Subgroups — C₁₃₇×#33631 #46883017

Order 35072.

556 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3164×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#2948×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2228×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2228×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2226×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2224×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2159×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2158×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#2151×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#2140×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₂×#357×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	#544×C₁₃₇	—	2	1	no	—
14	#518×C₁₃₇	—	2	1	no	—
15	C₂×M₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	#501×C₁₃₇	—	2	2	no	—
18	#500×C₁₃₇	C₂²	1	2	yes	complemented
19	#499×C₁₃₇	C₂²	1	2	yes	complemented
20	#442×C₁₃₇	—	2	2	no	—
21	C₄×D₈×C₁₃₇	C₂²	1	2	yes	—
22	C₄×D₈×C₁₃₇	C₂²	1	2	yes	—
23	#428×C₁₃₇	—	2	1	no	—
24	#427×C₁₃₇	C₂²	1	1	yes	characteristic
25	#427×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
27	#418×C₁₃₇	—	2	1	no	—
28	#405×C₁₃₇	C₂²	1	1	yes	characteristic
29	#367×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
30	#367×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
31	#367×C₁₃₇	C₂²	1	2	yes	complemented
32	#366×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
33	#366×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
34	#366×C₁₃₇	C₂²	1	2	yes	complemented
35	C₄⋊C₁₆×C₁₃₇	C₂²	1	2	yes	complemented
36	C₄⋊C₁₆×C₁₃₇	C₂²	1	2	yes	complemented
37	#357×C₁₃₇	C₂²	1	2	yes	—
38	#357×C₁₃₇	C₂²	1	2	yes	—
39	#357×C₁₃₇	C₂²	1	2	yes	—
40	#357×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃₇	—	2	1	no	—
42	C₂×D₈×C₁₃₇	—	2	1	no	—
43	C₂×D₈×C₁₃₇	—	2	2	no	—
44	C₂×D₈×C₁₃₇	Q₈	1	4	yes	complemented
45	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₃₇	—	4	1	no	—
50	#125×C₁₃₇	—	2	2	no	—
51	#125×C₁₃₇	—	4	1	no	—
52	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
53	C₄×D₄×C₁₃₇	—	2	2	no	—
54	C₄×D₄×C₁₃₇	—	2	2	no	—
55	C₄×D₄×C₁₃₇	—	4	1	no	—
56	C₄×D₄×C₁₃₇	—	4	1	no	—
57	#117×C₁₃₇	—	2	1	no	—
58	#117×C₁₃₇	—	2	1	no	—
59	#117×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	4	2	no	—
62	M₃₂×C₁₃₇	—	2	2	no	—
63	C₂×C₁₆×C₁₃₇	—	2	2	no	—
64	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
67	#107×C₁₃₇	—	2	1	no	—
68	#107×C₁₃₇	—	2	2	no	—
69	#107×C₁₃₇	C₂³	1	1	yes	characteristic
70	#107×C₁₃₇	C₂³	1	1	yes	characteristic
71	#107×C₁₃₇	C₂³	1	2	yes	—
72	#107×C₁₃₇	C₂³	1	1	yes	characteristic
73	#107×C₁₃₇	C₂³	1	1	yes	characteristic
74	#106×C₁₃₇	—	2	1	no	—
75	#106×C₁₃₇	—	2	1	no	—
76	#106×C₁₃₇	—	2	2	no	—
77	#102×C₁₃₇	—	2	2	no	—
78	#102×C₁₃₇	—	2	2	no	—
79	#97×C₁₃₇	D₄	1	2	yes	—
80	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
81	C₂⁴×C₁₃₇	—	4	1	no	—
82	C₂×Q₈×C₁₃₇	—	4	2	no	—
83	C₂×D₄×C₁₃₇	—	2	4	no	—
84	C₂×D₄×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	4	1	no	—
