Subgroups — C₁₃₇×#33842 #46883228

Order 35072.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	D₄×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3283×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2247×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2219×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2209×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#2208×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2189×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2188×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#2169×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₇	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₁₃₇	C₂²	1	2	yes	—
14	D₄×Q₈×C₁₃₇	—	2	1	no	—
15	#547×C₁₃₇	—	2	1	no	—
16	#510×C₁₃₇	—	2	8	no	—
17	C₂×Q₃₂×C₁₃₇	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₁₃₇	C₂²	1	2	yes	—
19	C₂×Q₃₂×C₁₃₇	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	—
21	C₂×SD₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×M₃₂×C₁₃₇	C₂²	1	2	yes	—
23	#494×C₁₃₇	C₂²	1	1	yes	characteristic
24	#494×C₁₃₇	C₂²	1	1	yes	characteristic
25	#467×C₁₃₇	C₂²	1	2	yes	—
26	#467×C₁₃₇	C₂²	1	2	yes	—
27	#462×C₁₃₇	—	2	1	no	—
28	#461×C₁₃₇	—	2	1	no	—
29	#452×C₁₃₇	—	2	2	no	—
30	#451×C₁₃₇	—	2	2	no	—
31	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	#367×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
36	#358×C₁₃₇	C₂²	1	1	yes	characteristic
37	#358×C₁₃₇	C₂²	1	2	yes	—
38	#358×C₁₃₇	C₂²	1	2	yes	—
39	#357×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂²⋊C₁₆×C₁₃₇	C₂²	1	2	yes	—
41	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₂×#41×C₁₃₇	—	2	2	no	—
43	C₂²×Q₈×C₁₃₇	—	2	2	no	—
44	#135×C₁₃₇	—	2	4	no	—
45	#135×C₁₃₇	—	4	2	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
48	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
49	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
50	C₂×Q₁₆×C₁₃₇	—	4	2	no	—
51	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
55	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₁₃₇	—	4	1	no	—
60	#123×C₁₃₇	—	4	2	no	—
61	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
63	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
64	#121×C₁₃₇	—	4	1	no	—
65	C₄×Q₈×C₁₃₇	—	2	1	no	—
66	C₄×D₄×C₁₃₇	—	2	1	no	—
67	C₄×D₄×C₁₃₇	—	4	1	no	—
68	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₃₇	—	4	1	no	—
70	Q₃₂×C₁₃₇	—	2	4	no	—
71	Q₃₂×C₁₃₇	—	2	4	no	—
72	Q₃₂×C₁₃₇	—	4	2	no	—
73	SD₃₂×C₁₃₇	—	2	4	no	—
74	SD₃₂×C₁₃₇	D₄	1	4	yes	complemented
75	M₃₂×C₁₃₇	—	2	4	no	—
76	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
77	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
79	#107×C₁₃₇	C₂³	1	1	yes	characteristic
80	#107×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
82	#103×C₁₃₇	—	2	1	no	—
83	#103×C₁₃₇	—	2	2	no	—
84	#103×C₁₃₇	—	2	2	no	—
85	#102×C₁₃₇	—	2	1	no	—
86	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
87	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
88	#41×C₁₃₇	—	4	4	no	—
89	#41×C₁₃₇	—	8	2	no	—
90	C₂×Q₈×C₁₃₇	—	2	1	no	—
91	C₂×Q₈×C₁₃₇	—	2	2	no	—
92	C₂×Q₈×C₁₃₇	—	2	2	no	—
93	C₂×Q₈×C₁₃₇	—	4	4	no	—
94	C₂×Q₈×C₁₃₇	—	4	2	no	—
95	C₂×Q₈×C₁₃₇	—	8	2	no	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	—	4	2	no	—
98	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	—	4	2	no	—
100	C₂²×C₄×C₁₃₇	—	4	1	no	—
101	C₂²×C₄×C₁₃₇	—	4	2	no	—
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	Q₁₆×C₁₃₇	—	2	2	no	—
104	Q₁₆×C₁₃₇	—	2	2	no	—
105	Q₁₆×C₁₃₇	—	2	1	no	—
106	Q₁₆×C₁₃₇	—	2	2	no	—
107	Q₁₆×C₁₃₇	—	2	2	no	—
108	Q₁₆×C₁₃₇	—	4	4	no	—
109	Q₁₆×C₁₃₇	—	8	1	no	—
110	Q₁₆×C₁₃₇	—	8	1	no	—
111	Q₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
