Subgroups — C₁₃₇×#20802 #46870188

Order 35072.

1070 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×#427×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#405×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2317×C₁₃₇	C₂	1	2	yes	maximal
6	#1847×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1846×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1844×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
14	#428×C₁₃₇	—	2	8	no	—
15	#427×C₁₃₇	—	2	4	no	—
16	C₂×#107×C₁₃₇	C₂²	1	4	yes	—
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₇	—	2	4	no	—
19	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#106×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
24	#405×C₁₃₇	C₄	1	8	yes	complemented
25	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
27	#389×C₁₃₇	—	2	4	no	—
28	#385×C₁₃₇	—	2	4	no	—
29	#384×C₁₃₇	C₂²	1	4	yes	—
30	#382×C₁₃₇	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃₇	—	2	2	no	—
32	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
34	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
35	C₂×M₁₆×C₁₃₇	Q₈	1	4	yes	—
36	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
38	C₂²×C₈×C₁₃₇	Q₈	1	4	yes	—
39	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	#117×C₁₃₇	—	2	4	no	—
43	#117×C₁₃₇	—	2	4	no	—
44	#117×C₁₃₇	C₂×C₄	1	4	yes	—
45	#117×C₁₃₇	Q₈	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
56	C₂×C₄²×C₁₃₇	—	2	2	no	—
57	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
58	#107×C₁₃₇	—	2	4	no	—
59	#107×C₁₃₇	—	2	8	no	—
60	#106×C₁₃₇	—	2	4	no	—
61	#106×C₁₃₇	—	2	4	no	—
62	#106×C₁₃₇	—	2	2	no	—
63	#106×C₁₃₇	—	2	2	no	—
64	#106×C₁₃₇	—	2	8	no	—
65	#97×C₁₃₇	C₂×C₄	1	8	yes	complemented
66	C₄×C₈×C₁₃₇	C₂×C₄	1	8	yes	complemented
67	#95×C₁₃₇	—	2	8	no	—
68	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₇	—	2	2	no	—
70	C₂²×C₄×C₁₃₇	—	2	4	no	—
71	C₂²×C₄×C₁₃₇	—	2	2	no	—
72	C₂²×C₄×C₁₃₇	—	4	4	no	—
73	C₂²×C₄×C₁₃₇	—	8	4	no	—
74	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
76	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
83	M₁₆×C₁₃₇	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₈×C₁₃₇	C₄⋊C₄	1	16	yes	complemented
85	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
89	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
92	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
93	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
94	C₄⋊C₄×C₁₃₇	—	2	4	no	—
95	C₄⋊C₄×C₁₃₇	—	2	2	no	—
96	C₄⋊C₄×C₁₃₇	—	2	4	no	—
97	C₄⋊C₄×C₁₃₇	—	2	2	no	—
98	C₄⋊C₄×C₁₃₇	—	2	2	no	—
99	C₄⋊C₄×C₁₃₇	—	2	2	no	—
100	C₄⋊C₄×C₁₃₇	—	4	4	no	—
101	C₄⋊C₄×C₁₃₇	—	8	8	no	—
102	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
103	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
104	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
105	C₄²×C₁₃₇	—	4	4	no	—
106	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
107	C₄²×C₁₃₇	C₂×Q₈	1	4	yes	—
108	C₂³×C₁₃₇	—	2	4	no	—
109	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
110	C₂³×C₁₃₇	#127	1	2	yes	—
111	C₂³×C₁₃₇	C₄⋊Q₈	1	2	yes	—
112	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₃₇	—	2	8	no	—
114	C₂×C₄×C₁₃₇	—	4	2	no	—
115	C₂×C₄×C₁₃₇	—	4	2	no	—
116	C₂×C₄×C₁₃₇	—	4	4	no	—
117	C₂×C₄×C₁₃₇	—	4	4	no	—
118	C₂×C₄×C₁₃₇	—	4	8	no	—
119	C₂×C₄×C₁₃₇	—	4	4	no	—
120	C₂×C₄×C₁₃₇	—	8	8	no	—
121	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
122	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
123	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
124	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₁₃₇	#127	1	2	yes	—
126	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	4	yes	—
127	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	4	yes	—
128	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
129	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
135	C₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
136	C₈×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₈×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	—
138	C₂²×C₁₃₇	—	2	4	no	—
139	C₂²×C₁₃₇	—	2	4	no	—
140	C₂²×C₁₃₇	—	2	4	no	—
141	C₂²×C₁₃₇	#384	1	4	yes	—
142	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×C₁₃₇	C₂×#127	1	1	yes	characteristic
144	C₂²×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
145	C₂²×C₁₃₇	#577	1	4	yes	—
146	C₄×C₁₃₇	—	2	8	no	—
147	C₄×C₁₃₇	—	8	2	no	—
148	C₄×C₁₃₇	—	8	2	no	—
149	C₄×C₁₃₇	—	8	4	no	—
150	C₄×C₁₃₇	#384	1	4	yes	—
151	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
152	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
153	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
154	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
155	C₂×C₁₃₇	—	2	4	no	—
156	C₂×C₁₃₇	C₂×#384	1	1	yes	characteristic
157	C₂×C₁₃₇	#2912	1	2	yes	—
158	C₂×C₁₃₇	#3154	1	2	yes	—
159	C₂×C₁₃₇	#3163	1	2	yes	—
160	#20802	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₁₃₇	#20802	1	1	yes	characteristic, direct product factor, Sylow
162	C₂×#428	C₂×C₁₃₇	1	2	yes	—
163	C₂×#427	C₂×C₁₃₇	1	1	yes	characteristic
164	C₂²×#106	C₂×C₁₃₇	1	1	yes	characteristic
165	C₂×#405	C₂×C₁₃₇	1	1	yes	characteristic
166	#2317	C₂×C₁₃₇	1	2	yes	—
167	#1847	C₂×C₁₃₇	1	4	yes	complemented
168	#1846	C₂×C₁₃₇	1	2	yes	complemented
169	#1844	C₂×C₁₃₇	1	2	yes	complemented
170	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
172	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
173	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
174	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
175	#428	—	2	8	no	—
176	#427	—	2	4	no	—
177	C₂×#107	C₂²×C₁₃₇	1	4	yes	—
178	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
179	C₂×#106	—	2	4	no	—
180	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
