Subgroups — C₁₃₇×#10869 #46860255

Order 35072.

774 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	C₂²×#108×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#343×C₁₃₇	C₂	1	2	yes	maximal
5	#1736×C₁₃₇	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
11	C₂×#108×C₁₃₇	—	2	2	no	—
12	C₂×#108×C₁₃₇	—	2	2	no	—
13	C₂×#108×C₁₃₇	C₄	1	4	yes	complemented
14	C₂×#106×C₁₃₇	—	2	1	no	—
15	C₂×#106×C₁₃₇	—	2	1	no	—
16	C₂×#106×C₁₃₇	—	2	2	no	—
17	C₂×#106×C₁₃₇	C₄	1	4	yes	complemented
18	#405×C₁₃₇	—	2	2	no	—
19	#405×C₁₃₇	C₄	1	4	yes	complemented
20	C₂×#97×C₁₃₇	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
22	#343×C₁₃₇	—	2	4	no	—
23	#340×C₁₃₇	—	2	4	no	—
24	C₂³×C₄×C₁₃₇	—	2	2	no	—
25	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₁₃₇	—	2	1	no	—
27	C₂×M₁₆×C₁₃₇	—	2	1	no	—
28	C₂×M₁₆×C₁₃₇	—	2	1	no	—
29	C₂×M₁₆×C₁₃₇	—	2	2	no	—
30	C₂×M₁₆×C₁₃₇	—	2	2	no	—
31	C₂×M₁₆×C₁₃₇	—	2	2	no	—
32	C₂×M₁₆×C₁₃₇	—	2	2	no	—
33	C₂×M₁₆×C₁₃₇	—	2	2	no	—
34	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
35	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
36	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
37	C₂×M₁₆×C₁₃₇	Q₈	1	2	yes	—
38	C₂²×C₈×C₁₃₇	—	2	1	no	—
39	C₂²×C₈×C₁₃₇	—	2	2	no	—
40	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
46	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
47	C₂²×C₈×C₁₃₇	Q₈	1	2	yes	—
48	#117×C₁₃₇	—	2	1	no	—
49	#117×C₁₃₇	—	2	1	no	—
50	#117×C₁₃₇	C₂×C₄	1	2	yes	—
51	#117×C₁₃₇	Q₈	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄²×C₁₃₇	—	2	1	no	—
61	#108×C₁₃₇	—	2	8	no	—
62	#106×C₁₃₇	—	2	4	no	—
63	#106×C₁₃₇	—	2	4	no	—
64	#97×C₁₃₇	—	2	4	no	—
65	C₄×C₈×C₁₃₇	—	2	4	no	—
66	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
67	C₂²×C₄×C₁₃₇	—	2	2	no	—
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	—	8	4	no	—
72	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
86	M₁₆×C₁₃₇	—	2	2	no	—
87	M₁₆×C₁₃₇	—	2	2	no	—
88	M₁₆×C₁₃₇	—	2	2	no	—
89	M₁₆×C₁₃₇	—	2	4	no	—
90	M₁₆×C₁₃₇	—	2	4	no	—
91	M₁₆×C₁₃₇	—	4	2	no	—
92	M₁₆×C₁₃₇	—	4	2	no	—
93	M₁₆×C₁₃₇	C₄⋊C₄	1	4	yes	—
94	C₂×C₈×C₁₃₇	—	2	2	no	—
95	C₂×C₈×C₁₃₇	—	2	2	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	4	2	no	—
99	C₂×C₈×C₁₃₇	—	4	2	no	—
100	C₂×C₈×C₁₃₇	C₄²	1	4	yes	—
101	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
104	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	2	yes	—
105	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
106	C₂×C₈×C₁₃₇	C₄⋊C₄	1	4	yes	—
107	C₂×C₈×C₁₃₇	C₄⋊C₄	1	4	yes	—
108	C₂×C₈×C₁₃₇	C₄⋊C₄	1	2	yes	—
109	C₂×C₈×C₁₃₇	C₄⋊C₄	1	2	yes	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	4	no	—
112	C₄⋊C₄×C₁₃₇	—	2	4	no	—
113	C₄⋊C₄×C₁₃₇	—	4	2	no	—
114	C₄⋊C₄×C₁₃₇	—	4	2	no	—
115	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	4	yes	—
116	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
117	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄²×C₁₃₇	—	2	2	no	—
119	C₄²×C₁₃₇	—	2	2	no	—
120	C₂³×C₁₃₇	—	2	4	no	—
121	C₂³×C₁₃₇	#117	1	1	yes	characteristic
122	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
123	C₂³×C₁₃₇	C₄×Q₈	1	1	yes	characteristic
124	C₂³×C₁₃₇	#121	1	1	yes	characteristic
125	C₂³×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₁₃₇	#124	1	1	yes	characteristic
127	C₂³×C₁₃₇	#125	1	1	yes	characteristic
128	C₂×C₄×C₁₃₇	—	2	4	no	—
129	C₂×C₄×C₁₃₇	—	4	4	no	—
130	C₂×C₄×C₁₃₇	—	4	4	no	—
131	C₂×C₄×C₁₃₇	—	8	4	no	—
132	C₂×C₄×C₁₃₇	—	8	4	no	—
