Subgroups — #31794272

Order 17536.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22578071	C₂	1	1	yes	maximal, characteristic, complemented
4	#22578066	C₂	1	1	yes	maximal, characteristic, complemented
5	#22578063	C₂	1	1	yes	maximal, characteristic, complemented
6	#22578059	C₂	1	1	yes	maximal, characteristic, complemented
7	#22578055	C₂	1	1	yes	maximal, characteristic, complemented
8	#22578051	C₂	1	2	yes	maximal, complemented
9	#22578050	C₂	1	1	yes	maximal, characteristic, complemented
10	#22578045	C₂	1	2	yes	maximal, complemented
11	#22578044	C₂	1	1	yes	maximal, characteristic, complemented
12	#22578040	C₂	1	2	yes	maximal, complemented
13	#22578037	C₂	1	1	yes	maximal, characteristic, complemented
14	#22578035	C₂	1	2	yes	maximal, complemented
15	#22577950	C₂	1	2	yes	maximal, complemented
16	#22577949	C₂	1	1	yes	maximal, characteristic, complemented
17	#22577915	C₂	1	1	yes	maximal, characteristic, complemented
18	#22577912	C₂	1	2	yes	maximal, complemented
19	#22577912	C₂	1	2	yes	maximal, complemented
20	#22577871	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₃₇	C₂	1	2	yes	maximal, complemented
23	#525×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14555511	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14555510	—	2	8	no	—
26	C₂×#14555510	C₂²	1	1	yes	characteristic
27	C₂×#14555510	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14555510	C₂²	1	2	yes	complemented
29	C₂×#14555510	C₂²	1	2	yes	complemented
30	C₂×#14555510	C₂²	1	2	yes	complemented
31	C₂×#14555510	C₂²	1	1	yes	characteristic, complemented
32	C₂×#14555510	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14555509	C₂²	1	2	yes	complemented
34	C₂×#14555509	C₂²	1	1	yes	characteristic, complemented
35	#41×D₁₃₇	—	2	8	no	—
36	C₂²×Dic₂₇₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₅₄₈	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊D₁₃₇	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₃₇	C₂²	1	2	yes	—
42	C₂×D₄×D₁₃₇	C₂²	1	2	yes	complemented
43	C₂×D₄×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₁₃₇	C₂²	1	2	yes	complemented
45	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄×D₁₃₇	C₂²	1	2	yes	complemented
47	#17984087	C₂²	1	2	yes	complemented
48	#17984086	C₂²	1	1	yes	characteristic, complemented
49	#17984084	C₂²	1	1	yes	characteristic, complemented
50	#17984084	C₂²	1	2	yes	complemented
51	#17984077	C₂²	1	1	yes	characteristic, complemented
52	#17984075	C₂²	1	1	yes	characteristic, complemented
53	#17984074	C₂²	1	2	yes	complemented
54	#17984074	C₂²	1	2	yes	complemented
55	#17984073	C₂²	1	2	yes	complemented
56	#17984073	C₂²	1	2	yes	complemented
57	#17984072	C₂²	1	2	yes	complemented
58	#17984070	C₂²	1	2	yes	complemented
59	#17984070	C₂²	1	2	yes	complemented
60	#17984068	C₂²	1	1	yes	characteristic, complemented
61	#17984068	C₂²	1	1	yes	characteristic, complemented
62	#17984066	C₂²	1	2	yes	complemented
63	#17984066	C₂²	1	2	yes	complemented
64	#17984065	C₂²	1	2	yes	complemented
65	#17984065	C₂²	1	2	yes	complemented
66	#17984063	C₂²	1	2	yes	complemented
67	#17984063	C₂²	1	1	yes	characteristic, complemented
68	#17984063	C₂²	1	1	yes	characteristic, complemented
69	#17984061	C₂²	1	2	yes	complemented
70	#17984061	C₂²	1	2	yes	complemented
71	#17984061	C₂²	1	2	yes	complemented
72	#17984061	C₂²	1	2	yes	complemented
73	#17984060	C₂²	1	2	yes	complemented
74	#17984060	C₂²	1	2	yes	complemented
75	#17984060	C₂²	1	2	yes	complemented
76	#17984060	C₂²	1	2	yes	complemented
