Subgroups — #18008027

Order 4736.

1012 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558160	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558157	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558156	C₂	1	1	yes	maximal, characteristic, complemented
4	#14558153	C₂	1	2	yes	maximal, complemented
5	#14558144	C₂	1	1	yes	maximal, characteristic, complemented
6	#14558143	C₂	1	1	yes	maximal, characteristic, complemented
7	#14558142	C₂	1	2	yes	maximal, complemented
8	#14558131	C₂	1	2	yes	maximal, complemented
9	#14558129	C₂	1	2	yes	maximal, complemented
10	#14558113	C₂	1	1	yes	maximal, characteristic
11	#14558108	C₂	1	1	yes	maximal, characteristic, complemented
12	#14558106	C₂	1	1	yes	maximal, characteristic, complemented
13	#14558087	C₂	1	1	yes	maximal, characteristic, complemented
14	#14558087	C₂	1	2	yes	maximal, complemented
15	#14558070	C₂	1	2	yes	maximal, complemented
16	#14558070	C₂	1	1	yes	maximal, characteristic, complemented
17	#14558067	C₂	1	1	yes	maximal, characteristic, complemented
18	#14558061	C₂	1	2	yes	maximal, complemented
19	#14558061	C₂	1	2	yes	maximal, complemented
20	C₄×#10596966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#10596962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10596966	C₂²	1	1	yes	characteristic
25	C₂×#10596962	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₃₇	C₂²	1	1	yes	characteristic
27	#11924535	C₂²	1	2	yes	—
28	#11924535	C₂²	1	1	yes	characteristic
29	#11924534	C₂²	1	1	yes	characteristic
30	#11924534	C₂²	1	2	yes	—
31	#11924531	C₂²	1	2	yes	—
32	#11924531	C₂²	1	2	yes	—
33	#11924531	C₂²	1	2	yes	—
34	#11924531	C₂²	1	2	yes	—
35	#11924531	C₂²	1	2	yes	—
36	#11924530	C₂²	1	2	yes	—
37	#11924529	C₂²	1	2	yes	—
38	#11924529	C₂²	1	2	yes	—
39	#11924528	C₂²	1	1	yes	characteristic
40	#11924527	C₂²	1	2	yes	—
41	#11924527	C₂²	1	1	yes	characteristic
42	#11924526	C₂²	1	2	yes	—
43	#11924526	C₂²	1	2	yes	—
44	#11924526	C₂²	1	2	yes	—
45	#11924526	C₂²	1	2	yes	—
46	#11924526	C₂²	1	2	yes	—
47	#11924525	C₂²	1	1	yes	characteristic
48	#11924525	C₂²	1	2	yes	—
49	#11924524	C₂²	1	1	yes	characteristic
50	#11924522	C₂²	1	2	yes	—
51	#11924522	C₂²	1	2	yes	—
52	#11924521	C₂²	1	2	yes	—
53	#11924521	C₂²	1	2	yes	—
54	#11924521	C₂²	1	2	yes	—
55	#11924521	C₂²	1	2	yes	—
56	#11924521	C₂²	1	2	yes	—
57	#11924519	C₂²	1	2	yes	—
58	#11924518	C₂²	1	2	yes	—
59	#11924518	C₂²	1	2	yes	—
60	#11924516	C₂²	1	1	yes	characteristic
61	#11924516	C₂²	1	2	yes	—
62	#11924515	C₂²	1	1	yes	characteristic
63	#11924514	C₂²	1	2	yes	—
64	#11924514	C₂²	1	2	yes	—
65	#11924514	C₂²	1	2	yes	—
66	#11924514	C₂²	1	2	yes	—
67	#11924514	C₂²	1	2	yes	—
