Subgroups — #532×D₁₃₇ #31794066

Order 17536.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₃₇	C₂	1	2	yes	maximal, complemented
2	#22577954	C₂	1	1	yes	maximal, characteristic, complemented
3	#22577953	C₂	1	1	yes	maximal, characteristic, complemented
4	#22577952	C₂	1	2	yes	maximal, complemented
5	#22577951	C₂	1	1	yes	maximal, characteristic, complemented
6	#22577950	C₂	1	4	yes	maximal, complemented
7	#22577949	C₂	1	2	yes	maximal, complemented
8	#22577948	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#127×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#124×D₁₃₇	C₂	1	2	yes	maximal, complemented
12	#121×D₁₃₇	C₂	1	4	yes	maximal, complemented
13	C₄×D₄×D₁₃₇	C₂	1	4	yes	maximal, complemented
14	C₂×C₄²×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#532×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555511	C₂²	1	2	yes	complemented
17	C₂×#14555510	C₂²	1	2	yes	complemented
18	C₂×#14555510	C₂²	1	4	yes	complemented
19	C₂×#14555509	C₂²	1	4	yes	complemented
20	C₂×#14555509	C₂²	1	2	yes	complemented
21	#41×D₁₃₇	—	2	16	no	—
22	C₂×Q₈×D₁₃₇	C₂²	1	2	yes	—
23	C₂×D₄×D₁₃₇	C₂²	1	2	yes	—
24	C₂×D₄×D₁₃₇	C₂²	1	4	yes	—
25	C₂×D₄×D₁₃₇	C₂²	1	4	yes	—
26	C₂²×C₄×D₁₃₇	C₂²	1	4	yes	—
27	C₂²×C₄×D₁₃₇	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
29	#17984088	C₂²	1	1	yes	characteristic, complemented
30	#17984087	C₂²	1	4	yes	complemented
31	#17984086	C₂²	1	2	yes	complemented
32	#17984085	C₂²	1	1	yes	characteristic, complemented
33	#17984084	C₂²	1	4	yes	complemented
34	#17984084	C₂²	1	2	yes	complemented
35	#17984077	C₂²	1	2	yes	complemented
36	#17984076	C₂²	1	2	yes	complemented
37	#17984075	C₂²	1	2	yes	complemented
38	#17984074	C₂²	1	8	yes	complemented
39	#17984063	C₂²	1	4	yes	complemented
40	#17984062	C₂²	1	4	yes	complemented
41	#17984061	C₂²	1	8	yes	complemented
42	#17984060	C₂²	1	8	yes	complemented
43	#17984059	C₂²	1	4	yes	complemented
44	C₄×D₅₄₈	C₂²	1	4	yes	complemented
45	D₄×Dic₁₃₇	C₂²	1	4	yes	complemented
46	#17984050	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₁₃₇	C₂²	1	8	yes	complemented
48	#17984048	C₂²	1	8	yes	complemented
49	C₄⋊C₄×D₁₃₇	C₂²	1	4	yes	—
50	C₂²⋊C₄×D₁₃₇	C₂²	1	8	yes	—
51	C₂×C₄×Dic₁₃₇	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
53	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic
54	C₄²×D₁₃₇	C₂²	1	2	yes	—
55	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic
56	C₄²×D₁₃₇	C₂²	1	2	yes	complemented
57	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
58	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₃₇	C₂²	1	2	yes	complemented
