Subgroups — D₄×#117×C₁₃₇ #46883508

Order 35072.

3562 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2354×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2352×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	D₄×C₄⋊C₄×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2344×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2342×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	D₄×C₂²⋊C₄×C₁₃₇	C₂	1	2	yes	maximal
9	#2293×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2290×C₁₃₇	C₂	1	4	yes	maximal, complemented
11	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#2280×C₁₃₇	C₂	1	2	yes	maximal, complemented
13	C₄²×D₄×C₁₃₇	C₂	1	2	yes	maximal, complemented
14	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃₇	C₄	1	16	yes	complemented
18	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₇	—	2	16	no	—
26	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₇	C₂²	1	4	yes	—
29	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₇	C₂²	1	4	yes	complemented
31	C₂×#117×C₁₃₇	C₂²	1	4	yes	complemented
32	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
34	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
35	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃₇	C₂²	1	4	yes	complemented
38	#390×C₁₃₇	C₂²	1	4	yes	—
39	#389×C₁₃₇	C₂²	1	4	yes	complemented
40	#388×C₁₃₇	C₂²	1	8	yes	complemented
41	#388×C₁₃₇	C₂²	1	8	yes	complemented
42	#387×C₁₃₇	C₂²	1	8	yes	complemented
43	#386×C₁₃₇	C₂²	1	8	yes	—
44	#385×C₁₃₇	C₂²	1	8	yes	complemented
45	#384×C₁₃₇	C₂²	1	2	yes	complemented
46	#382×C₁₃₇	C₂²	1	2	yes	complemented
47	#381×C₁₃₇	C₂²	1	4	yes	—
48	#380×C₁₃₇	C₂²	1	2	yes	—
49	#380×C₁₃₇	C₂²	1	2	yes	—
50	#380×C₁₃₇	C₂²	1	4	yes	complemented
51	#380×C₁₃₇	C₂²	1	4	yes	complemented
52	#379×C₁₃₇	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
54	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
55	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
56	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
57	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
59	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	8	yes	complemented
62	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
63	#376×C₁₃₇	C₂²	1	2	yes	complemented
64	C₄³×C₁₃₇	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₃₇	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₇	—	2	8	no	—
67	C₂²×D₄×C₁₃₇	C₂×C₄	1	8	yes	—
68	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₇	—	2	8	no	—
72	C₂³×C₄×C₁₃₇	—	2	8	no	—
73	C₂³×C₄×C₁₃₇	C₂×C₄	1	16	yes	complemented
74	C₂³×C₄×C₁₃₇	C₂³	1	8	yes	—
75	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₁₃₇	—	2	16	no	—
84	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	—
85	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	—
86	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
87	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
88	C₄×D₄×C₁₃₇	C₂×C₄	1	16	yes	complemented
89	C₄×D₄×C₁₃₇	C₂×C₄	1	16	yes	complemented
90	#117×C₁₃₇	—	2	8	no	—
91	#117×C₁₃₇	—	2	4	no	—
92	#117×C₁₃₇	—	2	16	no	—
93	#117×C₁₃₇	—	2	16	no	—
94	#117×C₁₃₇	—	2	16	no	—
95	#117×C₁₃₇	D₄	1	8	yes	direct product factor
96	C₂×C₄⋊C₄×C₁₃₇	—	2	16	no	—
97	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₃₇	—	2	16	no	—
108	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	16	yes	complemented
109	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₇	—	2	16	no	—
120	C₂×C₄²×C₁₃₇	C₂×C₄	1	8	yes	complemented
121	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₇	C₂³	1	8	yes	—
123	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
131	#95×C₁₃₇	C₂³	1	4	yes	—
132	#95×C₁₃₇	C₂³	1	4	yes	—
133	#95×C₁₃₇	C₂³	1	4	yes	—
134	#95×C₁₃₇	C₂³	1	8	yes	—
135	#95×C₁₃₇	C₂³	1	8	yes	—
136	#95×C₁₃₇	C₂³	1	4	yes	—
137	C₂⁴×C₁₃₇	—	2	4	no	—
138	C₂⁴×C₁₃₇	—	2	4	no	—
139	C₂⁴×C₁₃₇	—	2	8	no	—
