Subgroups — C₂×#14271888 #16833061

Order 3712.

1048 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271888	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11745306	C₂	1	2	yes	maximal
3	C₂×#11745252	C₂	1	2	yes	maximal
4	C₂×#11745251	C₂	1	4	yes	maximal
5	C₂×Q₈×Dic₂₉	C₂	1	2	yes	maximal
6	C₂×C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
8	C₂×#11745249	C₂	1	2	yes	maximal
9	C₂×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₂₉	C₂²	1	2	yes	—
11	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
12	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
13	C₂₉×C₄⋊Q₈	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
16	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
17	Q₈×Dic₂₉	C₂²	1	16	yes	—
18	#11745306	C₂²	1	16	yes	—
19	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
22	C₂×#90779	C₂²	1	4	yes	—
23	C₂×#90779	C₂²	1	2	yes	—
24	C₂×#90779	C₂²	1	2	yes	—
25	C₂×#90779	C₂²	1	4	yes	—
26	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
27	C₂×C₄×Dic₂₉	C₂²	1	4	yes	—
28	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
29	#11745252	C₂²	1	16	yes	—
30	#11745251	C₂²	1	32	yes	—
31	#11745249	C₂²	1	16	yes	—
32	C₄×Dic₅₈	C₂²	1	8	yes	—
33	C₄×Dic₅₈	C₂²	1	8	yes	—
34	C₂×Q₈×C₂₉	—	2	8	no	—
35	C₂×Q₈×C₂₉	C₂³	1	8	yes	—
36	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
37	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂²×Dic₂₉	C₂³	1	2	yes	—
41	C₂²×Dic₂₉	C₂³	1	2	yes	—
42	C₂²×Dic₂₉	C₂³	1	2	yes	—
43	C₂²×Dic₂₉	C₂³	1	2	yes	—
44	C₂×Dic₅₈	—	2	4	no	—
45	C₂×Dic₅₈	Q₈	1	8	yes	complemented
46	C₂×Dic₅₈	C₂³	1	4	yes	—
47	C₂×Dic₅₈	C₂³	1	4	yes	—
48	C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
49	C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
50	C₄²×C₂₉	C₂³	1	4	yes	—
51	C₄⋊Dic₂₉	C₂³	1	4	yes	—
52	C₄⋊Dic₂₉	C₂³	1	16	yes	—
53	C₄⋊Dic₂₉	C₂³	1	4	yes	—
54	#90779	C₂³	1	16	yes	—
55	#90779	C₂³	1	16	yes	—
56	#90779	C₂³	1	8	yes	—
57	#90779	C₂³	1	8	yes	—
58	C₄×Dic₂₉	C₂³	1	8	yes	—
59	C₄×Dic₂₉	C₂³	1	16	yes	—
60	C₄×Dic₂₉	C₂³	1	8	yes	—
61	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
62	Q₈×C₂₉	—	2	16	no	—
63	C₂×C₄×C₂₉	—	2	8	no	—
64	C₂×C₄×C₂₉	—	2	2	no	—
65	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
66	C₂×C₄×C₂₉	#41	1	4	yes	—
67	C₂×C₄×C₂₉	C₂⁴	1	8	yes	—
68	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
69	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
70	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
71	C₂×Dic₂₉	—	2	4	no	—
72	C₂×Dic₂₉	—	2	4	no	—
73	C₂×Dic₂₉	—	2	4	no	—
74	C₂×Dic₂₉	C₂×Q₈	1	8	yes	—
75	C₂×Dic₂₉	C₂⁴	1	4	yes	—
76	C₂×Dic₂₉	C₂⁴	1	4	yes	—
77	C₂×Dic₂₉	C₂⁴	1	4	yes	—
78	C₂×Dic₂₉	C₂⁴	1	4	yes	—
79	Dic₅₈	—	2	8	no	—
80	Dic₅₈	C₂×Q₈	1	16	yes	complemented
81	C₂×#557	—	29	1	no	maximal, Sylow
82	C₂²×C₂₉	C₂²×Q₈	1	2	yes	—
83	C₂²×C₂₉	C₂×#41	1	2	yes	—
84	C₂²×C₂₉	2₋¹⁺⁴	1	2	yes	—
85	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
86	C₄×C₂₉	—	2	8	no	—
87	C₄×C₂₉	—	2	2	no	—
88	C₄×C₂₉	C₂²×Q₈	1	4	yes	—
89	C₄×C₂₉	C₂×#41	1	4	yes	—
90	Dic₂₉	—	2	4	no	—
91	Dic₂₉	—	2	4	no	—
92	Dic₂₉	—	2	4	no	—
93	Dic₂₉	C₂²×Q₈	1	8	yes	—
94	#557	—	29	16	no	—
95	C₂×C₄⋊Q₈	—	29	2	no	—
96	C₂×C₄⋊Q₈	D₂₉	1	1	yes	characteristic
97	C₂×#125	—	29	4	no	—
98	C₂×#125	—	29	2	no	—
99	C₂×C₄×Q₈	—	29	2	no	—
100	C₂×C₄×Q₈	—	29	2	no	—
101	C₂×C₄×Q₈	—	29	1	no	—
102	C₂×C₄×Q₈	—	29	1	no	—
103	C₂×C₂₉	#557	1	4	yes	complemented
104	C₂×C₂₉	C₂³×Q₈	1	1	yes	characteristic