60	C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
61	#127×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
62	#124×C₁₃₇	C₂²	1	2	yes	complemented
63	#121×C₁₃₇	C₂²	1	4	yes	complemented
64	C₄×D₄×C₁₃₇	C₂²	1	4	yes	complemented
65	C₂×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
66	C₂³×D₁₃₇	C₂³	1	4	yes	—
67	C₂³×D₁₃₇	C₂³	1	1	yes	characteristic
68	#14555511	—	2	8	no	—
69	#14555510	—	2	16	no	—
70	#14555510	—	2	8	no	—
71	#14555509	—	2	16	no	—
72	#14555509	—	2	8	no	—
73	C₂×Dic₂₇₄	C₂³	1	4	yes	—
74	C₂×Dic₂₇₄	C₂³	1	2	yes	—
75	Q₈×D₁₃₇	—	2	8	no	—
76	C₂×D₅₄₈	C₂³	1	4	yes	—
77	C₂×D₅₄₈	C₂³	1	4	yes	—
78	C₂×D₅₄₈	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₁₃₇	C₂³	1	8	yes	—
80	C₂×C₂²⋊D₁₃₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₃₇	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₃₇	C₂³	1	4	yes	—
83	D₄×D₁₃₇	—	2	16	no	—
84	D₄×D₁₃₇	—	2	8	no	—
85	D₄×D₁₃₇	—	2	16	no	—
86	C₂²×Dic₁₃₇	C₂³	1	2	yes	—
87	C₂²×Dic₁₃₇	C₂³	1	4	yes	—
88	C₂²×Dic₁₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₃₇	—	2	16	no	—
90	C₂×C₄×D₁₃₇	—	2	8	no	—
91	C₂×C₄×D₁₃₇	D₄	1	8	yes	complemented
92	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
93	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
94	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
95	C₂×C₄×D₁₃₇	C₂³	1	4	yes	—
96	C₂×C₄×D₁₃₇	C₂³	1	4	yes	—
97	C₂×C₄×D₁₃₇	C₂³	1	4	yes	—
98	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₃₇	C₂³	1	2	yes	—
103	C₄⋊Dic₁₃₇	C₂³	1	4	yes	—
104	#14555489	C₂³	1	8	yes	—
105	C₂²⋊Dic₁₃₇	C₂³	1	8	yes	—
106	#14555487	C₂³	1	8	yes	—
107	#14555487	C₂³	1	8	yes	—
108	C₄×Dic₁₃₇	C₂³	1	2	yes	—
109	C₄×Dic₁₃₇	C₂³	1	2	yes	—
110	C₄×Dic₁₃₇	C₂³	1	2	yes	—
111	C₄×Dic₁₃₇	C₂³	1	2	yes	—
112	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
114	C₄×Dic₁₃₇	C₂³	1	2	yes	—
115	#41×C₁₃₇	—	2	8	no	—
116	C₂×Q₈×C₁₃₇	C₂³	1	2	yes	—
117	C₂×D₄×C₁₃₇	C₂³	1	4	yes	—
118	C₂×D₄×C₁₃₇	C₂³	1	4	yes	—
119	C₂×D₄×C₁₃₇	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₃₇	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₃₇	C₂³	1	4	yes	—
122	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
125	C₄²×C₁₃₇	C₂³	1	2	yes	—
126	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
127	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
128	C₂²×D₁₃₇	—	2	4	no	—
129	C₂²×D₁₃₇	—	2	8	no	—
130	C₂²×D₁₃₇	—	2	16	no	—
131	C₂²×D₁₃₇	C₂×D₄	1	4	yes	—
132	C₂²×D₁₃₇	C₂⁴	1	4	yes	—
133	C₂²×D₁₃₇	C₂⁴	1	1	yes	characteristic
134	C₂²×D₁₃₇	C₂⁴	1	1	yes	characteristic
135	Dic₂₇₄	—	2	4	no	—
