Subgroups — C₂×#2223×C₁₃₇ #46883002

Order 35072.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SD₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#504×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#473×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#472×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2223×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#368×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#362×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#361×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#137×C₁₃₇	—	2	1	no	—
10	C₂×AGL(1,ℤ/8)×C₁₃₇	—	2	1	no	—
11	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×SD₃₂×C₁₃₇	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₇	—	2	1	no	—
16	C₂×SD₃₂×C₁₃₇	—	2	2	no	—
17	C₂×SD₃₂×C₁₃₇	C₂²	1	4	yes	complemented
18	#504×C₁₃₇	—	2	2	no	—
19	#504×C₁₃₇	C₂²	1	4	yes	complemented
20	C₂×M₃₂×C₁₃₇	—	2	1	no	—
21	C₂×M₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₁₃₇	—	2	1	no	—
23	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
24	#473×C₁₃₇	—	2	2	no	—
25	#473×C₁₃₇	C₂²	1	4	yes	complemented
26	#472×C₁₃₇	—	2	2	no	—
27	#472×C₁₃₇	C₂²	1	4	yes	—
28	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×#101×C₁₃₇	—	2	1	no	—
31	C₂×#100×C₁₃₇	—	2	1	no	—
32	#368×C₁₃₇	C₂²	1	4	yes	complemented
33	#362×C₁₃₇	C₂²	1	4	yes	complemented
34	#361×C₁₃₇	C₂²	1	4	yes	complemented
35	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃₇	—	2	1	no	—
37	C₂²×D₄×C₁₃₇	—	2	1	no	—
38	#137×C₁₃₇	—	2	4	no	—
39	#137×C₁₃₇	—	4	2	no	—
40	AGL(1,ℤ/8)×C₁₃₇	—	2	4	no	—
41	AGL(1,ℤ/8)×C₁₃₇	—	4	2	no	—
42	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
43	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
44	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
45	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
47	C₂×Q₁₆×C₁₃₇	—	4	1	no	—
48	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
49	C₂×SD₁₆×C₁₃₇	—	4	1	no	—
50	C₂×SD₁₆×C₁₃₇	—	4	1	no	—
51	C₂×D₈×C₁₃₇	—	2	1	no	—
52	C₂×D₈×C₁₃₇	—	2	1	no	—
53	C₂×D₈×C₁₃₇	—	2	1	no	—
54	C₂×D₈×C₁₃₇	—	2	1	no	—
55	C₂×D₈×C₁₃₇	—	2	1	no	—
56	C₂×D₈×C₁₃₇	—	4	1	no	—
57	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
58	#131×C₁₃₇	—	2	1	no	—
59	#131×C₁₃₇	—	2	1	no	—
60	#131×C₁₃₇	D₄	1	2	yes	—
61	#131×C₁₃₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₃₇	—	2	1	no	—
63	C₂×M₁₆×C₁₃₇	—	2	1	no	—
64	C₂×M₁₆×C₁₃₇	—	2	1	no	—
65	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃₇	—	2	1	no	—
67	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
68	SD₃₂×C₁₃₇	—	2	4	no	—
69	SD₃₂×C₁₃₇	—	2	4	no	—
70	M₃₂×C₁₃₇	—	2	1	no	—
71	M₃₂×C₁₃₇	—	2	4	no	—
72	M₃₂×C₁₃₇	C₂³	1	2	yes	—
73	C₂×C₁₆×C₁₃₇	—	2	1	no	—
74	C₂×C₁₆×C₁₃₇	—	2	4	no	—
75	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
76	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
77	C₂×C₁₆×C₁₃₇	D₄	1	2	yes	—
78	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
79	#108×C₁₃₇	—	2	1	no	—
80	#108×C₁₃₇	—	2	1	no	—
