Subgroups — #16828156

Order 3712.

392 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271631	C₂	1	1	yes	maximal, characteristic
2	#14271225	C₂	1	2	yes	maximal, complemented
3	#14271222	C₂	1	2	yes	maximal, complemented
4	#14271218	C₂	1	2	yes	maximal, complemented
5	#14271214	C₂	1	2	yes	maximal, complemented
6	#14271186	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11745162	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271131	C₂	1	1	yes	maximal, characteristic
9	#14271129	C₂	1	1	yes	maximal, characteristic
10	#14271119	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#90805	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂×#90777	C₂²	1	1	yes	characteristic
18	C₂²×#6597	C₂²	1	1	yes	characteristic
19	#11745255	C₄	1	1	yes	characteristic
20	#11745255	C₄	1	1	yes	characteristic
21	#11745249	C₄	1	1	yes	characteristic
22	#11745249	C₄	1	1	yes	characteristic
23	#11745243	C₄	1	2	yes	—
24	#11745243	C₄	1	2	yes	—
25	#11745234	C₂²	1	2	yes	—
26	C₄²×D₂₉	C₂²	1	2	yes	—
27	C₂₉×#97	C₂²	1	2	yes	—
28	C₄×C₈×C₂₉	C₂²	1	2	yes	—
29	#11745168	C₂²	1	2	yes	—
30	#11745168	C₂²	1	2	yes	—
31	#11745168	C₂²	1	2	yes	—
32	#11745168	C₂²	1	2	yes	—
33	#11745162	C₂²	1	1	yes	characteristic
34	#11745162	C₂²	1	1	yes	characteristic
35	#11745162	C₂²	1	1	yes	characteristic
36	#11745162	C₂²	1	1	yes	characteristic
37	#11745162	C₂²	1	2	yes	—
38	#11745162	C₂²	1	2	yes	—
39	#11745151	C₂²	1	2	yes	—
40	C₄×#6597	C₂²	1	2	yes	—
41	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
42	C₂×C₂²⋊D₂₉	C₂×C₄	1	2	yes	—
43	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
45	#90805	—	2	2	no	—
46	#90805	—	2	2	no	—
47	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
49	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
50	C₂×C₄×D₂₉	C₂³	1	2	yes	—
51	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
52	M₁₆×C₂₉	—	2	2	no	—
53	C₂×C₈×C₂₉	—	2	2	no	—
54	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
55	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₂₉	C₂³	1	2	yes	—
57	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
58	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
59	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
60	C₄²×C₂₉	C₂³	1	2	yes	—
61	#90781	C₂×C₄	1	2	yes	—
62	#90781	C₂×C₄	1	2	yes	—
63	#90779	C₂×C₄	1	2	yes	—
64	#90779	C₂×C₄	1	2	yes	—
65	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
68	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
69	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
70	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
71	#90777	—	2	2	no	—
72	C₂×#6597	—	2	2	no	—
73	C₂×#6597	C₂³	1	1	yes	characteristic
74	C₂×#6597	C₂³	1	1	yes	characteristic
75	C₂×#6597	C₂³	1	2	yes	—
76	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
79	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
80	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	#41	1	2	yes	—
82	C₂×C₄×C₂₉	#41	1	2	yes	—
83	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
84	C₂²⋊D₂₉	—	2	4	no	—
85	C₂×Dic₂₉	—	2	2	no	—
86	C₂×Dic₂₉	—	4	1	no	—
87	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
88	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
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	D₁₁₆	—	2	2	no	—
93	C₄×D₂₉	—	2	2	no	—
94	C₄×D₂₉	—	2	2	no	—
95	C₄×D₂₉	—	2	4	no	—
96	C₄×D₂₉	—	4	2	no	—
97	Dic₅₈	—	2	2	no	—
98	C₈×C₂₉	—	2	1	no	—
99	C₈×C₂₉	—	2	1	no	—
100	C₈×C₂₉	—	2	2	no	—
101	#6597	—	2	1	no	—
102	#6597	—	2	1	no	—
103	#6597	—	2	2	no	—
104	#2925	—	29	1	no	maximal, Sylow
105	C₂²×C₂₉	—	2	1	no	—
106	C₂²×C₂₉	—	2	1	no	—
107	C₂²×C₂₉	#117	1	2	yes	—
108	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
109	C₂×D₂₉	—	2	2	no	—
110	C₂×D₂₉	—	2	2	no	—
111	C₂×D₂₉	—	2	2	no	—
112	C₄×C₂₉	—	2	2	no	—
113	C₄×C₂₉	—	2	2	no	—
114	C₄×C₂₉	#117	1	2	yes	—
115	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
116	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
117	Dic₂₉	—	2	2	no	—
118	Dic₂₉	—	2	1	no	—
119	Dic₂₉	—	2	1	no	—
120	Dic₂₉	—	2	1	no	—
121	Dic₂₉	#131	1	2	yes	—
122	C₄×#41	—	29	1	no	—
123	#433	—	29	2	no	—
124	#433	—	29	2	no	—
125	#432	—	29	2	no	—
126	#431	—	29	2	no	—
