Subgroups — C₄×#432×C₁₃₇ #46869852

Order 35072.

1206 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#432×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×C₄³×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1767×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₄×C₄⋊C₈×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1749×C₁₃₇	C₂	1	2	yes	maximal
6	C₄×C₂²⋊C₈×C₁₃₇	C₂	1	2	yes	maximal
7	#1745×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₄×#97×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄²×C₁₃₇	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃₇	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
14	#432×C₁₃₇	C₄	1	16	yes	direct product factor
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	4	yes	—
17	C₂×#97×C₁₃₇	C₂²	1	4	yes	—
18	C₂×#97×C₁₃₇	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₁₃₇	C₂²	1	4	yes	—
20	C₄³×C₁₃₇	C₄	1	2	yes	—
21	C₄³×C₁₃₇	C₄	1	2	yes	—
22	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
26	#336×C₁₃₇	C₂²	1	4	yes	—
27	#336×C₁₃₇	C₂²	1	4	yes	—
28	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₃₇	C₂³	1	8	yes	—
34	C₂×C₄²×C₁₃₇	—	2	8	no	—
35	C₂×C₄²×C₁₃₇	—	2	8	no	—
36	C₂×C₄²×C₁₃₇	—	2	4	no	—
37	C₂×C₄²×C₁₃₇	—	2	4	no	—
38	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃₇	C₂×C₄	1	8	yes	—
50	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₁₃₇	C₂×C₄	1	16	yes	complemented
58	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	16	yes	—
59	#97×C₁₃₇	—	2	8	no	—
60	#97×C₁₃₇	C₂×C₄	1	16	yes	complemented
61	C₄×C₈×C₁₃₇	—	2	8	no	—
62	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃₇	—	2	4	no	—
64	C₂²×C₄×C₁₃₇	—	2	4	no	—
65	C₂²×C₄×C₁₃₇	—	2	4	no	—
66	C₂²×C₄×C₁₃₇	—	2	4	no	—
67	C₂²×C₄×C₁₃₇	—	2	4	no	—
68	C₂²×C₄×C₁₃₇	—	2	4	no	—
69	C₂²×C₄×C₁₃₇	—	2	4	no	—
70	C₂²×C₄×C₁₃₇	—	2	2	no	—
71	C₂²×C₄×C₁₃₇	—	2	2	no	—
72	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
73	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
74	C₂²×C₄×C₁₃₇	M₁₆	1	8	yes	—
75	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₃₇	—	2	8	no	—
87	C₂×C₈×C₁₃₇	—	2	8	no	—
88	C₂×C₈×C₁₃₇	C₂²×C₄	1	16	yes	—
89	C₄²×C₁₃₇	—	2	4	no	—
90	C₄²×C₁₃₇	—	2	4	no	—
91	C₄²×C₁₃₇	—	2	4	no	—
92	C₄²×C₁₃₇	—	2	4	no	—
93	C₄²×C₁₃₇	—	2	4	no	—
94	C₄²×C₁₃₇	—	2	4	no	—
95	C₄²×C₁₃₇	—	2	4	no	—
96	C₄²×C₁₃₇	—	2	4	no	—
97	C₄²×C₁₃₇	—	2	4	no	—
98	C₄²×C₁₃₇	—	2	2	no	—
99	C₄²×C₁₃₇	—	2	2	no	—
100	C₄²×C₁₃₇	C₄²	1	4	yes	—
101	C₄²×C₁₃₇	C₄²	1	4	yes	—
102	C₄²×C₁₃₇	M₁₆	1	8	yes	—
103	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
104	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
105	C₄²×C₁₃₇	#41	1	4	yes	—
106	C₄²×C₁₃₇	#41	1	4	yes	—
107	C₂³×C₁₃₇	—	2	1	no	—
108	C₂³×C₁₃₇	—	2	1	no	—
109	C₂³×C₁₃₇	—	2	2	no	—
110	C₂³×C₁₃₇	C₂×C₄²	1	2	yes	—
111	C₂³×C₁₃₇	C₂×M₁₆	1	4	yes	—
112	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₃₇	—	2	16	no	—
114	C₂×C₄×C₁₃₇	—	2	2	no	—
115	C₂×C₄×C₁₃₇	—	2	2	no	—
116	C₂×C₄×C₁₃₇	—	2	1	no	—
117	C₂×C₄×C₁₃₇	—	2	1	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	8	no	—
126	C₂×C₄×C₁₃₇	—	2	8	no	—
127	C₂×C₄×C₁₃₇	—	2	8	no	—
128	C₂×C₄×C₁₃₇	—	2	16	no	—
129	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₁₃₇	#117	1	4	yes	—
135	C₂×C₄×C₁₃₇	#117	1	4	yes	—
136	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
137	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
138	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
139	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
