Subgroups — #18008647

Order 4736.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558256	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558240	C₂	1	2	yes	maximal, complemented
3	#14558221	C₂	1	2	yes	maximal, complemented
4	#14558206	C₂	1	4	yes	maximal, complemented
5	Q₈×D₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#14558191	C₂	1	2	yes	maximal, complemented
7	#14558188	C₂	1	1	yes	maximal, characteristic, complemented
8	#14558187	C₂	1	1	yes	maximal, characteristic, complemented
9	#14558179	C₂	1	2	yes	maximal, complemented
10	#14558154	C₂	1	2	yes	maximal, complemented
11	#14558124	C₂	1	4	yes	maximal, complemented
12	#14558090	C₂	1	1	yes	maximal, characteristic, complemented
13	#14558043	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₃₇	C₂	1	2	yes	maximal, complemented
15	#14558013	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10596962	C₂²	1	2	yes	—
19	C₂×#10596964	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₃₇	C₂²	1	2	yes	complemented
21	C₂²×D₁₄₈	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₃₇	C₂²	1	2	yes	—
23	#11924536	C₂²	1	2	yes	complemented
24	#11924536	C₂²	1	1	yes	characteristic, complemented
25	#11924536	C₂²	1	1	yes	characteristic, complemented
26	#11924531	C₂²	1	4	yes	complemented
27	#11924531	C₂²	1	4	yes	complemented
28	#11924528	C₂²	1	2	yes	complemented
29	#11924527	C₂²	1	4	yes	complemented
30	#11924524	C₂²	1	2	yes	—
31	#11924522	C₂²	1	4	yes	complemented
32	#11924521	C₂²	1	4	yes	—
33	#11924520	C₂²	1	4	yes	complemented
34	#11924518	C₂²	1	4	yes	complemented
35	#11924518	C₂²	1	4	yes	complemented
36	#11924516	C₂²	1	2	yes	complemented
37	#11924516	C₂²	1	2	yes	complemented
38	#11924516	C₂²	1	4	yes	complemented
39	#11924515	C₂²	1	2	yes	—
40	#11924515	C₂²	1	2	yes	—
41	#11924515	C₂²	1	2	yes	complemented
42	#11924514	C₂²	1	4	yes	complemented
43	#11924513	C₂²	1	4	yes	—
44	#11924513	C₂²	1	4	yes	complemented
45	#11924512	C₂²	1	2	yes	complemented
46	#11924510	C₂²	1	2	yes	—
47	#11924509	C₂²	1	4	yes	—
48	#11924507	C₂²	1	2	yes	complemented
49	#11924504	C₂²	1	4	yes	—
50	C₄×Dic₇₄	C₂²	1	2	yes	complemented
51	C₄×Dic₇₄	C₂²	1	2	yes	complemented
52	C₄×Dic₇₄	C₂²	1	2	yes	complemented
53	C₄×D₁₄₈	C₂²	1	2	yes	—
54	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
55	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
56	C₄×D₁₄₈	C₂²	1	2	yes	—
57	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
58	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
59	C₄×D₁₄₈	C₂²	1	2	yes	—
