Subgroups — C₂²×#327×C₁₃₇ #46866913

Order 35072.

2190 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#95×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#327×C₁₃₇	C₂	1	12	yes	maximal, direct product factor
5	C₂³×D₄×C₁₃₇	—	2	1	no	—
6	C₂³×D₄×C₁₃₇	C₄	1	1	yes	characteristic, complemented
7	C₂⁴×C₄×C₁₃₇	—	2	1	no	—
8	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃₇	—	2	1	no	—
10	C₂×#121×C₁₃₇	—	2	3	no	—
11	C₂×#121×C₁₃₇	—	2	3	no	—
12	C₂×#121×C₁₃₇	C₄	1	6	yes	complemented
13	C₂×#121×C₁₃₇	C₂²	1	6	yes	—
14	C₂²×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
16	C₂×C₂²⋊C₈×C₁₃₇	—	2	3	no	—
17	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	6	yes	complemented
18	C₂×#95×C₁₃₇	—	2	3	no	—
19	C₂×#95×C₁₃₇	C₂²	1	6	yes	complemented
20	#327×C₁₃₇	C₂²	1	16	yes	direct product factor
21	C₂⁵×C₁₃₇	—	2	1	no	—
22	C₂⁵×C₁₃₇	D₄	1	1	yes	characteristic
23	C₂²×D₄×C₁₃₇	—	2	6	no	—
24	C₂²×D₄×C₁₃₇	—	2	6	no	—
25	C₂²×D₄×C₁₃₇	—	2	3	no	—
26	C₂²×D₄×C₁₃₇	—	4	4	no	—
27	C₂²×D₄×C₁₃₇	—	4	4	no	—
28	C₂²×D₄×C₁₃₇	—	4	4	no	—
29	C₂²×D₄×C₁₃₇	C₂×C₄	1	6	yes	complemented
30	C₂³×C₄×C₁₃₇	—	2	8	no	—
31	C₂³×C₄×C₁₃₇	—	2	1	no	—
32	C₂³×C₄×C₁₃₇	—	2	6	no	—
33	C₂³×C₄×C₁₃₇	—	4	4	no	—
34	C₂³×C₄×C₁₃₇	—	4	4	no	—
35	C₂³×C₄×C₁₃₇	—	4	4	no	—
36	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₇	C₂×C₄	1	3	yes	—
38	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₇	D₄	1	3	yes	—
40	C₂³×C₄×C₁₃₇	D₄	1	3	yes	—
41	C₂³×C₄×C₁₃₇	C₂³	1	3	yes	—
42	C₂²×C₈×C₁₃₇	—	2	6	no	—
43	C₂²×C₈×C₁₃₇	—	4	4	no	—
44	#121×C₁₃₇	—	2	12	no	—
45	#121×C₁₃₇	—	2	6	no	—
46	#121×C₁₃₇	—	2	6	no	—
47	#121×C₁₃₇	C₂×C₄	1	12	yes	complemented
48	#121×C₁₃₇	C₂³	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	3	no	—
50	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	6	yes	complemented
51	C₂×C₂²⋊C₄×C₁₃₇	—	2	6	no	—
52	C₂×C₂²⋊C₄×C₁₃₇	—	2	6	no	—
53	C₂²⋊C₈×C₁₃₇	—	2	6	no	—
54	C₂²⋊C₈×C₁₃₇	C₂³	1	4	yes	complemented
55	#95×C₁₃₇	—	2	6	no	—
56	#95×C₁₃₇	C₂³	1	4	yes	complemented
57	C₂⁴×C₁₃₇	—	2	4	no	—
58	C₂⁴×C₁₃₇	—	2	4	no	—
59	C₂⁴×C₁₃₇	—	2	6	no	—
60	C₂⁴×C₁₃₇	—	4	4	no	—
61	C₂⁴×C₁₃₇	—	4	4	no	—
62	C₂⁴×C₁₃₇	—	4	4	no	—
63	C₂⁴×C₁₃₇	C₂²⋊C₄	1	3	yes	—
64	C₂⁴×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂⁴×C₁₃₇	D₈	1	4	yes	—
66	C₂⁴×C₁₃₇	SD₁₆	1	4	yes	—
67	C₂⁴×C₁₃₇	C₂×D₄	1	3	yes	—
68	C₂×D₄×C₁₃₇	—	2	12	no	—
69	C₂×D₄×C₁₃₇	—	2	4	no	—
70	C₂×D₄×C₁₃₇	—	2	6	no	—
71	C₂×D₄×C₁₃₇	—	4	12	no	—
72	C₂×D₄×C₁₃₇	—	4	12	no	—
73	C₂×D₄×C₁₃₇	—	4	24	no	—
74	C₂×D₄×C₁₃₇	—	4	12	no	—
75	C₂×D₄×C₁₃₇	—	4	12	no	—
76	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	complemented
77	C₂²×C₄×C₁₃₇	—	2	4	no	—
78	C₂²×C₄×C₁₃₇	—	2	4	no	—
79	C₂²×C₄×C₁₃₇	—	2	24	no	—
