Subgroups — C₂×#1502×C₁₃₇ #46866917

Order 35072.

1474 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1502×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#327×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₃₇	—	2	1	no	—
7	#532×C₁₃₇	—	2	2	no	—
8	#532×C₁₃₇	—	2	2	no	—
9	#532×C₁₃₇	C₄	1	4	yes	complemented
10	#532×C₁₃₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
12	C₂×#127×C₁₃₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₁₃₇	—	2	1	no	—
14	C₂×#121×C₁₃₇	—	2	1	no	—
15	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₇	C₄	1	2	yes	complemented
18	C₂²×C₄⋊C₄×C₁₃₇	—	2	1	no	—
19	C₂²×C₄²×C₁₃₇	—	2	1	no	—
20	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
21	#431×C₁₃₇	—	2	2	no	—
22	#431×C₁₃₇	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
24	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₃₇	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
28	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
29	#327×C₁₃₇	C₂²	1	16	yes	complemented
30	C₂×#41×C₁₃₇	—	2	4	no	—
31	C₂×#41×C₁₃₇	—	2	4	no	—
32	C₂×#41×C₁₃₇	—	4	4	no	—
33	C₂×#41×C₁₃₇	—	4	4	no	—
34	C₂²×Q₈×C₁₃₇	—	2	1	no	—
35	C₂²×D₄×C₁₃₇	—	2	2	no	—
36	C₂²×D₄×C₁₃₇	—	2	1	no	—
37	C₂²×D₄×C₁₃₇	—	2	1	no	—
38	C₂²×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₃₇	—	2	2	no	—
40	C₂³×C₄×C₁₃₇	—	2	2	no	—
41	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
47	#127×C₁₃₇	—	2	2	no	—
48	#127×C₁₃₇	C₂×C₄	1	4	yes	complemented
49	#124×C₁₃₇	—	2	4	no	—
50	#124×C₁₃₇	—	2	4	no	—
51	#121×C₁₃₇	—	2	4	no	—
52	#121×C₁₃₇	—	2	4	no	—
53	#121×C₁₃₇	—	2	2	no	—
54	#121×C₁₃₇	—	2	2	no	—
55	#121×C₁₃₇	C₂×C₄	1	4	yes	—
56	#121×C₁₃₇	C₂³	1	4	yes	—
57	C₄×D₄×C₁₃₇	—	2	4	no	—
58	C₄×D₄×C₁₃₇	—	2	4	no	—
59	C₄×D₄×C₁₃₇	—	2	4	no	—
60	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
61	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₄²×C₁₃₇	—	2	4	no	—
68	C₂×C₄²×C₁₃₇	—	4	4	no	—
69	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
77	C₄⋊C₈×C₁₃₇	—	2	4	no	—
78	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
79	C₂²⋊C₈×C₁₃₇	C₂³	1	4	yes	—
80	C₄×C₈×C₁₃₇	—	2	4	no	—
81	#95×C₁₃₇	—	2	2	no	—
82	#95×C₁₃₇	C₂³	1	4	yes	—
83	C₂⁴×C₁₃₇	—	2	2	no	—
84	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
85	#41×C₁₃₇	—	4	16	no	—
86	#41×C₁₃₇	—	4	8	no	—
87	#41×C₁₃₇	—	4	8	no	—
88	C₂×Q₈×C₁₃₇	—	2	4	no	—
89	C₂×Q₈×C₁₃₇	—	4	4	no	—
90	C₂×D₄×C₁₃₇	—	2	4	no	—
91	C₂×D₄×C₁₃₇	—	2	4	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	4	no	—
94	C₂×D₄×C₁₃₇	—	2	4	no	—
95	C₂×D₄×C₁₃₇	—	4	4	no	—
96	C₂×D₄×C₁₃₇	—	4	4	no	—
97	C₂×D₄×C₁₃₇	—	4	4	no	—
98	C₂×D₄×C₁₃₇	—	4	4	no	—
99	C₂×D₄×C₁₃₇	—	4	4	no	—
100	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₇	—	2	4	no	—
102	C₂²×C₄×C₁₃₇	—	2	8	no	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	2	4	no	—
105	C₂²×C₄×C₁₃₇	—	2	8	no	—
106	C₂²×C₄×C₁₃₇	—	4	2	no	—
107	C₂²×C₄×C₁₃₇	—	4	4	no	—
108	C₂²×C₄×C₁₃₇	—	4	4	no	—
109	C₂²×C₄×C₁₃₇	—	4	8	no	—
110	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₇	D₈	1	4	yes	—
