Subgroups — C₄×#11763898 #17981629

Order 4352.

470 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	C₄×C₄⋊#3633	C₂	1	2	yes	maximal
2	C₂×#11763898	C₂	1	2	yes	maximal
3	#14545790	C₂	1	2	yes	maximal
4	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#3633	C₂²	1	4	yes	—
6	C₂×C₄×#3633	—	2	2	no	—
7	(C₂×#3633)⋊C₄	—	2	2	no	—
8	#11763898	C₄	1	8	yes	direct product factor
9	C₄×#63242	C₄	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	C₂²	1	1	yes	characteristic
15	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
16	C₂²×#3633	—	2	4	no	—
17	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×#595	D₄	1	1	yes	characteristic
19	C₂×C₄×#595	D₄	1	1	yes	characteristic
20	C₂×C₄×#595	Q₈	1	1	yes	characteristic
21	C₂×C₄×#595	Q₈	1	1	yes	characteristic
22	C₂×C₄×#595	C₂³	1	1	yes	characteristic
23	C₂×#63242	C₂×C₄	1	1	yes	characteristic
24	C₂×#63242	C₂×C₄	1	1	yes	characteristic
25	C₄⋊#3633	—	2	4	no	—
26	C₄⋊#3633	C₂×C₄	1	8	yes	—
27	C₄×#3633	—	4	4	no	—
28	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
30	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
31	C₄×#3624	—	2	1	no	—
32	C₄×#3624	—	2	1	no	—
33	C₈×#595	—	2	2	no	—
34	C₈×#595	—	2	2	no	—
35	C₈×#595	C₈	1	4	yes	complemented
36	C₈×#595	C₂×C₄	1	4	yes	—
37	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic, complemented
38	C₈×Dic₁₇	C₈	1	1	yes	characteristic, complemented
39	C₈×Dic₁₇	C₈	1	1	yes	characteristic, complemented
40	C₄×#3622	C₈	1	1	yes	characteristic, complemented
41	C₂²×#595	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×#595	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×#595	C₂×D₄	1	1	yes	characteristic
44	C₂²×#595	C₂×Q₈	1	1	yes	characteristic
45	C₂×#3633	—	2	8	no	—
46	C₂×#3633	—	4	4	no	—
47	C₂×#3633	—	4	4	no	—
48	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
51	C₂×#3624	—	2	1	no	—
52	C₂×#3624	—	2	1	no	—
53	C₄×#595	—	2	2	no	—
54	C₄×#595	—	2	2	no	—
55	C₄×#595	—	2	2	no	—
56	C₄×#595	C₂×C₈	1	2	yes	—
57	C₄×#595	M₁₆	1	2	yes	—
58	C₄×#595	SD₁₆	1	4	yes	—
59	C₄×#595	C₂²×C₄	1	2	yes	—
60	C₄×#595	#41	1	2	yes	—
61	#63242	—	2	1	no	—
62	#63242	—	2	1	no	—
63	#63242	C₄²	1	2	yes	—
64	#63242	C₂×C₈	1	2	yes	—
65	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
66	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
67	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
68	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
69	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
70	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
71	C₂×#3622	C₂×C₈	1	1	yes	characteristic
72	C₂×#3622	C₂×C₈	1	1	yes	characteristic
73	C₈×D₁₇	—	2	1	no	—
74	C₈×D₁₇	—	2	1	no	—
75	C₈×D₁₇	C₄²	1	2	yes	—
76	C₈×D₁₇	C₂×C₈	1	2	yes	—
77	C₄×#334	—	17	1	no	maximal, Sylow
78	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×#595	—	2	1	no	—
80	C₂×#595	—	2	1	no	—
81	C₂×#595	—	2	1	no	—
82	C₂×#595	—	2	1	no	—
83	C₂×#595	C₄⋊C₈	1	2	yes	—
84	C₂×#595	C₄⋊C₈	1	2	yes	—
85	C₂×#595	#106	1	2	yes	—
86	C₂×#595	#108	1	2	yes	—
87	C₂×#595	C₄×D₄	1	2	yes	—
88	C₂×#595	C₄×Q₈	1	2	yes	—
89	C₂×#595	C₂×SD₁₆	1	2	yes	—