86	C₂×D₄×C₁₃₇	—	4	2	no	—
87	C₂²×C₄×C₁₃₇	—	4	1	no	—
88	C₂²×C₄×C₁₃₇	—	4	2	no	—
89	C₂²×C₄×C₁₃₇	—	4	2	no	—
90	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
91	D₈×C₁₃₇	—	2	4	no	—
92	D₈×C₁₃₇	—	2	2	no	—
93	D₈×C₁₃₇	C₂×Q₈	1	4	yes	—
94	M₁₆×C₁₃₇	—	2	2	no	—
95	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
98	C₂×C₈×C₁₃₇	#41	1	2	yes	—
99	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
100	C₄⋊C₄×C₁₃₇	—	2	1	no	—
101	C₄⋊C₄×C₁₃₇	—	2	1	no	—
102	C₄⋊C₄×C₁₃₇	—	2	1	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	1	no	—
105	C₄⋊C₄×C₁₃₇	—	4	1	no	—
106	C₄⋊C₄×C₁₃₇	—	4	2	no	—
107	C₄⋊C₄×C₁₃₇	—	4	2	no	—
108	C₄⋊C₄×C₁₃₇	—	4	2	no	—
109	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
112	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
113	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
114	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
116	C₄²×C₁₃₇	—	4	1	no	—
117	C₄²×C₁₃₇	—	4	1	no	—
118	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₁₆×C₁₃₇	—	2	1	no	—
120	C₁₆×C₁₃₇	—	2	1	no	—
121	C₁₆×C₁₃₇	—	2	2	no	—
122	C₂³×C₁₃₇	—	4	2	no	—
123	C₂³×C₁₃₇	—	4	4	no	—
124	C₂³×C₁₃₇	—	16	1	no	—
125	C₂³×C₁₃₇	—	16	1	no	—
126	C₂³×C₁₃₇	C₂×D₈	1	1	yes	characteristic
127	Q₈×C₁₃₇	—	16	2	no	—
128	D₄×C₁₃₇	—	2	4	no	—
129	D₄×C₁₃₇	—	4	2	no	—
130	D₄×C₁₃₇	—	4	4	no	—
131	C₂×C₄×C₁₃₇	—	4	1	no	—
132	C₂×C₄×C₁₃₇	—	4	1	no	—
133	C₂×C₄×C₁₃₇	—	4	1	no	—
134	C₂×C₄×C₁₃₇	—	4	1	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	16	2	no	—
137	C₂×C₄×C₁₃₇	—	16	2	no	—
138	C₂×C₄×C₁₃₇	—	16	1	no	—
139	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃₇	#137	1	2	yes	—
144	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
145	C₈×C₁₃₇	—	2	2	no	—
146	C₈×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
147	C₈×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
148	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
149	C₂²×C₁₃₇	—	2	1	no	—
150	C₂²×C₁₃₇	—	2	1	no	—
151	C₂²×C₁₃₇	—	4	4	no	—
152	C₂²×C₁₃₇	—	8	2	no	—
153	C₂²×C₁₃₇	—	8	2	no	—
154	C₂²×C₁₃₇	—	16	4	no	—
155	C₂²×C₁₃₇	#474	1	2	yes	—
156	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
157	C₄×C₁₃₇	—	2	2	no	—
158	C₄×C₁₃₇	—	2	2	no	—
159	C₄×C₁₃₇	—	8	1	no	—
160	C₄×C₁₃₇	—	8	2	no	—
161	C₄×C₁₃₇	—	8	1	no	—
162	C₄×C₁₃₇	—	8	1	no	—
163	C₄×C₁₃₇	—	8	1	no	—
164	C₄×C₁₃₇	#474	1	2	yes	—
165	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
166	C₄×C₁₃₇	C₂×#137	1	1	yes	characteristic
167	C₂×C₁₃₇	—	2	2	no	—
168	C₂×C₁₃₇	—	8	4	no	—
169	C₂×C₁₃₇	C₂×#474	1	1	yes	characteristic
170	C₂×C₁₃₇	#3415	1	1	yes	characteristic
171	C₂×C₁₃₇	#3416	1	1	yes	characteristic
172	#33631	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₁₃₇	#33631	1	1	yes	characteristic, direct product factor, Sylow
174	#3164	C₂×C₁₃₇	1	1	yes	characteristic, complemented
175	#2948	C₂×C₁₃₇	1	1	yes	characteristic
176	#2228	C₂×C₁₃₇	1	2	yes	complemented
177	#2228	C₂×C₁₃₇	1	2	yes	complemented
178	#2226	C₂×C₁₃₇	1	2	yes	complemented
179	#2224	C₂×C₁₃₇	1	2	yes	complemented
180	#2159	C₂×C₁₃₇	1	1	yes	characteristic, complemented
