Subgroups — #18008157

Order 4736.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558248	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558243	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558227	C₂	1	2	yes	maximal, complemented
4	#14558224	C₂	1	2	yes	maximal, complemented
5	#14558217	C₂	1	2	yes	maximal, complemented
6	#14558208	C₂	1	4	yes	maximal, complemented
7	#14558186	C₂	1	1	yes	maximal, characteristic, complemented
8	#14558176	C₂	1	2	yes	maximal, complemented
9	#14558088	C₂	1	1	yes	maximal, characteristic, complemented
10	#14558066	C₂	1	4	yes	maximal, complemented
11	#14558062	C₂	1	2	yes	maximal, complemented
12	#14558046	C₂	1	2	yes	maximal, complemented
13	C₄×#10596966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#10596966	C₂	1	2	yes	maximal, complemented
15	C₄×D₄×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₃₇	C₂	1	2	yes	maximal, complemented
17	C₃₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10596966	C₂²	1	1	yes	characteristic
19	C₂×#10596966	C₂²	1	2	yes	—
20	C₂×D₄×D₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₃₇	C₂²	1	2	yes	—
22	#11924536	C₂²	1	1	yes	characteristic, complemented
23	#11924530	C₂²	1	4	yes	complemented
24	#11924529	C₂²	1	4	yes	complemented
25	#11924528	C₂²	1	2	yes	complemented
26	#11924527	C₂²	1	2	yes	complemented
27	#11924526	C₂²	1	4	yes	complemented
28	#11924522	C₂²	1	4	yes	complemented
29	#11924521	C₂²	1	4	yes	—
30	#11924521	C₂²	1	4	yes	complemented
31	#11924518	C₂²	1	4	yes	—
32	#11924518	C₂²	1	4	yes	complemented
33	#11924516	C₂²	1	2	yes	—
34	#11924514	C₂²	1	4	yes	complemented
35	#11924512	C₂²	1	2	yes	—
36	#11924512	C₂²	1	2	yes	complemented
37	#11924512	C₂²	1	2	yes	complemented
38	#11924511	C₂²	1	2	yes	complemented
39	#11924510	C₂²	1	2	yes	complemented
40	#11924509	C₂²	1	4	yes	—
41	#11924507	C₂²	1	2	yes	—
42	#11924506	C₂²	1	4	yes	—
43	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃₇	C₂²	1	2	yes	complemented
45	#11924501	C₂²	1	2	yes	complemented
46	C₄×D₁₄₈	C₂²	1	2	yes	—
47	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
48	C₄×D₁₄₈	C₂²	1	2	yes	—
49	C₄×D₁₄₈	C₂²	1	4	yes	complemented
50	C₄×D₁₄₈	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₃₇	C₂²	1	1	yes	characteristic
52	#11924498	C₂²	1	2	yes	—
53	#11924498	C₂²	1	1	yes	characteristic
54	#11924498	C₂²	1	1	yes	characteristic, complemented
55	#11924498	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	—
57	#11924496	C₂²	1	2	yes	—
58	#11924496	C₂²	1	4	yes	complemented
59	#11924495	C₂²	1	2	yes	complemented
60	#11924494	C₂²	1	1	yes	characteristic