90	C₂×#595	#135	1	2	yes	—
91	#3633	—	4	8	no	—
92	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
94	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
95	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
96	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
97	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
98	C₄×D₁₇	—	2	1	no	—
99	C₄×D₁₇	—	2	1	no	—
100	C₄×D₁₇	#106	1	2	yes	—
101	C₄×D₁₇	#108	1	2	yes	—
102	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
103	C₄×D₁₇	#117	1	1	yes	characteristic
104	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
105	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
106	#3624	—	2	2	no	—
107	#3624	—	2	2	no	—
108	C₈×C₁₇	—	2	1	no	—
109	C₈×C₁₇	C₄×C₈	1	2	yes	complemented
110	#3622	—	2	1	no	—
111	#3622	C₄×C₈	1	2	yes	complemented
112	C₄×C₄⋊C₈	—	17	2	no	—
113	C₄²×C₈	—	17	1	no	—
114	C₂×#334	—	17	2	no	—
115	#1277	—	17	2	no	—
116	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
117	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
118	C₂×D₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
119	C₂×D₁₇	C₂×#106	1	1	yes	characteristic
120	C₂×D₁₇	#427	1	1	yes	characteristic
121	C₂×D₁₇	C₂×#108	1	1	yes	characteristic
122	C₂×D₁₇	C₂×#108	1	1	yes	characteristic
123	#595	—	2	2	no	—
124	#595	—	2	2	no	—
125	#595	#334	1	4	yes	complemented
126	#595	C₄×SD₁₆	1	4	yes	—
127	C₄×C₁₇	—	2	1	no	—
128	C₄×C₁₇	#334	1	2	yes	complemented
129	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
130	C₄×C₁₇	#431	1	1	yes	characteristic
131	Dic₁₇	—	2	1	no	—
132	Dic₁₇	#334	1	2	yes	complemented
133	Dic₁₇	C₄×M₁₆	1	1	yes	characteristic
134	Dic₁₇	#431	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	17	4	no	—
136	C₂×C₄×C₈	—	17	1	no	—
137	C₂×C₄×C₈	—	17	1	no	—
138	C₂×C₄×C₈	—	17	1	no	—
139	C₂×C₄×C₈	—	17	1	no	—
140	C₂×C₄×C₈	—	17	1	no	—
141	C₂×C₄×C₈	—	17	1	no	—
142	C₂×C₄×C₈	—	34	2	no	—
143	C₄³	—	17	1	no	—
144	#336	—	34	2	no	—
145	#334	—	17	8	no	—
146	C₂×C₁₇	C₂×#334	1	1	yes	characteristic
147	C₂×C₁₇	#1564	1	1	yes	characteristic
148	C₂×C₁₇	C₄×C₄⋊C₈	1	1	yes	characteristic
149	D₁₇	C₂×#334	1	1	yes	characteristic
150	D₁₇	#1564	1	1	yes	characteristic
151	D₁₇	C₄×#106	1	1	yes	characteristic
152	D₁₇	C₄×#108	1	1	yes	characteristic
153	C₂²×C₈	—	17	1	no	—
154	C₂²×C₈	—	17	1	no	—
155	C₂²×C₈	—	17	1	no	—
156	C₂²×C₈	—	17	1	no	—
157	C₂²×C₈	—	34	4	no	—
158	C₂×C₄²	—	17	1	no	—
159	C₂×C₄²	—	17	1	no	—
160	C₂×C₄²	—	17	1	no	—
161	C₂×C₄²	—	17	1	no	—
162	C₂×C₄²	—	17	1	no	—
163	C₂×C₄²	—	17	1	no	—
164	C₂×C₄²	—	17	1	no	—
165	C₄⋊C₈	—	17	8	no	—
166	C₄⋊C₈	—	34	4	no	—
167	C₄×C₈	—	17	4	no	—
168	C₄×C₈	—	17	4	no	—
169	C₄×C₈	—	17	1	no	—
170	C₄×C₈	—	17	1	no	—
171	C₄×C₈	—	17	1	no	—
172	C₄×C₈	—	34	2	no	—
173	C₄×C₈	—	34	2	no	—
174	C₄×C₈	—	34	1	no	—
175	C₄×C₈	—	34	1	no	—
176	C₄×C₈	—	68	4	no	—
177	C₄×C₈	#3633	1	1	yes	characteristic, complemented
178	C₁₇	C₄×#334	1	1	yes	characteristic, complemented, Sylow
179	C₂²×C₄	—	17	1	no	—
180	C₂²×C₄	—	17	1	no	—
181	C₂²×C₄	—	17	1	no	—
182	C₂²×C₄	—	17	1	no	—
183	C₂²×C₄	—	17	1	no	—
184	C₂²×C₄	—	17	1	no	—
185	C₂²×C₄	—	17	1	no	—
