Subgroups — C₁₃₇×#17834 #46867220

Order 35072.

616 conjugacy classes of subgroups.

The subgroup lattice has 334 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	#1566×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1564×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#334×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	2	yes	—
28	#335×C₁₃₇	C₂²	1	4	yes	—
29	#334×C₁₃₇	C₂²	1	1	yes	characteristic
30	#334×C₁₃₇	C₂²	1	2	yes	—
31	#334×C₁₃₇	C₂²	1	4	yes	—
32	#334×C₁₃₇	C₂²	1	1	yes	characteristic
33	#334×C₁₃₇	C₂²	1	2	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	4	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
135	C₈×C₁₃₇	—	2	2	no	—
136	C₈×C₁₃₇	—	2	1	no	—
137	C₈×C₁₃₇	—	2	1	no	—
138	C₈×C₁₃₇	—	2	2	no	—
139	C₈×C₁₃₇	—	2	1	no	—
140	C₈×C₁₃₇	—	4	2	no	—
141	C₈×C₁₃₇	—	4	2	no	—
142	C₈×C₁₃₇	—	4	4	no	—
143	C₈×C₁₃₇	#131	1	2	yes	—
144	C₂²×C₁₃₇	—	2	2	no	—
145	C₂²×C₁₃₇	—	2	2	no	—
146	C₂²×C₁₃₇	—	2	1	no	—
147	C₂²×C₁₃₇	—	2	1	no	—
148	C₂²×C₁₃₇	—	2	1	no	—
149	C₂²×C₁₃₇	C₂×#108	1	4	yes	—
150	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₄×C₁₃₇	—	2	2	no	—
152	C₄×C₁₃₇	—	2	1	no	—
153	C₄×C₁₃₇	—	2	2	no	—
154	C₄×C₁₃₇	—	2	1	no	—
155	C₄×C₁₃₇	—	2	1	no	—
156	C₄×C₁₃₇	—	2	2	no	—
157	C₄×C₁₃₇	C₂×#108	1	2	yes	—
158	C₄×C₁₃₇	C₂×#131	1	1	yes	characteristic
159	C₄×C₁₃₇	#568	1	1	yes	characteristic
160	C₄×C₁₃₇	#577	1	2	yes	—
161	C₂×C₁₃₇	—	2	4	no	—
162	C₂×C₁₃₇	—	4	1	no	—
163	C₂×C₁₃₇	#2906	1	1	yes	characteristic
164	C₂×C₁₃₇	#2912	1	1	yes	characteristic
165	C₂×C₁₃₇	C₂²×#108	1	1	yes	characteristic
166	#17834	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₁₃₇	#17834	1	1	yes	characteristic, direct product factor, Sylow
168	#2990	C₂×C₁₃₇	1	2	yes	—
169	C₈×#41	C₂×C₁₃₇	1	1	yes	characteristic
170	#1574	C₂×C₁₃₇	1	2	yes	complemented
171	#1573	C₂×C₁₃₇	1	4	yes	complemented
172	#1568	C₂×C₁₃₇	1	2	yes	complemented
173	#1566	C₂×C₁₃₇	1	1	yes	characteristic, complemented
174	#1564	C₂×C₁₃₇	1	1	yes	characteristic, complemented
175	C₂×#334	C₂×C₁₃₇	1	2	yes	complemented
176	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
177	#446	—	2	2	no	—
178	C₈×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
179	C₈×Q₈	C₄×C₁₃₇	1	1	yes	characteristic
180	#435	—	2	4	no	—
181	C₈×D₄	—	2	2	no	—
182	C₈×D₄	C₄×C₁₃₇	1	2	yes	—
183	C₈×D₄	C₄×C₁₃₇	1	1	yes	characteristic
184	C₈×D₄	C₄×C₁₃₇	1	2	yes	—
185	C₈×D₄	C₄×C₁₃₇	1	1	yes	characteristic
186	#432	C₂²×C₁₃₇	1	4	yes	—
187	#431	C₂²×C₁₃₇	1	2	yes	—
188	#431	C₂²×C₁₃₇	1	2	yes	—
189	#431	C₂²×C₁₃₇	1	1	yes	characteristic
190	#423	C₂²×C₁₃₇	1	2	yes	—
191	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
192	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
194	#335	C₂²×C₁₃₇	1	2	yes	—
195	#335	C₂²×C₁₃₇	1	4	yes	—
196	#334	C₂²×C₁₃₇	1	1	yes	characteristic
197	#334	C₂²×C₁₃₇	1	2	yes	—
198	#334	C₂²×C₁₃₇	1	4	yes	—
199	#334	C₂²×C₁₃₇	1	1	yes	characteristic
200	#334	C₂²×C₁₃₇	1	2	yes	—
201	C₂×#41	Q₈×C₁₃₇	1	1	yes	characteristic
202	C₂×M₁₆	—	2	2	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
205	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
208	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
209	C₄×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
211	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
212	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
213	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
214	#117	Q₈×C₁₃₇	1	1	yes	characteristic
215	#117	Q₈×C₁₃₇	1	2	yes	—
216	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
217	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
218	C₄⋊C₈	—	2	4	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
221	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
222	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
223	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
224	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
225	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
226	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	—	2	4	no	—
229	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
