Subgroups — C₈×#14519847 #30598079

Order 15616.

374 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14519847	C₂	1	1	yes	maximal, characteristic
2	#21461367	C₂	1	1	yes	maximal, characteristic
3	C₈×#11758213	C₂	1	2	yes	maximal
4	#21460651	C₂	1	2	yes	maximal
5	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic
6	#16840781	C₂²	1	2	yes	—
7	C₂×#14519847	C₄	1	2	yes	—
8	C₄×#11758213	C₂²	1	2	yes	—
9	#16840638	C₄	1	2	yes	—
10	#16840626	C₄	1	2	yes	—
11	#16840623	C₄	1	2	yes	—
12	#92420⋊C₈	—	2	2	no	—
13	C₈×#92420	—	2	2	no	—
14	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
16	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
17	C₈×#92418	C₄	1	1	yes	characteristic
18	C₈×#92418	C₄	1	1	yes	characteristic
19	C₈×#92418	C₄	1	1	yes	characteristic
20	C₈²×C₆₁	C₄	1	1	yes	characteristic
21	C₂×#11758213	C₂×C₄	1	4	yes	—
22	#14519847	C₈	1	8	yes	direct product factor
23	C₄⋊#92420	C₂×C₄	1	4	yes	—
24	#14519834	—	2	2	no	—
25	#14519832	—	2	2	no	—
26	C₄×#92420	—	2	2	no	—
27	C₄×#92420	—	2	2	no	—
28	C₂×C₈×D₆₁	—	2	1	no	—
29	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
32	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
33	C₄²×D₆₁	C₂³	1	1	yes	characteristic
34	C₄×#92418	C₂×C₄	1	1	yes	characteristic
35	C₄×#92418	C₂×C₄	1	1	yes	characteristic
36	C₄×#92418	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₆₁	—	2	1	no	—
38	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
39	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
40	C₈×Dic₆₁	D₄	1	1	yes	characteristic
41	C₈×Dic₆₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
48	C₂×#92420	—	2	4	no	—
49	C₂×#92420	—	2	4	no	—
50	#11758213	—	2	4	no	—
51	#11758213	C₂×C₈	1	8	yes	—
52	C₂×C₈×C₆₁	—	2	1	no	—
53	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
54	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
57	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
58	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
59	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
60	C₄×Dic₆₁	#41	1	1	yes	characteristic
61	C₂×#92418	—	2	1	no	—
62	C₂×#92418	C₄²	1	1	yes	characteristic
63	C₂×#92418	C₄²	1	1	yes	characteristic
64	C₂×#92418	C₄⋊C₄	1	1	yes	characteristic
65	C₂×#92418	C₄⋊C₄	1	1	yes	characteristic
66	C₈×D₆₁	—	2	4	no	—
67	C₈×D₆₁	—	2	2	no	—
68	C₈×D₆₁	—	2	2	no	—
69	C₈×D₆₁	—	2	2	no	—
70	C₈×D₆₁	C₂×C₈	1	4	yes	—
71	C₂²×D₆₁	C₄×Q₈	1	1	yes	characteristic
72	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
73	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
75	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
76	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
77	C₂×Dic₆₁	C₄×Q₈	1	1	yes	characteristic
78	C₄×D₆₁	—	2	1	no	—
79	C₄×D₆₁	—	2	1	no	—
80	C₄×D₆₁	—	2	2	no	—
81	C₄×D₆₁	C₂²×C₈	1	2	yes	—
82	C₄×D₆₁	#131	1	2	yes	—
83	#92420	—	2	8	no	—
84	#92420	—	4	4	no	—
85	C₈×C₆₁	—	2	2	no	—
86	C₈×C₆₁	—	2	1	no	—
87	C₈×C₆₁	—	2	1	no	—
88	C₈×C₆₁	C₄×C₈	1	2	yes	—
89	C₈×C₆₁	#108	1	2	yes	complemented
90	#92418	—	2	2	no	—
91	#92418	—	2	1	no	—
92	#92418	—	2	1	no	—
93	#92418	C₄×C₈	1	2	yes	—
94	#92418	#108	1	2	yes	complemented
95	C₈×#108	—	61	1	no	maximal, Sylow
96	C₂²×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
97	C₂×D₆₁	—	2	1	no	—
98	C₂×D₆₁	—	2	1	no	—
99	C₂×D₆₁	C₈×Q₈	1	2	yes	—
100	C₄×C₆₁	—	2	1	no	—
101	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
102	C₄×C₆₁	#405	1	1	yes	characteristic
103	C₄×C₆₁	C₂×#108	1	1	yes	characteristic
104	C₄×C₆₁	C₂×#108	1	1	yes	characteristic
105	Dic₆₁	—	2	1	no	—
106	Dic₆₁	C₈×D₄	1	2	yes	—
107	Dic₆₁	#443	1	2	yes	—
108	C₄×#108	—	61	1	no	—
109	#1564	—	61	1	no	—
110	C₈×M₁₆	—	61	2	no	—
111	C₂×C₈²	—	61	1	no	—
112	#1278	—	61	2	no	—
