Subgroups — C₁₃₇×#33846 #46883232

Order 35072.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#508×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3280×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2249×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2216×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#2215×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#2210×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2187×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2186×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₄×D₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₁₃₇	C₂²	1	2	yes	—
14	#546×C₁₃₇	—	2	2	no	—
15	#508×C₁₃₇	—	2	4	no	—
16	C₂×Q₃₂×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
18	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
19	C₂×D₁₆×C₁₃₇	—	2	4	no	—
20	C₂×D₁₆×C₁₃₇	C₂²	1	2	yes	—
21	C₂×D₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×D₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
25	#495×C₁₃₇	C₂²	1	2	yes	complemented
26	#467×C₁₃₇	C₂²	1	2	yes	—
27	#466×C₁₃₇	C₂²	1	2	yes	complemented
28	#463×C₁₃₇	—	2	2	no	—
29	#450×C₁₃₇	—	2	2	no	—
30	#449×C₁₃₇	—	2	2	no	—
31	C₄×D₈×C₁₃₇	C₂²	1	2	yes	complemented
32	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	#366×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
34	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
35	#358×C₁₃₇	C₂²	1	2	yes	complemented
36	#357×C₁₃₇	C₂²	1	2	yes	complemented
37	#357×C₁₃₇	C₂²	1	2	yes	complemented
38	C₂²⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#41×C₁₃₇	—	2	2	no	—
42	C₂²×D₄×C₁₃₇	—	2	2	no	—
43	#135×C₁₃₇	—	2	4	no	—
44	#135×C₁₃₇	—	4	2	no	—
45	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
47	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
48	C₂×D₈×C₁₃₇	—	2	4	no	—
49	C₂×D₈×C₁₃₇	—	2	2	no	—
50	C₂×D₈×C₁₃₇	—	4	2	no	—
51	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
52	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	#124×C₁₃₇	—	2	2	no	—
56	#123×C₁₃₇	—	4	2	no	—
57	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
58	#121×C₁₃₇	—	2	2	no	—
59	#121×C₁₃₇	—	4	2	no	—
60	#120×C₁₃₇	—	4	2	no	—
61	C₄×D₄×C₁₃₇	—	2	2	no	—
62	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₃₇	—	4	2	no	—
64	Q₃₂×C₁₃₇	—	2	2	no	—
65	SD₃₂×C₁₃₇	—	2	4	no	—
66	SD₃₂×C₁₃₇	—	4	2	no	—
67	D₁₆×C₁₃₇	—	2	4	no	—
68	D₁₆×C₁₃₇	—	2	2	no	—
69	D₁₆×C₁₃₇	D₄	1	4	yes	complemented
70	C₂×C₁₆×C₁₃₇	—	2	2	no	—
71	C₂×C₁₆×C₁₃₇	—	2	2	no	—
72	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
76	#107×C₁₃₇	C₂³	1	2	yes	—
77	C₄⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
78	#103×C₁₃₇	—	2	2	no	—
79	#102×C₁₃₇	—	2	2	no	—
80	#102×C₁₃₇	—	2	2	no	—
81	C₂²⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
82	C₂²⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₂⁴×C₁₃₇	—	4	2	no	—
85	#41×C₁₃₇	—	4	4	no	—
86	#41×C₁₃₇	—	8	2	no	—
87	C₂×Q₈×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	4	4	no	—
91	C₂×D₄×C₁₃₇	—	4	2	no	—
92	C₂×D₄×C₁₃₇	—	4	2	no	—
93	C₂×D₄×C₁₃₇	—	4	2	no	—
94	C₂×D₄×C₁₃₇	—	8	2	no	—
95	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	—	4	2	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₁₃₇	—	2	2	no	—
101	Q₁₆×C₁₃₇	—	2	2	no	—
102	SD₁₆×C₁₃₇	—	4	4	no	—
103	SD₁₆×C₁₃₇	—	8	2	no	—
104	D₈×C₁₃₇	—	2	2	no	—
105	D₈×C₁₃₇	—	2	2	no	—
106	D₈×C₁₃₇	—	2	2	no	—
107	D₈×C₁₃₇	—	4	4	no	—
108	D₈×C₁₃₇	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	—	2	1	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄⋊C₄×C₁₃₇	—	4	2	no	—
119	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
120	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
122	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
123	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
124	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
125	C₂²⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
126	C₂²⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
127	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₁₃₇	—	2	1	no	—
129	C₁₆×C₁₃₇	—	2	1	no	—
130	C₁₆×C₁₃₇	—	2	1	no	—
131	C₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
