Subgroups — #31789522

Order 17536.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#22577479	C₂	1	1	yes	maximal, characteristic, complemented
5	#22577478	C₂	1	1	yes	maximal, characteristic, complemented
6	#22577476	C₂	1	1	yes	maximal, characteristic, complemented
7	#22577475	C₂	1	1	yes	maximal, characteristic, complemented
8	#22577473	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#22577466	C₂	1	1	yes	maximal, characteristic, complemented
11	#22577425	C₂	1	1	yes	maximal, characteristic, complemented
12	#22577365	C₂	1	1	yes	maximal, characteristic, complemented
13	#22577365	C₂	1	1	yes	maximal, characteristic, complemented
14	#22577355	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₃₇	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#14555494	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555493	—	2	4	no	—
21	C₂×#14555493	C₂²	1	1	yes	characteristic
22	C₂×#14555493	C₂²	1	1	yes	characteristic
23	C₂×#14555493	C₂²	1	1	yes	characteristic
24	C₂×#14555493	C₂²	1	1	yes	characteristic
25	C₂×#14555493	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14555493	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₁₃₇	—	2	4	no	—
28	C₂²×#11764040	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₅₄₈	C₂²	1	1	yes	characteristic
32	D₄×Dic₁₃₇	C₄	1	1	yes	characteristic
33	#17984050	C₄	1	1	yes	characteristic
34	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
36	#17984048	C₄	1	1	yes	characteristic
37	#17984048	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
39	C₂²⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
40	C₂²⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
41	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic
42	C₄⋊#11764040	C₂²	1	1	yes	characteristic, complemented
43	#17984017	C₂²	1	1	yes	characteristic, complemented
44	#17984017	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11764040	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊#11764040	C₂²	1	1	yes	characteristic, complemented
47	#17984000	C₂²	1	1	yes	characteristic, complemented
48	#17984000	C₂²	1	1	yes	characteristic, complemented
49	#17984000	C₂²	1	1	yes	characteristic, complemented
50	#17984000	C₂²	1	1	yes	characteristic, complemented
51	#17983999	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
60	#97×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₂×D₅₄₈	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
66	D₄×D₁₃₇	—	2	4	no	—
67	C₂²×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₁₃₇	—	2	2	no	—
70	C₂×C₄×D₁₃₇	—	2	2	no	—
71	C₂×C₄×D₁₃₇	—	2	2	no	—
72	C₂×C₄×D₁₃₇	—	2	2	no	—
