Subgroups — #16828186

Order 3712.

520 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745263	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271674	C₂	1	1	yes	maximal, characteristic
3	#14271234	C₂	1	4	yes	maximal, complemented
4	C₈×C₂²⋊D₂₉	C₂	1	4	yes	maximal, complemented
5	#14271189	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271129	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271127	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271118	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90805	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₂₉	—	2	4	no	—
13	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
14	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
16	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	#11745315	C₄	1	2	yes	—
18	#11745292	C₄	1	2	yes	—
19	#11745291	C₄	1	2	yes	—
20	C₄×C₂²⋊D₂₉	C₂²	1	4	yes	—
21	#11745288	C₂²	1	1	yes	characteristic
22	#11745286	C₄	1	2	yes	—
23	C₂×#90777	C₂²	1	1	yes	characteristic
24	C₂×#90777	C₂²	1	1	yes	characteristic
25	#11745263	—	2	4	no	—
26	C₂×#90772	C₂²	1	2	yes	complemented
27	C₂×C₈×D₂₉	C₂²	1	2	yes	complemented
28	C₂²⋊#6597	C₂²	1	4	yes	—
29	#11745168	C₂²	1	4	yes	complemented
30	#11745163	C₂²	1	2	yes	complemented
31	#11745162	C₂²	1	4	yes	complemented
32	C₈×Dic₂₉	C₂²	1	2	yes	complemented
33	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₂₉	—	2	2	no	—
35	C₂²×C₄×C₂₉	—	2	2	no	—
36	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
37	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₂₉	C₂×C₄	1	4	yes	—
41	C₂×C₂²⋊D₂₉	C₂×C₄	1	2	yes	—
42	#90805	—	2	2	no	—
43	#90805	—	2	2	no	—
44	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₂₉	C₂³	1	2	yes	—
46	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×C₂₉	—	2	2	no	—
48	C₂×C₈×C₂₉	—	2	4	no	—
49	C₂×C₈×C₂₉	—	2	4	no	—
50	C₂×C₈×C₂₉	D₄	1	4	yes	complemented
51	C₂×C₈×C₂₉	C₂³	1	2	yes	—
52	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
54	C₂²⋊Dic₂₉	C₂×C₄	1	4	yes	—
55	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
56	#90781	C₂×C₄	1	4	yes	—
57	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
58	#90779	C₂×C₄	1	4	yes	—
59	C₄×Dic₂₉	C₂³	1	2	yes	—
60	#90777	—	2	2	no	—
61	#90777	—	2	2	no	—
62	C₂×#6597	C₂³	1	2	yes	—
63	C₂×#6597	C₂³	1	2	yes	—
64	#90772	—	2	4	no	—
65	C₈×D₂₉	—	2	4	no	—
66	C₂³×C₂₉	—	2	2	no	—
67	C₂³×C₂₉	—	2	4	no	—
68	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
69	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
70	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₂₉	—	2	2	no	—
72	C₂×C₄×C₂₉	—	2	4	no	—
73	C₂×C₄×C₂₉	—	2	2	no	—
74	C₂×C₄×C₂₉	—	2	2	no	—
75	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₂₉	#41	1	2	yes	—
79	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
80	C₂²⋊D₂₉	—	2	4	no	—
81	C₂²⋊D₂₉	—	2	8	no	—
82	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
83	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
84	D₁₁₆	—	2	2	no	—
85	C₄×D₂₉	—	2	2	no	—
86	C₄×D₂₉	—	2	2	no	—
87	Dic₅₈	—	2	2	no	—
88	C₈×C₂₉	—	2	2	no	—
89	C₈×C₂₉	C₂×D₄	1	2	yes	—
90	C₈×C₂₉	C₂×D₄	1	2	yes	—
91	#6597	—	2	2	no	—
92	#6597	—	2	2	no	—
93	#2929	—	29	1	no	maximal, Sylow
94	C₂²×C₂₉	—	2	8	no	—
95	C₂²×C₂₉	—	2	2	no	—
96	C₂²×C₂₉	—	2	2	no	—
97	C₂²×C₂₉	—	2	2	no	—
98	C₂²×C₂₉	C₄×D₄	1	2	yes	—
99	C₂²×C₂₉	#131	1	4	yes	complemented
100	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
101	C₂×D₂₉	—	2	2	no	—
102	C₂×D₂₉	—	2	4	no	—
103	C₄×C₂₉	—	2	2	no	—
104	C₄×C₂₉	C₄×D₄	1	2	yes	—
105	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
107	Dic₂₉	—	2	2	no	—
108	Dic₂₉	—	2	4	no	—
109	C₂×#131	—	29	1	no	—
110	C₂³×C₈	D₂₉	1	1	yes	characteristic, complemented
111	#525	—	29	1	no	—
112	#435	—	29	4	no	—
113	C₈×D₄	—	29	4	no	—
114	#424	—	29	1	no	—
115	#408	—	29	1	no	—
116	#407	—	29	1	no	—
117	#405	—	29	1	no	—
118	C₂×C₂₉	—	2	2	no	—
119	C₂×C₂₉	—	2	4	no	—