136	Dic₂₇₄	—	2	8	no	—
137	D₅₄₈	—	2	8	no	—
138	D₅₄₈	—	2	4	no	—
139	D₅₄₈	—	2	8	no	—
140	C₂²⋊D₁₃₇	—	2	8	no	—
141	C₂²⋊D₁₃₇	—	2	8	no	—
142	C₂²⋊D₁₃₇	—	2	8	no	—
143	C₂²⋊D₁₃₇	—	2	16	no	—
144	C₂×Dic₁₃₇	—	2	8	no	—
145	C₂×Dic₁₃₇	—	2	4	no	—
146	C₂×Dic₁₃₇	C₂×D₄	1	4	yes	complemented
147	C₂×Dic₁₃₇	C₂⁴	1	2	yes	—
148	C₂×Dic₁₃₇	C₂⁴	1	4	yes	—
149	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
150	C₂×Dic₁₃₇	C₂⁴	1	1	yes	characteristic
151	C₂×Dic₁₃₇	C₂⁴	1	2	yes	—
152	C₄×D₁₃₇	—	2	8	no	—
153	C₄×D₁₃₇	—	2	4	no	—
154	C₄×D₁₃₇	—	2	8	no	—
155	C₄×D₁₃₇	—	2	4	no	—
156	C₄×D₁₃₇	—	2	8	no	—
157	C₄×D₁₃₇	—	2	4	no	—
158	C₄×D₁₃₇	C₂×D₄	1	4	yes	—
159	C₄×D₁₃₇	C₂×D₄	1	4	yes	—
160	C₄×D₁₃₇	C₂×D₄	1	4	yes	complemented
161	C₄×D₁₃₇	C₂×D₄	1	4	yes	complemented
162	C₄×D₁₃₇	#41	1	8	yes	complemented
163	C₂³×C₁₃₇	C₂⁴	1	4	yes	—
164	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
165	Q₈×C₁₃₇	—	2	4	no	—
166	D₄×C₁₃₇	—	2	8	no	—
167	D₄×C₁₃₇	—	2	4	no	—
168	D₄×C₁₃₇	—	2	8	no	—
169	C₂×C₄×C₁₃₇	—	2	8	no	—
170	C₂×C₄×C₁₃₇	—	2	4	no	—
171	C₂×C₄×C₁₃₇	C₂×D₄	1	4	yes	complemented
172	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₃₇	C₂⁴	1	4	yes	—
174	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
177	C₂²×C₁₃₇	—	2	2	no	—
178	C₂²×C₁₃₇	—	2	4	no	—
179	C₂²×C₁₃₇	—	2	8	no	—
180	C₂²×C₁₃₇	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₃₇	C₂⁵	1	1	yes	characteristic
182	C₂×D₁₃₇	—	2	2	no	—
183	C₂×D₁₃₇	—	2	8	no	—
184	C₂×D₁₃₇	—	2	4	no	—
185	C₂×D₁₃₇	—	2	8	no	—
186	C₂×D₁₃₇	—	4	16	no	—
187	C₂×D₁₃₇	C₂²×D₄	1	2	yes	—
188	C₂×D₁₃₇	C₂²×D₄	1	2	yes	—
189	C₂×D₁₃₇	C₂×#41	1	4	yes	—
190	C₄×C₁₃₇	—	2	4	no	—
191	C₄×C₁₃₇	—	2	2	no	—
192	C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
193	C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
194	C₄×C₁₃₇	C₂×#41	1	4	yes	complemented
195	Dic₁₃₇	—	2	4	no	—
196	Dic₁₃₇	—	2	2	no	—
197	Dic₁₃₇	C₂²×D₄	1	2	yes	—
198	Dic₁₃₇	C₂²×D₄	1	2	yes	—
199	Dic₁₃₇	C₂×#41	1	4	yes	complemented
200	C₂×C₁₃₇	—	2	2	no	—
201	C₂×C₁₃₇	—	4	4	no	—
202	C₂×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
203	C₂×C₁₃₇	C₂²×#41	1	2	yes	—
204	D₁₃₇	—	2	2	no	—
205	D₁₃₇	—	4	4	no	—
206	D₁₃₇	#532	1	4	yes	direct product factor
207	C₁₃₇	C₂×#532	1	1	yes	characteristic, complemented, Sylow
208	C₂×#532	—	137	1	no	maximal, Sylow
209	C₂²×#41	—	137	2	no	—
210	#532	—	137	2	no	—
211	#532	—	137	1	no	—
212	#532	—	137	1	no	—
213	#532	—	137	2	no	—
214	#532	—	137	4	no	—
215	#532	—	137	4	no	—
216	#532	—	137	1	no	—
217	#532	D₁₃₇	1	1	yes	characteristic, direct product factor
218	C₂×C₄⋊Q₈	—	137	1	no	—
219	C₂×#127	—	137	1	no	—