73	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
82	#14555494	—	2	2	no	—
83	#14555493	—	2	2	no	—
84	#14555493	—	2	2	no	—
85	#14555493	—	2	2	no	—
86	#14555493	—	2	2	no	—
87	#14555493	—	2	2	no	—
88	#14555493	D₄	1	4	yes	complemented
89	C₂×#11764040	—	2	2	no	—
90	C₂×#11764040	C₂³	1	1	yes	characteristic
91	C₂×#11764040	C₂³	1	1	yes	characteristic
92	C₂×#11764040	C₂³	1	1	yes	characteristic
93	C₂×#11764040	C₂³	1	1	yes	characteristic
94	C₈×D₁₃₇	—	2	2	no	—
95	C₈×D₁₃₇	—	2	2	no	—
96	C₄⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
97	#14555489	C₂×C₄	1	1	yes	characteristic
98	#14555489	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
101	#14555487	C₂×C₄	1	1	yes	characteristic
102	#14555487	C₂×C₄	1	1	yes	characteristic
103	#14555487	C₂×C₄	1	1	yes	characteristic
104	#14555487	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
107	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
111	M₁₆×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
120	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
121	C₂²×D₁₃₇	—	2	2	no	—
122	C₂²×D₁₃₇	—	2	2	no	—
123	C₂²×D₁₃₇	—	2	2	no	—
124	C₂²×D₁₃₇	—	2	2	no	—
125	C₂²×D₁₃₇	—	4	1	no	—
126	C₂²×D₁₃₇	—	4	1	no	—
127	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
130	D₅₄₈	—	2	2	no	—
131	C₂²⋊D₁₃₇	—	2	2	no	—
132	C₂²⋊D₁₃₇	M₁₆	1	4	yes	complemented
133	C₂×Dic₁₃₇	—	2	2	no	—
134	C₂×Dic₁₃₇	—	2	2	no	—
135	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
140	C₄×D₁₃₇	—	2	2	no	—
141	C₄×D₁₃₇	—	2	2	no	—
142	C₄×D₁₃₇	—	2	1	no	—
143	C₄×D₁₃₇	—	2	1	no	—
144	C₄×D₁₃₇	—	2	1	no	—
145	C₄×D₁₃₇	—	2	1	no	—
146	C₄×D₁₃₇	—	2	2	no	—
147	C₄×D₁₃₇	—	2	2	no	—
148	C₄×D₁₃₇	—	2	2	no	—
149	C₄×D₁₃₇	—	4	1	no	—
150	C₄×D₁₃₇	C₂×D₄	1	2	yes	—
151	C₄×D₁₃₇	#41	1	2	yes	—
152	#11764040	—	2	1	no	—
153	#11764040	—	2	1	no	—
154	#11764040	—	2	1	no	—
155	#11764040	C₂×D₄	1	2	yes	complemented
156	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
157	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
158	D₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	2	1	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
168	C₈×C₁₃₇	—	2	1	no	—
169	C₈×C₁₃₇	—	2	1	no	—
170	C₈×C₁₃₇	—	2	1	no	—
171	C₈×C₁₃₇	C₂×D₄	1	2	yes	complemented
172	C₂²×C₁₃₇	—	2	1	no	—
173	C₂²×C₁₃₇	—	2	1	no	—
174	C₂²×C₁₃₇	—	2	1	no	—
175	C₂²×C₁₃₇	—	2	1	no	—
176	C₂²×C₁₃₇	—	2	1	no	—
177	C₂²×C₁₃₇	C₂×M₁₆	1	2	yes	complemented
178	C₂²×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×D₁₃₇	—	2	1	no	—
180	C₂×D₁₃₇	—	2	1	no	—
181	C₂×D₁₃₇	—	2	1	no	—
182	C₂×D₁₃₇	—	2	1	no	—
183	C₂×D₁₃₇	—	2	1	no	—
184	C₂×D₁₃₇	—	2	1	no	—
185	C₂×D₁₃₇	—	2	1	no	—
186	C₂×D₁₃₇	—	4	4	no	—
