Subgroups — C₄×Q₈×#3633 #17982886

Order 4352.

1070 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#3633	C₂	1	2	yes	maximal
2	C₄⋊C₄×#3633	C₂	1	6	yes	maximal
3	C₄×C₄⋊#3633	C₂	1	3	yes	maximal
4	C₄²×#3633	C₂	1	3	yes	maximal
5	C₄×Q₈×#595	C₂	1	1	yes	maximal, characteristic
6	Q₈×#3633	C₄	1	16	yes	direct product factor
7	C₂×C₄⋊#3633	C₂²	1	6	yes	—
8	C₂×C₄×#3633	C₂²	1	3	yes	—
9	C₂×C₄×#3633	C₂²	1	6	yes	—
10	C₂×C₄×#3633	C₂²	1	6	yes	—
11	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
12	(C₂×#3633)⋊C₄	C₂²	1	6	yes	—
13	C₂×Q₈×#595	C₄	1	1	yes	characteristic
14	C₂×Q₈×#595	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×#595	C₄	1	3	yes	—
16	C₄⋊C₄×#595	C₂²	1	3	yes	—
17	C₄×C₄⋊#595	C₄	1	3	yes	—
18	C₄²×#595	C₂²	1	3	yes	—
19	C₄×Q₈×D₁₇	C₄	1	1	yes	characteristic
20	C₂²×#3633	C₂³	1	6	yes	—
21	C₂²×#3633	C₂³	1	2	yes	—
22	C₂×Q₈×D₁₇	C₂×C₄	1	1	yes	characteristic
23	Q₈×#595	C₈	1	8	yes	complemented
24	Q₈×#595	C₂×C₄	1	8	yes	—
25	C₂×C₄⋊#595	C₂×C₄	1	3	yes	—
26	C₂×C₄⋊#595	C₂×C₄	1	3	yes	—
27	C₂×C₄×#595	C₂×C₄	1	3	yes	—
28	C₂×C₄×#595	C₂×C₄	1	3	yes	—
29	C₂×C₄×#595	C₂×C₄	1	3	yes	—
30	C₂×C₄×#595	C₂³	1	3	yes	—
31	C₂×C₄×#595	C₂³	1	3	yes	—
32	C₂×C₄×#595	C₂³	1	1	yes	characteristic
33	C₄⋊#3633	C₂×C₄	1	24	yes	—
34	C₄×#3633	—	2	12	no	—
35	C₄×#3633	—	2	6	no	—
36	C₄×#3633	C₂×C₄	1	24	yes	—
37	C₄×#3633	Q₈	1	4	yes	direct product factor
38	C₄×Q₈×C₁₇	C₈	1	1	yes	characteristic, complemented
39	Q₈×Dic₁₇	C₈	1	1	yes	characteristic, complemented
40	C₄⋊C₄×D₁₇	C₂×C₄	1	3	yes	—
41	#10587573	C₈	1	3	yes	complemented
42	C₄²×D₁₇	C₂×C₄	1	3	yes	—
43	C₄×Dic₃₄	C₈	1	3	yes	complemented
44	(C₂×#595)⋊C₄	C₂×C₄	1	6	yes	—
45	C₂²×#595	C₂²×C₄	1	3	yes	—
46	C₂²×#595	C₂²×C₄	1	3	yes	—
47	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
48	C₂²×#595	C₂⁴	1	1	yes	characteristic
49	C₂×#3633	—	2	6	no	—
50	C₂×#3633	—	2	6	no	—
51	C₂×#3633	C₂²×C₄	1	12	yes	—
52	C₂×#3633	C₂²×C₄	1	4	yes	—
53	C₂×#3633	C₂×Q₈	1	4	yes	—
54	C₂×#3633	#41	1	4	yes	—
55	C₂×Q₈×C₁₇	C₂×C₈	1	1	yes	characteristic
56	Q₈×D₁₇	C₄²	1	4	yes	—
57	Q₈×D₁₇	C₂×C₈	1	4	yes	—
58	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
59	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
60	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