220	C₂×#124	—	137	2	no	—
221	C₂×#121	—	137	4	no	—
222	C₂×C₄×D₄	—	137	4	no	—
223	C₂²×C₄²	—	137	1	no	—
224	C₂×#41	—	274	16	no	—
225	C₂×#41	—	137	2	no	—
226	C₂×#41	—	137	2	no	—
227	C₂×#41	—	137	4	no	—
228	C₂×#41	—	137	2	no	—
229	C₂×#41	—	137	4	no	—
230	C₂×#41	C₂×D₁₃₇	1	2	yes	complemented
231	C₂²×Q₈	—	137	2	no	—
232	C₂²×D₄	—	137	4	no	—
233	C₂²×D₄	—	137	4	no	—
234	C₂²×D₄	—	137	2	no	—
235	C₂³×C₄	—	137	4	no	—
236	C₂³×C₄	—	137	2	no	—
237	C₂³×C₄	—	137	1	no	—
238	C₄⋊Q₈	—	137	2	no	—
239	C₄⋊Q₈	—	137	4	no	—
240	C₄⋊Q₈	—	137	1	no	—
241	C₄⋊Q₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
242	#127	—	137	2	no	—
243	#127	—	137	4	no	—
244	#127	—	137	1	no	—
245	#127	C₂×D₁₃₇	1	1	yes	characteristic, complemented
246	#124	—	137	2	no	—
247	#124	—	137	2	no	—
248	#124	—	137	8	no	—
249	#124	—	137	2	no	—
250	#124	C₂×D₁₃₇	1	2	yes	complemented
251	#121	—	137	4	no	—
252	#121	—	137	8	no	—
253	#121	—	137	4	no	—
254	#121	—	137	4	no	—
255	#121	—	137	8	no	—
256	#121	C₂×D₁₃₇	1	4	yes	complemented
257	C₄×D₄	—	137	4	no	—
258	C₄×D₄	—	137	8	no	—
259	C₄×D₄	—	137	4	no	—
260	C₄×D₄	—	137	8	no	—
261	C₄×D₄	—	137	4	no	—
262	C₄×D₄	C₂×D₁₃₇	1	4	yes	complemented
263	C₂×C₄⋊C₄	—	137	4	no	—
264	C₂×C₂²⋊C₄	—	137	8	no	—
265	C₂×C₄²	—	137	2	no	—
266	C₂×C₄²	—	137	1	no	—
267	C₂×C₄²	—	137	2	no	—
268	C₂×C₄²	—	137	1	no	—
269	C₂×C₄²	—	137	1	no	—
270	C₂×C₄²	—	137	1	no	—
271	C₂×C₄²	—	137	1	no	—
272	C₂×C₄²	—	137	2	no	—
273	C₂×C₄²	C₂×D₁₃₇	1	1	yes	characteristic, complemented
274	C₂⁴	—	137	4	no	—
275	C₂⁴	—	137	1	no	—
276	#41	—	2	8	no	—
277	#41	—	274	16	no	—
278	#41	—	274	16	no	—
279	#41	—	274	8	no	—
280	#41	—	274	8	no	—
281	#41	—	274	8	no	—
282	C₂×Q₈	—	274	8	no	—
283	C₂×Q₈	—	137	2	no	—
284	C₂×Q₈	—	137	4	no	—
285	C₂×Q₈	C₂²×D₁₃₇	1	2	yes	—
286	C₂×D₄	—	274	16	no	—
287	C₂×D₄	—	274	16	no	—
288	C₂×D₄	—	274	8	no	—
289	C₂×D₄	—	137	8	no	—
290	C₂×D₄	—	137	4	no	—
291	C₂×D₄	—	137	4	no	—
292	C₂×D₄	—	137	4	no	—
293	C₂×D₄	—	137	4	no	—
294	C₂×D₄	—	137	4	no	—
295	C₂×D₄	—	137	2	no	—
296	C₂×D₄	C₂²×D₁₃₇	1	4	yes	—
297	C₂×D₄	C₂²×D₁₃₇	1	4	yes	—
298	C₂×D₄	C₂²×D₁₃₇	1	2	yes	—
299	C₂²×C₄	—	274	8	no	—
300	C₂²×C₄	—	274	16	no	—
301	C₂²×C₄	—	137	2	no	—
302	C₂²×C₄	—	137	4	no	—
303	C₂²×C₄	—	137	2	no	—
304	C₂²×C₄	—	137	2	no	—
305	C₂²×C₄	—	137	2	no	—
306	C₂²×C₄	—	137	4	no	—
307	C₂²×C₄	—	137	4	no	—
308	C₂²×C₄	—	137	4	no	—
309	C₂²×C₄	—	137	1	no	—
310	C₂²×C₄	—	137	8	no	—
311	C₂²×C₄	—	137	2	no	—
312	C₂²×C₄	—	137	1	no	—
313	C₂²×C₄	—	137	1	no	—
314	C₂²×C₄	—	137	1	no	—
315	C₂²×C₄	—	137	1	no	—
316	C₂²×C₄	C₂²×D₁₃₇	1	2	yes	—
317	C₂²×C₄	C₂²×D₁₃₇	1	4	yes	—