68	#11924512	C₂²	1	1	yes	characteristic
69	#11924512	C₂²	1	2	yes	—
70	#11924512	C₂²	1	1	yes	characteristic
71	#11924512	C₂²	1	2	yes	—
72	#11924511	C₂²	1	2	yes	—
73	#11924511	C₂²	1	1	yes	characteristic
74	#11924510	C₂²	1	1	yes	characteristic
75	#11924509	C₂²	1	2	yes	—
76	#11924509	C₂²	1	2	yes	—
77	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic
78	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic
79	C₄×Dic₇₄	C₂²	1	2	yes	—
80	C₄×Dic₇₄	C₂²	1	1	yes	characteristic
81	C₄×Dic₇₄	C₂²	1	1	yes	characteristic
82	C₄×Dic₇₄	C₂²	1	1	yes	characteristic
83	C₄×Dic₇₄	C₂²	1	2	yes	—
84	#11924501	C₂²	1	2	yes	—
85	#11924501	C₂²	1	1	yes	characteristic
86	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
87	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
88	C₄×D₁₄₈	C₂²	1	2	yes	—
89	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
90	C₄×D₁₄₈	C₂²	1	2	yes	—
91	#11924498	C₂²	1	2	yes	—
92	#11924498	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	—
98	#11924495	C₂²	1	1	yes	characteristic
99	#11924494	C₂²	1	1	yes	characteristic
100	#11924494	C₂²	1	2	yes	—
101	#11924493	C₂²	1	1	yes	characteristic
102	#11924493	C₂²	1	1	yes	characteristic
103	#11924493	C₂²	1	2	yes	—
104	#11924493	C₂²	1	2	yes	—
105	#11924493	C₂²	1	2	yes	—
106	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₃₇	C₂²	1	2	yes	—
108	C₄²×D₃₇	C₂²	1	1	yes	characteristic
109	C₄²×D₃₇	C₂²	1	2	yes	—
110	C₄²×D₃₇	C₂²	1	1	yes	characteristic
111	C₄²×D₃₇	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
114	#125×C₃₇	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
118	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₃₇	C₂²	1	2	yes	—
121	#117×C₃₇	C₂²	1	2	yes	—
122	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
126	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₃₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₃₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₃₇	C₂³	1	2	yes	—
132	#10596966	—	2	4	no	—
133	Q₈×D₃₇	—	2	4	no	—
134	#10596962	—	2	4	no	—
135	C₂×D₁₄₈	C₂³	1	2	yes	—
136	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
137	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
138	C₂×D₁₄₈	C₂³	1	2	yes	—
139	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₃₇	C₂³	1	2	yes	—
141	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₃₇	C₂³	1	2	yes	—
143	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₃₇	C₂³	1	2	yes	—
145	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₃₇	C₂³	1	2	yes	—
147	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₃₇	C₂³	1	2	yes	—
149	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
150	C₂×Dic₇₄	C₂³	1	2	yes	—