140	C₂⁴×C₁₃₇	—	4	4	no	—
141	C₂⁴×C₁₃₇	C₂²×C₄	1	8	yes	—
142	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
143	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
144	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
145	C₂×D₄×C₁₃₇	—	2	8	no	—
146	C₂×D₄×C₁₃₇	—	2	32	no	—
147	C₂×D₄×C₁₃₇	—	2	4	no	—
148	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
149	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
150	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
151	C₂×D₄×C₁₃₇	#41	1	8	yes	—
152	C₂²×C₄×C₁₃₇	—	2	4	no	—
153	C₂²×C₄×C₁₃₇	—	2	4	no	—
154	C₂²×C₄×C₁₃₇	—	2	64	no	—
155	C₂²×C₄×C₁₃₇	—	2	4	no	—
156	C₂²×C₄×C₁₃₇	—	2	4	no	—
157	C₂²×C₄×C₁₃₇	—	2	4	no	—
158	C₂²×C₄×C₁₃₇	—	2	4	no	—
159	C₂²×C₄×C₁₃₇	—	2	4	no	—
160	C₂²×C₄×C₁₃₇	—	2	4	no	—
161	C₂²×C₄×C₁₃₇	—	2	4	no	—
162	C₂²×C₄×C₁₃₇	—	2	4	no	—
163	C₂²×C₄×C₁₃₇	—	2	4	no	—
164	C₂²×C₄×C₁₃₇	—	2	16	no	—
165	C₂²×C₄×C₁₃₇	—	2	16	no	—
166	C₂²×C₄×C₁₃₇	—	4	2	no	—
167	C₂²×C₄×C₁₃₇	—	4	8	no	—
168	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
170	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
171	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
174	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
178	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃₇	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₁₃₇	—	2	16	no	—
190	C₄⋊C₄×C₁₃₇	—	2	8	no	—
191	C₄⋊C₄×C₁₃₇	—	2	4	no	—
192	C₄⋊C₄×C₁₃₇	—	2	8	no	—
193	C₄⋊C₄×C₁₃₇	—	4	4	no	—
194	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
195	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
196	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
197	C₄⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	complemented
198	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
199	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
200	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
201	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
202	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
203	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
204	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
205	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
206	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
207	C₂²⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
208	C₄²×C₁₃₇	—	2	16	no	—
209	C₄²×C₁₃₇	—	2	8	no	—
210	C₄²×C₁₃₇	—	2	4	no	—
211	C₄²×C₁₃₇	—	2	8	no	—
212	C₄²×C₁₃₇	—	4	4	no	—
213	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
214	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
215	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
216	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
217	C₄²×C₁₃₇	C₂×D₄	1	8	yes	complemented
218	C₂³×C₁₃₇	—	2	2	no	—
219	C₂³×C₁₃₇	—	2	2	no	—
220	C₂³×C₁₃₇	—	2	2	no	—
221	C₂³×C₁₃₇	—	2	4	no	—
222	C₂³×C₁₃₇	—	2	2	no	—
223	C₂³×C₁₃₇	—	2	16	no	—
224	C₂³×C₁₃₇	—	2	16	no	—
225	C₂³×C₁₃₇	—	2	2	no	—
226	C₂³×C₁₃₇	—	2	2	no	—
227	C₂³×C₁₃₇	—	2	4	no	—
228	C₂³×C₁₃₇	—	2	4	no	—
229	C₂³×C₁₃₇	—	4	8	no	—
230	C₂³×C₁₃₇	—	4	16	no	—
231	C₂³×C₁₃₇	—	4	16	no	—
232	C₂³×C₁₃₇	C₂³×C₄	1	4	yes	—
233	C₂³×C₁₃₇	C₂³×C₄	1	4	yes	—
234	C₂³×C₁₃₇	C₂³×C₄	1	2	yes	—
235	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
236	C₂³×C₁₃₇	C₂×#41	1	8	yes	—
237	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
238	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
239	D₄×C₁₃₇	—	2	16	no	—
240	D₄×C₁₃₇	—	2	8	no	—
241	D₄×C₁₃₇	#117	1	16	yes	direct product factor
242	C₂×C₄×C₁₃₇	—	2	16	no	—
243	C₂×C₄×C₁₃₇	—	2	2	no	—
244	C₂×C₄×C₁₃₇	—	2	2	no	—
245	C₂×C₄×C₁₃₇	—	2	4	no	—
246	C₂×C₄×C₁₃₇	—	2	2	no	—
247	C₂×C₄×C₁₃₇	—	2	2	no	—
248	C₂×C₄×C₁₃₇	—	2	2	no	—
249	C₂×C₄×C₁₃₇	—	2	2	no	—
250	C₂×C₄×C₁₃₇	—	2	4	no	—
251	C₂×C₄×C₁₃₇	—	2	2	no	—
252	C₂×C₄×C₁₃₇	—	2	8	no	—
253	C₂×C₄×C₁₃₇	—	2	16	no	—
254	C₂×C₄×C₁₃₇	—	2	16	no	—
255	C₂×C₄×C₁₃₇	—	2	16	no	—
