Subgroups — C₂×#552×C₁₃₇ #31778481

Order 17536.

1124 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#552×C₁₃₇	C₂	1	16	yes	maximal, direct product factor
2	C₂×#126×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×#125×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₂×#125×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#123×C₁₃₇	C₂	1	2	yes	maximal
6	C₂×C₂²⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂²⋊Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#117×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₃₇	C₂²	1	2	yes	—
16	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	#126×C₁₃₇	C₂²	1	16	yes	complemented
19	#125×C₁₃₇	C₂²	1	16	yes	complemented
20	#125×C₁₃₇	C₂²	1	8	yes	complemented
21	#123×C₁₃₇	C₂²	1	16	yes	—
22	C₂²⋊Q₈×C₁₃₇	C₂²	1	8	yes	complemented
23	C₂²⋊Q₈×C₁₃₇	C₂²	1	8	yes	complemented
24	C₄×Q₈×C₁₃₇	C₂²	1	8	yes	complemented
25	C₄×D₄×C₁₃₇	C₂²	1	8	yes	—
26	#117×C₁₃₇	C₂²	1	8	yes	complemented
27	#117×C₁₃₇	C₂²	1	16	yes	complemented
28	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
34	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	8	yes	complemented
39	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
44	C₂×C₄²×C₁₃₇	C₂²	1	2	yes	—
45	C₂×C₄²×C₁₃₇	C₂²	1	2	yes	—
46	C₂×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
47	C₂⁴×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂⁴×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂×Q₈×C₁₃₇	—	2	4	no	—
50	C₂×Q₈×C₁₃₇	C₂³	1	4	yes	—
51	C₂×D₄×C₁₃₇	—	2	4	no	—
52	C₂×D₄×C₁₃₇	C₂³	1	4	yes	—
53	C₂²×C₄×C₁₃₇	—	2	8	no	—
54	C₂²×C₄×C₁₃₇	—	2	4	no	—
55	C₂²×C₄×C₁₃₇	—	2	4	no	—
56	C₂²×C₄×C₁₃₇	C₂³	1	8	yes	—
57	C₂²×C₄×C₁₃₇	C₂³	1	4	yes	—
58	C₂²×C₄×C₁₃₇	C₂³	1	4	yes	—
59	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
63	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
67	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
69	C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
70	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
71	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
72	C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
73	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
74	C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
75	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
76	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
77	C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
78	C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
79	C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
82	C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
83	C₄²×C₁₃₇	C₂³	1	8	yes	—
84	C₄²×C₁₃₇	C₂³	1	8	yes	—
85	C₄²×C₁₃₇	C₂³	1	4	yes	—
86	C₂³×C₁₃₇	—	2	2	no	—
87	C₂³×C₁₃₇	—	2	2	no	—
88	C₂³×C₁₃₇	—	2	2	no	—
89	C₂³×C₁₃₇	—	2	2	no	—
90	C₂³×C₁₃₇	—	2	2	no	—
91	C₂³×C₁₃₇	#41	1	4	yes	—
92	C₂³×C₁₃₇	C₂⁴	1	2	yes	—
93	C₂³×C₁₃₇	C₂⁴	1	2	yes	—
