Subgroups — C₃×C₂²⋊#95 #72148

Order 384.

1088 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₃×#95	C₂	1	4	yes	maximal, complemented
4	C₂²⋊#95	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁵×C₃	C₂²	1	1	yes	characteristic
6	C₂³×C₃×C₄	—	2	4	no	—
7	C₂³×C₃×C₄	—	2	8	no	—
8	C₂³×C₃×C₄	C₄	1	4	yes	complemented
9	C₂³×C₃×C₄	C₂²	1	4	yes	—
10	C₂³×C₃×C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
12	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
13	C₂×C₃×C₂²⋊C₄	C₄	1	8	yes	complemented
14	C₃×#95	—	2	8	no	—
15	C₂⁴×C₄	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄	C₂×C₃	1	2	yes	—
17	C₂×#95	C₂×C₃	1	4	yes	complemented
18	C₂⁴×C₃	—	2	4	no	—
19	C₂⁴×C₃	—	2	4	no	—
20	C₂⁴×C₃	C₂×C₄	1	4	yes	—
21	C₂⁴×C₃	C₂×C₄	1	2	yes	—
22	C₂⁴×C₃	D₄	1	2	yes	—
23	C₂⁴×C₃	D₄	1	4	yes	—
24	C₂⁴×C₃	Q₈	1	2	yes	—
25	C₂⁴×C₃	C₂³	1	1	yes	characteristic
26	C₂²×C₃×C₄	—	2	32	no	—
27	C₂²×C₃×C₄	—	2	8	no	—
28	C₂²×C₃×C₄	—	2	4	no	—
29	C₂²×C₃×C₄	—	2	4	no	—
30	C₂²×C₃×C₄	—	2	16	no	—
31	C₂²×C₃×C₄	—	2	8	no	—
32	C₂²×C₃×C₄	—	2	4	no	—
33	C₂²×C₃×C₄	—	2	4	no	—
34	C₂²×C₃×C₄	—	2	8	no	—
35	C₂²×C₃×C₄	C₂×C₄	1	4	yes	—
36	C₂²×C₃×C₄	C₂×C₄	1	8	yes	complemented
37	C₂²×C₃×C₄	D₄	1	8	yes	—
38	C₃×C₂²⋊C₄	—	2	16	no	—
39	C₂⁵	C₂²×C₃	1	1	yes	characteristic
40	C₂³×C₄	—	2	4	no	—
41	C₂³×C₄	—	2	8	no	—
42	C₂³×C₄	C₃×C₄	1	4	yes	complemented
43	C₂³×C₄	C₂²×C₃	1	4	yes	—
44	C₂³×C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₂²⋊C₄	—	2	4	no	—
46	C₂×C₂²⋊C₄	—	2	4	no	—
47	C₂×C₂²⋊C₄	C₃×C₄	1	8	yes	complemented
48	#95	—	2	8	no	—
49	C₂³×C₃	—	2	4	no	—
50	C₂³×C₃	—	2	4	no	—
51	C₂³×C₃	—	2	16	no	—
52	C₂³×C₃	—	2	8	no	—
53	C₂³×C₃	—	2	8	no	—
54	C₂³×C₃	—	2	8	no	—
55	C₂³×C₃	—	2	8	no	—
56	C₂³×C₃	C₄²	1	4	yes	—
57	C₂³×C₃	C₂²⋊C₄	1	8	yes	—
58	C₂³×C₃	C₂²⋊C₄	1	4	yes	—
59	C₂³×C₃	C₄⋊C₄	1	4	yes	—
60	C₂³×C₃	C₄⋊C₄	1	8	yes	—
61	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
62	C₂³×C₃	C₂²×C₄	1	2	yes	—
63	C₂³×C₃	C₂×D₄	1	2	yes	—
64	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
65	C₂³×C₃	C₂×D₄	1	4	yes	—
66	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
67	C₂³×C₃	#41	1	4	yes	—
