Subgroups — C₁₃₇×#20007 #46869393

Order 35072.

570 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3395×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3381×C₁₃₇	C₂	1	2	yes	maximal
3	#3338×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1707×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1676×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1672×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1669×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1644×C₁₃₇	C₂	1	2	yes	maximal
9	#1636×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#557×C₁₃₇	C₂²	1	2	yes	—
13	#554×C₁₃₇	C₂²	1	2	yes	—
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#499×C₁₃₇	—	2	2	no	—
16	#498×C₁₃₇	C₂²	1	2	yes	—
17	#494×C₁₃₇	—	2	1	no	—
18	#494×C₁₃₇	C₂²	1	1	yes	characteristic
19	#487×C₁₃₇	C₂²	1	2	yes	—
20	#484×C₁₃₇	—	2	2	no	—
21	#479×C₁₃₇	—	2	2	no	—
22	#478×C₁₃₇	—	2	2	no	—
23	#477×C₁₃₇	C₂²	1	2	yes	—
24	#477×C₁₃₇	C₂²	1	2	yes	—
25	#474×C₁₃₇	C₂²	1	2	yes	—
26	#467×C₁₃₇	—	2	1	no	—
27	#462×C₁₃₇	—	2	2	no	—
28	#462×C₁₃₇	C₂²	1	2	yes	—
29	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
31	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
32	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×SD₁₆×C₁₃₇	—	2	2	no	—
34	C₄×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₁₃₇	—	2	1	no	—
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#334×C₁₃₇	C₂²	1	1	yes	characteristic
39	#333×C₁₃₇	C₂²	1	2	yes	—
40	#332×C₁₃₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
43	D₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
54	#125×C₁₃₇	—	2	2	no	—
55	#125×C₁₃₇	—	2	2	no	—
56	#125×C₁₃₇	—	4	2	no	—
57	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
58	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
59	C₄×Q₈×C₁₃₇	—	2	2	no	—
60	C₄×Q₈×C₁₃₇	—	2	2	no	—
61	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
66	#107×C₁₃₇	—	2	1	no	—
67	#107×C₁₃₇	—	2	1	no	—
68	#107×C₁₃₇	—	2	2	no	—
69	#107×C₁₃₇	—	2	2	no	—
70	#107×C₁₃₇	—	2	2	no	—
71	#107×C₁₃₇	D₄	1	1	yes	characteristic
72	#106×C₁₃₇	—	2	2	no	—
73	#106×C₁₃₇	—	2	2	no	—
74	#106×C₁₃₇	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₁₃₇	—	2	1	no	—
76	C₄⋊C₈×C₁₃₇	—	2	2	no	—
77	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
80	#103×C₁₃₇	—	2	2	no	—
81	#103×C₁₃₇	—	2	2	no	—
82	#103×C₁₃₇	—	2	2	no	—
83	#103×C₁₃₇	—	4	2	no	—
84	#103×C₁₃₇	D₄	1	1	yes	characteristic
85	#103×C₁₃₇	D₄	1	2	yes	—
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	—	2	2	no	—
90	C₄×C₈×C₁₃₇	—	2	1	no	—
91	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	—	2	1	no	—
100	C₂²×C₄×C₁₃₇	—	4	2	no	—
101	Q₁₆×C₁₃₇	—	2	2	no	—
102	Q₁₆×C₁₃₇	—	4	2	no	—
103	Q₁₆×C₁₃₇	—	8	1	no	—
104	Q₁₆×C₁₃₇	—	8	2	no	—
105	SD₁₆×C₁₃₇	Q₁₆	1	4	yes	complemented
106	C₂×C₈×C₁₃₇	—	2	2	no	—
107	C₂×C₈×C₁₃₇	—	2	1	no	—
108	C₂×C₈×C₁₃₇	—	2	1	no	—
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	—	4	2	no	—
111	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	1	no	—
