Subgroups — C₂²×D₁₃⋊M₃₂ #16809613

Order 3328.

2334 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88098	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₃⋊M₃₂	C₂	1	24	yes	maximal, direct product factor
3	C₂²×#88106	C₂	1	2	yes	maximal, complemented
4	C₂²×D₁₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂³×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×D₁₃	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
8	C₂³×#1055	C₂²	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₄	1	12	yes	—
10	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
12	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	12	yes	—
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×#88106	C₂²	1	24	yes	complemented
16	C₂²×#6092	C₂²	1	4	yes	complemented
17	D₁₃⋊M₃₂	C₂²	1	64	yes	direct product factor
18	C₂×#88098	C₂²	1	24	yes	complemented
19	C₂×D₁₃⋊C₁₆	C₂²	1	24	yes	complemented
20	C₂⁴×D₁₃	C₈	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×Dic₁₃	C₈	1	1	yes	characteristic
23	C₂²×C₄×D₁₃	C₈	1	1	yes	characteristic
24	C₂²×C₄×D₁₃	C₈	1	12	yes	—
25	C₂²×C₄×D₁₃	C₈	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂×C₄	1	12	yes	—
27	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂×C₄	1	12	yes	—
30	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂×C₄	1	6	yes	—
33	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
34	C₂²×#1055	C₂³	1	1	yes	characteristic
35	C₂²×#1055	C₂³	1	6	yes	—
36	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	48	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	12	yes	—
39	C₂×C₈×D₁₃	C₂×C₄	1	12	yes	—
40	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
41	C₂×C₈×D₁₃	C₂³	1	6	yes	—
42	C₂×C₈×D₁₃	C₂³	1	6	yes	—
43	C₂×C₈×D₁₃	C₂³	1	16	yes	—
44	#88106	C₂³	1	32	yes	complemented
45	C₂×#6092	C₂³	1	24	yes	complemented
46	#88098	C₂³	1	32	yes	complemented
47	D₁₃⋊C₁₆	C₂³	1	32	yes	complemented
48	C₂³×M₃₂	—	13	1	no	maximal, Sylow
49	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
50	C₂³×D₁₃	—	2	8	no	—
51	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
52	C₂³×D₁₃	C₂×C₈	1	12	yes	—
53	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
55	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	C₂×C₈	1	12	yes	—
59	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
60	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
61	C₂×C₄×D₁₃	C₂×C₈	1	12	yes	—
62	C₂×C₄×D₁₃	C₂×C₈	1	6	yes	—
63	C₂×C₄×D₁₃	C₂×C₈	1	48	yes	—
64	C₂×C₄×D₁₃	C₂×C₈	1	6	yes	—
65	C₂×C₄×D₁₃	C₂×C₈	1	12	yes	—
66	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
67	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	—
68	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	16	yes	—
71	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
72	C₂×#1055	C₂²×C₄	1	3	yes	—
73	C₂×#1055	C₂²×C₄	1	12	yes	—
74	C₂×#1055	C₂²×C₄	1	6	yes	—
75	C₂×#1055	C₂⁴	1	3	yes	—
76	C₂×#1055	C₂⁴	1	4	yes	—
77	C₈×D₁₃	C₂²×C₄	1	12	yes	—
78	C₈×D₁₃	C₂²×C₄	1	12	yes	—
79	C₈×D₁₃	C₂²×C₄	1	16	yes	—
80	C₈×D₁₃	C₂²×C₄	1	16	yes	—
81	C₈×D₁₃	C₂⁴	1	4	yes	—
82	C₈×D₁₃	C₂⁴	1	4	yes	—
83	#6092	C₂⁴	1	16	yes	complemented