68	C₂×C₃×C₄	—	2	32	no	—
69	C₂×C₃×C₄	—	2	4	no	—
70	C₂×C₃×C₄	—	2	4	no	—
71	C₂×C₃×C₄	—	2	16	no	—
72	C₂×C₃×C₄	—	2	8	no	—
73	C₂×C₃×C₄	—	2	16	no	—
74	C₂×C₃×C₄	—	4	4	no	—
75	C₂×C₃×C₄	—	4	8	no	—
76	C₂×C₃×C₄	—	4	4	no	—
77	C₂×C₃×C₄	C₂²⋊C₄	1	8	yes	complemented
78	C₂⁴	—	2	4	no	—
79	C₂⁴	—	2	4	no	—
80	C₂⁴	C₂×C₃×C₄	1	4	yes	—
81	C₂⁴	C₂×C₃×C₄	1	2	yes	—
82	C₂⁴	C₃×D₄	1	2	yes	—
83	C₂⁴	C₃×D₄	1	4	yes	—
84	C₂⁴	C₃×Q₈	1	2	yes	—
85	C₂⁴	C₂³×C₃	1	1	yes	characteristic
86	C₂²×C₄	—	2	32	no	—
87	C₂²×C₄	—	2	8	no	—
88	C₂²×C₄	—	2	4	no	—
89	C₂²×C₄	—	2	4	no	—
90	C₂²×C₄	—	2	16	no	—
91	C₂²×C₄	—	2	8	no	—
92	C₂²×C₄	—	2	4	no	—
93	C₂²×C₄	—	2	4	no	—
94	C₂²×C₄	—	2	8	no	—
95	C₂²×C₄	C₂×C₃×C₄	1	4	yes	—
96	C₂²×C₄	C₂×C₃×C₄	1	8	yes	complemented
97	C₂²×C₄	C₃×D₄	1	8	yes	—
98	C₂²⋊C₄	—	2	16	no	—
99	C₂²×C₃	—	2	8	no	—
100	C₂²×C₃	—	2	4	no	—
101	C₂²×C₃	—	2	8	no	—
102	C₂²×C₃	—	2	4	no	—
103	C₂²×C₃	—	2	16	no	—
104	C₂²×C₃	—	2	16	no	—
105	C₂²×C₃	#95	1	8	yes	complemented
106	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
107	C₂²×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₃	C₂×C₂²⋊C₄	1	2	yes	—
109	C₂²×C₃	C₂×C₂²⋊C₄	1	2	yes	—
110	C₂²×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₃	C₂×C₄⋊C₄	1	2	yes	—
112	C₂²×C₃	#117	1	2	yes	—
113	C₂²×C₃	C₄×D₄	1	8	yes	—
114	C₂²×C₃	#120	1	4	yes	—
115	C₂²×C₃	#121	1	4	yes	—
116	C₂²×C₃	C₂²⋊Q₈	1	4	yes	—
117	C₂²×C₃	#123	1	4	yes	—
118	C₃×C₄	—	2	8	no	—
119	C₃×C₄	—	4	8	no	—
120	C₂³	—	2	4	no	—
121	C₂³	—	2	4	no	—
122	C₂³	—	2	16	no	—
123	C₂³	—	2	8	no	—
124	C₂³	—	2	8	no	—
125	C₂³	—	2	8	no	—
126	C₂³	—	2	8	no	—
127	C₂³	C₃×C₄²	1	4	yes	—
128	C₂³	C₃×C₂²⋊C₄	1	8	yes	—
129	C₂³	C₃×C₂²⋊C₄	1	4	yes	—
130	C₂³	C₃×C₄⋊C₄	1	4	yes	—
131	C₂³	C₃×C₄⋊C₄	1	8	yes	—
132	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
133	C₂³	C₂²×C₃×C₄	1	2	yes	—
134	C₂³	C₂×C₃×D₄	1	2	yes	—
135	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
136	C₂³	C₂×C₃×D₄	1	4	yes	—
137	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
138	C₂³	C₃×#41	1	4	yes	—
139	C₂×C₄	—	2	32	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	2	16	no	—
143	C₂×C₄	—	2	8	no	—
