇	C₂	semidirect
6. #1567×C₁₃₇	C₂	semidirect
7. #1564×C₁₃₇	C₂	semidirect
8. C₂×#335×C₁₃₇	C₂	semidirect
169. #17836	C₁₃₇	direct (N × H)
170. C₁₃₇	#17836	direct (N × H)
173. #1574	C₂×C₁₃₇	semidirect
174. #1573	C₂×C₁₃₇	semidirect
175. #1568	C₂×C₁₃₇	semidirect
176. #1567	C₂×C₁₃₇	semidirect
177. #1564	C₂×C₁₃₇	semidirect
178. C₂×#335	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2990×C₁₃₇	2
C₈×#41×C₁₃₇	2
#1574×C₁₃₇	2
#1573×C₁₃₇	2
#1568×C₁₃₇	2
#1567×C₁₃₇	2
#1564×C₁₃₇	2
C₂×#335×C₁₃₇	2
#17836	137

Subgroups — C137×#17836 #46867222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17836 #46867222