Subgroups — C₄×#11763899 #17981630

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 282 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×#11763899	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	#11763899	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	D₈	1	2	yes	—
59	C₄×#595	Q₁₆	1	2	yes	—
60	C₄×#595	C₂²×C₄	1	2	yes	—
61	C₄×#595	#41	1	2	yes	—
62	#63242	—	2	1	no	—
63	#63242	—	2	1	no	—
64	#63242	C₄²	1	2	yes	—
65	#63242	C₂×C₈	1	2	yes	—
66	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
67	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
68	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
69	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
70	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
71	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
72	C₂×#3622	C₂×C₈	1	1	yes	characteristic
73	C₂×#3622	C₂×C₈	1	1	yes	characteristic
74	C₈×D₁₇	—	2	1	no	—
75	C₈×D₁₇	—	2	1	no	—
76	C₈×D₁₇	C₄²	1	2	yes	—
77	C₈×D₁₇	C₂×C₈	1	2	yes	—
78	C₄×#335	—	17	1	no	maximal, Sylow
79	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×#595	—	2	1	no	—
81	C₂×#595	—	2	1	no	—
82	C₂×#595	—	2	1	no	—
83	C₂×#595	—	2	1	no	—
84	C₂×#595	C₄⋊C₈	1	2	yes	—
85	C₂×#595	C₄⋊C₈	1	2	yes	—
86	C₂×#595	#107	1	2	yes	—
87	C₂×#595	#108	1	2	yes	—
88	C₂×#595	C₄×D₄	1	2	yes	—
89	C₂×#595	C₄×Q₈	1	2	yes	—
90	C₂×#595	C₂×D₈	1	1	yes	characteristic
91	C₂×#595	C₂×Q₁₆	1	1	yes	characteristic
92	C₂×#595	#135	1	2	yes	—
93	#3633	—	4	8	no	—
94	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
95	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
96	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
97	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
98	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
99	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
100	C₄×D₁₇	—	2	1	no	—
101	C₄×D₁₇	—	2	1	no	—
102	C₄×D₁₇	#107	1	2	yes	—
103	C₄×D₁₇	#108	1	2	yes	—
104	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
105	C₄×D₁₇	#117	1	1	yes	characteristic
106	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
107	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
108	#3624	—	2	2	no	—
109	#3624	—	2	2	no	—
110	C₈×C₁₇	—	2	1	no	—
111	C₈×C₁₇	C₄×C₈	1	2	yes	complemented
112	#3622	—	2	1	no	—
113	#3622	C₄×C₈	1	2	yes	complemented
114	C₄×C₄⋊C₈	—	17	2	no	—
115	C₄²×C₈	—	17	1	no	—
116	C₂×#335	—	17	2	no	—
117	#1277	—	17	2	no	—
118	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
119	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
120	C₂×D₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
121	C₂×D₁₇	C₂×#107	1	1	yes	characteristic
122	C₂×D₁₇	#427	1	1	yes	characteristic
123	C₂×D₁₇	C₂×#108	1	1	yes	characteristic
124	C₂×D₁₇	C₂×#108	1	1	yes	characteristic
125	#595	—	2	2	no	—
126	#595	—	2	2	no	—
127	#595	#335	1	4	yes	complemented
128	#595	C₄×D₈	1	2	yes	—
129	#595	C₄×Q₁₆	1	2	yes	—
130	C₄×C₁₇	—	2	1	no	—
131	C₄×C₁₇	#335	1	2	yes	complemented
132	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
133	C₄×C₁₇	#431	1	1	yes	characteristic
134	Dic₁₇	—	2	1	no	—
135	Dic₁₇	#335	1	2	yes	complemented
136	Dic₁₇	C₄×M₁₆	1	1	yes	characteristic
137	Dic₁₇	#431	1	1	yes	characteristic
138	C₂×C₄⋊C₈	—	17	4	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	—	17	1	no	—
143	C₂×C₄×C₈	—	17	1	no	—
144	C₂×C₄×C₈	—	17	1	no	—
145	C₂×C₄×C₈	—	34	2	no	—
146	C₄³	—	17	1	no	—
147	#336	—	34	2	no	—
148	#335	—	17	8	no	—
149	C₂×C₁₇	C₂×#335	1	1	yes	characteristic
150	C₂×C₁₇	#1564	1	1	yes	characteristic
151	C₂×C₁₇	C₄×C₄⋊C₈	1	1	yes	characteristic
152	D₁₇	C₂×#335	1	1	yes	characteristic
153	D₁₇	#1564	1	1	yes	characteristic
154	D₁₇	C₄×#107	1	1	yes	characteristic
