Subgroups — C₁₃₇×#11105 #46860491

Order 35072.

910 conjugacy classes of subgroups.

The subgroup lattice has 440 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, complemented
2	C₂×#417×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×#408×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#343×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	C₂×#340×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
11	C₂×#108×C₁₃₇	—	2	4	no	—
12	C₂×#108×C₁₃₇	—	2	2	no	—
13	#417×C₁₃₇	—	2	4	no	—
14	#417×C₁₃₇	—	2	4	no	—
15	C₂×#103×C₁₃₇	—	2	2	no	—
16	C₂×#102×C₁₃₇	—	2	2	no	—
17	#408×C₁₃₇	—	2	2	no	—
18	#408×C₁₃₇	C₄	1	4	yes	complemented
19	C₂×C₂²⋊C₈×C₁₃₇	—	2	2	no	—
20	#343×C₁₃₇	—	2	4	no	—
21	#340×C₁₃₇	—	2	2	no	—
22	C₂×#41×C₁₃₇	—	2	1	no	—
23	C₂×#41×C₁₃₇	—	2	1	no	—
24	C₂×#41×C₁₃₇	—	2	2	no	—
25	C₂×#41×C₁₃₇	—	2	2	no	—
26	C₂×#41×C₁₃₇	—	2	2	no	—
27	C₂×#41×C₁₃₇	—	2	2	no	—
28	C₂×#41×C₁₃₇	C₂×C₄	1	2	yes	—
29	C₂×#41×C₁₃₇	Q₈	1	2	yes	—
30	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃₇	—	2	1	no	—
32	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₇	—	2	1	no	—
34	C₂³×C₄×C₁₃₇	—	2	2	no	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₃₇	—	2	1	no	—
37	C₂×M₁₆×C₁₃₇	—	2	2	no	—
38	C₂×M₁₆×C₁₃₇	—	2	2	no	—
39	C₂×M₁₆×C₁₃₇	—	2	2	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	—	2	2	no	—
42	C₂×M₁₆×C₁₃₇	—	2	2	no	—
43	C₂×M₁₆×C₁₃₇	—	2	2	no	—
44	C₂×M₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	—	2	2	no	—
48	C₂²×C₈×C₁₃₇	—	2	1	no	—
49	C₂²×C₈×C₁₃₇	—	2	2	no	—
50	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
52	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
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	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
59	#108×C₁₃₇	—	2	8	no	—
60	#103×C₁₃₇	—	2	8	no	—
61	#102×C₁₃₇	—	2	8	no	—
62	C₂²⋊C₈×C₁₃₇	—	2	8	no	—
63	C₂⁴×C₁₃₇	—	2	1	no	—
64	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
65	#41×C₁₃₇	—	2	4	no	—
66	#41×C₁₃₇	—	2	4	no	—
67	#41×C₁₃₇	—	2	4	no	—
68	#41×C₁₃₇	—	2	4	no	—
69	#41×C₁₃₇	—	4	1	no	—
70	#41×C₁₃₇	—	4	2	no	—
71	#41×C₁₃₇	—	4	1	no	—
72	#41×C₁₃₇	—	4	1	no	—
73	#41×C₁₃₇	—	4	2	no	—
74	#41×C₁₃₇	—	4	1	no	—
75	C₂×Q₈×C₁₃₇	—	2	1	no	—
76	C₂×Q₈×C₁₃₇	—	2	2	no	—
77	C₂×Q₈×C₁₃₇	—	2	2	no	—
78	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	2	yes	—
79	C₂×D₄×C₁₃₇	—	2	2	no	—
80	C₂×D₄×C₁₃₇	—	2	2	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	—	2	1	no	—
83	C₂×D₄×C₁₃₇	—	2	2	no	—
84	C₂×D₄×C₁₃₇	—	4	2	no	—
85	C₂×D₄×C₁₃₇	—	4	2	no	—
86	C₂×D₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	—	2	1	no	—
88	C₂²×C₄×C₁₃₇	—	2	2	no	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	—	2	4	no	—
91	C₂²×C₄×C₁₃₇	—	4	2	no	—
92	C₂²×C₄×C₁₃₇	—	4	2	no	—
93	C₂²×C₄×C₁₃₇	—	4	2	no	—
94	C₂²×C₄×C₁₃₇	—	4	2	no	—
95	C₂²×C₄×C₁₃₇	—	8	2	no	—
96	C₂²×C₄×C₁₃₇	—	8	2	no	—
97	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
105	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
106	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
107	M₁₆×C₁₃₇	—	2	4	no	—
108	M₁₆×C₁₃₇	—	2	4	no	—
109	M₁₆×C₁₃₇	—	2	4	no	—
110	M₁₆×C₁₃₇	—	4	2	no	—
111	M₁₆×C₁₃₇	—	4	1	no	—
112	M₁₆×C₁₃₇	—	4	1	no	—
113	M₁₆×C₁₃₇	—	4	2	no	—
114	C₂×C₈×C₁₃₇	—	2	4	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	4	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	4	no	—
120	C₂×C₈×C₁₃₇	—	4	2	no	—
121	C₂×C₈×C₁₃₇	—	4	2	no	—
122	C₂×C₈×C₁₃₇	—	4	2	no	—
123	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	4	yes	—
124	C₄⋊C₄×C₁₃₇	—	2	4	no	—