61	#11924494	C₂²	1	2	yes	—
62	#11924494	C₂²	1	4	yes	complemented
63	#11924494	C₂²	1	2	yes	complemented
64	#11924494	C₂²	1	2	yes	complemented
65	#11924493	C₂²	1	4	yes	—
66	#11924492	C₂²	1	4	yes	complemented
67	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
68	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
70	C₂²⋊C₄×D₃₇	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₃₇	C₂²	1	4	yes	—
72	C₄²×D₃₇	C₂²	1	1	yes	characteristic
73	C₄²×D₃₇	C₂²	1	4	yes	complemented
74	C₄²×D₃₇	C₂²	1	2	yes	complemented
75	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
76	#126×C₃₇	C₂²	1	4	yes	complemented
77	#124×C₃₇	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₃₇	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
82	#117×C₃₇	C₂²	1	2	yes	complemented
83	C₂³×D₃₇	C₂³	1	2	yes	—
84	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
85	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₃₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₃₇	C₂³	1	4	yes	—
90	C₂²×Dic₃₇	C₂³	1	2	yes	—
91	#10596966	—	2	8	no	—
92	#10596966	—	2	4	no	—
93	D₄×D₃₇	—	2	4	no	—
94	C₂×D₁₄₈	C₂³	1	2	yes	—
95	C₂×D₁₄₈	C₂³	1	4	yes	—
96	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
97	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₃₇	—	2	8	no	—
99	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₃₇	C₂³	1	2	yes	—
101	C₂×C₄×D₃₇	C₂³	1	4	yes	—
102	C₂×C₄×D₃₇	C₂³	1	2	yes	—
103	C₂×C₄×D₃₇	C₂³	1	2	yes	—
104	C₂×C₄×D₃₇	C₂³	1	2	yes	—
105	C₂×C₄×D₃₇	C₂³	1	2	yes	—
106	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₃₇	C₂³	1	4	yes	—
108	C₂×C₄×D₃₇	C₂³	1	2	yes	—
109	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
110	C₂×Dic₇₄	C₂³	1	2	yes	—
111	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
114	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
115	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
116	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
120	C₄²×C₃₇	C₂³	1	1	yes	characteristic
121	C₄²×C₃₇	C₂³	1	4	yes	—
122	C₄²×C₃₇	C₂³	1	2	yes	—
123	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₃₇	C₂³	1	2	yes	—
125	#10596938	C₂³	1	2	yes	—
126	#10596938	C₂³	1	4	yes	—
127	#10596938	C₂³	1	2	yes	—
128	#10596938	C₂³	1	2	yes	—
129	#10596938	C₂³	1	2	yes	—
130	#10596938	C₂³	1	4	yes	—
131	#10596938	C₂³	1	2	yes	—
132	#10596938	C₂³	1	4	yes	—
133	#10596938	C₂³	1	4	yes	—
134	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₃₇	C₂³	1	2	yes	—
137	C₄⋊Dic₃₇	C₂³	1	2	yes	—
138	C₄⋊Dic₃₇	C₂³	1	2	yes	—
139	C₄⋊Dic₃₇	C₂³	1	4	yes	—
140	#10596936	C₂³	1	2	yes	—
141	#10596936	C₂³	1	4	yes	—
