Subgroups — D₄×SD₃₂×C₁₃₇ #46883233

Order 35072.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SD₃₂×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	D₄×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2248×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2217×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2208×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#2207×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2187×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2185×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₇	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₁₃₇	C₂²	1	2	yes	—
14	D₄×Q₈×C₁₃₇	—	2	1	no	—
15	D₄²×C₁₃₇	—	2	1	no	—
16	C₂×SD₃₂×C₁₃₇	—	2	8	no	—
17	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	—
18	C₂×SD₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
20	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
21	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
22	C₂²×C₁₆×C₁₃₇	C₂²	1	2	yes	complemented
23	#494×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
24	#493×C₁₃₇	C₂²	1	1	yes	characteristic
25	#467×C₁₃₇	C₂²	1	2	yes	complemented
26	#466×C₁₃₇	C₂²	1	2	yes	—
27	#462×C₁₃₇	—	2	1	no	—
28	#459×C₁₃₇	—	2	1	no	—
29	#451×C₁₃₇	—	2	2	no	—
30	#447×C₁₃₇	—	2	2	no	—
31	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
35	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
36	#358×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
37	#358×C₁₃₇	C₂²	1	2	yes	complemented
38	#357×C₁₃₇	C₂²	1	1	yes	characteristic
39	#357×C₁₃₇	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₁₃₇	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×Q₈×C₁₃₇	—	2	2	no	—
43	C₂²×D₄×C₁₃₇	—	2	2	no	—
44	C₂²×D₄×C₁₃₇	—	4	1	no	—
45	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
46	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₇	—	4	2	no	—
49	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₁₃₇	—	2	4	no	—
52	C₂×D₈×C₁₃₇	—	2	2	no	—
53	C₂×D₈×C₁₃₇	—	2	1	no	—
54	C₂×D₈×C₁₃₇	—	4	2	no	—
55	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
56	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₁₃₇	—	4	1	no	—
60	#127×C₁₃₇	—	2	1	no	—
61	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
63	#121×C₁₃₇	—	2	2	no	—
64	#121×C₁₃₇	—	4	1	no	—
65	#120×C₁₃₇	—	4	2	no	—
66	C₄×Q₈×C₁₃₇	—	2	1	no	—
67	C₄×D₄×C₁₃₇	—	2	1	no	—
68	C₄×D₄×C₁₃₇	—	4	1	no	—
69	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
70	SD₃₂×C₁₃₇	—	2	4	no	—
71	SD₃₂×C₁₃₇	—	2	4	no	—
72	SD₃₂×C₁₃₇	—	2	4	no	—
73	SD₃₂×C₁₃₇	—	4	2	no	—
74	SD₃₂×C₁₃₇	D₄	1	4	yes	direct product factor
75	C₂×C₁₆×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	#102×C₁₃₇	—	2	1	no	—
85	#102×C₁₃₇	—	2	2	no	—
86	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
87	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
88	C₂⁴×C₁₃₇	—	4	2	no	—
89	C₂×Q₈×C₁₃₇	—	2	1	no	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	4	4	no	—
92	C₂×Q₈×C₁₃₇	—	4	2	no	—
93	C₂×Q₈×C₁₃₇	—	8	2	no	—
94	C₂×D₄×C₁₃₇	—	2	1	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	4	4	no	—
97	C₂×D₄×C₁₃₇	—	4	2	no	—
98	C₂×D₄×C₁₃₇	—	4	2	no	—
99	C₂×D₄×C₁₃₇	—	4	1	no	—
100	C₂×D₄×C₁₃₇	—	4	1	no	—
101	C₂×D₄×C₁₃₇	—	8	2	no	—
102	C₂×D₄×C₁₃₇	—	8	4	no	—
