Subgroups — C₃×#3107 #84971

Order 384.

390 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₃×#485	C₂	1	2	yes	maximal, complemented
4	C₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#452	C₂	1	2	yes	maximal
9	C₃×C₄×Q₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	#3107	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×SD₁₆	C₂²	1	2	yes	—
16	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×#125	—	2	1	no	—
19	C₃×C₂²⋊Q₈	—	2	1	no	—
20	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₄×Q₈	—	2	1	no	—
22	C₃×C₄×Q₈	C₂²	1	2	yes	—
23	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₄×D₄	—	2	1	no	—
26	C₃×C₄×D₄	—	2	1	no	—
27	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₃×#117	—	2	1	no	—
30	C₃×#117	—	2	1	no	—
31	C₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²	—	2	1	no	—
33	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₃×#107	C₂²	1	2	yes	—
35	C₃×#106	C₂²	1	2	yes	—
36	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×#103	C₂²	1	2	yes	—
39	C₃×#103	C₂²	1	2	yes	—
40	C₃×#103	C₂²	1	2	yes	—
41	C₃×#102	C₂²	1	2	yes	—
42	C₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₃×C₄×C₈	C₂²	1	2	yes	—
44	#533	C₂×C₃	1	1	yes	characteristic, complemented
45	C₄×#41	C₂×C₃	1	1	yes	characteristic
46	#485	C₂×C₃	1	2	yes	complemented
47	#475	C₂×C₃	1	1	yes	characteristic, complemented
48	#474	C₂×C₃	1	1	yes	characteristic, complemented
49	#462	C₂×C₃	1	1	yes	characteristic, complemented
50	#461	C₂×C₃	1	1	yes	characteristic, complemented
51	#452	C₂×C₃	1	2	yes	—
52	C₄×Q₁₆	C₂×C₃	1	2	yes	complemented
53	C₄×SD₁₆	C₂×C₃	1	2	yes	complemented
54	#431	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#41	—	2	2	no	—
56	C₃×#41	—	2	2	no	—
57	C₂×C₃×Q₈	—	2	1	no	—
58	C₂×C₃×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×D₄	—	2	1	no	—
61	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄	—	2	1	no	—
63	C₂²×C₃×C₄	—	2	1	no	—
64	C₂²×C₃×C₄	—	2	1	no	—
65	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
68	C₃×Q₁₆	—	2	4	no	—
69	C₃×SD₁₆	—	2	4	no	—
70	C₂×C₃×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₈	C₂³	1	2	yes	—
72	C₃×C₄⋊C₄	—	2	1	no	—
73	C₃×C₄⋊C₄	—	2	1	no	—
74	C₃×C₄⋊C₄	—	2	1	no	—
75	C₃×C₄⋊C₄	—	2	1	no	—
76	C₃×C₄⋊C₄	—	2	1	no	—
77	C₃×C₄⋊C₄	—	2	2	no	—
78	C₃×C₄⋊C₄	—	2	2	no	—
79	C₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₄²	—	2	1	no	—
87	C₃×C₄²	—	2	1	no	—
88	C₃×C₄²	—	2	1	no	—
89	C₃×C₄²	—	2	2	no	—
90	C₃×C₄²	D₄	1	1	yes	characteristic
91	C₃×C₄²	D₄	1	1	yes	characteristic
92	C₃×C₄²	C₂³	1	1	yes	characteristic
93	C₃×C₄²	C₂³	1	1	yes	characteristic
94	C₂×#41	C₂²×C₃	1	1	yes	characteristic
95	C₂×Q₁₆	C₂²×C₃	1	2	yes	—
96	C₂×SD₁₆	C₂²×C₃	1	2	yes	—
97	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
99	#125	—	2	1	no	—
100	C₂²⋊Q₈	—	2	1	no	—
101	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
102	C₄×Q₈	—	2	1	no	—
103	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₄×Q₈	C₂²×C₃	1	2	yes	—
106	C₄×D₄	—	2	1	no	—
107	C₄×D₄	—	2	1	no	—
108	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
110	#117	—	2	1	no	—
111	#117	—	2	1	no	—
112	#117	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄²	—	2	1	no	—
114	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
115	#107	C₂²×C₃	1	2	yes	—
116	#106	C₂²×C₃	1	2	yes	—
117	C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
118	C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	#103	C₂²×C₃	1	2	yes	—
120	#103	C₂²×C₃	1	2	yes	—
121	#103	C₂²×C₃	1	2	yes	—
122	#102	C₂²×C₃	1	2	yes	—
123	C₂²⋊C₈	C₂²×C₃	1	2	yes	—
124	C₄×C₈	C₂²×C₃	1	2	yes	—
125	C₂³×C₃	—	2	1	no	—
126	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
127	C₃×Q₈	—	2	1	no	—
128	C₃×Q₈	—	2	2	no	—
129	C₃×Q₈	—	2	2	no	—
130	C₃×Q₈	—	4	2	no	—
131	C₃×Q₈	#41	1	2	yes	—
132	C₃×D₄	—	2	4	no	—
133	C₃×D₄	—	2	1	no	—
134	C₃×D₄	#41	1	2	yes	—
135	C₂×C₃×C₄	—	2	4	no	—
136	C₂×C₃×C₄	—	2	1	no	—