142	#10596936	C₂³	1	4	yes	—
143	#10596936	C₂³	1	4	yes	—
144	#10596936	C₂³	1	4	yes	—
145	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
146	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
147	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
148	C₄×Dic₃₇	C₂³	1	2	yes	—
149	C₄×Dic₃₇	C₂³	1	4	yes	—
150	C₄×Dic₃₇	C₂³	1	4	yes	—
151	C₄×Dic₃₇	C₂³	1	2	yes	—
152	C₂³×C₃₇	C₂⁴	1	2	yes	—
153	C₂²×D₃₇	—	2	4	no	—
154	C₂²×D₃₇	—	2	4	no	—
155	C₂²×D₃₇	—	4	2	no	—
156	C₂²×D₃₇	C₂⁴	1	2	yes	—
157	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
158	C₂²×D₃₇	C₂⁴	1	2	yes	—
159	Q₈×C₃₇	—	2	4	no	—
160	Q₈×C₃₇	—	2	2	no	—
161	D₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	4	no	—
163	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
164	C₂×C₄×C₃₇	C₂⁴	1	4	yes	—
165	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
166	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₃₇	—	2	4	no	—
171	C₂²⋊D₃₇	—	4	4	no	—
172	C₂×Dic₃₇	—	2	4	no	—
173	C₂×Dic₃₇	C₂⁴	1	2	yes	—
174	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₃₇	C₂⁴	1	4	yes	—
177	C₂×Dic₃₇	C₂⁴	1	2	yes	—
178	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
179	D₁₄₈	—	2	4	no	—
180	D₁₄₈	—	2	8	no	—
181	D₁₄₈	—	2	2	no	—
182	D₁₄₈	#41	1	4	yes	complemented
183	C₄×D₃₇	—	2	4	no	—
184	C₄×D₃₇	—	2	8	no	—
185	C₄×D₃₇	—	2	4	no	—
186	C₄×D₃₇	—	2	2	no	—
187	C₄×D₃₇	—	2	4	no	—
188	C₄×D₃₇	—	2	4	no	—
189	C₄×D₃₇	—	2	4	no	—
190	C₄×D₃₇	—	4	4	no	—
191	C₄×D₃₇	—	4	1	no	—
192	C₄×D₃₇	—	4	2	no	—
193	C₄×D₃₇	#41	1	4	yes	complemented
194	Dic₇₄	—	4	2	no	—
195	C₂²×C₃₇	—	2	2	no	—
196	C₂²×C₃₇	—	2	2	no	—
197	C₂²×C₃₇	—	2	2	no	—
198	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
199	C₂×D₃₇	—	2	2	no	—
200	C₂×D₃₇	—	2	1	no	—
201	C₂×D₃₇	—	2	2	no	—
202	C₂×D₃₇	—	2	1	no	—
203	C₂×D₃₇	—	2	2	no	—
204	C₂×D₃₇	—	2	2	no	—
205	C₂×D₃₇	—	2	2	no	—
206	C₂×D₃₇	—	4	8	no	—
207	C₂×D₃₇	C₂×#41	1	2	yes	—
208	C₂×D₃₇	C₂×#41	1	4	yes	—
209	C₄×C₃₇	—	2	2	no	—
210	C₄×C₃₇	—	2	4	no	—
211	C₄×C₃₇	—	2	2	no	—
212	C₄×C₃₇	—	2	1	no	—
213	C₄×C₃₇	—	2	2	no	—
214	C₄×C₃₇	C₂×#41	1	2	yes	—
215	C₄×C₃₇	C₂×#41	1	2	yes	—
216	Dic₃₇	—	2	2	no	—
217	Dic₃₇	—	2	2	no	—
218	Dic₃₇	—	2	1	no	—
219	Dic₃₇	—	2	4	no	—
220	Dic₃₇	—	2	1	no	—
221	Dic₃₇	C₂×#41	1	2	yes	—
222	#3475	—	37	1	no	maximal, Sylow
223	C₂×C₃₇	—	4	2	no	—
224	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
225	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
226	C₂×C₃₇	#585	1	1	yes	characteristic
227	D₃₇	—	2	2	no	—
228	D₃₇	—	2	4	no	—
229	D₃₇	—	4	2	no	—
230	#556	D₃₇	1	1	yes	characteristic, complemented
231	#555	—	37	1	no	—
232	#554	—	37	1	no	—
233	#553	—	37	2	no	—