103	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	—	4	2	no	—
105	C₂²×C₄×C₁₃₇	—	4	1	no	—
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	Q₁₆×C₁₃₇	—	2	2	no	—
108	Q₁₆×C₁₃₇	—	2	1	no	—
109	Q₁₆×C₁₃₇	—	2	2	no	—
110	Q₁₆×C₁₃₇	—	4	4	no	—
111	Q₁₆×C₁₃₇	—	8	1	no	—
112	Q₁₆×C₁₃₇	C₂×D₄	1	2	yes	complemented
113	D₈×C₁₃₇	—	2	2	no	—
114	D₈×C₁₃₇	—	2	1	no	—
115	D₈×C₁₃₇	—	2	2	no	—
116	D₈×C₁₃₇	—	4	4	no	—
117	D₈×C₁₃₇	—	8	1	no	—
118	D₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₁₃₇	—	2	1	no	—
125	C₄⋊C₄×C₁₃₇	—	2	1	no	—
126	C₄⋊C₄×C₁₃₇	—	4	1	no	—
127	C₄⋊C₄×C₁₃₇	—	4	1	no	—
128	C₄⋊C₄×C₁₃₇	—	4	2	no	—
129	C₄⋊C₄×C₁₃₇	—	4	1	no	—
130	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
133	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
135	C₄²×C₁₃₇	—	4	1	no	—
136	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₁₃₇	—	2	2	no	—
138	C₁₆×C₁₃₇	—	2	1	no	—
139	C₁₆×C₁₃₇	C₂×D₄	1	2	yes	complemented
140	C₂³×C₁₃₇	—	4	1	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	—	8	4	no	—
143	C₂³×C₁₃₇	—	8	4	no	—
144	C₂³×C₁₃₇	—	16	2	no	—
145	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
146	Q₈×C₁₃₇	—	2	2	no	—
147	Q₈×C₁₃₇	—	4	1	no	—
148	Q₈×C₁₃₇	—	4	2	no	—
149	Q₈×C₁₃₇	—	4	2	no	—
150	Q₈×C₁₃₇	—	8	4	no	—
151	D₄×C₁₃₇	—	2	2	no	—
152	D₄×C₁₃₇	—	4	2	no	—
153	D₄×C₁₃₇	—	4	1	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	D₄×C₁₃₇	—	8	4	no	—
156	D₄×C₁₃₇	—	8	4	no	—
157	D₄×C₁₃₇	—	8	2	no	—
158	D₄×C₁₃₇	—	16	1	no	—
159	D₄×C₁₃₇	SD₃₂	1	4	yes	direct product factor
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	4	1	no	—
163	C₂×C₄×C₁₃₇	—	4	1	no	—
164	C₂×C₄×C₁₃₇	—	4	1	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	8	4	no	—
167	C₂×C₄×C₁₃₇	—	8	2	no	—
168	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₁₃₇	—	2	2	no	—
173	C₈×C₁₃₇	—	2	1	no	—
174	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²×C₁₃₇	—	2	2	no	—
177	C₂²×C₁₃₇	—	2	2	no	—
178	C₂²×C₁₃₇	—	4	2	no	—
179	C₂²×C₁₃₇	—	8	1	no	—
180	C₂²×C₁₃₇	—	8	1	no	—
181	C₂²×C₁₃₇	—	8	2	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	—	8	2	no	—
184	C₂²×C₁₃₇	—	16	8	no	—
185	C₂²×C₁₃₇	C₂×SD₃₂	1	4	yes	complemented
186	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₁₃₇	—	2	1	no	—
188	C₄×C₁₃₇	—	2	2	no	—
189	C₄×C₁₃₇	—	4	2	no	—
190	C₄×C₁₃₇	—	8	1	no	—
191	C₄×C₁₃₇	—	8	1	no	—
192	C₄×C₁₃₇	—	8	2	no	—
193	C₄×C₁₃₇	C₂×SD₃₂	1	2	yes	complemented
194	C₄×C₁₃₇	D₄²	1	1	yes	characteristic
195	C₄×C₁₃₇	#576	1	1	yes	characteristic
196	C₂×C₁₃₇	—	2	4	no	—
197	C₂×C₁₃₇	—	8	2	no	—
198	C₂×C₁₃₇	—	16	2	no	—
199	C₂×C₁₃₇	D₄×D₈	1	1	yes	characteristic
200	C₂×C₁₃₇	C₂²×SD₃₂	1	1	yes	characteristic
201	C₂×C₁₃₇	#3416	1	1	yes	characteristic
202	D₄×SD₃₂	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₇	D₄×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×SD₃₂	C₂×C₁₃₇	1	2	yes	complemented
205	D₄×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	D₄×D₈	C₂×C₁₃₇	1	1	yes	characteristic
207	#2248	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	#2217	C₂×C₁₃₇	1	2	yes	complemented
209	#2208	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#2207	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	#2187	C₂×C₁₃₇	1	2	yes	complemented
212	#2185	C₂×C₁₃₇	1	2	yes	complemented