151	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
152	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
153	C₂×Dic₇₄	C₂³	1	2	yes	—
154	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
156	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
157	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
159	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
160	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
161	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
162	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
165	C₄²×C₃₇	C₂³	1	1	yes	characteristic
166	C₄²×C₃₇	C₂³	1	2	yes	—
167	C₄²×C₃₇	C₂³	1	2	yes	—
168	C₄²×C₃₇	C₂³	1	1	yes	characteristic
169	C₄²×C₃₇	C₂³	1	1	yes	characteristic
170	C₄²×C₃₇	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₃₇	C₂³	1	2	yes	—
174	#10596938	C₂³	1	1	yes	characteristic
175	#10596938	C₂³	1	1	yes	characteristic
176	#10596938	C₂³	1	1	yes	characteristic
177	#10596938	C₂³	1	1	yes	characteristic
178	#10596938	C₂³	1	2	yes	—
179	#10596938	C₂³	1	2	yes	—
180	#10596938	C₂³	1	2	yes	—
181	#10596938	C₂³	1	2	yes	—
182	#10596938	C₂³	1	2	yes	—
183	#10596938	C₂³	1	2	yes	—
184	#10596938	C₂³	1	2	yes	—
185	#10596938	C₂³	1	2	yes	—
186	#10596938	C₂³	1	2	yes	—
187	#10596938	C₂³	1	2	yes	—
188	#10596938	C₂³	1	2	yes	—
189	#10596938	C₂³	1	2	yes	—
190	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₃₇	C₂³	1	2	yes	—
192	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₃₇	C₂³	1	2	yes	—
194	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₃₇	C₂³	1	2	yes	—
197	C₄⋊Dic₃₇	C₂³	1	2	yes	—
198	#10596936	C₂³	1	2	yes	—
199	#10596936	C₂³	1	2	yes	—
200	#10596936	C₂³	1	2	yes	—
201	#10596936	C₂³	1	1	yes	characteristic
202	#10596936	C₂³	1	1	yes	characteristic
203	#10596936	C₂³	1	1	yes	characteristic
204	#10596936	C₂³	1	1	yes	characteristic
205	#10596936	C₂³	1	2	yes	—
206	#10596936	C₂³	1	2	yes	—
207	#10596936	C₂³	1	2	yes	—
208	#10596936	C₂³	1	2	yes	—
209	#10596936	C₂³	1	2	yes	—
210	#10596936	C₂³	1	2	yes	—
211	#10596936	C₂³	1	2	yes	—
212	#10596936	C₂³	1	2	yes	—
213	#10596936	C₂³	1	2	yes	—
214	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
215	C₄×Dic₃₇	C₂³	1	2	yes	—
216	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₇	C₂³	1	2	yes	—
221	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₃₇	C₂³	1	2	yes	—
223	C₄×Dic₃₇	C₂³	1	2	yes	—
224	C₄×Dic₃₇	C₂³	1	2	yes	—
225	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
226	C₂²×D₃₇	C₂⁴	1	2	yes	—
227	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
228	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
229	Q₈×C₃₇	—	2	2	no	—
230	Q₈×C₃₇	—	2	2	no	—
