Subgroups — #2943×C₁₄₉ #34041856

Order 19072.

492 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄×#41×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#442×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#441×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#440×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	#427×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#416×C₁₄₉	C₂	1	2	yes	maximal, complemented
8	C₂×#97×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#41×C₁₄₉	C₂²	1	2	yes	—
10	#135×C₁₄₉	C₄	1	8	yes	complemented
11	C₂×Q₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
12	C₂×SD₁₆×C₁₄₉	C₂²	1	2	yes	—
13	C₂×D₈×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₄×Q₈×C₁₄₉	C₂²	1	4	yes	—
17	C₄×D₄×C₁₄₉	—	2	4	no	—
18	C₄×D₄×C₁₄₉	C₂²	1	4	yes	—
19	#117×C₁₄₉	—	2	2	no	—
20	#117×C₁₄₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₄₉	—	2	2	no	—
22	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
23	#107×C₁₄₉	C₂²	1	2	yes	—
24	#106×C₁₄₉	C₂²	1	2	yes	—
25	#103×C₁₄₉	C₂²	1	4	yes	—
26	#102×C₁₄₉	C₂²	1	4	yes	—
27	#97×C₁₄₉	C₂²	1	2	yes	—
28	#97×C₁₄₉	C₂²	1	2	yes	—
29	#41×C₁₄₉	—	2	4	no	—
30	#41×C₁₄₉	C₂×C₄	1	8	yes	complemented
31	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
32	C₂×D₄×C₁₄₉	—	2	2	no	—
33	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₄₉	—	2	2	no	—
35	C₂²×C₄×C₁₄₉	—	2	4	no	—
36	C₂²×C₄×C₁₄₉	D₄	1	2	yes	—
37	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
38	Q₁₆×C₁₄₉	C₂×C₄	1	4	yes	complemented
39	SD₁₆×C₁₄₉	C₂×C₄	1	8	yes	complemented
40	D₈×C₁₄₉	C₂×C₄	1	4	yes	complemented
41	C₂×C₈×C₁₄₉	—	2	2	no	—
42	C₂×C₈×C₁₄₉	C₂×C₄	1	4	yes	complemented
43	C₂×C₈×C₁₄₉	C₂³	1	2	yes	—
44	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
45	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
46	C₄⋊C₄×C₁₄₉	—	2	4	no	—
47	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
48	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
49	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
50	C₄²×C₁₄₉	—	2	4	no	—
51	C₄²×C₁₄₉	—	2	2	no	—
52	C₄²×C₁₄₉	D₄	1	2	yes	—
53	C₄²×C₁₄₉	C₂³	1	2	yes	—
54	C₂³×C₁₄₉	—	2	2	no	—
55	C₂³×C₁₄₉	C₂×D₄	1	1	yes	characteristic
56	Q₈×C₁₄₉	—	2	2	no	—
57	Q₈×C₁₄₉	C₂²×C₄	1	4	yes	—
58	D₄×C₁₄₉	—	2	8	no	—
59	D₄×C₁₄₉	—	2	2	no	—
60	D₄×C₁₄₉	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₁₄₉	—	2	2	no	—
62	C₂×C₄×C₁₄₉	—	2	8	no	—
63	C₂×C₄×C₁₄₉	—	2	4	no	—
64	C₂×C₄×C₁₄₉	—	4	2	no	—
65	C₂×C₄×C₁₄₉	—	4	8	no	—
66	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