113	C₂×C₆₁	C₈×C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₆₁	#1772	1	1	yes	characteristic
115	C₂×C₆₁	C₄×#108	1	1	yes	characteristic
116	D₆₁	—	2	2	no	—
117	#431	—	61	2	no	—
118	C₂×#108	—	61	2	no	—
119	C₄×M₁₆	—	61	2	no	—
120	C₂×C₄×C₈	—	61	1	no	—
121	C₂×C₄×C₈	—	61	1	no	—
122	C₂×C₄×C₈	—	61	1	no	—
123	#341	—	61	2	no	—
124	#335	—	61	2	no	—
125	#334	—	61	2	no	—
126	#322	—	122	2	no	—
127	C₈²	—	61	1	no	—
128	C₈²	—	61	1	no	—
129	C₈²	—	61	1	no	—
130	C₈²	—	122	2	no	—
131	C₈²	#6923	1	1	yes	characteristic
132	C₆₁	C₈×#108	1	1	yes	characteristic, complemented, Sylow
133	C₂×M₁₆	—	61	4	no	—
134	C₂²×C₈	—	61	1	no	—
135	C₂²×C₈	—	61	1	no	—
136	C₂²×C₈	—	61	1	no	—
137	C₂²×C₈	—	61	1	no	—
138	C₂²×C₈	—	122	1	no	—
139	C₂×C₄²	—	61	1	no	—
140	#108	—	61	8	no	—
141	C₄⋊C₈	—	61	4	no	—
142	C₂²⋊C₈	—	122	2	no	—
143	#97	—	122	2	no	—
144	C₄×C₈	—	61	1	no	—
145	C₄×C₈	—	61	1	no	—
146	C₄×C₈	—	61	1	no	—
147	C₄×C₈	—	61	1	no	—
148	C₄×C₈	—	61	1	no	—
149	C₄×C₈	—	61	1	no	—
150	C₄×C₈	—	61	1	no	—
151	C₄×C₈	—	122	1	no	—
152	C₄×C₈	—	122	2	no	—
153	C₄×C₈	—	122	2	no	—
154	C₄×C₈	C₂×#6923	1	1	yes	characteristic
155	C₄×C₈	C₂×#6923	1	1	yes	characteristic
156	C₄×C₈	C₂×#6923	1	1	yes	characteristic
157	C₂²×C₄	—	61	1	no	—
158	C₂²×C₄	—	61	1	no	—
159	C₂²×C₄	—	61	1	no	—
160	M₁₆	—	61	8	no	—
161	M₁₆	—	122	4	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	61	1	no	—
164	C₂×C₈	—	61	1	no	—
165	C₂×C₈	—	61	4	no	—
166	C₂×C₈	—	61	1	no	—
167	C₂×C₈	—	61	1	no	—
168	C₂×C₈	—	122	2	no	—
169	C₂×C₈	—	122	2	no	—
170	C₂×C₈	—	122	4	no	—
171	C₂×C₈	—	122	4	no	—
172	C₂×C₈	—	122	1	no	—
173	C₂×C₈	—	122	2	no	—
174	C₂×C₈	—	122	4	no	—
175	C₂×C₈	C₄×#6923	1	1	yes	characteristic
176	C₂×C₈	C₄×#6923	1	1	yes	characteristic
177	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
178	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
179	C₄²	—	61	1	no	—
180	C₄²	—	61	1	no	—
181	C₄²	—	61	1	no	—
182	C₄²	C₂²×#6923	1	1	yes	characteristic
183	C₂³	—	61	1	no	—
184	C₂×C₄	—	61	1	no	—
185	C₂×C₄	—	61	1	no	—
186	C₂×C₄	—	61	2	no	—
187	C₂×C₄	—	61	2	no	—
188	C₂×C₄	—	61	1	no	—
189	C₂×C₄	—	122	2	no	—
190	C₂×C₄	—	122	1	no	—
191	C₂×C₄	—	122	1	no	—
192	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
193	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
194	C₂×C₄	#14519856	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	61	2	no	—
199	C₈	—	61	2	no	—
200	C₈	—	122	2	no	—
201	C₈	—	122	8	no	—
202	C₈	—	122	1	no	—
203	C₈	—	122	1	no	—
204	C₈	—	244	4	no	—
205	C₈	C₈×#6923	1	2	yes	—
206	C₈	#14519847	1	2	yes	direct product factor
207	C₂²	—	61	2	no	—
208	C₂²	—	122	1	no	—
209	C₂²	—	122	1	no	—
210	C₂²	C₄×C₄⋊#6923	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	61	2	no	—
213	C₄	—	61	2	no	—
214	C₄	—	122	1	no	—
215	C₄	C₂×C₈×#6923	1	1	yes	characteristic
216	C₄	#16840725	1	1	yes	characteristic
217	C₄	C₂×#14519847	1	1	yes	characteristic
218	C₄	D₆₁⋊#108	1	1	yes	characteristic
219	C₂	—	122	2	no	—
220	C₂	C₈×C₄⋊#6923	1	1	yes	characteristic
221	C₂	#21461621	1	1	yes	characteristic
222	C₂	C₄×#14519847	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₄²	C₂²×#6923
Fitting	C₈²×C₆₁	C₄
socle	C₂²×C₆₁	C₄×C₄⋊C₄
prime radical	C₂²×D₆₁	C₄×Q₈
cosocle	C₄²×D₆₁	C₂³
hypercenter	C₈²	#6923
hypocenter	C₆₁	C₈×#108
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
22. #14519847	C₈	direct (N × H)
89. C₈×C₆₁	#108	semidirect
94. #92418	#108	semidirect
132. C₆₁	C₈×#108	semidirect
206. C₈	#14519847	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#14519847	2
#21461367	2
C₈×#11758213	2
#21460651	2
C₈²×D₆₁	2
C₈×#108	61

Subgroups — C8×#14519847 #30598079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14519847 #30598079