Subgroups — #16836170

Order 3712.

484 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272186	C₂	1	2	yes	maximal, complemented
2	#14272185	C₂	1	2	yes	maximal, complemented
3	#14272182	C₂	1	2	yes	maximal, complemented
4	#14272181	C₂	1	2	yes	maximal, complemented
5	#14272166	C₂	1	2	yes	maximal, complemented
6	#14272135	C₂	1	2	yes	maximal
7	C₄×#90800	C₂	1	2	yes	maximal, complemented
8	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×D₂₉	C₄	1	1	yes	characteristic
10	C₂²×C₄×D₂₉	C₄	1	1	yes	characteristic
11	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
12	C₂×#90800	C₂²	1	4	yes	—
13	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₄²×D₂₉	C₄	1	1	yes	characteristic
18	C₄²×D₂₉	C₄	1	1	yes	characteristic
19	C₄²×D₂₉	C₄	1	1	yes	characteristic
20	C₄²×D₂₉	C₄	1	1	yes	characteristic
21	C₄²×D₂₉	C₂²	1	1	yes	characteristic
22	C₄²×D₂₉	C₂²	1	1	yes	characteristic
23	C₄²×D₂₉	C₂²	1	1	yes	characteristic
24	C₄²×D₂₉	C₂²	1	1	yes	characteristic
25	#11745220	C₂²	1	4	yes	complemented
26	#11745219	C₂²	1	4	yes	—
27	#11745219	C₂²	1	4	yes	—
28	#11745218	C₂²	1	4	yes	complemented
29	C₄⋊#6599	C₂²	1	4	yes	complemented
30	C₄×#6599	C₂²	1	4	yes	complemented
31	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₂₉	C₂×C₄	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	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₂₉	—	2	4	no	—
39	C₂×C₄×D₂₉	—	2	4	no	—
40	C₂×C₄×D₂₉	—	2	4	no	—
41	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
52	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
53	#90800	—	2	8	no	—
54	C₂×#6599	C₂³	1	8	yes	—
55	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
56	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
57	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
58	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
68	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
69	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
70	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×D₂₉	—	2	2	no	—
73	C₂²×D₂₉	—	2	2	no	—
74	C₂²×D₂₉	—	2	2	no	—
75	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₂₉	—	2	2	no	—
78	C₂×C₄×C₂₉	—	2	2	no	—
79	C₂×C₄×C₂₉	—	2	2	no	—
80	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
86	C₂×Dic₂₉	—	2	2	no	—
87	C₂×Dic₂₉	—	2	2	no	—
88	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
91	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
92	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
93	C₂×Dic₂₉	#41	1	4	yes	—
94	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
95	C₄×D₂₉	—	2	2	no	—
96	C₄×D₂₉	—	2	2	no	—
97	C₄×D₂₉	—	2	2	no	—
98	C₄×D₂₉	—	2	2	no	—
99	C₄×D₂₉	—	2	2	no	—
100	C₄×D₂₉	—	2	2	no	—
101	C₄×D₂₉	—	2	2	no	—