132	C₂³×C₁₃₇	—	4	2	no	—
133	C₂³×C₁₃₇	—	4	2	no	—
134	C₂³×C₁₃₇	—	8	4	no	—
135	C₂³×C₁₃₇	—	8	4	no	—
136	C₂³×C₁₃₇	—	16	2	no	—
137	C₂³×C₁₃₇	C₂×D₈	1	1	yes	characteristic
138	C₂³×C₁₃₇	C₂×D₈	1	1	yes	characteristic
139	Q₈×C₁₃₇	—	4	2	no	—
140	Q₈×C₁₃₇	—	4	2	no	—
141	D₄×C₁₃₇	—	2	2	no	—
142	D₄×C₁₃₇	—	2	4	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	D₄×C₁₃₇	—	4	2	no	—
146	D₄×C₁₃₇	—	8	4	no	—
147	D₄×C₁₃₇	—	8	4	no	—
148	D₄×C₁₃₇	—	16	2	no	—
149	C₂×C₄×C₁₃₇	—	2	1	no	—
150	C₂×C₄×C₁₃₇	—	2	1	no	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	1	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	—	8	4	no	—
156	C₂×C₄×C₁₃₇	—	16	2	no	—
157	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₁₃₇	—	2	1	no	—
163	C₈×C₁₃₇	—	2	1	no	—
164	C₈×C₁₃₇	—	2	1	no	—
165	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×C₁₃₇	—	2	1	no	—
168	C₂²×C₁₃₇	—	2	1	no	—
169	C₂²×C₁₃₇	—	2	1	no	—
170	C₂²×C₁₃₇	—	2	1	no	—
171	C₂²×C₁₃₇	—	2	1	no	—
172	C₂²×C₁₃₇	—	4	4	no	—
173	C₂²×C₁₃₇	—	8	2	no	—
174	C₂²×C₁₃₇	—	8	2	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	2	no	—
177	C₂²×C₁₃₇	—	8	2	no	—
178	C₂²×C₁₃₇	—	16	8	no	—
179	C₂²×C₁₃₇	#508	1	2	yes	complemented
180	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	2	1	no	—
183	C₄×C₁₃₇	—	2	1	no	—
184	C₄×C₁₃₇	—	2	1	no	—
185	C₄×C₁₃₇	—	8	2	no	—
186	C₄×C₁₃₇	—	8	2	no	—
187	C₄×C₁₃₇	D₄²	1	1	yes	characteristic
188	C₄×C₁₃₇	#576	1	1	yes	characteristic
189	C₂×C₁₃₇	—	2	2	no	—
190	C₂×C₁₃₇	—	4	1	no	—
191	C₂×C₁₃₇	—	8	4	no	—
192	C₂×C₁₃₇	—	16	2	no	—
193	C₂×C₁₃₇	D₄×D₈	1	1	yes	characteristic
194	C₂×C₁₃₇	C₂×#508	1	1	yes	characteristic
195	C₂×C₁₃₇	#3415	1	1	yes	characteristic
196	#33846	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₃₇	#33846	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#508	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	C₂²×D₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#3280	C₂×C₁₃₇	1	2	yes	complemented
201	#2249	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	#2216	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#2215	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#2210	C₂×C₁₃₇	1	2	yes	complemented
205	#2187	C₂×C₁₃₇	1	2	yes	complemented
206	#2186	C₂×C₁₃₇	1	2	yes	complemented
207	C₄×D₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	D₄×C₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	C₂×#135	C₂²×C₁₃₇	1	2	yes	complemented
210	C₂²×D₈	C₂²×C₁₃₇	1	2	yes	—
211	#546	—	2	2	no	—
212	#508	—	2	4	no	—
213	C₂×Q₃₂	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
214	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
215	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
216	C₂×D₁₆	—	2	4	no	—
217	C₂×D₁₆	C₂²×C₁₃₇	1	2	yes	—
218	C₂×D₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×D₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
222	#495	C₂²×C₁₃₇	1	2	yes	complemented
223	#467	C₂²×C₁₃₇	1	2	yes	—
224	#466	C₂²×C₁₃₇	1	2	yes	complemented
225	#463	—	2	2	no	—
226	#450	—	2	2	no	—
227	#449	—	2	2	no	—
228	C₄×D₈	C₂²×C₁₃₇	1	2	yes	complemented
229	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
230	#366	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
231	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
232	#358	C₂²×C₁₃₇	1	2	yes	complemented
233	#357	C₂²×C₁₃₇	1	2	yes	complemented
234	#357	C₂²×C₁₃₇	1	2	yes	complemented
235	C₂²⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂²⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
237	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
238	C₂×#41	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	#135	—	2	4	no	—
241	#135	—	4	2	no	—
242	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×D₈	—	2	4	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	—	4	2	no	—
248	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
249	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
252	#124	—	2	2	no	—
253	#123	—	4	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	#121	—	2	2	no	—
256	#121	—	4	2	no	—
257	#120	—	4	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	4	2	no	—
261	Q₃₂	—	2	2	no	—
262	SD₃₂	—	2	4	no	—
263	SD₃₂	—	4	2	no	—
