Subgroups — C₂×#1997×C₁₃₇ #46870721

Order 35072.

1342 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1997×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#343×C₁₃₇	C₂	1	4	yes	maximal
6	C₂³×Q₈×C₁₃₇	C₄	1	2	yes	—
7	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₁₃₇	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₁₃₇	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₁₃₇	C₄	1	4	yes	—
16	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₃₇	C₄	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
20	#423×C₁₃₇	—	2	2	no	—
21	#423×C₁₃₇	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
23	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
24	C₄×M₁₆×C₁₃₇	—	2	2	no	—
25	C₄×M₁₆×C₁₃₇	C₂²	1	4	yes	—
26	C₂×#97×C₁₃₇	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
28	#343×C₁₃₇	C₂²	1	16	yes	—
29	C₂²×Q₈×C₁₃₇	—	2	4	no	—
30	C₂²×Q₈×C₁₃₇	—	2	2	no	—
31	C₂²×Q₈×C₁₃₇	—	2	2	no	—
32	C₂²×Q₈×C₁₃₇	—	4	8	no	—
33	C₂²×Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₃₇	—	2	2	no	—
39	C₂×M₁₆×C₁₃₇	—	2	4	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	—	2	8	no	—
42	C₂×M₁₆×C₁₃₇	Q₈	1	8	yes	complemented
43	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
44	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₃₇	—	2	2	no	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
48	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
49	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
50	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
54	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	8	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	C₄⋊C₈×C₁₃₇	—	2	4	no	—
75	#97×C₁₃₇	—	2	4	no	—
76	C₄×C₈×C₁₃₇	—	2	4	no	—
77	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₃₇	—	2	8	no	—
79	C₂×Q₈×C₁₃₇	—	2	8	no	—
80	C₂×Q₈×C₁₃₇	—	4	16	no	—
81	C₂×Q₈×C₁₃₇	—	4	8	no	—
82	C₂×Q₈×C₁₃₇	—	4	16	no	—
83	C₂×Q₈×C₁₃₇	—	4	8	no	—
84	C₂²×C₄×C₁₃₇	—	2	4	no	—
85	C₂²×C₄×C₁₃₇	—	2	4	no	—
86	C₂²×C₄×C₁₃₇	—	2	4	no	—
87	C₂²×C₄×C₁₃₇	—	2	4	no	—
88	C₂²×C₄×C₁₃₇	—	4	8	no	—
89	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₁₃₇	C₂²×C₄	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	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₇	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
105	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₃₇	—	2	8	no	—
107	M₁₆×C₁₃₇	—	2	4	no	—
108	M₁₆×C₁₃₇	—	2	8	no	—
109	M₁₆×C₁₃₇	—	4	4	no	—
110	M₁₆×C₁₃₇	C₂×Q₈	1	8	yes	complemented
111	C₂×C₈×C₁₃₇	—	2	8	no	—
112	C₂×C₈×C₁₃₇	—	2	4	no	—
113	C₂×C₈×C₁₃₇	—	2	4	no	—
114	C₂×C₈×C₁₃₇	—	4	4	no	—
115	C₄⋊C₄×C₁₃₇	—	2	8	no	—
116	C₄⋊C₄×C₁₃₇	—	2	4	no	—
117	C₄⋊C₄×C₁₃₇	—	2	4	no	—
118	C₄⋊C₄×C₁₃₇	—	2	8	no	—
119	C₄⋊C₄×C₁₃₇	—	2	4	no	—
120	C₄⋊C₄×C₁₃₇	—	2	4	no	—
121	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
127	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂³×C₁₃₇	—	2	2	no	—
130	C₂³×C₁₃₇	—	2	2	no	—
131	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₃₇	C₄×Q₈	1	4	yes	—
134	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
135	Q₈×C₁₃₇	—	4	16	no	—
136	Q₈×C₁₃₇	—	4	16	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	2	4	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	2	4	no	—
143	C₂×C₄×C₁₃₇	—	2	8	no	—
144	C₂×C₄×C₁₃₇	—	4	8	no	—
145	C₂×C₄×C₁₃₇	—	4	8	no	—
146	C₂×C₄×C₁₃₇	—	4	8	no	—
147	C₂×C₄×C₁₃₇	#100	1	4	yes	—
148	C₂×C₄×C₁₃₇	#101	1	4	yes	—
149	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₄×Q₈	1	4	yes	—
156	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
157	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
158	C₂×C₄×C₁₃₇	#124	1	2	yes	—
159	C₂×C₄×C₁₃₇	#124	1	2	yes	—
160	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
161	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
162	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂²×Q₈	1	2	yes	—
165	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
166	C₈×C₁₃₇	—	2	8	no	—
167	C₈×C₁₃₇	—	4	4	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	—	2	8	no	—
173	C₂²×C₁₃₇	#391	1	2	yes	—
174	C₂²×C₁₃₇	#391	1	2	yes	—
175	C₂²×C₁₃₇	C₂×#100	1	2	yes	—
176	C₂²×C₁₃₇	C₂×#101	1	2	yes	—
177	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₃₇	C₂×C₄×Q₈	1	2	yes	—
179	C₄×C₁₃₇	—	2	2	no	—
180	C₄×C₁₃₇	—	2	2	no	—
181	C₄×C₁₃₇	—	4	8	no	—
182	C₄×C₁₃₇	#391	1	2	yes	—
183	C₄×C₁₃₇	#391	1	2	yes	—
184	C₄×C₁₃₇	C₂×#100	1	4	yes	—
185	C₄×C₁₃₇	C₂×#101	1	4	yes	—
186	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	2	yes	—
187	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
188	C₄×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	C₂×C₁₃₇	—	2	2	no	—
190	C₂×C₁₃₇	—	2	2	no	—
191	C₂×C₁₃₇	#1997	1	4	yes	direct product factor
192	C₂×C₁₃₇	C₂×#391	1	1	yes	characteristic
193	C₂×C₁₃₇	C₂²×#100	1	1	yes	characteristic
194	C₂×C₁₃₇	C₂²×#101	1	1	yes	characteristic
195	C₂×#1997	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₇	C₂×#1997	1	1	yes	characteristic, direct product factor, Sylow