187	C₂×D₁₃₇	—	4	4	no	—
188	C₂×D₁₃₇	C₄×D₄	1	2	yes	—
189	C₂×D₁₃₇	C₂×M₁₆	1	2	yes	complemented
190	C₄×C₁₃₇	—	2	1	no	—
191	C₄×C₁₃₇	—	2	1	no	—
192	C₄×C₁₃₇	—	2	1	no	—
193	C₄×C₁₃₇	—	2	1	no	—
194	C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
196	Dic₁₃₇	—	2	1	no	—
197	Dic₁₃₇	—	2	1	no	—
198	Dic₁₃₇	—	2	1	no	—
199	Dic₁₃₇	C₄×D₄	1	2	yes	—
200	Dic₁₃₇	C₂×M₁₆	1	2	yes	complemented
201	C₂×C₁₃₇	—	2	2	no	—
202	C₂×C₁₃₇	—	4	1	no	—
203	C₂×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
205	C₂×C₁₃₇	#568	1	1	yes	characteristic
206	D₁₃₇	—	2	2	no	—
207	D₁₃₇	—	2	2	no	—
208	D₁₃₇	—	4	1	no	—
209	C₁₃₇	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
210	D₄×M₁₆	—	137	1	no	maximal, Sylow
211	C₂²×M₁₆	—	137	1	no	—
212	C₂²×M₁₆	—	137	1	no	—
213	C₂×C₄×D₄	—	137	1	no	—
214	#436	—	137	1	no	—
215	#436	—	137	1	no	—
216	#435	—	137	1	no	—
217	#435	—	137	1	no	—
218	#435	—	137	1	no	—
219	#435	D₁₃₇	1	1	yes	characteristic, complemented
220	C₈×D₄	—	137	1	no	—
221	C₈×D₄	—	137	1	no	—
222	#423	—	137	1	no	—
223	#407	—	137	1	no	—
224	#407	—	137	1	no	—
225	C₄×M₁₆	—	137	1	no	—
226	C₂²×D₄	—	137	1	no	—
227	C₂³×C₄	—	137	1	no	—
228	C₂³×C₄	—	137	1	no	—
229	C₂×M₁₆	—	274	4	no	—
230	C₂×M₁₆	—	274	4	no	—
231	C₂×M₁₆	—	137	1	no	—
232	C₂×M₁₆	—	137	1	no	—
233	C₂×M₁₆	—	137	1	no	—
234	C₂×M₁₆	—	137	1	no	—
235	C₂×M₁₆	—	137	1	no	—
236	C₂×M₁₆	—	137	1	no	—
237	C₂×M₁₆	—	137	1	no	—
238	C₂×M₁₆	C₂×D₁₃₇	1	1	yes	characteristic, complemented
239	C₂²×C₈	—	137	1	no	—
240	C₂²×C₈	—	137	1	no	—
241	C₂²×C₈	—	137	1	no	—
242	C₂²×C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
243	C₄×D₄	—	137	1	no	—
244	C₄×D₄	—	137	1	no	—
245	C₄×D₄	—	137	1	no	—
246	C₄×D₄	—	137	1	no	—
247	C₄×D₄	—	137	1	no	—
248	C₄×D₄	—	137	1	no	—
249	C₄×D₄	—	137	1	no	—
250	C₄×D₄	C₂×D₁₃₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	137	1	no	—
252	C₂×C₂²⋊C₄	—	137	1	no	—
253	C₂×C₂²⋊C₄	—	137	1	no	—
254	C₂×C₄²	—	137	1	no	—
255	C₄⋊C₈	—	137	1	no	—
256	C₄⋊C₈	—	137	1	no	—
257	C₄⋊C₈	—	137	1	no	—
258	C₄⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
259	C₂²⋊C₈	—	137	1	no	—
260	C₂²⋊C₈	—	137	1	no	—
261	C₂²⋊C₈	—	137	1	no	—
262	C₂²⋊C₈	—	137	1	no	—
263	C₂²⋊C₈	—	137	1	no	—
264	C₂²⋊C₈	—	137	1	no	—
265	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
266	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
267	#97	—	137	1	no	—
268	#97	C₂×D₁₃₇	1	1	yes	characteristic, complemented
269	C₄×C₈	—	137	1	no	—
270	C₄×C₈	—	137	1	no	—
271	C₂⁴	—	137	1	no	—
272	C₂⁴	—	137	1	no	—
273	C₂×D₄	—	274	4	no	—
274	C₂×D₄	—	137	1	no	—
275	C₂×D₄	—	137	1	no	—
276	C₂×D₄	—	137	1	no	—
277	C₂×D₄	C₄×D₁₃₇	1	1	yes	characteristic