84	C₂⁴×C₈	—	13	1	no	—
85	C₂²×M₃₂	—	13	2	no	—
86	C₂²×M₃₂	—	13	24	no	—
87	C₂²×M₃₂	—	13	2	no	—
88	C₂³×C₁₆	—	13	2	no	—
89	C₂³×C₁₃	—	2	4	no	—
90	C₂³×C₁₃	C₂²×C₈	1	6	yes	—
91	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
92	C₂²×D₁₃	—	2	4	no	—
93	C₂²×D₁₃	—	2	48	no	—
94	C₂²×D₁₃	M₃₂	1	8	yes	complemented
95	C₂²×D₁₃	C₂²×C₈	1	6	yes	—
96	C₂²×D₁₃	C₂²×C₈	1	16	yes	—
97	C₂²×D₁₃	C₂²×C₈	1	6	yes	—
98	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
99	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
100	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
101	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
102	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
103	C₂×Dic₁₃	C₂²×C₈	1	16	yes	—
104	C₂×Dic₁₃	C₂²×C₈	1	6	yes	—
105	C₂×Dic₁₃	C₂²×C₈	1	6	yes	—
106	C₄×D₁₃	C₂²×C₈	1	12	yes	—
107	C₄×D₁₃	C₂²×C₈	1	16	yes	—
108	C₄×D₁₃	C₂²×C₈	1	12	yes	—
109	C₄×D₁₃	C₂²×C₈	1	16	yes	—
110	C₄×D₁₃	C₂³×C₄	1	4	yes	—
111	C₄×D₁₃	C₂³×C₄	1	4	yes	—
112	C₈×C₁₃	C₂³×C₄	1	4	yes	—
113	C₈×C₁₃	C₂³×C₄	1	4	yes	—
114	#1055	C₂³×C₄	1	3	yes	—
115	#1055	C₂³×C₄	1	4	yes	—
116	#1055	C₂⁵	1	1	yes	characteristic
117	C₂⁴×C₄	—	13	1	no	—
118	C₂³×C₈	—	13	1	no	—
119	C₂³×C₈	—	13	12	no	—
120	C₂³×C₈	—	13	1	no	—
121	C₂³×C₈	—	13	1	no	—
122	C₂³×C₈	—	13	12	no	—
123	C₂³×C₈	—	13	1	no	—
124	C₂³×C₈	—	13	1	no	—
125	C₂³×C₈	#261	1	1	yes	characteristic
126	C₂×M₃₂	—	13	24	no	—
127	C₂×M₃₂	—	13	64	no	—
128	C₂×M₃₂	—	13	24	no	—
129	C₂²×C₁₆	—	13	24	no	—
130	C₂²×C₁₆	—	13	4	no	—
131	C₂²×C₁₃	—	2	12	no	—
132	C₂²×C₁₃	C₂×M₃₂	1	4	yes	complemented
133	C₂²×C₁₃	C₂³×C₈	1	4	yes	—
134	C₂²×C₁₃	C₂³×C₈	1	3	yes	—
135	C₂×D₁₃	—	2	12	no	—
136	C₂×D₁₃	—	2	32	no	—
137	C₂×D₁₃	C₂×M₃₂	1	24	yes	complemented
138	C₂×D₁₃	C₂³×C₈	1	4	yes	—
139	C₂×D₁₃	C₂³×C₈	1	4	yes	—
140	C₄×C₁₃	C₂³×C₈	1	3	yes	—
141	C₄×C₁₃	C₂³×C₈	1	4	yes	—
142	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
143	Dic₁₃	C₂³×C₈	1	4	yes	—
144	Dic₁₃	C₂³×C₈	1	4	yes	—
145	C₂⁵	—	13	1	no	—
146	C₂³×C₄	—	13	1	no	—
147	C₂³×C₄	—	13	1	no	—
148	C₂³×C₄	—	13	12	no	—
149	C₂³×C₄	—	13	1	no	—
150	C₂³×C₄	—	13	12	no	—
151	C₂³×C₄	—	13	1	no	—
152	C₂³×C₄	—	13	1	no	—
153	C₂³×C₄	C₂×#261	1	1	yes	characteristic
154	C₂²×C₈	—	13	6	no	—
155	C₂²×C₈	—	13	1	no	—
156	C₂²×C₈	—	13	1	no	—
157	C₂²×C₈	—	13	6	no	—
158	C₂²×C₈	—	13	6	no	—
159	C₂²×C₈	—	13	48	no	—
160	C₂²×C₈	—	13	12	no	—
161	C₂²×C₈	—	13	6	no	—
162	C₂²×C₈	—	13	12	no	—
163	C₂²×C₈	—	13	6	no	—
164	C₂²×C₈	—	13	6	no	—
165	C₂²×C₈	—	13	16	no	—
166	C₂²×C₈	C₂×#261	1	1	yes	characteristic
167	C₂²×C₈	C₂×#261	1	12	yes	—
168	C₂²×C₈	C₂×#261	1	1	yes	characteristic
169	M₃₂	—	13	32	no	—
170	M₃₂	—	13	32	no	—
171	C₂×C₁₆	—	13	32	no	—
172	C₂×C₁₆	—	13	24	no	—
173	C₂×C₁₃	—	2	4	no	—
174	C₂×C₁₃	C₂²×M₃₂	1	6	yes	complemented
175	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
176	D₁₃	—	2	4	no	—
177	D₁₃	C₂²×M₃₂	1	8	yes	complemented
178	C₂⁴	—	13	1	no	—
179	C₂⁴	—	13	12	no	—
180	C₂⁴	—	13	1	no	—
181	C₂⁴	—	26	8	no	—
182	C₂⁴	D₁₃⋊C₈	1	1	yes	characteristic
183	C₂²×C₄	—	13	12	no	—
184	C₂²×C₄	—	13	1	no	—
185	C₂²×C₄	—	13	1	no	—
186	C₂²×C₄	—	13	12	no	—
187	C₂²×C₄	—	13	6	no	—
188	C₂²×C₄	—	13	48	no	—