197	C₂²×C₄⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic
198	C₂×#423	C₂×C₁₃₇	1	1	yes	characteristic
199	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
200	#1997	C₂×C₁₃₇	1	8	yes	direct product factor
201	C₂×#343	C₂×C₁₃₇	1	4	yes	—
202	C₂³×Q₈	C₄×C₁₃₇	1	2	yes	—
203	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
204	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	—	2	1	no	—
207	C₂×C₄⋊Q₈	—	2	2	no	—
208	C₂×C₄⋊Q₈	—	2	1	no	—
209	C₂×C₄⋊Q₈	—	2	1	no	—
210	C₂×C₄⋊Q₈	—	2	2	no	—
211	C₂×C₄⋊Q₈	C₄×C₁₃₇	1	4	yes	—
212	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	4	yes	—
213	C₂²×C₄⋊C₄	C₄×C₁₃₇	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
216	#423	—	2	2	no	—
217	#423	C₂²×C₁₃₇	1	4	yes	—
218	C₂×C₄⋊C₈	—	2	1	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₄×M₁₆	—	2	2	no	—
221	C₄×M₁₆	C₂²×C₁₃₇	1	4	yes	—
222	C₂×#97	—	2	1	no	—
223	C₂×C₄×C₈	—	2	1	no	—
224	#343	C₂²×C₁₃₇	1	16	yes	—
225	C₂²×Q₈	—	2	4	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	4	8	no	—
229	C₂²×Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
230	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×C₁₃₇	1	4	yes	—
233	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	8	no	—
238	C₂×M₁₆	Q₈×C₁₃₇	1	8	yes	complemented
239	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
240	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	—	2	4	no	—
246	C₄⋊Q₈	—	2	4	no	—
247	C₄⋊Q₈	—	2	4	no	—
248	C₄⋊Q₈	—	2	4	no	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	8	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
261	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
262	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
265	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
269	C₄⋊C₈	—	2	4	no	—
270	C₄⋊C₈	—	2	4	no	—
271	#97	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	4	16	no	—
277	C₂×Q₈	—	4	8	no	—
278	C₂×Q₈	—	4	16	no	—
279	C₂×Q₈	—	4	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₁₃₇	1	4	yes	—
300	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
302	M₁₆	—	2	8	no	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	2	8	no	—
305	M₁₆	—	4	4	no	—
306	M₁₆	C₂×Q₈×C₁₃₇	1	8	yes	complemented
307	C₂×C₈	—	2	8	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
318	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
319	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
320	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
321	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
322	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
323	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
324	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
328	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
329	C₂³	C₄×Q₈×C₁₃₇	1	4	yes	—
330	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
331	Q₈	—	4	16	no	—
332	Q₈	—	4	16	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	#100×C₁₃₇	1	4	yes	—
344	C₂×C₄	#101×C₁₃₇	1	4	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
351	C₂×C₄	C₄×Q₈×C₁₃₇	1	4	yes	—
352	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
353	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
354	C₂×C₄	#124×C₁₃₇	1	2	yes	—
355	C₂×C₄	#124×C₁₃₇	1	2	yes	—
356	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
357	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×Q₈×C₁₃₇	1	2	yes	—
361	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
362	C₈	—	2	8	no	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	8	no	—
369	C₂²	#391×C₁₃₇	1	2	yes	—
370	C₂²	#391×C₁₃₇	1	2	yes	—
371	C₂²	C₂×#100×C₁₃₇	1	2	yes	—
372	C₂²	C₂×#101×C₁₃₇	1	2	yes	—
373	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
374	C₂²	C₂×C₄×Q₈×C₁₃₇	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	8	no	—
378	C₄	#391×C₁₃₇	1	2	yes	—
379	C₄	#391×C₁₃₇	1	2	yes	—
380	C₄	C₂×#100×C₁₃₇	1	4	yes	—
381	C₄	C₂×#101×C₁₃₇	1	4	yes	—
382	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	2	yes	—
383	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
384	C₄	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	#1997×C₁₃₇	1	4	yes	direct product factor
388	C₂	C₂×#391×C₁₃₇	1	1	yes	characteristic
389	C₂	C₂²×#100×C₁₃₇	1	1	yes	characteristic
390	C₂	C₂²×#101×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1997×C₁₃₇	C₂	direct (N × H)
42. C₂×M₁₆×C₁₃₇	Q₈	semidirect
110. M₁₆×C₁₃₇	C₂×Q₈	semidirect
191. C₂×C₁₃₇	#1997	direct (N × H)
195. C₂×#1997	C₁₃₇	direct (N × H)
196. C₁₃₇	C₂×#1997	direct (N × H)
200. #1997	C₂×C₁₃₇	direct (N × H)
238. C₂×M₁₆	Q₈×C₁₃₇	semidirect
306. M₁₆	C₂×Q₈×C₁₃₇	semidirect
387. C₂	#1997×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×C₄⋊Q₈×C₁₃₇	2
C₂×#423×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
#1997×C₁₃₇	2
C₂×#343×C₁₃₇	2
C₂×#1997	137

Subgroups — C2×#1997×C137 #46870721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1997×C₁₃₇ #46870721