Subgroups — D₃₇⋊#444 #18011367

Order 4736.

464 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊#131	C₂	1	2	yes	maximal, complemented
2	#14558580	C₂	1	2	yes	maximal, complemented
3	#14558579	C₂	1	2	yes	maximal, complemented
4	#14558578	C₂	1	4	yes	maximal, complemented
5	D₃₇⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃₇⋊#104	C₂	1	2	yes	maximal, complemented
7	C₂×#11924590	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×D₃₇	C₂	1	1	yes	maximal, characteristic
9	#11924624	C₂²	1	4	yes	complemented
10	#11924623	—	2	4	no	—
11	#11924623	C₂²	1	4	yes	complemented
12	D₃₇⋊M₁₆	—	2	2	no	—
13	D₃₇⋊M₁₆	C₂²	1	2	yes	—
14	C₂×D₃₇⋊C₈	—	2	2	no	—
15	C₂×D₃₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×#3866	C₂²	1	1	yes	characteristic
17	#11924607	C₂²	1	2	yes	complemented
18	#11924606	C₂²	1	2	yes	complemented
19	#11924601	C₂²	1	4	yes	complemented
20	#11924600	C₂²	1	4	yes	complemented
21	#11924590	C₂²	1	2	yes	complemented
22	#11924590	C₂²	1	2	yes	complemented
23	#41×D₃₇	C₂²	1	2	yes	—
24	#11924559	C₂²	1	1	yes	characteristic
25	#11924558	C₄	1	1	yes	characteristic, complemented
26	#11924557	C₂²	1	2	yes	—
27	#11924556	C₄	1	2	yes	complemented
28	#11924555	C₂²	1	1	yes	characteristic
29	Q₁₆×D₃₇	C₄	1	1	yes	characteristic, complemented
30	SD₁₆×D₃₇	C₄	1	2	yes	complemented
31	D₈×D₃₇	C₄	1	1	yes	characteristic, complemented
32	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
33	#135×C₃₇	C₄	1	1	yes	characteristic, complemented
34	C₂²×#3866	—	2	1	no	—
35	#41×C₃₇	C₂×C₄	1	2	yes	—
36	#10596966	C₂³	1	2	yes	—
37	Q₈×D₃₇	C₂×C₄	1	2	yes	—
38	#10596964	—	2	2	no	—
39	#10596964	C₂³	1	2	yes	—
40	D₄×D₃₇	—	2	2	no	—
41	D₄×D₃₇	C₂×C₄	1	2	yes	—
42	#10596962	—	2	2	no	—
43	#10596962	C₂×C₄	1	2	yes	—
44	C₂×C₄×D₃₇	—	2	2	no	—
45	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
46	#10596957	—	2	2	no	—
47	#10596957	—	2	4	no	—
48	C₂×#64438	—	2	4	no	—
49	C₂×#64438	D₄	1	2	yes	—
50	C₄×#3866	—	2	1	no	—
51	C₄×#3866	C₂³	1	2	yes	—
52	#10596953	—	2	4	no	—
53	#10596953	C₂³	1	4	yes	—
54	D₃₇⋊C₈	—	2	2	no	—
55	D₃₇⋊C₈	—	2	4	no	—
56	D₃₇⋊C₈	D₄	1	2	yes	—
57	D₃₇⋊C₈	C₂³	1	2	yes	—
58	Q₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
59	SD₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
60	D₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
62	#10596942	C₂×C₄	1	2	yes	complemented
63	#10596941	C₂×C₄	1	2	yes	complemented
64	#10596940	C₂×C₄	1	2	yes	complemented
65	#10596939	C₂×C₄	1	2	yes	complemented
66	C₂×#64436	C₂×C₄	1	1	yes	characteristic
67	Dic₁₄₈	C₂×C₄	1	1	yes	characteristic, complemented
68	D₂₉₆	C₂×C₄	1	1	yes	characteristic, complemented
69	#10596930	C₂×C₄	1	2	yes	complemented
70	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
71	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
72	C₈×D₃₇	C₂³	1	1	yes	characteristic
73	C₈×D₃₇	C₂³	1	1	yes	characteristic
74	C₂²×D₃₇	—	2	2	no	—
75	C₂²×D₃₇	#41	1	1	yes	characteristic
76	C₂×#3866	—	2	2	no	—
77	C₂×#3866	—	4	2	no	—
78	Q₈×C₃₇	C₂²×C₄	1	2	yes	—
79	D₄×C₃₇	—	2	2	no	—
80	D₄×C₃₇	C₂²×C₄	1	2	yes	—
81	C₂×C₄×C₃₇	—	2	2	no	—
82	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²⋊D₃₇	—	2	2	no	—