117	C₂²×C₄×C₁₃₇	SD₁₆	1	4	yes	—
118	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₁₃₇	—	2	4	no	—
127	C₂×C₈×C₁₃₇	—	4	4	no	—
128	C₄⋊C₄×C₁₃₇	—	2	16	no	—
129	C₄⋊C₄×C₁₃₇	—	2	4	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
132	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
133	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
134	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
135	C₄²×C₁₃₇	—	4	8	no	—
136	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
137	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
140	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
141	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
144	C₂³×C₁₃₇	—	2	2	no	—
145	C₂³×C₁₃₇	—	2	2	no	—
146	C₂³×C₁₃₇	—	2	4	no	—
147	C₂³×C₁₃₇	—	4	4	no	—
148	C₂³×C₁₃₇	—	4	4	no	—
149	C₂³×C₁₃₇	—	4	4	no	—
150	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
153	C₂³×C₁₃₇	C₂×SD₁₆	1	2	yes	—
154	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃₇	—	4	8	no	—
156	D₄×C₁₃₇	—	4	4	no	—
157	D₄×C₁₃₇	—	4	4	no	—
158	D₄×C₁₃₇	—	4	4	no	—
159	D₄×C₁₃₇	—	4	4	no	—
160	D₄×C₁₃₇	—	4	8	no	—
161	D₄×C₁₃₇	—	4	8	no	—
162	D₄×C₁₃₇	—	4	8	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	2	2	no	—
166	C₂×C₄×C₁₃₇	—	2	4	no	—
167	C₂×C₄×C₁₃₇	—	2	4	no	—
168	C₂×C₄×C₁₃₇	—	2	8	no	—
169	C₂×C₄×C₁₃₇	—	2	4	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	1	no	—
173	C₂×C₄×C₁₃₇	—	4	1	no	—
174	C₂×C₄×C₁₃₇	—	4	4	no	—
175	C₂×C₄×C₁₃₇	—	4	16	no	—
176	C₂×C₄×C₁₃₇	—	4	4	no	—
177	C₂×C₄×C₁₃₇	—	4	4	no	—
178	C₂×C₄×C₁₃₇	—	4	16	no	—
179	C₂×C₄×C₁₃₇	#102	1	4	yes	—
180	C₂×C₄×C₁₃₇	#102	1	4	yes	—
181	C₂×C₄×C₁₃₇	#102	1	8	yes	—
182	C₂×C₄×C₁₃₇	#104	1	4	yes	—
183	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₃₇	C₂×D₈	1	4	yes	—
190	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₃₇	—	4	4	no	—
194	C₂²×C₁₃₇	—	2	1	no	—
195	C₂²×C₁₃₇	—	2	1	no	—
196	C₂²×C₁₃₇	—	2	1	no	—
197	C₂²×C₁₃₇	—	2	1	no	—
198	C₂²×C₁₃₇	—	2	4	no	—
199	C₂²×C₁₃₇	—	2	4	no	—
200	C₂²×C₁₃₇	—	4	4	no	—
201	C₂²×C₁₃₇	—	4	4	no	—
202	C₂²×C₁₃₇	—	4	4	no	—
203	C₂²×C₁₃₇	—	8	8	no	—
204	C₂²×C₁₃₇	#410	1	2	yes	—
205	C₂²×C₁₃₇	C₂×#102	1	2	yes	—
206	C₂²×C₁₃₇	C₂×#102	1	2	yes	—
207	C₂²×C₁₃₇	C₂×#104	1	2	yes	—
208	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
210	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
211	C₄×C₁₃₇	—	2	1	no	—
212	C₄×C₁₃₇	—	2	1	no	—
213	C₄×C₁₃₇	—	2	1	no	—
214	C₄×C₁₃₇	—	2	1	no	—
215	C₄×C₁₃₇	—	2	2	no	—
216	C₄×C₁₃₇	—	4	8	no	—
217	C₄×C₁₃₇	—	4	4	no	—
218	C₄×C₁₃₇	C₂×#102	1	4	yes	—
219	C₄×C₁₃₇	C₂×#102	1	4	yes	—
220	C₄×C₁₃₇	C₂×#104	1	4	yes	—
221	C₂×C₁₃₇	—	2	1	no	—
222	C₂×C₁₃₇	—	2	1	no	—
223	C₂×C₁₃₇	—	2	2	no	—
224	C₂×C₁₃₇	—	8	4	no	—
225	C₂×C₁₃₇	#1502	1	4	yes	direct product factor
226	C₂×C₁₃₇	C₂×#410	1	1	yes	characteristic
227	C₂×C₁₃₇	C₂²×#102	1	1	yes	characteristic
228	C₂×C₁₃₇	C₂²×#104	1	1	yes	characteristic
229	C₂×#1502	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃₇	C₂×#1502	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#532	C₂×C₁₃₇	1	1	yes	characteristic