60	D₄×Dic₃₇	C₂²	1	4	yes	—
61	#11924496	C₂²	1	4	yes	complemented
62	#11924496	C₂²	1	4	yes	complemented
63	#11924495	C₂²	1	2	yes	—
64	#11924494	C₂²	1	2	yes	complemented
65	#11924494	C₂²	1	4	yes	complemented
66	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₃₇	C₂²	1	4	yes	complemented
70	C₂×#10596938	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₃₇	C₂²	1	4	yes	—
72	#126×C₃₇	C₂²	1	2	yes	complemented
73	#125×C₃₇	C₂²	1	1	yes	characteristic, complemented
74	#124×C₃₇	C₂²	1	1	yes	characteristic, complemented
75	#123×C₃₇	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
77	#121×C₃₇	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₃₇	C₂²	1	2	yes	—
80	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
81	#117×C₃₇	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
83	C₂³×D₃₇	C₂³	1	2	yes	—
84	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₃₇	C₂³	1	2	yes	—
86	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
90	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₃₇	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₃₇	C₂³	1	4	yes	—
93	C₂²×Dic₃₇	C₂³	1	2	yes	—
94	C₂²×Dic₃₇	C₂³	1	4	yes	—
95	Q₈×D₃₇	—	4	4	no	—
96	#10596964	—	4	4	no	—
97	#10596962	—	2	8	no	—
98	C₂×D₁₄₈	—	2	4	no	—
99	C₂×D₁₄₈	C₂³	1	2	yes	—
100	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
101	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₃₇	—	4	4	no	—
103	C₂×C₄×D₃₇	C₂³	1	4	yes	—
104	C₂×C₄×D₃₇	C₂³	1	2	yes	—
105	C₂×C₄×D₃₇	C₂³	1	2	yes	—
106	C₂×C₄×D₃₇	C₂³	1	4	yes	—
107	C₂×C₄×D₃₇	C₂³	1	2	yes	—
108	C₂×C₄×D₃₇	C₂³	1	2	yes	—
109	C₂×Dic₇₄	C₂³	1	2	yes	—
110	C₂×Dic₇₄	C₂³	1	2	yes	—
111	C₂×Dic₇₄	C₂³	1	4	yes	—
112	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
113	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
116	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
117	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
123	C₄²×C₃₇	C₂³	1	1	yes	characteristic
124	C₄²×C₃₇	C₂³	1	1	yes	characteristic
125	C₄²×C₃₇	C₂³	1	1	yes	characteristic
126	C₄²×C₃₇	C₂³	1	1	yes	characteristic
127	C₄²×C₃₇	C₂³	1	2	yes	—
128	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
129	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
130	#10596938	C₂³	1	4	yes	—
131	#10596938	C₂³	1	4	yes	—
132	#10596938	C₂³	1	2	yes	—
133	#10596938	C₂³	1	2	yes	—
134	#10596938	C₂³	1	2	yes	—
135	#10596938	C₂³	1	2	yes	—
136	#10596938	C₂³	1	4	yes	—
137	#10596938	C₂³	1	4	yes	—
138	C₄⋊Dic₃₇	C₂³	1	4	yes	—
139	C₄⋊Dic₃₇	C₂³	1	2	yes	—
140	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₃₇	C₂³	1	2	yes	—
