Subgroups — C₁₃₇×#17808 #46867194

Order 35072.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2920×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2920×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#431×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1574×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1572×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1565×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
8	#432×C₁₃₇	—	2	1	no	—
9	#432×C₁₃₇	C₄	1	2	yes	—
10	#432×C₁₃₇	C₄	1	2	yes	—
11	#432×C₁₃₇	C₂²	1	2	yes	—
12	#431×C₁₃₇	—	2	1	no	—
13	#431×C₁₃₇	—	2	1	no	—
14	#431×C₁₃₇	—	2	1	no	—
15	#431×C₁₃₇	C₂²	1	2	yes	—
16	#431×C₁₃₇	C₂²	1	2	yes	—
17	#431×C₁₃₇	C₂²	1	2	yes	—
18	#431×C₁₃₇	C₂²	1	2	yes	—
19	#431×C₁₃₇	C₂²	1	2	yes	—
20	#423×C₁₃₇	C₄	1	2	yes	—
21	#423×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
23	#407×C₁₃₇	—	2	1	no	—
24	#407×C₁₃₇	C₄	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
26	C₄×M₁₆×C₁₃₇	—	2	1	no	—
27	C₄×M₁₆×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
29	#335×C₁₃₇	C₂²	1	8	yes	complemented
30	#334×C₁₃₇	C₂²	1	8	yes	complemented
31	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₇	Q₈	1	1	yes	characteristic
34	C₂×M₁₆×C₁₃₇	—	2	2	no	—
35	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
36	C₂²×C₈×C₁₃₇	—	2	2	no	—
37	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₃₇	—	2	2	no	—
50	C₄⋊C₈×C₁₃₇	—	2	2	no	—
51	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
52	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
53	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
54	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
55	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
56	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
57	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
58	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
59	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
60	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
61	#97×C₁₃₇	—	2	2	no	—
62	#97×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₄×C₈×C₁₃₇	—	2	2	no	—
64	C₄×C₈×C₁₃₇	—	2	2	no	—
65	C₄×C₈×C₁₃₇	—	2	2	no	—
66	C₄×C₈×C₁₃₇	C₂³	1	4	yes	—
67	C₂⁴×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃₇	—	2	4	no	—
69	C₂²×C₄×C₁₃₇	—	4	2	no	—
70	C₂²×C₄×C₁₃₇	—	4	2	no	—
71	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
89	M₁₆×C₁₃₇	—	2	8	no	—
90	M₁₆×C₁₃₇	—	4	4	no	—
91	C₂×C₈×C₁₃₇	—	2	4	no	—
92	C₂×C₈×C₁₃₇	—	2	4	no	—
93	C₂×C₈×C₁₃₇	—	4	4	no	—
94	C₂×C₈×C₁₃₇	C₂²×C₄	1	8	yes	—
95	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
111	C₂³×C₁₃₇	—	2	2	no	—
112	C₂³×C₁₃₇	—	4	1	no	—
113	C₂³×C₁₃₇	—	4	1	no	—
114	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	2	no	—
120	C₂×C₄×C₁₃₇	—	2	2	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	2	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	4	1	no	—
129	C₂×C₄×C₁₃₇	—	4	1	no	—
130	C₂×C₄×C₁₃₇	—	4	1	no	—
131	C₂×C₄×C₁₃₇	—	4	1	no	—
132	C₂×C₄×C₁₃₇	—	4	1	no	—
133	C₂×C₄×C₁₃₇	—	4	1	no	—
134	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	#131	1	4	yes	—
144	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
147	C₈×C₁₃₇	—	2	8	no	—
148	C₈×C₁₃₇	—	4	4	no	—
149	C₈×C₁₃₇	—	4	4	no	—
150	C₂²×C₁₃₇	—	2	1	no	—
151	C₂²×C₁₃₇	—	2	1	no	—
152	C₂²×C₁₃₇	—	2	1	no	—
153	C₂²×C₁₃₇	—	2	1	no	—
154	C₂²×C₁₃₇	—	2	1	no	—
155	C₂²×C₁₃₇	—	2	1	no	—
156	C₂²×C₁₃₇	—	2	1	no	—
157	C₂²×C₁₃₇	—	2	1	no	—
158	C₂²×C₁₃₇	—	4	4	no	—
159	C₂²×C₁₃₇	#424	1	2	yes	—
160	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₄×C₁₃₇	—	2	1	no	—
162	C₄×C₁₃₇	—	2	1	no	—
163	C₄×C₁₃₇	—	2	1	no	—
164	C₄×C₁₃₇	—	2	1	no	—
165	C₄×C₁₃₇	—	2	1	no	—
166	C₄×C₁₃₇	—	2	1	no	—
167	C₄×C₁₃₇	—	2	1	no	—
168	C₄×C₁₃₇	—	2	1	no	—
169	C₄×C₁₃₇	#424	1	2	yes	—
170	C₄×C₁₃₇	#430	1	2	yes	—
171	C₄×C₁₃₇	C₂×#131	1	2	yes	—
172	C₄×C₁₃₇	#575	1	2	yes	—
173	C₂×C₁₃₇	—	2	2	no	—
174	C₂×C₁₃₇	—	4	1	no	—
175	C₂×C₁₃₇	—	4	1	no	—
176	C₂×C₁₃₇	C₂×#424	1	1	yes	characteristic
177	C₂×C₁₃₇	#2911	1	1	yes	characteristic
178	C₂×C₁₃₇	C₂×#430	1	1	yes	characteristic
179	#17808	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₃₇	#17808	1	1	yes	characteristic, direct product factor, Sylow