84	C₂²⋊D₃₇	—	2	2	no	—
85	C₂²⋊D₃₇	—	2	2	no	—
86	C₂×Dic₃₇	—	2	2	no	—
87	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
88	D₁₄₈	—	2	2	no	—
89	D₁₄₈	C₂²×C₄	1	2	yes	—
90	C₄×D₃₇	—	2	2	no	—
91	C₄×D₃₇	—	2	2	no	—
92	C₄×D₃₇	—	2	2	no	—
93	C₄×D₃₇	C₂²×C₄	1	1	yes	characteristic
94	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
95	C₄×D₃₇	#41	1	1	yes	characteristic
96	C₄×D₃₇	C₂⁴	1	1	yes	characteristic
97	Dic₇₄	—	2	2	no	—
98	Dic₇₄	C₂²×C₄	1	2	yes	—
99	#64438	—	2	4	no	—
100	#64438	C₂×D₄	1	4	yes	—
101	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
102	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
103	#64436	C₂²×C₄	1	1	yes	characteristic
104	#64436	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₃₇	—	2	2	no	—
106	C₂²×C₃₇	C₄×D₄	1	1	yes	characteristic
107	C₂×D₃₇	—	2	2	no	—
108	C₂×D₃₇	—	2	2	no	—
109	C₂×D₃₇	—	4	4	no	—
110	C₂×D₃₇	C₄×D₄	1	1	yes	characteristic
111	C₂×D₃₇	C₂×#41	1	1	yes	characteristic
112	#3866	—	4	2	no	—
113	C₄×C₃₇	—	2	2	no	—
114	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
115	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
116	Dic₃₇	—	2	2	no	—
117	Dic₃₇	C₄×D₄	1	1	yes	characteristic
118	Dic₃₇	C₂²×D₄	1	1	yes	characteristic
119	C₂×#444	—	37	1	no	maximal, Sylow
120	C₂×C₃₇	—	2	1	no	—
121	C₂×C₃₇	—	4	2	no	—
122	C₂×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
123	D₃₇	—	2	1	no	—
124	D₃₇	—	4	2	no	—
125	D₃₇	#444	1	2	yes	complemented
126	C₂×#135	—	37	1	no	—
127	C₂×#131	—	37	2	no	—
128	#444	—	37	4	no	—
129	#444	—	37	2	no	—
130	#444	—	37	2	no	—
131	C₂×#108	—	37	1	no	—
132	C₂×#104	—	37	2	no	—
133	C₂×#97	—	37	1	no	—
134	C₃₇	C₂×#444	1	1	yes	characteristic, complemented, Sylow
135	C₂×#41	—	37	2	no	—
136	#135	—	37	2	no	—
137	#135	—	37	1	no	—
138	#135	—	37	2	no	—
139	#135	—	37	1	no	—
140	#135	—	37	1	no	—
141	#135	#3866	1	1	yes	characteristic, complemented
142	C₂×Q₁₆	—	37	1	no	—
143	C₂×SD₁₆	—	37	2	no	—
144	C₂×D₈	—	37	1	no	—
145	#131	—	37	4	no	—
146	#131	—	37	4	no	—
147	#131	—	74	4	no	—
148	C₂×M₁₆	—	37	2	no	—
149	C₂×M₁₆	—	74	2	no	—
150	C₂²×C₈	—	37	1	no	—
151	C₂²×C₈	—	37	1	no	—
152	C₂²×C₈	—	74	2	no	—
153	C₂×C₄²	—	37	1	no	—
154	#108	—	37	2	no	—
155	#108	—	37	2	no	—
156	#104	—	37	4	no	—
157	#104	—	37	4	no	—
158	#97	—	37	2	no	—
159	#97	—	37	2	no	—
160	#41	—	37	2	no	—
161	#41	—	37	2	no	—
162	#41	—	37	2	no	—
163	#41	—	74	2	no	—
164	#41	—	74	2	no	—
165	#41	C₂×#3866	1	2	yes	—
166	C₂×Q₈	—	37	2	no	—
167	C₂×D₄	—	37	2	no	—
168	C₂×D₄	—	74	2	no	—
169	C₂²×C₄	—	37	1	no	—
170	C₂²×C₄	—	74	2	no	—
171	C₂²×C₄	—	74	1	no	—
172	Q₁₆	—	37	2	no	—
173	Q₁₆	—	37	1	no	—
174	Q₁₆	C₂×#3866	1	1	yes	characteristic, complemented
175	SD₁₆	—	37	2	no	—
176	SD₁₆	—	37	2	no	—
177	SD₁₆	—	37	2	no	—
178	SD₁₆	C₂×#3866	1	2	yes	complemented
179	D₈	—	37	2	no	—
180	D₈	—	37	1	no	—
181	D₈	C₂×#3866	1	1	yes	characteristic, complemented
182	M₁₆	—	37	4	no	—
183	M₁₆	—	74	4	no	—
184	M₁₆	—	74	4	no	—
185	M₁₆	—	74	2	no	—
186	C₂×C₈	—	37	2	no	—
187	C₂×C₈	—	37	2	no	—
188	C₂×C₈	—	37	2	no	—
189	C₂×C₈	—	37	1	no	—
190	C₂×C₈	—	37	1	no	—
191	C₂×C₈	—	37	1	no	—
192	C₂×C₈	—	37	1	no	—