102	C₄×D₂₉	—	2	2	no	—
103	C₄×D₂₉	—	2	2	no	—
104	C₄×D₂₉	—	2	2	no	—
105	C₄×D₂₉	M₁₆	1	4	yes	complemented
106	C₄×D₂₉	M₁₆	1	4	yes	complemented
107	#6599	—	2	8	no	—
108	#2920	—	29	1	no	maximal, Sylow
109	C₂²×C₂₉	—	2	1	no	—
110	C₂²×C₂₉	—	2	1	no	—
111	C₂²×C₂₉	#117	1	2	yes	—
112	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
113	C₂×D₂₉	—	2	8	no	—
114	C₂×D₂₉	—	2	1	no	—
115	C₂×D₂₉	—	2	1	no	—
116	C₂×D₂₉	—	2	1	no	—
117	C₂×D₂₉	—	2	1	no	—
118	C₂×D₂₉	C₂×M₁₆	1	2	yes	—
119	C₂×D₂₉	C₂×M₁₆	1	2	yes	—
120	C₄×C₂₉	—	2	1	no	—
121	C₄×C₂₉	—	2	1	no	—
122	C₄×C₂₉	—	2	1	no	—
123	C₄×C₂₉	—	2	1	no	—
124	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
125	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
126	Dic₂₉	—	2	1	no	—
127	Dic₂₉	—	2	1	no	—
128	Dic₂₉	#117	1	2	yes	—
129	Dic₂₉	C₂×M₁₆	1	2	yes	—
130	Dic₂₉	C₂×M₁₆	1	2	yes	—
131	Dic₂₉	C₂×#41	1	2	yes	—
132	C₂²×C₄²	—	29	1	no	—
133	#432	—	29	2	no	—
134	#432	—	29	2	no	—
135	#431	—	29	2	no	—
136	#431	—	29	2	no	—
137	#423	—	29	2	no	—
138	#407	—	29	2	no	—
139	C₄×M₁₆	—	29	2	no	—
140	C₂×C₂₉	—	2	2	no	—
141	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
142	C₂×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
143	C₂×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
144	D₂₉	—	2	2	no	—
145	D₂₉	—	2	2	no	—
146	C₂³×C₄	—	29	1	no	—
147	C₂³×C₄	—	29	1	no	—
148	C₂³×C₄	—	29	1	no	—
149	C₂×M₁₆	—	29	4	no	—
150	C₂×C₄²	—	29	1	no	—
151	C₂×C₄²	—	29	1	no	—
152	C₂×C₄²	—	29	1	no	—
153	C₂×C₄²	—	29	1	no	—
154	C₂×C₄²	—	29	1	no	—
155	C₂×C₄²	—	29	1	no	—
156	C₂×C₄²	—	29	1	no	—
157	C₂×C₄²	—	29	1	no	—
158	C₂×C₄²	—	29	1	no	—
159	C₂×C₄²	—	29	1	no	—
160	C₂×C₄²	—	29	1	no	—
161	C₂×C₄²	#1181	1	1	yes	characteristic
162	C₄⋊C₈	—	29	4	no	—
163	C₄⋊C₈	—	29	4	no	—
164	C₂²⋊C₈	—	29	4	no	—
165	C₂²⋊C₈	—	29	4	no	—
166	#97	—	29	4	no	—
167	C₄×C₈	—	29	4	no	—
168	C₂₉	#2920	1	1	yes	characteristic, complemented, Sylow
169	C₂⁴	—	29	1	no	—
170	C₂²×C₄	—	29	1	no	—
171	C₂²×C₄	—	29	1	no	—
172	C₂²×C₄	—	29	1	no	—
173	C₂²×C₄	—	29	1	no	—
174	C₂²×C₄	—	29	1	no	—
175	C₂²×C₄	—	29	1	no	—
176	C₂²×C₄	—	29	1	no	—
177	C₂²×C₄	—	29	1	no	—
178	C₂²×C₄	—	29	1	no	—
179	C₂²×C₄	—	29	1	no	—
180	C₂²×C₄	—	29	1	no	—
181	C₂²×C₄	—	29	1	no	—
182	C₂²×C₄	—	29	1	no	—
183	C₂²×C₄	—	29	1	no	—
184	C₂²×C₄	—	29	1	no	—
185	C₂²×C₄	—	58	4	no	—
186	C₂²×C₄	—	58	4	no	—
187	C₂²×C₄	—	58	4	no	—
188	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
189	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
190	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
191	M₁₆	—	58	8	no	—
192	C₂×C₈	—	29	8	no	—
193	C₄²	—	29	1	no	—
194	C₄²	—	29	1	no	—
195	C₄²	—	29	1	no	—
196	C₄²	—	29	1	no	—
197	C₄²	—	29	1	no	—
198	C₄²	—	29	1	no	—
199	C₄²	—	29	1	no	—
200	C₄²	—	29	1	no	—