67	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
68	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₄₉	#41	1	2	yes	—
70	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
71	C₈×C₁₄₉	—	2	2	no	—
72	C₈×C₁₄₉	C₂²×C₄	1	2	yes	—
73	C₈×C₁₄₉	C₂²×C₄	1	2	yes	—
74	C₂²×C₁₄₉	—	2	2	no	—
75	C₂²×C₁₄₉	—	2	4	no	—
76	C₂²×C₁₄₉	—	4	4	no	—
77	C₂²×C₁₄₉	C₄×D₄	1	2	yes	—
78	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
79	C₄×C₁₄₉	—	2	4	no	—
80	C₄×C₁₄₉	—	2	4	no	—
81	C₄×C₁₄₉	—	4	4	no	—
82	C₄×C₁₄₉	C₄×D₄	1	2	yes	—
83	C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
84	C₄×C₁₄₉	C₂×#41	1	1	yes	characteristic
85	C₂×C₁₄₉	—	2	2	no	—
86	C₂×C₁₄₉	—	4	4	no	—
87	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
88	C₂×C₁₄₉	#575	1	2	yes	—
89	C₁₄₉	#2943	1	1	yes	characteristic, direct product factor, Sylow
90	#2943	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂×#135	C₂×C₁₄₉	1	1	yes	characteristic
92	C₄×#41	C₂×C₁₄₉	1	2	yes	complemented
93	#442	C₂×C₁₄₉	1	2	yes	complemented
94	#441	C₂×C₁₄₉	1	2	yes	complemented
95	#440	C₂×C₁₄₉	1	4	yes	complemented
96	#427	C₂×C₁₄₉	1	1	yes	characteristic, complemented
97	#416	C₂×C₁₄₉	1	2	yes	complemented
98	C₂×#97	C₂×C₁₄₉	1	1	yes	characteristic, complemented
99	C₂×#41	C₂²×C₁₄₉	1	2	yes	—
100	#135	C₄×C₁₄₉	1	8	yes	complemented
101	C₂×Q₁₆	C₂²×C₁₄₉	1	1	yes	characteristic
102	C₂×SD₁₆	C₂²×C₁₄₉	1	2	yes	—
103	C₂×D₈	C₂²×C₁₄₉	1	1	yes	characteristic
104	C₂²×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
105	C₂²×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
106	C₄×Q₈	C₂²×C₁₄₉	1	4	yes	—
107	C₄×D₄	—	2	4	no	—
108	C₄×D₄	C₂²×C₁₄₉	1	4	yes	—
109	#117	—	2	2	no	—
110	#117	C₂²×C₁₄₉	1	2	yes	—
111	C₂×C₄²	—	2	2	no	—
112	C₂×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
113	#107	C₂²×C₁₄₉	1	2	yes	—
114	#106	C₂²×C₁₄₉	1	2	yes	—
115	#103	C₂²×C₁₄₉	1	4	yes	—
116	#102	C₂²×C₁₄₉	1	4	yes	—
117	#97	C₂²×C₁₄₉	1	2	yes	—
118	#97	C₂²×C₁₄₉	1	2	yes	—
119	#41	—	2	4	no	—
120	#41	C₂×C₄×C₁₄₉	1	8	yes	complemented
121	C₂×Q₈	C₂³×C₁₄₉	1	2	yes	—
122	C₂×D₄	—	2	2	no	—
123	C₂×D₄	C₂³×C₁₄₉	1	2	yes	—
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	D₄×C₁₄₉	1	2	yes	—
127	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
128	Q₁₆	C₂×C₄×C₁₄₉	1	4	yes	complemented
129	SD₁₆	C₂×C₄×C₁₄₉	1	8	yes	complemented
130	D₈	C₂×C₄×C₁₄₉	1	4	yes	complemented
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	C₂×C₄×C₁₄₉	1	4	yes	complemented
133	C₂×C₈	C₂³×C₁₄₉	1	2	yes	—
134	C₂×C₈	C₂³×C₁₄₉	1	1	yes	characteristic
135	C₂×C₈	C₂³×C₁₄₉	1	1	yes	characteristic
