Subgroups — C₁₃₇×#17832 #46867218

Order 35072.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2965×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2925×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2906×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1574×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1573×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1571×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1570×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1569×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1566×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1565×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₂×#335×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₃₇	—	2	1	no	—
13	C₄×#41×C₁₃₇	C₂²	1	1	yes	characteristic
14	#446×C₁₃₇	C₄	1	1	yes	characteristic
15	#446×C₁₃₇	C₄	1	1	yes	characteristic
16	#436×C₁₃₇	C₄	1	1	yes	characteristic
17	#436×C₁₃₇	C₄	1	1	yes	characteristic
18	#435×C₁₃₇	C₄	1	2	yes	—
19	#435×C₁₃₇	C₄	1	2	yes	—
20	#433×C₁₃₇	—	2	2	no	—
21	#432×C₁₃₇	C₂²	1	2	yes	—
22	#431×C₁₃₇	C₂²	1	2	yes	—
23	#431×C₁₃₇	C₂²	1	1	yes	characteristic
24	#431×C₁₃₇	C₂²	1	2	yes	—
25	#424×C₁₃₇	—	2	1	no	—
26	#424×C₁₃₇	—	2	2	no	—
27	#423×C₁₃₇	C₂²	1	1	yes	characteristic
28	#423×C₁₃₇	C₂²	1	1	yes	characteristic
29	#423×C₁₃₇	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
33	#408×C₁₃₇	—	2	1	no	—
34	#405×C₁₃₇	—	2	1	no	—
35	C₄×M₁₆×C₁₃₇	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#335×C₁₃₇	C₂²	1	1	yes	characteristic
39	#335×C₁₃₇	C₂²	1	1	yes	characteristic
40	#335×C₁₃₇	C₂²	1	1	yes	characteristic
41	#335×C₁₃₇	C₂²	1	2	yes	—
42	#335×C₁₃₇	C₂²	1	2	yes	—
43	#334×C₁₃₇	C₂²	1	2	yes	—
44	#334×C₁₃₇	C₂²	1	2	yes	—
45	#334×C₁₃₇	C₂²	1	2	yes	—
46	#334×C₁₃₇	C₂²	1	2	yes	—
47	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
48	#131×C₁₃₇	—	4	4	no	—
49	C₂×M₁₆×C₁₃₇	—	2	1	no	—
50	C₂×M₁₆×C₁₃₇	—	2	2	no	—
51	C₂×M₁₆×C₁₃₇	—	2	1	no	—
52	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃₇	—	2	1	no	—
55	C₂²×C₈×C₁₃₇	—	2	2	no	—
56	C₂²×C₈×C₁₃₇	—	2	1	no	—
57	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₃₇	Q₈	1	1	yes	characteristic
61	C₄×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃₇	Q₈	1	2	yes	—
64	C₄×D₄×C₁₃₇	Q₈	1	1	yes	characteristic
65	#117×C₁₃₇	D₄	1	1	yes	characteristic
66	#117×C₁₃₇	D₄	1	2	yes	—
67	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₃₇	—	2	2	no	—
70	C₄⋊C₈×C₁₃₇	—	2	1	no	—
71	C₄⋊C₈×C₁₃₇	—	2	1	no	—
72	C₄⋊C₈×C₁₃₇	—	2	2	no	—
73	C₄⋊C₈×C₁₃₇	—	2	1	no	—
74	C₄⋊C₈×C₁₃₇	—	2	1	no	—
75	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
76	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
77	C₄⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
79	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
85	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
86	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
87	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
88	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
90	#97×C₁₃₇	—	2	2	no	—
91	#97×C₁₃₇	C₂×C₄	1	2	yes	—
92	#97×C₁₃₇	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₁₃₇	—	2	2	no	—
94	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
99	#41×C₁₃₇	—	2	2	no	—
100	#41×C₁₃₇	—	2	2	no	—
101	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
103	C₂×D₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
110	M₁₆×C₁₃₇	—	2	4	no	—
111	M₁₆×C₁₃₇	—	4	2	no	—
112	M₁₆×C₁₃₇	—	4	4	no	—
113	M₁₆×C₁₃₇	—	4	2	no	—
114	M₁₆×C₁₃₇	—	4	2	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	—	2	1	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	1	no	—
122	C₂×C₈×C₁₃₇	—	4	1	no	—
123	C₂×C₈×C₁₃₇	—	4	4	no	—
124	C₂×C₈×C₁₃₇	—	4	2	no	—
125	C₂×C₈×C₁₃₇	—	4	2	no	—
126	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
139	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
141	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