234	#552	—	37	2	no	—
235	#552	—	37	2	no	—
236	#551	—	37	4	no	—
237	#547	—	37	1	no	—
238	#546	—	37	2	no	—
239	#533	—	37	1	no	—
240	#529	—	37	4	no	—
241	#529	—	37	2	no	—
242	#525	—	37	2	no	—
243	C₄×#41	—	37	2	no	—
244	C₄×#41	—	37	1	no	—
245	C₂×C₄×D₄	—	37	1	no	—
246	C₂×#117	—	37	2	no	—
247	C₃₇	#3475	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	37	1	no	—
249	C₂×#41	—	37	2	no	—
250	C₂²×D₄	—	37	1	no	—
251	C₂³×C₄	—	37	2	no	—
252	C₄⋊Q₈	—	37	1	no	—
253	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
254	#126	—	37	4	no	—
255	#126	—	37	4	no	—
256	#126	C₂×D₃₇	1	4	yes	complemented
257	#125	—	37	4	no	—
258	#125	—	37	2	no	—
259	#125	—	37	2	no	—
260	#124	—	37	4	no	—
261	#124	C₂×D₃₇	1	2	yes	—
262	#123	—	37	4	no	—
263	#123	—	37	4	no	—
264	#123	—	37	4	no	—
265	#123	—	37	4	no	—
266	C₂²⋊Q₈	—	37	2	no	—
267	C₂²⋊Q₈	—	37	2	no	—
268	C₂²⋊Q₈	—	37	2	no	—
269	C₂²⋊Q₈	—	37	4	no	—
270	C₂²⋊Q₈	—	37	2	no	—
271	C₂²⋊Q₈	C₂×D₃₇	1	2	yes	complemented
272	#121	—	37	2	no	—
273	#121	—	37	2	no	—
274	#121	—	37	2	no	—
275	#121	—	37	4	no	—
276	#120	—	37	4	no	—
277	C₄×Q₈	—	37	2	no	—
278	C₄×Q₈	—	37	1	no	—
279	C₄×Q₈	—	37	2	no	—
280	C₄×Q₈	C₂×D₃₇	1	2	yes	complemented
281	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
282	C₄×D₄	—	37	1	no	—
283	C₄×D₄	—	37	2	no	—
284	C₄×D₄	—	37	1	no	—
285	C₄×D₄	—	37	4	no	—
286	C₄×D₄	—	37	2	no	—
287	C₄×D₄	—	37	1	no	—
288	C₄×D₄	—	37	2	no	—
289	C₄×D₄	—	37	4	no	—
290	C₄×D₄	—	37	1	no	—
291	C₄×D₄	—	37	2	no	—
292	C₄×D₄	—	37	2	no	—
293	C₄×D₄	—	37	1	no	—
294	C₄×D₄	—	37	4	no	—
295	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic
296	#117	—	37	2	no	—
297	#117	—	37	1	no	—
298	#117	—	37	2	no	—
299	#117	—	37	2	no	—
300	#117	—	37	4	no	—
301	#117	—	37	2	no	—
302	#117	—	37	4	no	—
303	#117	—	37	4	no	—
304	#117	C₂×D₃₇	1	2	yes	complemented
305	C₂×C₄⋊C₄	—	37	2	no	—
306	C₂×C₄⋊C₄	—	37	2	no	—
307	C₂×C₄⋊C₄	—	37	1	no	—
308	C₂×C₂²⋊C₄	—	37	4	no	—
309	C₂×C₂²⋊C₄	—	37	2	no	—
310	C₂×C₄²	—	37	4	no	—
311	C₂×C₄²	—	37	1	no	—
312	C₂×C₄²	—	37	2	no	—
313	C₂⁴	—	37	2	no	—
314	#41	—	74	4	no	—
315	#41	—	74	8	no	—
316	C₂×Q₈	—	37	2	no	—
317	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
319	C₂×D₄	—	37	2	no	—
320	C₂×D₄	—	37	4	no	—
321	C₂×D₄	—	37	1	no	—
322	C₂×D₄	—	37	2	no	—
323	C₂×D₄	—	37	4	no	—
324	C₂×D₄	—	37	1	no	—
325	C₂×D₄	—	74	4	no	—
326	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
327	C₂²×C₄	—	37	1	no	—
328	C₂²×C₄	—	37	2	no	—
329	C₂²×C₄	—	37	2	no	—
330	C₂²×C₄	—	37	4	no	—
331	C₂²×C₄	—	37	1	no	—
332	C₂²×C₄	—	37	2	no	—
333	C₂²×C₄	—	37	2	no	—
334	C₂²×C₄	—	37	2	no	—
335	C₂²×C₄	—	37	2	no	—