77	#17984059	C₂²	1	2	yes	complemented
78	#17984058	C₂²	1	2	yes	complemented
79	#17984058	C₂²	1	2	yes	complemented
80	#17984058	C₂²	1	2	yes	complemented
81	#17984056	C₂²	1	2	yes	complemented
82	#17984056	C₂²	1	2	yes	complemented
83	#17984053	C₂²	1	1	yes	characteristic, complemented
84	#17984053	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₅₄₈	C₂²	1	2	yes	complemented
86	C₄×D₅₄₈	C₂²	1	2	yes	complemented
87	D₄×Dic₁₃₇	C₂²	1	2	yes	complemented
88	#17984050	C₂²	1	1	yes	characteristic, complemented
89	#17984050	C₂²	1	1	yes	characteristic, complemented
90	#17984050	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₃₇	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₁₃₇	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic, complemented
101	#17984048	C₂²	1	2	yes	—
102	#17984048	C₂²	1	2	yes	complemented
103	#17984048	C₂²	1	2	yes	complemented
104	#17984048	C₂²	1	2	yes	complemented
105	#17984045	C₂²	1	2	yes	complemented
106	C₂×#14555489	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₃₇	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14555487	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₁₃₇	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₃₇	C₂²	1	2	yes	complemented
112	C₂×C₄×Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
113	C₄²×D₁₃₇	C₂²	1	2	yes	complemented
114	C₂×#41×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
115	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₃₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
120	#121×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₃₇	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₃₇	C₂²	1	2	yes	complemented
123	C₄×D₄×C₁₃₇	C₂²	1	2	yes	complemented
124	#117×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
125	C₂³×D₁₃₇	C₂³	1	2	yes	—
126	C₂³×D₁₃₇	C₂³	1	2	yes	—
127	C₂³×D₁₃₇	C₂³	1	1	yes	characteristic
128	#14555511	—	2	4	no	—
129	#14555510	—	2	4	no	—
130	#14555510	—	2	4	no	—
131	#14555510	—	2	8	no	—
132	#14555510	—	2	8	no	—
133	#14555510	—	2	8	no	—
134	#14555510	—	2	4	no	—
135	#14555510	D₄	1	8	yes	complemented
136	#14555509	—	2	4	no	—
137	#14555509	—	2	8	no	—
138	C₂×Dic₂₇₄	—	2	4	no	—
139	C₂×Dic₂₇₄	C₂³	1	2	yes	—
140	C₂×Dic₂₇₄	C₂³	1	2	yes	—
141	C₂×Dic₂₇₄	C₂³	1	1	yes	characteristic
142	C₂×Dic₂₇₄	C₂³	1	1	yes	characteristic
143	Q₈×D₁₃₇	—	2	4	no	—
144	C₂×D₅₄₈	—	2	4	no	—
145	C₂×D₅₄₈	C₂³	1	2	yes	—
146	C₂×D₅₄₈	C₂³	1	2	yes	—
147	C₂×D₅₄₈	C₂³	1	2	yes	—
148	C₂×D₅₄₈	C₂³	1	1	yes	characteristic
149	C₂×D₅₄₈	C₂³	1	2	yes	—
150	C₂×D₅₄₈	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₃₇	—	2	8	no	—
152	C₂×C₂²⋊D₁₃₇	—	2	4	no	—
153	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₃₇	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₁₃₇	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₁₃₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊D₁₃₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊D₁₃₇	C₂³	1	1	yes	characteristic
165	D₄×D₁₃₇	—	2	4	no	—
166	D₄×D₁₃₇	—	2	8	no	—
167	D₄×D₁₃₇	—	2	8	no	—
168	C₂²×Dic₁₃₇	C₂³	1	1	yes	characteristic
169	C₂²×Dic₁₃₇	C₂³	1	1	yes	characteristic
170	C₂²×Dic₁₃₇	C₂³	1	2	yes	—
171	C₂²×Dic₁₃₇	C₂³	1	2	yes	—
172	C₂²×Dic₁₃₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₃₇	—	2	8	no	—
174	C₂×C₄×D₁₃₇	—	2	8	no	—
175	C₂×C₄×D₁₃₇	—	2	4	no	—
176	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
177	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
178	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
