Subgroups — C₄×#11763913 #17982469

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763913	C₂	1	2	yes	maximal
2	C₄×#10587666	C₂	1	2	yes	maximal
3	#14545859	C₂	1	2	yes	maximal
4	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587666	C₂²	1	4	yes	—
6	#11763913	C₄	1	8	yes	direct product factor
7	#11763903	—	2	2	no	—
8	C₄×#63241	—	2	2	no	—
9	C₄×#63242	C₂²	1	1	yes	characteristic
10	C₂×C₈×#595	C₄	1	1	yes	characteristic
11	C₂×C₈×#595	C₄	1	1	yes	characteristic
12	C₂×C₈×#595	C₂²	1	1	yes	characteristic
13	C₂×C₈×#595	C₂²	1	1	yes	characteristic
14	C₄²×#595	C₄	1	1	yes	characteristic
15	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
16	C₂×C₄×#595	—	2	1	no	—
17	C₂×C₄×#595	—	2	1	no	—
18	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
20	C₂×#63242	C₂×C₄	1	1	yes	characteristic
21	C₂×#63242	C₂³	1	1	yes	characteristic
22	C₂×#63241	—	2	4	no	—
23	#10587666	—	2	4	no	—
24	#10587666	C₂×C₄	1	8	yes	—
25	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
28	C₄×#3624	D₄	1	1	yes	characteristic
29	C₄×#3624	D₄	1	1	yes	characteristic
30	C₄×#3624	Q₈	1	1	yes	characteristic
31	C₄×#3624	Q₈	1	1	yes	characteristic
32	C₈×#595	—	2	2	no	—
33	C₈×#595	—	2	2	no	—
34	C₈×#595	C₈	1	4	yes	—
35	C₈×#595	C₂×C₄	1	4	yes	—
36	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
37	C₈×Dic₁₇	C₈	1	1	yes	characteristic
38	C₈×Dic₁₇	C₈	1	1	yes	characteristic
39	C₄×#3622	C₈	1	1	yes	characteristic
40	C₂²×#595	—	2	1	no	—
41	C₂²×#595	—	2	1	no	—
42	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
43	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
44	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×#3624	C₄⋊C₄	1	1	yes	characteristic
46	C₂×#3624	C₄⋊C₄	1	1	yes	characteristic
47	C₂×#3624	C₂×D₄	1	1	yes	characteristic
48	C₂×#3624	C₂×Q₈	1	1	yes	characteristic
49	C₄×#595	—	2	4	no	—
50	C₄×#595	—	2	4	no	—
51	C₄×#595	—	2	1	no	—
52	C₄×#595	—	2	1	no	—
53	C₄×#595	C₄²	1	2	yes	—
54	C₄×#595	C₂×C₈	1	2	yes	—
55	#63242	C₂×C₈	1	2	yes	—
56	#63242	M₁₆	1	2	yes	—
57	#63242	C₂²×C₄	1	2	yes	—
58	#63242	#41	1	2	yes	—
59	#63241	—	2	8	no	—
60	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
61	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
62	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
63	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
64	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
65	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
66	C₂×#3622	C₂×C₈	1	1	yes	characteristic
67	C₂×#3622	C₂×C₈	1	1	yes	characteristic
68	C₈×D₁₇	—	2	1	no	—
69	C₈×D₁₇	—	2	1	no	—
70	C₈×D₁₇	C₄²	1	2	yes	—
71	C₈×D₁₇	C₂×C₈	1	2	yes	—
72	C₄×#364	—	17	1	no	maximal, Sylow