201	C₄²	—	29	1	no	—
202	C₄²	—	29	1	no	—
203	C₄²	—	29	1	no	—
204	C₄²	—	29	1	no	—
205	C₄²	C₂×#1181	1	1	yes	characteristic
206	C₄²	C₂×#1181	1	1	yes	characteristic
207	C₄²	C₂×#1181	1	1	yes	characteristic
208	C₄²	C₂×#1181	1	1	yes	characteristic
209	C₂³	—	29	1	no	—
210	C₂³	—	29	1	no	—
211	C₂³	—	58	2	no	—
212	C₂³	—	58	2	no	—
213	C₂³	—	58	2	no	—
214	C₂³	C₂²×#1181	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	29	4	no	—
219	C₂×C₄	—	29	1	no	—
220	C₂×C₄	—	29	1	no	—
221	C₂×C₄	—	29	1	no	—
222	C₂×C₄	—	29	1	no	—
223	C₂×C₄	—	29	4	no	—
224	C₂×C₄	—	29	4	no	—
225	C₂×C₄	—	29	1	no	—
226	C₂×C₄	—	29	1	no	—
227	C₂×C₄	—	58	2	no	—
228	C₂×C₄	—	58	2	no	—
229	C₂×C₄	—	58	2	no	—
230	C₂×C₄	—	58	2	no	—
231	C₂×C₄	—	58	2	no	—
232	C₂×C₄	—	58	2	no	—
233	C₂×C₄	—	58	2	no	—
234	C₂×C₄	—	58	2	no	—
235	C₂×C₄	—	58	2	no	—
236	C₂×C₄	—	58	2	no	—
237	C₂×C₄	—	58	2	no	—
238	C₂×C₄	—	58	2	no	—
239	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
240	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
241	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
242	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
243	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
244	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
245	C₈	—	58	8	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	29	2	no	—
249	C₂²	—	29	2	no	—
250	C₂²	—	58	8	no	—
251	C₂²	—	58	1	no	—
252	C₂²	—	58	1	no	—
253	C₂²	—	58	1	no	—
254	C₂²	—	58	1	no	—
255	C₂²	#11745345	1	2	yes	—
256	C₂²	C₂³×#1181	1	1	yes	characteristic
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	29	2	no	—
262	C₄	—	29	2	no	—
263	C₄	—	29	2	no	—
264	C₄	—	29	2	no	—
265	C₄	—	58	1	no	—
266	C₄	—	58	1	no	—
267	C₄	D₂₉⋊M₁₆	1	2	yes	—
268	C₄	D₂₉⋊M₁₆	1	2	yes	—
269	C₂	—	2	2	no	—
270	C₂	—	58	2	no	—
271	C₂	—	58	2	no	—
272	C₂	C₂×#11745345	1	1	yes	characteristic
273	C₂	C₂×D₂₉⋊M₁₆	1	1	yes	characteristic
274	C₂	C₂×D₂₉⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Frattini	C₂²	C₂³×#1181
Fitting	C₂×C₄²×C₂₉	C₄
prime radical	C₂³×D₂₉	C₂×C₄
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	#2920
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #14272186	C₂	semidirect
2. #14272185	C₂	semidirect
3. #14272182	C₂	semidirect
4. #14272181	C₂	semidirect
5. #14272166	C₂	semidirect
7. C₄×#90800	C₂	semidirect
25. #11745220	C₂²	semidirect
28. #11745218	C₂²	semidirect
29. C₄⋊#6599	C₂²	semidirect
30. C₄×#6599	C₂²	semidirect
105. C₄×D₂₉	M₁₆	semidirect
106. C₄×D₂₉	M₁₆	semidirect
168. C₂₉	#2920	semidirect

Maximal subgroups

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

subgroup	index
#14272186	2
#14272185	2
#14272182	2
#14272181	2
#14272166	2
#14272135	2
C₄×#90800	2
C₂×C₄²×D₂₉	2
#2920	29