Subgroups — C₂×#1809×C₁₃₇ #46870045

Order 35072.

1662 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#380×C₁₃₇	C₂	1	2	yes	maximal
5	#1809×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₃₇	—	2	4	no	—
9	C₂²×M₁₆×C₁₃₇	—	2	4	no	—
10	C₂²×M₁₆×C₁₃₇	C₄	1	8	yes	complemented
11	C₂²×M₁₆×C₁₃₇	C₂²	1	4	yes	—
12	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
17	C₂×#107×C₁₃₇	—	2	4	no	—
18	C₂×#107×C₁₃₇	C₂²	1	4	yes	complemented
19	C₂×#106×C₁₃₇	—	2	4	no	—
20	C₂×#106×C₁₃₇	C₂²	1	4	yes	complemented
21	#380×C₁₃₇	—	2	4	no	—
22	#380×C₁₃₇	C₂²	1	8	yes	—
23	C₂×#95×C₁₃₇	—	2	2	no	—
24	#340×C₁₃₇	C₂²	1	8	yes	complemented
25	C₂⁵×C₁₃₇	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₇	—	2	2	no	—
27	C₂³×C₄×C₁₃₇	—	2	2	no	—
28	C₂³×C₄×C₁₃₇	—	2	2	no	—
29	C₂³×C₄×C₁₃₇	—	2	2	no	—
30	C₂³×C₄×C₁₃₇	—	2	2	no	—
31	C₂³×C₄×C₁₃₇	—	2	2	no	—
32	C₂³×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
34	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₇	Q₈	1	4	yes	—
36	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₃₇	—	2	32	no	—
39	C₂×M₁₆×C₁₃₇	—	2	8	no	—
40	C₂×M₁₆×C₁₃₇	—	2	8	no	—
41	C₂×M₁₆×C₁₃₇	C₂×C₄	1	16	yes	complemented
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
47	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	4	8	no	—
60	#107×C₁₃₇	—	2	8	no	—
61	#106×C₁₃₇	—	2	8	no	—
62	#95×C₁₃₇	—	2	8	no	—
63	C₂⁴×C₁₃₇	—	2	2	no	—
64	C₂⁴×C₁₃₇	—	2	2	no	—
65	C₂⁴×C₁₃₇	—	2	4	no	—
66	C₂⁴×C₁₃₇	—	2	4	no	—
67	C₂⁴×C₁₃₇	C₄⋊C₄	1	4	yes	—
68	C₂⁴×C₁₃₇	C₂×D₄	1	2	yes	—
69	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	—	2	2	no	—
71	C₂²×C₄×C₁₃₇	—	2	2	no	—
72	C₂²×C₄×C₁₃₇	—	2	8	no	—
73	C₂²×C₄×C₁₃₇	—	2	8	no	—
74	C₂²×C₄×C₁₃₇	—	2	4	no	—
75	C₂²×C₄×C₁₃₇	—	2	4	no	—
76	C₂²×C₄×C₁₃₇	—	2	8	no	—
77	C₂²×C₄×C₁₃₇	—	2	8	no	—
78	C₂²×C₄×C₁₃₇	—	2	2	no	—
79	C₂²×C₄×C₁₃₇	—	2	2	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	4	no	—
83	C₂²×C₄×C₁₃₇	—	2	4	no	—
84	C₂²×C₄×C₁₃₇	—	4	4	no	—
85	C₂²×C₄×C₁₃₇	—	4	4	no	—
86	C₂²×C₄×C₁₃₇	—	4	4	no	—
87	C₂²×C₄×C₁₃₇	—	4	4	no	—
88	C₂²×C₄×C₁₃₇	—	4	4	no	—
89	C₂²×C₄×C₁₃₇	—	4	4	no	—
90	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
91	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
92	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
101	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
102	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
103	M₁₆×C₁₃₇	—	2	32	no	—
104	C₂×C₈×C₁₃₇	—	2	8	no	—
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	2	no	—
107	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	16	yes	complemented
108	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
110	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₁₃₇	—	2	4	no	—
113	C₄⋊C₄×C₁₃₇	—	2	4	no	—
114	C₄⋊C₄×C₁₃₇	—	2	4	no	—
115	C₄⋊C₄×C₁₃₇	—	2	4	no	—
116	C₄⋊C₄×C₁₃₇	—	4	4	no	—
117	C₄⋊C₄×C₁₃₇	—	4	4	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	16	no	—
119	C₂³×C₁₃₇	—	2	2	no	—
120	C₂³×C₁₃₇	—	2	2	no	—
121	C₂³×C₁₃₇	—	2	4	no	—
122	C₂³×C₁₃₇	—	2	4	no	—
123	C₂³×C₁₃₇	—	2	8	no	—
124	C₂³×C₁₃₇	—	2	16	no	—
125	C₂³×C₁₃₇	—	4	8	no	—
126	C₂³×C₁₃₇	—	4	4	no	—
127	C₂³×C₁₃₇	—	4	4	no	—
128	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
129	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂³×C₁₃₇	#121	1	2	yes	—
131	C₂³×C₁₃₇	#121	1	2	yes	—
132	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
133	C₂³×C₁₃₇	#137	1	4	yes	—
134	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	8	no	—
138	C₂×C₄×C₁₃₇	—	2	4	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	2	4	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	2	16	no	—