73	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
74	C₂×#595	—	2	2	no	—
75	C₂×#595	—	2	2	no	—
76	C₂×#595	—	2	2	no	—
77	C₂×#595	—	2	2	no	—
78	C₂×#595	—	2	2	no	—
79	C₂×#595	—	2	2	no	—
80	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
83	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
84	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
85	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₄×D₁₇	—	2	2	no	—
87	C₄×D₁₇	—	2	2	no	—
88	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
89	C₄×D₁₇	#117	1	1	yes	characteristic
90	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
91	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
92	#3624	C₄⋊C₈	1	2	yes	—
93	#3624	C₄⋊C₈	1	2	yes	—
94	#3624	C₄×D₄	1	2	yes	—
95	#3624	C₄×Q₈	1	2	yes	—
96	C₈×C₁₇	—	2	1	no	—
97	C₈×C₁₇	C₄×C₈	1	2	yes	—
98	#3622	—	2	1	no	—
99	#3622	C₄×C₈	1	2	yes	—
100	C₂×#364	—	17	2	no	—
101	C₄×M₃₂	—	17	2	no	—
102	C₄²×C₈	—	17	1	no	—
103	#1376	—	17	2	no	—
104	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
105	C₂×D₁₇	—	2	1	no	—
106	C₂×D₁₇	—	2	1	no	—
107	C₂×D₁₇	C₄×M₁₆	1	1	yes	characteristic
108	C₂×D₁₇	#431	1	1	yes	characteristic
109	#595	—	2	4	no	—
110	#595	—	2	4	no	—
111	C₄×C₁₇	—	2	1	no	—
112	C₄×C₁₇	#364	1	2	yes	complemented
113	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
114	C₄×C₁₇	#431	1	1	yes	characteristic
115	Dic₁₇	—	2	1	no	—
116	Dic₁₇	#364	1	2	yes	complemented
117	Dic₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
118	Dic₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
119	C₂×M₃₂	—	17	4	no	—
120	C₂×C₄×C₈	—	17	1	no	—
121	C₂×C₄×C₈	—	17	1	no	—
122	C₂×C₄×C₈	—	17	1	no	—
123	C₂×C₄×C₈	—	17	1	no	—
124	C₂×C₄×C₈	—	17	1	no	—
125	C₂×C₄×C₈	—	17	1	no	—
126	C₄³	—	17	1	no	—
127	#364	—	17	8	no	—
128	#346	—	34	2	no	—
129	C₄×C₁₆	—	34	2	no	—
130	C₂×C₁₇	C₄×C₄⋊C₈	1	1	yes	characteristic
131	C₂×C₁₇	C₂×#364	1	1	yes	characteristic
132	C₂×C₁₇	C₂×#364	1	1	yes	characteristic
133	D₁₇	—	2	1	no	—
134	D₁₇	—	2	1	no	—
135	C₂²×C₈	—	17	1	no	—
136	C₂²×C₈	—	17	1	no	—
137	C₂²×C₈	—	17	1	no	—
138	C₂²×C₈	—	17	1	no	—
139	C₂×C₄²	—	17	1	no	—
140	C₂×C₄²	—	17	1	no	—
141	C₂×C₄²	—	17	1	no	—
142	C₂×C₄²	—	34	1	no	—
143	C₂×C₄²	—	34	1	no	—
144	M₃₂	—	17	8	no	—
145	M₃₂	—	34	4	no	—
146	C₂×C₁₆	—	34	4	no	—
147	C₄×C₈	—	17	1	no	—
148	C₄×C₈	—	17	1	no	—
149	C₄×C₈	—	17	4	no	—
150	C₄×C₈	—	17	4	no	—
151	C₄×C₈	—	17	1	no	—
152	C₄×C₈	—	17	1	no	—
153	C₄×C₈	—	17	1	no	—
154	C₄×C₈	—	17	1	no	—
155	C₄×C₈	—	17	1	no	—
156	C₄×C₈	—	34	2	no	—
157	C₄×C₈	—	34	2	no	—
158	C₄×C₈	#3633	1	1	yes	characteristic
159	C₁₇	C₄×#364	1	1	yes	characteristic, complemented, Sylow
160	C₂²×C₄	—	17	1	no	—