94	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
95	Q₈×C₁₃₇	—	2	8	no	—
96	D₄×C₁₃₇	—	2	8	no	—
97	C₂×C₄×C₁₃₇	—	2	16	no	—
98	C₂×C₄×C₁₃₇	—	2	4	no	—
99	C₂×C₄×C₁₃₇	—	2	4	no	—
100	C₂×C₄×C₁₃₇	—	2	2	no	—
101	C₂×C₄×C₁₃₇	—	2	2	no	—
102	C₂×C₄×C₁₃₇	—	2	2	no	—
103	C₂×C₄×C₁₃₇	—	2	4	no	—
104	C₂×C₄×C₁₃₇	—	2	2	no	—
105	C₂×C₄×C₁₃₇	—	2	4	no	—
106	C₂×C₄×C₁₃₇	—	2	8	no	—
107	C₂×C₄×C₁₃₇	—	2	8	no	—
108	C₂×C₄×C₁₃₇	#41	1	4	yes	—
109	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
110	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
111	C₂×C₄×C₁₃₇	C₂⁴	1	4	yes	—
112	C₂×C₄×C₁₃₇	C₂⁴	1	4	yes	—
113	C₂×C₄×C₁₃₇	C₂⁴	1	4	yes	—
114	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
115	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
116	C₂×C₄×C₁₃₇	C₂⁴	1	4	yes	—
117	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
118	C₂²×C₁₃₇	—	2	8	no	—
119	C₂²×C₁₃₇	—	2	2	no	—
120	C₂²×C₁₃₇	—	2	2	no	—
121	C₂²×C₁₃₇	—	2	2	no	—
122	C₂²×C₁₃₇	—	2	2	no	—
123	C₂²×C₁₃₇	—	2	2	no	—
124	C₂²×C₁₃₇	—	4	4	no	—
125	C₂²×C₁₃₇	C₂×#41	1	4	yes	—
126	C₂²×C₁₃₇	C₂×#41	1	2	yes	—
127	C₂²×C₁₃₇	C₂×#41	1	2	yes	—
128	C₂²×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
129	C₂²×C₁₃₇	C₂⁵	1	1	yes	characteristic
130	C₄×C₁₃₇	—	2	4	no	—
131	C₄×C₁₃₇	—	2	4	no	—
132	C₄×C₁₃₇	—	2	2	no	—
133	C₄×C₁₃₇	—	2	2	no	—
134	C₄×C₁₃₇	—	2	2	no	—
135	C₄×C₁₃₇	—	2	4	no	—
136	C₄×C₁₃₇	—	2	2	no	—
137	C₄×C₁₃₇	—	2	4	no	—
138	C₄×C₁₃₇	C₂×#41	1	4	yes	—
139	C₂×C₁₃₇	—	2	4	no	—
140	C₂×C₁₃₇	—	4	2	no	—
141	C₂×C₁₃₇	#552	1	4	yes	direct product factor
142	C₂×C₁₃₇	C₂²×#41	1	1	yes	characteristic
143	C₂×C₁₃₇	C₂²×#41	1	1	yes	characteristic
144	C₂×C₁₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
145	C₁₃₇	C₂×#552	1	1	yes	characteristic, direct product factor, Sylow
146	C₂×#552	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	#552	C₂×C₁₃₇	1	16	yes	direct product factor
148	C₂×#126	C₂×C₁₃₇	1	2	yes	complemented
149	C₂×#125	C₂×C₁₃₇	1	2	yes	complemented
150	C₂×#125	C₂×C₁₃₇	1	1	yes	characteristic, complemented
151	C₂×#123	C₂×C₁₃₇	1	2	yes	—
152	C₂×C₂²⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
153	C₂×C₂²⋊Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
154	C₂×C₄×Q₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
155	C₂×C₄×D₄	C₂×C₁₃₇	1	1	yes	characteristic
156	C₂×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
157	C₂×#117	C₂×C₁₃₇	1	2	yes	complemented
158	C₂²×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
159	C₂²×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
160	C₂²×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
161	C₂³×C₄	C₂²×C₁₃₇	1	2	yes	—
162	C₂³×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
163	C₂³×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
164	#126	C₂²×C₁₃₇	1	16	yes	complemented
165	#125	C₂²×C₁₃₇	1	16	yes	complemented
166	#125	C₂²×C₁₃₇	1	8	yes	complemented
167	#123	C₂²×C₁₃₇	1	16	yes	—