117	C₄⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄⋊C₄×C₁₃₇	—	2	2	no	—
119	C₄⋊C₄×C₁₃₇	—	2	2	no	—
120	C₄⋊C₄×C₁₃₇	—	2	2	no	—
121	C₄⋊C₄×C₁₃₇	—	4	2	no	—
122	C₄⋊C₄×C₁₃₇	—	4	2	no	—
123	C₄⋊C₄×C₁₃₇	—	4	2	no	—
124	C₄⋊C₄×C₁₃₇	—	4	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₄²×C₁₃₇	—	2	2	no	—
132	C₄²×C₁₃₇	—	2	1	no	—
133	C₄²×C₁₃₇	—	4	2	no	—
134	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
135	C₂³×C₁₃₇	—	2	1	no	—
136	Q₈×C₁₃₇	—	2	1	no	—
137	Q₈×C₁₃₇	—	2	2	no	—
138	Q₈×C₁₃₇	—	2	2	no	—
139	Q₈×C₁₃₇	—	4	2	no	—
140	Q₈×C₁₃₇	—	4	2	no	—
141	Q₈×C₁₃₇	—	8	2	no	—
142	Q₈×C₁₃₇	C₂×Q₁₆	1	2	yes	—
143	D₄×C₁₃₇	—	2	1	no	—
144	D₄×C₁₃₇	C₂×Q₁₆	1	2	yes	—
145	C₂×C₄×C₁₃₇	—	2	1	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	2	1	no	—
149	C₂×C₄×C₁₃₇	—	2	1	no	—
150	C₂×C₄×C₁₃₇	—	4	1	no	—
151	C₂×C₄×C₁₃₇	—	4	1	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	16	2	no	—
155	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
158	C₈×C₁₃₇	—	2	1	no	—
159	C₈×C₁₃₇	—	2	1	no	—
160	C₈×C₁₃₇	—	4	1	no	—
161	C₈×C₁₃₇	—	4	1	no	—
162	C₈×C₁₃₇	—	4	1	no	—
163	C₈×C₁₃₇	—	4	2	no	—
164	C₈×C₁₃₇	C₂×Q₁₆	1	2	yes	—
165	C₈×C₁₃₇	#135	1	2	yes	—
166	C₂²×C₁₃₇	—	2	2	no	—
167	C₂²×C₁₃₇	—	4	1	no	—
168	C₂²×C₁₃₇	—	4	1	no	—
169	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	—	2	1	no	—
172	C₄×C₁₃₇	—	4	1	no	—
173	C₄×C₁₃₇	—	4	2	no	—
174	C₄×C₁₃₇	—	4	1	no	—
175	C₄×C₁₃₇	—	4	2	no	—
176	C₄×C₁₃₇	—	8	2	no	—
177	C₄×C₁₃₇	—	8	2	no	—
178	C₄×C₁₃₇	C₂²×Q₁₆	1	1	yes	characteristic
179	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
180	C₄×C₁₃₇	#577	1	1	yes	characteristic
181	C₄×C₁₃₇	#578	1	1	yes	characteristic
182	C₂×C₁₃₇	—	4	2	no	—
183	C₂×C₁₃₇	#3284	1	1	yes	characteristic
184	C₂×C₁₃₇	D₄×Q₁₆	1	1	yes	characteristic
185	C₂×C₁₃₇	#3290	1	1	yes	characteristic
186	#20007	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₁₃₇	#20007	1	1	yes	characteristic, direct product factor, Sylow
188	#3395	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#3381	C₂×C₁₃₇	1	2	yes	—
190	#3338	C₂×C₁₃₇	1	1	yes	characteristic
191	#1707	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#1676	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	#1672	C₂×C₁₃₇	1	2	yes	complemented
194	#1669	C₂×C₁₃₇	1	1	yes	characteristic
195	#1644	C₂×C₁₃₇	1	2	yes	—
196	#1636	C₂×C₁₃₇	1	2	yes	complemented
197	C₈×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	C₈×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic
199	#557	C₂²×C₁₃₇	1	2	yes	—
200	#554	C₂²×C₁₃₇	1	2	yes	—
201	#500	C₂²×C₁₃₇	1	1	yes	characteristic
202	#499	—	2	2	no	—
203	#498	C₂²×C₁₃₇	1	2	yes	—
204	#494	—	2	1	no	—
205	#494	C₂²×C₁₃₇	1	1	yes	characteristic
206	#487	C₂²×C₁₃₇	1	2	yes	—
207	#484	—	2	2	no	—
208	#479	—	2	2	no	—
209	#478	—	2	2	no	—
210	#477	C₂²×C₁₃₇	1	2	yes	—
211	#477	C₂²×C₁₃₇	1	2	yes	—
212	#474	C₂²×C₁₃₇	1	2	yes	—
213	#467	—	2	1	no	—
214	#462	—	2	2	no	—
215	#462	C₂²×C₁₃₇	1	2	yes	—
216	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₄×SD₁₆	—	2	2	no	—
