Subgroups — #16827878

Order 3712.

400 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271062	C₂	1	1	yes	maximal, characteristic
2	#14271061	C₂	1	1	yes	maximal, characteristic
3	#14271059	C₂	1	1	yes	maximal, characteristic
4	#14271049	C₂	1	2	yes	maximal
5	#14271048	C₂	1	2	yes	maximal
6	#14271045	C₂	1	2	yes	maximal
7	#14271044	C₂	1	2	yes	maximal
8	#14271028	C₂	1	1	yes	maximal, characteristic
9	#14271028	C₂	1	1	yes	maximal, characteristic
10	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#389	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
19	C₂×#90779	C₂²	1	2	yes	—
20	C₂×#90779	C₂²	1	2	yes	—
21	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#95	C₂²	1	2	yes	—
28	#11745179	C₂²	1	2	yes	—
29	#11745179	C₂²	1	2	yes	—
30	#11745179	C₂²	1	2	yes	—
31	#11745179	C₂²	1	2	yes	—
32	#11745179	C₂²	1	2	yes	—
33	#11745179	C₂²	1	2	yes	—
34	#11745179	C₂²	1	2	yes	—
35	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₂₉	C₂³	1	2	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	1	yes	characteristic
43	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
44	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
45	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
46	C₄⋊C₄×C₂₉	—	2	2	no	—
47	C₄⋊C₄×C₂₉	—	2	4	no	—
48	C₄⋊C₄×C₂₉	—	2	2	no	—
49	C₄²×C₂₉	—	2	2	no	—
50	C₄⋊Dic₂₉	—	2	2	no	—
51	C₄⋊Dic₂₉	—	2	2	no	—
52	C₄⋊Dic₂₉	—	2	4	no	—
53	#90779	—	2	4	no	—
54	#90779	—	2	4	no	—
55	C₄×Dic₂₉	—	2	2	no	—
56	C₄×Dic₂₉	—	2	2	no	—
57	C₄×Dic₂₉	—	2	2	no	—
58	C₄×Dic₂₉	—	2	2	no	—
59	C₄×Dic₂₉	—	2	2	no	—
60	C₄×Dic₂₉	Q₈	1	4	yes	—
61	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
62	C₂×C₄×C₂₉	—	2	1	no	—
63	C₂×C₄×C₂₉	—	2	1	no	—
64	C₂×C₄×C₂₉	—	2	1	no	—
65	C₂×C₄×C₂₉	—	2	1	no	—
66	C₂×C₄×C₂₉	—	2	2	no	—
67	C₂×C₄×C₂₉	—	2	2	no	—
68	C₂×C₄×C₂₉	—	2	2	no	—
69	C₂×C₄×C₂₉	—	2	2	no	—
70	C₂×C₄×C₂₉	—	2	2	no	—
71	C₂×C₄×C₂₉	—	2	2	no	—
72	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
73	C₂×C₄×C₂₉	#41	1	2	yes	—
74	C₂×C₄×C₂₉	#41	1	2	yes	—
75	C₂×C₄×C₂₉	#41	1	2	yes	—
76	C₂×C₄×C₂₉	#41	1	2	yes	—
77	C₂×Dic₂₉	—	2	1	no	—
78	C₂×Dic₂₉	—	2	1	no	—
79	C₂×Dic₂₉	—	2	1	no	—
80	C₂×Dic₂₉	—	2	1	no	—
81	C₂×Dic₂₉	—	2	1	no	—
82	C₂×Dic₂₉	—	2	1	no	—
83	C₂×Dic₂₉	—	2	1	no	—
84	C₂×Dic₂₉	—	2	1	no	—
85	C₂×Dic₂₉	—	2	2	no	—
86	C₂×Dic₂₉	—	2	2	no	—
87	C₂×Dic₂₉	—	2	2	no	—
88	C₂×Dic₂₉	—	2	2	no	—
89	C₂×Dic₂₉	—	2	2	no	—
90	C₂×Dic₂₉	—	2	2	no	—
91	C₂×Dic₂₉	C₂×Q₈	1	2	yes	—
92	C₂×Dic₂₉	C₂×Q₈	1	2	yes	—
93	C₂×Dic₂₉	#41	1	2	yes	—
94	C₂×Dic₂₉	#41	1	2	yes	—
95	#2864	—	29	1	no	maximal, Sylow
96	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
97	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
98	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
99	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
100	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
101	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
102	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
103	C₄×C₂₉	—	2	2	no	—
104	C₄×C₂₉	—	2	2	no	—
105	C₄×C₂₉	—	4	2	no	—
106	C₄×C₂₉	—	4	2	no	—
107	C₄×C₂₉	#125	1	4	yes	—
108	Dic₂₉	—	2	2	no	—
109	Dic₂₉	—	2	2	no	—
110	Dic₂₉	—	2	2	no	—
111	Dic₂₉	—	2	2	no	—
112	Dic₂₉	—	4	2	no	—
113	Dic₂₉	—	4	2	no	—
114	#389	—	29	1	no	—
115	#389	—	29	1	no	—
116	#389	—	29	1	no	—
117	#389	D₂₉	1	1	yes	characteristic
118	#387	—	29	2	no	—
119	#387	—	29	2	no	—
120	#387	—	29	2	no	—
121	#387	—	29	2	no	—
122	#382	—	29	1	no	—
123	#382	—	29	1	no	—
124	C₄³	—	29	1	no	—
125	C₂×C₂₉	C₂×#125	1	1	yes	characteristic