168	C₂²⋊Q₈	C₂²×C₁₃₇	1	8	yes	complemented
169	C₂²⋊Q₈	C₂²×C₁₃₇	1	8	yes	complemented
170	C₄×Q₈	C₂²×C₁₃₇	1	8	yes	complemented
171	C₄×D₄	C₂²×C₁₃₇	1	8	yes	—
172	#117	C₂²×C₁₃₇	1	8	yes	complemented
173	#117	C₂²×C₁₃₇	1	16	yes	complemented
174	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
176	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
177	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
178	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
179	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
180	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
182	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
184	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	8	yes	complemented
185	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
190	C₂×C₄²	C₂²×C₁₃₇	1	2	yes	—
191	C₂×C₄²	C₂²×C₁₃₇	1	2	yes	—
192	C₂×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
193	C₂⁴	C₂³×C₁₃₇	1	1	yes	characteristic
194	C₂⁴	C₂³×C₁₃₇	1	1	yes	characteristic
195	C₂×Q₈	—	2	4	no	—
196	C₂×Q₈	C₂³×C₁₃₇	1	4	yes	—
197	C₂×D₄	—	2	4	no	—
198	C₂×D₄	C₂³×C₁₃₇	1	4	yes	—
199	C₂²×C₄	—	2	8	no	—
200	C₂²×C₄	—	2	4	no	—
201	C₂²×C₄	—	2	4	no	—
202	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
203	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
204	C₂²×C₄	C₂³×C₁₃₇	1	2	yes	—
205	C₂²×C₄	C₂³×C₁₃₇	1	2	yes	—
206	C₂²×C₄	C₂³×C₁₃₇	1	2	yes	—
207	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
208	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
209	C₂²×C₄	C₂³×C₁₃₇	1	2	yes	—
210	C₂²×C₄	C₂³×C₁₃₇	1	8	yes	—
211	C₂²×C₄	C₂³×C₁₃₇	1	4	yes	—
212	C₂²×C₄	C₂³×C₁₃₇	1	4	yes	—
213	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
214	C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
215	C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
216	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
217	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
218	C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
219	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
220	C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
221	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
222	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
223	C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
224	C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
225	C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
226	C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
227	C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
228	C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
229	C₄²	C₂³×C₁₃₇	1	8	yes	—
230	C₄²	C₂³×C₁₃₇	1	8	yes	—
231	C₄²	C₂³×C₁₃₇	1	4	yes	—
232	C₂³	—	2	2	no	—
233	C₂³	—	2	2	no	—
234	C₂³	—	2	2	no	—
235	C₂³	—	2	2	no	—
236	C₂³	—	2	2	no	—
237	C₂³	#41×C₁₃₇	1	4	yes	—
238	C₂³	C₂⁴×C₁₃₇	1	2	yes	—
239	C₂³	C₂⁴×C₁₃₇	1	2	yes	—
240	C₂³	C₂⁴×C₁₃₇	1	1	yes	characteristic
241	Q₈	—	2	8	no	—