80	C₂²×C₄×C₁₃₇	—	2	6	no	—
81	C₂²×C₄×C₁₃₇	—	2	4	no	—
82	C₂²×C₄×C₁₃₇	—	4	6	no	—
83	C₂²×C₄×C₁₃₇	—	4	6	no	—
84	C₂²×C₄×C₁₃₇	—	4	6	no	—
85	C₂²×C₄×C₁₃₇	—	4	6	no	—
86	C₂²×C₄×C₁₃₇	—	4	32	no	—
87	C₂²×C₄×C₁₃₇	—	4	12	no	—
88	C₂²×C₄×C₁₃₇	—	4	4	no	—
89	C₂²×C₄×C₁₃₇	—	4	12	no	—
90	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	3	yes	—
91	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	3	yes	—
92	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	6	yes	—
93	C₂²×C₄×C₁₃₇	C₂²×C₄	1	3	yes	—
94	C₂²×C₄×C₁₃₇	C₂²×C₄	1	3	yes	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	—	4	12	no	—
101	C₄⋊C₄×C₁₃₇	—	2	6	no	—
102	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	complemented
103	C₂²⋊C₄×C₁₃₇	—	2	12	no	—
104	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
105	C₂³×C₁₃₇	—	2	16	no	—
106	C₂³×C₁₃₇	—	2	16	no	—
107	C₂³×C₁₃₇	—	2	6	no	—
108	C₂³×C₁₃₇	—	2	6	no	—
109	C₂³×C₁₃₇	—	2	6	no	—
110	C₂³×C₁₃₇	—	2	6	no	—
111	C₂³×C₁₃₇	—	2	4	no	—
112	C₂³×C₁₃₇	—	4	12	no	—
113	C₂³×C₁₃₇	—	4	12	no	—
114	C₂³×C₁₃₇	—	4	12	no	—
115	C₂³×C₁₃₇	—	8	16	no	—
116	C₂³×C₁₃₇	#99	1	4	yes	—
117	C₂³×C₁₃₇	#102	1	12	yes	—
118	C₂³×C₁₃₇	#102	1	4	yes	—
119	C₂³×C₁₃₇	#104	1	4	yes	—
120	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	3	yes	—
121	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	3	yes	—
122	C₂³×C₁₃₇	C₂×D₈	1	6	yes	—
123	C₂³×C₁₃₇	C₂×SD₁₆	1	6	yes	—
124	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
125	D₄×C₁₃₇	—	4	4	no	—
126	D₄×C₁₃₇	—	4	12	no	—
127	D₄×C₁₃₇	—	4	4	no	—
128	D₄×C₁₃₇	—	4	4	no	—
129	D₄×C₁₃₇	—	4	24	no	—
130	C₂×C₄×C₁₃₇	—	2	6	no	—
131	C₂×C₄×C₁₃₇	—	2	6	no	—
132	C₂×C₄×C₁₃₇	—	2	6	no	—
133	C₂×C₄×C₁₃₇	—	2	6	no	—
134	C₂×C₄×C₁₃₇	—	2	8	no	—
135	C₂×C₄×C₁₃₇	—	2	4	no	—
136	C₂×C₄×C₁₃₇	—	4	6	no	—
137	C₂×C₄×C₁₃₇	—	4	3	no	—
138	C₂×C₄×C₁₃₇	—	4	3	no	—
139	C₂×C₄×C₁₃₇	—	4	3	no	—
140	C₂×C₄×C₁₃₇	—	4	1	no	—
141	C₂×C₄×C₁₃₇	—	4	4	no	—
142	C₂×C₄×C₁₃₇	—	4	48	no	—
143	C₂×C₄×C₁₃₇	—	4	4	no	—
144	C₂×C₄×C₁₃₇	—	4	12	no	—
145	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	3	yes	—
146	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
149	C₈×C₁₃₇	—	4	4	no	—
150	C₂²×C₁₃₇	—	2	1	no	—
151	C₂²×C₁₃₇	—	2	3	no	—
152	C₂²×C₁₃₇	—	2	1	no	—
153	C₂²×C₁₃₇	—	2	3	no	—
154	C₂²×C₁₃₇	—	2	12	no	—
155	C₂²×C₁₃₇	—	2	24	no	—
156	C₂²×C₁₃₇	—	2	12	no	—
157	C₂²×C₁₃₇	—	4	4	no	—
158	C₂²×C₁₃₇	—	4	4	no	—
159	C₂²×C₁₃₇	—	4	4	no	—
160	C₂²×C₁₃₇	—	8	24	no	—
161	C₂²×C₁₃₇	#327	1	16	yes	direct product factor
162	C₂²×C₁₃₇	C₂×#99	1	6	yes	—
163	C₂²×C₁₃₇	C₂×#102	1	6	yes	—
164	C₂²×C₁₃₇	C₂×#102	1	6	yes	—
165	C₂²×C₁₃₇	C₂×#104	1	6	yes	—
166	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
168	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