61	C₂×Dic₃₄	C₂×C₈	1	3	yes	—
62	C₄⋊#595	C₄²	1	12	yes	—
63	C₄⋊#595	C₂×C₈	1	12	yes	—
64	C₄×#595	—	2	6	no	—
65	C₄×#595	—	2	6	no	—
66	C₄×#595	—	2	6	no	—
67	C₄×#595	C₂×C₈	1	12	yes	—
68	C₄×#595	C₂²×C₄	1	12	yes	—
69	C₄×#595	C₂×Q₈	1	2	yes	—
70	C₄×#595	#41	1	2	yes	—
71	C₄⋊C₄×C₁₇	C₂×C₈	1	3	yes	—
72	C₄²×C₁₇	C₂×C₈	1	3	yes	—
73	C₄⋊Dic₁₇	C₂×C₈	1	3	yes	—
74	#63225	C₂×C₈	1	6	yes	—
75	C₄×Dic₁₇	C₂×C₈	1	3	yes	—
76	C₄×Dic₁₇	C₂×C₈	1	3	yes	—
77	C₄×Dic₁₇	C₂×C₈	1	3	yes	—
78	C₄×C₈×Q₈	—	17	1	no	maximal, Sylow
79	C₂²×D₁₇	C₂³×C₄	1	1	yes	characteristic
80	C₂×#595	—	2	3	no	—
81	C₂×#595	—	2	3	no	—
82	C₂×#595	—	2	3	no	—
83	C₂×#595	—	2	3	no	—
84	C₂×#595	C₂×C₄²	1	6	yes	—
85	C₂×#595	C₄×Q₈	1	2	yes	—
86	C₂×#595	C₂²×C₈	1	6	yes	—
87	C₂×#595	C₂²×C₈	1	2	yes	—
88	C₂×#595	#131	1	2	yes	—
89	C₂×#595	C₂³×C₄	1	2	yes	—
90	C₂×#595	C₂²×Q₈	1	1	yes	characteristic
91	C₂×#595	C₂×#41	1	2	yes	—
92	C₂×#595	C₂×#41	1	1	yes	characteristic
93	#3633	—	2	12	no	—
94	#3633	C₄×Q₈	1	8	yes	direct product factor
95	Q₈×C₁₇	C₄×C₈	1	4	yes	complemented
96	C₂×C₄×C₁₇	C₂²×C₈	1	3	yes	—
97	C₂×C₄×C₁₇	C₂²×C₈	1	3	yes	—
98	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
99	C₂×Dic₁₇	C₂²×C₈	1	3	yes	—
100	C₂×Dic₁₇	C₂²×C₈	1	3	yes	—
101	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
102	C₄×D₁₇	—	2	3	no	—
103	C₄×D₁₇	—	2	3	no	—
104	C₄×D₁₇	C₂×C₄²	1	6	yes	—
105	C₄×D₁₇	C₄×Q₈	1	2	yes	—
106	C₄×D₁₇	C₂²×C₈	1	6	yes	—
107	C₄×D₁₇	#131	1	2	yes	—
108	Dic₃₄	C₄×C₈	1	12	yes	complemented
109	C₂×C₈×Q₈	—	17	2	no	—
110	C₄²×Q₈	—	17	1	no	—
111	C₈×C₄⋊C₄	—	17	6	no	—
112	C₄×C₄⋊C₈	—	17	3	no	—
113	C₄²×C₈	—	17	3	no	—
114	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
115	C₂×D₁₇	C₂²×C₄²	1	1	yes	characteristic
116	C₂×D₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
117	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
118	C₂×D₁₇	C₂³×C₈	1	1	yes	characteristic
119	C₂×D₁₇	C₂×#131	1	1	yes	characteristic
120	C₂×D₁₇	C₂×#131	1	1	yes	characteristic
121	#595	—	2	6	no	—
122	#595	—	2	6	no	—
123	#595	C₈×Q₈	1	4	yes	complemented
124	#595	C₂×C₄×Q₈	1	2	yes	—
125	#595	C₄×#41	1	2	yes	—
126	C₄×C₁₇	—	2	3	no	—
127	C₄×C₁₇	C₂×C₄×C₈	1	6	yes	—
128	C₄×C₁₇	C₈×Q₈	1	2	yes	complemented
129	Dic₁₇	—	2	3	no	—
130	Dic₁₇	C₂×C₄×C₈	1	6	yes	—
131	Dic₁₇	C₈×Q₈	1	2	yes	complemented