127	#423	—	29	1	no	—
128	C₂×C₄⋊C₈	—	29	1	no	—
129	#408	—	29	1	no	—
130	#408	—	29	1	no	—
131	#405	—	29	1	no	—
132	#405	D₂₉	1	1	yes	characteristic, complemented
133	C₂×C₂₉	—	2	2	no	—
134	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
135	C₂×C₂₉	C₂×#131	1	1	yes	characteristic
136	C₂×C₂₉	#568	1	1	yes	characteristic
137	D₂₉	—	4	2	no	—
138	C₂×#41	—	29	1	no	—
139	C₂×M₁₆	—	29	1	no	—
140	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
141	C₂²×C₈	—	29	1	no	—
142	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
143	C₄×Q₈	—	29	1	no	—
144	C₄×Q₈	—	29	1	no	—
145	C₄×D₄	—	29	1	no	—
146	C₄×D₄	—	29	1	no	—
147	C₄×D₄	—	29	2	no	—
148	C₄×D₄	—	29	2	no	—
149	#117	—	29	2	no	—
150	#117	C₂×D₂₉	1	1	yes	characteristic
151	C₂×C₄²	—	29	1	no	—
152	C₂×C₄²	—	29	2	no	—
153	C₄⋊C₈	—	29	1	no	—
154	C₄⋊C₈	—	29	1	no	—
155	C₄⋊C₈	—	29	1	no	—
156	C₄⋊C₈	—	29	1	no	—
157	C₄⋊C₈	—	29	2	no	—
158	C₄⋊C₈	—	29	2	no	—
159	C₂²⋊C₈	—	29	2	no	—
160	C₂²⋊C₈	—	29	2	no	—
161	C₂²⋊C₈	—	29	2	no	—
162	C₂²⋊C₈	—	29	2	no	—
163	#97	—	29	2	no	—
164	#97	C₂×D₂₉	1	2	yes	—
165	C₄×C₈	—	29	2	no	—
166	C₄×C₈	C₂×D₂₉	1	2	yes	—
167	C₂₉	#2925	1	1	yes	characteristic, complemented, Sylow
168	#41	—	58	2	no	—
169	#41	—	58	2	no	—
170	C₂×Q₈	—	29	1	no	—
171	C₂×D₄	—	29	2	no	—
172	C₂×D₄	—	29	1	no	—
173	C₂²×C₄	—	29	1	no	—
174	C₂²×C₄	—	29	1	no	—
175	C₂²×C₄	—	29	2	no	—
176	C₂²×C₄	—	29	2	no	—
177	C₂²×C₄	—	29	2	no	—
178	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
179	M₁₆	—	2	2	no	—
180	M₁₆	—	58	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	29	1	no	—
183	C₂×C₈	—	29	2	no	—
184	C₂×C₈	—	29	1	no	—
185	C₂×C₈	—	58	2	no	—
186	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
187	C₂×C₈	C₂²×D₂₉	1	2	yes	—
188	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
189	C₄⋊C₄	—	29	2	no	—
190	C₄⋊C₄	—	29	2	no	—
191	C₄⋊C₄	C₄×D₂₉	1	1	yes	characteristic
192	C₄⋊C₄	C₄×D₂₉	1	1	yes	characteristic
193	C₂²⋊C₄	—	29	2	no	—
194	C₂²⋊C₄	—	29	2	no	—
195	C₂²⋊C₄	C₄×D₂₉	1	2	yes	—
196	C₄²	—	29	1	no	—
197	C₄²	—	29	2	no	—
198	C₄²	—	29	1	no	—
199	C₄²	—	29	2	no	—
200	C₄²	—	29	1	no	—
201	C₄²	—	29	1	no	—
202	C₄²	C₂²×D₂₉	1	2	yes	—
203	C₂³	—	29	2	no	—
204	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
205	Q₈	—	58	2	no	—
206	D₄	—	58	4	no	—
207	D₄	—	58	2	no	—
208	C₂×C₄	—	29	1	no	—
209	C₂×C₄	—	29	1	no	—
210	C₂×C₄	—	29	1	no	—
211	C₂×C₄	—	29	1	no	—
212	C₂×C₄	—	29	2	no	—
213	C₂×C₄	—	58	4	no	—
214	C₂×C₄	—	58	2	no	—
215	C₂×C₄	—	58	2	no	—
216	C₂×C₄	—	58	2	no	—
217	C₂×C₄	—	116	2	no	—
218	C₂×C₄	—	116	1	no	—
219	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
220	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
221	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
222	C₂×C₄	#90805	1	2	yes	—
223	C₂×C₄	#90805	1	2	yes	—
224	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	2	2	no	—
228	C₈	—	58	1	no	—
229	C₈	—	58	1	no	—
230	C₈	—	58	2	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	58	2	no	—
234	C₂²	—	58	2	no	—
235	C₂²	—	58	2	no	—
236	C₂²	#11745234	1	2	yes	—
237	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	2	2	no	—
240	C₄	—	29	2	no	—
241	C₄	—	58	2	no	—
242	C₄	—	58	1	no	—
243	C₄	—	58	1	no	—
244	C₄	—	58	1	no	—
245	C₄	#11745234	1	2	yes	—
246	C₄	C₂×#90805	1	1	yes	characteristic
247	C₄	C₂×#90805	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	116	2	no	—
250	C₂	C₂×#11745234	1	1	yes	characteristic
251	C₂	#131×D₂₉	1	1	yes	characteristic
252	C₂	#14271928	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#405	C₂
prime radical	C₂×#90805	C₂²
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	#405	D₂₉
hypocenter	C₂₉	#2925
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #14271225	C₂	semidirect
3. #14271222	C₂	semidirect
4. #14271218	C₂	semidirect
5. #14271214	C₂	semidirect
6. #14271186	C₂	semidirect
7. C₂×#11745162	C₂	semidirect
10. #14271119	C₂	semidirect
11. C₂₉×#405	C₂	semidirect
132. #405	D₂₉	semidirect
167. C₂₉	#2925	semidirect

Maximal subgroups

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

subgroup	index
#14271631	2
#14271225	2
#14271222	2
#14271218	2
#14271214	2
#14271186	2
C₂×#11745162	2
#14271131	2
#14271129	2
#14271119	2
C₂₉×#405	2
#2925	29