105	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
106	C₂×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
107	C₂²×Q₈	—	29	1	no	—
108	C₂²×Q₈	—	29	1	no	—
109	C₂²×Q₈	C₂×D₂₉	1	2	yes	—
110	C₄⋊Q₈	—	29	16	no	—
111	C₄⋊Q₈	C₂×D₂₉	1	8	yes	—
112	#125	—	29	32	no	—
113	#125	—	29	16	no	—
114	C₄×Q₈	—	29	16	no	—
115	C₄×Q₈	—	29	16	no	—
116	C₄×Q₈	—	29	8	no	—
117	C₄×Q₈	—	29	8	no	—
118	C₂×C₄⋊C₄	—	29	1	no	—
119	C₂×C₄⋊C₄	—	29	2	no	—
120	C₂×C₄⋊C₄	—	29	2	no	—
121	C₂×C₄⋊C₄	—	29	4	no	—
122	C₂×C₄⋊C₄	—	29	4	no	—
123	C₂×C₄⋊C₄	—	29	1	no	—
124	C₂×C₄⋊C₄	—	29	4	no	—
125	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
126	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
127	C₂×C₄²	—	29	4	no	—
128	C₂×C₄²	—	29	2	no	—
129	C₂×C₄²	—	29	2	no	—
130	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
131	C₂₉	C₂×#557	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₈	—	2	8	no	—
133	C₂×Q₈	—	29	8	no	—
134	C₂×Q₈	—	29	4	no	—
135	C₂×Q₈	—	29	4	no	—
136	C₂×Q₈	—	58	4	no	—
137	C₂×Q₈	C₂²×D₂₉	1	8	yes	—
138	C₂²×C₄	—	29	2	no	—
139	C₂²×C₄	—	29	2	no	—
140	C₂²×C₄	—	29	2	no	—
141	C₂²×C₄	—	29	2	no	—
142	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
143	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
144	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
146	C₄⋊C₄	—	29	4	no	—
147	C₄⋊C₄	—	29	8	no	—
148	C₄⋊C₄	—	29	8	no	—
149	C₄⋊C₄	—	29	16	no	—
150	C₄⋊C₄	—	29	4	no	—
151	C₄⋊C₄	—	29	16	no	—
152	C₄⋊C₄	—	29	16	no	—
153	C₄⋊C₄	C₂²×D₂₉	1	8	yes	—
154	C₄⋊C₄	C₂²×D₂₉	1	8	yes	—
155	C₄²	—	29	16	no	—
156	C₄²	—	29	8	no	—
157	C₄²	—	29	8	no	—
158	C₄²	C₂²×D₂₉	1	4	yes	—
159	C₂³	C₂³×D₂₉	1	1	yes	characteristic
160	Q₈	—	2	16	no	—
161	Q₈	—	29	16	no	—
162	Q₈	—	58	8	no	—
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	29	8	no	—
166	C₂×C₄	—	29	4	no	—
167	C₂×C₄	—	29	4	no	—
168	C₂×C₄	—	29	4	no	—
169	C₂×C₄	—	29	4	no	—
170	C₂×C₄	—	58	4	no	—
171	C₂×C₄	—	58	4	no	—
172	C₂×C₄	—	58	4	no	—
173	C₂×C₄	#90807	1	4	yes	—
174	C₂×C₄	Q₈×D₂₉	1	4	yes	—
175	C₂×C₄	C₂³×D₂₉	1	8	yes	—
176	C₂×C₄	C₂³×D₂₉	1	2	yes	—
177	C₂×C₄	C₂³×D₂₉	1	2	yes	—
178	C₂×C₄	C₂³×D₂₉	1	2	yes	—
179	C₂²	C₂×#90807	1	2	yes	—
180	C₂²	C₂×Q₈×D₂₉	1	2	yes	—
181	C₂²	#11745362	1	2	yes	—
182	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
183	C₄	—	2	8	no	—
184	C₄	—	2	2	no	—
185	C₄	—	29	8	no	—
186	C₄	—	58	4	no	—
187	C₄	—	58	4	no	—
188	C₄	—	58	4	no	—
189	C₄	C₂×#90807	1	4	yes	—
190	C₄	C₂×Q₈×D₂₉	1	4	yes	—
191	C₂	#14271888	1	4	yes	direct product factor
192	C₂	C₂²×Q₈×D₂₉	1	1	yes	characteristic
193	C₂	C₂²×#90807	1	1	yes	characteristic
194	C₂	C₂×#11745362	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₉
commutator, cosocle	C₂²×C₂₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₉
Fitting	C₂×C₂₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₂₉	C₂⁴
hypercenter	C₂×C₄⋊Q₈	D₂₉
hypocenter	C₂₉	C₂×#557
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14271888	C₂	direct (N × H)
45. C₂×Dic₅₈	Q₈	semidirect
80. Dic₅₈	C₂×Q₈	semidirect
103. C₂×C₂₉	#557	semidirect
131. C₂₉	C₂×#557	semidirect
191. C₂	#14271888	direct (N × H)

Maximal subgroups

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

subgroup	index
#14271888	2
C₂×#11745306	2
C₂×#11745252	2
C₂×#11745251	2
C₂×Q₈×Dic₂₉	2
C₂×C₄×Dic₅₈	2
C₂×#11745249	2
C₂×C₂₉×C₄⋊Q₈	2
C₂×#557	29

Subgroups — C2×#14271888 #16833061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271888 #16833061