133	C₂×C₄×C₁₃₇	—	8	4	no	—
134	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	C₂×C₂²⋊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	#117	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	#125	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	1	yes	characteristic
162	C₈×C₁₃₇	—	2	4	no	—
163	C₈×C₁₃₇	—	4	4	no	—
164	C₈×C₁₃₇	#95	1	4	yes	—
165	C₈×C₁₃₇	#95	1	4	yes	—
166	C₂²×C₁₃₇	—	2	2	no	—
167	C₂²×C₁₃₇	—	2	2	no	—
168	C₂²×C₁₃₇	—	2	2	no	—
169	C₂²×C₁₃₇	—	2	2	no	—
170	C₂²×C₁₃₇	—	2	2	no	—
171	C₂²×C₁₃₇	—	2	2	no	—
172	C₂²×C₁₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₃₇	#380	1	1	yes	characteristic
174	C₂²×C₁₃₇	#382	1	1	yes	characteristic
175	C₂²×C₁₃₇	#389	1	1	yes	characteristic
176	C₂²×C₁₃₇	#389	1	1	yes	characteristic
177	C₂²×C₁₃₇	#390	1	1	yes	characteristic
178	C₂²×C₁₃₇	#391	1	1	yes	characteristic
179	C₂²×C₁₃₇	#471	1	4	yes	—
180	C₄×C₁₃₇	—	4	4	no	—
181	C₄×C₁₃₇	—	8	4	no	—
182	C₄×C₁₃₇	C₂×#95	1	1	yes	characteristic
183	C₄×C₁₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
184	C₄×C₁₃₇	#380	1	1	yes	characteristic
185	C₄×C₁₃₇	#384	1	1	yes	characteristic
186	C₄×C₁₃₇	#389	1	1	yes	characteristic
187	C₄×C₁₃₇	#389	1	1	yes	characteristic
188	C₄×C₁₃₇	#390	1	1	yes	characteristic
189	C₄×C₁₃₇	#391	1	1	yes	characteristic
190	C₂×C₁₃₇	—	2	1	no	—
191	C₂×C₁₃₇	—	2	1	no	—
192	C₂×C₁₃₇	—	2	1	no	—
193	C₂×C₁₃₇	—	2	1	no	—
194	C₂×C₁₃₇	C₄⋊#95	1	1	yes	characteristic
195	C₂×C₁₃₇	#1815	1	2	yes	—
196	C₂×C₁₃₇	#1951	1	2	yes	—
197	C₂×C₁₃₇	#1977	1	2	yes	—
198	#10869	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₇	#10869	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×#108	C₂×C₁₃₇	1	1	yes	characteristic
201	C₂²×#106	C₂×C₁₃₇	1	1	yes	characteristic
202	C₂×#405	C₂×C₁₃₇	1	1	yes	characteristic
203	C₂×#343	C₂×C₁₃₇	1	2	yes	—
204	#1736	C₂×C₁₃₇	1	2	yes	—
205	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
206	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
210	C₂×#108	—	2	2	no	—
211	C₂×#108	—	2	2	no	—
212	C₂×#108	C₄×C₁₃₇	1	4	yes	complemented
213	C₂×#106	—	2	1	no	—
214	C₂×#106	—	2	1	no	—
215	C₂×#106	—	2	2	no	—
216	C₂×#106	C₄×C₁₃₇	1	4	yes	complemented
217	#405	—	2	2	no	—
218	#405	C₄×C₁₃₇	1	4	yes	complemented
219	C₂×#97	—	2	1	no	—
220	C₂×C₄×C₈	—	2	1	no	—
221	#343	—	2	4	no	—
222	#340	—	2	4	no	—
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂×M₁₆	—	2	1	no	—
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	1	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
234	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
235	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
236	C₂×M₁₆	Q₈×C₁₃₇	1	2	yes	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
241	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
242	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
243	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
244	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
245	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
246	C₂²×C₈	Q₈×C₁₃₇	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	—	2	1	no	—
249	#117	C₂×C₄×C₁₃₇	1	2	yes	—
250	#117	Q₈×C₁₃₇	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
257	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	#108	—	2	8	no	—
261	#106	—	2	4	no	—
262	#106	—	2	4	no	—
263	#97	—	2	4	no	—
264	C₄×C₈	—	2	4	no	—
265	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	8	4	no	—