181	#2158	C₂×C₁₃₇	1	1	yes	characteristic, complemented
182	#2151	C₂×C₁₃₇	1	1	yes	characteristic, complemented
183	#2140	C₂×C₁₃₇	1	1	yes	characteristic
184	C₂×#357	C₂×C₁₃₇	1	1	yes	characteristic
185	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
186	#544	—	2	1	no	—
187	#518	—	2	1	no	—
188	C₂×M₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
189	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
190	#501	—	2	2	no	—
191	#500	C₂²×C₁₃₇	1	2	yes	complemented
192	#499	C₂²×C₁₃₇	1	2	yes	complemented
193	#442	—	2	2	no	—
194	C₄×D₈	C₂²×C₁₃₇	1	2	yes	—
195	C₄×D₈	C₂²×C₁₃₇	1	2	yes	—
196	#428	—	2	1	no	—
197	#427	C₂²×C₁₃₇	1	1	yes	characteristic
198	#427	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
200	#418	—	2	1	no	—
201	#405	C₂²×C₁₃₇	1	1	yes	characteristic
202	#367	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
203	#367	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
204	#367	C₂²×C₁₃₇	1	2	yes	complemented
205	#366	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
206	#366	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
207	#366	C₂²×C₁₃₇	1	2	yes	complemented
208	C₄⋊C₁₆	C₂²×C₁₃₇	1	2	yes	complemented
209	C₄⋊C₁₆	C₂²×C₁₃₇	1	2	yes	complemented
210	#357	C₂²×C₁₃₇	1	2	yes	—
211	#357	C₂²×C₁₃₇	1	2	yes	—
212	#357	C₂²×C₁₃₇	1	2	yes	—
213	#357	C₂²×C₁₃₇	1	2	yes	—
214	C₂²×D₄	—	2	1	no	—
215	C₂×D₈	—	2	1	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	Q₈×C₁₃₇	1	4	yes	complemented
218	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
219	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
221	C₄⋊Q₈	—	2	2	no	—
222	C₄⋊Q₈	—	4	1	no	—
223	#125	—	2	2	no	—
224	#125	—	4	1	no	—
225	C₂²⋊Q₈	—	4	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	4	1	no	—
229	C₄×D₄	—	4	1	no	—
230	#117	—	2	1	no	—
231	#117	—	2	1	no	—
232	#117	D₄×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	4	2	no	—
235	M₃₂	—	2	2	no	—
236	C₂×C₁₆	—	2	2	no	—
237	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
238	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
239	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
240	#107	—	2	1	no	—
241	#107	—	2	2	no	—
242	#107	C₂³×C₁₃₇	1	2	yes	—
243	#107	C₂³×C₁₃₇	1	1	yes	characteristic
244	#107	C₂³×C₁₃₇	1	1	yes	characteristic
245	#107	C₂³×C₁₃₇	1	1	yes	characteristic
246	#107	C₂³×C₁₃₇	1	1	yes	characteristic
247	#106	—	2	1	no	—
248	#106	—	2	1	no	—
249	#106	—	2	2	no	—
250	#102	—	2	2	no	—
251	#102	—	2	2	no	—
252	#97	D₄×C₁₃₇	1	2	yes	—
253	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
254	C₂⁴	—	4	1	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
264	D₈	—	2	4	no	—
265	D₈	—	2	2	no	—
266	D₈	C₂×Q₈×C₁₃₇	1	4	yes	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
269	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
270	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
271	C₂×C₈	#41×C₁₃₇	1	2	yes	—
272	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
283	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
289	C₄²	—	4	1	no	—
290	C₄²	—	4	1	no	—