213	C₄×SD₃₂	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	D₄×C₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	C₂²×Q₁₆	C₂²×C₁₃₇	1	2	yes	complemented
216	C₂²×D₈	C₂²×C₁₃₇	1	2	yes	—
217	D₄×Q₈	—	2	1	no	—
218	D₄²	—	2	1	no	—
219	C₂×SD₃₂	—	2	8	no	—
220	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	—
221	C₂×SD₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
223	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
224	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
225	C₂²×C₁₆	C₂²×C₁₃₇	1	2	yes	complemented
226	#494	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
227	#493	C₂²×C₁₃₇	1	1	yes	characteristic
228	#467	C₂²×C₁₃₇	1	2	yes	complemented
229	#466	C₂²×C₁₃₇	1	2	yes	—
230	#462	—	2	1	no	—
231	#459	—	2	1	no	—
232	#451	—	2	2	no	—
233	#447	—	2	2	no	—
234	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
235	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
237	#367	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
238	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
239	#358	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
240	#358	C₂²×C₁₃₇	1	2	yes	complemented
241	#357	C₂²×C₁₃₇	1	1	yes	characteristic
242	#357	C₂²×C₁₃₇	1	2	yes	complemented
243	C₂²⋊C₁₆	C₂²×C₁₃₇	1	2	yes	complemented
244	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	4	1	no	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	4	2	no	—
252	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
253	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	4	2	no	—
258	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
259	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	4	1	no	—
263	#127	—	2	1	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	C₂²⋊Q₈	—	4	2	no	—
266	#121	—	2	2	no	—
267	#121	—	4	1	no	—
268	#120	—	4	2	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	4	1	no	—
272	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
273	SD₃₂	—	2	4	no	—
274	SD₃₂	—	2	4	no	—
275	SD₃₂	—	2	4	no	—
276	SD₃₂	—	4	2	no	—
277	SD₃₂	D₄×C₁₃₇	1	4	yes	direct product factor
278	C₂×C₁₆	—	2	4	no	—
279	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
280	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
281	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
282	#107	C₂³×C₁₃₇	1	1	yes	characteristic
283	#107	C₂³×C₁₃₇	1	1	yes	characteristic
284	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
285	#103	—	2	1	no	—
286	#103	—	2	2	no	—
287	#102	—	2	1	no	—
288	#102	—	2	2	no	—
289	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
290	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂⁴	—	4	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	4	no	—
306	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	4	4	no	—
314	Q₁₆	—	8	1	no	—
315	Q₁₆	C₂×D₄×C₁₃₇	1	2	yes	complemented
316	D₈	—	2	2	no	—
317	D₈	—	2	1	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	4	no	—
320	D₈	—	8	1	no	—
321	D₈	C₂×D₄×C₁₃₇	1	2	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
326	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
338	C₄²	—	4	1	no	—
339	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	1	no	—
342	C₁₆	C₂×D₄×C₁₃₇	1	2	yes	complemented
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	16	2	no	—