231	Q₈×C₃₇	—	4	2	no	—
232	C₂×C₄×C₃₇	—	2	2	no	—
233	C₂×C₄×C₃₇	—	2	2	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
237	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
238	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
240	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₃₇	—	2	2	no	—
246	C₂²⋊D₃₇	—	2	2	no	—
247	C₂²⋊D₃₇	—	4	2	no	—
248	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₃₇	C₂⁴	1	2	yes	—
252	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₃₇	C₂⁴	1	2	yes	—
254	C₂×Dic₃₇	C₂⁴	1	2	yes	—
255	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
257	D₁₄₈	—	2	2	no	—
258	D₁₄₈	—	2	4	no	—
259	D₁₄₈	—	2	2	no	—
260	D₁₄₈	—	4	2	no	—
261	C₄×D₃₇	—	2	4	no	—
262	C₄×D₃₇	—	2	2	no	—
263	C₄×D₃₇	—	2	2	no	—
264	C₄×D₃₇	—	2	2	no	—
265	C₄×D₃₇	—	2	4	no	—
266	C₄×D₃₇	—	2	4	no	—
267	C₄×D₃₇	—	4	1	no	—
268	C₄×D₃₇	—	4	2	no	—
269	C₄×D₃₇	—	4	2	no	—
270	C₄×D₃₇	—	4	1	no	—
271	C₄×D₃₇	#41	1	4	yes	—
272	Dic₇₄	—	2	2	no	—
273	Dic₇₄	—	2	2	no	—
274	Dic₇₄	—	2	4	no	—
275	Dic₇₄	—	4	2	no	—
276	C₂²×C₃₇	—	2	1	no	—
277	C₂²×C₃₇	—	2	1	no	—
278	C₂²×C₃₇	—	2	1	no	—
279	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
280	C₂×D₃₇	—	2	1	no	—
281	C₂×D₃₇	—	2	1	no	—
282	C₂×D₃₇	—	2	2	no	—
283	C₂×D₃₇	—	2	1	no	—
284	C₂×D₃₇	—	2	2	no	—
285	C₂×D₃₇	—	2	1	no	—
286	C₂×D₃₇	—	2	1	no	—
287	C₂×D₃₇	—	2	2	no	—
288	C₂×D₃₇	C₂×#41	1	2	yes	—
289	C₄×C₃₇	—	2	2	no	—
290	C₄×C₃₇	—	2	1	no	—
291	C₄×C₃₇	—	2	2	no	—
292	C₄×C₃₇	—	2	1	no	—
293	C₄×C₃₇	—	2	2	no	—
294	C₄×C₃₇	—	2	1	no	—
295	C₄×C₃₇	—	2	2	no	—
296	C₄×C₃₇	—	2	1	no	—
297	C₄×C₃₇	C₂×#41	1	2	yes	—
298	C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
299	Dic₃₇	—	2	2	no	—
300	Dic₃₇	—	2	1	no	—
301	Dic₃₇	—	2	1	no	—
302	Dic₃₇	—	2	1	no	—
303	Dic₃₇	—	2	2	no	—
304	Dic₃₇	—	2	1	no	—
305	Dic₃₇	—	2	2	no	—
306	Dic₃₇	—	2	1	no	—
307	Dic₃₇	C₂×#41	1	2	yes	—
308	#3461	—	37	1	no	maximal, Sylow
309	C₂×C₃₇	—	4	1	no	—
310	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
311	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
312	C₂×C₃₇	#585	1	1	yes	characteristic
313	D₃₇	—	2	2	no	—
314	D₃₇	—	4	2	no	—
315	D₃₇	—	4	1	no	—
316	#544	—	37	1	no	—
317	#542	—	37	1	no	—
318	#542	—	37	2	no	—
319	#542	—	37	1	no	—
320	#541	—	37	1	no	—
321	#541	—	37	2	no	—
322	#541	—	37	1	no	—
323	#539	—	37	2	no	—
324	#539	—	37	2	no	—
325	#537	—	37	1	no	—
326	#536	—	37	1	no	—
327	#536	—	37	1	no	—
328	#533	—	37	2	no	—
329	#533	—	37	1	no	—
330	#533	D₃₇	1	1	yes	characteristic, complemented
331	#529	—	37	2	no	—
332	#529	—	37	1	no	—
333	#529	—	37	2	no	—
334	#529	—	37	2	no	—
335	#529	—	37	1	no	—
336	C₄×#41	—	37	1	no	—
337	C₄×#41	—	37	1	no	—
338	C₂×C₄×Q₈	—	37	1	no	—
