Subgroups — C₃×#3283 #85147

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#135	C₂	1	2	yes	maximal, complemented
2	C₃×#547	C₂	1	2	yes	maximal, complemented
3	C₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#467	C₂	1	2	yes	maximal, complemented
5	C₃×#461	C₂	1	2	yes	maximal, complemented
6	C₃×#452	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	#3283	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×#41	C₂²	1	4	yes	—
11	C₃×#135	—	2	8	no	—
12	C₂×C₃×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₃×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×SD₁₆	C₂²	1	4	yes	—
15	C₂×C₃×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₈	C₂²	1	2	yes	—
17	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×#123	—	2	4	no	—
19	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₃×#121	—	2	2	no	—
21	C₃×C₄×D₄	C₂²	1	2	yes	—
22	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊C₄	—	2	2	no	—
24	C₃×#107	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₃×#103	C₂²	1	4	yes	—
27	C₃×#102	C₂²	1	2	yes	—
28	C₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
30	C₂×#135	C₂×C₃	1	2	yes	complemented
31	#547	C₂×C₃	1	2	yes	complemented
32	#494	C₂×C₃	1	1	yes	characteristic, complemented
33	#467	C₂×C₃	1	2	yes	complemented
34	#461	C₂×C₃	1	2	yes	complemented
35	#452	C₂×C₃	1	4	yes	complemented
36	C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
38	C₃×#41	—	2	8	no	—
39	C₃×#41	—	4	4	no	—
40	C₂×C₃×Q₈	C₂³	1	4	yes	—
41	C₂×C₃×D₄	—	2	4	no	—
42	C₂×C₃×D₄	D₄	1	1	yes	characteristic
43	C₂×C₃×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄	—	2	2	no	—
45	C₂²×C₃×C₄	—	2	4	no	—
46	C₂²×C₃×C₄	C₂³	1	2	yes	—
47	C₃×Q₁₆	—	2	4	no	—
48	C₃×Q₁₆	—	4	2	no	—
49	C₃×SD₁₆	—	2	8	no	—
50	C₃×D₈	D₄	1	4	yes	complemented
51	C₂×C₃×C₈	—	2	4	no	—
52	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
55	C₃×C₄⋊C₄	—	2	2	no	—
56	C₃×C₄⋊C₄	—	2	4	no	—
57	C₃×C₄⋊C₄	—	2	2	no	—
58	C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₃×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₂²⋊C₄	—	2	2	no	—
62	C₃×C₂²⋊C₄	D₄	1	2	yes	—
63	C₃×C₄²	C₂³	1	1	yes	characteristic
64	C₂×#41	C₂²×C₃	1	4	yes	—
65	#135	—	2	8	no	—
66	C₂×Q₁₆	C₂²×C₃	1	2	yes	—
67	C₂×Q₁₆	C₂²×C₃	1	2	yes	—
68	C₂×SD₁₆	C₂²×C₃	1	4	yes	—
69	C₂×D₈	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₈	C₂²×C₃	1	2	yes	—
71	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
72	#123	—	2	4	no	—
73	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
74	#121	—	2	2	no	—
75	C₄×D₄	C₂²×C₃	1	2	yes	—
76	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄⋊C₄	—	2	2	no	—
78	#107	C₂²×C₃	1	1	yes	characteristic
79	C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
80	#103	C₂²×C₃	1	4	yes	—
81	#102	C₂²×C₃	1	2	yes	—
82	C₂²⋊C₈	C₂²×C₃	1	2	yes	—
83	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₃	—	2	2	no	—
85	C₂³×C₃	C₂×D₄	1	2	yes	—
86	C₃×Q₈	—	2	4	no	—
87	C₃×Q₈	—	2	4	no	—
88	C₃×D₄	—	2	2	no	—
89	C₃×D₄	—	2	2	no	—
90	C₃×D₄	—	4	8	no	—
91	C₃×D₄	C₂×D₄	1	4	yes	—
92	C₂×C₃×C₄	—	2	2	no	—
93	C₂×C₃×C₄	—	2	2	no	—
94	C₂×C₃×C₄	—	2	2	no	—
95	C₂×C₃×C₄	—	2	4	no	—
96	C₂×C₃×C₄	—	4	8	no	—
97	C₂×C₃×C₄	—	4	4	no	—
98	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
102	C₃×C₈	—	2	2	no	—
103	C₃×C₈	—	2	1	no	—