142	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₃₇	C₂³	1	2	yes	—
144	C₄⋊Dic₃₇	C₂³	1	2	yes	—
145	C₄⋊Dic₃₇	C₂³	1	2	yes	—
146	C₄⋊Dic₃₇	C₂³	1	4	yes	—
147	#10596936	C₂³	1	4	yes	—
148	#10596936	C₂³	1	4	yes	—
149	#10596936	C₂³	1	4	yes	—
150	#10596936	C₂³	1	4	yes	—
151	C₄×Dic₃₇	C₂³	1	4	yes	—
152	C₄×Dic₃₇	C₂³	1	4	yes	—
153	C₂³×C₃₇	C₂⁴	1	2	yes	—
154	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
155	C₂²×D₃₇	—	2	4	no	—
156	C₂²×D₃₇	—	2	4	no	—
157	C₂²×D₃₇	—	4	2	no	—
158	C₂²×D₃₇	C₂⁴	1	2	yes	—
159	C₂²×D₃₇	C₂⁴	1	2	yes	—
160	Q₈×C₃₇	—	2	2	no	—
161	D₄×C₃₇	—	2	4	no	—
162	D₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	2	4	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
172	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
173	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
176	C₂²⋊D₃₇	—	2	8	no	—
177	C₂²⋊D₃₇	—	4	4	no	—
178	C₂×Dic₃₇	—	4	2	no	—
179	C₂×Dic₃₇	—	4	4	no	—
180	C₂×Dic₃₇	C₂⁴	1	4	yes	—
181	C₂×Dic₃₇	C₂⁴	1	2	yes	—
182	C₂×Dic₃₇	C₂⁴	1	4	yes	—
183	C₂×Dic₃₇	C₂⁴	1	2	yes	—
184	D₁₄₈	—	2	4	no	—
185	D₁₄₈	—	2	2	no	—
186	D₁₄₈	#41	1	4	yes	complemented
187	C₄×D₃₇	—	2	8	no	—
188	C₄×D₃₇	—	2	4	no	—
189	C₄×D₃₇	—	2	4	no	—
190	C₄×D₃₇	—	4	2	no	—
191	C₄×D₃₇	—	4	2	no	—
192	C₄×D₃₇	—	4	4	no	—
193	Dic₇₄	—	2	4	no	—
194	Dic₇₄	—	2	4	no	—
195	Dic₇₄	—	4	4	no	—
196	C₂²×C₃₇	—	2	1	no	—
197	C₂²×C₃₇	—	2	1	no	—
198	C₂²×C₃₇	—	2	2	no	—
199	C₂²×C₃₇	—	2	2	no	—
200	C₂²×C₃₇	—	2	2	no	—
201	C₂²×C₃₇	2₋¹⁺⁴	1	2	yes	—
202	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
203	C₂×D₃₇	—	2	2	no	—
204	C₂×D₃₇	—	2	2	no	—
205	C₂×D₃₇	—	2	2	no	—
206	C₂×D₃₇	—	2	2	no	—
207	C₂×D₃₇	—	2	2	no	—
208	C₂×D₃₇	—	4	8	no	—
209	C₂×D₃₇	C₂×#41	1	4	yes	—
210	C₄×C₃₇	—	2	2	no	—
211	C₄×C₃₇	—	2	1	no	—
212	C₄×C₃₇	—	2	2	no	—
213	C₄×C₃₇	—	2	1	no	—
214	C₄×C₃₇	—	2	1	no	—
215	C₄×C₃₇	—	2	1	no	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	C₂×#41	1	2	yes	—
218	C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
219	Dic₃₇	—	2	4	no	—
220	Dic₃₇	—	2	4	no	—
221	Dic₃₇	—	2	2	no	—
222	Dic₃₇	—	2	2	no	—
223	#3520	—	37	1	no	maximal, Sylow
224	C₂×C₃₇	—	2	2	no	—
225	C₂×C₃₇	—	4	2	no	—
226	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
227	C₂×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
229	D₃₇	—	2	4	no	—
230	D₃₇	—	4	2	no	—
231	#556	—	37	1	no	—
232	#554	—	37	2	no	—
233	#552	—	37	2	no	—
234	#551	—	37	4	no	—
235	D₄×Q₈	—	37	1	no	—
236	#548	—	37	2	no	—
237	#547	—	37	1	no	—
238	#547	—	37	1	no	—
239	#546	—	37	2	no	—
240	#542	—	37	2	no	—