144	C₄²×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
146	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	2	2	no	—
149	D₄×C₁₃₇	—	2	4	no	—
150	D₄×C₁₃₇	—	2	2	no	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	2	2	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₁₃₇	#137	1	2	yes	—
167	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₁₃₇	—	2	1	no	—
171	C₈×C₁₃₇	—	2	2	no	—
172	C₈×C₁₃₇	—	2	1	no	—
173	C₈×C₁₃₇	—	2	1	no	—
174	C₈×C₁₃₇	—	2	2	no	—
175	C₈×C₁₃₇	—	4	1	no	—
176	C₈×C₁₃₇	—	4	1	no	—
177	C₈×C₁₃₇	—	4	1	no	—
178	C₈×C₁₃₇	—	4	2	no	—
179	C₈×C₁₃₇	—	4	1	no	—
180	C₈×C₁₃₇	—	4	2	no	—
181	C₈×C₁₃₇	#131	1	2	yes	complemented
182	C₂²×C₁₃₇	—	2	1	no	—
183	C₂²×C₁₃₇	—	2	1	no	—
184	C₂²×C₁₃₇	—	2	2	no	—
185	C₂²×C₁₃₇	—	2	2	no	—
186	C₂²×C₁₃₇	—	2	2	no	—
187	C₂²×C₁₃₇	#428	1	2	yes	—
188	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₁₃₇	—	2	1	no	—
190	C₄×C₁₃₇	—	2	2	no	—
191	C₄×C₁₃₇	—	2	2	no	—
192	C₄×C₁₃₇	—	2	1	no	—
193	C₄×C₁₃₇	—	2	1	no	—
194	C₄×C₁₃₇	—	2	2	no	—
195	C₄×C₁₃₇	#428	1	2	yes	—
196	C₄×C₁₃₇	C₂×#131	1	1	yes	characteristic
197	C₄×C₁₃₇	#568	1	1	yes	characteristic
198	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
200	C₂×C₁₃₇	—	2	2	no	—
201	C₂×C₁₃₇	—	4	2	no	—
202	C₂×C₁₃₇	#2906	1	1	yes	characteristic
203	C₂×C₁₃₇	C₂×#428	1	1	yes	characteristic
204	C₂×C₁₃₇	#2916	1	1	yes	characteristic
205	#17832	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₁₃₇	#17832	1	1	yes	characteristic, direct product factor, Sylow
207	#2965	C₂×C₁₃₇	1	1	yes	characteristic
208	#2925	C₂×C₁₃₇	1	1	yes	characteristic
209	#2906	C₂×C₁₃₇	1	1	yes	characteristic
210	#1574	C₂×C₁₃₇	1	2	yes	complemented
211	#1573	C₂×C₁₃₇	1	2	yes	complemented
212	#1571	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	#1570	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	#1569	C₂×C₁₃₇	1	2	yes	complemented
215	#1566	C₂×C₁₃₇	1	1	yes	characteristic, complemented
216	#1565	C₂×C₁₃₇	1	2	yes	complemented
217	C₂×#335	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	C₂×#131	—	2	1	no	—
219	C₄×#41	C₂²×C₁₃₇	1	1	yes	characteristic
220	#446	C₄×C₁₃₇	1	1	yes	characteristic
221	#446	C₄×C₁₃₇	1	1	yes	characteristic
222	#436	C₄×C₁₃₇	1	1	yes	characteristic
223	#436	C₄×C₁₃₇	1	1	yes	characteristic
224	#435	C₄×C₁₃₇	1	2	yes	—
225	#435	C₄×C₁₃₇	1	2	yes	—
226	#433	—	2	2	no	—
227	#432	C₂²×C₁₃₇	1	2	yes	—
228	#431	C₂²×C₁₃₇	1	2	yes	—
229	#431	C₂²×C₁₃₇	1	1	yes	characteristic
230	#431	C₂²×C₁₃₇	1	2	yes	—
231	#424	—	2	1	no	—
232	#424	—	2	2	no	—
233	#423	C₂²×C₁₃₇	1	1	yes	characteristic
234	#423	C₂²×C₁₃₇	1	1	yes	characteristic
235	#423	C₂²×C₁₃₇	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
239	#408	—	2	1	no	—
240	#405	—	2	1	no	—
241	C₄×M₁₆	C₂²×C₁₃₇	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
243	#335	C₂²×C₁₃₇	1	1	yes	characteristic
244	#335	C₂²×C₁₃₇	1	1	yes	characteristic
245	#335	C₂²×C₁₃₇	1	1	yes	characteristic
246	#335	C₂²×C₁₃₇	1	1	yes	characteristic
247	#335	C₂²×C₁₃₇	1	2	yes	—
248	#335	C₂²×C₁₃₇	1	2	yes	—
249	#334	C₂²×C₁₃₇	1	2	yes	—
250	#334	C₂²×C₁₃₇	1	2	yes	—
251	#334	C₂²×C₁₃₇	1	2	yes	—
252	#334	C₂²×C₁₃₇	1	2	yes	—
253	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
254	#131	—	4	4	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
259	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
265	C₄×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
266	C₄×Q₈	Q₈×C₁₃₇	1	1	yes	characteristic
267	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
268	C₄×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
269	C₄×D₄	Q₈×C₁₃₇	1	2	yes	—
270	C₄×D₄	Q₈×C₁₃₇	1	1	yes	characteristic
271	#117	D₄×C₁₃₇	1	1	yes	characteristic
272	#117	D₄×C₁₃₇	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
282	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
283	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