336	C₂²×C₄	—	37	1	no	—
337	C₂²×C₄	—	37	4	no	—
338	C₂²×C₄	—	37	2	no	—
339	C₂²×C₄	—	74	8	no	—
340	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
341	C₄⋊C₄	—	37	4	no	—
342	C₄⋊C₄	—	37	4	no	—
343	C₄⋊C₄	—	37	2	no	—
344	C₄⋊C₄	—	37	4	no	—
345	C₄⋊C₄	—	37	4	no	—
346	C₄⋊C₄	—	37	1	no	—
347	C₄⋊C₄	—	37	2	no	—
348	C₄⋊C₄	—	37	1	no	—
349	C₄⋊C₄	—	37	2	no	—
350	C₄⋊C₄	—	37	4	no	—
351	C₄⋊C₄	—	37	2	no	—
352	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
355	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
356	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
357	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
358	C₂²⋊C₄	—	37	4	no	—
359	C₂²⋊C₄	—	37	2	no	—
360	C₂²⋊C₄	—	37	2	no	—
361	C₂²⋊C₄	—	37	2	no	—
362	C₂²⋊C₄	—	37	4	no	—
363	C₂²⋊C₄	—	37	2	no	—
364	C₂²⋊C₄	—	37	4	no	—
365	C₂²⋊C₄	—	37	2	no	—
366	C₂²⋊C₄	—	37	4	no	—
367	C₂²⋊C₄	—	37	2	no	—
368	C₂²⋊C₄	—	37	4	no	—
369	C₂²⋊C₄	C₂²×D₃₇	1	4	yes	—
370	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₃₇	1	4	yes	—
372	C₄²	—	37	2	no	—
373	C₄²	—	37	1	no	—
374	C₄²	—	37	4	no	—
375	C₄²	—	37	4	no	—
376	C₄²	—	37	1	no	—
377	C₄²	—	37	2	no	—
378	C₄²	—	37	1	no	—
379	C₄²	C₂²×D₃₇	1	4	yes	—
380	C₄²	C₂²×D₃₇	1	1	yes	characteristic
381	C₄²	C₂²×D₃₇	1	2	yes	—
382	C₂³	—	37	1	no	—
383	C₂³	—	37	2	no	—
384	C₂³	—	37	2	no	—
385	C₂³	—	74	4	no	—
386	C₂³	—	74	4	no	—
387	C₂³	—	148	2	no	—
388	C₂³	C₂³×D₃₇	1	2	yes	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	148	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	37	4	no	—
394	D₄	—	74	4	no	—
395	D₄	—	74	8	no	—
396	D₄	—	74	4	no	—
397	D₄	—	74	2	no	—
398	D₄	—	148	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	37	1	no	—
401	C₂×C₄	—	37	4	no	—
402	C₂×C₄	—	37	2	no	—
403	C₂×C₄	—	37	1	no	—
404	C₂×C₄	—	37	4	no	—
405	C₂×C₄	—	37	1	no	—
406	C₂×C₄	—	37	2	no	—
407	C₂×C₄	—	74	4	no	—
408	C₂×C₄	—	74	4	no	—
409	C₂×C₄	—	74	4	no	—
410	C₂×C₄	—	74	8	no	—
411	C₂×C₄	—	74	4	no	—
412	C₂×C₄	—	74	4	no	—
413	C₂×C₄	—	74	2	no	—
414	C₂×C₄	—	74	4	no	—
415	C₂×C₄	—	148	2	no	—
416	C₂×C₄	—	148	4	no	—
417	C₂×C₄	—	148	1	no	—
418	C₂×C₄	C₂³×D₃₇	1	2	yes	—
419	C₂×C₄	C₂³×D₃₇	1	2	yes	—
420	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₃₇	1	4	yes	—
422	C₂×C₄	C₂³×D₃₇	1	2	yes	—
423	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	37	2	no	—
429	C₂²	—	37	4	no	—
430	C₂²	—	74	2	no	—
431	C₂²	—	74	1	no	—
432	C₂²	—	74	2	no	—
433	C₂²	—	74	1	no	—
434	C₂²	—	74	2	no	—
435	C₂²	—	74	2	no	—
436	C₂²	—	74	2	no	—
437	C₂²	—	148	8	no	—
438	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	1	no	—
444	C₄	—	37	2	no	—
445	C₄	—	74	2	no	—
446	C₄	—	74	2	no	—