339	C₃₇	#3461	1	1	yes	characteristic, complemented, Sylow
340	C₂×#41	—	37	1	no	—
341	C₂×#41	—	37	1	no	—
342	C₂²×Q₈	—	37	1	no	—
343	C₄⋊Q₈	—	37	1	no	—
344	C₄⋊Q₈	—	37	2	no	—
345	C₄⋊Q₈	—	37	2	no	—
346	C₄⋊Q₈	—	37	1	no	—
347	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
348	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
349	#126	—	37	2	no	—
350	#126	—	37	2	no	—
351	#126	—	37	2	no	—
352	#126	—	37	2	no	—
353	#126	—	37	2	no	—
354	#126	—	37	2	no	—
355	#126	—	37	2	no	—
356	#126	—	37	2	no	—
357	#125	—	37	2	no	—
358	#125	—	37	2	no	—
359	#125	—	37	2	no	—
360	#125	—	37	1	no	—
361	#125	—	37	2	no	—
362	#125	—	37	2	no	—
363	#125	—	37	2	no	—
364	#125	—	37	1	no	—
365	#125	C₂×D₃₇	1	2	yes	—
366	#124	—	37	1	no	—
367	#124	—	37	2	no	—
368	#124	—	37	2	no	—
369	#124	—	37	2	no	—
370	#124	—	37	1	no	—
371	#123	—	37	2	no	—
372	#123	—	37	2	no	—
373	#123	—	37	2	no	—
374	#123	—	37	2	no	—
375	#123	—	37	2	no	—
376	#123	—	37	2	no	—
377	#123	—	37	2	no	—
378	#123	—	37	2	no	—
379	C₂²⋊Q₈	—	37	1	no	—
380	C₂²⋊Q₈	—	37	2	no	—
381	C₂²⋊Q₈	—	37	1	no	—
382	C₂²⋊Q₈	—	37	2	no	—
383	C₂²⋊Q₈	—	37	1	no	—
384	C₂²⋊Q₈	—	37	2	no	—
385	C₂²⋊Q₈	—	37	2	no	—
386	C₂²⋊Q₈	—	37	2	no	—
387	C₂²⋊Q₈	—	37	1	no	—
388	C₂²⋊Q₈	—	37	2	no	—
389	C₂²⋊Q₈	—	37	2	no	—
390	C₂²⋊Q₈	—	37	2	no	—
391	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
393	C₂²⋊Q₈	C₂×D₃₇	1	2	yes	—
394	#121	—	37	1	no	—
395	#121	—	37	2	no	—
396	#121	—	37	1	no	—
397	#121	—	37	2	no	—
398	#121	—	37	2	no	—
399	C₄×Q₈	—	37	1	no	—
400	C₄×Q₈	—	37	1	no	—
401	C₄×Q₈	—	37	2	no	—
402	C₄×Q₈	—	37	1	no	—
403	C₄×Q₈	—	37	2	no	—
404	C₄×Q₈	—	37	1	no	—
405	C₄×Q₈	—	37	1	no	—
406	C₄×Q₈	—	37	1	no	—
407	C₄×Q₈	—	37	2	no	—
408	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic
409	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic
410	C₄×Q₈	C₂×D₃₇	1	2	yes	—
411	C₄×D₄	—	37	1	no	—
412	C₄×D₄	—	37	1	no	—
413	C₄×D₄	—	37	1	no	—
414	C₄×D₄	—	37	1	no	—
415	C₄×D₄	—	37	2	no	—
416	C₄×D₄	—	37	2	no	—
417	C₄×D₄	—	37	1	no	—
418	C₄×D₄	—	37	1	no	—
419	C₄×D₄	—	37	2	no	—
420	C₄×D₄	—	37	1	no	—
421	C₄×D₄	—	37	1	no	—
422	C₄×D₄	—	37	2	no	—
423	#117	—	37	1	no	—
424	#117	—	37	1	no	—
425	#117	—	37	2	no	—
426	#117	—	37	1	no	—
427	#117	—	37	1	no	—
428	#117	—	37	2	no	—
429	#117	—	37	2	no	—
430	#117	—	37	2	no	—
431	#117	C₂×D₃₇	1	2	yes	—
432	C₂×C₄⋊C₄	—	37	1	no	—
433	C₂×C₄⋊C₄	—	37	2	no	—
434	C₂×C₄²	—	37	1	no	—
435	C₂×C₄²	—	37	2	no	—
436	C₂×C₄²	—	37	2	no	—
437	C₂×C₄²	—	37	1	no	—
438	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
439	#41	—	74	4	no	—
440	#41	—	74	4	no	—
441	C₂×Q₈	—	37	2	no	—
442	C₂×Q₈	—	37	1	no	—
443	C₂×Q₈	—	37	1	no	—
444	C₂×Q₈	—	37	2	no	—
445	C₂×Q₈	—	74	4	no	—