169	C₄×C₁₃₇	—	2	1	no	—
170	C₄×C₁₃₇	—	2	3	no	—
171	C₄×C₁₃₇	—	2	3	no	—
172	C₄×C₁₃₇	—	2	1	no	—
173	C₄×C₁₃₇	—	4	8	no	—
174	C₄×C₁₃₇	—	4	4	no	—
175	C₂×C₁₃₇	—	2	1	no	—
176	C₂×C₁₃₇	—	2	1	no	—
177	C₂×C₁₃₇	—	2	6	no	—
178	C₂×C₁₃₇	—	8	4	no	—
179	C₂×C₁₃₇	C₂×#327	1	12	yes	direct product factor
180	C₂×C₁₃₇	C₂²×#99	1	1	yes	characteristic
181	C₂×C₁₃₇	C₂²×#102	1	1	yes	characteristic
182	C₂×C₁₃₇	C₂²×#104	1	1	yes	characteristic
183	C₂²×#327	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₇	C₂²×#327	1	1	yes	characteristic, direct product factor, Sylow
185	C₂²×#121	C₂×C₁₃₇	1	1	yes	characteristic
186	C₂²×C₂²⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	C₂²×#95	C₂×C₁₃₇	1	1	yes	characteristic, complemented
188	C₂×#327	C₂×C₁₃₇	1	12	yes	direct product factor
189	C₂³×D₄	—	2	1	no	—
190	C₂³×D₄	C₄×C₁₃₇	1	1	yes	characteristic, complemented
191	C₂⁴×C₄	—	2	1	no	—
192	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
193	C₂³×C₈	—	2	1	no	—
194	C₂×#121	—	2	3	no	—
195	C₂×#121	—	2	3	no	—
196	C₂×#121	C₄×C₁₃₇	1	6	yes	complemented
197	C₂×#121	C₂²×C₁₃₇	1	6	yes	—
198	C₂²×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic, complemented
199	C₂²×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₂²⋊C₈	—	2	3	no	—
201	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	6	yes	complemented
202	C₂×#95	—	2	3	no	—
203	C₂×#95	C₂²×C₁₃₇	1	6	yes	complemented
204	#327	C₂²×C₁₃₇	1	16	yes	direct product factor
205	C₂⁵	—	2	1	no	—
206	C₂⁵	D₄×C₁₃₇	1	1	yes	characteristic
207	C₂²×D₄	—	2	6	no	—
208	C₂²×D₄	—	2	6	no	—
209	C₂²×D₄	—	2	3	no	—
210	C₂²×D₄	—	4	4	no	—
211	C₂²×D₄	—	4	4	no	—
212	C₂²×D₄	—	4	4	no	—
213	C₂²×D₄	C₂×C₄×C₁₃₇	1	6	yes	complemented
214	C₂³×C₄	—	2	8	no	—
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	—	2	6	no	—
217	C₂³×C₄	—	4	4	no	—
218	C₂³×C₄	—	4	4	no	—
219	C₂³×C₄	—	4	4	no	—
220	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₁₃₇	1	3	yes	—
222	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₃₇	1	3	yes	—
224	C₂³×C₄	D₄×C₁₃₇	1	3	yes	—
225	C₂³×C₄	C₂³×C₁₃₇	1	3	yes	—
226	C₂²×C₈	—	2	6	no	—
227	C₂²×C₈	—	4	4	no	—
228	#121	—	2	12	no	—
229	#121	—	2	6	no	—
230	#121	—	2	6	no	—
231	#121	C₂×C₄×C₁₃₇	1	12	yes	complemented
232	#121	C₂³×C₁₃₇	1	4	yes	—
233	C₂×C₄⋊C₄	—	2	3	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	6	yes	complemented
235	C₂×C₂²⋊C₄	—	2	6	no	—
236	C₂×C₂²⋊C₄	—	2	6	no	—
237	C₂²⋊C₈	—	2	6	no	—
238	C₂²⋊C₈	C₂³×C₁₃₇	1	4	yes	complemented
239	#95	—	2	6	no	—
240	#95	C₂³×C₁₃₇	1	4	yes	complemented
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	—	2	6	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	C₂²⋊C₄×C₁₃₇	1	3	yes	—