232	C₂×#431	C₂×C₁₃₇	1	1	yes	characteristic, complemented
233	C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
234	#1502	C₂×C₁₃₇	1	8	yes	direct product factor
235	C₂×#327	C₂×C₁₃₇	1	4	yes	complemented
236	C₂²×#41	—	2	1	no	—
237	#532	—	2	2	no	—
238	#532	—	2	2	no	—
239	#532	C₄×C₁₃₇	1	4	yes	complemented
240	#532	C₂²×C₁₃₇	1	4	yes	—
241	C₂×C₄⋊Q₈	C₄×C₁₃₇	1	1	yes	characteristic, complemented
242	C₂×#127	C₄×C₁₃₇	1	1	yes	characteristic, complemented
243	C₂×#124	—	2	1	no	—
244	C₂×#121	—	2	1	no	—
245	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
246	C₂×C₄×D₄	—	2	1	no	—
247	C₂×C₄×D₄	C₄×C₁₃₇	1	2	yes	complemented
248	C₂²×C₄⋊C₄	—	2	1	no	—
249	C₂²×C₄²	—	2	1	no	—
250	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
251	#431	—	2	2	no	—
252	#431	C₂²×C₁₃₇	1	4	yes	complemented
253	C₂×C₄⋊C₈	—	2	1	no	—
254	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
255	C₂×C₄×C₈	—	2	1	no	—
256	C₄×C₄⋊C₄	—	2	2	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
258	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
259	#327	C₂²×C₁₃₇	1	16	yes	complemented
260	C₂×#41	—	2	4	no	—
261	C₂×#41	—	2	4	no	—
262	C₂×#41	—	4	4	no	—
263	C₂×#41	—	4	4	no	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
277	#127	—	2	2	no	—
278	#127	C₂×C₄×C₁₃₇	1	4	yes	complemented
279	#124	—	2	4	no	—
280	#124	—	2	4	no	—
281	#121	—	2	4	no	—
282	#121	—	2	4	no	—
283	#121	—	2	2	no	—
284	#121	—	2	2	no	—
285	#121	C₂×C₄×C₁₃₇	1	4	yes	—
286	#121	C₂³×C₁₃₇	1	4	yes	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	4	no	—
298	C₂×C₄²	—	4	4	no	—
299	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
301	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
302	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
303	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
307	C₄⋊C₈	—	2	4	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	C₂³×C₁₃₇	1	4	yes	—
310	C₄×C₈	—	2	4	no	—
311	#95	—	2	2	no	—
312	#95	C₂³×C₁₃₇	1	4	yes	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	#41	—	4	16	no	—
316	#41	—	4	8	no	—
317	#41	—	4	8	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
344	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
346	C₂²×C₄	D₈×C₁₃₇	1	4	yes	—
347	C₂²×C₄	SD₁₆×C₁₃₇	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	4	4	no	—
358	C₄⋊C₄	—	2	16	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₄²	—	4	8	no	—
366	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
367	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
368	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
369	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
370	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
371	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
372	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
373	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
381	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
382	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