186	C₂×C₈	—	17	1	no	—
187	C₂×C₈	—	17	2	no	—
188	C₂×C₈	—	17	2	no	—
189	C₂×C₈	—	17	2	no	—
190	C₂×C₈	—	17	2	no	—
191	C₂×C₈	—	17	1	no	—
192	C₂×C₈	—	34	1	no	—
193	C₂×C₈	—	34	1	no	—
194	C₂×C₈	—	34	1	no	—
195	C₂×C₈	—	34	1	no	—
196	C₂×C₈	—	34	1	no	—
197	C₂×C₈	—	34	1	no	—
198	C₂×C₈	—	34	8	no	—
199	C₂×C₈	—	68	4	no	—
200	C₂×C₈	—	68	4	no	—
201	C₂×C₈	C₂×#3633	1	1	yes	characteristic
202	C₂×C₈	C₂×#3633	1	1	yes	characteristic
203	C₄²	—	17	2	no	—
204	C₄²	—	17	2	no	—
205	C₄²	—	17	4	no	—
206	C₄²	—	17	2	no	—
207	C₄²	—	17	2	no	—
208	C₄²	—	17	1	no	—
209	C₄²	—	17	1	no	—
210	C₄²	—	17	1	no	—
211	C₄²	—	34	2	no	—
212	C₄²	—	34	2	no	—
213	C₄²	—	34	2	no	—
214	C₄²	C₂×#3633	1	1	yes	characteristic
215	C₂³	—	17	1	no	—
216	C₂×C₄	—	17	2	no	—
217	C₂×C₄	—	17	2	no	—
218	C₂×C₄	—	17	2	no	—
219	C₂×C₄	—	17	2	no	—
220	C₂×C₄	—	17	2	no	—
221	C₂×C₄	—	17	2	no	—
222	C₂×C₄	—	17	1	no	—
223	C₂×C₄	—	17	1	no	—
224	C₂×C₄	—	17	2	no	—
225	C₂×C₄	—	17	2	no	—
226	C₂×C₄	—	17	1	no	—
227	C₂×C₄	—	17	1	no	—
228	C₂×C₄	—	17	1	no	—
229	C₂×C₄	—	17	1	no	—
230	C₂×C₄	—	17	2	no	—
231	C₂×C₄	—	17	2	no	—
232	C₂×C₄	—	17	1	no	—
233	C₂×C₄	—	34	1	no	—
234	C₂×C₄	—	34	1	no	—
235	C₂×C₄	—	34	1	no	—
236	C₂×C₄	—	34	1	no	—
237	C₂×C₄	—	34	1	no	—
238	C₂×C₄	—	34	1	no	—
239	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
240	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
241	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
242	C₈	—	2	1	no	—
243	C₈	—	17	2	no	—
244	C₈	—	34	2	no	—
245	C₈	—	34	2	no	—
246	C₈	—	34	1	no	—
247	C₈	—	68	8	no	—
248	C₈	C₄×#3633	1	2	yes	complemented
249	C₂²	—	17	1	no	—
250	C₂²	—	17	1	no	—
251	C₂²	—	17	1	no	—
252	C₂²	—	17	1	no	—
253	C₂²	—	17	1	no	—
254	C₂²	—	17	1	no	—
255	C₂²	C₂×C₄⋊#3633	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	17	4	no	—
258	C₄	—	17	4	no	—
259	C₄	—	17	1	no	—
260	C₄	—	17	1	no	—
261	C₄	—	17	2	no	—
262	C₄	—	34	2	no	—
263	C₄	—	34	2	no	—
264	C₄	—	34	1	no	—
265	C₄	#11763898	1	2	yes	direct product factor
266	C₄	C₂×C₄×#3633	1	1	yes	characteristic
267	C₄	#11763922	1	1	yes	characteristic
268	C₂	—	17	1	no	—
269	C₂	—	17	1	no	—
270	C₂	—	17	1	no	—
271	C₂	—	17	1	no	—
272	C₂	C₂×#11763898	1	1	yes	characteristic
273	C₂	#14545908	1	1	yes	characteristic
274	C₂	C₄×C₄⋊#3633	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×C₄⋊C₄
cosocle	C₂×C₄×#595	C₂³
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	C₄×#334
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
8. #11763898	C₄	direct (N × H)
35. C₈×#595	C₈	semidirect
37. C₄×C₈×C₁₇	C₈	semidirect
38. C₈×Dic₁₇	C₈	semidirect
39. C₈×Dic₁₇	C₈	semidirect
40. C₄×#3622	C₈	semidirect
109. C₈×C₁₇	C₄×C₈	semidirect
111. #3622	C₄×C₈	semidirect
125. #595	#334	semidirect
128. C₄×C₁₇	#334	semidirect
132. Dic₁₇	#334	semidirect
177. C₄×C₈	#3633	semidirect
178. C₁₇	C₄×#334	semidirect
248. C₈	C₄×#3633	semidirect
265. C₄	#11763898	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₄⋊#3633	2
C₂×#11763898	2
#14545790	2
C₄×C₈×#595	2
C₄×#334	17

Subgroups — C4×#11763898 #17981629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763898 #17981629