446	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
449	C₂×D₄	—	37	1	no	—
450	C₂×D₄	—	37	1	no	—
451	C₂×D₄	—	37	2	no	—
452	C₂×D₄	—	37	2	no	—
453	C₂×D₄	—	37	1	no	—
454	C₂×D₄	—	37	1	no	—
455	C₂×D₄	—	37	2	no	—
456	C₂²×C₄	—	37	1	no	—
457	C₂²×C₄	—	37	2	no	—
458	C₂²×C₄	—	37	2	no	—
459	C₂²×C₄	—	37	1	no	—
460	C₂²×C₄	—	37	1	no	—
461	C₂²×C₄	—	37	1	no	—
462	C₂²×C₄	—	37	2	no	—
463	C₂²×C₄	—	37	1	no	—
464	C₂²×C₄	—	37	2	no	—
465	C₂²×C₄	—	37	2	no	—
466	C₂²×C₄	—	37	1	no	—
467	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
470	C₄⋊C₄	—	37	2	no	—
471	C₄⋊C₄	—	37	2	no	—
472	C₄⋊C₄	—	37	2	no	—
473	C₄⋊C₄	—	37	1	no	—
474	C₄⋊C₄	—	37	1	no	—
475	C₄⋊C₄	—	37	1	no	—
476	C₄⋊C₄	—	37	1	no	—
477	C₄⋊C₄	—	37	2	no	—
478	C₄⋊C₄	—	37	2	no	—
479	C₄⋊C₄	—	37	2	no	—
480	C₄⋊C₄	—	37	2	no	—
481	C₄⋊C₄	—	37	2	no	—
482	C₄⋊C₄	—	37	2	no	—
483	C₄⋊C₄	—	37	2	no	—
484	C₄⋊C₄	—	37	2	no	—
485	C₄⋊C₄	—	37	2	no	—
486	C₄⋊C₄	—	37	1	no	—
487	C₄⋊C₄	—	37	2	no	—
488	C₄⋊C₄	—	37	1	no	—
489	C₄⋊C₄	—	37	1	no	—
490	C₄⋊C₄	—	37	2	no	—
491	C₄⋊C₄	—	37	1	no	—
492	C₄⋊C₄	—	37	2	no	—
493	C₄⋊C₄	—	37	2	no	—
494	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
496	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
497	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
499	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
500	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
502	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
503	C₂²⋊C₄	—	37	1	no	—
504	C₂²⋊C₄	—	37	1	no	—
505	C₂²⋊C₄	—	37	2	no	—
506	C₂²⋊C₄	—	37	2	no	—
507	C₂²⋊C₄	—	37	1	no	—
508	C₂²⋊C₄	—	37	1	no	—
509	C₂²⋊C₄	—	37	1	no	—
510	C₂²⋊C₄	—	37	2	no	—
511	C₂²⋊C₄	—	37	2	no	—
512	C₂²⋊C₄	—	37	1	no	—
513	C₂²⋊C₄	—	37	2	no	—
514	C₂²⋊C₄	—	37	2	no	—
515	C₂²⋊C₄	—	37	2	no	—
516	C₂²⋊C₄	—	37	2	no	—
517	C₂²⋊C₄	—	37	2	no	—
518	C₂²⋊C₄	—	37	2	no	—
519	C₂²⋊C₄	—	37	2	no	—
520	C₂²⋊C₄	—	37	2	no	—
521	C₂²⋊C₄	—	37	2	no	—
522	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
524	C₄²	—	37	1	no	—
525	C₄²	—	37	1	no	—
526	C₄²	—	37	2	no	—
527	C₄²	—	37	1	no	—
528	C₄²	—	37	2	no	—
529	C₄²	—	37	1	no	—
530	C₄²	—	37	2	no	—
531	C₄²	—	37	2	no	—
532	C₄²	—	37	1	no	—
533	C₄²	—	37	2	no	—
534	C₄²	—	37	1	no	—
535	C₄²	C₂²×D₃₇	1	1	yes	characteristic
536	C₄²	C₂²×D₃₇	1	1	yes	characteristic
537	C₄²	C₂²×D₃₇	1	1	yes	characteristic
538	C₄²	C₂²×D₃₇	1	2	yes	—
539	C₄²	C₂²×D₃₇	1	2	yes	—
540	C₄²	C₂²×D₃₇	1	1	yes	characteristic
541	C₂³	—	37	1	no	—
542	C₂³	—	37	1	no	—
543	C₂³	—	37	2	no	—
544	C₂³	C₂³×D₃₇	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	74	4	no	—
549	Q₈	—	74	2	no	—
550	Q₈	—	74	2	no	—
551	Q₈	—	148	2	no	—
552	D₄	—	74	2	no	—
553	D₄	—	74	4	no	—
554	D₄	—	74	2	no	—
555	D₄	—	74	2	no	—