179	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
180	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
181	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
184	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
187	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
188	C₄⋊Dic₁₃₇	C₂³	1	2	yes	—
189	C₄⋊Dic₁₃₇	C₂³	1	2	yes	—
190	#14555489	C₂³	1	1	yes	characteristic
191	#14555489	C₂³	1	2	yes	—
192	#14555489	C₂³	1	1	yes	characteristic
193	#14555489	C₂³	1	1	yes	characteristic
194	#14555489	C₂³	1	1	yes	characteristic
195	#14555489	C₂³	1	2	yes	—
196	#14555489	C₂³	1	2	yes	—
197	#14555489	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₃₇	C₂³	1	1	yes	characteristic
199	C₂²⋊Dic₁₃₇	C₂³	1	2	yes	—
200	C₂²⋊Dic₁₃₇	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₁₃₇	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₃₇	C₂³	1	1	yes	characteristic
203	C₂²⋊Dic₁₃₇	C₂³	1	2	yes	—
204	#14555487	C₂³	1	1	yes	characteristic
205	#14555487	C₂³	1	2	yes	—
206	#14555487	C₂³	1	2	yes	—
207	#14555487	C₂³	1	2	yes	—
208	#14555487	C₂³	1	1	yes	characteristic
209	#14555487	C₂³	1	1	yes	characteristic
210	#14555487	C₂³	1	1	yes	characteristic
211	#14555487	C₂³	1	2	yes	—
212	#14555487	C₂³	1	2	yes	—
213	#14555487	C₂³	1	2	yes	—
214	#14555487	C₂³	1	2	yes	—
215	#14555487	C₂³	1	2	yes	—
216	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₃₇	C₂³	1	2	yes	—
218	C₄×Dic₁₃₇	C₂³	1	2	yes	—
219	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
222	C₂⁴×C₁₃₇	C₂³	1	1	yes	characteristic
223	#41×C₁₃₇	—	2	4	no	—
224	C₂×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
225	C₂×D₄×C₁₃₇	C₂³	1	2	yes	—
226	C₂×D₄×C₁₃₇	C₂³	1	2	yes	—
227	C₂×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
228	C₂×D₄×C₁₃₇	C₂³	1	2	yes	—
229	C₂²×C₄×C₁₃₇	—	2	4	no	—
230	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
234	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
238	C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
241	C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
242	C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
245	C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
246	C₄²×C₁₃₇	C₂³	1	2	yes	—
247	C₂²×D₁₃₇	—	2	2	no	—
248	C₂²×D₁₃₇	—	2	4	no	—
249	C₂²×D₁₃₇	—	2	4	no	—
250	C₂²×D₁₃₇	—	2	4	no	—
251	C₂²×D₁₃₇	—	2	4	no	—
252	C₂²×D₁₃₇	—	2	2	no	—
253	C₂²×D₁₃₇	—	4	2	no	—
254	C₂²×D₁₃₇	—	4	2	no	—
255	C₂²×D₁₃₇	—	4	1	no	—
256	C₂²×D₁₃₇	C₂⁴	1	1	yes	characteristic
257	C₂²×D₁₃₇	C₂⁴	1	2	yes	—
258	C₂²×D₁₃₇	C₂⁴	1	2	yes	—
259	C₂²×D₁₃₇	C₂⁴	1	1	yes	characteristic
260	Dic₂₇₄	—	2	2	no	—
261	Dic₂₇₄	—	2	4	no	—
262	Dic₂₇₄	—	2	4	no	—
263	Dic₂₇₄	C₂×D₄	1	4	yes	complemented
264	D₅₄₈	—	2	4	no	—
265	D₅₄₈	—	2	4	no	—
266	D₅₄₈	—	2	4	no	—
267	D₅₄₈	—	2	2	no	—
268	D₅₄₈	—	4	2	no	—
269	D₅₄₈	C₂×D₄	1	4	yes	complemented
270	C₂²⋊D₁₃₇	—	2	4	no	—
271	C₂²⋊D₁₃₇	—	2	2	no	—
272	C₂²⋊D₁₃₇	—	2	4	no	—
273	C₂²⋊D₁₃₇	—	2	4	no	—
274	C₂²⋊D₁₃₇	—	2	2	no	—
275	C₂²⋊D₁₃₇	—	2	4	no	—
276	C₂²⋊D₁₃₇	—	2	4	no	—
277	C₂²⋊D₁₃₇	—	2	4	no	—
278	C₂²⋊D₁₃₇	—	2	2	no	—
279	C₂²⋊D₁₃₇	—	4	2	no	—
280	C₂²⋊D₁₃₇	C₂×D₄	1	8	yes	complemented
281	C₂²⋊D₁₃₇	#41	1	4	yes	complemented
282	C₂×Dic₁₃₇	—	2	2	no	—
283	C₂×Dic₁₃₇	—	2	4	no	—
284	C₂×Dic₁₃₇	—	2	4	no	—
285	C₂×Dic₁₃₇	—	2	2	no	—
286	C₂×Dic₁₃₇	—	4	1	no	—
287	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₁₃₇	C₂⁴	1	2	yes	—
292	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₁₃₇	C₂⁴	1	2	yes	—
294	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
295	C₄×D₁₃₇	—	2	4	no	—
296	C₄×D₁₃₇	—	2	4	no	—
