Subgroups — C₁₃₇×#33612 #46882998

Order 35072.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#509×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#504×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3061×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#3058×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2220×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2218×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2217×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2215×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2159×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#2138×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#357×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#131×C₁₃₇	C₂²	1	1	yes	characteristic
15	#537×C₁₃₇	—	2	1	no	—
16	#535×C₁₃₇	—	2	1	no	—
17	#509×C₁₃₇	—	2	4	no	—
18	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	—
19	C₂×D₁₆×C₁₃₇	C₂²	1	2	yes	—
20	#504×C₁₃₇	—	2	4	no	—
21	C₂×M₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×M₃₂×C₁₃₇	C₂²	1	2	yes	complemented
23	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₁₃₇	C₂²	1	2	yes	complemented
25	#469×C₁₃₇	—	2	2	no	—
26	#468×C₁₃₇	—	2	2	no	—
27	#467×C₁₃₇	C₂²	1	2	yes	complemented
28	#466×C₁₃₇	C₂²	1	2	yes	—
29	#466×C₁₃₇	C₂²	1	2	yes	—
30	#466×C₁₃₇	C₂²	1	2	yes	complemented
31	#427×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
33	#418×C₁₃₇	—	2	1	no	—
34	#417×C₁₃₇	—	2	1	no	—
35	#367×C₁₃₇	C₂²	1	2	yes	complemented
36	#366×C₁₃₇	C₂²	1	2	yes	complemented
37	#358×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
38	#358×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
39	#357×C₁₃₇	C₂²	1	2	yes	—
40	#357×C₁₃₇	C₂²	1	2	yes	—
41	#357×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
42	#357×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₁₃₇	—	2	1	no	—
44	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₇	—	2	1	no	—
46	#135×C₁₃₇	—	2	2	no	—
47	#135×C₁₃₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₇	—	2	1	no	—
50	C₂×D₈×C₁₃₇	—	2	2	no	—
51	C₂×D₈×C₁₃₇	—	2	1	no	—
52	C₂×D₈×C₁₃₇	—	2	2	no	—
53	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
54	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	#131×C₁₃₇	—	2	2	no	—
56	#131×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
59	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
61	#127×C₁₃₇	—	4	1	no	—
62	#124×C₁₃₇	—	4	1	no	—
63	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
64	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
65	#121×C₁₃₇	—	2	2	no	—
66	#121×C₁₃₇	—	2	2	no	—
67	#121×C₁₃₇	—	2	2	no	—
68	#121×C₁₃₇	—	4	1	no	—
69	#121×C₁₃₇	—	4	2	no	—
70	#120×C₁₃₇	—	4	2	no	—
71	#117×C₁₃₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
73	SD₃₂×C₁₃₇	—	2	4	no	—
74	D₁₆×C₁₃₇	—	2	4	no	—
75	M₃₂×C₁₃₇	—	2	4	no	—
76	M₃₂×C₁₃₇	D₄	1	4	yes	complemented
77	C₂×C₁₆×C₁₃₇	—	2	2	no	—
78	C₂×C₁₆×C₁₃₇	—	2	4	no	—
79	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
82	#107×C₁₃₇	—	2	1	no	—
83	#107×C₁₃₇	C₂³	1	1	yes	characteristic
84	#107×C₁₃₇	C₂³	1	2	yes	—
85	#107×C₁₃₇	C₂³	1	1	yes	characteristic
86	#106×C₁₃₇	—	2	1	no	—
87	#103×C₁₃₇	—	2	2	no	—
88	#102×C₁₃₇	—	2	2	no	—