241	#539	—	37	4	no	—
242	#533	—	37	1	no	—
243	#529	D₃₇	1	1	yes	characteristic, complemented
244	#525	—	37	2	no	—
245	C₂×C₂²⋊Q₈	—	37	2	no	—
246	#520	—	37	2	no	—
247	C₂×C₄×D₄	—	37	1	no	—
248	C₃₇	#3520	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	37	2	no	—
250	C₂×#41	—	37	2	no	—
251	C₂²×Q₈	—	37	2	no	—
252	C₂²×D₄	—	37	1	no	—
253	C₂³×C₄	—	37	2	no	—
254	C₄⋊Q₈	—	37	1	no	—
255	C₄⋊Q₈	—	37	1	no	—
256	C₄⋊Q₈	—	37	2	no	—
257	#126	—	37	4	no	—
258	#126	—	37	4	no	—
259	#126	C₂×D₃₇	1	2	yes	complemented
260	#125	—	37	4	no	—
261	#125	—	37	2	no	—
262	#125	C₂×D₃₇	1	1	yes	characteristic, complemented
263	#124	—	37	4	no	—
264	#124	—	37	2	no	—
265	#124	C₂×D₃₇	1	1	yes	characteristic, complemented
266	#123	—	37	4	no	—
267	#123	—	37	4	no	—
268	#123	—	37	4	no	—
269	#123	—	37	4	no	—
270	#123	C₂×D₃₇	1	2	yes	—
271	C₂²⋊Q₈	—	37	2	no	—
272	C₂²⋊Q₈	—	37	2	no	—
273	C₂²⋊Q₈	—	37	2	no	—
274	C₂²⋊Q₈	—	37	2	no	—
275	C₂²⋊Q₈	—	37	4	no	—
276	C₂²⋊Q₈	—	37	2	no	—
277	C₂²⋊Q₈	—	37	2	no	—
278	C₂²⋊Q₈	—	37	4	no	—
279	C₂²⋊Q₈	—	37	4	no	—
280	C₂²⋊Q₈	—	37	4	no	—
281	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
282	#121	—	37	2	no	—
283	#121	—	37	2	no	—
284	#121	—	37	4	no	—
285	#121	C₂×D₃₇	1	1	yes	characteristic
286	#120	—	37	4	no	—
287	C₄×Q₈	—	37	2	no	—
288	C₄×Q₈	—	37	2	no	—
289	C₄×Q₈	—	37	2	no	—
290	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
291	C₄×D₄	—	37	4	no	—
292	C₄×D₄	—	37	4	no	—
293	C₄×D₄	—	37	4	no	—
294	C₄×D₄	—	37	1	no	—
295	C₄×D₄	—	37	2	no	—
296	C₄×D₄	—	37	1	no	—
297	C₄×D₄	—	37	1	no	—
298	C₄×D₄	—	37	1	no	—
299	C₄×D₄	—	37	2	no	—
300	C₄×D₄	—	37	2	no	—
301	C₄×D₄	C₂×D₃₇	1	2	yes	—
302	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic, complemented
303	#117	—	37	2	no	—
304	#117	—	37	4	no	—
305	#117	—	37	2	no	—
306	#117	C₂×D₃₇	1	2	yes	complemented
307	C₂×C₄⋊C₄	—	37	1	no	—
308	C₂×C₄⋊C₄	—	37	2	no	—
309	C₂×C₄⋊C₄	—	37	4	no	—
310	C₂×C₄⋊C₄	—	37	2	no	—
311	C₂×C₂²⋊C₄	—	37	2	no	—
312	C₂×C₂²⋊C₄	—	37	4	no	—
313	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
314	C₂⁴	—	37	2	no	—
315	#41	—	74	8	no	—
316	#41	—	148	4	no	—
317	C₂×Q₈	—	37	2	no	—
318	C₂×Q₈	—	37	2	no	—
319	C₂×Q₈	—	37	4	no	—
320	C₂×Q₈	—	148	4	no	—
321	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
322	C₂×D₄	—	37	4	no	—
323	C₂×D₄	—	37	4	no	—
324	C₂×D₄	—	37	1	no	—
325	C₂×D₄	—	37	2	no	—
326	C₂×D₄	—	37	1	no	—
327	C₂×D₄	—	74	4	no	—
328	C₂×D₄	C₂²×D₃₇	1	2	yes	—
329	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
330	C₂²×C₄	—	37	2	no	—
331	C₂²×C₄	—	37	4	no	—
332	C₂²×C₄	—	37	4	no	—