242	D₄	—	2	8	no	—
243	C₂×C₄	—	2	16	no	—
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	2	4	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	8	no	—
253	C₂×C₄	—	2	8	no	—
254	C₂×C₄	#41×C₁₃₇	1	4	yes	—
255	C₂×C₄	C₂⁴×C₁₃₇	1	2	yes	—
256	C₂×C₄	C₂⁴×C₁₃₇	1	2	yes	—
257	C₂×C₄	C₂⁴×C₁₃₇	1	4	yes	—
258	C₂×C₄	C₂⁴×C₁₃₇	1	4	yes	—
259	C₂×C₄	C₂⁴×C₁₃₇	1	4	yes	—
260	C₂×C₄	C₂⁴×C₁₃₇	1	2	yes	—
261	C₂×C₄	C₂⁴×C₁₃₇	1	2	yes	—
262	C₂×C₄	C₂⁴×C₁₃₇	1	4	yes	—
263	C₂×C₄	C₂⁴×C₁₃₇	1	2	yes	—
264	C₂²	—	2	8	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	2	no	—
270	C₂²	—	4	4	no	—
271	C₂²	C₂×#41×C₁₃₇	1	4	yes	—
272	C₂²	C₂×#41×C₁₃₇	1	2	yes	—
273	C₂²	C₂×#41×C₁₃₇	1	2	yes	—
274	C₂²	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
275	C₂²	C₂⁵×C₁₃₇	1	1	yes	characteristic
276	C₄	—	2	4	no	—
277	C₄	—	2	4	no	—
278	C₄	—	2	2	no	—
279	C₄	—	2	2	no	—
280	C₄	—	2	2	no	—
281	C₄	—	2	4	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	4	no	—
284	C₄	C₂×#41×C₁₃₇	1	4	yes	—
285	C₂	—	2	4	no	—
286	C₂	—	4	2	no	—
287	C₂	#552×C₁₃₇	1	4	yes	direct product factor
288	C₂	C₂²×#41×C₁₃₇	1	1	yes	characteristic
289	C₂	C₂²×#41×C₁₃₇	1	1	yes	characteristic
290	C₂	C₂×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #552×C₁₃₇	C₂	direct (N × H)
2. C₂×#126×C₁₃₇	C₂	semidirect
3. C₂×#125×C₁₃₇	C₂	semidirect
4. C₂×#125×C₁₃₇	C₂	semidirect
6. C₂×C₂²⋊Q₈×C₁₃₇	C₂	semidirect
7. C₂×C₂²⋊Q₈×C₁₃₇	C₂	semidirect
8. C₂×C₄×Q₈×C₁₃₇	C₂	semidirect
10. C₂×#117×C₁₃₇	C₂	semidirect
11. C₂×#117×C₁₃₇	C₂	semidirect
12. C₂²×C₄⋊C₄×C₁₃₇	C₂	semidirect
18. #126×C₁₃₇	C₂²	semidirect
19. #125×C₁₃₇	C₂²	semidirect
20. #125×C₁₃₇	C₂²	semidirect
22. C₂²⋊Q₈×C₁₃₇	C₂²	semidirect
23. C₂²⋊Q₈×C₁₃₇	C₂²	semidirect
24. C₄×Q₈×C₁₃₇	C₂²	semidirect
26. #117×C₁₃₇	C₂²	semidirect
27. #117×C₁₃₇	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₃₇	C₂²	semidirect
141. C₂×C₁₃₇	#552	direct (N × H)
145. C₁₃₇	C₂×#552	direct (N × H)
146. C₂×#552	C₁₃₇	direct (N × H)
147. #552	C₂×C₁₃₇	direct (N × H)
148. C₂×#126	C₂×C₁₃₇	semidirect
149. C₂×#125	C₂×C₁₃₇	semidirect
150. C₂×#125	C₂×C₁₃₇	semidirect
152. C₂×C₂²⋊Q₈	C₂×C₁₃₇	semidirect
153. C₂×C₂²⋊Q₈	C₂×C₁₃₇	semidirect
154. C₂×C₄×Q₈	C₂×C₁₃₇	semidirect
156. C₂×#117	C₂×C₁₃₇	semidirect
157. C₂×#117	C₂×C₁₃₇	semidirect
158. C₂²×C₄⋊C₄	C₂×C₁₃₇	semidirect
164. #126	C₂²×C₁₃₇	semidirect
165. #125	C₂²×C₁₃₇	semidirect
166. #125	C₂²×C₁₃₇	semidirect
168. C₂²⋊Q₈	C₂²×C₁₃₇	semidirect
169. C₂²⋊Q₈	C₂²×C₁₃₇	semidirect
170. C₄×Q₈	C₂²×C₁₃₇	semidirect
172. #117	C₂²×C₁₃₇	semidirect
173. #117	C₂²×C₁₃₇	semidirect
184. C₂×C₄⋊C₄	C₂²×C₁₃₇	semidirect
287. C₂	#552×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
#552×C₁₃₇	2
C₂×#126×C₁₃₇	2
C₂×#125×C₁₃₇	2
C₂×#123×C₁₃₇	2
C₂×C₂²⋊Q₈×C₁₃₇	2
C₂×C₄×Q₈×C₁₃₇	2
C₂×C₄×D₄×C₁₃₇	2
C₂×#117×C₁₃₇	2
C₂²×C₄⋊C₄×C₁₃₇	2
C₂×#552	137

Subgroups — C2×#552×C137 #31778481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#552×C₁₃₇ #31778481