181	#2920	C₂×C₁₃₇	1	1	yes	characteristic
182	#2920	C₂×C₁₃₇	1	1	yes	characteristic
183	C₂×#431	C₂×C₁₃₇	1	1	yes	characteristic
184	#1574	C₂×C₁₃₇	1	4	yes	complemented
185	#1572	C₂×C₁₃₇	1	4	yes	complemented
186	#1565	C₂×C₁₃₇	1	4	yes	complemented
187	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
188	#432	—	2	1	no	—
189	#432	C₄×C₁₃₇	1	2	yes	—
190	#432	C₄×C₁₃₇	1	2	yes	—
191	#432	C₂²×C₁₃₇	1	2	yes	—
192	#431	—	2	1	no	—
193	#431	—	2	1	no	—
194	#431	—	2	1	no	—
195	#431	C₂²×C₁₃₇	1	2	yes	—
196	#431	C₂²×C₁₃₇	1	2	yes	—
197	#431	C₂²×C₁₃₇	1	2	yes	—
198	#431	C₂²×C₁₃₇	1	2	yes	—
199	#431	C₂²×C₁₃₇	1	2	yes	—
200	#423	C₄×C₁₃₇	1	2	yes	—
201	#423	C₂²×C₁₃₇	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
203	#407	—	2	1	no	—
204	#407	C₄×C₁₃₇	1	2	yes	—
205	C₂×C₂²⋊C₈	—	2	1	no	—
206	C₄×M₁₆	—	2	1	no	—
207	C₄×M₁₆	C₂²×C₁₃₇	1	2	yes	—
208	C₂×C₄×C₈	—	2	1	no	—
209	#335	C₂²×C₁₃₇	1	8	yes	complemented
210	#334	C₂²×C₁₃₇	1	8	yes	complemented
211	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
213	C₂³×C₄	Q₈×C₁₃₇	1	1	yes	characteristic
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
216	C₂²×C₈	—	2	2	no	—
217	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
223	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
224	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
232	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
233	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
234	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
240	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
241	#97	—	2	2	no	—
242	#97	C₂×C₄×C₁₃₇	1	4	yes	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	C₄×C₈	C₂³×C₁₃₇	1	4	yes	—
247	C₂⁴	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
269	M₁₆	—	2	8	no	—
270	M₁₆	—	4	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	4	4	no	—
274	C₂×C₈	C₂²×C₄×C₁₃₇	1	8	yes	—
275	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
276	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
277	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
278	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
279	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
280	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
281	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
283	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
284	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
286	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
288	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
289	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
290	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
291	C₂³	—	2	2	no	—
292	C₂³	—	4	1	no	—
293	C₂³	—	4	1	no	—
294	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
295	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
296	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	#131×C₁₃₇	1	4	yes	—
324	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
327	C₈	—	2	8	no	—
328	C₈	—	4	4	no	—
329	C₈	—	4	4	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	4	4	no	—
339	C₂²	#424×C₁₃₇	1	2	yes	—
340	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	#424×C₁₃₇	1	2	yes	—
350	C₄	#430×C₁₃₇	1	2	yes	—
351	C₄	C₂×#131×C₁₃₇	1	2	yes	—
352	C₄	#575×C₁₃₇	1	2	yes	—
353	C₂	—	2	2	no	—
354	C₂	—	4	1	no	—
355	C₂	—	4	1	no	—
356	C₂	C₂×#424×C₁₃₇	1	1	yes	characteristic
357	C₂	#2911×C₁₃₇	1	1	yes	characteristic
358	C₂	C₂×#430×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	C₂⁴×C₁₃₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1574×C₁₃₇	C₂	semidirect
5. #1572×C₁₃₇	C₂	semidirect
6. #1565×C₁₃₇	C₂	semidirect
29. #335×C₁₃₇	C₂²	semidirect
30. #334×C₁₃₇	C₂²	semidirect
179. #17808	C₁₃₇	direct (N × H)
180. C₁₃₇	#17808	direct (N × H)
184. #1574	C₂×C₁₃₇	semidirect
185. #1572	C₂×C₁₃₇	semidirect
186. #1565	C₂×C₁₃₇	semidirect
209. #335	C₂²×C₁₃₇	semidirect
210. #334	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2920×C₁₃₇	2
C₂×#431×C₁₃₇	2
#1574×C₁₃₇	2
#1572×C₁₃₇	2
#1565×C₁₃₇	2
#17808	137

Subgroups — C137×#17808 #46867194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17808 #46867194