140	C₂×C₄×C₁₃₇	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
143	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
144	C₈×C₁₃₇	—	2	16	no	—
145	C₂²×C₁₃₇	—	2	2	no	—
146	C₂²×C₁₃₇	—	2	4	no	—
147	C₂²×C₁₃₇	—	2	4	no	—
148	C₂²×C₁₃₇	—	2	2	no	—
149	C₂²×C₁₃₇	C₄×M₁₆	1	4	yes	—
150	C₂²×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
151	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
152	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
153	C₂²×C₁₃₇	C₂²×M₁₆	1	2	yes	—
154	C₂²×C₁₃₇	C₂²×M₁₆	1	2	yes	—
155	C₄×C₁₃₇	—	2	2	no	—
156	C₄×C₁₃₇	—	2	2	no	—
157	C₄×C₁₃₇	—	2	2	no	—
158	C₄×C₁₃₇	—	2	4	no	—
159	C₄×C₁₃₇	—	2	4	no	—
160	C₄×C₁₃₇	—	2	4	no	—
161	C₄×C₁₃₇	—	2	2	no	—
162	C₄×C₁₃₇	C₄×M₁₆	1	4	yes	—
163	C₄×C₁₃₇	#432	1	8	yes	direct product factor
164	C₄×C₁₃₇	C₄×#41	1	4	yes	—
165	C₂×C₁₃₇	—	2	4	no	—
166	C₂×C₁₃₇	C₄×#117	1	1	yes	characteristic
167	C₂×C₁₃₇	C₂×C₄×M₁₆	1	1	yes	characteristic
168	C₂×C₁₃₇	C₂×C₄×M₁₆	1	1	yes	characteristic
169	C₂×C₁₃₇	C₂×#432	1	2	yes	—
170	C₂×C₁₃₇	#2920	1	2	yes	—
171	C₄×#432	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₁₃₇	C₄×#432	1	1	yes	characteristic, direct product factor, Sylow
173	C₂×#432	C₂×C₁₃₇	1	2	yes	—
174	C₂×C₄³	C₂×C₁₃₇	1	1	yes	characteristic
175	#1767	C₂×C₁₃₇	1	2	yes	complemented
176	C₄×C₄⋊C₈	C₂×C₁₃₇	1	2	yes	complemented
177	#1749	C₂×C₁₃₇	1	2	yes	—
178	C₄×C₂²⋊C₈	C₂×C₁₃₇	1	2	yes	—
179	#1745	C₂×C₁₃₇	1	2	yes	complemented
180	C₄×#97	C₂×C₁₃₇	1	2	yes	complemented
181	C₂²×C₄²	C₄×C₁₃₇	1	2	yes	—
182	C₂²×C₄²	C₄×C₁₃₇	1	2	yes	—
183	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
184	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
185	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
186	#432	C₄×C₁₃₇	1	16	yes	direct product factor
187	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	4	yes	—
189	C₂×#97	C₂²×C₁₃₇	1	4	yes	—
190	C₂×#97	C₂²×C₁₃₇	1	4	yes	—
191	C₂×C₄×C₈	C₂²×C₁₃₇	1	4	yes	—
192	C₄³	C₄×C₁₃₇	1	2	yes	—
193	C₄³	C₄×C₁₃₇	1	2	yes	—
194	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
195	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
196	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
198	#336	C₂²×C₁₃₇	1	4	yes	—
199	#336	C₂²×C₁₃₇	1	4	yes	—
200	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
201	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
202	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
203	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
204	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₁₃₇	1	8	yes	—
206	C₂×C₄²	—	2	8	no	—
207	C₂×C₄²	—	2	8	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	—	2	4	no	—
210	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
211	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
212	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
214	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
215	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
216	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
217	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
218	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₁₃₇	1	8	yes	—
222	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
223	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄²	C₂³×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	C₂×C₄×C₁₃₇	1	16	yes	complemented
230	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	16	yes	—
231	#97	—	2	8	no	—