89	#102×C₁₃₇	—	2	2	no	—
90	#102×C₁₃₇	—	2	2	no	—
91	C₂⁴×C₁₃₇	—	4	1	no	—
92	#41×C₁₃₇	—	2	2	no	—
93	#41×C₁₃₇	—	2	2	no	—
94	#41×C₁₃₇	—	4	2	no	—
95	#41×C₁₃₇	—	4	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	D₈	1	1	yes	characteristic
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	1	no	—
100	C₂×D₄×C₁₃₇	—	4	1	no	—
101	C₂×D₄×C₁₃₇	—	4	2	no	—
102	C₂×D₄×C₁₃₇	—	4	2	no	—
103	C₂×D₄×C₁₃₇	—	4	2	no	—
104	C₂×D₄×C₁₃₇	—	4	2	no	—
105	C₂×D₄×C₁₃₇	—	4	1	no	—
106	C₂×D₄×C₁₃₇	—	4	2	no	—
107	C₂×D₄×C₁₃₇	D₈	1	2	yes	—
108	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	—	4	1	no	—
110	C₂²×C₄×C₁₃₇	—	4	1	no	—
111	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₁₃₇	—	2	1	no	—
114	Q₁₆×C₁₃₇	—	2	1	no	—
115	SD₁₆×C₁₃₇	—	4	2	no	—
116	D₈×C₁₃₇	—	2	1	no	—
117	D₈×C₁₃₇	—	2	2	no	—
118	D₈×C₁₃₇	—	2	2	no	—
119	D₈×C₁₃₇	—	2	1	no	—
120	D₈×C₁₃₇	—	4	2	no	—
121	M₁₆×C₁₃₇	—	2	2	no	—
122	M₁₆×C₁₃₇	—	2	4	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃₇	#41	1	2	yes	—
129	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	2	1	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	4	1	no	—
134	C₄⋊C₄×C₁₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
137	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
140	C₄²×C₁₃₇	—	4	1	no	—
141	C₁₆×C₁₃₇	—	2	1	no	—
142	C₁₆×C₁₃₇	—	2	1	no	—
143	C₁₆×C₁₃₇	C₂×D₄	1	4	yes	—
144	C₂³×C₁₃₇	—	4	1	no	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	—	8	2	no	—
147	C₂³×C₁₃₇	—	16	1	no	—
148	C₂³×C₁₃₇	—	16	1	no	—
149	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
150	C₂³×C₁₃₇	C₂×D₈	1	1	yes	characteristic
151	Q₈×C₁₃₇	—	2	2	no	—
152	Q₈×C₁₃₇	—	4	1	no	—
153	Q₈×C₁₃₇	—	4	1	no	—
154	D₄×C₁₃₇	—	2	4	no	—
155	D₄×C₁₃₇	—	2	2	no	—
156	D₄×C₁₃₇	—	4	2	no	—
157	D₄×C₁₃₇	—	4	1	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	4	1	no	—
160	D₄×C₁₃₇	—	8	2	no	—
161	D₄×C₁₃₇	—	8	2	no	—
162	D₄×C₁₃₇	—	16	2	no	—
163	D₄×C₁₃₇	—	16	2	no	—
164	D₄×C₁₃₇	—	16	2	no	—
165	C₂×C₄×C₁₃₇	—	2	2	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	8	2	no	—
172	C₂×C₄×C₁₃₇	—	16	1	no	—
173	C₂×C₄×C₁₃₇	#121	1	2	yes	—
174	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	#135	1	2	yes	—
177	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃₇	—	2	2	no	—
179	C₈×C₁₃₇	#121	1	2	yes	—
180	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
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	—	8	1	no	—
188	C₂²×C₁₃₇	—	8	2	no	—
189	C₂²×C₁₃₇	—	8	2	no	—
190	C₂²×C₁₃₇	—	8	1	no	—
191	C₂²×C₁₃₇	—	8	1	no	—
192	C₂²×C₁₃₇	—	8	2	no	—
193	C₂²×C₁₃₇	—	16	4	no	—
194	C₂²×C₁₃₇	#466	1	2	yes	—
195	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
196	C₄×C₁₃₇	—	2	2	no	—
197	C₄×C₁₃₇	—	8	2	no	—
198	C₄×C₁₃₇	—	8	1	no	—
199	C₄×C₁₃₇	—	8	1	no	—
200	C₄×C₁₃₇	—	8	1	no	—
201	C₄×C₁₃₇	#466	1	2	yes	—
202	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
203	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
204	C₂×C₁₃₇	—	2	2	no	—
205	C₂×C₁₃₇	—	4	2	no	—
206	C₂×C₁₃₇	—	16	1	no	—
207	C₂×C₁₃₇	—	16	2	no	—
208	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
209	C₂×C₁₃₇	#3415	1	1	yes	characteristic
210	C₂×C₁₃₇	#3416	1	1	yes	characteristic
