Subgroups — C₂×#14271221 #16828115

Order 3712.

412 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745288	C₂	1	1	yes	maximal, characteristic
2	#14271221	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11745162	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11745162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊#6597	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₂₉	C₄	1	1	yes	characteristic
13	C₂×C₂²⋊Dic₂₉	C₄	1	1	yes	characteristic
14	#11745288	C₄	1	4	yes	—
15	#11745288	C₂²	1	4	yes	—
16	C₂×C₄⋊Dic₂₉	C₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₂₉	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
20	C₂²×#6597	C₂²	1	1	yes	characteristic
21	C₂²×#6597	C₂²	1	1	yes	characteristic
22	C₂₉×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₂²⋊#6597	C₂²	1	4	yes	—
24	#11745163	C₂²	1	4	yes	complemented
25	#11745162	C₂²	1	4	yes	complemented
26	#11745162	C₂²	1	4	yes	complemented
27	C₈×Dic₂₉	C₂²	1	4	yes	complemented
28	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₂₉	—	2	2	no	—
30	C₂²×C₄×C₂₉	—	2	2	no	—
31	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×C₂₉	—	2	2	no	—
40	C₂×C₈×C₂₉	—	2	2	no	—
41	C₂×C₈×C₂₉	C₂³	1	2	yes	—
42	C₂×C₈×C₂₉	C₂³	1	2	yes	—
43	C₂²⋊Dic₂₉	C₂×C₄	1	4	yes	—
44	C₂²⋊Dic₂₉	C₂×C₄	1	4	yes	—
45	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
46	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
47	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
48	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
49	C₄×Dic₂₉	C₂³	1	2	yes	—
50	C₄×Dic₂₉	C₂³	1	2	yes	—
51	C₂×#6597	—	2	2	no	—
52	C₂×#6597	—	2	2	no	—
53	C₂×#6597	C₂³	1	2	yes	—
54	C₂×#6597	C₂³	1	2	yes	—
55	C₂³×C₂₉	—	2	2	no	—
56	C₂³×C₂₉	—	2	2	no	—
57	C₂³×C₂₉	—	2	2	no	—
58	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
59	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₂₉	—	2	2	no	—
61	C₂×C₄×C₂₉	—	2	4	no	—
62	C₂×C₄×C₂₉	—	2	2	no	—
63	C₂×C₄×C₂₉	—	2	2	no	—
64	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₂₉	#41	1	2	yes	—
67	C₂×C₄×C₂₉	#41	1	2	yes	—
68	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
69	C₂×Dic₂₉	—	2	2	no	—
70	C₂×Dic₂₉	—	2	2	no	—
71	C₂×Dic₂₉	—	2	2	no	—
72	C₂×Dic₂₉	—	2	2	no	—
73	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
74	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
75	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
76	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
77	C₈×C₂₉	—	2	2	no	—
78	C₈×C₂₉	—	2	2	no	—
79	#6597	—	2	2	no	—
80	#6597	—	2	2	no	—
81	C₂×#433	—	29	1	no	maximal, Sylow
82	C₂²×C₂₉	—	2	2	no	—
83	C₂²×C₂₉	—	2	2	no	—
84	C₂²×C₂₉	—	2	2	no	—
85	C₂²×C₂₉	—	4	4	no	—
86	C₂²×C₂₉	#117	1	2	yes	—
87	C₂²×C₂₉	#131	1	2	yes	—
88	C₂²×C₂₉	#131	1	2	yes	—
89	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
90	C₄×C₂₉	—	2	2	no	—
91	C₄×C₂₉	#117	1	2	yes	—
92	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
93	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
94	Dic₂₉	—	2	2	no	—
95	Dic₂₉	—	2	2	no	—
96	Dic₂₉	—	2	2	no	—
97	Dic₂₉	—	2	2	no	—
98	C₂×#117	—	29	1	no	—
99	#433	—	29	8	no	—
100	C₂×C₄⋊C₈	—	29	1	no	—
101	C₂×C₄⋊C₈	—	29	1	no	—
102	C₂×C₂²⋊C₈	—	29	1	no	—
103	C₂×C₂²⋊C₈	D₂₉	1	1	yes	characteristic
104	C₂×#97	—	29	1	no	—
105	C₂×C₄×C₈	—	29	1	no	—
106	C₂×C₂₉	—	4	2	no	—
107	C₂×C₂₉	#433	1	4	yes	complemented
108	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
109	C₂×C₂₉	C₂×#131	1	1	yes	characteristic
