Subgroups — C₄×#63394 #11783798

Order 1152.

444 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#63394	C₂	1	2	yes	maximal
3	C₄×#3667	C₂	1	2	yes	maximal
4	#10588207	C₂	1	2	yes	maximal
5	C₄×#836	—	3	1	no	maximal
6	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
7	C₄×Q₈×C₉	—	2	2	no	—
8	C₄×Q₈×C₉	—	2	2	no	—
9	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₄	1	2	yes	—
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₂×#3667	C₂²	1	4	yes	—
14	#63394	C₄	1	8	yes	direct product factor
15	#63362	—	2	2	no	—
16	C₄×C₉⋊C₈	—	2	2	no	—
17	C₂×C₃×C₄×Q₈	D₃	1	1	yes	characteristic
18	C₂×#836	—	3	2	no	—
19	C₄×#208	—	3	2	no	—
20	#4530	—	3	2	no	—
21	C₂×Q₈×C₉	—	2	2	no	—
22	C₂×Q₈×C₉	—	2	2	no	—
23	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₉×C₄⋊C₄	—	2	4	no	—
30	C₉×C₄⋊C₄	—	2	2	no	—
31	C₄²×C₉	—	2	2	no	—
32	C₄²×C₉	—	2	2	no	—
33	C₄²×C₉	D₄	1	2	yes	—
34	C₄²×C₉	D₄	1	2	yes	—
35	#3667	—	2	4	no	—
36	#3667	C₂×C₄	1	8	yes	—
37	C₂×C₉⋊C₈	—	2	4	no	—
38	C₄×#101	—	9	1	no	Sylow
39	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
40	C₃×C₄×Q₈	—	2	2	no	—
41	C₃×C₄×Q₈	—	2	2	no	—
42	C₂×C₃×C₄⋊C₄	Dic₃	1	2	yes	—
43	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
44	C₂×C₃×C₄²	Dic₃	1	2	yes	—
45	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
46	C₂×#208	—	3	4	no	—
47	#836	—	3	8	no	—
48	#803	—	6	2	no	—
49	C₄×C₃⋊C₈	—	6	2	no	—
50	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
51	Q₈×C₉	—	2	8	no	—
52	C₂×C₄×C₉	—	2	2	no	—
53	C₂×C₄×C₉	—	2	2	no	—
54	C₂×C₄×C₉	—	2	2	no	—
55	C₂×C₄×C₉	—	2	2	no	—
56	C₂×C₄×C₉	—	4	1	no	—
57	C₂×C₄×C₉	—	4	2	no	—
58	C₂×C₄×C₉	C₄²	1	4	yes	—
59	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₉	#41	1	2	yes	—
65	C₉⋊C₈	—	2	8	no	—
66	C₂×C₄×Q₈	D₉	1	1	yes	characteristic
67	C₂×#101	—	9	2	no	—
68	C₄×M₁₆	—	9	2	no	—
69	#343	—	9	2	no	—
70	C₂×C₃×Q₈	—	2	2	no	—
71	C₂×C₃×Q₈	—	2	2	no	—
72	C₂×C₃×Q₈	C₄×D₃	1	4	yes	—
73	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
74	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
76	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
78	C₃×C₄⋊C₄	—	2	4	no	—
79	C₃×C₄⋊C₄	—	2	2	no	—
80	C₃×C₄²	—	2	2	no	—
81	C₃×C₄²	—	2	2	no	—
82	C₃×C₄²	#67	1	2	yes	—
83	C₃×C₄²	#67	1	2	yes	—
84	#208	—	3	8	no	—
85	#208	—	6	4	no	—
86	C₂×C₃⋊C₈	—	6	4	no	—
87	C₂²×C₉	—	2	1	no	—
88	C₂²×C₉	—	2	1	no	—
89	C₂²×C₉	C₂×C₄²	1	1	yes	characteristic
90	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₉	#117	1	1	yes	characteristic
92	C₄×C₉	—	2	4	no	—
93	C₄×C₉	—	2	1	no	—
94	C₄×C₉	—	2	2	no	—
95	C₄×C₉	—	4	2	no	—
96	C₄×C₉	#101	1	2	yes	complemented
97	C₄×C₉	C₄×D₄	1	4	yes	—
98	C₂²×Q₈	C₂×D₉	1	1	yes	characteristic
99	C₂×M₁₆	—	9	4	no	—
100	C₄×Q₈	—	2	2	no	—
101	C₄×Q₈	—	2	2	no	—
102	C₂×C₄⋊C₄	Dic₉	1	2	yes	—
103	C₂×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
104	C₂×C₄²	Dic₉	1	2	yes	—
105	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
106	#101	—	9	8	no	—
107	#97	—	18	2	no	—
108	C₄×C₈	—	18	2	no	—
109	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
110	C₃×Q₈	—	2	8	no	—
111	C₂×C₃×C₄	—	2	2	no	—
112	C₂×C₃×C₄	—	2	2	no	—
113	C₂×C₃×C₄	—	2	2	no	—
114	C₂×C₃×C₄	—	2	2	no	—