221	C₄×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₂×#107	—	2	1	no	—
224	#335	C₂²×C₁₃₇	1	1	yes	characteristic
225	#334	C₂²×C₁₃₇	1	1	yes	characteristic
226	#333	C₂²×C₁₃₇	1	2	yes	—
227	#332	C₂²×C₁₃₇	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
229	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
230	D₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
236	C₂×SD₁₆	D₄×C₁₃₇	1	1	yes	characteristic
237	C₂²×C₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
241	#125	—	2	2	no	—
242	#125	—	2	2	no	—
243	#125	—	4	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
249	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	—	2	2	no	—
253	#107	—	2	1	no	—
254	#107	—	2	1	no	—
255	#107	—	2	2	no	—
256	#107	—	2	2	no	—
257	#107	—	2	2	no	—
258	#107	D₄×C₁₃₇	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	#106	—	2	2	no	—
261	#106	D₄×C₁₃₇	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	4	2	no	—
271	#103	D₄×C₁₃₇	1	1	yes	characteristic
272	#103	D₄×C₁₃₇	1	2	yes	—
273	#102	—	2	2	no	—
274	#102	D₄×C₁₃₇	1	1	yes	characteristic
275	C₂²⋊C₈	—	2	1	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
284	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
285	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	2	no	—
290	Q₁₆	—	8	1	no	—
291	Q₁₆	—	8	2	no	—
292	SD₁₆	Q₁₆×C₁₃₇	1	4	yes	complemented
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
322	C₂³	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	2	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	C₂×Q₁₆×C₁₃₇	1	2	yes	—
330	D₄	—	2	1	no	—
331	D₄	C₂×Q₁₆×C₁₃₇	1	2	yes	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	2	no	—
351	C₈	C₂×Q₁₆×C₁₃₇	1	2	yes	—
352	C₈	#135×C₁₃₇	1	2	yes	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	2	no	—
365	C₄	C₂²×Q₁₆×C₁₃₇	1	1	yes	characteristic
366	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
367	C₄	#577×C₁₃₇	1	1	yes	characteristic
368	C₄	#578×C₁₃₇	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	#3284×C₁₃₇	1	1	yes	characteristic
371	C₂	D₄×Q₁₆×C₁₃₇	1	1	yes	characteristic
372	C₂	#3290×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂×D₄×C₁₃₇	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3395×C₁₃₇	C₂	semidirect
4. #1707×C₁₃₇	C₂	semidirect
5. #1676×C₁₃₇	C₂	semidirect
6. #1672×C₁₃₇	C₂	semidirect
9. #1636×C₁₃₇	C₂	semidirect
10. C₈×Q₁₆×C₁₃₇	C₂	semidirect
105. SD₁₆×C₁₃₇	Q₁₆	semidirect
186. #20007	C₁₃₇	direct (N × H)
187. C₁₃₇	#20007	direct (N × H)
188. #3395	C₂×C₁₃₇	semidirect
191. #1707	C₂×C₁₃₇	semidirect
192. #1676	C₂×C₁₃₇	semidirect
193. #1672	C₂×C₁₃₇	semidirect
196. #1636	C₂×C₁₃₇	semidirect
197. C₈×Q₁₆	C₂×C₁₃₇	semidirect
292. SD₁₆	Q₁₆×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3395×C₁₃₇	2
#3381×C₁₃₇	2
#3338×C₁₃₇	2
#1707×C₁₃₇	2
#1676×C₁₃₇	2
#1672×C₁₃₇	2
#1669×C₁₃₇	2
#1644×C₁₃₇	2
#1636×C₁₃₇	2
C₈×Q₁₆×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#20007	137

Subgroups — C137×#20007 #46869393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20007 #46869393