348	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	1	no	—
362	D₄	SD₃₂×C₁₃₇	1	4	yes	direct product factor
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
378	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×SD₃₂×C₁₃₇	1	4	yes	complemented
389	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂×SD₃₂×C₁₃₇	1	2	yes	complemented
397	C₄	D₄²×C₁₃₇	1	1	yes	characteristic
398	C₄	#576×C₁₃₇	1	1	yes	characteristic
399	C₂	—	2	4	no	—
400	C₂	—	8	2	no	—
401	C₂	—	16	2	no	—
402	C₂	D₄×D₈×C₁₃₇	1	1	yes	characteristic
403	C₂	C₂²×SD₃₂×C₁₃₇	1	1	yes	characteristic
404	C₂	#3416×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
prime radical	D₄×D₈×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. C₂²×SD₃₂×C₁₃₇	C₂	semidirect
2. D₄×Q₁₆×C₁₃₇	C₂	semidirect
4. #2248×C₁₃₇	C₂	semidirect
5. #2217×C₁₃₇	C₂	semidirect
6. #2208×C₁₃₇	C₂	semidirect
7. #2207×C₁₃₇	C₂	semidirect
8. #2187×C₁₃₇	C₂	semidirect
9. #2185×C₁₃₇	C₂	semidirect
10. C₄×SD₃₂×C₁₃₇	C₂	semidirect
11. D₄×C₁₆×C₁₃₇	C₂	semidirect
12. C₂²×Q₁₆×C₁₃₇	C₂²	semidirect
19. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
20. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
21. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
22. C₂²×C₁₆×C₁₃₇	C₂²	semidirect
23. #494×C₁₃₇	C₂²	semidirect
25. #467×C₁₃₇	C₂²	semidirect
31. C₄×Q₁₆×C₁₃₇	C₂²	semidirect
34. #367×C₁₃₇	C₂²	semidirect
35. C₄⋊C₁₆×C₁₃₇	C₂²	semidirect
36. #358×C₁₃₇	C₂²	semidirect
37. #358×C₁₃₇	C₂²	semidirect
39. #357×C₁₃₇	C₂²	semidirect
40. C₂²⋊C₁₆×C₁₃₇	C₂²	semidirect
41. C₄×C₁₆×C₁₃₇	C₂²	semidirect
74. SD₃₂×C₁₃₇	D₄	direct (N × H)
112. Q₁₆×C₁₃₇	C₂×D₄	semidirect
139. C₁₆×C₁₃₇	C₂×D₄	semidirect
159. D₄×C₁₃₇	SD₃₂	direct (N × H)
185. C₂²×C₁₃₇	C₂×SD₃₂	semidirect
193. C₄×C₁₃₇	C₂×SD₃₂	semidirect
202. D₄×SD₃₂	C₁₃₇	direct (N × H)
203. C₁₃₇	D₄×SD₃₂	direct (N × H)
204. C₂²×SD₃₂	C₂×C₁₃₇	semidirect
205. D₄×Q₁₆	C₂×C₁₃₇	semidirect
207. #2248	C₂×C₁₃₇	semidirect
208. #2217	C₂×C₁₃₇	semidirect
209. #2208	C₂×C₁₃₇	semidirect
210. #2207	C₂×C₁₃₇	semidirect
211. #2187	C₂×C₁₃₇	semidirect
212. #2185	C₂×C₁₃₇	semidirect
213. C₄×SD₃₂	C₂×C₁₃₇	semidirect
214. D₄×C₁₆	C₂×C₁₃₇	semidirect
215. C₂²×Q₁₆	C₂²×C₁₃₇	semidirect
222. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
223. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
224. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
225. C₂²×C₁₆	C₂²×C₁₃₇	semidirect
226. #494	C₂²×C₁₃₇	semidirect
228. #467	C₂²×C₁₃₇	semidirect
234. C₄×Q₁₆	C₂²×C₁₃₇	semidirect
237. #367	C₂²×C₁₃₇	semidirect
238. C₄⋊C₁₆	C₂²×C₁₃₇	semidirect
239. #358	C₂²×C₁₃₇	semidirect
240. #358	C₂²×C₁₃₇	semidirect
242. #357	C₂²×C₁₃₇	semidirect
243. C₂²⋊C₁₆	C₂²×C₁₃₇	semidirect
244. C₄×C₁₆	C₂²×C₁₃₇	semidirect
277. SD₃₂	D₄×C₁₃₇	direct (N × H)
315. Q₁₆	C₂×D₄×C₁₃₇	semidirect
342. C₁₆	C₂×D₄×C₁₃₇	semidirect
362. D₄	SD₃₂×C₁₃₇	direct (N × H)
388. C₂²	C₂×SD₃₂×C₁₃₇	semidirect
396. C₄	C₂×SD₃₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×SD₃₂×C₁₃₇	2
D₄×Q₁₆×C₁₃₇	2
D₄×D₈×C₁₃₇	2
#2248×C₁₃₇	2
#2217×C₁₃₇	2
#2208×C₁₃₇	2
#2207×C₁₃₇	2
#2187×C₁₃₇	2
#2185×C₁₃₇	2
C₄×SD₃₂×C₁₃₇	2
D₄×C₁₆×C₁₃₇	2
D₄×SD₃₂	137

Subgroups — D4×SD32×C137 #46883233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×SD₃₂×C₁₃₇ #46883233