110	C₂×C₂₉	C₂×#131	1	1	yes	characteristic
111	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
112	C₂²×C₈	—	29	1	no	—
113	C₂²×C₈	—	29	1	no	—
114	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
115	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
116	#117	—	29	4	no	—
117	#117	—	29	4	no	—
118	C₂×C₄⋊C₄	—	29	1	no	—
119	C₂×C₄⋊C₄	—	29	1	no	—
120	C₂×C₂²⋊C₄	—	29	1	no	—
121	C₂×C₂²⋊C₄	—	29	1	no	—
122	C₂×C₄²	—	29	1	no	—
123	C₂×C₄²	—	29	1	no	—
124	C₄⋊C₈	—	29	4	no	—
125	C₄⋊C₈	—	29	4	no	—
126	C₂²⋊C₈	—	29	4	no	—
127	C₂²⋊C₈	C₂×D₂₉	1	4	yes	—
128	#97	—	29	4	no	—
129	C₄×C₈	—	29	4	no	—
130	C₂₉	C₂×#433	1	1	yes	characteristic, complemented, Sylow
131	C₂⁴	C₄×D₂₉	1	1	yes	characteristic
132	C₂²×C₄	—	2	2	no	—
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	29	1	no	—
135	C₂²×C₄	—	29	1	no	—
136	C₂²×C₄	—	29	1	no	—
137	C₂²×C₄	—	29	1	no	—
138	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
139	C₂²×C₄	C₄×D₂₉	1	2	yes	—
140	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
141	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	29	2	no	—
145	C₂×C₈	—	29	2	no	—
146	C₂×C₈	—	58	2	no	—
147	C₂×C₈	—	58	2	no	—
148	C₂×C₈	C₂²×D₂₉	1	2	yes	—
149	C₂×C₈	C₂²×D₂₉	1	2	yes	—
150	C₄⋊C₄	—	29	4	no	—
151	C₄⋊C₄	—	29	4	no	—
152	C₂²⋊C₄	—	29	4	no	—
153	C₂²⋊C₄	—	29	4	no	—
154	C₄²	—	29	2	no	—
155	C₄²	—	29	2	no	—
156	C₄²	—	29	2	no	—
157	C₄²	—	29	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	C₂×C₄×D₂₉	1	2	yes	—
162	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	29	2	no	—
168	C₂×C₄	—	29	2	no	—
169	C₂×C₄	—	29	2	no	—
170	C₂×C₄	—	29	2	no	—
171	C₂×C₄	—	58	2	no	—
172	C₂×C₄	—	58	2	no	—
173	C₂×C₄	—	58	2	no	—
174	C₂×C₄	—	58	2	no	—
175	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
176	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
177	C₂×C₄	#90807	1	2	yes	—
178	C₂×C₄	#90807	1	2	yes	—
179	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
180	C₈	—	2	2	no	—
181	C₈	—	2	2	no	—
182	C₈	—	58	2	no	—
183	C₈	—	58	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	4	4	no	—
188	C₂²	#11745239	1	2	yes	—
189	C₂²	#11745263	1	2	yes	—
190	C₂²	#11745269	1	2	yes	—
191	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
192	C₄	—	2	2	no	—
193	C₄	—	58	2	no	—
194	C₄	—	58	2	no	—
195	C₄	—	58	2	no	—
196	C₄	—	58	2	no	—
197	C₄	#11745239	1	2	yes	—
198	C₄	C₂×#90807	1	1	yes	characteristic
199	C₄	C₂×#90807	1	1	yes	characteristic
200	C₂	—	4	2	no	—
201	C₂	#14271221	1	4	yes	direct product factor
202	C₂	C₂×#11745239	1	1	yes	characteristic
203	C₂	C₂×#11745263	1	1	yes	characteristic
204	C₂	C₂×#11745269	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×C₂²⋊C₈	C₂
socle	C₂³×C₂₉	C₂²×C₄
prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂×C₂²⋊C₈	D₂₉
hypocenter	C₂₉	C₂×#433
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #14271221	C₂	direct (N × H)
3. C₂×#11745162	C₂	semidirect
4. C₂×#11745162	C₂	semidirect
6. C₂×#11745163	C₂	semidirect
7. C₂×C₈×Dic₂₉	C₂	semidirect
24. #11745163	C₂²	semidirect
25. #11745162	C₂²	semidirect
26. #11745162	C₂²	semidirect
27. C₈×Dic₂₉	C₂²	semidirect
107. C₂×C₂₉	#433	semidirect
130. C₂₉	C₂×#433	semidirect
201. C₂	#14271221	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×#11745288	2
#14271221	2
C₂×#11745162	2
C₂×C₂²⋊#6597	2
C₂×#11745163	2
C₂×C₈×Dic₂₉	2
C₂×C₂₉×C₂²⋊C₈	2
C₂×#433	29

Subgroups — C2×#14271221 #16828115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271221 #16828115