112	SD₁₆×C₁₃₇	—	4	4	no	—
113	D₈×C₁₃₇	—	2	1	no	—
114	D₈×C₁₃₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	4	1	no	—
123	C₄⋊C₄×C₁₃₇	—	4	2	no	—
124	C₄⋊C₄×C₁₃₇	—	4	1	no	—
125	C₄⋊C₄×C₁₃₇	—	4	1	no	—
126	C₄⋊C₄×C₁₃₇	—	4	2	no	—
127	C₄⋊C₄×C₁₃₇	—	4	1	no	—
128	C₄⋊C₄×C₁₃₇	—	4	1	no	—
129	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
133	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
134	C₄²×C₁₃₇	—	4	1	no	—
135	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₁₃₇	—	2	2	no	—
137	C₁₆×C₁₃₇	—	2	1	no	—
138	C₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
139	C₂³×C₁₃₇	—	4	1	no	—
140	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
141	Q₈×C₁₃₇	—	2	2	no	—
142	Q₈×C₁₃₇	—	4	1	no	—
143	Q₈×C₁₃₇	—	4	2	no	—
144	Q₈×C₁₃₇	—	4	2	no	—
145	Q₈×C₁₃₇	—	4	2	no	—
146	Q₈×C₁₃₇	—	4	2	no	—
147	Q₈×C₁₃₇	—	8	4	no	—
148	D₄×C₁₃₇	—	2	2	no	—
149	D₄×C₁₃₇	—	2	2	no	—
150	D₄×C₁₃₇	—	4	1	no	—
151	D₄×C₁₃₇	—	8	4	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	4	1	no	—
155	C₂×C₄×C₁₃₇	—	4	1	no	—
156	C₂×C₄×C₁₃₇	—	4	1	no	—
157	C₂×C₄×C₁₃₇	—	4	2	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	8	4	no	—
160	C₂×C₄×C₁₃₇	—	8	4	no	—
161	C₂×C₄×C₁₃₇	—	8	2	no	—
162	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₁₃₇	—	2	2	no	—
167	C₈×C₁₃₇	—	2	1	no	—
168	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×C₁₃₇	—	2	2	no	—
171	C₂²×C₁₃₇	—	2	2	no	—
172	C₂²×C₁₃₇	—	2	2	no	—
173	C₂²×C₁₃₇	—	4	2	no	—
174	C₂²×C₁₃₇	—	8	1	no	—
175	C₂²×C₁₃₇	—	8	1	no	—
176	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
177	C₄×C₁₃₇	—	2	1	no	—
178	C₄×C₁₃₇	—	2	2	no	—
179	C₄×C₁₃₇	—	4	2	no	—
180	C₄×C₁₃₇	—	8	1	no	—
181	C₄×C₁₃₇	—	8	1	no	—
182	C₄×C₁₃₇	—	8	2	no	—
183	C₄×C₁₃₇	—	8	2	no	—
184	C₄×C₁₃₇	#510	1	2	yes	complemented
185	C₄×C₁₃₇	D₄²	1	1	yes	characteristic
186	C₄×C₁₃₇	#576	1	1	yes	characteristic
187	C₂×C₁₃₇	—	4	2	no	—
188	C₂×C₁₃₇	—	8	2	no	—
189	C₂×C₁₃₇	D₄×D₈	1	1	yes	characteristic
190	C₂×C₁₃₇	C₂×#510	1	1	yes	characteristic
191	C₂×C₁₃₇	#3417	1	1	yes	characteristic
192	#33842	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₇	#33842	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#510	C₂×C₁₃₇	1	2	yes	complemented
195	D₄×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#3283	C₂×C₁₃₇	1	1	yes	characteristic
197	#2247	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#2219	C₂×C₁₃₇	1	2	yes	complemented
199	#2209	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#2208	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	#2189	C₂×C₁₃₇	1	2	yes	complemented
202	#2188	C₂×C₁₃₇	1	2	yes	complemented
203	C₄×SD₃₂	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#2169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
205	C₂×#135	C₂²×C₁₃₇	1	2	yes	—
206	C₂²×Q₁₆	C₂²×C₁₃₇	1	2	yes	—
207	D₄×Q₈	—	2	1	no	—
208	#547	—	2	1	no	—
209	#510	—	2	8	no	—
210	C₂×Q₃₂	C₂²×C₁₃₇	1	2	yes	—
211	C₂×Q₃₂	C₂²×C₁₃₇	1	2	yes	—
212	C₂×Q₃₂	C₂²×C₁₃₇	1	2	yes	—
213	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	—
214	C₂×SD₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×M₃₂	C₂²×C₁₃₇	1	2	yes	—
216	#494	C₂²×C₁₃₇	1	1	yes	characteristic
217	#494	C₂²×C₁₃₇	1	1	yes	characteristic
218	#467	C₂²×C₁₃₇	1	2	yes	—
219	#467	C₂²×C₁₃₇	1	2	yes	—
220	#462	—	2	1	no	—
221	#461	—	2	1	no	—
222	#452	—	2	2	no	—
223	#451	—	2	2	no	—
224	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
227	#367	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
229	#358	C₂²×C₁₃₇	1	1	yes	characteristic
230	#358	C₂²×C₁₃₇	1	2	yes	—
231	#358	C₂²×C₁₃₇	1	2	yes	—
232	#357	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂²⋊C₁₆	C₂²×C₁₃₇	1	2	yes	—
234	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×#41	—	2	2	no	—
