Subgroups — C₄×#950 #82505

Order 384.

500 conjugacy classes of subgroups.

The subgroup lattice has 270 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, complemented
2	C₂×#950	C₂	1	1	yes	maximal, characteristic
3	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
4	#5233	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#216	C₂	1	2	yes	maximal, complemented
6	C₄×#215	C₂	1	2	yes	maximal, complemented
7	C₄×#214	C₂	1	2	yes	maximal, complemented
8	C₄×#213	C₂	1	2	yes	maximal, complemented
9	#5002	C₂	1	1	yes	maximal, characteristic, complemented
10	#4998	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#135	—	3	1	no	maximal, Sylow
13	C₂×C₃×#41	C₂²	1	1	yes	characteristic
14	C₂×#235	C₂²	1	1	yes	characteristic
15	C₃×C₄×Q₈	C₂²	1	2	yes	—
16	C₃×C₄×D₄	—	2	2	no	—
17	C₃×C₄×D₄	C₂²	1	2	yes	—
18	C₃×#117	—	2	1	no	—
19	C₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²	—	2	1	no	—
21	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
22	#950	C₄	1	8	yes	direct product factor
23	C₂×#216	C₂²	1	1	yes	characteristic
24	C₂×#215	C₂²	1	1	yes	characteristic
25	C₂×#214	C₂²	1	1	yes	characteristic
26	C₂×#213	C₂²	1	1	yes	characteristic
27	C₄×#67	—	2	2	no	—
28	#926	C₂²	1	1	yes	characteristic
29	C₂²×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂²×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₄×D₁₂	C₂²	1	2	yes	—
32	#872	—	2	1	no	—
33	C₄²×D₃	—	2	1	no	—
34	C₄×Dic₆	C₂²	1	2	yes	—
35	#835	C₂²	1	2	yes	—
36	#832	C₂²	1	2	yes	—
37	#810	C₂²	1	2	yes	—
38	#809	C₂²	1	2	yes	—
39	#808	C₂²	1	2	yes	—
40	#807	C₂²	1	2	yes	—
41	C₄×C₃⋊C₈	C₂²	1	2	yes	—
42	C₄×C₃⋊C₈	C₂²	1	2	yes	—
43	C₂×#135	—	3	1	no	—
44	C₄×#41	—	3	1	no	—
45	C₄×#41	D₃	1	1	yes	characteristic, complemented
46	C₄×Q₁₆	—	3	2	no	—
47	C₄×SD₁₆	—	3	2	no	—
48	C₄×SD₁₆	—	3	2	no	—
49	C₄×D₈	—	3	2	no	—
50	#427	—	3	1	no	—
51	#416	—	3	1	no	—
52	#416	—	3	1	no	—
53	C₂×C₄×C₈	—	3	1	no	—
54	C₃×#41	—	2	2	no	—
55	C₃×#41	C₂×C₄	1	4	yes	complemented
56	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×D₄	—	2	1	no	—
58	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄	—	2	1	no	—
60	C₂²×C₃×C₄	—	2	2	no	—
61	C₂²×C₃×C₄	D₄	1	2	yes	—
62	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
63	C₂×#67	—	2	1	no	—
64	#235	—	2	2	no	—
65	#235	C₂×C₄	1	4	yes	complemented
66	C₂×D₁₂	C₂³	1	1	yes	characteristic
67	C₂×C₄×D₃	—	2	1	no	—
68	C₂×C₄×D₃	—	2	2	no	—
69	C₂×Dic₆	C₂³	1	1	yes	characteristic
70	C₃×C₄⋊C₄	—	2	2	no	—
71	C₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₄²	—	2	1	no	—
75	C₃×C₄²	—	2	2	no	—
76	C₃×C₄²	D₄	1	1	yes	characteristic
77	C₃×C₄²	D₄	1	1	yes	characteristic
78	C₃×C₄²	C₂³	1	2	yes	—
79	#217	—	2	1	no	—
80	#216	C₂×C₄	1	4	yes	complemented
81	#215	C₂×C₄	1	4	yes	complemented
82	#214	C₂×C₄	1	4	yes	complemented
83	#213	C₂×C₄	1	4	yes	complemented
84	(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₄⋊Dic₃	C₂³	1	2	yes	—
86	Dic₃⋊C₄	—	2	2	no	—
87	C₄×Dic₃	—	2	2	no	—
88	C₄×Dic₃	—	2	1	no	—
89	C₂×C₃⋊C₈	—	2	2	no	—
90	C₂×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
91	C₂×C₃⋊C₈	C₂³	1	2	yes	—
92	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×#41	—	3	1	no	—
95	C₂×#41	C₂×D₃	1	1	yes	characteristic
96	#135	—	3	8	no	—
97	C₂×Q₁₆	—	3	1	no	—
98	C₂×SD₁₆	—	3	1	no	—
99	C₂×SD₁₆	—	3	1	no	—
100	C₂×D₈	—	3	1	no	—
101	C₂²×C₈	—	3	1	no	—
102	C₂²×C₈	—	3	1	no	—
103	C₄×Q₈	—	3	2	no	—
104	C₄×Q₈	C₂×D₃	1	2	yes	—
105	C₄×D₄	—	2	2	no	—
106	C₄×D₄	—	3	2	no	—
107	C₄×D₄	—	6	2	no	—
108	C₄×D₄	C₂×D₃	1	2	yes	—
109	#117	—	2	1	no	—
110	#117	—	3	1	no	—
111	#117	—	6	1	no	—
112	#117	C₂×D₃	1	1	yes	characteristic
113	C₂×C₄²	—	2	1	no	—
114	C₂×C₄²	—	6	1	no	—
115	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
116	#107	—	3	2	no	—
117	#106	—	3	2	no	—
118	#103	—	3	2	no	—
119	#103	—	3	2	no	—