81	#108×C₁₃₇	C₂³	1	2	yes	—
82	#108×C₁₃₇	C₂³	1	2	yes	—
83	#101×C₁₃₇	—	2	4	no	—
84	#100×C₁₃₇	—	2	4	no	—
85	C₂⁴×C₁₃₇	—	4	1	no	—
86	#41×C₁₃₇	—	2	1	no	—
87	#41×C₁₃₇	—	2	1	no	—
88	#41×C₁₃₇	D₈	1	2	yes	—
89	#41×C₁₃₇	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	4	1	no	—
92	C₂×Q₈×C₁₃₇	—	4	1	no	—
93	C₂×Q₈×C₁₃₇	—	4	1	no	—
94	C₂×Q₈×C₁₃₇	—	4	1	no	—
95	C₂×Q₈×C₁₃₇	—	4	1	no	—
96	C₂×Q₈×C₁₃₇	D₈	1	1	yes	characteristic
97	C₂×D₄×C₁₃₇	—	2	1	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	4	1	no	—
100	C₂×D₄×C₁₃₇	—	4	1	no	—
101	C₂×D₄×C₁₃₇	—	4	1	no	—
102	C₂×D₄×C₁₃₇	—	4	1	no	—
103	C₂×D₄×C₁₃₇	—	4	1	no	—
104	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	—	2	1	no	—
106	C₂²×C₄×C₁₃₇	—	4	1	no	—
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₁₃₇	—	2	2	no	—
109	Q₁₆×C₁₃₇	—	2	2	no	—
110	Q₁₆×C₁₃₇	—	4	4	no	—
111	Q₁₆×C₁₃₇	—	4	1	no	—
112	Q₁₆×C₁₃₇	—	4	1	no	—
113	SD₁₆×C₁₃₇	—	4	4	no	—
114	SD₁₆×C₁₃₇	—	4	4	no	—
115	D₈×C₁₃₇	—	2	2	no	—
116	D₈×C₁₃₇	—	2	2	no	—
117	D₈×C₁₃₇	—	4	4	no	—
118	D₈×C₁₃₇	—	4	1	no	—
119	D₈×C₁₃₇	—	4	1	no	—
120	M₁₆×C₁₃₇	—	2	1	no	—
121	M₁₆×C₁₃₇	—	2	2	no	—
122	M₁₆×C₁₃₇	—	2	2	no	—
123	M₁₆×C₁₃₇	—	2	2	no	—
124	M₁₆×C₁₃₇	—	2	2	no	—
125	M₁₆×C₁₃₇	—	4	1	no	—
126	M₁₆×C₁₃₇	—	4	1	no	—
127	M₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃₇	—	2	1	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	—	4	1	no	—
132	C₂×C₈×C₁₃₇	—	4	1	no	—
133	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃₇	#41	1	1	yes	characteristic
137	C₂×C₈×C₁₃₇	#41	1	1	yes	characteristic
138	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
139	C₁₆×C₁₃₇	—	2	2	no	—
140	C₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
141	C₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
142	C₂³×C₁₃₇	—	2	1	no	—
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	8	1	no	—
145	C₂³×C₁₃₇	—	8	1	no	—
146	C₂³×C₁₃₇	—	16	2	no	—
147	C₂³×C₁₃₇	#135	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	2	1	no	—
149	Q₈×C₁₃₇	—	4	2	no	—
150	Q₈×C₁₃₇	—	4	2	no	—
151	Q₈×C₁₃₇	—	8	1	no	—
152	Q₈×C₁₃₇	—	8	1	no	—
153	Q₈×C₁₃₇	C₂×D₈	1	2	yes	—
154	D₄×C₁₃₇	—	2	2	no	—
155	D₄×C₁₃₇	—	2	2	no	—
156	D₄×C₁₃₇	—	2	1	no	—
157	D₄×C₁₃₇	—	4	2	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	8	1	no	—
160	D₄×C₁₃₇	—	8	1	no	—
161	D₄×C₁₃₇	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	8	1	no	—
167	C₂×C₄×C₁₃₇	—	8	1	no	—
168	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₃₇	—	2	2	no	—
175	C₈×C₁₃₇	—	4	2	no	—
176	C₈×C₁₃₇	—	4	2	no	—
177	C₈×C₁₃₇	#121	1	1	yes	characteristic
178	C₈×C₁₃₇	#121	1	1	yes	characteristic
179	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
181	C₂²×C₁₃₇	—	2	2	no	—
182	C₂²×C₁₃₇	—	2	2	no	—
183	C₂²×C₁₃₇	—	4	2	no	—
184	C₂²×C₁₃₇	—	8	2	no	—
185	C₂²×C₁₃₇	—	16	2	no	—
186	C₂²×C₁₃₇	—	16	2	no	—
187	C₂²×C₁₃₇	—	16	2	no	—
188	C₂²×C₁₃₇	#466	1	1	yes	characteristic
189	C₂²×C₁₃₇	#466	1	1	yes	characteristic
190	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₁₃₇	—	2	2	no	—
192	C₄×C₁₃₇	—	8	2	no	—
193	C₄×C₁₃₇	#466	1	1	yes	characteristic