256	C₂×C₄×C₁₃₇	—	2	16	no	—
257	C₂×C₄×C₁₃₇	—	2	8	no	—
258	C₂×C₄×C₁₃₇	—	2	4	no	—
259	C₂×C₄×C₁₃₇	—	2	4	no	—
260	C₂×C₄×C₁₃₇	—	2	8	no	—
261	C₂×C₄×C₁₃₇	—	2	4	no	—
262	C₂×C₄×C₁₃₇	—	2	8	no	—
263	C₂×C₄×C₁₃₇	—	4	4	no	—
264	C₂×C₄×C₁₃₇	—	4	32	no	—
265	C₂×C₄×C₁₃₇	C₄×D₄	1	16	yes	complemented
266	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
270	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₁₃₇	C₂²×D₄	1	8	yes	—
275	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
278	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
279	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
280	C₂²×C₁₃₇	—	2	2	no	—
281	C₂²×C₁₃₇	—	2	4	no	—
282	C₂²×C₁₃₇	—	2	2	no	—
283	C₂²×C₁₃₇	—	2	4	no	—
284	C₂²×C₁₃₇	—	2	8	no	—
285	C₂²×C₁₃₇	—	2	4	no	—
286	C₂²×C₁₃₇	—	2	4	no	—
287	C₂²×C₁₃₇	—	2	8	no	—
288	C₂²×C₁₃₇	—	2	4	no	—
289	C₂²×C₁₃₇	—	2	4	no	—
290	C₂²×C₁₃₇	—	2	4	no	—
291	C₂²×C₁₃₇	—	4	32	no	—
292	C₂²×C₁₃₇	—	4	4	no	—
293	C₂²×C₁₃₇	—	4	4	no	—
294	C₂²×C₁₃₇	C₂×#117	1	8	yes	complemented
295	C₂²×C₁₃₇	C₂×C₄×D₄	1	4	yes	—
296	C₂²×C₁₃₇	C₂⁴×C₄	1	1	yes	characteristic
297	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
299	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃₇	#585	1	2	yes	—
301	C₄×C₁₃₇	—	2	2	no	—
302	C₄×C₁₃₇	—	2	4	no	—
303	C₄×C₁₃₇	—	2	4	no	—
304	C₄×C₁₃₇	—	2	2	no	—
305	C₄×C₁₃₇	—	2	2	no	—
306	C₄×C₁₃₇	—	2	8	no	—
307	C₄×C₁₃₇	—	4	8	no	—
308	C₄×C₁₃₇	—	4	4	no	—
309	C₄×C₁₃₇	C₂×#117	1	4	yes	complemented
310	C₄×C₁₃₇	C₂×C₄×D₄	1	4	yes	—
311	C₄×C₁₃₇	C₂×C₄×D₄	1	4	yes	—
312	C₂×C₁₃₇	—	2	4	no	—
313	C₂×C₁₃₇	—	2	8	no	—
314	C₂×C₁₃₇	—	4	4	no	—
315	C₂×C₁₃₇	C₂²×#117	1	1	yes	characteristic
316	C₂×C₁₃₇	C₂²×C₄×D₄	1	1	yes	characteristic
317	C₂×C₁₃₇	#3428	1	1	yes	characteristic
318	C₂×C₁₃₇	D₄×#41	1	2	yes	—
319	C₂×C₁₃₇	#3475	1	2	yes	—
320	D₄×#117	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₁₃₇	D₄×#117	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²×C₄×D₄	C₂×C₁₃₇	1	1	yes	characteristic
323	C₂²×#117	C₂×C₁₃₇	1	2	yes	complemented
324	#2354	C₂×C₁₃₇	1	2	yes	complemented
325	#2352	C₂×C₁₃₇	1	4	yes	complemented
326	D₄×C₄⋊C₄	C₂×C₁₃₇	1	2	yes	complemented
327	#2344	C₂×C₁₃₇	1	2	yes	complemented
328	#2342	C₂×C₁₃₇	1	4	yes	complemented
329	D₄×C₂²⋊C₄	C₂×C₁₃₇	1	2	yes	—
330	#2293	C₂×C₁₃₇	1	2	yes	complemented
331	#2290	C₂×C₁₃₇	1	4	yes	complemented
332	#2285	C₂×C₁₃₇	1	1	yes	characteristic, complemented
333	#2280	C₂×C₁₃₇	1	2	yes	complemented
334	C₄²×D₄	C₂×C₁₃₇	1	2	yes	complemented
335	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
336	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×C₁₃₇	1	2	yes	—
338	C₂×C₄×D₄	C₄×C₁₃₇	1	16	yes	complemented
339	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
340	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
343	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
345	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
346	C₂×#117	—	2	16	no	—
347	C₂×#117	C₂²×C₁₃₇	1	4	yes	—
348	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
349	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
350	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
351	C₂×#117	C₂²×C₁₃₇	1	4	yes	complemented
352	C₂×#117	C₂²×C₁₃₇	1	4	yes	complemented
353	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
355	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
356	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
357	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
358	C₂²×C₄²	C₂²×C₁₃₇	1	4	yes	complemented
359	#390	C₂²×C₁₃₇	1	4	yes	—
360	#389	C₂²×C₁₃₇	1	4	yes	complemented
361	#388	C₂²×C₁₃₇	1	8	yes	complemented
362	#388	C₂²×C₁₃₇	1	8	yes	complemented
363	#387	C₂²×C₁₃₇	1	8	yes	complemented
364	#386	C₂²×C₁₃₇	1	8	yes	—
365	#385	C₂²×C₁₃₇	1	8	yes	complemented
366	#384	C₂²×C₁₃₇	1	2	yes	complemented
367	#382	C₂²×C₁₃₇	1	2	yes	complemented
368	#381	C₂²×C₁₃₇	1	4	yes	—