297	C₄×D₁₃₇	—	2	2	no	—
298	C₄×D₁₃₇	—	2	2	no	—
299	C₄×D₁₃₇	—	2	2	no	—
300	C₄×D₁₃₇	—	2	4	no	—
301	C₄×D₁₃₇	—	2	2	no	—
302	C₄×D₁₃₇	—	2	4	no	—
303	C₄×D₁₃₇	—	2	4	no	—
304	C₄×D₁₃₇	—	2	4	no	—
305	C₄×D₁₃₇	—	4	2	no	—
306	C₄×D₁₃₇	C₂×D₄	1	8	yes	complemented
307	C₂³×C₁₃₇	—	2	2	no	—
308	C₂³×C₁₃₇	—	2	2	no	—
309	C₂³×C₁₃₇	—	4	1	no	—
310	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
311	C₂³×C₁₃₇	C₂⁴	1	2	yes	—
312	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
313	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
314	Q₈×C₁₃₇	—	2	2	no	—
315	D₄×C₁₃₇	—	2	4	no	—
316	D₄×C₁₃₇	—	2	4	no	—
317	D₄×C₁₃₇	—	2	2	no	—
318	D₄×C₁₃₇	—	4	2	no	—
319	C₂×C₄×C₁₃₇	—	2	2	no	—
320	C₂×C₄×C₁₃₇	—	2	2	no	—
321	C₂×C₄×C₁₃₇	—	2	2	no	—
322	C₂×C₄×C₁₃₇	—	2	2	no	—
323	C₂×C₄×C₁₃₇	—	2	2	no	—
324	C₂×C₄×C₁₃₇	—	2	4	no	—
325	C₂×C₄×C₁₃₇	C₂×D₄	1	4	yes	complemented
326	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
327	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
328	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
329	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
330	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
331	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₁₃₇	—	2	1	no	—
334	C₂²×C₁₃₇	—	2	1	no	—
335	C₂²×C₁₃₇	—	2	1	no	—
336	C₂²×C₁₃₇	—	2	1	no	—
337	C₂²×C₁₃₇	—	2	1	no	—
338	C₂²×C₁₃₇	—	2	2	no	—
339	C₂²×C₁₃₇	—	2	2	no	—
340	C₂²×C₁₃₇	—	2	1	no	—
341	C₂²×C₁₃₇	—	2	1	no	—
342	C₂²×C₁₃₇	—	2	2	no	—
343	C₂²×C₁₃₇	—	4	4	no	—
344	C₂²×C₁₃₇	C₂²×D₄	1	2	yes	—
345	C₂²×C₁₃₇	C₂×#41	1	2	yes	complemented
346	C₂²×C₁₃₇	C₂⁵	1	1	yes	characteristic
347	C₂×D₁₃₇	—	2	1	no	—
348	C₂×D₁₃₇	—	2	2	no	—
349	C₂×D₁₃₇	—	2	2	no	—
350	C₂×D₁₃₇	—	2	1	no	—
351	C₂×D₁₃₇	—	2	1	no	—
352	C₂×D₁₃₇	—	2	2	no	—
353	C₂×D₁₃₇	—	2	1	no	—
354	C₂×D₁₃₇	—	2	2	no	—
355	C₂×D₁₃₇	—	2	2	no	—
356	C₂×D₁₃₇	—	2	1	no	—
357	C₂×D₁₃₇	—	4	8	no	—
358	C₂×D₁₃₇	—	4	4	no	—
359	C₂×D₁₃₇	—	4	8	no	—
360	C₂×D₁₃₇	C₂²×D₄	1	4	yes	—
361	C₂×D₁₃₇	C₂×#41	1	2	yes	complemented
362	C₄×C₁₃₇	—	2	1	no	—
363	C₄×C₁₃₇	—	2	1	no	—
364	C₄×C₁₃₇	—	2	2	no	—
365	C₄×C₁₃₇	—	2	2	no	—
366	C₄×C₁₃₇	—	2	2	no	—
367	C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
368	C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
369	Dic₁₃₇	—	2	1	no	—
370	Dic₁₃₇	—	2	2	no	—
371	Dic₁₃₇	—	2	1	no	—
372	Dic₁₃₇	—	2	1	no	—
373	Dic₁₃₇	—	2	1	no	—
374	Dic₁₃₇	—	2	1	no	—
375	Dic₁₃₇	C₂²×D₄	1	4	yes	—
376	Dic₁₃₇	C₂×#41	1	2	yes	complemented
377	C₂×C₁₃₇	—	2	2	no	—
378	C₂×C₁₃₇	—	2	2	no	—
379	C₂×C₁₃₇	—	4	2	no	—
380	C₂×C₁₃₇	—	4	1	no	—
381	C₂×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
382	C₂×C₁₃₇	C₂²×#41	1	1	yes	characteristic
383	C₂×C₁₃₇	#585	1	1	yes	characteristic
384	D₁₃₇	—	2	2	no	—
385	D₁₃₇	—	2	4	no	—
386	D₁₃₇	—	4	1	no	—
387	D₁₃₇	—	4	2	no	—
388	C₁₃₇	D₄×#41	1	1	yes	characteristic, complemented, Sylow
389	D₄×#41	—	137	1	no	maximal, Sylow
390	C₂²×#41	—	137	1	no	—
391	C₂²×#41	—	137	1	no	—
392	#550	—	137	1	no	—
393	D₄×Q₈	—	137	1	no	—
394	#548	—	137	1	no	—
395	#548	—	137	1	no	—
396	#547	—	137	2	no	—
397	#547	—	137	1	no	—
398	#546	—	137	2	no	—
399	#546	—	137	1	no	—
400	#546	—	137	1	no	—
401	#546	—	137	2	no	—
402	D₄²	—	137	1	no	—
403	D₄²	—	137	2	no	—
404	#532	—	137	1	no	—
405	#532	—	137	2	no	—
406	#525	—	137	2	no	—
407	#525	—	137	2	no	—
408	#525	—	137	1	no	—
409	#525	D₁₃₇	1	1	yes	characteristic, complemented
410	C₄×#41	—	137	1	no	—
411	C₂×C₄×D₄	—	137	1	no	—
412	C₂×C₄×D₄	—	137	2	no	—
413	C₂×#41	—	274	8	no	—
414	C₂×#41	—	274	8	no	—
415	C₂×#41	—	137	1	no	—
416	C₂×#41	—	137	2	no	—