447	C₄	—	74	1	no	—
448	C₄	—	74	1	no	—
449	C₄	—	74	4	no	—
450	C₄	#41×D₃₇	1	2	yes	—
451	C₄	#41×D₃₇	1	2	yes	—
452	C₂	—	4	2	no	—
453	C₂	—	74	2	no	—
454	C₂	—	74	4	no	—
455	C₂	—	148	2	no	—
456	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
457	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
458	C₂	#14558370	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁵
Fitting	C₃₇×#556	C₂
hypercenter	#556	D₃₇
hypocenter	C₃₇	#3475
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #14558248	C₂	semidirect
2. #14558243	C₂	semidirect
3. #14558227	C₂	semidirect
4. #14558224	C₂	semidirect
5. #14558217	C₂	semidirect
6. #14558208	C₂	semidirect
7. #14558186	C₂	semidirect
8. #14558176	C₂	semidirect
9. #14558088	C₂	semidirect
10. #14558066	C₂	semidirect
11. #14558062	C₂	semidirect
12. #14558046	C₂	semidirect
13. C₄×#10596966	C₂	semidirect
14. C₄×#10596966	C₂	semidirect
15. C₄×D₄×D₃₇	C₂	semidirect
16. #117×D₃₇	C₂	semidirect
17. C₃₇×#556	C₂	semidirect
22. #11924536	C₂²	semidirect
23. #11924530	C₂²	semidirect
24. #11924529	C₂²	semidirect
25. #11924528	C₂²	semidirect
26. #11924527	C₂²	semidirect
27. #11924526	C₂²	semidirect
28. #11924522	C₂²	semidirect
30. #11924521	C₂²	semidirect
32. #11924518	C₂²	semidirect
34. #11924514	C₂²	semidirect
36. #11924512	C₂²	semidirect
37. #11924512	C₂²	semidirect
38. #11924511	C₂²	semidirect
39. #11924510	C₂²	semidirect
43. Q₈×Dic₃₇	C₂²	semidirect
44. Q₈×Dic₃₇	C₂²	semidirect
45. #11924501	C₂²	semidirect
49. C₄×D₁₄₈	C₂²	semidirect
50. C₄×D₁₄₈	C₂²	semidirect
54. #11924498	C₂²	semidirect
55. #11924498	C₂²	semidirect
58. #11924496	C₂²	semidirect
59. #11924495	C₂²	semidirect
62. #11924494	C₂²	semidirect
63. #11924494	C₂²	semidirect
64. #11924494	C₂²	semidirect
66. #11924492	C₂²	semidirect
68. C₄⋊C₄×D₃₇	C₂²	semidirect
69. C₄⋊C₄×D₃₇	C₂²	semidirect
73. C₄²×D₃₇	C₂²	semidirect
74. C₄²×D₃₇	C₂²	semidirect
75. C₄⋊Q₈×C₃₇	C₂²	semidirect
76. #126×C₃₇	C₂²	semidirect
78. C₂²⋊Q₈×C₃₇	C₂²	semidirect
79. C₄×Q₈×C₃₇	C₂²	semidirect
80. C₄×Q₈×C₃₇	C₂²	semidirect
82. #117×C₃₇	C₂²	semidirect
182. D₁₄₈	#41	semidirect
193. C₄×D₃₇	#41	semidirect
230. #556	D₃₇	semidirect
247. C₃₇	#3475	semidirect
253. C₄⋊Q₈	C₂×D₃₇	semidirect
256. #126	C₂×D₃₇	semidirect
271. C₂²⋊Q₈	C₂×D₃₇	semidirect
280. C₄×Q₈	C₂×D₃₇	semidirect
281. C₄×Q₈	C₂×D₃₇	semidirect
304. #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
#14558248	2
#14558243	2
#14558227	2
#14558224	2
#14558217	2
#14558208	2
#14558186	2
#14558176	2
#14558088	2
#14558066	2
#14558062	2
#14558046	2
C₄×#10596966	2
C₄×D₄×D₃₇	2
#117×D₃₇	2
C₃₇×#556	2
#3475	37