556	D₄	—	74	2	no	—
557	D₄	—	148	2	no	—
558	D₄	—	148	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	37	1	no	—
563	C₂×C₄	—	37	4	no	—
564	C₂×C₄	—	37	1	no	—
565	C₂×C₄	—	37	1	no	—
566	C₂×C₄	—	37	1	no	—
567	C₂×C₄	—	37	2	no	—
568	C₂×C₄	—	37	2	no	—
569	C₂×C₄	—	37	1	no	—
570	C₂×C₄	—	37	1	no	—
571	C₂×C₄	—	37	2	no	—
572	C₂×C₄	—	74	4	no	—
573	C₂×C₄	—	74	4	no	—
574	C₂×C₄	—	74	2	no	—
575	C₂×C₄	—	74	2	no	—
576	C₂×C₄	—	74	2	no	—
577	C₂×C₄	—	74	4	no	—
578	C₂×C₄	—	148	1	no	—
579	C₂×C₄	—	148	1	no	—
580	C₂×C₄	—	148	2	no	—
581	C₂×C₄	—	148	2	no	—
582	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₃₇	1	2	yes	—
584	C₂×C₄	C₂³×D₃₇	1	2	yes	—
585	C₂×C₄	C₂³×D₃₇	1	2	yes	—
586	C₂×C₄	C₂³×D₃₇	1	2	yes	—
587	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	37	2	no	—
596	C₂²	—	74	1	no	—
597	C₂²	—	74	1	no	—
598	C₂²	—	74	2	no	—
599	C₂²	—	74	1	no	—
600	C₂²	—	74	1	no	—
601	C₂²	—	74	2	no	—
602	C₂²	—	74	1	no	—
603	C₂²	—	74	2	no	—
604	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	37	2	no	—
614	C₄	—	74	1	no	—
615	C₄	—	74	2	no	—
616	C₄	—	74	1	no	—
617	C₄	—	74	1	no	—
618	C₄	—	74	2	no	—
619	C₄	—	74	1	no	—
620	C₄	—	74	2	no	—
621	C₄	—	74	1	no	—
622	C₄	#41×D₃₇	1	2	yes	—
623	C₄	#11924584	1	2	yes	—
624	C₂	—	4	1	no	—
625	C₂	—	74	2	no	—
626	C₂	—	148	2	no	—
627	C₂	—	148	1	no	—
628	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
629	C₂	C₂×#11924584	1	1	yes	characteristic
630	C₂	#14558369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₃₇
Fitting	C₃₇×#533	C₂
prime radical	#14558113	C₂
hypercenter	#533	D₃₇
hypocenter	C₃₇	#3461
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #14558160	C₂	semidirect
2. #14558157	C₂	semidirect
3. #14558156	C₂	semidirect
4. #14558153	C₂	semidirect
5. #14558144	C₂	semidirect
6. #14558143	C₂	semidirect
7. #14558142	C₂	semidirect
8. #14558131	C₂	semidirect
9. #14558129	C₂	semidirect
11. #14558108	C₂	semidirect
12. #14558106	C₂	semidirect
13. #14558087	C₂	semidirect
14. #14558087	C₂	semidirect
15. #14558070	C₂	semidirect
16. #14558070	C₂	semidirect
17. #14558067	C₂	semidirect
18. #14558061	C₂	semidirect
19. #14558061	C₂	semidirect
20. C₄×#10596966	C₂	semidirect
21. C₄×#10596962	C₂	semidirect
22. C₄×Q₈×D₃₇	C₂	semidirect
23. C₃₇×#533	C₂	semidirect
330. #533	D₃₇	semidirect
339. C₃₇	#3461	semidirect

Maximal subgroups

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

subgroup	index
#14558160	2
#14558157	2
#14558156	2
#14558153	2
#14558144	2
#14558143	2
#14558142	2
#14558131	2
#14558129	2
#14558113	2
#14558108	2
#14558106	2
#14558087	2
#14558070	2
#14558067	2
#14558061	2
C₄×#10596966	2
C₄×#10596962	2
C₄×Q₈×D₃₇	2
C₃₇×#533	2
#3461	37