417	C₂×#41	—	137	1	no	—
418	C₂×#41	—	137	1	no	—
419	C₂×#41	—	137	2	no	—
420	C₂×#41	—	137	2	no	—
421	C₂×#41	—	137	1	no	—
422	C₂×#41	—	137	2	no	—
423	C₂×#41	—	137	1	no	—
424	C₂×#41	—	137	1	no	—
425	C₂×#41	C₂×D₁₃₇	1	1	yes	characteristic, complemented
426	C₂²×Q₈	—	137	1	no	—
427	C₂²×Q₈	—	137	1	no	—
428	C₂²×D₄	—	137	1	no	—
429	C₂²×D₄	—	137	2	no	—
430	C₂²×D₄	—	137	2	no	—
431	C₂²×D₄	—	137	1	no	—
432	C₂²×D₄	—	137	2	no	—
433	C₂²×D₄	—	137	1	no	—
434	C₂³×C₄	—	137	2	no	—
435	C₂³×C₄	—	137	2	no	—
436	C₂³×C₄	—	137	1	no	—
437	C₂³×C₄	C₂×D₁₃₇	1	1	yes	characteristic, complemented
438	C₄⋊Q₈	—	137	1	no	—
439	C₄⋊Q₈	—	137	2	no	—
440	#127	—	137	2	no	—
441	#127	—	137	1	no	—
442	#124	—	137	1	no	—
443	#124	—	137	1	no	—
444	#124	—	137	2	no	—
445	#124	—	137	2	no	—
446	#123	—	137	2	no	—
447	#123	—	137	2	no	—
448	#123	—	137	2	no	—
449	#123	—	137	2	no	—
450	#123	—	137	2	no	—
451	#123	C₂×D₁₃₇	1	2	yes	complemented
452	C₂²⋊Q₈	—	137	2	no	—
453	C₂²⋊Q₈	—	137	1	no	—
454	C₂²⋊Q₈	—	137	2	no	—
455	C₂²⋊Q₈	—	137	1	no	—
456	C₂²⋊Q₈	—	137	2	no	—
457	C₂²⋊Q₈	—	137	2	no	—
458	C₂²⋊Q₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
459	C₂²⋊Q₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
460	#121	—	137	2	no	—
461	#121	—	137	2	no	—
462	#121	—	137	2	no	—
463	#121	—	137	2	no	—
464	#121	—	137	2	no	—
465	#121	—	137	1	no	—
466	#121	—	137	1	no	—
467	#121	—	137	2	no	—
468	#121	—	137	2	no	—
469	#121	—	137	2	no	—
470	#121	—	137	2	no	—
471	#121	—	137	2	no	—
472	#121	C₂×D₁₃₇	1	1	yes	characteristic, complemented
473	#121	C₂×D₁₃₇	1	1	yes	characteristic, complemented
474	#120	—	137	2	no	—
475	#120	—	137	2	no	—
476	#120	—	137	2	no	—
477	#120	—	137	2	no	—
478	#120	—	137	2	no	—
479	#120	C₂×D₁₃₇	1	2	yes	complemented
480	C₄×Q₈	—	137	1	no	—
481	C₄×Q₈	—	137	1	no	—
482	C₄×D₄	—	137	2	no	—
483	C₄×D₄	—	137	1	no	—
484	C₄×D₄	—	137	1	no	—
485	C₄×D₄	—	137	1	no	—
486	C₄×D₄	—	137	2	no	—
487	C₄×D₄	—	137	1	no	—
488	C₄×D₄	—	137	1	no	—
489	C₄×D₄	—	137	1	no	—
490	C₄×D₄	—	137	1	no	—
491	C₄×D₄	—	137	1	no	—
492	C₄×D₄	—	137	2	no	—
493	C₄×D₄	—	137	2	no	—
494	C₄×D₄	—	137	1	no	—
495	C₄×D₄	—	137	1	no	—
496	C₄×D₄	—	137	2	no	—
497	C₄×D₄	—	137	2	no	—
498	C₄×D₄	—	137	2	no	—
499	C₄×D₄	—	137	2	no	—
500	C₄×D₄	—	137	2	no	—
501	C₄×D₄	—	137	2	no	—
502	C₄×D₄	C₂×D₁₃₇	1	2	yes	complemented
503	C₄×D₄	C₂×D₁₃₇	1	2	yes	complemented
504	#117	—	137	2	no	—
505	#117	C₂×D₁₃₇	1	1	yes	characteristic, complemented
506	C₂×C₄⋊C₄	—	137	1	no	—
507	C₂×C₄⋊C₄	—	137	2	no	—
508	C₂×C₂²⋊C₄	—	137	1	no	—
509	C₂×C₂²⋊C₄	—	137	1	no	—
510	C₂×C₂²⋊C₄	—	137	2	no	—
511	C₂×C₂²⋊C₄	—	137	2	no	—
512	C₂×C₄²	—	137	1	no	—
513	C₂×C₄²	—	137	2	no	—
514	C₂⁴	—	137	2	no	—
515	C₂⁴	—	137	2	no	—
516	C₂⁴	—	137	1	no	—
517	C₂⁴	C₂²×D₁₃₇	1	1	yes	characteristic
518	#41	—	2	4	no	—
519	#41	—	274	4	no	—
520	#41	—	274	8	no	—
521	#41	—	274	4	no	—
522	#41	—	274	8	no	—
523	#41	—	274	8	no	—
524	#41	—	274	4	no	—
525	#41	—	274	8	no	—
526	#41	—	274	4	no	—
527	#41	—	274	4	no	—
528	#41	—	137	8	no	—
529	C₂×Q₈	—	274	4	no	—
530	C₂×Q₈	—	274	4	no	—
531	C₂×Q₈	—	137	1	no	—
532	C₂×Q₈	—	137	2	no	—
533	C₂×Q₈	—	137	2	no	—
534	C₂×Q₈	—	137	1	no	—
535	C₂×Q₈	C₂²×D₁₃₇	1	1	yes	characteristic
536	C₂×D₄	—	274	4	no	—
537	C₂×D₄	—	274	8	no	—
538	C₂×D₄	—	274	8	no	—
539	C₂×D₄	—	274	4	no	—
540	C₂×D₄	—	274	4	no	—
541	C₂×D₄	—	274	8	no	—
542	C₂×D₄	—	137	1	no	—
543	C₂×D₄	—	137	1	no	—
544	C₂×D₄	—	137	2	no	—
545	C₂×D₄	—	137	1	no	—
546	C₂×D₄	—	137	2	no	—
547	C₂×D₄	—	137	2	no	—
548	C₂×D₄	—	137	2	no	—
549	C₂×D₄	—	137	2	no	—
550	C₂×D₄	—	137	2	no	—
