Subgroups — C₁₃₇×#23641 #46873027

Order 35072.

1014 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#408×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2311×C₁₃₇	C₂	1	2	yes	maximal
4	#2077×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#2076×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2075×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1736×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	C₂×#340×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
14	#427×C₁₃₇	—	2	4	no	—
15	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
18	#408×C₁₃₇	—	2	4	no	—
19	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
21	#391×C₁₃₇	—	2	2	no	—
22	#390×C₁₃₇	—	2	2	no	—
23	#386×C₁₃₇	—	2	4	no	—
24	#380×C₁₃₇	C₂²	1	4	yes	—
25	#380×C₁₃₇	C₂²	1	4	yes	—
26	#340×C₁₃₇	C₂²	1	2	yes	—
27	#340×C₁₃₇	C₂²	1	4	yes	—
28	#340×C₁₃₇	C₂²	1	4	yes	—
29	#340×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	2	2	no	—
32	C₂×#41×C₁₃₇	—	2	4	no	—
33	C₂×#41×C₁₃₇	—	2	4	no	—
34	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
36	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₇	—	2	2	no	—
38	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	—	2	4	no	—
42	C₂²×C₈×C₁₃₇	—	2	4	no	—
43	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
44	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	#117×C₁₃₇	—	2	4	no	—
48	#117×C₁₃₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
58	C₂×C₄²×C₁₃₇	—	2	2	no	—
59	#107×C₁₃₇	—	2	2	no	—
60	#107×C₁₃₇	—	2	2	no	—
61	#106×C₁₃₇	—	2	4	no	—
62	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
63	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
64	#95×C₁₃₇	—	2	4	no	—
65	#95×C₁₃₇	—	2	4	no	—
66	C₂⁴×C₁₃₇	C₂×D₄	1	2	yes	—
67	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
68	#41×C₁₃₇	—	4	4	no	—
69	#41×C₁₃₇	—	4	4	no	—
70	#41×C₁₃₇	—	4	8	no	—
71	C₂×Q₈×C₁₃₇	—	2	2	no	—
72	C₂×Q₈×C₁₃₇	—	2	4	no	—
73	C₂×D₄×C₁₃₇	—	2	4	no	—
74	C₂×D₄×C₁₃₇	—	2	8	no	—
75	C₂×D₄×C₁₃₇	—	2	2	no	—
76	C₂×D₄×C₁₃₇	—	2	4	no	—
77	C₂²×C₄×C₁₃₇	—	2	2	no	—
78	C₂²×C₄×C₁₃₇	—	2	2	no	—
79	C₂²×C₄×C₁₃₇	—	2	4	no	—
80	C₂²×C₄×C₁₃₇	—	2	4	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	2	no	—
83	C₂²×C₄×C₁₃₇	—	2	4	no	—
84	C₂²×C₄×C₁₃₇	—	4	4	no	—
85	C₂²×C₄×C₁₃₇	—	8	2	no	—
86	C₂²×C₄×C₁₃₇	—	8	2	no	—
87	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
91	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
92	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
93	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₃₇	—	4	4	no	—
95	C₂×C₈×C₁₃₇	—	2	8	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	2	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	4	no	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	4	4	no	—
109	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
110	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
111	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
112	C₄²×C₁₃₇	—	4	4	no	—
113	C₂³×C₁₃₇	—	2	1	no	—
114	C₂³×C₁₃₇	—	2	2	no	—
115	C₂³×C₁₃₇	—	2	1	no	—
116	C₂³×C₁₃₇	—	2	2	no	—
117	C₂³×C₁₃₇	—	2	4	no	—
118	C₂³×C₁₃₇	—	2	2	no	—