144	C₂×C₄	—	2	16	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	—	4	8	no	—
147	C₂×C₄	—	4	4	no	—
148	C₂×C₄	C₃×C₂²⋊C₄	1	8	yes	complemented
149	C₂×C₃	—	2	8	no	—
150	C₂×C₃	C₂×#95	1	1	yes	characteristic
151	C₂×C₃	C₄×C₂²⋊C₄	1	2	yes	—
152	C₂×C₃	#379	1	1	yes	characteristic
153	C₂×C₃	#380	1	2	yes	—
154	C₂×C₃	#381	1	1	yes	characteristic
155	C₂×C₃	#385	1	4	yes	—
156	C₂×C₃	#386	1	4	yes	—
157	C₂²	—	2	8	no	—
158	C₂²	—	2	4	no	—
159	C₂²	—	2	8	no	—
160	C₂²	—	2	4	no	—
161	C₂²	—	2	16	no	—
162	C₂²	—	2	16	no	—
163	C₂²	C₃×#95	1	8	yes	complemented
164	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
165	C₂²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
166	C₂²	C₂×C₃×C₂²⋊C₄	1	2	yes	—
167	C₂²	C₂×C₃×C₂²⋊C₄	1	2	yes	—
168	C₂²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂²	C₂×C₃×C₄⋊C₄	1	2	yes	—
170	C₂²	C₃×#117	1	2	yes	—
171	C₂²	C₃×C₄×D₄	1	8	yes	—
172	C₂²	C₃×#120	1	4	yes	—
173	C₂²	C₃×#121	1	4	yes	—
174	C₂²	C₃×C₂²⋊Q₈	1	4	yes	—
175	C₂²	C₃×#123	1	4	yes	—
176	C₄	—	2	8	no	—
177	C₄	—	4	8	no	—
178	C₃	C₂²⋊#95	1	1	yes	characteristic, direct product factor, Sylow
179	C₂	—	2	8	no	—
180	C₂	C₂×C₃×#95	1	1	yes	characteristic
181	C₂	C₃×C₄×C₂²⋊C₄	1	2	yes	—
182	C₂	C₃×#379	1	1	yes	characteristic
183	C₂	C₃×#380	1	2	yes	—
184	C₂	C₃×#381	1	1	yes	characteristic
185	C₂	C₃×#385	1	4	yes	—
186	C₂	C₃×#386	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂³
commutator	C₂²	C₂×C₃×C₄²
Frattini, cosocle	C₂⁴	C₂³×C₃
prime radical	C₂⁵×C₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#95	C₂	semidirect
4. C₂²⋊#95	C₃	direct (N × H)
8. C₂³×C₃×C₄	C₄	semidirect
13. C₂×C₃×C₂²⋊C₄	C₄	semidirect
17. C₂×#95	C₂×C₃	semidirect
36. C₂²×C₃×C₄	C₂×C₄	semidirect
42. C₂³×C₄	C₃×C₄	semidirect
47. C₂×C₂²⋊C₄	C₃×C₄	semidirect
77. C₂×C₃×C₄	C₂²⋊C₄	semidirect
96. C₂²×C₄	C₂×C₃×C₄	semidirect
105. C₂²×C₃	#95	semidirect
148. C₂×C₄	C₃×C₂²⋊C₄	semidirect
163. C₂²	C₃×#95	semidirect
178. C₃	C₂²⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₄	2
C₂²×C₃×C₂²⋊C₄	2
C₂×C₃×#95	2
C₂²⋊#95	3

Subgroups — C3×C22⋊#95 #72148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊#95 #72148