291	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₁₆	—	2	1	no	—
293	C₁₆	—	2	1	no	—
294	C₁₆	—	2	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	16	1	no	—
298	C₂³	—	16	1	no	—
299	C₂³	C₂×D₈×C₁₃₇	1	1	yes	characteristic
300	Q₈	—	16	2	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	4	no	—
303	D₄	—	4	2	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	16	2	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	—	16	1	no	—
312	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
313	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
314	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
315	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄	#137×C₁₃₇	1	2	yes	—
317	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
320	C₈	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
321	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	16	4	no	—
328	C₂²	#474×C₁₃₇	1	2	yes	—
329	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	8	1	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	1	no	—
335	C₄	—	8	1	no	—
336	C₄	—	8	1	no	—
337	C₄	#474×C₁₃₇	1	2	yes	—
338	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
339	C₄	C₂×#137×C₁₃₇	1	1	yes	characteristic
340	C₂	—	2	2	no	—
341	C₂	—	8	4	no	—
342	C₂	C₂×#474×C₁₃₇	1	1	yes	characteristic
343	C₂	#3415×C₁₃₇	1	1	yes	characteristic
344	C₂	#3416×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
prime radical	C₂²×D₈×C₁₃₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ #117×C₁₃₇ ◁ #405×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3164×C₁₃₇	C₂	semidirect
3. #2228×C₁₃₇	C₂	semidirect
4. #2228×C₁₃₇	C₂	semidirect
5. #2226×C₁₃₇	C₂	semidirect
6. #2224×C₁₃₇	C₂	semidirect
7. #2159×C₁₃₇	C₂	semidirect
8. #2158×C₁₃₇	C₂	semidirect
9. #2151×C₁₃₇	C₂	semidirect
18. #500×C₁₃₇	C₂²	semidirect
19. #499×C₁₃₇	C₂²	semidirect
29. #367×C₁₃₇	C₂²	semidirect
30. #367×C₁₃₇	C₂²	semidirect
31. #367×C₁₃₇	C₂²	semidirect
32. #366×C₁₃₇	C₂²	semidirect
33. #366×C₁₃₇	C₂²	semidirect
34. #366×C₁₃₇	C₂²	semidirect
35. C₄⋊C₁₆×C₁₃₇	C₂²	semidirect
36. C₄⋊C₁₆×C₁₃₇	C₂²	semidirect
44. C₂×D₈×C₁₃₇	Q₈	semidirect
172. #33631	C₁₃₇	direct (N × H)
173. C₁₃₇	#33631	direct (N × H)
174. #3164	C₂×C₁₃₇	semidirect
176. #2228	C₂×C₁₃₇	semidirect
177. #2228	C₂×C₁₃₇	semidirect
178. #2226	C₂×C₁₃₇	semidirect
179. #2224	C₂×C₁₃₇	semidirect
180. #2159	C₂×C₁₃₇	semidirect
181. #2158	C₂×C₁₃₇	semidirect
182. #2151	C₂×C₁₃₇	semidirect
191. #500	C₂²×C₁₃₇	semidirect
192. #499	C₂²×C₁₃₇	semidirect
202. #367	C₂²×C₁₃₇	semidirect
203. #367	C₂²×C₁₃₇	semidirect
204. #367	C₂²×C₁₃₇	semidirect
205. #366	C₂²×C₁₃₇	semidirect
206. #366	C₂²×C₁₃₇	semidirect
207. #366	C₂²×C₁₃₇	semidirect
208. C₄⋊C₁₆	C₂²×C₁₃₇	semidirect
209. C₄⋊C₁₆	C₂²×C₁₃₇	semidirect
217. C₂×D₈	Q₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3164×C₁₃₇	2
#2948×C₁₃₇	2
#2228×C₁₃₇	2
#2226×C₁₃₇	2
#2224×C₁₃₇	2
#2159×C₁₃₇	2
#2158×C₁₃₇	2
#2151×C₁₃₇	2
#2140×C₁₃₇	2
C₂×#357×C₁₃₇	2
#33631	137

Subgroups — C137×#33631 #46883017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33631 #46883017