161	C₂²×C₄	—	17	1	no	—
162	C₂²×C₄	—	17	1	no	—
163	C₂²×C₄	—	34	1	no	—
164	C₂²×C₄	—	34	1	no	—
165	C₂×C₈	—	17	2	no	—
166	C₂×C₈	—	17	2	no	—
167	C₂×C₈	—	17	2	no	—
168	C₂×C₈	—	17	2	no	—
169	C₂×C₈	—	17	1	no	—
170	C₂×C₈	—	17	1	no	—
171	C₂×C₈	—	17	1	no	—
172	C₂×C₈	—	17	1	no	—
173	C₂×C₈	—	17	1	no	—
174	C₂×C₈	—	17	2	no	—
175	C₂×C₈	—	17	2	no	—
176	C₂×C₈	—	17	1	no	—
177	C₂×C₈	—	34	1	no	—
178	C₂×C₈	—	34	1	no	—
179	C₂×C₈	C₂×#3633	1	1	yes	characteristic
180	C₂×C₈	C₂×#3633	1	1	yes	characteristic
181	C₄²	—	17	1	no	—
182	C₄²	—	17	1	no	—
183	C₄²	—	17	1	no	—
184	C₄²	—	17	2	no	—
185	C₄²	—	17	2	no	—
186	C₄²	—	34	1	no	—
187	C₄²	—	34	1	no	—
188	C₄²	—	34	4	no	—
189	C₄²	—	34	4	no	—
190	C₄²	C₂×#3633	1	1	yes	characteristic
191	C₁₆	—	34	8	no	—
192	C₂³	—	17	1	no	—
193	C₂×C₄	—	17	1	no	—
194	C₂×C₄	—	17	1	no	—
195	C₂×C₄	—	17	1	no	—
196	C₂×C₄	—	17	1	no	—
197	C₂×C₄	—	17	1	no	—
198	C₂×C₄	—	17	1	no	—
199	C₂×C₄	—	17	1	no	—
200	C₂×C₄	—	34	2	no	—
201	C₂×C₄	—	34	2	no	—
202	C₂×C₄	—	34	2	no	—
203	C₂×C₄	—	34	2	no	—
204	C₂×C₄	—	34	2	no	—
205	C₂×C₄	—	34	2	no	—
206	C₂×C₄	—	34	2	no	—
207	C₂×C₄	—	34	2	no	—
208	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
209	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
210	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
211	C₈	—	2	1	no	—
212	C₈	—	17	2	no	—
213	C₈	—	17	2	no	—
214	C₈	—	17	2	no	—
215	C₈	—	17	2	no	—
216	C₈	—	17	2	no	—
217	C₈	—	34	1	no	—
218	C₈	C₄×#3633	1	2	yes	—
219	C₂²	—	17	1	no	—
220	C₂²	—	17	1	no	—
221	C₂²	—	34	1	no	—
222	C₂²	—	34	1	no	—
223	C₂²	C₂×C₄⋊#3633	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	17	1	no	—
226	C₄	—	17	1	no	—
227	C₄	—	17	2	no	—
228	C₄	—	34	4	no	—
229	C₄	—	34	4	no	—
230	C₄	—	34	1	no	—
231	C₄	#11763913	1	2	yes	direct product factor
232	C₄	C₂×C₄×#3633	1	1	yes	characteristic
233	C₄	#11763922	1	1	yes	characteristic
234	C₂	—	34	1	no	—
235	C₂	—	34	1	no	—
236	C₂	C₄×C₄⋊#3633	1	1	yes	characteristic
237	C₂	C₂×#11763913	1	1	yes	characteristic
238	C₂	#14545978	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#3633
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₄⋊C₈
prime radical	C₂²×D₁₇	C₂×M₁₆
cosocle	C₂×#63242	C₂³
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	C₄×#364
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #11763913	C₄	direct (N × H)
112. C₄×C₁₇	#364	semidirect
116. Dic₁₇	#364	semidirect
159. C₁₇	C₄×#364	semidirect
231. C₄	#11763913	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11763913	2
C₄×#10587666	2
#14545859	2
C₄×C₈×#595	2
C₄×#364	17

Subgroups — C4×#11763913 #17982469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763913 #17982469