155	D₁₇	C₄×#108	1	1	yes	characteristic
156	C₂²×C₈	—	17	1	no	—
157	C₂²×C₈	—	17	1	no	—
158	C₂²×C₈	—	17	1	no	—
159	C₂²×C₈	—	17	1	no	—
160	C₂²×C₈	—	34	4	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	C₂×C₄²	—	17	1	no	—
166	C₂×C₄²	—	17	1	no	—
167	C₂×C₄²	—	17	1	no	—
168	C₄⋊C₈	—	17	8	no	—
169	C₄⋊C₈	—	34	4	no	—
170	C₄×C₈	—	17	4	no	—
171	C₄×C₈	—	17	4	no	—
172	C₄×C₈	—	17	1	no	—
173	C₄×C₈	—	17	1	no	—
174	C₄×C₈	—	17	1	no	—
175	C₄×C₈	—	34	2	no	—
176	C₄×C₈	—	34	2	no	—
177	C₄×C₈	—	34	1	no	—
178	C₄×C₈	—	34	1	no	—
179	C₄×C₈	—	68	4	no	—
180	C₄×C₈	#3633	1	1	yes	characteristic, complemented
181	C₁₇	C₄×#335	1	1	yes	characteristic, complemented, Sylow
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	C₂²×C₄	—	17	1	no	—
187	C₂²×C₄	—	17	1	no	—
188	C₂²×C₄	—	17	1	no	—
189	C₂×C₈	—	17	1	no	—
190	C₂×C₈	—	17	2	no	—
191	C₂×C₈	—	17	2	no	—
192	C₂×C₈	—	17	2	no	—
193	C₂×C₈	—	17	2	no	—
194	C₂×C₈	—	17	1	no	—
195	C₂×C₈	—	34	1	no	—
196	C₂×C₈	—	34	1	no	—
197	C₂×C₈	—	34	1	no	—
198	C₂×C₈	—	34	1	no	—
199	C₂×C₈	—	34	1	no	—
200	C₂×C₈	—	34	1	no	—
201	C₂×C₈	—	34	8	no	—
202	C₂×C₈	—	68	4	no	—
203	C₂×C₈	—	68	4	no	—
204	C₂×C₈	C₂×#3633	1	1	yes	characteristic
205	C₂×C₈	C₂×#3633	1	1	yes	characteristic
206	C₄²	—	17	2	no	—
207	C₄²	—	17	2	no	—
208	C₄²	—	17	2	no	—
209	C₄²	—	17	2	no	—
210	C₄²	—	17	2	no	—
211	C₄²	—	17	2	no	—
212	C₄²	—	17	1	no	—
213	C₄²	—	17	1	no	—
214	C₄²	—	17	1	no	—
215	C₄²	—	34	2	no	—
216	C₄²	—	34	2	no	—
217	C₄²	—	34	2	no	—
218	C₄²	C₂×#3633	1	1	yes	characteristic
219	C₂³	—	17	1	no	—
220	C₂×C₄	—	17	2	no	—
221	C₂×C₄	—	17	1	no	—
222	C₂×C₄	—	17	2	no	—
223	C₂×C₄	—	17	2	no	—
224	C₂×C₄	—	17	1	no	—
225	C₂×C₄	—	17	2	no	—
226	C₂×C₄	—	17	2	no	—
227	C₂×C₄	—	17	1	no	—
228	C₂×C₄	—	17	1	no	—
229	C₂×C₄	—	17	2	no	—
230	C₂×C₄	—	17	2	no	—
231	C₂×C₄	—	17	1	no	—
232	C₂×C₄	—	17	1	no	—
233	C₂×C₄	—	17	1	no	—
234	C₂×C₄	—	17	1	no	—
235	C₂×C₄	—	17	2	no	—
236	C₂×C₄	—	17	2	no	—
237	C₂×C₄	—	17	1	no	—
238	C₂×C₄	—	34	1	no	—
239	C₂×C₄	—	34	1	no	—
240	C₂×C₄	—	34	1	no	—
241	C₂×C₄	—	34	1	no	—
242	C₂×C₄	—	34	1	no	—
243	C₂×C₄	—	34	1	no	—
244	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
245	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
246	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
247	C₈	—	2	1	no	—
248	C₈	—	17	2	no	—
249	C₈	—	34	2	no	—
250	C₈	—	34	2	no	—
251	C₈	—	34	1	no	—
252	C₈	—	68	8	no	—
253	C₈	C₄×#3633	1	2	yes	complemented
254	C₂²	—	17	1	no	—
255	C₂²	—	17	1	no	—
256	C₂²	—	17	1	no	—
257	C₂²	—	17	1	no	—
258	C₂²	—	17	1	no	—
259	C₂²	—	17	1	no	—
260	C₂²	C₂×C₄⋊#3633	1	1	yes	characteristic
261	C₄	—	2	1	no	—
262	C₄	—	17	2	no	—
263	C₄	—	17	4	no	—
264	C₄	—	17	2	no	—
265	C₄	—	17	1	no	—
266	C₄	—	17	1	no	—
267	C₄	—	17	2	no	—
268	C₄	—	34	2	no	—
269	C₄	—	34	2	no	—
270	C₄	—	34	1	no	—
271	C₄	#11763899	1	2	yes	direct product factor
272	C₄	C₂×C₄×#3633	1	1	yes	characteristic
273	C₄	#11763922	1	1	yes	characteristic
274	C₂	—	17	1	no	—
275	C₂	—	17	1	no	—
276	C₂	—	17	1	no	—
277	C₂	—	17	1	no	—
278	C₂	C₂×#11763899	1	1	yes	characteristic
279	C₂	#14545908	1	1	yes	characteristic
280	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×#335
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. #11763899	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
111. C₈×C₁₇	C₄×C₈	semidirect
113. #3622	C₄×C₈	semidirect
127. #595	#335	semidirect
131. C₄×C₁₇	#335	semidirect
135. Dic₁₇	#335	semidirect
180. C₄×C₈	#3633	semidirect
181. C₁₇	C₄×#335	semidirect
253. C₈	C₄×#3633	semidirect
271. C₄	#11763899	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×#11763899	2
#14545790	2
C₄×C₈×#595	2
C₄×#335	17

Subgroups — C4×#11763899 #17981630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763899 #17981630