143	C₂×C₄×C₁₃₇	—	4	4	no	—
144	C₂×C₄×C₁₃₇	—	4	4	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	4	4	no	—
148	C₂×C₄×C₁₃₇	—	4	4	no	—
149	C₂×C₄×C₁₃₇	—	8	8	no	—
150	C₂×C₄×C₁₃₇	—	8	8	no	—
151	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃₇	#117	1	4	yes	—
155	C₂×C₄×C₁₃₇	#121	1	2	yes	—
156	C₂×C₄×C₁₃₇	#121	1	2	yes	—
157	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
158	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₃₇	—	2	4	no	—
166	C₈×C₁₃₇	C₂×C₂²⋊C₄	1	8	yes	complemented
167	C₂²×C₁₃₇	—	2	8	no	—
168	C₂²×C₁₃₇	—	2	4	no	—
169	C₂²×C₁₃₇	—	4	16	no	—
170	C₂²×C₁₃₇	—	4	4	no	—
171	C₂²×C₁₃₇	—	4	2	no	—
172	C₂²×C₁₃₇	—	4	2	no	—
173	C₂²×C₁₃₇	#380	1	4	yes	—
174	C₂²×C₁₃₇	#428	1	8	yes	—
175	C₂²×C₁₃₇	#468	1	8	yes	—
176	C₂²×C₁₃₇	#469	1	4	yes	—
177	C₂²×C₁₃₇	#470	1	4	yes	—
178	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
180	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
181	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
182	C₂²×C₁₃₇	C₂×#137	1	2	yes	—
183	C₄×C₁₃₇	—	2	4	no	—
184	C₄×C₁₃₇	—	8	4	no	—
185	C₄×C₁₃₇	—	8	4	no	—
186	C₄×C₁₃₇	#380	1	4	yes	—
187	C₄×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
188	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₁₃₇	—	4	4	no	—
192	C₂×C₁₃₇	#1809	1	8	yes	direct product factor
193	C₂×C₁₃₇	C₂×#380	1	1	yes	characteristic
194	C₂×C₁₃₇	C₂×#428	1	2	yes	—
195	C₂×C₁₃₇	C₂×#468	1	2	yes	—
196	C₂×C₁₃₇	C₂×#469	1	1	yes	characteristic
197	C₂×C₁₃₇	C₂×#470	1	1	yes	characteristic
198	C₂×#1809	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₇	C₂×#1809	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
201	C₂²×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	C₂²×#106	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	C₂×#380	C₂×C₁₃₇	1	2	yes	—
204	#1809	C₂×C₁₃₇	1	8	yes	direct product factor
205	C₂×#340	C₂×C₁₃₇	1	2	yes	complemented
206	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
207	C₂²×M₁₆	—	2	4	no	—
208	C₂²×M₁₆	—	2	4	no	—
209	C₂²×M₁₆	C₄×C₁₃₇	1	8	yes	complemented
210	C₂²×M₁₆	C₂²×C₁₃₇	1	4	yes	—
211	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
215	C₂²×C₂²⋊C₄	—	2	2	no	—
216	C₂×#107	—	2	4	no	—
217	C₂×#107	C₂²×C₁₃₇	1	4	yes	complemented
218	C₂×#106	—	2	4	no	—
219	C₂×#106	C₂²×C₁₃₇	1	4	yes	complemented
220	#380	—	2	4	no	—
221	#380	C₂²×C₁₃₇	1	8	yes	—
222	C₂×#95	—	2	2	no	—
223	#340	C₂²×C₁₃₇	1	8	yes	complemented
224	C₂⁵	D₄×C₁₃₇	1	1	yes	characteristic
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	C₂×C₄×C₁₃₇	1	4	yes	—
232	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
233	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
234	C₂³×C₄	Q₈×C₁₃₇	1	4	yes	—
235	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
237	C₂×M₁₆	—	2	32	no	—
238	C₂×M₁₆	—	2	8	no	—
239	C₂×M₁₆	—	2	8	no	—
240	C₂×M₁₆	C₂×C₄×C₁₃₇	1	16	yes	complemented
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
244	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
245	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
246	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
247	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
249	C₂×C₄⋊C₄	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
257	C₂×C₂²⋊C₄	—	2	8	no	—
258	C₂×C₂²⋊C₄	—	4	8	no	—
259	#107	—	2	8	no	—
260	#106	—	2	8	no	—
261	#95	—	2	8	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	C₄⋊C₄×C₁₃₇	1	4	yes	—
267	C₂⁴	C₂×D₄×C₁₃₇	1	2	yes	—
268	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
290	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×Q₈×C₁₃₇	1	4	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