333	C₂²×C₄	—	37	2	no	—
334	C₂²×C₄	—	37	2	no	—
335	C₂²×C₄	—	37	4	no	—
336	C₂²×C₄	—	37	2	no	—
337	C₂²×C₄	—	37	2	no	—
338	C₂²×C₄	—	148	4	no	—
339	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
343	C₄⋊C₄	—	37	4	no	—
344	C₄⋊C₄	—	37	4	no	—
345	C₄⋊C₄	—	37	4	no	—
346	C₄⋊C₄	—	37	4	no	—
347	C₄⋊C₄	—	37	1	no	—
348	C₄⋊C₄	—	37	4	no	—
349	C₄⋊C₄	—	37	2	no	—
350	C₄⋊C₄	—	37	2	no	—
351	C₄⋊C₄	—	37	1	no	—
352	C₄⋊C₄	—	37	2	no	—
353	C₄⋊C₄	—	37	2	no	—
354	C₄⋊C₄	—	37	2	no	—
355	C₄⋊C₄	—	37	4	no	—
356	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
357	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
359	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
361	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
362	C₂²⋊C₄	—	37	4	no	—
363	C₂²⋊C₄	—	37	4	no	—
364	C₂²⋊C₄	—	37	2	no	—
365	C₂²⋊C₄	—	37	2	no	—
366	C₂²⋊C₄	—	37	2	no	—
367	C₂²⋊C₄	—	37	2	no	—
368	C₂²⋊C₄	—	37	4	no	—
369	C₂²⋊C₄	—	37	4	no	—
370	C₂²⋊C₄	—	37	4	no	—
371	C₂²⋊C₄	—	37	4	no	—
372	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
373	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
377	C₄²	—	37	4	no	—
378	C₄²	—	37	4	no	—
379	C₄²	C₂²×D₃₇	1	1	yes	characteristic
380	C₄²	C₂²×D₃₇	1	1	yes	characteristic
381	C₄²	C₂²×D₃₇	1	1	yes	characteristic
382	C₄²	C₂²×D₃₇	1	1	yes	characteristic
383	C₄²	C₂²×D₃₇	1	2	yes	—
384	C₂³	—	37	2	no	—
385	C₂³	—	37	2	no	—
386	C₂³	—	74	4	no	—
387	C₂³	—	74	4	no	—
388	C₂³	—	148	2	no	—
389	C₂³	C₂³×D₃₇	1	2	yes	—
390	C₂³	C₂³×D₃₇	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	74	4	no	—
393	Q₈	—	74	4	no	—
394	Q₈	—	148	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	37	4	no	—
398	D₄	—	74	4	no	—
399	D₄	—	74	8	no	—
400	D₄	—	74	2	no	—
401	D₄	—	148	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	37	4	no	—
407	C₂×C₄	—	37	2	no	—
408	C₂×C₄	—	37	4	no	—
409	C₂×C₄	—	37	2	no	—
410	C₂×C₄	—	74	8	no	—
411	C₂×C₄	—	74	4	no	—
412	C₂×C₄	—	74	4	no	—
413	C₂×C₄	—	148	2	no	—
414	C₂×C₄	—	148	2	no	—
415	C₂×C₄	—	148	4	no	—
416	C₂×C₄	—	148	2	no	—
417	C₂×C₄	—	148	4	no	—
418	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₃₇	1	2	yes	—
420	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₃₇	1	2	yes	—
424	C₂×C₄	C₂³×D₃₇	1	2	yes	—
425	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	37	4	no	—
433	C₂²	—	74	2	no	—
434	C₂²	—	74	2	no	—
435	C₂²	—	74	2	no	—
436	C₂²	—	74	2	no	—
437	C₂²	—	74	2	no	—
438	C₂²	—	148	8	no	—
439	C₂²	#11924583	1	2	yes	—
440	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	74	4	no	—
449	C₄	—	74	2	no	—
450	C₄	—	74	2	no	—
451	C₄	—	74	4	no	—