248	C₂⁴	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
249	C₂⁴	D₈×C₁₃₇	1	4	yes	—
250	C₂⁴	SD₁₆×C₁₃₇	1	4	yes	—
251	C₂⁴	C₂×D₄×C₁₃₇	1	3	yes	—
252	C₂×D₄	—	2	12	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	6	no	—
255	C₂×D₄	—	4	12	no	—
256	C₂×D₄	—	4	12	no	—
257	C₂×D₄	—	4	24	no	—
258	C₂×D₄	—	4	12	no	—
259	C₂×D₄	—	4	12	no	—
260	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	complemented
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	24	no	—
264	C₂²×C₄	—	2	6	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	6	no	—
267	C₂²×C₄	—	4	6	no	—
268	C₂²×C₄	—	4	6	no	—
269	C₂²×C₄	—	4	6	no	—
270	C₂²×C₄	—	4	12	no	—
271	C₂²×C₄	—	4	32	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	4	12	no	—
274	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	3	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	3	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	6	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₃₇	1	3	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₃₇	1	3	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₇	1	3	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	3	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	3	yes	—
282	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	4	12	no	—
285	C₄⋊C₄	—	2	6	no	—
286	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	complemented
287	C₂²⋊C₄	—	2	12	no	—
288	C₂²⋊C₄	—	2	4	no	—
289	C₂³	—	2	6	no	—
290	C₂³	—	2	6	no	—
291	C₂³	—	2	6	no	—
292	C₂³	—	2	6	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	16	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	12	no	—
297	C₂³	—	4	12	no	—
298	C₂³	—	4	12	no	—
299	C₂³	—	8	16	no	—
300	C₂³	#99×C₁₃₇	1	4	yes	—
301	C₂³	#102×C₁₃₇	1	12	yes	—
302	C₂³	#102×C₁₃₇	1	4	yes	—
303	C₂³	#104×C₁₃₇	1	4	yes	—
304	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	3	yes	—
305	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	3	yes	—
306	C₂³	C₂×D₈×C₁₃₇	1	6	yes	—
307	C₂³	C₂×SD₁₆×C₁₃₇	1	6	yes	—
308	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
309	D₄	—	4	4	no	—
310	D₄	—	4	12	no	—
311	D₄	—	4	24	no	—
312	D₄	—	4	4	no	—
313	D₄	—	4	4	no	—
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	6	no	—
316	C₂×C₄	—	2	6	no	—
317	C₂×C₄	—	2	6	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	6	no	—
321	C₂×C₄	—	4	3	no	—
322	C₂×C₄	—	4	3	no	—
323	C₂×C₄	—	4	3	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	48	no	—
327	C₂×C₄	—	4	12	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	3	yes	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	3	yes	—
331	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