271	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
283	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
284	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	4	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	2	no	—
292	M₁₆	C₄⋊C₄×C₁₃₇	1	4	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₄²×C₁₃₇	1	4	yes	—
300	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
301	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
302	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
303	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	2	yes	—
304	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
305	C₂×C₈	C₄⋊C₄×C₁₃₇	1	4	yes	—
306	C₂×C₈	C₄⋊C₄×C₁₃₇	1	4	yes	—
307	C₂×C₈	C₄⋊C₄×C₁₃₇	1	2	yes	—
308	C₂×C₈	C₄⋊C₄×C₁₃₇	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	4	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₂³	—	2	4	no	—
320	C₂³	#117×C₁₃₇	1	1	yes	characteristic
321	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
322	C₂³	C₄×Q₈×C₁₃₇	1	1	yes	characteristic
323	C₂³	#121×C₁₃₇	1	1	yes	characteristic
324	C₂³	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
325	C₂³	#124×C₁₃₇	1	1	yes	characteristic
326	C₂³	#125×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	C₄×Q₈×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄	C₄×Q₈×C₁₃₇	1	1	yes	characteristic
348	C₂×C₄	C₄×Q₈×C₁₃₇	1	1	yes	characteristic
349	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
350	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
352	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	#125×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
361	C₈	—	2	4	no	—
362	C₈	—	4	4	no	—
363	C₈	#95×C₁₃₇	1	4	yes	—
364	C₈	#95×C₁₃₇	1	4	yes	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	C₄×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
372	C₂²	#380×C₁₃₇	1	1	yes	characteristic
373	C₂²	#382×C₁₃₇	1	1	yes	characteristic
374	C₂²	#389×C₁₃₇	1	1	yes	characteristic
375	C₂²	#389×C₁₃₇	1	1	yes	characteristic
376	C₂²	#390×C₁₃₇	1	1	yes	characteristic
377	C₂²	#391×C₁₃₇	1	1	yes	characteristic
378	C₂²	#471×C₁₃₇	1	4	yes	—
379	C₄	—	4	4	no	—
380	C₄	—	8	4	no	—
381	C₄	C₂×#95×C₁₃₇	1	1	yes	characteristic
382	C₄	C₄×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
383	C₄	#380×C₁₃₇	1	1	yes	characteristic
384	C₄	#384×C₁₃₇	1	1	yes	characteristic
385	C₄	#389×C₁₃₇	1	1	yes	characteristic
386	C₄	#389×C₁₃₇	1	1	yes	characteristic
387	C₄	#390×C₁₃₇	1	1	yes	characteristic
388	C₄	#391×C₁₃₇	1	1	yes	characteristic
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	C₄⋊#95×C₁₃₇	1	1	yes	characteristic
394	C₂	#1815×C₁₃₇	1	2	yes	—
395	C₂	#1951×C₁₃₇	1	2	yes	—
396	C₂	#1977×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#121
commutator	C₂×C₄	C₂×C₄²×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
prime radical	C₂⁴×C₁₃₇	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂³×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×#108×C₁₃₇	C₄	semidirect
17. C₂×#106×C₁₃₇	C₄	semidirect
19. #405×C₁₃₇	C₄	semidirect
198. #10869	C₁₃₇	direct (N × H)
199. C₁₃₇	#10869	direct (N × H)
212. C₂×#108	C₄×C₁₃₇	semidirect
216. C₂×#106	C₄×C₁₃₇	semidirect
218. #405	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#108×C₁₃₇	2
C₂²×#106×C₁₃₇	2
C₂×#405×C₁₃₇	2
C₂×#343×C₁₃₇	2
#1736×C₁₃₇	2
#10869	137

Subgroups — C137×#10869 #46860255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10869 #46860255