452	C₄	#41×D₃₇	1	2	yes	—
453	C₄	#11924582	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	4	2	no	—
456	C₂	—	74	4	no	—
457	C₂	—	148	2	no	—
458	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
459	C₂	C₂×#11924582	1	1	yes	characteristic
460	C₂	C₂×#11924583	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁵
Fitting	C₃₇×#529	C₂
hypercenter	#529	D₃₇
hypocenter	C₃₇	#3520
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14558256	C₂	semidirect
2. #14558240	C₂	semidirect
3. #14558221	C₂	semidirect
4. #14558206	C₂	semidirect
5. Q₈×D₁₄₈	C₂	semidirect
6. #14558191	C₂	semidirect
7. #14558188	C₂	semidirect
8. #14558187	C₂	semidirect
9. #14558179	C₂	semidirect
10. #14558154	C₂	semidirect
11. #14558124	C₂	semidirect
12. #14558090	C₂	semidirect
13. #14558043	C₂	semidirect
14. C₂²⋊Q₈×D₃₇	C₂	semidirect
15. #14558013	C₂	semidirect
16. C₂×C₄×D₁₄₈	C₂	semidirect
17. C₃₇×#529	C₂	semidirect
19. C₂×#10596964	C₂²	semidirect
20. C₂×Q₈×D₃₇	C₂²	semidirect
23. #11924536	C₂²	semidirect
24. #11924536	C₂²	semidirect
25. #11924536	C₂²	semidirect
26. #11924531	C₂²	semidirect
27. #11924531	C₂²	semidirect
28. #11924528	C₂²	semidirect
29. #11924527	C₂²	semidirect
31. #11924522	C₂²	semidirect
33. #11924520	C₂²	semidirect
34. #11924518	C₂²	semidirect
35. #11924518	C₂²	semidirect
36. #11924516	C₂²	semidirect
37. #11924516	C₂²	semidirect
38. #11924516	C₂²	semidirect
41. #11924515	C₂²	semidirect
42. #11924514	C₂²	semidirect
44. #11924513	C₂²	semidirect
45. #11924512	C₂²	semidirect
48. #11924507	C₂²	semidirect
50. C₄×Dic₇₄	C₂²	semidirect
51. C₄×Dic₇₄	C₂²	semidirect
52. C₄×Dic₇₄	C₂²	semidirect
61. #11924496	C₂²	semidirect
62. #11924496	C₂²	semidirect
64. #11924494	C₂²	semidirect
65. #11924494	C₂²	semidirect
67. C₂×C₄⋊Dic₃₇	C₂²	semidirect
68. C₄⋊C₄×D₃₇	C₂²	semidirect
69. C₄⋊C₄×D₃₇	C₂²	semidirect
72. #126×C₃₇	C₂²	semidirect
73. #125×C₃₇	C₂²	semidirect
74. #124×C₃₇	C₂²	semidirect
78. C₄×Q₈×C₃₇	C₂²	semidirect
80. C₄×D₄×C₃₇	C₂²	semidirect
81. #117×C₃₇	C₂²	semidirect
186. D₁₄₈	#41	semidirect
243. #529	D₃₇	semidirect
248. C₃₇	#3520	semidirect
259. #126	C₂×D₃₇	semidirect
262. #125	C₂×D₃₇	semidirect
265. #124	C₂×D₃₇	semidirect
290. C₄×Q₈	C₂×D₃₇	semidirect
302. C₄×D₄	C₂×D₃₇	semidirect
306. #117	C₂×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14558256	2
#14558240	2
#14558221	2
#14558206	2
Q₈×D₁₄₈	2
#14558191	2
#14558188	2
#14558187	2
#14558179	2
#14558154	2
#14558124	2
#14558090	2
#14558043	2
C₂²⋊Q₈×D₃₇	2
#14558013	2
C₂×C₄×D₁₄₈	2
C₃₇×#529	2
#3520	37