194	C₄×C₁₃₇	#466	1	1	yes	characteristic
195	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
196	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
197	C₂×C₁₃₇	—	2	1	no	—
198	C₂×C₁₃₇	—	2	1	no	—
199	C₂×C₁₃₇	—	4	2	no	—
200	C₂×C₁₃₇	—	16	2	no	—
201	C₂×C₁₃₇	#2223	1	2	yes	direct product factor
202	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
203	C₂×#2223	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₇	C₂×#2223	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×SD₃₂	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	C₂×#504	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	C₂×#473	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	C₂×#472	C₂×C₁₃₇	1	1	yes	characteristic
209	#2223	C₂×C₁₃₇	1	8	yes	direct product factor
210	C₂×#368	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	C₂×#362	C₂×C₁₃₇	1	1	yes	characteristic, complemented
212	C₂×#361	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	C₂×#137	—	2	1	no	—
214	C₂×AGL(1,ℤ/8)	—	2	1	no	—
215	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₂×#131	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₂×SD₃₂	—	2	1	no	—
219	C₂×SD₃₂	—	2	1	no	—
220	C₂×SD₃₂	—	2	2	no	—
221	C₂×SD₃₂	C₂²×C₁₃₇	1	4	yes	complemented
222	#504	—	2	2	no	—
223	#504	C₂²×C₁₃₇	1	4	yes	complemented
224	C₂×M₃₂	—	2	1	no	—
225	C₂×M₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂²×C₁₆	—	2	1	no	—
227	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
228	#473	—	2	2	no	—
229	#473	C₂²×C₁₃₇	1	4	yes	complemented
230	#472	—	2	2	no	—
231	#472	C₂²×C₁₃₇	1	4	yes	—
232	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×#101	—	2	1	no	—
235	C₂×#100	—	2	1	no	—
236	#368	C₂²×C₁₃₇	1	4	yes	complemented
237	#362	C₂²×C₁₃₇	1	4	yes	complemented
238	#361	C₂²×C₁₃₇	1	4	yes	complemented
239	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	#137	—	2	4	no	—
243	#137	—	4	2	no	—
244	AGL(1,ℤ/8)	—	2	4	no	—
245	AGL(1,ℤ/8)	—	4	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	4	1	no	—
252	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
253	C₂×SD₁₆	—	4	1	no	—
254	C₂×SD₁₆	—	4	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	4	1	no	—
261	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	#131	D₄×C₁₃₇	1	2	yes	—
265	#131	C₂³×C₁₃₇	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
272	SD₃₂	—	2	4	no	—
273	SD₃₂	—	2	4	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	2	4	no	—
276	M₃₂	C₂³×C₁₃₇	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	4	no	—
279	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
280	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
281	C₂×C₁₆	D₄×C₁₃₇	1	2	yes	—
282	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
283	#108	—	2	1	no	—
284	#108	—	2	1	no	—
285	#108	C₂³×C₁₃₇	1	2	yes	—
286	#108	C₂³×C₁₃₇	1	2	yes	—
287	#101	—	2	4	no	—
288	#100	—	2	4	no	—
289	C₂⁴	—	4	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	D₈×C₁₃₇	1	2	yes	—