299	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
300	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
302	M₁₆	—	2	32	no	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	16	yes	complemented
307	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
308	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
309	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₂²⋊C₄	—	4	16	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	16	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
328	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
329	C₂³	#121×C₁₃₇	1	2	yes	—
330	C₂³	#121×C₁₃₇	1	2	yes	—
331	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
332	C₂³	#137×C₁₃₇	1	4	yes	—
333	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	8	8	no	—
349	C₂×C₄	—	8	8	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
351	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
352	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
353	C₂×C₄	#117×C₁₃₇	1	4	yes	—
354	C₂×C₄	#121×C₁₃₇	1	2	yes	—
355	C₂×C₄	#121×C₁₃₇	1	2	yes	—
356	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
358	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	C₂×C₂²⋊C₄×C₁₃₇	1	8	yes	complemented
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	16	no	—
372	C₂²	#380×C₁₃₇	1	4	yes	—
373	C₂²	#428×C₁₃₇	1	8	yes	—
374	C₂²	#468×C₁₃₇	1	8	yes	—
375	C₂²	#469×C₁₃₇	1	4	yes	—
376	C₂²	#470×C₁₃₇	1	4	yes	—
377	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
378	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
379	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
380	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
381	C₂²	C₂×#137×C₁₃₇	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	8	4	no	—
384	C₄	—	8	4	no	—
385	C₄	#380×C₁₃₇	1	4	yes	—
386	C₄	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
387	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
388	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
389	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	#1809×C₁₃₇	1	8	yes	direct product factor
392	C₂	C₂×#380×C₁₃₇	1	1	yes	characteristic
393	C₂	C₂×#428×C₁₃₇	1	2	yes	—
394	C₂	C₂×#468×C₁₃₇	1	2	yes	—
395	C₂	C₂×#469×C₁₃₇	1	1	yes	characteristic
396	C₂	C₂×#470×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂⁵×C₁₃₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ C₂⁴×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#107×C₁₃₇	C₂	semidirect
3. C₂²×#106×C₁₃₇	C₂	semidirect
5. #1809×C₁₃₇	C₂	direct (N × H)
6. C₂×#340×C₁₃₇	C₂	semidirect
10. C₂²×M₁₆×C₁₃₇	C₄	semidirect
18. C₂×#107×C₁₃₇	C₂²	semidirect
20. C₂×#106×C₁₃₇	C₂²	semidirect
24. #340×C₁₃₇	C₂²	semidirect
41. C₂×M₁₆×C₁₃₇	C₂×C₄	semidirect
107. C₂×C₈×C₁₃₇	C₂²⋊C₄	semidirect
166. C₈×C₁₃₇	C₂×C₂²⋊C₄	semidirect
192. C₂×C₁₃₇	#1809	direct (N × H)
198. C₂×#1809	C₁₃₇	direct (N × H)
199. C₁₃₇	C₂×#1809	direct (N × H)
201. C₂²×#107	C₂×C₁₃₇	semidirect
202. C₂²×#106	C₂×C₁₃₇	semidirect
204. #1809	C₂×C₁₃₇	direct (N × H)
205. C₂×#340	C₂×C₁₃₇	semidirect
209. C₂²×M₁₆	C₄×C₁₃₇	semidirect
217. C₂×#107	C₂²×C₁₃₇	semidirect
219. C₂×#106	C₂²×C₁₃₇	semidirect
223. #340	C₂²×C₁₃₇	semidirect
240. C₂×M₁₆	C₂×C₄×C₁₃₇	semidirect
306. C₂×C₈	C₂²⋊C₄×C₁₃₇	semidirect
365. C₈	C₂×C₂²⋊C₄×C₁₃₇	semidirect
391. C₂	#1809×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
C₂³×M₁₆×C₁₃₇	2
C₂²×#107×C₁₃₇	2
C₂²×#106×C₁₃₇	2
C₂×#380×C₁₃₇	2
#1809×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₂×#1809	137

Subgroups — C2×#1809×C137 #46870045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1809×C₁₃₇ #46870045