551	C₂×D₄	—	137	2	no	—
552	C₂×D₄	—	137	1	no	—
553	C₂×D₄	—	137	2	no	—
554	C₂×D₄	—	137	2	no	—
555	C₂×D₄	—	137	2	no	—
556	C₂×D₄	—	137	2	no	—
557	C₂×D₄	—	137	1	no	—
558	C₂×D₄	—	137	2	no	—
559	C₂×D₄	—	137	1	no	—
560	C₂×D₄	C₂²×D₁₃₇	1	2	yes	—
561	C₂×D₄	C₂²×D₁₃₇	1	2	yes	—
562	C₂×D₄	C₂²×D₁₃₇	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₁₃₇	1	2	yes	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	274	8	no	—
566	C₂²×C₄	—	274	8	no	—
567	C₂²×C₄	—	274	4	no	—
568	C₂²×C₄	—	137	1	no	—
569	C₂²×C₄	—	137	1	no	—
570	C₂²×C₄	—	137	2	no	—
571	C₂²×C₄	—	137	2	no	—
572	C₂²×C₄	—	137	2	no	—
573	C₂²×C₄	—	137	2	no	—
574	C₂²×C₄	—	137	2	no	—
575	C₂²×C₄	—	137	2	no	—
576	C₂²×C₄	—	137	1	no	—
577	C₂²×C₄	—	137	2	no	—
578	C₂²×C₄	—	137	1	no	—
579	C₂²×C₄	—	137	1	no	—
580	C₂²×C₄	—	137	1	no	—
581	C₂²×C₄	—	137	2	no	—
582	C₂²×C₄	—	137	1	no	—
583	C₂²×C₄	—	137	2	no	—
584	C₂²×C₄	—	137	2	no	—
585	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
586	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
587	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
588	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
589	C₂²×C₄	C₂²×D₁₃₇	1	2	yes	—
590	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
591	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
592	C₄⋊C₄	—	137	1	no	—
593	C₄⋊C₄	—	137	2	no	—
594	C₄⋊C₄	—	137	1	no	—
595	C₄⋊C₄	—	137	1	no	—
596	C₄⋊C₄	—	137	1	no	—
597	C₄⋊C₄	—	137	2	no	—
598	C₄⋊C₄	—	137	2	no	—
599	C₄⋊C₄	—	137	2	no	—
600	C₄⋊C₄	—	137	2	no	—
601	C₄⋊C₄	—	137	2	no	—
602	C₄⋊C₄	C₂²×D₁₃₇	1	2	yes	—
603	C₄⋊C₄	C₂²×D₁₃₇	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×D₁₃₇	1	1	yes	characteristic
605	C₄⋊C₄	C₂²×D₁₃₇	1	2	yes	—
606	C₂²⋊C₄	—	137	1	no	—
607	C₂²⋊C₄	—	137	1	no	—
608	C₂²⋊C₄	—	137	1	no	—
609	C₂²⋊C₄	—	137	2	no	—
610	C₂²⋊C₄	—	137	1	no	—
611	C₂²⋊C₄	—	137	2	no	—
612	C₂²⋊C₄	—	137	1	no	—
613	C₂²⋊C₄	—	137	1	no	—
614	C₂²⋊C₄	—	137	2	no	—
615	C₂²⋊C₄	—	137	1	no	—
616	C₂²⋊C₄	—	137	2	no	—
617	C₂²⋊C₄	—	137	2	no	—
618	C₂²⋊C₄	—	137	1	no	—
619	C₂²⋊C₄	—	137	2	no	—
620	C₂²⋊C₄	—	137	2	no	—
621	C₂²⋊C₄	—	137	2	no	—
622	C₂²⋊C₄	—	137	2	no	—
623	C₂²⋊C₄	—	137	2	no	—
624	C₂²⋊C₄	C₂²×D₁₃₇	1	2	yes	—
625	C₂²⋊C₄	C₂²×D₁₃₇	1	2	yes	—
626	C₂²⋊C₄	C₂²×D₁₃₇	1	2	yes	—
627	C₂²⋊C₄	C₂²×D₁₃₇	1	2	yes	—
628	C₂²⋊C₄	C₂²×D₁₃₇	1	2	yes	—
629	C₄²	—	137	1	no	—
630	C₄²	—	137	2	no	—
631	C₄²	—	137	1	no	—
632	C₄²	—	137	2	no	—
633	C₄²	—	137	1	no	—
634	C₄²	—	137	1	no	—
635	C₄²	C₂²×D₁₃₇	1	2	yes	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	274	4	no	—
640	C₂³	—	274	4	no	—
641	C₂³	—	274	2	no	—
642	C₂³	—	274	4	no	—
643	C₂³	—	274	2	no	—
644	C₂³	—	274	4	no	—
645	C₂³	—	548	1	no	—
646	C₂³	—	548	2	no	—
647	C₂³	—	548	2	no	—
648	C₂³	—	137	1	no	—
649	C₂³	—	137	2	no	—
650	C₂³	—	137	1	no	—
651	C₂³	—	137	2	no	—
652	C₂³	C₂³×D₁₃₇	1	2	yes	—
653	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
654	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
655	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	274	4	no	—
658	Q₈	—	274	4	no	—
659	Q₈	—	274	2	no	—
660	Q₈	—	137	4	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	274	4	no	—
666	D₄	—	274	4	no	—
667	D₄	—	274	4	no	—
668	D₄	—	274	4	no	—
669	D₄	—	274	4	no	—
670	D₄	—	274	2	no	—
671	D₄	—	274	4	no	—
672	D₄	—	274	2	no	—
673	D₄	—	274	4	no	—
674	D₄	—	274	4	no	—
675	D₄	—	274	4	no	—
676	D₄	—	274	2	no	—
677	D₄	—	274	2	no	—
678	D₄	—	548	2	no	—
679	D₄	—	548	2	no	—
680	D₄	—	137	8	no	—
681	D₄	—	137	4	no	—
682	D₄	—	137	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	274	4	no	—