293	#41	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	D₈×C₁₃₇	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	4	4	no	—
315	Q₁₆	—	4	1	no	—
316	Q₁₆	—	4	1	no	—
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	4	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	4	no	—
322	D₈	—	4	1	no	—
323	D₈	—	4	1	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
340	C₂×C₈	#41×C₁₃₇	1	1	yes	characteristic
341	C₂×C₈	#41×C₁₃₇	1	1	yes	characteristic
342	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
345	C₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	16	2	no	—
351	C₂³	#135×C₁₃₇	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	8	1	no	—
356	Q₈	—	8	1	no	—
357	Q₈	C₂×D₈×C₁₃₇	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	C₂×D₈×C₁₃₇	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
376	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	#121×C₁₃₇	1	1	yes	characteristic
382	C₈	#121×C₁₃₇	1	1	yes	characteristic
383	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
384	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	16	2	no	—
392	C₂²	#466×C₁₃₇	1	1	yes	characteristic
393	C₂²	#466×C₁₃₇	1	1	yes	characteristic
394	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	8	2	no	—
397	C₄	#466×C₁₃₇	1	1	yes	characteristic
398	C₄	#466×C₁₃₇	1	1	yes	characteristic
399	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
400	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	16	2	no	—
405	C₂	#2223×C₁₃₇	1	2	yes	direct product factor
406	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
prime radical	C₂×#472×C₁₃₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂²×C₄×C₁₃₇ ◁ C₂×#131×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×SD₃₂×C₁₃₇	C₂	semidirect
2. C₂×#504×C₁₃₇	C₂	semidirect
3. C₂×#473×C₁₃₇	C₂	semidirect
5. #2223×C₁₃₇	C₂	direct (N × H)
6. C₂×#368×C₁₃₇	C₂	semidirect
7. C₂×#362×C₁₃₇	C₂	semidirect
8. C₂×#361×C₁₃₇	C₂	semidirect
17. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
19. #504×C₁₃₇	C₂²	semidirect
25. #473×C₁₃₇	C₂²	semidirect
32. #368×C₁₃₇	C₂²	semidirect
33. #362×C₁₃₇	C₂²	semidirect
34. #361×C₁₃₇	C₂²	semidirect
201. C₂×C₁₃₇	#2223	direct (N × H)
203. C₂×#2223	C₁₃₇	direct (N × H)
204. C₁₃₇	C₂×#2223	direct (N × H)
205. C₂²×SD₃₂	C₂×C₁₃₇	semidirect
206. C₂×#504	C₂×C₁₃₇	semidirect
207. C₂×#473	C₂×C₁₃₇	semidirect
209. #2223	C₂×C₁₃₇	direct (N × H)
210. C₂×#368	C₂×C₁₃₇	semidirect
211. C₂×#362	C₂×C₁₃₇	semidirect
212. C₂×#361	C₂×C₁₃₇	semidirect
221. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
223. #504	C₂²×C₁₃₇	semidirect
229. #473	C₂²×C₁₃₇	semidirect
236. #368	C₂²×C₁₃₇	semidirect
237. #362	C₂²×C₁₃₇	semidirect
238. #361	C₂²×C₁₃₇	semidirect
405. C₂	#2223×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×SD₃₂×C₁₃₇	2
C₂×#504×C₁₃₇	2
C₂×#473×C₁₃₇	2
C₂×#472×C₁₃₇	2
#2223×C₁₃₇	2
C₂×#368×C₁₃₇	2
C₂×#362×C₁₃₇	2
C₂×#361×C₁₃₇	2
C₂×#2223	137

Subgroups — C2×#2223×C137 #46883002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2223×C₁₃₇ #46883002