230	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
231	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	2	no	—
234	C₄×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
235	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
236	C₄×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
237	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
238	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
239	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
240	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
241	#41	—	2	4	no	—
242	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
243	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
244	C₂×D₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
248	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
250	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
251	M₁₆	—	8	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	1	no	—
259	C₂×C₈	—	8	4	no	—
260	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
261	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
262	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
263	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
264	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
266	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
267	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
268	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
269	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
270	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
271	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
272	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
273	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
274	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
275	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
276	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
277	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
278	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
279	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
280	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
281	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
282	Q₈	—	2	2	no	—
283	D₄	—	2	4	no	—
284	D₄	#108×C₁₃₇	1	4	yes	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
294	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
295	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
296	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
297	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
298	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
299	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
300	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
302	C₈	—	2	2	no	—
303	C₈	—	2	1	no	—
304	C₈	—	2	1	no	—
305	C₈	—	2	2	no	—
306	C₈	—	2	1	no	—
307	C₈	—	4	2	no	—
308	C₈	—	4	4	no	—
309	C₈	—	4	2	no	—
310	C₈	#131×C₁₃₇	1	2	yes	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	1	no	—
316	C₂²	C₂×#108×C₁₃₇	1	4	yes	—
317	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
318	C₄	—	2	2	no	—
319	C₄	—	2	1	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	2	2	no	—
324	C₄	C₂×#108×C₁₃₇	1	2	yes	—
325	C₄	C₂×#131×C₁₃₇	1	1	yes	characteristic
326	C₄	#568×C₁₃₇	1	1	yes	characteristic
327	C₄	#577×C₁₃₇	1	2	yes	—
328	C₂	—	2	4	no	—
329	C₂	—	4	1	no	—
330	C₂	#2906×C₁₃₇	1	1	yes	characteristic
331	C₂	#2912×C₁₃₇	1	1	yes	characteristic
332	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. #1566×C₁₃₇	C₂	semidirect
7. #1564×C₁₃₇	C₂	semidirect
8. C₂×#334×C₁₃₇	C₂	semidirect
166. #17834	C₁₃₇	direct (N × H)
167. C₁₃₇	#17834	direct (N × H)
170. #1574	C₂×C₁₃₇	semidirect
171. #1573	C₂×C₁₃₇	semidirect
172. #1568	C₂×C₁₃₇	semidirect
173. #1566	C₂×C₁₃₇	semidirect
174. #1564	C₂×C₁₃₇	semidirect
175. C₂×#334	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
#1566×C₁₃₇	2
#1564×C₁₃₇	2
C₂×#334×C₁₃₇	2
#17834	137

Subgroups — C137×#17834 #46867220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17834 #46867220