318	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
319	C₄⋊C₄	—	137	8	no	—
320	C₄⋊C₄	—	137	4	no	—
321	C₄⋊C₄	C₂²×D₁₃₇	1	4	yes	—
322	C₂²⋊C₄	—	137	8	no	—
323	C₂²⋊C₄	—	137	8	no	—
324	C₂²⋊C₄	—	137	8	no	—
325	C₂²⋊C₄	C₂²×D₁₃₇	1	8	yes	—
326	C₄²	—	137	2	no	—
327	C₄²	—	137	2	no	—
328	C₄²	—	137	1	no	—
329	C₄²	—	137	2	no	—
330	C₄²	—	137	1	no	—
331	C₄²	—	137	2	no	—
332	C₄²	—	137	2	no	—
333	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
334	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
335	C₄²	C₂²×D₁₃₇	1	2	yes	—
336	C₂³	—	274	4	no	—
337	C₂³	—	274	8	no	—
338	C₂³	—	274	16	no	—
339	C₂³	—	137	4	no	—
340	C₂³	—	137	4	no	—
341	C₂³	—	137	1	no	—
342	C₂³	—	137	1	no	—
343	C₂³	C₂³×D₁₃₇	1	4	yes	—
344	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	274	8	no	—
347	Q₈	—	274	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	274	8	no	—
352	D₄	—	274	8	no	—
353	D₄	—	274	8	no	—
354	D₄	—	274	8	no	—
355	D₄	—	274	16	no	—
356	D₄	—	274	4	no	—
357	D₄	—	274	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	274	8	no	—
361	C₂×C₄	—	274	4	no	—
362	C₂×C₄	—	274	8	no	—
363	C₂×C₄	—	274	4	no	—
364	C₂×C₄	—	274	8	no	—
365	C₂×C₄	—	274	4	no	—
366	C₂×C₄	—	274	8	no	—
367	C₂×C₄	—	274	4	no	—
368	C₂×C₄	—	137	2	no	—
369	C₂×C₄	—	137	4	no	—
370	C₂×C₄	—	137	4	no	—
371	C₂×C₄	—	137	2	no	—
372	C₂×C₄	—	137	1	no	—
373	C₂×C₄	—	137	1	no	—
374	C₂×C₄	—	137	4	no	—
375	C₂×C₄	—	137	4	no	—
376	C₂×C₄	—	137	4	no	—
377	C₂×C₄	—	137	4	no	—
378	C₂×C₄	—	137	8	no	—
379	C₂×C₄	D₄×D₁₃₇	1	4	yes	complemented
380	C₂×C₄	C₂³×D₁₃₇	1	2	yes	—
381	C₂×C₄	C₂³×D₁₃₇	1	4	yes	—
382	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₁₃₇	1	2	yes	—
384	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	274	8	no	—
389	C₂²	—	274	2	no	—
390	C₂²	—	274	4	no	—
391	C₂²	—	274	8	no	—
392	C₂²	—	548	16	no	—
393	C₂²	—	137	2	no	—
394	C₂²	—	137	2	no	—
395	C₂²	—	137	4	no	—
396	C₂²	C₂×D₄×D₁₃₇	1	2	yes	—
397	C₂²	C₂⁴×D₁₃₇	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	274	4	no	—
401	C₄	—	274	2	no	—
402	C₄	—	137	2	no	—
403	C₄	—	137	2	no	—
404	C₄	—	137	4	no	—
405	C₄	C₂×D₄×D₁₃₇	1	2	yes	—
406	C₄	C₂×D₄×D₁₃₇	1	2	yes	—
407	C₄	#41×D₁₃₇	1	4	yes	complemented
408	C₂	—	2	2	no	—
409	C₂	—	4	4	no	—
410	C₂	—	274	2	no	—
411	C₂	—	548	4	no	—
412	C₂	—	137	4	no	—
413	C₂	C₂²×D₄×D₁₃₇	1	1	yes	characteristic
414	C₂	C₂×#41×D₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃₇
commutator, socle, cosocle	C₂²×C₁₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₇
Fitting	#532×C₁₃₇	C₂
hypercenter	#532	D₁₃₇
hypocenter	C₁₃₇	C₂×#532