193	C₂×C₈	—	37	1	no	—
194	C₂×C₈	—	74	4	no	—
195	C₂×C₈	—	74	4	no	—
196	C₂×C₈	—	74	2	no	—
197	C₂×C₈	C₂×#3866	1	1	yes	characteristic
198	C₄²	—	37	2	no	—
199	C₄²	—	74	1	no	—
200	C₂³	—	37	1	no	—
201	C₂³	—	74	2	no	—
202	Q₈	—	37	2	no	—
203	Q₈	—	74	2	no	—
204	Q₈	C₂²×#3866	1	2	yes	—
205	D₄	—	2	2	no	—
206	D₄	—	37	2	no	—
207	D₄	—	74	2	no	—
208	D₄	—	74	2	no	—
209	D₄	—	74	2	no	—
210	D₄	—	74	2	no	—
211	D₄	C₂²×#3866	1	2	yes	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	37	1	no	—
214	C₂×C₄	—	37	1	no	—
215	C₂×C₄	—	37	1	no	—
216	C₂×C₄	—	37	1	no	—
217	C₂×C₄	—	37	1	no	—
218	C₂×C₄	—	74	2	no	—
219	C₂×C₄	—	74	2	no	—
220	C₂×C₄	—	74	2	no	—
221	C₂×C₄	—	74	2	no	—
222	C₂×C₄	—	74	2	no	—
223	C₂×C₄	—	148	2	no	—
224	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
225	C₈	—	37	4	no	—
226	C₈	—	37	1	no	—
227	C₈	—	37	1	no	—
228	C₈	—	74	4	no	—
229	C₈	C₂²×#3866	1	1	yes	characteristic
230	C₈	C₂²×#3866	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	37	1	no	—
233	C₂²	—	37	1	no	—
234	C₂²	—	74	2	no	—
235	C₂²	—	74	2	no	—
236	C₂²	—	148	4	no	—
237	C₂²	D₄×#3866	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	37	1	no	—
240	C₄	—	37	1	no	—
241	C₄	—	74	2	no	—
242	C₄	—	148	2	no	—
243	C₄	D₄×#3866	1	1	yes	characteristic
244	C₄	C₂³×#3866	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	4	2	no	—
247	C₂	—	37	2	no	—
248	C₂	—	74	1	no	—
249	C₂	—	148	2	no	—
250	C₂	C₂×D₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×#3866
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₄	C₂³×#3866
Fitting	#135×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄×D₄
prime radical	#135×D₃₇	C₂
cosocle	C₄×D₃₇	C₂⁴
hypercenter	#135	#3866
hypocenter	C₃₇	C₂×#444
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. D₃₇⋊#131	C₂	semidirect
2. #14558580	C₂	semidirect
3. #14558579	C₂	semidirect
4. #14558578	C₂	semidirect
5. D₃₇⋊#108	C₂	semidirect
6. D₃₇⋊#104	C₂	semidirect
7. C₂×#11924590	C₂	semidirect
9. #11924624	C₂²	semidirect
11. #11924623	C₂²	semidirect
17. #11924607	C₂²	semidirect
18. #11924606	C₂²	semidirect
19. #11924601	C₂²	semidirect
20. #11924600	C₂²	semidirect
21. #11924590	C₂²	semidirect
22. #11924590	C₂²	semidirect
25. #11924558	C₄	semidirect
27. #11924556	C₄	semidirect
29. Q₁₆×D₃₇	C₄	semidirect
30. SD₁₆×D₃₇	C₄	semidirect
31. D₈×D₃₇	C₄	semidirect
33. #135×C₃₇	C₄	semidirect
58. Q₁₆×C₃₇	C₂×C₄	semidirect
59. SD₁₆×C₃₇	C₂×C₄	semidirect
60. D₈×C₃₇	C₂×C₄	semidirect
62. #10596942	C₂×C₄	semidirect
63. #10596941	C₂×C₄	semidirect
64. #10596940	C₂×C₄	semidirect
65. #10596939	C₂×C₄	semidirect
67. Dic₁₄₈	C₂×C₄	semidirect
68. D₂₉₆	C₂×C₄	semidirect
69. #10596930	C₂×C₄	semidirect
125. D₃₇	#444	semidirect
134. C₃₇	C₂×#444	semidirect
141. #135	#3866	semidirect
174. Q₁₆	C₂×#3866	semidirect
178. SD₁₆	C₂×#3866	semidirect
181. D₈	C₂×#3866	semidirect

Maximal subgroups

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

subgroup	index
D₃₇⋊#131	2
#14558580	2
#14558579	2
#14558578	2
D₃₇⋊#108	2
D₃₇⋊#104	2
C₂×#11924590	2
#135×D₃₇	2
C₂×#444	37

Subgroups — D37⋊#444 #18011367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇⋊#444 #18011367