211	#33612	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₁₃₇	#33612	1	1	yes	characteristic, direct product factor, Sylow
213	C₂×#509	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	C₂×#504	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	#3061	C₂×C₁₃₇	1	1	yes	characteristic, complemented
216	#3058	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	#2220	C₂×C₁₃₇	1	2	yes	complemented
218	#2218	C₂×C₁₃₇	1	2	yes	complemented
219	#2217	C₂×C₁₃₇	1	2	yes	complemented
220	#2215	C₂×C₁₃₇	1	2	yes	complemented
221	#2159	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#2138	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	C₂×#357	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	C₂×#135	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#131	C₂²×C₁₃₇	1	1	yes	characteristic
227	#537	—	2	1	no	—
228	#535	—	2	1	no	—
229	#509	—	2	4	no	—
230	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	—
231	C₂×D₁₆	C₂²×C₁₃₇	1	2	yes	—
232	#504	—	2	4	no	—
233	C₂×M₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×M₃₂	C₂²×C₁₃₇	1	2	yes	complemented
235	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂²×C₁₆	C₂²×C₁₃₇	1	2	yes	complemented
237	#469	—	2	2	no	—
238	#468	—	2	2	no	—
239	#467	C₂²×C₁₃₇	1	2	yes	complemented
240	#466	C₂²×C₁₃₇	1	2	yes	—
241	#466	C₂²×C₁₃₇	1	2	yes	—
242	#466	C₂²×C₁₃₇	1	2	yes	complemented
243	#427	C₂²×C₁₃₇	1	1	yes	characteristic
244	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
245	#418	—	2	1	no	—
246	#417	—	2	1	no	—
247	#367	C₂²×C₁₃₇	1	2	yes	complemented
248	#366	C₂²×C₁₃₇	1	2	yes	complemented
249	#358	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
250	#358	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
251	#357	C₂²×C₁₃₇	1	2	yes	—
252	#357	C₂²×C₁₃₇	1	2	yes	—
253	#357	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
254	#357	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
255	C₂×#41	—	2	1	no	—
256	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	#135	—	2	2	no	—
259	#135	—	2	2	no	—
260	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
266	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
267	#131	—	2	2	no	—
268	#131	—	2	2	no	—
269	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
270	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
273	#127	—	4	1	no	—
274	#124	—	4	1	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	—	4	1	no	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	#121	—	2	2	no	—
280	#121	—	4	1	no	—
281	#121	—	4	2	no	—
282	#120	—	4	2	no	—
283	#117	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	SD₃₂	—	2	4	no	—
286	D₁₆	—	2	4	no	—
287	M₃₂	—	2	4	no	—
288	M₃₂	D₄×C₁₃₇	1	4	yes	complemented
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	2	4	no	—
291	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
294	#107	—	2	1	no	—
295	#107	C₂³×C₁₃₇	1	2	yes	—
296	#107	C₂³×C₁₃₇	1	1	yes	characteristic
297	#107	C₂³×C₁₃₇	1	1	yes	characteristic
298	#106	—	2	1	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂⁴	—	4	1	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	D₈×C₁₃₇	1	1	yes	characteristic
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	D₈×C₁₃₇	1	2	yes	—
320	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	Q₁₆	—	2	1	no	—