125	C₄⋊C₄×C₁₃₇	—	2	4	no	—
126	C₄⋊C₄×C₁₃₇	—	4	2	no	—
127	C₄⋊C₄×C₁₃₇	—	4	2	no	—
128	C₂³×C₁₃₇	—	2	2	no	—
129	C₂³×C₁₃₇	—	2	1	no	—
130	C₂³×C₁₃₇	—	2	1	no	—
131	C₂³×C₁₃₇	—	2	2	no	—
132	C₂³×C₁₃₇	—	4	2	no	—
133	C₂³×C₁₃₇	—	4	2	no	—
134	C₂³×C₁₃₇	—	4	1	no	—
135	C₂³×C₁₃₇	—	4	1	no	—
136	C₂³×C₁₃₇	#117	1	1	yes	characteristic
137	C₂³×C₁₃₇	#121	1	1	yes	characteristic
138	C₂³×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂³×C₁₃₇	#123	1	2	yes	—
140	C₂³×C₁₃₇	#124	1	2	yes	—
141	Q₈×C₁₃₇	—	2	4	no	—
142	Q₈×C₁₃₇	—	4	1	no	—
143	Q₈×C₁₃₇	—	4	1	no	—
144	D₄×C₁₃₇	—	2	4	no	—
145	D₄×C₁₃₇	—	4	4	no	—
146	D₄×C₁₃₇	—	4	2	no	—
147	D₄×C₁₃₇	—	4	2	no	—
148	D₄×C₁₃₇	—	4	1	no	—
149	D₄×C₁₃₇	—	4	1	no	—
150	C₂×C₄×C₁₃₇	—	2	2	no	—
151	C₂×C₄×C₁₃₇	—	4	2	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	4	no	—
155	C₂×C₄×C₁₃₇	—	4	4	no	—
156	C₂×C₄×C₁₃₇	—	8	4	no	—
157	C₂×C₄×C₁₃₇	—	8	2	no	—
158	C₂×C₄×C₁₃₇	—	8	2	no	—
159	C₂×C₄×C₁₃₇	—	8	4	no	—
160	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₃₇	#120	1	2	yes	—
165	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	#121	1	2	yes	—
167	C₂×C₄×C₁₃₇	#121	1	2	yes	—
168	C₂×C₄×C₁₃₇	#121	1	2	yes	—
169	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	#123	1	2	yes	—
174	C₂×C₄×C₁₃₇	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	#126	1	2	yes	—
177	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
178	C₈×C₁₃₇	—	2	4	no	—
179	C₈×C₁₃₇	—	4	2	no	—
180	C₈×C₁₃₇	—	4	4	no	—
181	C₂²×C₁₃₇	—	2	2	no	—
182	C₂²×C₁₃₇	—	2	2	no	—
183	C₂²×C₁₃₇	—	2	2	no	—
184	C₂²×C₁₃₇	—	2	2	no	—
185	C₂²×C₁₃₇	—	2	1	no	—
186	C₂²×C₁₃₇	—	2	1	no	—
187	C₂²×C₁₃₇	—	2	1	no	—
188	C₂²×C₁₃₇	—	2	1	no	—
189	C₂²×C₁₃₇	—	4	2	no	—
190	C₂²×C₁₃₇	—	4	2	no	—
191	C₂²×C₁₃₇	—	4	2	no	—
192	C₂²×C₁₃₇	—	8	2	no	—
193	C₂²×C₁₃₇	—	8	2	no	—
194	C₂²×C₁₃₇	#380	1	1	yes	characteristic
195	C₂²×C₁₃₇	#388	1	2	yes	—
196	C₂²×C₁₃₇	#393	1	1	yes	characteristic
197	C₂²×C₁₃₇	#394	1	2	yes	—
198	C₂²×C₁₃₇	#399	1	1	yes	characteristic
199	C₂²×C₁₃₇	#471	1	2	yes	—
200	C₂²×C₁₃₇	#472	1	1	yes	characteristic
201	C₂²×C₁₃₇	#473	1	1	yes	characteristic
202	C₄×C₁₃₇	—	4	2	no	—
203	C₄×C₁₃₇	—	8	4	no	—
204	C₄×C₁₃₇	#385	1	2	yes	—
205	C₄×C₁₃₇	#386	1	1	yes	characteristic
206	C₄×C₁₃₇	#390	1	1	yes	characteristic
207	C₄×C₁₃₇	#392	1	1	yes	characteristic
208	C₄×C₁₃₇	#396	1	2	yes	—
209	C₄×C₁₃₇	#397	1	1	yes	characteristic
210	C₂×C₁₃₇	—	2	2	no	—
211	C₂×C₁₃₇	—	2	1	no	—
212	C₂×C₁₃₇	—	2	1	no	—
213	C₂×C₁₃₇	—	8	2	no	—
214	C₂×C₁₃₇	#1439	1	1	yes	characteristic
215	C₂×C₁₃₇	#1815	1	1	yes	characteristic
216	C₂×C₁₃₇	#1816	1	1	yes	characteristic
217	C₂×C₁₃₇	#2051	1	2	yes	—
218	C₂×C₁₃₇	#2052	1	2	yes	—
219	#11105	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₁₃₇	#11105	1	1	yes	characteristic, direct product factor, Sylow
221	C₂²×#108	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	C₂×#417	C₂×C₁₃₇	1	2	yes	—
223	C₂×#408	C₂×C₁₃₇	1	1	yes	characteristic
224	C₂×#343	C₂×C₁₃₇	1	2	yes	complemented
225	C₂×#340	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
229	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
231	C₂×#108	—	2	4	no	—
232	C₂×#108	—	2	2	no	—
233	#417	—	2	4	no	—
234	#417	—	2	4	no	—
235	C₂×#103	—	2	2	no	—
236	C₂×#102	—	2	2	no	—
237	#408	—	2	2	no	—
238	#408	C₄×C₁₃₇	1	4	yes	complemented
239	C₂×C₂²⋊C₈	—	2	2	no	—
240	#343	—	2	4	no	—
241	#340	—	2	2	no	—
242	C₂×#41	—	2	1	no	—
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	C₂×C₄×C₁₃₇	1	2	yes	—
249	C₂×#41	Q₈×C₁₃₇	1	2	yes	—
250	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