119	C₂³×C₁₃₇	—	2	4	no	—
120	C₂³×C₁₃₇	—	2	2	no	—
121	C₂³×C₁₃₇	#121	1	2	yes	—
122	C₂³×C₁₃₇	#123	1	4	yes	—
123	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
124	Q₈×C₁₃₇	—	4	4	no	—
125	D₄×C₁₃₇	—	4	8	no	—
126	D₄×C₁₃₇	—	4	4	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	2	4	no	—
129	C₂×C₄×C₁₃₇	—	4	2	no	—
130	C₂×C₄×C₁₃₇	—	4	2	no	—
131	C₂×C₄×C₁₃₇	—	4	4	no	—
132	C₂×C₄×C₁₃₇	—	4	2	no	—
133	C₂×C₄×C₁₃₇	—	4	2	no	—
134	C₂×C₄×C₁₃₇	—	4	4	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	4	4	no	—
137	C₂×C₄×C₁₃₇	—	4	2	no	—
138	C₂×C₄×C₁₃₇	—	4	4	no	—
139	C₂×C₄×C₁₃₇	—	4	2	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	8	8	no	—
142	C₂×C₄×C₁₃₇	#121	1	2	yes	—
143	C₂×C₄×C₁₃₇	#123	1	4	yes	—
144	C₂×C₄×C₁₃₇	#123	1	4	yes	—
145	C₂×C₄×C₁₃₇	#124	1	4	yes	—
146	C₂×C₄×C₁₃₇	#126	1	8	yes	—
147	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₃₇	—	2	2	no	—
152	C₈×C₁₃₇	—	2	2	no	—
153	C₈×C₁₃₇	—	4	2	no	—
154	C₂²×C₁₃₇	—	2	4	no	—
155	C₂²×C₁₃₇	—	2	4	no	—
156	C₂²×C₁₃₇	—	2	2	no	—
157	C₂²×C₁₃₇	—	2	2	no	—
158	C₂²×C₁₃₇	—	4	4	no	—
159	C₂²×C₁₃₇	—	4	4	no	—
160	C₂²×C₁₃₇	—	4	2	no	—
161	C₂²×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	4	2	no	—
163	C₂²×C₁₃₇	#397	1	4	yes	—
164	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
165	C₂²×C₁₃₇	C₂×#123	1	2	yes	—
166	C₂²×C₁₃₇	#576	1	1	yes	characteristic
167	C₂²×C₁₃₇	#577	1	2	yes	—
168	C₂²×C₁₃₇	#578	1	1	yes	characteristic
169	C₄×C₁₃₇	—	4	2	no	—
170	C₄×C₁₃₇	—	8	4	no	—
171	C₄×C₁₃₇	—	8	2	no	—
172	C₄×C₁₃₇	—	8	2	no	—
173	C₄×C₁₃₇	#397	1	4	yes	—
174	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
175	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
176	C₄×C₁₃₇	C₂×#126	1	2	yes	—
177	C₂×C₁₃₇	—	2	4	no	—
178	C₂×C₁₃₇	—	8	2	no	—
179	C₂×C₁₃₇	C₂×#397	1	1	yes	characteristic
180	C₂×C₁₃₇	#3060	1	1	yes	characteristic
181	C₂×C₁₃₇	#3061	1	1	yes	characteristic
182	C₂×C₁₃₇	#3096	1	2	yes	—
183	C₂×C₁₃₇	#3097	1	2	yes	—
184	#23641	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₇	#23641	1	1	yes	characteristic, direct product factor, Sylow
186	C₂×#427	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	C₂×#408	C₂×C₁₃₇	1	1	yes	characteristic
188	#2311	C₂×C₁₃₇	1	2	yes	—
189	#2077	C₂×C₁₃₇	1	4	yes	complemented
190	#2076	C₂×C₁₃₇	1	2	yes	complemented
191	#2075	C₂×C₁₃₇	1	2	yes	complemented
192	#1736	C₂×C₁₃₇	1	2	yes	complemented
193	C₂×#340	C₂×C₁₃₇	1	1	yes	characteristic, complemented
194	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
199	#427	—	2	4	no	—
200	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
203	#408	—	2	4	no	—
204	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
206	#391	—	2	2	no	—
207	#390	—	2	2	no	—
208	#386	—	2	4	no	—
209	#380	C₂²×C₁₃₇	1	4	yes	—
210	#380	C₂²×C₁₃₇	1	4	yes	—
211	#340	C₂²×C₁₃₇	1	2	yes	—
212	#340	C₂²×C₁₃₇	1	4	yes	—
213	#340	C₂²×C₁₃₇	1	4	yes	—
214	#340	C₂²×C₁₃₇	1	2	yes	—
215	C₂×#41	—	2	2	no	—
216	C₂×#41	—	2	2	no	—
217	C₂×#41	—	2	4	no	—
218	C₂×#41	—	2	4	no	—
219	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
220	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
221	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