181	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
182	C₂×#106	C₂²×C₁₃₇	1	4	yes	—
183	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
184	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
185	#405	C₄×C₁₃₇	1	8	yes	complemented
186	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
188	#389	—	2	4	no	—
189	#385	—	2	4	no	—
190	#384	C₂²×C₁₃₇	1	4	yes	—
191	#382	C₂²×C₁₃₇	1	4	yes	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
194	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
195	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
196	C₂×M₁₆	Q₈×C₁₃₇	1	4	yes	—
197	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
198	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
199	C₂²×C₈	Q₈×C₁₃₇	1	4	yes	—
200	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
203	#117	—	2	4	no	—
204	#117	—	2	4	no	—
205	#117	C₂×C₄×C₁₃₇	1	4	yes	—
206	#117	Q₈×C₁₃₇	1	4	yes	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	8	no	—
211	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
212	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
217	C₂×C₄²	—	2	2	no	—
218	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
219	#107	—	2	4	no	—
220	#107	—	2	8	no	—
221	#106	—	2	4	no	—
222	#106	—	2	4	no	—
223	#106	—	2	2	no	—
224	#106	—	2	2	no	—
225	#106	—	2	8	no	—
226	#97	C₂×C₄×C₁₃₇	1	8	yes	complemented
227	C₄×C₈	C₂×C₄×C₁₃₇	1	8	yes	complemented
228	#95	—	2	8	no	—
229	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	—	8	4	no	—
235	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
236	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
237	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
238	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
239	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
240	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
241	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
242	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
243	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
244	M₁₆	C₄⋊C₄×C₁₃₇	1	16	yes	complemented
245	C₂×C₈	C₄⋊C₄×C₁₃₇	1	16	yes	complemented
246	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
247	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
248	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
249	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
250	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
251	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
252	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
253	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
254	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	4	4	no	—
262	C₄⋊C₄	—	8	8	no	—
263	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
264	C₂²⋊C₄	—	4	4	no	—
265	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
266	C₄²	—	4	4	no	—
267	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
268	C₄²	C₂×Q₈×C₁₃₇	1	4	yes	—
269	C₂³	—	2	4	no	—
270	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
271	C₂³	#127×C₁₃₇	1	2	yes	—
272	C₂³	C₄⋊Q₈×C₁₃₇	1	2	yes	—
273	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	4	8	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	8	8	no	—
282	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
283	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
284	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
285	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
286	C₂×C₄	#127×C₁₃₇	1	2	yes	—
287	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
288	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	4	yes	—
289	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	4	yes	—
290	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
295	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
296	C₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
297	C₈	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
298	C₈	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	—
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	#384×C₁₃₇	1	4	yes	—
303	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
304	C₂²	C₂×#127×C₁₃₇	1	1	yes	characteristic
305	C₂²	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
306	C₂²	#577×C₁₃₇	1	4	yes	—
307	C₄	—	2	8	no	—
308	C₄	—	8	4	no	—
309	C₄	—	8	2	no	—
310	C₄	—	8	2	no	—
311	C₄	#384×C₁₃₇	1	4	yes	—
312	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
313	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
314	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
315	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
316	C₂	—	2	4	no	—
317	C₂	C₂×#384×C₁₃₇	1	1	yes	characteristic
318	C₂	#2912×C₁₃₇	1	2	yes	—
319	C₂	#3154×C₁₃₇	1	2	yes	—
320	C₂	#3163×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×#117×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
6. #1847×C₁₃₇	C₂	semidirect
7. #1846×C₁₃₇	C₂	semidirect
8. #1844×C₁₃₇	C₂	semidirect
24. #405×C₁₃₇	C₄	semidirect
65. #97×C₁₃₇	C₂×C₄	semidirect
66. C₄×C₈×C₁₃₇	C₂×C₄	semidirect
83. M₁₆×C₁₃₇	C₄⋊C₄	semidirect
84. C₂×C₈×C₁₃₇	C₄⋊C₄	semidirect
160. #20802	C₁₃₇	direct (N × H)
161. C₁₃₇	#20802	direct (N × H)
167. #1847	C₂×C₁₃₇	semidirect
168. #1846	C₂×C₁₃₇	semidirect
169. #1844	C₂×C₁₃₇	semidirect
185. #405	C₄×C₁₃₇	semidirect
226. #97	C₂×C₄×C₁₃₇	semidirect
227. C₄×C₈	C₂×C₄×C₁₃₇	semidirect
244. M₁₆	C₄⋊C₄×C₁₃₇	semidirect
245. C₂×C₈	C₄⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#428×C₁₃₇	2
C₂×#427×C₁₃₇	2
C₂²×#106×C₁₃₇	2
C₂×#405×C₁₃₇	2
#2317×C₁₃₇	2
#1847×C₁₃₇	2
#1846×C₁₃₇	2
#1844×C₁₃₇	2
#20802	137

Subgroups — C137×#20802 #46870188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20802 #46870188