120	#102	—	3	2	no	—
121	#102	—	3	2	no	—
122	C₄×C₈	—	3	2	no	—
123	C₄×C₈	—	3	2	no	—
124	C₂³×C₃	—	2	1	no	—
125	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₃	—	2	1	no	—
127	C₃×Q₈	—	2	1	no	—
128	C₃×Q₈	C₂²×C₄	1	2	yes	—
129	C₃×D₄	—	2	4	no	—
130	C₃×D₄	—	2	1	no	—
131	C₃×D₄	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄	—	2	1	no	—
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	—	2	4	no	—
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	4	4	no	—
137	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄	#41	1	2	yes	—
142	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
143	#67	—	2	4	no	—
144	C₂×Dic₃	—	2	1	no	—
145	C₂×Dic₃	—	2	2	no	—
146	D₁₂	—	2	1	no	—
147	D₁₂	C₂²×C₄	1	2	yes	—
148	C₄×D₃	—	2	4	no	—
149	C₄×D₃	—	4	4	no	—
150	Dic₆	—	2	1	no	—
151	Dic₆	C₂²×C₄	1	2	yes	—
152	C₃⋊C₈	—	2	2	no	—
153	C₃⋊C₈	C₂²×C₄	1	2	yes	—
154	C₃⋊C₈	C₂²×C₄	1	2	yes	—
155	#41	—	2	2	no	—
156	#41	—	3	4	no	—
157	#41	—	6	2	no	—
158	#41	C₄×D₃	1	4	yes	complemented
159	C₂×Q₈	—	3	1	no	—
160	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
161	C₂×D₄	—	2	1	no	—
162	C₂×D₄	—	3	1	no	—
163	C₂×D₄	—	6	1	no	—
164	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	6	1	no	—
168	C₂²×C₄	—	6	2	no	—
169	C₂²×C₄	#67	1	2	yes	—
170	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
171	Q₁₆	—	3	4	no	—
172	SD₁₆	—	3	4	no	—
173	SD₁₆	—	3	4	no	—
174	D₈	—	3	4	no	—
175	C₂×C₈	—	3	4	no	—
176	C₂×C₈	—	3	1	no	—
177	C₂×C₈	—	3	1	no	—
178	C₂×C₈	—	3	2	no	—
179	C₂×C₈	—	6	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	3	2	no	—
182	C₄⋊C₄	—	6	2	no	—
183	C₄⋊C₄	C₂²×D₃	1	2	yes	—
184	C₂²⋊C₄	—	2	1	no	—
185	C₂²⋊C₄	—	2	2	no	—
186	C₂²⋊C₄	—	6	1	no	—
187	C₂²⋊C₄	—	6	2	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	6	1	no	—
191	C₄²	—	6	2	no	—
192	C₄²	#67	1	1	yes	characteristic
193	C₄²	#67	1	1	yes	characteristic
194	C₄²	C₂²×D₃	1	2	yes	—
195	C₂²×C₃	—	2	2	no	—
196	C₂²×C₃	—	2	2	no	—
197	C₂²×C₃	—	4	2	no	—
198	C₂²×C₃	C₄×D₄	1	2	yes	—
199	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×D₃	—	2	2	no	—
201	C₂×D₃	—	4	2	no	—
202	C₃×C₄	—	2	2	no	—
203	C₃×C₄	—	2	2	no	—
204	C₃×C₄	—	4	2	no	—
205	C₃×C₄	C₄×D₄	1	2	yes	—
206	C₃×C₄	#135	1	4	yes	complemented
207	C₃×C₄	C₂³×C₄	1	1	yes	characteristic
208	C₃×C₄	C₂×#41	1	1	yes	characteristic
209	Dic₃	—	2	2	no	—
210	Dic₃	—	4	2	no	—
211	C₂³	—	2	1	no	—
212	C₂³	—	6	1	no	—
213	C₂³	C₂×#67	1	1	yes	characteristic
214	Q₈	—	2	1	no	—
215	Q₈	—	3	2	no	—
216	Q₈	—	6	1	no	—
217	Q₈	C₂×C₄×D₃	1	2	yes	—
218	D₄	—	2	4	no	—
219	D₄	—	2	1	no	—
220	D₄	—	3	2	no	—
221	D₄	—	6	4	no	—
222	D₄	—	6	1	no	—
223	D₄	C₂×C₄×D₃	1	2	yes	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	4	no	—
229	C₂×C₄	—	6	1	no	—
230	C₂×C₄	—	6	4	no	—
231	C₂×C₄	—	6	2	no	—
232	C₂×C₄	—	12	4	no	—
233	C₂×C₄	C₂×C₄×D₃	1	2	yes	—
234	C₂×C₄	#235	1	2	yes	—
235	C₂×C₄	C₂×#67	1	2	yes	—
236	C₂×C₄	C₂×#67	1	1	yes	characteristic
237	C₂×C₄	C₂×#67	1	2	yes	—
238	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
239	C₈	—	3	2	no	—
240	C₈	—	3	2	no	—
241	C₈	—	6	2	no	—
242	C₂×C₃	—	2	2	no	—
243	C₂×C₃	—	4	2	no	—
244	C₂×C₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂×C₃	C₂×#135	1	2	yes	—
246	D₃	—	4	2	no	—
247	C₂²	—	2	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	6	2	no	—
251	C₂²	—	12	2	no	—
252	C₂²	C₄×#67	1	2	yes	—
253	C₂²	C₂²×#67	1	1	yes	characteristic
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	4	2	no	—
257	C₄	—	6	2	no	—
258	C₄	—	12	2	no	—
259	C₄	C₄×#67	1	2	yes	—
260	C₄	#950	1	4	yes	direct product factor
261	C₄	C₂²×C₄×D₃	1	1	yes	characteristic
262	C₄	C₂×#235	1	1	yes	characteristic
263	C₃	C₄×#135	1	1	yes	characteristic, complemented, Sylow
264	C₂	—	2	2	no	—
265	C₂	—	4	2	no	—
266	C₂	—	12	2	no	—
267	C₂	C₂×C₄×#67	1	1	yes	characteristic
268	C₂	C₂×#950	1	2	yes	—