120	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
121	C₂×C₂₉	C₂×#131	1	2	yes	—
122	D₂₉	—	4	2	no	—
123	C₂×#41	—	29	1	no	—
124	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
125	#131	—	58	4	no	—
126	C₂×M₁₆	—	29	1	no	—
127	C₂×M₁₆	—	29	1	no	—
128	C₂×M₁₆	—	29	2	no	—
129	C₂²×C₈	—	2	4	no	—
130	C₂²×C₈	—	29	2	no	—
131	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
132	C₂²×C₈	C₂×D₂₉	1	2	yes	—
133	C₂²×C₈	C₂×D₂₉	1	2	yes	—
134	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
135	#123	—	29	2	no	—
136	C₂²⋊Q₈	—	29	2	no	—
137	#121	—	29	2	no	—
138	#120	—	29	2	no	—
139	C₄×D₄	—	29	4	no	—
140	#117	—	29	1	no	—
141	C₄⋊C₈	—	29	4	no	—
142	C₂²⋊C₈	—	29	4	no	—
143	C₂²⋊C₈	—	29	4	no	—
144	#97	—	29	2	no	—
145	C₄×C₈	—	29	2	no	—
146	C₂₉	#2929	1	1	yes	characteristic, complemented, Sylow
147	C₂⁴	C₄×D₂₉	1	1	yes	characteristic
148	#41	—	58	2	no	—
149	#41	—	58	2	no	—
150	C₂×Q₈	—	29	1	no	—
151	C₂×D₄	—	29	4	no	—
152	C₂×D₄	—	29	2	no	—
153	C₂×D₄	—	29	1	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	29	2	no	—
157	C₂²×C₄	C₄×D₂₉	1	2	yes	—
158	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
160	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
161	M₁₆	—	58	2	no	—
162	M₁₆	—	58	2	no	—
163	M₁₆	—	58	4	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	2	4	no	—
166	C₂×C₈	—	2	4	no	—
167	C₂×C₈	—	29	2	no	—
168	C₂×C₈	—	29	2	no	—
169	C₂×C₈	—	58	4	no	—
170	C₂×C₈	C₂²⋊D₂₉	1	4	yes	complemented
171	C₂×C₈	C₂²×D₂₉	1	2	yes	—
172	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
174	C₄⋊C₄	—	29	2	no	—
175	C₄⋊C₄	—	29	4	no	—
176	C₂²⋊C₄	—	29	2	no	—
177	C₂²⋊C₄	—	29	4	no	—
178	C₂²⋊C₄	—	29	4	no	—
179	C₄²	—	29	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	4	no	—
182	C₂³	—	29	2	no	—
183	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
184	C₂³	C₂×C₄×D₂₉	1	2	yes	—
185	Q₈	—	58	2	no	—
186	D₄	—	58	4	no	—
187	D₄	—	58	8	no	—
188	D₄	—	58	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	29	4	no	—
194	C₂×C₄	—	29	2	no	—
195	C₂×C₄	—	58	2	no	—
196	C₂×C₄	—	58	2	no	—
197	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
198	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
199	C₂×C₄	#90805	1	2	yes	—
200	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
201	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	58	2	no	—
204	C₈	—	58	2	no	—
205	C₈	C₂×C₂²⋊D₂₉	1	2	yes	—
206	C₈	C₂×C₂²⋊D₂₉	1	2	yes	—
207	C₂²	—	2	8	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	58	2	no	—
212	C₂²	—	58	4	no	—
213	C₂²	#11745263	1	4	yes	complemented
214	C₂²	C₄×C₂²⋊D₂₉	1	2	yes	—
215	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	58	2	no	—
218	C₄	—	58	4	no	—
219	C₄	C₄×C₂²⋊D₂₉	1	2	yes	—
220	C₄	C₂×#90805	1	1	yes	characteristic
221	C₄	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
222	C₂	—	2	2	no	—
223	C₂	—	2	4	no	—
224	C₂	—	116	2	no	—
225	C₂	C₂×C₄×C₂²⋊D₂₉	1	1	yes	characteristic
226	C₂	C₂×#11745263	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂³×C₈×C₂₉	C₂
prime radical	#14271674	C₂
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂³×C₈	D₂₉
hypocenter	C₂₉	#2929
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11745263	C₂	semidirect
3. #14271234	C₂	semidirect
4. C₈×C₂²⋊D₂₉	C₂	semidirect
5. #14271189	C₂	semidirect
6. #14271129	C₂	semidirect
7. #14271127	C₂	semidirect
8. #14271118	C₂	semidirect
9. C₂³×C₈×C₂₉	C₂	semidirect
26. C₂×#90772	C₂²	semidirect
27. C₂×C₈×D₂₉	C₂²	semidirect
29. #11745168	C₂²	semidirect
30. #11745163	C₂²	semidirect
31. #11745162	C₂²	semidirect
32. C₈×Dic₂₉	C₂²	semidirect
50. C₂×C₈×C₂₉	D₄	semidirect
99. C₂²×C₂₉	#131	semidirect
110. C₂³×C₈	D₂₉	semidirect
146. C₂₉	#2929	semidirect
170. C₂×C₈	C₂²⋊D₂₉	semidirect
213. C₂²	#11745263	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745263	2
#14271674	2
#14271234	2
C₈×C₂²⋊D₂₉	2
#14271189	2
#14271129	2
#14271127	2
#14271118	2
C₂³×C₈×C₂₉	2
#2929	29