264	D₁₆	—	2	4	no	—
265	D₁₆	—	2	2	no	—
266	D₁₆	D₄×C₁₃₇	1	4	yes	complemented
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	2	2	no	—
269	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
272	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
273	#107	C₂³×C₁₃₇	1	2	yes	—
274	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
275	#103	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	C₂²⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
279	C₂²⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
281	C₂⁴	—	4	2	no	—
282	#41	—	4	4	no	—
283	#41	—	8	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	8	2	no	—
292	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	SD₁₆	—	4	4	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	4	4	no	—
305	D₈	C₂×D₄×C₁₃₇	1	4	yes	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
323	C₂²⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	1	no	—
328	C₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	8	4	no	—
332	C₂³	—	8	4	no	—
333	C₂³	—	16	2	no	—
334	C₂³	C₂×D₈×C₁₃₇	1	1	yes	characteristic
335	C₂³	C₂×D₈×C₁₃₇	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	4	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	4	no	—
344	D₄	—	8	4	no	—
345	D₄	—	16	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	16	2	no	—
354	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
363	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	16	8	no	—
376	C₂²	#508×C₁₃₇	1	2	yes	complemented
377	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	D₄²×C₁₃₇	1	1	yes	characteristic
385	C₄	#576×C₁₃₇	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	8	4	no	—
389	C₂	—	16	2	no	—
390	C₂	D₄×D₈×C₁₃₇	1	1	yes	characteristic
391	C₂	C₂×#508×C₁₃₇	1	1	yes	characteristic
392	C₂	#3415×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 ◁ C₄×D₄×C₁₃₇ ◁ C₈×D₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#508×C₁₃₇	C₂	semidirect
2. C₂²×D₁₆×C₁₃₇	C₂	semidirect
3. #3280×C₁₃₇	C₂	semidirect
4. #2249×C₁₃₇	C₂	semidirect
5. #2216×C₁₃₇	C₂	semidirect
6. #2215×C₁₃₇	C₂	semidirect
7. #2210×C₁₃₇	C₂	semidirect
8. #2187×C₁₃₇	C₂	semidirect
9. #2186×C₁₃₇	C₂	semidirect
10. C₄×D₁₆×C₁₃₇	C₂	semidirect
11. D₄×C₁₆×C₁₃₇	C₂	semidirect
12. C₂×#135×C₁₃₇	C₂²	semidirect
16. C₂×Q₃₂×C₁₃₇	C₂²	semidirect
17. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
18. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
24. C₂²×C₁₆×C₁₃₇	C₂²	semidirect
25. #495×C₁₃₇	C₂²	semidirect
27. #466×C₁₃₇	C₂²	semidirect
31. C₄×D₈×C₁₃₇	C₂²	semidirect
33. #366×C₁₃₇	C₂²	semidirect
34. C₄⋊C₁₆×C₁₃₇	C₂²	semidirect
35. #358×C₁₃₇	C₂²	semidirect
36. #357×C₁₃₇	C₂²	semidirect
37. #357×C₁₃₇	C₂²	semidirect
39. C₂²⋊C₁₆×C₁₃₇	C₂²	semidirect
40. C₄×C₁₆×C₁₃₇	C₂²	semidirect
69. D₁₆×C₁₃₇	D₄	semidirect
179. C₂²×C₁₃₇	#508	semidirect
196. #33846	C₁₃₇	direct (N × H)
197. C₁₃₇	#33846	direct (N × H)
198. C₂×#508	C₂×C₁₃₇	semidirect
199. C₂²×D₁₆	C₂×C₁₃₇	semidirect
200. #3280	C₂×C₁₃₇	semidirect
201. #2249	C₂×C₁₃₇	semidirect
202. #2216	C₂×C₁₃₇	semidirect
203. #2215	C₂×C₁₃₇	semidirect
204. #2210	C₂×C₁₃₇	semidirect
205. #2187	C₂×C₁₃₇	semidirect
206. #2186	C₂×C₁₃₇	semidirect
207. C₄×D₁₆	C₂×C₁₃₇	semidirect
208. D₄×C₁₆	C₂×C₁₃₇	semidirect
209. C₂×#135	C₂²×C₁₃₇	semidirect
213. C₂×Q₃₂	C₂²×C₁₃₇	semidirect
214. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
215. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
221. C₂²×C₁₆	C₂²×C₁₃₇	semidirect
222. #495	C₂²×C₁₃₇	semidirect
224. #466	C₂²×C₁₃₇	semidirect
228. C₄×D₈	C₂²×C₁₃₇	semidirect
230. #366	C₂²×C₁₃₇	semidirect
231. C₄⋊C₁₆	C₂²×C₁₃₇	semidirect
232. #358	C₂²×C₁₃₇	semidirect
233. #357	C₂²×C₁₃₇	semidirect
234. #357	C₂²×C₁₃₇	semidirect
236. C₂²⋊C₁₆	C₂²×C₁₃₇	semidirect
237. C₄×C₁₆	C₂²×C₁₃₇	semidirect
266. D₁₆	D₄×C₁₃₇	semidirect
376. C₂²	#508×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#508×C₁₃₇	2
C₂²×D₁₆×C₁₃₇	2
#3280×C₁₃₇	2
#2249×C₁₃₇	2
#2216×C₁₃₇	2
#2215×C₁₃₇	2
#2210×C₁₃₇	2
#2187×C₁₃₇	2
#2186×C₁₃₇	2
C₄×D₁₆×C₁₃₇	2
D₄×C₁₆×C₁₃₇	2
#33846	137

Subgroups — C137×#33846 #46883232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33846 #46883232