690	C₂×C₄	—	274	4	no	—
691	C₂×C₄	—	274	4	no	—
692	C₂×C₄	—	274	4	no	—
693	C₂×C₄	—	274	4	no	—
694	C₂×C₄	—	274	2	no	—
695	C₂×C₄	—	274	4	no	—
696	C₂×C₄	—	274	4	no	—
697	C₂×C₄	—	274	2	no	—
698	C₂×C₄	—	274	2	no	—
699	C₂×C₄	—	274	2	no	—
700	C₂×C₄	—	274	2	no	—
701	C₂×C₄	—	274	4	no	—
702	C₂×C₄	—	274	2	no	—
703	C₂×C₄	—	548	2	no	—
704	C₂×C₄	—	548	1	no	—
705	C₂×C₄	—	137	1	no	—
706	C₂×C₄	—	137	1	no	—
707	C₂×C₄	—	137	1	no	—
708	C₂×C₄	—	137	1	no	—
709	C₂×C₄	—	137	1	no	—
710	C₂×C₄	—	137	2	no	—
711	C₂×C₄	—	137	1	no	—
712	C₂×C₄	—	137	2	no	—
713	C₂×C₄	—	137	8	no	—
714	C₂×C₄	D₄×D₁₃₇	1	4	yes	complemented
715	C₂×C₄	C₂³×D₁₃₇	1	2	yes	—
716	C₂×C₄	C₂³×D₁₃₇	1	2	yes	—
717	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
718	C₂×C₄	C₂³×D₁₃₇	1	2	yes	—
719	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
720	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
721	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	274	1	no	—
734	C₂²	—	274	2	no	—
735	C₂²	—	274	2	no	—
736	C₂²	—	274	1	no	—
737	C₂²	—	274	2	no	—
738	C₂²	—	274	1	no	—
739	C₂²	—	274	2	no	—
740	C₂²	—	274	1	no	—
741	C₂²	—	274	1	no	—
742	C₂²	—	274	2	no	—
743	C₂²	—	548	8	no	—
744	C₂²	—	548	4	no	—
745	C₂²	—	548	8	no	—
746	C₂²	—	137	4	no	—
747	C₂²	—	137	2	no	—
748	C₂²	C₂×D₄×D₁₃₇	1	2	yes	—
749	C₂²	#41×D₁₃₇	1	2	yes	complemented
750	C₂²	C₂⁴×D₁₃₇	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	274	1	no	—
757	C₄	—	274	2	no	—
758	C₄	—	274	1	no	—
759	C₄	—	274	1	no	—
760	C₄	—	274	1	no	—
761	C₄	—	274	1	no	—
762	C₄	—	137	4	no	—
763	C₄	—	137	2	no	—
764	C₄	C₂×D₄×D₁₃₇	1	2	yes	—
765	C₄	C₂×D₄×D₁₃₇	1	2	yes	—
766	C₂	—	2	2	no	—
767	C₂	—	2	2	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	2	no	—
770	C₂	—	274	2	no	—
771	C₂	—	274	4	no	—
772	C₂	—	548	2	no	—
773	C₂	—	548	1	no	—
774	C₂	C₂²×D₄×D₁₃₇	1	1	yes	characteristic
775	C₂	C₂×#41×D₁₃₇	1	1	yes	characteristic
776	C₂	#22578239	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃₇
commutator, socle, cosocle	C₂²×C₁₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₇
Fitting	#525×C₁₃₇	C₂
hypercenter	#525	D₁₃₇
hypocenter	C₁₃₇	D₄×#41
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555510	C₂	semidirect
2. C₂×#41×D₁₃₇	C₂	semidirect
3. #22578071	C₂	semidirect
4. #22578066	C₂	semidirect
5. #22578063	C₂	semidirect
6. #22578059	C₂	semidirect
7. #22578055	C₂	semidirect
8. #22578051	C₂	semidirect
9. #22578050	C₂	semidirect
10. #22578045	C₂	semidirect
11. #22578044	C₂	semidirect
12. #22578040	C₂	semidirect
13. #22578037	C₂	semidirect
14. #22578035	C₂	semidirect
15. #22577950	C₂	semidirect
16. #22577949	C₂	semidirect
17. #22577915	C₂	semidirect
18. #22577912	C₂	semidirect
19. #22577912	C₂	semidirect
20. #22577871	C₂	semidirect
21. C₂×C₄×C₂²⋊D₁₃₇	C₂	semidirect
22. C₄×D₄×D₁₃₇	C₂	semidirect
23. #525×C₁₃₇	C₂	semidirect
24. C₂×#14555511	C₂²	semidirect
27. C₂×#14555510	C₂²	semidirect
28. C₂×#14555510	C₂²	semidirect
29. C₂×#14555510	C₂²	semidirect
30. C₂×#14555510	C₂²	semidirect
31. C₂×#14555510	C₂²	semidirect
32. C₂×#14555510	C₂²	semidirect
33. C₂×#14555509	C₂²	semidirect
34. C₂×#14555509	C₂²	semidirect
36. C₂²×Dic₂₇₄	C₂²	semidirect
37. C₂×Q₈×D₁₃₇	C₂²	semidirect
38. C₂²×D₅₄₈	C₂²	semidirect
40. C₂²×C₂²⋊D₁₃₇	C₂²	semidirect
42. C₂×D₄×D₁₃₇	C₂²	semidirect
43. C₂×D₄×D₁₃₇	C₂²	semidirect
44. C₂²×C₄×D₁₃₇	C₂²	semidirect
45. C₂²×C₄×D₁₃₇	C₂²	semidirect
46. C₂²×C₄×D₁₃₇	C₂²	semidirect
47. #17984087	C₂²	semidirect
48. #17984086	C₂²	semidirect
49. #17984084	C₂²	semidirect