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	C₂³×C₁₄₉	1	4	yes	—
138	C₂²⋊C₄	—	2	2	no	—
139	C₂²⋊C₄	—	2	4	no	—
140	C₄²	—	2	2	no	—
141	C₄²	—	2	4	no	—
142	C₄²	D₄×C₁₄₉	1	2	yes	—
143	C₄²	C₂³×C₁₄₉	1	2	yes	—
144	C₂³	—	2	2	no	—
145	C₂³	C₂×D₄×C₁₄₉	1	1	yes	characteristic
146	Q₈	—	2	2	no	—
147	Q₈	C₂²×C₄×C₁₄₉	1	4	yes	—
148	D₄	—	2	8	no	—
149	D₄	—	2	2	no	—
150	D₄	C₂²×C₄×C₁₄₉	1	4	yes	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	8	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	8	no	—
156	C₂×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
157	C₂×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
158	C₂×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
159	C₂×C₄	#41×C₁₄₉	1	2	yes	—
160	C₂×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
161	C₈	—	2	2	no	—
162	C₈	C₂²×C₄×C₁₄₉	1	2	yes	—
163	C₈	C₂²×C₄×C₁₄₉	1	2	yes	—
164	C₂²	—	2	2	no	—
165	C₂²	—	2	4	no	—
166	C₂²	—	4	4	no	—
167	C₂²	C₄×D₄×C₁₄₉	1	2	yes	—
168	C₂²	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
169	C₄	—	2	4	no	—
170	C₄	—	2	4	no	—
171	C₄	—	4	4	no	—
172	C₄	C₄×D₄×C₁₄₉	1	2	yes	—
173	C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
174	C₄	C₂×#41×C₁₄₉	1	1	yes	characteristic
175	C₂	—	2	2	no	—
176	C₂	—	4	4	no	—
177	C₂	C₂×C₄×D₄×C₁₄₉	1	1	yes	characteristic
178	C₂	#575×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×D₄
prime radical	C₂×#135×C₁₄₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#41×C₁₄₉	C₂	semidirect
3. #442×C₁₄₉	C₂	semidirect
4. #441×C₁₄₉	C₂	semidirect
5. #440×C₁₄₉	C₂	semidirect
6. #427×C₁₄₉	C₂	semidirect
7. #416×C₁₄₉	C₂	semidirect
8. C₂×#97×C₁₄₉	C₂	semidirect
10. #135×C₁₄₉	C₄	semidirect
30. #41×C₁₄₉	C₂×C₄	semidirect
38. Q₁₆×C₁₄₉	C₂×C₄	semidirect
39. SD₁₆×C₁₄₉	C₂×C₄	semidirect
40. D₈×C₁₄₉	C₂×C₄	semidirect
42. C₂×C₈×C₁₄₉	C₂×C₄	semidirect
89. C₁₄₉	#2943	direct (N × H)
90. #2943	C₁₄₉	direct (N × H)
92. C₄×#41	C₂×C₁₄₉	semidirect
93. #442	C₂×C₁₄₉	semidirect
94. #441	C₂×C₁₄₉	semidirect
95. #440	C₂×C₁₄₉	semidirect
96. #427	C₂×C₁₄₉	semidirect
97. #416	C₂×C₁₄₉	semidirect
98. C₂×#97	C₂×C₁₄₉	semidirect
100. #135	C₄×C₁₄₉	semidirect
120. #41	C₂×C₄×C₁₄₉	semidirect
128. Q₁₆	C₂×C₄×C₁₄₉	semidirect
129. SD₁₆	C₂×C₄×C₁₄₉	semidirect
130. D₈	C₂×C₄×C₁₄₉	semidirect
132. C₂×C₈	C₂×C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#135×C₁₄₉	2
C₄×#41×C₁₄₉	2
#442×C₁₄₉	2
#441×C₁₄₉	2
#440×C₁₄₉	2
#427×C₁₄₉	2
#416×C₁₄₉	2
C₂×#97×C₁₄₉	2
#2943	149

Subgroups — #2943×C149 #34041856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2943×C₁₄₉ #34041856