Subgroups — C₂×#10588759 #11873389

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#63431	C₂	1	1	yes	maximal, characteristic
3	C₂×#63395	C₂	1	4	yes	maximal
4	#10588759	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#5079	—	3	1	no	maximal
7	C₂²×Q₈×C₉	C₂²	1	2	yes	—
8	C₂²×Dic₁₈	—	2	1	no	—
9	C₉×C₄⋊Q₈	—	2	2	no	—
10	C₉×C₄⋊Q₈	C₂²	1	4	yes	—
11	C₂×C₉×C₄⋊C₄	—	2	1	no	—
12	C₂×C₉×C₄⋊C₄	—	2	1	no	—
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₉	—	2	1	no	—
15	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
16	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
17	#63431	—	2	2	no	—
18	#63431	C₂²	1	4	yes	—
19	#63395	C₂²	1	16	yes	—
20	C₄×C₉⋊C₈	C₂²	1	4	yes	—
21	C₂×C₃×C₄⋊Q₈	D₃	1	1	yes	characteristic
22	C₂×#869	—	3	1	no	—
23	C₂×#835	—	3	4	no	—
24	#5079	—	3	8	no	—
25	C₂×C₄×C₃⋊C₈	—	3	1	no	—
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	—	2	8	no	—
28	C₂×Q₈×C₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₉	—	2	2	no	—
30	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₉	—	2	2	no	—
34	C₂×Dic₁₈	—	2	4	no	—
35	C₂×Dic₁₈	—	4	4	no	—
36	C₉×C₄⋊C₄	—	2	4	no	—
37	C₉×C₄⋊C₄	—	2	4	no	—
38	C₄²×C₉	D₄	1	2	yes	—
39	C₄²×C₉	C₂³	1	2	yes	—
40	C₄⋊Dic₉	—	2	2	no	—
41	C₄⋊Dic₉	—	2	4	no	—
42	C₄⋊Dic₉	C₂³	1	4	yes	—
43	C₂×C₉⋊C₈	—	2	4	no	—
44	C₂×C₉⋊C₈	C₂³	1	4	yes	—
45	C₂×#487	—	9	1	no	Sylow
46	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
47	C₂²×Dic₆	—	6	1	no	—
48	C₃×C₄⋊Q₈	—	2	2	no	—
49	C₃×C₄⋊Q₈	C₂×D₃	1	4	yes	—
50	C₂×C₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
53	C₂×C₄⋊Dic₃	—	3	2	no	—
54	C₂×C₄⋊Dic₃	—	6	1	no	—
55	C₂²×C₃⋊C₈	—	3	2	no	—
56	#869	—	3	4	no	—
57	#869	—	6	2	no	—
58	#835	—	3	16	no	—
59	C₄×C₃⋊C₈	—	3	4	no	—
60	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
61	Q₈×C₉	—	2	8	no	—
62	Q₈×C₉	—	4	4	no	—
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	—	4	4	no	—
65	C₂×C₄×C₉	SD₁₆	1	4	yes	—
66	C₂×C₄×C₉	Q₁₆	1	4	yes	—
67	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₉	#41	1	4	yes	—
71	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
72	C₂×Dic₉	—	2	4	no	—
73	C₂×Dic₉	—	4	4	no	—
74	Dic₁₈	—	4	8	no	—
75	C₉⋊C₈	—	2	4	no	—
76	C₂×C₄⋊Q₈	—	9	1	no	—
77	C₂×C₄⋊Q₈	D₉	1	1	yes	characteristic
78	#487	—	9	8	no	—
79	C₂×#103	—	9	4	no	—
80	C₂×C₄×C₈	—	9	1	no	—
81	C₂×C₃×Q₈	—	2	2	no	—
82	C₂×C₃×Q₈	—	2	8	no	—
83	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
84	C₂²×C₃×C₄	—	2	2	no	—
85	C₂²×C₃×C₄	#67	1	1	yes	characteristic
86	C₂²×C₃×C₄	#67	1	1	yes	characteristic
87	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
88	C₂²×Dic₃	—	6	2	no	—
89	C₂×Dic₆	—	6	4	no	—
90	C₂×Dic₆	—	12	4	no	—
91	C₃×C₄⋊C₄	—	2	4	no	—
92	C₃×C₄⋊C₄	—	2	4	no	—
93	C₃×C₄²	#67	1	2	yes	—
94	C₃×C₄²	C₂²×D₃	1	2	yes	—
95	C₄⋊Dic₃	—	3	4	no	—
96	C₄⋊Dic₃	—	6	4	no	—
97	C₄⋊Dic₃	—	6	2	no	—
98	C₂×C₃⋊C₈	—	3	4	no	—
99	C₂×C₃⋊C₈	—	6	4	no	—
100	C₂²×C₉	#124	1	2	yes	—
101	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
102	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
103	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₉	—	4	4	no	—
105	C₄×C₉	#124	1	2	yes	—
106	C₄×C₉	C₂×SD₁₆	1	4	yes	—
107	C₄×C₉	C₂×Q₁₆	1	4	yes	—
108	C₄×C₉	C₂×#41	1	2	yes	—
109	Dic₉	—	4	4	no	—
110	C₂²×Q₈	—	18	1	no	—
111	C₂²×Q₈	C₂×D₉	1	2	yes	—
112	C₂²×C₈	—	9	2	no	—
113	C₄⋊Q₈	—	2	2	no	—
114	C₄⋊Q₈	—	9	4	no	—
115	C₄⋊Q₈	—	18	2	no	—
116	C₄⋊Q₈	C₂×D₉	1	4	yes	—
117	C₂×C₄⋊C₄	—	2	1	no	—