383	C₂³	C₂×SD₁₆×C₁₃₇	1	2	yes	—
384	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
385	Q₈	—	4	8	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	8	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	8	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	16	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	16	no	—
409	C₂×C₄	#102×C₁₃₇	1	4	yes	—
410	C₂×C₄	#102×C₁₃₇	1	4	yes	—
411	C₂×C₄	#102×C₁₃₇	1	8	yes	—
412	C₂×C₄	#104×C₁₃₇	1	4	yes	—
413	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
414	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
415	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
419	C₂×C₄	C₂×D₈×C₁₃₇	1	4	yes	—
420	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
423	C₈	—	4	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	8	no	—
434	C₂²	#410×C₁₃₇	1	2	yes	—
435	C₂²	C₂×#102×C₁₃₇	1	2	yes	—
436	C₂²	C₂×#102×C₁₃₇	1	2	yes	—
437	C₂²	C₂×#104×C₁₃₇	1	2	yes	—
438	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
439	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
440	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	8	no	—
447	C₄	—	4	4	no	—
448	C₄	C₂×#102×C₁₃₇	1	4	yes	—
449	C₄	C₂×#102×C₁₃₇	1	4	yes	—
450	C₄	C₂×#104×C₁₃₇	1	4	yes	—
451	C₂	—	2	1	no	—
452	C₂	—	2	2	no	—
453	C₂	—	2	1	no	—
454	C₂	—	8	4	no	—
455	C₂	#1502×C₁₃₇	1	4	yes	direct product factor
456	C₂	C₂×#410×C₁₃₇	1	1	yes	characteristic
457	C₂	C₂²×#102×C₁₃₇	1	1	yes	characteristic
458	C₂	C₂²×#104×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₃₇	C₂	semidirect
3. C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	semidirect
4. #1502×C₁₃₇	C₂	direct (N × H)
5. C₂×#327×C₁₃₇	C₂	semidirect
9. #532×C₁₃₇	C₄	semidirect
11. C₂×C₄⋊Q₈×C₁₃₇	C₄	semidirect
12. C₂×#127×C₁₃₇	C₄	semidirect
17. C₂×C₄×D₄×C₁₃₇	C₄	semidirect
22. #431×C₁₃₇	C₂²	semidirect
27. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
29. #327×C₁₃₇	C₂²	semidirect
46. C₄⋊Q₈×C₁₃₇	C₂×C₄	semidirect
48. #127×C₁₃₇	C₂×C₄	semidirect
60. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
225. C₂×C₁₃₇	#1502	direct (N × H)
229. C₂×#1502	C₁₃₇	direct (N × H)
230. C₁₃₇	C₂×#1502	direct (N × H)
232. C₂×#431	C₂×C₁₃₇	semidirect
233. C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	semidirect
234. #1502	C₂×C₁₃₇	direct (N × H)
235. C₂×#327	C₂×C₁₃₇	semidirect
239. #532	C₄×C₁₃₇	semidirect
241. C₂×C₄⋊Q₈	C₄×C₁₃₇	semidirect
242. C₂×#127	C₄×C₁₃₇	semidirect
247. C₂×C₄×D₄	C₄×C₁₃₇	semidirect
252. #431	C₂²×C₁₃₇	semidirect
257. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
259. #327	C₂²×C₁₃₇	semidirect
276. C₄⋊Q₈	C₂×C₄×C₁₃₇	semidirect
278. #127	C₂×C₄×C₁₃₇	semidirect
290. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
455. C₂	#1502×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
C₂×#532×C₁₃₇	2
C₂×#431×C₁₃₇	2
C₂×C₄×C₄⋊C₄×C₁₃₇	2
#1502×C₁₃₇	2
C₂×#327×C₁₃₇	2
C₂×#1502	137

Subgroups — C2×#1502×C137 #46866917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1502×C₁₃₇ #46866917