137	C₂×C₃×C₄	—	2	2	no	—
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	1	no	—
140	C₂×C₃×C₄	—	2	1	no	—
141	C₂×C₃×C₄	—	2	1	no	—
142	C₂×C₃×C₄	—	2	1	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	4	2	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
153	C₃×C₈	—	2	2	no	—
154	C₃×C₈	—	2	2	no	—
155	#41	—	2	2	no	—
156	#41	—	2	2	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	C₂³×C₃	1	2	yes	—
159	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
160	C₂×D₄	—	2	1	no	—
161	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
166	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
167	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
168	Q₁₆	—	2	4	no	—
169	SD₁₆	—	2	4	no	—
170	C₂×C₈	C₂³×C₃	1	2	yes	—
171	C₂×C₈	C₂³×C₃	1	2	yes	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	2	1	no	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	1	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	C₂³×C₃	1	2	yes	—
180	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
181	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	1	no	—
184	C₂²⋊C₄	—	2	1	no	—
185	C₂²⋊C₄	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	2	no	—
190	C₄²	C₃×D₄	1	1	yes	characteristic
191	C₄²	C₃×D₄	1	1	yes	characteristic
192	C₄²	C₂³×C₃	1	1	yes	characteristic
193	C₄²	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃	—	2	1	no	—
195	C₂²×C₃	—	2	2	no	—
196	C₂²×C₃	—	2	1	no	—
197	C₂²×C₃	—	2	1	no	—
198	C₂²×C₃	—	4	1	no	—
199	C₂²×C₃	—	4	1	no	—
200	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
201	C₃×C₄	—	2	1	no	—
202	C₃×C₄	—	2	2	no	—
203	C₃×C₄	—	2	1	no	—
204	C₃×C₄	—	2	1	no	—
205	C₃×C₄	—	4	2	no	—
206	C₃×C₄	—	4	1	no	—
207	C₃×C₄	—	4	2	no	—
208	C₃×C₄	—	4	1	no	—
209	C₃×C₄	#135	1	2	yes	—
210	C₃×C₄	#137	1	2	yes	—
211	C₃×C₄	C₂×#41	1	1	yes	characteristic
212	C₃×C₄	C₂×#41	1	1	yes	characteristic
213	C₂³	—	2	1	no	—
214	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
215	Q₈	—	2	1	no	—
216	Q₈	—	2	2	no	—
217	Q₈	—	2	2	no	—
218	Q₈	—	4	2	no	—
219	Q₈	C₃×#41	1	2	yes	—
220	D₄	—	2	4	no	—
221	D₄	—	2	1	no	—
222	D₄	C₃×#41	1	2	yes	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
241	C₈	—	2	2	no	—
242	C₈	—	2	2	no	—
243	C₂×C₃	—	4	1	no	—
244	C₂×C₃	—	4	2	no	—
245	C₂×C₃	#525	1	1	yes	characteristic
246	C₂×C₃	C₂×#135	1	1	yes	characteristic
247	C₂×C₃	C₂×#137	1	1	yes	characteristic
248	C₂²	—	2	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	4	1	no	—
253	C₂²	—	4	1	no	—
254	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	2	no	—
259	C₄	—	4	1	no	—
260	C₄	—	4	2	no	—
261	C₄	—	4	1	no	—
262	C₄	—	4	2	no	—
263	C₄	C₃×#135	1	2	yes	—
264	C₄	C₃×#137	1	2	yes	—
265	C₄	C₂×C₃×#41	1	1	yes	characteristic
266	C₄	C₂×C₃×#41	1	1	yes	characteristic
267	C₃	#3107	1	1	yes	characteristic, direct product factor, Sylow
268	C₂	—	4	1	no	—
269	C₂	—	4	2	no	—
270	C₂	C₃×#525	1	1	yes	characteristic
271	C₂	C₂×C₃×#135	1	1	yes	characteristic
272	C₂	C₂×C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×D₄
prime radical	C₂×C₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#533	C₂	semidirect
3. C₃×#485	C₂	semidirect
4. C₃×#475	C₂	semidirect
5. C₃×#474	C₂	semidirect
6. C₃×#462	C₂	semidirect
7. C₃×#461	C₂	semidirect
9. C₃×C₄×Q₁₆	C₂	semidirect
10. C₃×C₄×SD₁₆	C₂	semidirect
11. C₃×#431	C₂	semidirect
12. #3107	C₃	direct (N × H)
44. #533	C₂×C₃	semidirect
46. #485	C₂×C₃	semidirect
47. #475	C₂×C₃	semidirect
48. #474	C₂×C₃	semidirect
49. #462	C₂×C₃	semidirect
50. #461	C₂×C₃	semidirect
52. C₄×Q₁₆	C₂×C₃	semidirect
53. C₄×SD₁₆	C₂×C₃	semidirect
54. #431	C₂×C₃	semidirect
267. C₃	#3107	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×#533	2
C₃×C₄×#41	2
C₃×#485	2
C₃×#475	2
C₃×#474	2
C₃×#462	2
C₃×#461	2
C₃×#452	2
C₃×C₄×Q₁₆	2
C₃×C₄×SD₁₆	2
C₃×#431	2
#3107	3

Subgroups — C3×#3107 #84971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3107 #84971