118	C₂×C₄⋊C₄	—	2	1	no	—
119	C₂×C₄⋊C₄	—	9	2	no	—
120	C₂×C₄⋊C₄	—	18	1	no	—
121	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
122	#103	—	9	16	no	—
123	C₄×C₈	—	9	4	no	—
124	C₂³×C₃	C₂×#67	1	1	yes	characteristic
125	C₃×Q₈	—	2	8	no	—
126	C₃×Q₈	—	4	4	no	—
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	—	4	4	no	—
129	C₂×C₃×C₄	#215	1	4	yes	—
130	C₂×C₃×C₄	#216	1	4	yes	—
131	C₂×C₃×C₄	#237	1	4	yes	—
132	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂×#67	1	2	yes	—
134	C₂×C₃×C₄	C₂×#67	1	2	yes	—
135	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
136	C₂×Dic₃	—	6	4	no	—
137	C₂×Dic₃	—	12	4	no	—
138	Dic₆	—	12	8	no	—
139	C₃⋊C₈	—	6	4	no	—
140	C₂×C₉	#487	1	4	yes	complemented
141	C₂×C₉	C₂×#124	1	1	yes	characteristic
142	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
143	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
144	C₂×Q₈	—	2	2	no	—
145	C₂×Q₈	—	2	8	no	—
146	C₂×Q₈	—	18	4	no	—
147	C₂×Q₈	—	36	4	no	—
148	C₂×Q₈	C₂²×D₉	1	4	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	18	2	no	—
151	C₂²×C₄	#611	1	1	yes	characteristic
152	C₂²×C₄	#611	1	1	yes	characteristic
153	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
154	C₂×C₈	—	9	4	no	—
155	C₂×C₈	—	18	4	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	9	4	no	—
159	C₄⋊C₄	—	18	2	no	—
160	C₄⋊C₄	—	18	4	no	—
161	C₄²	#611	1	2	yes	—
162	C₄²	C₂²×D₉	1	2	yes	—
163	C₂²×C₃	#936	1	2	yes	—
164	C₂²×C₃	C₂×#215	1	2	yes	—
165	C₂²×C₃	C₂×#216	1	2	yes	—
166	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
167	C₃×C₄	—	4	4	no	—
168	C₃×C₄	#936	1	2	yes	—
169	C₃×C₄	C₂×#215	1	4	yes	—
170	C₃×C₄	C₂×#216	1	4	yes	—
171	C₃×C₄	C₂×#237	1	2	yes	—
172	Dic₃	—	12	4	no	—
173	C₉	C₂×#487	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×#611	1	1	yes	characteristic
175	Q₈	—	2	8	no	—
176	Q₈	—	4	4	no	—
177	Q₈	—	36	8	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	18	4	no	—
181	C₂×C₄	—	36	4	no	—
182	C₂×C₄	#3674	1	4	yes	—
183	C₂×C₄	#3675	1	4	yes	—
184	C₂×C₄	#3699	1	4	yes	—
185	C₂×C₄	C₂×#611	1	1	yes	characteristic
186	C₂×C₄	C₂×#611	1	2	yes	—
187	C₂×C₄	C₂×#611	1	2	yes	—
188	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
189	C₈	—	18	4	no	—
190	C₂×C₃	#5079	1	4	yes	—
191	C₂×C₃	C₂×#936	1	1	yes	characteristic
192	C₂×C₃	C₂²×#215	1	1	yes	characteristic
193	C₂×C₃	C₂²×#216	1	1	yes	characteristic
194	C₂²	#63498	1	2	yes	—
195	C₂²	C₂×#3674	1	2	yes	—
196	C₂²	C₂×#3675	1	2	yes	—
197	C₂²	C₂²×#611	1	1	yes	characteristic
198	C₄	—	4	4	no	—
199	C₄	—	36	4	no	—
200	C₄	#63498	1	2	yes	—
201	C₄	C₂×#3674	1	4	yes	—
202	C₄	C₂×#3675	1	4	yes	—
203	C₄	C₂×#3699	1	2	yes	—
204	C₃	C₂×#5079	1	1	yes	characteristic
205	C₂	#10588759	1	4	yes	direct product factor
206	C₂	C₂×#63498	1	1	yes	characteristic
207	C₂	C₂²×#3674	1	1	yes	characteristic
208	C₂	C₂²×#3675	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#611
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₃	C₂×#67
hypercenter	C₂×C₄⋊Q₈	D₉
hypocenter	C₉	C₂×#487
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
4. #10588759	C₂	direct (N × H)
140. C₂×C₉	#487	semidirect
173. C₉	C₂×#487	semidirect
205. C₂	#10588759	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×C₉×C₄⋊Q₈	2
C₂×#63431	2
C₂×#63395	2
#10588759	2
C₂×C₄×C₉⋊C₈	2
C₂×#5079	3

Subgroups — C2×#10588759 #11873389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588759 #11873389