115	C₂×C₃×C₄	—	4	1	no	—
116	C₂×C₃×C₄	—	4	2	no	—
117	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
118	C₂×C₃×C₄	#217	1	1	yes	characteristic
119	C₂×C₃×C₄	#217	1	2	yes	—
120	C₂×C₃×C₄	#217	1	1	yes	characteristic
121	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
122	C₂×C₃×C₄	#235	1	2	yes	—
123	C₂×C₃×C₄	C₂×#67	1	2	yes	—
124	C₃⋊C₈	—	6	8	no	—
125	C₂×C₉	—	2	1	no	—
126	C₂×C₉	—	2	1	no	—
127	C₂×C₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₉	C₂×#101	1	1	yes	characteristic
129	C₂×C₉	#413	1	1	yes	characteristic
130	C₂×Q₈	—	2	2	no	—
131	C₂×Q₈	—	2	2	no	—
132	C₂×Q₈	C₄×D₉	1	4	yes	—
133	C₂²×C₄	C₂×Dic₉	1	2	yes	—
134	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
135	C₂²×C₄	C₂×Dic₉	1	2	yes	—
136	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
137	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
138	M₁₆	—	9	8	no	—
139	M₁₆	—	18	4	no	—
140	C₂×C₈	—	18	4	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	2	no	—
145	C₄²	#611	1	2	yes	—
146	C₄²	#611	1	2	yes	—
147	C₂²×C₃	—	2	1	no	—
148	C₂²×C₃	—	2	1	no	—
149	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
150	C₂²×C₃	#926	1	1	yes	characteristic
151	C₂²×C₃	C₂×#217	1	1	yes	characteristic
152	C₃×C₄	—	2	4	no	—
153	C₃×C₄	—	2	1	no	—
154	C₃×C₄	—	2	2	no	—
155	C₃×C₄	—	4	2	no	—
156	C₃×C₄	#836	1	2	yes	—
157	C₃×C₄	C₄×#67	1	4	yes	—
158	C₉	C₄×#101	1	1	yes	characteristic, complemented, Sylow
159	C₂³	C₂²×Dic₉	1	1	yes	characteristic
160	Q₈	—	2	8	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	—	4	2	no	—
167	C₂×C₄	C₄×Dic₉	1	4	yes	—
168	C₂×C₄	#3676	1	1	yes	characteristic
169	C₂×C₄	#3676	1	2	yes	—
170	C₂×C₄	#3676	1	1	yes	characteristic
171	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
172	C₂×C₄	#3697	1	2	yes	—
173	C₂×C₄	C₂×#611	1	2	yes	—
174	C₈	—	18	8	no	—
175	C₂×C₃	—	2	1	no	—
176	C₂×C₃	—	2	1	no	—
177	C₂×C₃	C₄×#217	1	1	yes	characteristic
178	C₂×C₃	C₂×#836	1	1	yes	characteristic
179	C₂×C₃	#5237	1	1	yes	characteristic
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	C₂×C₄×Dic₉	1	1	yes	characteristic
183	C₂²	#63488	1	1	yes	characteristic
184	C₂²	C₂×#3676	1	1	yes	characteristic
185	C₄	—	2	4	no	—
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	4	2	no	—
189	C₄	#63394	1	2	yes	direct product factor
190	C₄	C₄×#611	1	4	yes	—
191	C₃	C₄×#836	1	1	yes	characteristic
192	C₂	—	2	1	no	—
193	C₂	—	2	1	no	—
194	C₂	C₄×#3676	1	1	yes	characteristic
195	C₂	C₂×#63394	1	1	yes	characteristic
196	C₂	#10588915	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3676
commutator	C₂²×C₉	C₂×C₄²
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₄×Q₈×C₉	C₂
socle	C₂²×C₃	C₂×#217
prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×C₄×Q₈	D₉
hypocenter	C₉	C₄×#101
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
14. #63394	C₄	direct (N × H)
96. C₄×C₉	#101	semidirect
158. C₉	C₄×#101	semidirect
189. C₄	#63394	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×C₄×Q₈×C₉	2
C₂×#63394	2
C₄×#3667	2
#10588207	2
C₄×#836	3

Subgroups — C4×#63394 #11783798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63394 #11783798