132	C₂×C₄×Q₈	—	17	1	no	—
133	C₂×C₄×Q₈	—	17	1	no	—
134	C₂×C₄×Q₈	—	17	1	no	—
135	C₈×Q₈	—	17	16	no	—
136	C₂×C₄⋊C₈	—	17	6	no	—
137	C₂×C₄×C₈	—	17	6	no	—
138	C₂×C₄×C₈	—	17	1	no	—
139	C₂×C₄×C₈	—	17	3	no	—
140	C₂×C₄×C₈	—	17	6	no	—
141	C₄×C₄⋊C₄	—	17	3	no	—
142	C₄×C₄⋊C₄	—	17	3	no	—
143	C₄×C₄⋊C₄	—	17	3	no	—
144	C₄³	—	17	3	no	—
145	#336	—	17	6	no	—
146	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
147	C₂×C₁₇	C₂×C₈×Q₈	1	1	yes	characteristic
148	C₂×C₁₇	C₈×#41	1	1	yes	characteristic
149	D₁₇	C₄²×Q₈	1	1	yes	characteristic
150	D₁₇	C₄×#131	1	1	yes	characteristic
151	D₁₇	C₂×C₈×Q₈	1	1	yes	characteristic
152	D₁₇	C₈×#41	1	1	yes	characteristic
153	C₂²×Q₈	—	17	1	no	—
154	C₂²×C₈	—	17	2	no	—
155	C₂²×C₈	—	17	6	no	—
156	C₄×Q₈	—	17	8	no	—
157	C₄×Q₈	—	17	8	no	—
158	C₄×Q₈	—	17	1	no	—
159	C₄×Q₈	—	17	3	no	—
160	C₄×Q₈	—	17	3	no	—
161	C₄×Q₈	#3633	1	1	yes	characteristic, direct product factor
162	C₂×C₄⋊C₄	—	17	3	no	—
163	C₂×C₄⋊C₄	—	17	3	no	—
164	C₂×C₄⋊C₄	—	17	3	no	—
165	C₂×C₄²	—	17	3	no	—
166	C₂×C₄²	—	17	3	no	—
167	C₂×C₄²	—	17	1	no	—
168	C₂×C₄²	—	17	3	no	—
169	C₂×C₄²	—	17	3	no	—
170	C₂×C₄²	—	17	3	no	—
171	C₂×C₄²	—	17	3	no	—
172	C₄⋊C₈	—	17	24	no	—
173	C₄×C₈	—	17	24	no	—
174	C₄×C₈	—	17	4	no	—
175	C₄×C₈	—	34	6	no	—
176	C₄×C₈	—	34	12	no	—
177	#95	—	17	6	no	—
178	C₁₇	C₄×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
179	C₂×Q₈	—	17	4	no	—
180	C₂×Q₈	—	17	4	no	—
181	C₂×Q₈	—	17	3	no	—
182	C₂×Q₈	C₂×#3633	1	1	yes	characteristic
183	C₂²×C₄	—	17	1	no	—
184	C₂²×C₄	—	17	1	no	—
185	C₂²×C₄	—	17	3	no	—
186	C₂²×C₄	—	17	1	no	—
187	C₂²×C₄	—	17	3	no	—
188	C₂²×C₄	—	17	3	no	—
189	C₂²×C₄	—	17	3	no	—
190	C₂×C₈	—	17	4	no	—
191	C₂×C₈	—	17	4	no	—
192	C₂×C₈	—	17	4	no	—
193	C₂×C₈	—	17	12	no	—
194	C₂×C₈	—	34	6	no	—
195	C₂×C₈	—	34	6	no	—
196	C₄⋊C₄	—	17	12	no	—
197	C₄⋊C₄	—	17	12	no	—
198	C₄⋊C₄	—	17	6	no	—
199	C₄⋊C₄	—	17	3	no	—
200	C₄⋊C₄	C₂×#3633	1	3	yes	—
201	C₄²	—	17	12	no	—
202	C₄²	—	17	12	no	—
203	C₄²	—	17	2	no	—
204	C₄²	—	17	2	no	—
205	C₄²	—	17	3	no	—
206	C₄²	—	17	3	no	—
207	C₄²	—	17	3	no	—
208	C₄²	—	34	6	no	—
209	C₄²	—	34	6	no	—
210	C₄²	—	34	6	no	—
211	C₄²	C₂×#3633	1	3	yes	—
212	C₂³	—	17	1	no	—
213	Q₈	—	17	12	no	—
214	Q₈	C₄×#3633	1	4	yes	direct product factor
215	C₂×C₄	—	17	2	no	—