	subgroup	G/H
center	C₄²	#67
commutator	C₃×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₃×C₄×#41	C₂
socle	C₂²×C₃	C₂²×D₄
prime radical	C₂×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	C₄×#41	D₃
hypocenter	C₃	C₄×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×#41	C₂	semidirect
3. C₄×#235	C₂	semidirect
4. #5233	C₂	semidirect
5. C₄×#216	C₂	semidirect
6. C₄×#215	C₂	semidirect
7. C₄×#214	C₂	semidirect
8. C₄×#213	C₂	semidirect
9. #5002	C₂	semidirect
10. #4998	C₂	semidirect
11. C₂×C₄×C₃⋊C₈	C₂	semidirect
22. #950	C₄	direct (N × H)
45. C₄×#41	D₃	semidirect
55. C₃×#41	C₂×C₄	semidirect
65. #235	C₂×C₄	semidirect
80. #216	C₂×C₄	semidirect
81. #215	C₂×C₄	semidirect
82. #214	C₂×C₄	semidirect
83. #213	C₂×C₄	semidirect
90. C₂×C₃⋊C₈	C₂×C₄	semidirect
158. #41	C₄×D₃	semidirect
206. C₃×C₄	#135	semidirect
260. C₄	#950	direct (N × H)
263. C₃	C₄×#135	semidirect

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
C₂×#950	2
C₄×#235	2
#5233	2
C₄×#216	2
C₄×#215	2
C₄×#214	2
C₄×#213	2
#5002	2
#4998	2
C₂×C₄×C₃⋊C₈	2
C₄×#135	3

Subgroups — C4×#950 #82505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#950 #82505