232	#97	C₂×C₄×C₁₃₇	1	16	yes	complemented
233	C₄×C₈	—	2	8	no	—
234	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
245	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
246	C₂²×C₄	M₁₆×C₁₃₇	1	8	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
257	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
258	C₂×C₈	—	2	8	no	—
259	C₂×C₈	—	2	8	no	—
260	C₂×C₈	C₂²×C₄×C₁₃₇	1	16	yes	—
261	C₄²	—	2	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₄²	—	2	4	no	—
267	C₄²	—	2	4	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	C₄²×C₁₃₇	1	4	yes	—
273	C₄²	C₄²×C₁₃₇	1	4	yes	—
274	C₄²	M₁₆×C₁₃₇	1	8	yes	—
275	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
276	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
277	C₄²	#41×C₁₃₇	1	4	yes	—
278	C₄²	#41×C₁₃₇	1	4	yes	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	2	no	—
282	C₂³	C₂×C₄²×C₁₃₇	1	2	yes	—
283	C₂³	C₂×M₁₆×C₁₃₇	1	4	yes	—
284	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
302	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
303	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
304	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
305	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
306	C₂×C₄	#117×C₁₃₇	1	4	yes	—
307	C₂×C₄	#117×C₁₃₇	1	4	yes	—
308	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
309	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
310	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
311	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
312	C₂×C₄	C₂×M₁₆×C₁₃₇	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
314	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
315	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
316	C₈	—	2	16	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	C₄×M₁₆×C₁₃₇	1	4	yes	—
322	C₂²	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
323	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
324	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
325	C₂²	C₂²×M₁₆×C₁₃₇	1	2	yes	—
326	C₂²	C₂²×M₁₆×C₁₃₇	1	2	yes	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	2	4	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	4	no	—
334	C₄	C₄×M₁₆×C₁₃₇	1	4	yes	—
335	C₄	#432×C₁₃₇	1	8	yes	direct product factor
336	C₄	C₄×#41×C₁₃₇	1	4	yes	—
337	C₂	—	2	4	no	—
338	C₂	C₄×#117×C₁₃₇	1	1	yes	characteristic
339	C₂	C₂×C₄×M₁₆×C₁₃₇	1	1	yes	characteristic
340	C₂	C₂×C₄×M₁₆×C₁₃₇	1	1	yes	characteristic
341	C₂	C₂×#432×C₁₃₇	1	2	yes	—
342	C₂	#2920×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1767×C₁₃₇	C₂	semidirect
4. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
7. #1745×C₁₃₇	C₂	semidirect
8. C₄×#97×C₁₃₇	C₂	semidirect
14. #432×C₁₃₇	C₄	direct (N × H)
57. C₄⋊C₈×C₁₃₇	C₂×C₄	semidirect
60. #97×C₁₃₇	C₂×C₄	semidirect
163. C₄×C₁₃₇	#432	direct (N × H)
171. C₄×#432	C₁₃₇	direct (N × H)
172. C₁₃₇	C₄×#432	direct (N × H)
175. #1767	C₂×C₁₃₇	semidirect
176. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
179. #1745	C₂×C₁₃₇	semidirect
180. C₄×#97	C₂×C₁₃₇	semidirect
186. #432	C₄×C₁₃₇	direct (N × H)
229. C₄⋊C₈	C₂×C₄×C₁₃₇	semidirect
232. #97	C₂×C₄×C₁₃₇	semidirect
335. C₄	#432×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#432×C₁₃₇	2
C₂×C₄³×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1749×C₁₃₇	2
C₄×C₂²⋊C₈×C₁₃₇	2
#1745×C₁₃₇	2
C₄×#97×C₁₃₇	2
C₄×#432	137

Subgroups — C4×#432×C137 #46869852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#432×C₁₃₇ #46869852