Subgroups — C₃×#2925 #84789

Order 384.

392 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#433	C₂	1	4	yes	maximal, complemented
3	C₃×#432	C₂	1	2	yes	maximal, complemented
4	C₃×#431	C₂	1	2	yes	maximal, complemented
5	C₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#408	C₂	1	2	yes	maximal
8	C₃×#405	C₂	1	2	yes	maximal, complemented
9	#2925	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×#41	C₂²	1	1	yes	characteristic
11	C₂×C₃×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₃×C₈	C₂²	1	2	yes	—
13	C₃×C₄×Q₈	C₄	1	1	yes	characteristic
14	C₃×C₄×Q₈	C₄	1	1	yes	characteristic
15	C₃×C₄×D₄	C₄	1	2	yes	—
16	C₃×C₄×D₄	C₄	1	1	yes	characteristic
17	C₃×C₄×D₄	C₄	1	2	yes	—
18	C₃×C₄×D₄	C₄	1	1	yes	characteristic
19	C₃×#117	C₂²	1	1	yes	characteristic
20	C₃×#117	C₂²	1	2	yes	—
21	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²	C₂²	1	2	yes	—
23	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₃×C₄⋊C₈	C₂²	1	2	yes	—
28	C₃×C₂²⋊C₈	C₂²	1	4	yes	—
29	C₃×C₂²⋊C₈	C₂²	1	4	yes	—
30	C₃×#97	C₂²	1	4	yes	—
31	C₃×C₄×C₈	C₂²	1	4	yes	—
32	C₄×#41	C₂×C₃	1	1	yes	characteristic
33	#433	C₂×C₃	1	4	yes	complemented
34	#432	C₂×C₃	1	2	yes	complemented
35	#431	C₂×C₃	1	2	yes	complemented
36	#423	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
38	#408	C₂×C₃	1	2	yes	—
39	#405	C₂×C₃	1	2	yes	complemented
40	C₃×#41	—	2	2	no	—
41	C₃×#41	—	2	2	no	—
42	C₂×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×D₄	C₂×C₄	1	2	yes	—
44	C₂×C₃×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
46	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
48	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
51	C₃×M₁₆	—	2	4	no	—
52	C₂×C₃×C₈	—	2	4	no	—
53	C₂×C₃×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₈	C₂³	1	4	yes	—
55	C₂×C₃×C₈	C₂³	1	2	yes	—
56	C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₄²	C₂×C₄	1	2	yes	—
64	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²	C₂×C₄	1	2	yes	—
66	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
67	C₃×C₄²	C₂³	1	2	yes	—
68	C₃×C₄²	C₂³	1	1	yes	characteristic
69	C₃×C₄²	C₂³	1	1	yes	characteristic
70	C₂×#41	C₂²×C₃	1	1	yes	characteristic
71	C₂×M₁₆	C₂²×C₃	1	2	yes	—
72	C₂²×C₈	C₂²×C₃	1	2	yes	—
73	C₄×Q₈	C₃×C₄	1	1	yes	characteristic
74	C₄×Q₈	C₃×C₄	1	1	yes	characteristic
75	C₄×D₄	C₃×C₄	1	2	yes	—
76	C₄×D₄	C₃×C₄	1	1	yes	characteristic
77	C₄×D₄	C₃×C₄	1	2	yes	—
78	C₄×D₄	C₃×C₄	1	1	yes	characteristic
79	#117	C₂²×C₃	1	1	yes	characteristic
80	#117	C₂²×C₃	1	2	yes	—
81	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄²	C₂²×C₃	1	2	yes	—
83	C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
84	C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
85	C₄⋊C₈	C₂²×C₃	1	2	yes	—
86	C₄⋊C₈	C₂²×C₃	1	2	yes	—
87	C₄⋊C₈	C₂²×C₃	1	2	yes	—
88	C₂²⋊C₈	C₂²×C₃	1	4	yes	—
89	C₂²⋊C₈	C₂²×C₃	1	4	yes	—
90	#97	C₂²×C₃	1	4	yes	—
91	C₄×C₈	C₂²×C₃	1	4	yes	—
92	C₂³×C₃	C₂²×C₄	1	2	yes	—
93	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
94	C₃×Q₈	—	2	2	no	—
95	C₃×D₄	—	2	4	no	—
96	C₃×D₄	—	2	2	no	—
97	C₂×C₃×C₄	—	2	2	no	—
98	C₂×C₃×C₄	—	2	4	no	—
99	C₂×C₃×C₄	—	2	2	no	—
100	C₂×C₃×C₄	—	2	2	no	—
101	C₂×C₃×C₄	—	4	1	no	—
102	C₂×C₃×C₄	—	4	2	no	—
103	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄	#41	1	2	yes	—
112	C₂×C₃×C₄	#41	1	2	yes	—
113	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
114	C₃×C₈	—	2	2	no	—
115	C₃×C₈	—	2	2	no	—
116	C₃×C₈	—	2	4	no	—
117	#41	—	2	2	no	—
118	#41	—	2	2	no	—
119	C₂×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂×D₄	C₂×C₃×C₄	1	2	yes	—
121	C₂×D₄	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
123	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