278	C₂²×C₄	—	274	2	no	—
279	C₂²×C₄	—	274	2	no	—
280	C₂²×C₄	—	274	2	no	—
281	C₂²×C₄	—	274	2	no	—
282	C₂²×C₄	—	137	1	no	—
283	C₂²×C₄	—	137	1	no	—
284	C₂²×C₄	—	137	1	no	—
285	C₂²×C₄	—	137	1	no	—
286	C₂²×C₄	—	137	1	no	—
287	C₂²×C₄	—	137	1	no	—
288	C₂²×C₄	—	137	1	no	—
289	C₂²×C₄	—	137	1	no	—
290	C₂²×C₄	—	137	1	no	—
291	C₂²×C₄	—	137	1	no	—
292	C₂²×C₄	—	137	1	no	—
293	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	274	2	no	—
297	M₁₆	—	274	2	no	—
298	M₁₆	—	274	2	no	—
299	M₁₆	—	274	2	no	—
300	M₁₆	—	274	2	no	—
301	M₁₆	—	274	2	no	—
302	M₁₆	—	137	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	274	2	no	—
305	C₂×C₈	—	274	2	no	—
306	C₂×C₈	—	274	2	no	—
307	C₂×C₈	—	137	1	no	—
308	C₂×C₈	—	137	1	no	—
309	C₂×C₈	—	137	1	no	—
310	C₂×C₈	—	137	1	no	—
311	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
315	C₄⋊C₄	—	137	1	no	—
316	C₄⋊C₄	—	137	1	no	—
317	C₄⋊C₄	—	137	1	no	—
318	C₄⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
319	C₂²⋊C₄	—	137	1	no	—
320	C₂²⋊C₄	—	137	1	no	—
321	C₂²⋊C₄	—	137	1	no	—
322	C₂²⋊C₄	—	137	1	no	—
323	C₂²⋊C₄	—	137	1	no	—
324	C₂²⋊C₄	—	137	1	no	—
325	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
326	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
327	C₄²	—	137	1	no	—
328	C₄²	—	137	1	no	—
329	C₄²	—	137	1	no	—
330	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
331	C₂³	—	274	2	no	—
332	C₂³	—	274	2	no	—
333	C₂³	—	274	2	no	—
334	C₂³	—	274	2	no	—
335	C₂³	—	548	1	no	—
336	C₂³	—	548	1	no	—
337	C₂³	—	137	1	no	—
338	C₂³	—	137	1	no	—
339	C₂³	—	137	1	no	—
340	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	274	2	no	—
344	D₄	—	274	2	no	—
345	D₄	—	137	4	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	274	2	no	—
351	C₂×C₄	—	274	2	no	—
352	C₂×C₄	—	274	2	no	—
353	C₂×C₄	—	274	2	no	—
354	C₂×C₄	—	274	2	no	—
355	C₂×C₄	—	274	2	no	—
356	C₂×C₄	—	274	2	no	—
357	C₂×C₄	—	274	1	no	—
358	C₂×C₄	—	274	1	no	—
359	C₂×C₄	—	274	1	no	—
360	C₂×C₄	—	274	1	no	—
361	C₂×C₄	—	548	1	no	—
362	C₂×C₄	—	137	1	no	—
363	C₂×C₄	—	137	1	no	—
364	C₂×C₄	—	137	1	no	—
365	C₂×C₄	—	137	1	no	—
366	C₂×C₄	—	137	1	no	—
367	C₂×C₄	—	137	2	no	—
368	C₂×C₄	—	137	2	no	—
369	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	274	1	no	—
378	C₈	—	274	1	no	—
379	C₈	—	274	1	no	—
380	C₈	—	137	2	no	—
381	C₈	D₄×D₁₃₇	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	274	1	no	—
388	C₂²	—	274	1	no	—
389	C₂²	—	274	1	no	—
390	C₂²	—	274	1	no	—
391	C₂²	—	274	1	no	—
392	C₂²	—	274	1	no	—
393	C₂²	—	274	1	no	—
394	C₂²	—	548	4	no	—
395	C₂²	—	548	4	no	—
396	C₂²	—	137	2	no	—
397	C₂²	—	137	2	no	—