236	C₂²×Q₈	—	2	2	no	—
237	#135	—	2	4	no	—
238	#135	—	4	2	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	4	2	no	—
244	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
245	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
246	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	4	1	no	—
253	#123	—	4	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	#121	—	4	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	4	1	no	—
261	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	4	1	no	—
263	Q₃₂	—	2	4	no	—
264	Q₃₂	—	2	4	no	—
265	Q₃₂	—	4	2	no	—
266	SD₃₂	—	2	4	no	—
267	SD₃₂	D₄×C₁₃₇	1	4	yes	complemented
268	M₃₂	—	2	4	no	—
269	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
271	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
272	#107	C₂³×C₁₃₇	1	1	yes	characteristic
273	#107	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
275	#103	—	2	1	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#102	—	2	1	no	—
279	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
280	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
281	#41	—	4	4	no	—
282	#41	—	8	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	8	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	1	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	4	4	no	—
302	Q₁₆	—	8	1	no	—
303	Q₁₆	—	8	1	no	—
304	Q₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
305	SD₁₆	—	4	4	no	—
306	D₈	—	2	1	no	—
307	D₈	C₂×D₄×C₁₃₇	1	2	yes	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
312	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
327	C₄²	—	4	1	no	—
328	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₁₆	—	2	2	no	—
330	C₁₆	—	2	1	no	—
331	C₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
332	C₂³	—	4	1	no	—
333	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	8	4	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	8	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
357	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	1	no	—
361	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
362	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	#510×C₁₃₇	1	2	yes	complemented
378	C₄	D₄²×C₁₃₇	1	1	yes	characteristic
379	C₄	#576×C₁₃₇	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	D₄×D₈×C₁₃₇	1	1	yes	characteristic
383	C₂	C₂×#510×C₁₃₇	1	1	yes	characteristic
384	C₂	#3417×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
prime radical	#3283×C₁₃₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄×D₄×C₁₃₇ ◁ C₈×D₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#510×C₁₃₇	C₂	semidirect
2. D₄×Q₁₆×C₁₃₇	C₂	semidirect
4. #2247×C₁₃₇	C₂	semidirect
5. #2219×C₁₃₇	C₂	semidirect
6. #2209×C₁₃₇	C₂	semidirect
7. #2208×C₁₃₇	C₂	semidirect
8. #2189×C₁₃₇	C₂	semidirect
9. #2188×C₁₃₇	C₂	semidirect
10. C₄×SD₃₂×C₁₃₇	C₂	semidirect
11. #2169×C₁₃₇	C₂	semidirect
74. SD₃₂×C₁₃₇	D₄	semidirect
184. C₄×C₁₃₇	#510	semidirect
192. #33842	C₁₃₇	direct (N × H)
193. C₁₃₇	#33842	direct (N × H)
194. C₂×#510	C₂×C₁₃₇	semidirect
195. D₄×Q₁₆	C₂×C₁₃₇	semidirect
197. #2247	C₂×C₁₃₇	semidirect
198. #2219	C₂×C₁₃₇	semidirect
199. #2209	C₂×C₁₃₇	semidirect
200. #2208	C₂×C₁₃₇	semidirect
201. #2189	C₂×C₁₃₇	semidirect
202. #2188	C₂×C₁₃₇	semidirect
203. C₄×SD₃₂	C₂×C₁₃₇	semidirect
204. #2169	C₂×C₁₃₇	semidirect
267. SD₃₂	D₄×C₁₃₇	semidirect
377. C₄	#510×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#510×C₁₃₇	2
D₄×Q₁₆×C₁₃₇	2
#3283×C₁₃₇	2
#2247×C₁₃₇	2
#2219×C₁₃₇	2
#2209×C₁₃₇	2
#2208×C₁₃₇	2
#2189×C₁₃₇	2
#2188×C₁₃₇	2
C₄×SD₃₂×C₁₃₇	2
#2169×C₁₃₇	2
#33842	137

Subgroups — C137×#33842 #46883228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33842 #46883228