369	#380	C₂²×C₁₃₇	1	2	yes	—
370	#380	C₂²×C₁₃₇	1	2	yes	—
371	#380	C₂²×C₁₃₇	1	4	yes	complemented
372	#380	C₂²×C₁₃₇	1	4	yes	complemented
373	#379	C₂²×C₁₃₇	1	4	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
375	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
376	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
377	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
378	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
379	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	8	yes	complemented
382	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
383	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
384	#376	C₂²×C₁₃₇	1	2	yes	complemented
385	C₄³	C₂²×C₁₃₇	1	2	yes	complemented
386	C₂⁵	C₂³×C₁₃₇	1	2	yes	—
387	C₂²×D₄	—	2	8	no	—
388	C₂²×D₄	C₂×C₄×C₁₃₇	1	8	yes	—
389	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
390	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
391	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	2	8	no	—
394	C₂³×C₄	C₂×C₄×C₁₃₇	1	16	yes	complemented
395	C₂³×C₄	C₂³×C₁₃₇	1	8	yes	—
396	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
401	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
404	C₄×D₄	—	2	16	no	—
405	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	—
406	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	—
407	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
408	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
409	C₄×D₄	C₂×C₄×C₁₃₇	1	16	yes	complemented
410	C₄×D₄	C₂×C₄×C₁₃₇	1	16	yes	complemented
411	#117	—	2	8	no	—
412	#117	—	2	4	no	—
413	#117	—	2	16	no	—
414	#117	—	2	16	no	—
415	#117	—	2	16	no	—
416	#117	D₄×C₁₃₇	1	8	yes	direct product factor
417	C₂×C₄⋊C₄	—	2	16	no	—
418	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
419	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
428	C₂×C₂²⋊C₄	—	2	16	no	—
429	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	16	yes	complemented
430	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
440	C₂×C₄²	—	2	16	no	—
441	C₂×C₄²	C₂×C₄×C₁₃₇	1	8	yes	complemented
442	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
443	C₂×C₄²	C₂³×C₁₃₇	1	8	yes	—
444	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
445	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
446	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
447	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
452	#95	C₂³×C₁₃₇	1	4	yes	—
453	#95	C₂³×C₁₃₇	1	4	yes	—
454	#95	C₂³×C₁₃₇	1	4	yes	—
455	#95	C₂³×C₁₃₇	1	8	yes	—
456	#95	C₂³×C₁₃₇	1	8	yes	—
457	#95	C₂³×C₁₃₇	1	4	yes	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	2	8	no	—
461	C₂⁴	—	4	4	no	—
462	C₂⁴	C₂²×C₄×C₁₃₇	1	8	yes	—
463	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
464	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
465	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	32	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
470	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
471	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
472	C₂×D₄	#41×C₁₃₇	1	8	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	64	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	16	no	—
486	C₂²×C₄	—	2	16	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
490	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
491	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
492	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
493	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
494	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
497	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
498	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₁₃₇	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
510	C₄⋊C₄	—	2	16	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