126	C₂×C₂₉	#529	1	1	yes	characteristic
127	C₂×C₂₉	#529	1	1	yes	characteristic
128	C₂×C₂₉	#529	1	1	yes	characteristic
129	C₂×C₂₉	#529	1	1	yes	characteristic
130	C₂×C₂₉	#533	1	1	yes	characteristic
131	C₂×C₂₉	#533	1	1	yes	characteristic
132	C₂×C₄⋊C₄	—	29	2	no	—
133	C₂×C₄⋊C₄	—	29	2	no	—
134	C₂×C₄⋊C₄	—	29	1	no	—
135	C₂×C₄⋊C₄	—	29	1	no	—
136	C₂×C₄⋊C₄	—	29	2	no	—
137	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
138	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
139	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
140	C₂×C₄²	—	29	1	no	—
141	C₂×C₄²	—	29	1	no	—
142	C₂×C₄²	—	29	1	no	—
143	C₂×C₄²	—	29	1	no	—
144	C₂×C₄²	—	29	1	no	—
145	C₂×C₄²	—	29	1	no	—
146	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
147	#95	—	29	2	no	—
148	#95	—	29	2	no	—
149	#95	—	29	2	no	—
150	#95	—	29	2	no	—
151	#95	—	29	2	no	—
152	#95	—	29	2	no	—
153	#95	—	29	2	no	—
154	#95	C₂×D₂₉	1	2	yes	—
155	C₂₉	#2864	1	1	yes	characteristic, complemented, Sylow
156	C₂²×C₄	—	29	1	no	—
157	C₂²×C₄	—	29	1	no	—
158	C₂²×C₄	—	29	1	no	—
159	C₂²×C₄	—	29	1	no	—
160	C₂²×C₄	—	29	2	no	—
161	C₂²×C₄	—	29	2	no	—
162	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
163	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
164	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
166	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	4	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	58	4	no	—
171	C₄⋊C₄	—	58	4	no	—
172	C₄⋊C₄	—	58	2	no	—
173	C₄⋊C₄	—	58	2	no	—
174	C₄⋊C₄	—	58	4	no	—
175	C₄²	—	2	2	no	—
176	C₄²	—	29	4	no	—
177	C₄²	—	58	2	no	—
178	C₄²	—	58	2	no	—
179	C₄²	—	58	2	no	—
180	C₄²	—	58	2	no	—
181	C₄²	—	58	2	no	—
182	C₂³	C₂³×D₂₉	1	1	yes	characteristic
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	29	2	no	—
194	C₂×C₄	—	29	2	no	—
195	C₂×C₄	—	29	2	no	—
196	C₂×C₄	—	29	2	no	—
197	C₂×C₄	—	58	1	no	—
198	C₂×C₄	—	58	1	no	—
199	C₂×C₄	—	58	1	no	—
200	C₂×C₄	—	58	1	no	—
201	C₂×C₄	—	58	1	no	—
202	C₂×C₄	—	58	1	no	—
203	C₂×C₄	—	58	1	no	—
204	C₂×C₄	—	58	1	no	—
205	C₂×C₄	—	58	2	no	—
206	C₂×C₄	—	58	2	no	—
207	C₂×C₄	—	58	2	no	—
208	C₂×C₄	—	58	2	no	—
209	C₂×C₄	—	58	2	no	—
210	C₂×C₄	—	58	2	no	—
211	C₂×C₄	#90805	1	2	yes	—
212	C₂×C₄	#90807	1	2	yes	—
213	C₂×C₄	#90807	1	2	yes	—
214	C₂×C₄	Q₈×D₂₉	1	2	yes	—
215	C₂×C₄	#90809	1	2	yes	—
216	C₂²	C₂×#90805	1	1	yes	characteristic
217	C₂²	C₂×#90807	1	1	yes	characteristic
218	C₂²	C₂×#90807	1	1	yes	characteristic
219	C₂²	C₂×Q₈×D₂₉	1	1	yes	characteristic
220	C₂²	C₂×#90809	1	1	yes	characteristic
221	C₂²	#41×D₂₉	1	1	yes	characteristic
222	C₂²	#41×D₂₉	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	2	no	—
226	C₄	—	4	2	no	—
227	C₄	—	58	2	no	—
228	C₄	—	58	2	no	—
229	C₄	—	58	2	no	—
230	C₄	—	58	2	no	—
231	C₄	—	116	2	no	—
232	C₄	—	116	2	no	—
233	C₄	#11745251	1	4	yes	—
234	C₂	C₂×#11745251	1	1	yes	characteristic
235	C₂	#14271694	1	1	yes	characteristic
236	C₂	#14271695	1	1	yes	characteristic
237	C₂	#14271699	1	1	yes	characteristic
238	C₂	#14271700	1	1	yes	characteristic
239	C₂	#14271718	1	1	yes	characteristic
240	C₂	#14271719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂₉×#389	C₂
hypercenter	#389	D₂₉
hypocenter	C₂₉	#2864
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
155. C₂₉	#2864	semidirect

Maximal subgroups

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

subgroup	index
#14271062	2
#14271061	2
#14271059	2
#14271049	2
#14271048	2
#14271045	2
#14271044	2
#14271028	2
C₄²×Dic₂₉	2
C₂₉×#389	2
#2864	29