125	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂²×C₄	C₂³×C₃	1	2	yes	—
127	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
128	M₁₆	—	2	4	no	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	C₂³×C₃	1	2	yes	—
131	C₂×C₈	C₂³×C₃	1	4	yes	—
132	C₂×C₈	C₂³×C₃	1	2	yes	—
133	C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
134	C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
135	C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
136	C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
138	C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
139	C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
140	C₄²	C₂×C₃×C₄	1	2	yes	—
141	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
142	C₄²	C₂×C₃×C₄	1	2	yes	—
143	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
144	C₄²	C₂³×C₃	1	2	yes	—
145	C₄²	C₂³×C₃	1	1	yes	characteristic
146	C₄²	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₃	—	2	1	no	—
148	C₂²×C₃	—	2	1	no	—
149	C₂²×C₃	—	2	2	no	—
150	C₂²×C₃	—	2	2	no	—
151	C₂²×C₃	—	2	2	no	—
152	C₂²×C₃	#117	1	2	yes	—
153	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
154	C₃×C₄	—	2	2	no	—
155	C₃×C₄	—	2	1	no	—
156	C₃×C₄	—	2	2	no	—
157	C₃×C₄	—	2	1	no	—
158	C₃×C₄	—	2	1	no	—
159	C₃×C₄	—	2	2	no	—
160	C₃×C₄	#117	1	2	yes	—
161	C₃×C₄	#131	1	2	yes	—
162	C₃×C₄	C₂×#41	1	1	yes	characteristic
163	C₃×C₄	C₂×#41	1	1	yes	characteristic
164	C₂³	C₂²×C₃×C₄	1	2	yes	—
165	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
166	Q₈	—	2	2	no	—
167	D₄	—	2	4	no	—
168	D₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
176	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
177	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
178	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
179	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
180	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
182	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
183	C₂×C₄	C₃×#41	1	2	yes	—
184	C₂×C₄	C₃×#41	1	2	yes	—
185	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
186	C₈	—	2	2	no	—
187	C₈	—	2	2	no	—
188	C₈	—	2	4	no	—
189	C₂×C₃	—	2	2	no	—
190	C₂×C₃	—	4	2	no	—
191	C₂×C₃	C₂×#117	1	1	yes	characteristic
192	C₂×C₃	C₂×#131	1	1	yes	characteristic
193	C₂×C₃	#568	1	1	yes	characteristic
194	C₂²	—	2	1	no	—
195	C₂²	—	2	1	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	2	no	—
199	C₂²	C₃×#117	1	2	yes	—
200	C₂²	C₂³×C₃×C₄	1	1	yes	characteristic
201	C₄	—	2	1	no	—
202	C₄	—	2	2	no	—
203	C₄	—	2	1	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	C₃×#117	1	2	yes	—
208	C₄	C₃×#131	1	2	yes	—
209	C₄	C₂×C₃×#41	1	1	yes	characteristic
210	C₄	C₂×C₃×#41	1	1	yes	characteristic
211	C₃	#2925	1	1	yes	characteristic, direct product factor, Sylow
212	C₂	—	2	2	no	—
213	C₂	—	4	2	no	—
214	C₂	C₂×C₃×#117	1	1	yes	characteristic
215	C₂	C₂×C₃×#131	1	1	yes	characteristic
216	C₂	C₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁴
commutator	C₂²	C₂³×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₄
prime radical	C₂×C₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#433	C₂	semidirect
3. C₃×#432	C₂	semidirect
4. C₃×#431	C₂	semidirect
5. C₃×#423	C₂	semidirect
6. C₂×C₃×C₄⋊C₈	C₂	semidirect
8. C₃×#405	C₂	semidirect
9. #2925	C₃	direct (N × H)
33. #433	C₂×C₃	semidirect
34. #432	C₂×C₃	semidirect
35. #431	C₂×C₃	semidirect
36. #423	C₂×C₃	semidirect
37. C₂×C₄⋊C₈	C₂×C₃	semidirect
39. #405	C₂×C₃	semidirect
211. C₃	#2925	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#41	2
C₃×#433	2
C₃×#432	2
C₃×#431	2
C₃×#423	2
C₂×C₃×C₄⋊C₈	2
C₃×#408	2
C₃×#405	2
#2925	3

Subgroups — C3×#2925 #84789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2925 #84789