50. #17984084	C₂²	semidirect
51. #17984077	C₂²	semidirect
52. #17984075	C₂²	semidirect
53. #17984074	C₂²	semidirect
54. #17984074	C₂²	semidirect
55. #17984073	C₂²	semidirect
56. #17984073	C₂²	semidirect
57. #17984072	C₂²	semidirect
58. #17984070	C₂²	semidirect
59. #17984070	C₂²	semidirect
60. #17984068	C₂²	semidirect
61. #17984068	C₂²	semidirect
62. #17984066	C₂²	semidirect
63. #17984066	C₂²	semidirect
64. #17984065	C₂²	semidirect
65. #17984065	C₂²	semidirect
66. #17984063	C₂²	semidirect
67. #17984063	C₂²	semidirect
68. #17984063	C₂²	semidirect
69. #17984061	C₂²	semidirect
70. #17984061	C₂²	semidirect
71. #17984061	C₂²	semidirect
72. #17984061	C₂²	semidirect
73. #17984060	C₂²	semidirect
74. #17984060	C₂²	semidirect
75. #17984060	C₂²	semidirect
76. #17984060	C₂²	semidirect
77. #17984059	C₂²	semidirect
78. #17984058	C₂²	semidirect
79. #17984058	C₂²	semidirect
80. #17984058	C₂²	semidirect
81. #17984056	C₂²	semidirect
82. #17984056	C₂²	semidirect
83. #17984053	C₂²	semidirect
84. #17984053	C₂²	semidirect
85. C₄×D₅₄₈	C₂²	semidirect
86. C₄×D₅₄₈	C₂²	semidirect
87. D₄×Dic₁₃₇	C₂²	semidirect
88. #17984050	C₂²	semidirect
89. #17984050	C₂²	semidirect
90. #17984050	C₂²	semidirect
93. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
94. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
95. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
96. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
97. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
98. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
99. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
100. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
102. #17984048	C₂²	semidirect
103. #17984048	C₂²	semidirect
104. #17984048	C₂²	semidirect
105. #17984045	C₂²	semidirect
106. C₂×#14555489	C₂²	semidirect
107. C₄⋊C₄×D₁₃₇	C₂²	semidirect
108. C₂×C₂²⋊Dic₁₃₇	C₂²	semidirect
109. C₂×#14555487	C₂²	semidirect
110. C₂²⋊C₄×D₁₃₇	C₂²	semidirect
111. C₂²⋊C₄×D₁₃₇	C₂²	semidirect
112. C₂×C₄×Dic₁₃₇	C₂²	semidirect
113. C₄²×D₁₃₇	C₂²	semidirect
114. C₂×#41×C₁₃₇	C₂²	semidirect
115. C₂³×C₄×C₁₃₇	C₂²	semidirect
116. #123×C₁₃₇	C₂²	semidirect
117. C₂²⋊Q₈×C₁₃₇	C₂²	semidirect
118. C₂²⋊Q₈×C₁₃₇	C₂²	semidirect
119. #121×C₁₃₇	C₂²	semidirect
120. #121×C₁₃₇	C₂²	semidirect
121. #120×C₁₃₇	C₂²	semidirect
122. C₄×D₄×C₁₃₇	C₂²	semidirect
123. C₄×D₄×C₁₃₇	C₂²	semidirect
124. #117×C₁₃₇	C₂²	semidirect
135. #14555510	D₄	semidirect
263. Dic₂₇₄	C₂×D₄	semidirect
269. D₅₄₈	C₂×D₄	semidirect
280. C₂²⋊D₁₃₇	C₂×D₄	semidirect
281. C₂²⋊D₁₃₇	#41	semidirect
306. C₄×D₁₃₇	C₂×D₄	semidirect
325. C₂×C₄×C₁₃₇	C₂×D₄	semidirect
345. C₂²×C₁₃₇	C₂×#41	semidirect
361. C₂×D₁₃₇	C₂×#41	semidirect
376. Dic₁₃₇	C₂×#41	semidirect
388. C₁₃₇	D₄×#41	semidirect
409. #525	D₁₃₇	semidirect
425. C₂×#41	C₂×D₁₃₇	semidirect
437. C₂³×C₄	C₂×D₁₃₇	semidirect
451. #123	C₂×D₁₃₇	semidirect
458. C₂²⋊Q₈	C₂×D₁₃₇	semidirect
459. C₂²⋊Q₈	C₂×D₁₃₇	semidirect
472. #121	C₂×D₁₃₇	semidirect
473. #121	C₂×D₁₃₇	semidirect
479. #120	C₂×D₁₃₇	semidirect
502. C₄×D₄	C₂×D₁₃₇	semidirect
503. C₄×D₄	C₂×D₁₃₇	semidirect
505. #117	C₂×D₁₃₇	semidirect
714. C₂×C₄	D₄×D₁₃₇	semidirect
749. C₂²	#41×D₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14555510	2
C₂×#41×D₁₃₇	2
#22578071	2
#22578066	2
#22578063	2
#22578059	2
#22578055	2
#22578051	2
#22578050	2
#22578045	2
#22578044	2
#22578040	2
#22578037	2
#22578035	2
#22577950	2
#22577949	2
#22577915	2
#22577912	2
#22577871	2
C₂×C₄×C₂²⋊D₁₃₇	2
C₄×D₄×D₁₃₇	2
#525×C₁₃₇	2
D₄×#41	137