516	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
517	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	complemented
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
525	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
526	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
527	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
528	C₂²⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
529	C₄²	—	2	16	no	—
530	C₄²	—	2	8	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	8	no	—
533	C₄²	—	4	4	no	—
534	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
535	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
536	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
537	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
538	C₄²	C₂×D₄×C₁₃₇	1	8	yes	complemented
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	16	no	—
545	C₂³	—	2	16	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	16	no	—
552	C₂³	—	4	16	no	—
553	C₂³	C₂³×C₄×C₁₃₇	1	4	yes	—
554	C₂³	C₂³×C₄×C₁₃₇	1	4	yes	—
555	C₂³	C₂³×C₄×C₁₃₇	1	2	yes	—
556	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
557	C₂³	C₂×#41×C₁₃₇	1	8	yes	—
558	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
559	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
560	D₄	—	2	16	no	—
561	D₄	—	2	8	no	—
562	D₄	#117×C₁₃₇	1	16	yes	direct product factor
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	16	no	—
575	C₂×C₄	—	2	16	no	—
576	C₂×C₄	—	2	16	no	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	8	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	32	no	—
586	C₂×C₄	C₄×D₄×C₁₃₇	1	16	yes	complemented
587	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
589	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
590	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
591	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
592	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
593	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
594	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃₇	1	8	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
598	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
599	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
600	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	8	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	4	32	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	4	no	—
615	C₂²	C₂×#117×C₁₃₇	1	8	yes	complemented
616	C₂²	C₂×C₄×D₄×C₁₃₇	1	4	yes	—
617	C₂²	C₂⁴×C₄×C₁₃₇	1	1	yes	characteristic
618	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
620	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
621	C₂²	#585×C₁₃₇	1	2	yes	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	8	no	—
628	C₄	—	4	8	no	—
629	C₄	—	4	4	no	—
630	C₄	C₂×#117×C₁₃₇	1	4	yes	complemented
631	C₄	C₂×C₄×D₄×C₁₃₇	1	4	yes	—
632	C₄	C₂×C₄×D₄×C₁₃₇	1	4	yes	—
633	C₂	—	2	4	no	—
634	C₂	—	2	8	no	—
635	C₂	—	4	4	no	—
636	C₂	C₂²×#117×C₁₃₇	1	1	yes	characteristic
637	C₂	C₂²×C₄×D₄×C₁₃₇	1	1	yes	characteristic
638	C₂	#3428×C₁₃₇	1	1	yes	characteristic
639	C₂	D₄×#41×C₁₃₇	1	2	yes	—
640	C₂	#3475×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃₇
Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
socle	C₂³×C₁₃₇	C₂⁵
prime radical	C₂³×D₄×C₁₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₃₇	C₂	semidirect
3. #2354×C₁₃₇	C₂	semidirect
4. #2352×C₁₃₇	C₂	semidirect
5. D₄×C₄⋊C₄×C₁₃₇	C₂	semidirect
6. #2344×C₁₃₇	C₂	semidirect
7. #2342×C₁₃₇	C₂	semidirect
9. #2293×C₁₃₇	C₂	semidirect
10. #2290×C₁₃₇	C₂	semidirect
11. #2285×C₁₃₇	C₂	semidirect
12. #2280×C₁₃₇	C₂	semidirect
13. C₄²×D₄×C₁₃₇	C₂	semidirect
14. C₄×#117×C₁₃₇	C₂	semidirect
17. C₂×C₄×D₄×C₁₃₇	C₄	semidirect
30. C₂×#117×C₁₃₇	C₂²	semidirect
31. C₂×#117×C₁₃₇	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₁₃₇	C₂²	semidirect