333	C₈	—	4	4	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	3	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	3	no	—
338	C₂²	—	2	12	no	—
339	C₂²	—	2	24	no	—
340	C₂²	—	2	12	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	8	24	no	—
345	C₂²	#327×C₁₃₇	1	16	yes	direct product factor
346	C₂²	C₂×#99×C₁₃₇	1	6	yes	—
347	C₂²	C₂×#102×C₁₃₇	1	6	yes	—
348	C₂²	C₂×#102×C₁₃₇	1	6	yes	—
349	C₂²	C₂×#104×C₁₃₇	1	6	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
351	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
352	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	3	no	—
355	C₄	—	2	3	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	8	no	—
358	C₄	—	4	4	no	—
359	C₂	—	2	1	no	—
360	C₂	—	2	6	no	—
361	C₂	—	2	1	no	—
362	C₂	—	8	4	no	—
363	C₂	C₂×#327×C₁₃₇	1	12	yes	direct product factor
364	C₂	C₂²×#99×C₁₃₇	1	1	yes	characteristic
365	C₂	C₂²×#102×C₁₃₇	1	1	yes	characteristic
366	C₂	C₂²×#104×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#121×C₁₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ C₂⁴×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊C₈×C₁₃₇	C₂	semidirect
3. C₂²×#95×C₁₃₇	C₂	semidirect
4. C₂×#327×C₁₃₇	C₂	direct (N × H)
6. C₂³×D₄×C₁₃₇	C₄	semidirect
12. C₂×#121×C₁₃₇	C₄	semidirect
14. C₂²×C₄⋊C₄×C₁₃₇	C₄	semidirect
17. C₂×C₂²⋊C₈×C₁₃₇	C₂²	semidirect
19. C₂×#95×C₁₃₇	C₂²	semidirect
20. #327×C₁₃₇	C₂²	direct (N × H)
29. C₂²×D₄×C₁₃₇	C₂×C₄	semidirect
47. #121×C₁₃₇	C₂×C₄	semidirect
50. C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	semidirect
54. C₂²⋊C₈×C₁₃₇	C₂³	semidirect
56. #95×C₁₃₇	C₂³	semidirect
76. C₂×D₄×C₁₃₇	C₂²×C₄	semidirect
102. C₄⋊C₄×C₁₃₇	C₂²×C₄	semidirect
161. C₂²×C₁₃₇	#327	direct (N × H)
179. C₂×C₁₃₇	C₂×#327	direct (N × H)
183. C₂²×#327	C₁₃₇	direct (N × H)
184. C₁₃₇	C₂²×#327	direct (N × H)
186. C₂²×C₂²⋊C₈	C₂×C₁₃₇	semidirect
187. C₂²×#95	C₂×C₁₃₇	semidirect
188. C₂×#327	C₂×C₁₃₇	direct (N × H)
190. C₂³×D₄	C₄×C₁₃₇	semidirect
196. C₂×#121	C₄×C₁₃₇	semidirect
198. C₂²×C₄⋊C₄	C₄×C₁₃₇	semidirect
201. C₂×C₂²⋊C₈	C₂²×C₁₃₇	semidirect
203. C₂×#95	C₂²×C₁₃₇	semidirect
204. #327	C₂²×C₁₃₇	direct (N × H)
213. C₂²×D₄	C₂×C₄×C₁₃₇	semidirect
231. #121	C₂×C₄×C₁₃₇	semidirect
234. C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	semidirect
238. C₂²⋊C₈	C₂³×C₁₃₇	semidirect
240. #95	C₂³×C₁₃₇	semidirect
260. C₂×D₄	C₂²×C₄×C₁₃₇	semidirect
286. C₄⋊C₄	C₂²×C₄×C₁₃₇	semidirect
345. C₂²	#327×C₁₃₇	direct (N × H)
363. C₂	C₂×#327×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×#121×C₁₃₇	2
C₂²×C₂²⋊C₈×C₁₃₇	2
C₂²×#95×C₁₃₇	2
C₂×#327×C₁₃₇	2
C₂²×#327	137

Subgroups — C22×#327×C137 #46866913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#327×C₁₃₇ #46866913