284	C₄⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
285	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
286	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
288	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
290	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
294	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
295	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
296	#97	—	2	2	no	—
297	#97	C₂×C₄×C₁₃₇	1	2	yes	—
298	#97	C₂×C₄×C₁₃₇	1	2	yes	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
301	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
308	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
309	C₂×D₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
315	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
316	M₁₆	—	2	4	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	4	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	4	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
334	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
335	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
336	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
337	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
338	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
339	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
340	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
341	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
342	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
343	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
344	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
345	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
346	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
347	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
348	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
349	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
350	C₄²	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
351	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
352	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
353	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
367	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
368	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
369	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
372	C₂×C₄	#137×C₁₃₇	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	#131×C₁₃₇	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#428×C₁₃₇	1	2	yes	—
394	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#428×C₁₃₇	1	2	yes	—
402	C₄	C₂×#131×C₁₃₇	1	1	yes	characteristic
403	C₄	#568×C₁₃₇	1	1	yes	characteristic
404	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
405	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#2906×C₁₃₇	1	1	yes	characteristic
409	C₂	C₂×#428×C₁₃₇	1	1	yes	characteristic
410	C₂	#2916×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	D₄
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
4. #1574×C₁₃₇	C₂	semidirect
5. #1573×C₁₃₇	C₂	semidirect
6. #1571×C₁₃₇	C₂	semidirect
7. #1570×C₁₃₇	C₂	semidirect
8. #1569×C₁₃₇	C₂	semidirect
9. #1566×C₁₃₇	C₂	semidirect
10. #1565×C₁₃₇	C₂	semidirect
11. C₂×#335×C₁₃₇	C₂	semidirect
181. C₈×C₁₃₇	#131	semidirect
205. #17832	C₁₃₇	direct (N × H)
206. C₁₃₇	#17832	direct (N × H)
210. #1574	C₂×C₁₃₇	semidirect
211. #1573	C₂×C₁₃₇	semidirect
212. #1571	C₂×C₁₃₇	semidirect
213. #1570	C₂×C₁₃₇	semidirect
214. #1569	C₂×C₁₃₇	semidirect
215. #1566	C₂×C₁₃₇	semidirect
216. #1565	C₂×C₁₃₇	semidirect
217. C₂×#335	C₂×C₁₃₇	semidirect
387. C₈	#131×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2965×C₁₃₇	2
#2925×C₁₃₇	2
#2906×C₁₃₇	2
#1574×C₁₃₇	2
#1573×C₁₃₇	2
#1571×C₁₃₇	2
#1570×C₁₃₇	2
#1569×C₁₃₇	2
#1566×C₁₃₇	2
#1565×C₁₃₇	2
C₂×#335×C₁₃₇	2
#17832	137

Subgroups — C137×#17832 #46867218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17832 #46867218