104	C₃×C₈	C₂×D₄	1	2	yes	—
105	#41	—	2	8	no	—
106	#41	—	4	4	no	—
107	C₂×Q₈	C₂³×C₃	1	4	yes	—
108	C₂×D₄	—	2	4	no	—
109	C₂×D₄	C₃×D₄	1	1	yes	characteristic
110	C₂×D₄	C₂³×C₃	1	2	yes	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	2	4	no	—
113	C₂²×C₄	C₂³×C₃	1	2	yes	—
114	Q₁₆	—	2	4	no	—
115	Q₁₆	—	4	2	no	—
116	SD₁₆	—	2	8	no	—
117	D₈	C₃×D₄	1	4	yes	complemented
118	C₂×C₈	—	2	4	no	—
119	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₈	C₂³×C₃	1	2	yes	—
121	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
122	C₄⋊C₄	—	2	2	no	—
123	C₄⋊C₄	—	2	4	no	—
124	C₄⋊C₄	—	2	2	no	—
125	C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
126	C₄⋊C₄	C₂³×C₃	1	2	yes	—
127	C₂²⋊C₄	—	2	4	no	—
128	C₂²⋊C₄	—	2	2	no	—
129	C₂²⋊C₄	C₃×D₄	1	2	yes	—
130	C₄²	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₃	—	2	2	no	—
132	C₂²×C₃	—	2	4	no	—
133	C₂²×C₃	—	2	2	no	—
134	C₂²×C₃	—	2	2	no	—
135	C₂²×C₃	—	4	2	no	—
136	C₂²×C₃	—	4	2	no	—
137	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
138	C₃×C₄	—	2	2	no	—
139	C₃×C₄	—	2	1	no	—
140	C₃×C₄	—	4	4	no	—
141	C₃×C₄	—	4	2	no	—
142	C₃×C₄	#135	1	2	yes	complemented
143	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
144	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂³	—	2	2	no	—
146	C₂³	C₂×C₃×D₄	1	2	yes	—
147	Q₈	—	2	4	no	—
148	Q₈	—	2	4	no	—
149	D₄	—	2	2	no	—
150	D₄	—	2	2	no	—
151	D₄	—	4	8	no	—
152	D₄	C₂×C₃×D₄	1	4	yes	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
160	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
161	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
163	C₈	—	2	2	no	—
164	C₈	—	2	1	no	—
165	C₈	C₂×C₃×D₄	1	2	yes	—
166	C₂×C₃	—	4	2	no	—
167	C₂×C₃	—	4	4	no	—
168	C₂×C₃	D₄²	1	1	yes	characteristic
169	C₂×C₃	C₂×#135	1	1	yes	characteristic
170	C₂×C₃	#578	1	1	yes	characteristic
171	C₂²	—	2	2	no	—
172	C₂²	—	2	2	no	—
173	C₂²	—	2	2	no	—
174	C₂²	—	2	4	no	—
175	C₂²	—	4	2	no	—
176	C₂²	—	4	2	no	—
177	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
178	C₄	—	2	1	no	—
179	C₄	—	2	2	no	—
180	C₄	—	4	2	no	—
181	C₄	—	4	4	no	—
182	C₄	C₃×#135	1	2	yes	complemented
183	C₄	C₂²×C₃×D₄	1	1	yes	characteristic
184	C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
185	C₃	#3283	1	1	yes	characteristic, direct product factor, Sylow
186	C₂	—	4	2	no	—
187	C₂	—	4	4	no	—
188	C₂	C₃×D₄²	1	1	yes	characteristic
189	C₂	C₂×C₃×#135	1	1	yes	characteristic
190	C₂	C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#135	C₂	semidirect
2. C₃×#547	C₂	semidirect
3. C₃×#494	C₂	semidirect
4. C₃×#467	C₂	semidirect
5. C₃×#461	C₂	semidirect
6. C₃×#452	C₂	semidirect
7. C₃×C₄×D₈	C₂	semidirect
8. C₃×C₈×D₄	C₂	semidirect
9. #3283	C₃	direct (N × H)
30. C₂×#135	C₂×C₃	semidirect
31. #547	C₂×C₃	semidirect
32. #494	C₂×C₃	semidirect
33. #467	C₂×C₃	semidirect
34. #461	C₂×C₃	semidirect
35. #452	C₂×C₃	semidirect
36. C₄×D₈	C₂×C₃	semidirect
37. C₈×D₄	C₂×C₃	semidirect
50. C₃×D₈	D₄	semidirect
117. D₈	C₃×D₄	semidirect
142. C₃×C₄	#135	semidirect
182. C₄	C₃×#135	semidirect
185. C₃	#3283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#135	2
C₃×#547	2
C₃×#494	2
C₃×#467	2
C₃×#461	2
C₃×#452	2
C₃×C₄×D₈	2
C₃×C₈×D₄	2
#3283	3

Subgroups — C3×#3283 #85147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3283 #85147