189	C₂²×C₄	—	13	12	no	—
190	C₂²×C₄	—	13	6	no	—
191	C₂²×C₄	—	13	6	no	—
192	C₂²×C₄	—	13	16	no	—
193	C₂²×C₄	—	13	6	no	—
194	C₂²×C₄	D₁₃⋊C₈	1	6	yes	—
195	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
196	C₂²×C₄	C₂²×#261	1	6	yes	—
197	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
198	C₂×C₈	—	13	3	no	—
199	C₂×C₈	—	13	4	no	—
200	C₂×C₈	—	13	3	no	—
201	C₂×C₈	—	13	12	no	—
202	C₂×C₈	—	13	6	no	—
203	C₂×C₈	—	13	4	no	—
204	C₂×C₈	—	13	4	no	—
205	C₂×C₈	—	13	12	no	—
206	C₂×C₈	—	13	12	no	—
207	C₂×C₈	—	13	16	no	—
208	C₂×C₈	—	13	16	no	—
209	C₂×C₈	C₂²×#261	1	16	yes	—
210	C₂×C₈	C₂²×#261	1	6	yes	—
211	C₂×C₈	C₂²×#261	1	6	yes	—
212	C₁₆	—	13	16	no	—
213	C₁₃	C₂³×M₃₂	1	1	yes	characteristic, complemented, Sylow
214	C₂³	—	2	4	no	—
215	C₂³	—	13	8	no	—
216	C₂³	—	13	6	no	—
217	C₂³	—	13	16	no	—
218	C₂³	—	13	6	no	—
219	C₂³	—	26	48	no	—
220	C₂³	—	26	4	no	—
221	C₂³	C₂×D₁₃⋊C₈	1	6	yes	—
222	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
223	C₂×C₄	—	13	16	no	—
224	C₂×C₄	—	13	6	no	—
225	C₂×C₄	—	13	6	no	—
226	C₂×C₄	—	13	16	no	—
227	C₂×C₄	—	13	12	no	—
228	C₂×C₄	—	13	12	no	—
229	C₂×C₄	—	13	16	no	—
230	C₂×C₄	—	13	4	no	—
231	C₂×C₄	—	13	4	no	—
232	C₂×C₄	C₂×D₁₃⋊C₈	1	12	yes	—
233	C₂×C₄	C₂×D₁₃⋊C₈	1	6	yes	—
234	C₂×C₄	C₂×D₁₃⋊C₈	1	3	yes	—
235	C₂×C₄	C₂³×#261	1	4	yes	—
236	C₂×C₄	C₂³×#261	1	3	yes	—
237	C₈	—	13	1	no	—
238	C₈	—	13	3	no	—
239	C₈	—	13	4	no	—
240	C₈	C₂³×#261	1	4	yes	—
241	C₈	C₂³×#261	1	4	yes	—
242	C₂²	—	2	12	no	—
243	C₂²	—	13	24	no	—
244	C₂²	—	13	4	no	—
245	C₂²	—	13	4	no	—
246	C₂²	—	26	32	no	—
247	C₂²	—	26	12	no	—
248	C₂²	D₁₃⋊M₃₂	1	4	yes	direct product factor
249	C₂²	C₂²×D₁₃⋊C₈	1	4	yes	—
250	C₂²	C₂²×D₁₃⋊C₈	1	3	yes	—
251	C₄	—	13	4	no	—
252	C₄	—	13	4	no	—
253	C₄	C₂²×D₁₃⋊C₈	1	3	yes	—
254	C₄	C₂²×D₁₃⋊C₈	1	4	yes	—
255	C₄	C₂⁴×#261	1	1	yes	characteristic
256	C₂	—	2	4	no	—
257	C₂	—	13	8	no	—
258	C₂	—	26	4	no	—
259	C₂	C₂×D₁₃⋊M₃₂	1	6	yes	direct product factor
260	C₂	C₂³×D₁₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×#261
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₄	C₂⁴×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×D₁₃	C₈
cosocle	#1055	C₂⁵
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂³×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#88098	C₂	semidirect
2. C₂×D₁₃⋊M₃₂	C₂	direct (N × H)
3. C₂²×#88106	C₂	semidirect
4. C₂²×D₁₃⋊C₁₆	C₂	semidirect
15. C₂×#88106	C₂²	semidirect
16. C₂²×#6092	C₂²	semidirect
17. D₁₃⋊M₃₂	C₂²	direct (N × H)
18. C₂×#88098	C₂²	semidirect
19. C₂×D₁₃⋊C₁₆	C₂²	semidirect
44. #88106	C₂³	semidirect
45. C₂×#6092	C₂³	semidirect
46. #88098	C₂³	semidirect
47. D₁₃⋊C₁₆	C₂³	semidirect
83. #6092	C₂⁴	semidirect
94. C₂²×D₁₃	M₃₂	semidirect
132. C₂²×C₁₃	C₂×M₃₂	semidirect
137. C₂×D₁₃	C₂×M₃₂	semidirect
174. C₂×C₁₃	C₂²×M₃₂	semidirect
177. D₁₃	C₂²×M₃₂	semidirect
213. C₁₃	C₂³×M₃₂	semidirect
248. C₂²	D₁₃⋊M₃₂	direct (N × H)
259. C₂	C₂×D₁₃⋊M₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88098	2
C₂×D₁₃⋊M₃₂	2
C₂²×#88106	2
C₂²×D₁₃⋊C₁₆	2
C₂³×C₈×D₁₃	2
C₂³×M₃₂	13

Subgroups — C22×D13⋊M32 #16809613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃⋊M₃₂ #16809613