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₃₇	C₂	semidirect
2. #22577954	C₂	semidirect
3. #22577953	C₂	semidirect
4. #22577952	C₂	semidirect
5. #22577951	C₂	semidirect
6. #22577950	C₂	semidirect
7. #22577949	C₂	semidirect
8. #22577948	C₂	semidirect
9. C₄⋊Q₈×D₁₃₇	C₂	semidirect
10. #127×D₁₃₇	C₂	semidirect
11. #124×D₁₃₇	C₂	semidirect
12. #121×D₁₃₇	C₂	semidirect
13. C₄×D₄×D₁₃₇	C₂	semidirect
14. C₂×C₄²×D₁₃₇	C₂	semidirect
15. #532×C₁₃₇	C₂	semidirect
16. C₂×#14555511	C₂²	semidirect
17. C₂×#14555510	C₂²	semidirect
18. C₂×#14555510	C₂²	semidirect
19. C₂×#14555509	C₂²	semidirect
20. C₂×#14555509	C₂²	semidirect
29. #17984088	C₂²	semidirect
30. #17984087	C₂²	semidirect
31. #17984086	C₂²	semidirect
32. #17984085	C₂²	semidirect
33. #17984084	C₂²	semidirect
34. #17984084	C₂²	semidirect
35. #17984077	C₂²	semidirect
36. #17984076	C₂²	semidirect
37. #17984075	C₂²	semidirect
38. #17984074	C₂²	semidirect
39. #17984063	C₂²	semidirect
40. #17984062	C₂²	semidirect
41. #17984061	C₂²	semidirect
42. #17984060	C₂²	semidirect
43. #17984059	C₂²	semidirect
44. C₄×D₅₄₈	C₂²	semidirect
45. D₄×Dic₁₃₇	C₂²	semidirect
46. #17984050	C₂²	semidirect
47. C₄×C₂²⋊D₁₃₇	C₂²	semidirect
48. #17984048	C₂²	semidirect
51. C₂×C₄×Dic₁₃₇	C₂²	semidirect
52. C₂×C₄×Dic₁₃₇	C₂²	semidirect
56. C₄²×D₁₃₇	C₂²	semidirect
57. C₄²×D₁₃₇	C₂²	semidirect
58. C₄²×D₁₃₇	C₂²	semidirect
59. C₂×#41×C₁₃₇	C₂²	semidirect
60. C₄⋊Q₈×C₁₃₇	C₂²	semidirect
61. #127×C₁₃₇	C₂²	semidirect
62. #124×C₁₃₇	C₂²	semidirect
63. #121×C₁₃₇	C₂²	semidirect
64. C₄×D₄×C₁₃₇	C₂²	semidirect
65. C₂×C₄²×C₁₃₇	C₂²	semidirect
91. C₂×C₄×D₁₃₇	D₄	semidirect
146. C₂×Dic₁₃₇	C₂×D₄	semidirect
160. C₄×D₁₃₇	C₂×D₄	semidirect
161. C₄×D₁₃₇	C₂×D₄	semidirect
162. C₄×D₁₃₇	#41	semidirect
171. C₂×C₄×C₁₃₇	C₂×D₄	semidirect
194. C₄×C₁₃₇	C₂×#41	semidirect
199. Dic₁₃₇	C₂×#41	semidirect
206. D₁₃₇	#532	direct (N × H)
207. C₁₃₇	C₂×#532	semidirect
217. #532	D₁₃₇	direct (N × H)
230. C₂×#41	C₂×D₁₃₇	semidirect
241. C₄⋊Q₈	C₂×D₁₃₇	semidirect
245. #127	C₂×D₁₃₇	semidirect
250. #124	C₂×D₁₃₇	semidirect
256. #121	C₂×D₁₃₇	semidirect
262. C₄×D₄	C₂×D₁₃₇	semidirect
273. C₂×C₄²	C₂×D₁₃₇	semidirect
379. C₂×C₄	D₄×D₁₃₇	semidirect
407. C₄	#41×D₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₃₇	2
#22577954	2
#22577953	2
#22577952	2
#22577951	2
#22577950	2
#22577949	2
#22577948	2
C₄⋊Q₈×D₁₃₇	2
#127×D₁₃₇	2
#124×D₁₃₇	2
#121×D₁₃₇	2
C₄×D₄×D₁₃₇	2
C₂×C₄²×D₁₃₇	2
#532×C₁₃₇	2
C₂×#532	137

Subgroups — #532×D137 #31794066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #532×D₁₃₇ #31794066