229	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
232	#117	—	2	4	no	—
233	#117	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₄²	—	2	2	no	—
244	#107	—	2	2	no	—
245	#107	—	2	2	no	—
246	#106	—	2	4	no	—
247	C₂²⋊C₈	—	2	4	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	#95	—	2	4	no	—
250	#95	—	2	4	no	—
251	C₂⁴	C₂×D₄×C₁₃₇	1	2	yes	—
252	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
253	#41	—	4	4	no	—
254	#41	—	4	4	no	—
255	#41	—	4	8	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	8	2	no	—
271	C₂²×C₄	—	8	2	no	—
272	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
275	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
276	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
277	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
286	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	8	4	no	—
296	C₂²⋊C₄	—	8	4	no	—
297	C₄²	—	4	4	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	2	no	—
306	C₂³	#121×C₁₃₇	1	2	yes	—
307	C₂³	#123×C₁₃₇	1	4	yes	—
308	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
309	Q₈	—	4	4	no	—
310	D₄	—	4	8	no	—
311	D₄	—	4	4	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	#121×C₁₃₇	1	2	yes	—
328	C₂×C₄	#123×C₁₃₇	1	4	yes	—
329	C₂×C₄	#123×C₁₃₇	1	4	yes	—
330	C₂×C₄	#124×C₁₃₇	1	4	yes	—
331	C₂×C₄	#126×C₁₃₇	1	8	yes	—
332	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
334	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
335	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	4	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	2	no	—
348	C₂²	#397×C₁₃₇	1	4	yes	—
349	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
350	C₂²	C₂×#123×C₁₃₇	1	2	yes	—
351	C₂²	#576×C₁₃₇	1	1	yes	characteristic
352	C₂²	#577×C₁₃₇	1	2	yes	—
353	C₂²	#578×C₁₃₇	1	1	yes	characteristic
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	4	no	—
358	C₄	#397×C₁₃₇	1	4	yes	—
359	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
360	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
361	C₄	C₂×#126×C₁₃₇	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	—	8	2	no	—
364	C₂	C₂×#397×C₁₃₇	1	1	yes	characteristic
365	C₂	#3060×C₁₃₇	1	1	yes	characteristic
366	C₂	#3061×C₁₃₇	1	1	yes	characteristic
367	C₂	#3096×C₁₃₇	1	2	yes	—
368	C₂	#3097×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×#41×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#427×C₁₃₇	C₂	semidirect
4. #2077×C₁₃₇	C₂	semidirect
5. #2076×C₁₃₇	C₂	semidirect
6. #2075×C₁₃₇	C₂	semidirect
7. #1736×C₁₃₇	C₂	semidirect
8. C₂×#340×C₁₃₇	C₂	semidirect
184. #23641	C₁₃₇	direct (N × H)
185. C₁₃₇	#23641	direct (N × H)
186. C₂×#427	C₂×C₁₃₇	semidirect
189. #2077	C₂×C₁₃₇	semidirect
190. #2076	C₂×C₁₃₇	semidirect
191. #2075	C₂×C₁₃₇	semidirect
192. #1736	C₂×C₁₃₇	semidirect
193. C₂×#340	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#427×C₁₃₇	2
C₂×#408×C₁₃₇	2
#2311×C₁₃₇	2
#2077×C₁₃₇	2
#2076×C₁₃₇	2
#2075×C₁₃₇	2
#1736×C₁₃₇	2
C₂×#340×C₁₃₇	2
#23641	137

Subgroups — C137×#23641 #46873027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#23641 #46873027