398	C₂²	M₁₆×D₁₃₇	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₁₃₇	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	274	1	no	—
405	C₄	—	274	1	no	—
406	C₄	—	274	1	no	—
407	C₄	—	137	2	no	—
408	C₄	—	137	2	no	—
409	C₄	C₂×D₄×D₁₃₇	1	1	yes	characteristic
410	C₄	#41×D₁₃₇	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	274	2	no	—
414	C₂	—	274	2	no	—
415	C₂	—	548	1	no	—
416	C₂	C₄×D₄×D₁₃₇	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₁₃₇	1	1	yes	characteristic
418	C₂	#22578168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃₇
commutator, socle	C₂²×C₁₃₇	C₂³×C₄
Fitting	#435×C₁₃₇	C₂
prime radical	C₂×D₄×D₁₃₇	C₄
cosocle	C₂×C₄×C₁₃₇	C₂⁴
hypercenter	#435	D₁₃₇
hypocenter	C₁₃₇	D₄×M₁₆
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555493	C₂	semidirect
2. C₂×M₁₆×D₁₃₇	C₂	semidirect
4. #22577479	C₂	semidirect
5. #22577478	C₂	semidirect
6. #22577476	C₂	semidirect
7. #22577475	C₂	semidirect
8. #22577473	C₂	semidirect
9. C₈×C₂²⋊D₁₃₇	C₂	semidirect
10. #22577466	C₂	semidirect
11. #22577425	C₂	semidirect
12. #22577365	C₂	semidirect
13. #22577365	C₂	semidirect
14. #22577355	C₂	semidirect
15. #435×C₁₃₇	C₂	semidirect
19. C₂×#14555494	C₂²	semidirect
25. C₂×#14555493	C₂²	semidirect
26. C₂×#14555493	C₂²	semidirect
28. C₂²×#11764040	C₂²	semidirect
29. C₂×C₈×D₁₃₇	C₂²	semidirect
30. C₂×C₈×D₁₃₇	C₂²	semidirect
42. C₄⋊#11764040	C₂²	semidirect
43. #17984017	C₂²	semidirect
44. #17984017	C₂²	semidirect
45. C₂²⋊#11764040	C₂²	semidirect
46. C₂²⋊#11764040	C₂²	semidirect
47. #17984000	C₂²	semidirect
48. #17984000	C₂²	semidirect
49. #17984000	C₂²	semidirect
50. #17984000	C₂²	semidirect
51. #17983999	C₂²	semidirect
52. C₈×Dic₁₃₇	C₂²	semidirect
53. C₈×Dic₁₃₇	C₂²	semidirect
54. C₂×M₁₆×C₁₃₇	C₂²	semidirect
55. C₂²×C₈×C₁₃₇	C₂²	semidirect
57. C₄⋊C₈×C₁₃₇	C₂²	semidirect
58. C₂²⋊C₈×C₁₃₇	C₂²	semidirect
59. C₂²⋊C₈×C₁₃₇	C₂²	semidirect
60. #97×C₁₃₇	C₂²	semidirect
88. #14555493	D₄	semidirect
132. C₂²⋊D₁₃₇	M₁₆	semidirect
155. #11764040	C₂×D₄	semidirect
171. C₈×C₁₃₇	C₂×D₄	semidirect
177. C₂²×C₁₃₇	C₂×M₁₆	semidirect
189. C₂×D₁₃₇	C₂×M₁₆	semidirect
200. Dic₁₃₇	C₂×M₁₆	semidirect
209. C₁₃₇	D₄×M₁₆	semidirect
219. #435	D₁₃₇	semidirect
238. C₂×M₁₆	C₂×D₁₃₇	semidirect
242. C₂²×C₈	C₂×D₁₃₇	semidirect
258. C₄⋊C₈	C₂×D₁₃₇	semidirect
265. C₂²⋊C₈	C₂×D₁₃₇	semidirect
266. C₂²⋊C₈	C₂×D₁₃₇	semidirect
268. #97	C₂×D₁₃₇	semidirect
381. C₈	D₄×D₁₃₇	semidirect
398. C₂²	M₁₆×D₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14555493	2
C₂×M₁₆×D₁₃₇	2
C₄×D₄×D₁₃₇	2
#22577479	2
#22577478	2
#22577476	2
#22577475	2
#22577473	2
C₈×C₂²⋊D₁₃₇	2
#22577466	2
#22577425	2
#22577365	2
#22577355	2
#435×C₁₃₇	2
D₄×M₁₆	137