37. C₂²×C₄²×C₁₃₇	C₂²	semidirect
39. #389×C₁₃₇	C₂²	semidirect
40. #388×C₁₃₇	C₂²	semidirect
41. #388×C₁₃₇	C₂²	semidirect
42. #387×C₁₃₇	C₂²	semidirect
44. #385×C₁₃₇	C₂²	semidirect
45. #384×C₁₃₇	C₂²	semidirect
46. #382×C₁₃₇	C₂²	semidirect
50. #380×C₁₃₇	C₂²	semidirect
51. #380×C₁₃₇	C₂²	semidirect
53. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
54. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
55. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
56. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
57. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
63. #376×C₁₃₇	C₂²	semidirect
64. C₄³×C₁₃₇	C₂²	semidirect
73. C₂³×C₄×C₁₃₇	C₂×C₄	semidirect
86. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
87. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
88. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
89. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
95. #117×C₁₃₇	D₄	direct (N × H)
97. C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	semidirect
108. C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	semidirect
120. C₂×C₄²×C₁₃₇	C₂×C₄	semidirect
197. C₄⋊C₄×C₁₃₇	C₂×D₄	semidirect
217. C₄²×C₁₃₇	C₂×D₄	semidirect
241. D₄×C₁₃₇	#117	direct (N × H)
265. C₂×C₄×C₁₃₇	C₄×D₄	semidirect
294. C₂²×C₁₃₇	C₂×#117	semidirect
309. C₄×C₁₃₇	C₂×#117	semidirect
320. D₄×#117	C₁₃₇	direct (N × H)
321. C₁₃₇	D₄×#117	direct (N × H)
323. C₂²×#117	C₂×C₁₃₇	semidirect
324. #2354	C₂×C₁₃₇	semidirect
325. #2352	C₂×C₁₃₇	semidirect
326. D₄×C₄⋊C₄	C₂×C₁₃₇	semidirect
327. #2344	C₂×C₁₃₇	semidirect
328. #2342	C₂×C₁₃₇	semidirect
330. #2293	C₂×C₁₃₇	semidirect
331. #2290	C₂×C₁₃₇	semidirect
332. #2285	C₂×C₁₃₇	semidirect
333. #2280	C₂×C₁₃₇	semidirect
334. C₄²×D₄	C₂×C₁₃₇	semidirect
335. C₄×#117	C₂×C₁₃₇	semidirect
338. C₂×C₄×D₄	C₄×C₁₃₇	semidirect
351. C₂×#117	C₂²×C₁₃₇	semidirect
352. C₂×#117	C₂²×C₁₃₇	semidirect
354. C₂²×C₄⋊C₄	C₂²×C₁₃₇	semidirect
358. C₂²×C₄²	C₂²×C₁₃₇	semidirect
360. #389	C₂²×C₁₃₇	semidirect
361. #388	C₂²×C₁₃₇	semidirect
362. #388	C₂²×C₁₃₇	semidirect
363. #387	C₂²×C₁₃₇	semidirect
365. #385	C₂²×C₁₃₇	semidirect
366. #384	C₂²×C₁₃₇	semidirect
367. #382	C₂²×C₁₃₇	semidirect
371. #380	C₂²×C₁₃₇	semidirect
372. #380	C₂²×C₁₃₇	semidirect
374. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
375. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
376. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
377. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
378. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
381. C₄×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
382. C₄×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
383. C₄×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
384. #376	C₂²×C₁₃₇	semidirect
385. C₄³	C₂²×C₁₃₇	semidirect
394. C₂³×C₄	C₂×C₄×C₁₃₇	semidirect
407. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
408. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
409. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
410. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
416. #117	D₄×C₁₃₇	direct (N × H)
418. C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	semidirect
429. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	semidirect
441. C₂×C₄²	C₂×C₄×C₁₃₇	semidirect
518. C₄⋊C₄	C₂×D₄×C₁₃₇	semidirect
538. C₄²	C₂×D₄×C₁₃₇	semidirect
562. D₄	#117×C₁₃₇	direct (N × H)
586. C₂×C₄	C₄×D₄×C₁₃₇	semidirect
615. C₂²	C₂×#117×C₁₃₇	semidirect
630. C₄	C₂×#117×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃₇	2
C₂²×#117×C₁₃₇	2
#2354×C₁₃₇	2
#2352×C₁₃₇	2
D₄×C₄⋊C₄×C₁₃₇	2
#2344×C₁₃₇	2
#2342×C₁₃₇	2
D₄×C₂²⋊C₄×C₁₃₇	2
#2293×C₁₃₇	2
#2290×C₁₃₇	2
#2285×C₁₃₇	2
#2280×C₁₃₇	2
C₄²×D₄×C₁₃₇	2
C₄×#117×C₁₃₇	2
D₄×#117	137

Subgroups — D4×#117×C137 #46883508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#117×C₁₃₇ #46883508