216	C₂×C₄	—	17	2	no	—
217	C₂×C₄	—	17	1	no	—
218	C₂×C₄	—	17	1	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	3	no	—
224	C₂×C₄	—	17	6	no	—
225	C₂×C₄	—	17	6	no	—
226	C₂×C₄	—	17	2	no	—
227	C₂×C₄	—	17	2	no	—
228	C₂×C₄	—	17	6	no	—
229	C₂×C₄	—	17	6	no	—
230	C₂×C₄	—	17	3	no	—
231	C₂×C₄	—	34	3	no	—
232	C₂×C₄	—	34	3	no	—
233	C₂×C₄	—	34	3	no	—
234	C₂×C₄	—	34	3	no	—
235	C₂×C₄	—	34	3	no	—
236	C₂×C₄	—	34	3	no	—
237	C₂×C₄	C₂²×#3633	1	3	yes	—
238	C₂×C₄	C₂²×#3633	1	3	yes	—
239	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
240	C₈	—	17	8	no	—
241	C₈	—	34	12	no	—
242	C₂²	—	17	1	no	—
243	C₂²	—	17	1	no	—
244	C₂²	—	17	1	no	—
245	C₂²	—	17	1	no	—
246	C₂²	—	17	1	no	—
247	C₂²	—	17	1	no	—
248	C₂²	C₂³×#3633	1	1	yes	characteristic
249	C₄	—	2	3	no	—
250	C₄	—	17	2	no	—
251	C₄	—	17	2	no	—
252	C₄	—	17	4	no	—
253	C₄	—	17	6	no	—
254	C₄	—	17	2	no	—
255	C₄	—	34	6	no	—
256	C₄	—	34	6	no	—
257	C₄	—	34	3	no	—
258	C₄	C₂×C₄×#3633	1	6	yes	—
259	C₄	Q₈×#3633	1	2	yes	direct product factor
260	C₂	—	17	1	no	—
261	C₂	—	17	1	no	—
262	C₂	—	17	1	no	—
263	C₂	—	17	1	no	—
264	C₂	C₂²×C₄×#3633	1	1	yes	characteristic
265	C₂	C₂×Q₈×#3633	1	1	yes	characteristic
266	C₂	#41×#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#3633
commutator	C₂×C₁₇	C₂²×C₄×C₈
Frattini	C₂²	C₂³×#3633
Fitting	C₄×Q₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂³×C₈
prime radical	C₂²×D₁₇	C₂³×C₄
cosocle	C₂²×#595	C₂⁴
hypercenter	C₄×Q₈	#3633
hypocenter	C₁₇	C₄×C₈×Q₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
6. Q₈×#3633	C₄	direct (N × H)
23. Q₈×#595	C₈	semidirect
37. C₄×#3633	Q₈	direct (N × H)
38. C₄×Q₈×C₁₇	C₈	semidirect
39. Q₈×Dic₁₇	C₈	semidirect
41. #10587573	C₈	semidirect
43. C₄×Dic₃₄	C₈	semidirect
94. #3633	C₄×Q₈	direct (N × H)
95. Q₈×C₁₇	C₄×C₈	semidirect
108. Dic₃₄	C₄×C₈	semidirect
123. #595	C₈×Q₈	semidirect
128. C₄×C₁₇	C₈×Q₈	semidirect
131. Dic₁₇	C₈×Q₈	semidirect
161. C₄×Q₈	#3633	direct (N × H)
178. C₁₇	C₄×C₈×Q₈	semidirect
214. Q₈	C₄×#3633	direct (N × H)
259. C₄	Q₈×#3633	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×Q₈×#3633	2
C₄⋊C₄×#3633	2
C₄×C₄⋊#3633	2
C₄²×#3633	2
C₄×Q₈×#595	2
C₄×C₈×Q₈	17

Subgroups — C4×Q8×#3633 #17982886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×#3633 #17982886