265	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
271	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
272	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
279	#108	—	2	8	no	—
280	#103	—	2	8	no	—
281	#102	—	2	8	no	—
282	C₂²⋊C₈	—	2	8	no	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	4	1	no	—
290	#41	—	4	2	no	—
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	2	yes	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	8	2	no	—
316	C₂²×C₄	—	8	2	no	—
317	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
324	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
325	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
326	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	4	2	no	—
331	M₁₆	—	4	1	no	—
332	M₁₆	—	4	1	no	—
333	M₁₆	—	4	2	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	4	yes	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	#117×C₁₃₇	1	1	yes	characteristic
357	C₂³	#121×C₁₃₇	1	1	yes	characteristic
358	C₂³	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
359	C₂³	#123×C₁₃₇	1	2	yes	—
360	C₂³	#124×C₁₃₇	1	2	yes	—
361	Q₈	—	2	4	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	8	4	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
382	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
383	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
384	C₂×C₄	#120×C₁₃₇	1	2	yes	—
385	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
386	C₂×C₄	#121×C₁₃₇	1	2	yes	—
387	C₂×C₄	#121×C₁₃₇	1	2	yes	—
388	C₂×C₄	#121×C₁₃₇	1	2	yes	—
389	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
390	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
391	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
392	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
393	C₂×C₄	#123×C₁₃₇	1	2	yes	—
394	C₂×C₄	#123×C₁₃₇	1	1	yes	characteristic
395	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
396	C₂×C₄	#126×C₁₃₇	1	2	yes	—
397	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	4	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	#380×C₁₃₇	1	1	yes	characteristic
415	C₂²	#388×C₁₃₇	1	2	yes	—
416	C₂²	#393×C₁₃₇	1	1	yes	characteristic
417	C₂²	#394×C₁₃₇	1	2	yes	—
418	C₂²	#399×C₁₃₇	1	1	yes	characteristic
419	C₂²	#471×C₁₃₇	1	2	yes	—
420	C₂²	#472×C₁₃₇	1	1	yes	characteristic
421	C₂²	#473×C₁₃₇	1	1	yes	characteristic
422	C₄	—	4	2	no	—
423	C₄	—	8	4	no	—
424	C₄	#385×C₁₃₇	1	2	yes	—
425	C₄	#386×C₁₃₇	1	1	yes	characteristic
426	C₄	#390×C₁₃₇	1	1	yes	characteristic
427	C₄	#392×C₁₃₇	1	1	yes	characteristic
428	C₄	#396×C₁₃₇	1	2	yes	—
429	C₄	#397×C₁₃₇	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	8	2	no	—
434	C₂	#1439×C₁₃₇	1	1	yes	characteristic
435	C₂	#1815×C₁₃₇	1	1	yes	characteristic
436	C₂	#1816×C₁₃₇	1	1	yes	characteristic
437	C₂	#2051×C₁₃₇	1	2	yes	—
438	C₂	#2052×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂²×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
1. C₂²×#108×C₁₃₇	C₂	semidirect
4. C₂×#343×C₁₃₇	C₂	semidirect
5. C₂×#340×C₁₃₇	C₂	semidirect
18. #408×C₁₃₇	C₄	semidirect
219. #11105	C₁₃₇	direct (N × H)
220. C₁₃₇	#11105	direct (N × H)
221. C₂²×#108	C₂×C₁₃₇	semidirect
224. C₂×#343	C₂×C₁₃₇	semidirect
225. C₂×#340	C₂×C₁₃₇	semidirect
238. #408	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
C₂×#417×C₁₃₇	2
C₂×#408×C₁₃₇	2
C₂×#343×C₁₃₇	2
C₂×#340×C₁₃₇	2
#11105	137

Subgroups — C137×#11105 #46860491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#11105 #46860491