326	Q₁₆	—	2	1	no	—
327	SD₁₆	—	4	2	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	2	1	no	—
332	D₈	—	4	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
340	C₂×C₈	#41×C₁₃₇	1	2	yes	—
341	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	4	1	no	—
353	C₁₆	—	2	1	no	—
354	C₁₆	—	2	1	no	—
355	C₁₆	C₂×D₄×C₁₃₇	1	4	yes	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	16	1	no	—
360	C₂³	—	16	1	no	—
361	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
362	C₂³	C₂×D₈×C₁₃₇	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	16	2	no	—
375	D₄	—	16	2	no	—
376	D₄	—	16	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	16	1	no	—
385	C₂×C₄	#121×C₁₃₇	1	2	yes	—
386	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
387	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
388	C₂×C₄	#135×C₁₃₇	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	#121×C₁₃₇	1	2	yes	—
392	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
393	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	16	4	no	—
406	C₂²	#466×C₁₃₇	1	2	yes	—
407	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	#466×C₁₃₇	1	2	yes	—
414	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
415	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic
421	C₂	#3415×C₁₃₇	1	1	yes	characteristic
422	C₂	#3416×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×#41×C₁₃₇ ◁ C₂×#131×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#509×C₁₃₇	C₂	semidirect
2. C₂×#504×C₁₃₇	C₂	semidirect
3. #3061×C₁₃₇	C₂	semidirect
4. #3058×C₁₃₇	C₂	semidirect
5. #2220×C₁₃₇	C₂	semidirect
6. #2218×C₁₃₇	C₂	semidirect
7. #2217×C₁₃₇	C₂	semidirect
8. #2215×C₁₃₇	C₂	semidirect
9. #2159×C₁₃₇	C₂	semidirect
10. #2138×C₁₃₇	C₂	semidirect
11. C₂×#357×C₁₃₇	C₂	semidirect
22. C₂×M₃₂×C₁₃₇	C₂²	semidirect
24. C₂²×C₁₆×C₁₃₇	C₂²	semidirect
27. #467×C₁₃₇	C₂²	semidirect
30. #466×C₁₃₇	C₂²	semidirect
35. #367×C₁₃₇	C₂²	semidirect
36. #366×C₁₃₇	C₂²	semidirect
37. #358×C₁₃₇	C₂²	semidirect
38. #358×C₁₃₇	C₂²	semidirect
41. #357×C₁₃₇	C₂²	semidirect
42. #357×C₁₃₇	C₂²	semidirect
76. M₃₂×C₁₃₇	D₄	semidirect
211. #33612	C₁₃₇	direct (N × H)
212. C₁₃₇	#33612	direct (N × H)
213. C₂×#509	C₂×C₁₃₇	semidirect
214. C₂×#504	C₂×C₁₃₇	semidirect
215. #3061	C₂×C₁₃₇	semidirect
216. #3058	C₂×C₁₃₇	semidirect
217. #2220	C₂×C₁₃₇	semidirect
218. #2218	C₂×C₁₃₇	semidirect
219. #2217	C₂×C₁₃₇	semidirect
220. #2215	C₂×C₁₃₇	semidirect
221. #2159	C₂×C₁₃₇	semidirect
222. #2138	C₂×C₁₃₇	semidirect
223. C₂×#357	C₂×C₁₃₇	semidirect
234. C₂×M₃₂	C₂²×C₁₃₇	semidirect
236. C₂²×C₁₆	C₂²×C₁₃₇	semidirect
239. #467	C₂²×C₁₃₇	semidirect
242. #466	C₂²×C₁₃₇	semidirect
247. #367	C₂²×C₁₃₇	semidirect
248. #366	C₂²×C₁₃₇	semidirect
249. #358	C₂²×C₁₃₇	semidirect
250. #358	C₂²×C₁₃₇	semidirect
253. #357	C₂²×C₁₃₇	semidirect
254. #357	C₂²×C₁₃₇	semidirect
288. M₃₂	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#509×C₁₃₇	2
C₂×#504×C₁₃₇	2
#3061×C₁₃₇	2
#3058×C₁₃₇	2
#2220×C₁₃₇	2
#2218×C₁₃₇	2
#2217×C₁₃₇	2
#2215×C₁₃₇	2
#2159×C₁₃₇	2
#2138×C₁₃₇	2
C₂×#357×C₁₃₇	2
#33612	137

Subgroups — C137×#33612 #46882998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33612 #46882998