Subgroups — C₂×D₁₇×#518 #17940901

Order 4352.

14590 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763284	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11763283	C₂	1	2	yes	maximal, complemented
4	C₂×#11763282	C₂	1	4	yes	maximal, complemented
5	C₂×#11763281	C₂	1	8	yes	maximal, complemented
6	D₁₇×#518	C₂	1	32	yes	maximal, direct product factor
7	C₂×C₄×D₄×D₁₇	C₂	1	8	yes	maximal, complemented
8	C₂×#117×D₁₇	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₁₇	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₇	C₂²	1	2	yes	—
12	C₂³×D₆₈	C₂²	1	1	yes	characteristic
13	C₂³×C₂²⋊D₁₇	C₂²	1	2	yes	—
14	C₂²×D₄×D₁₇	C₄	1	32	yes	complemented
15	C₂²×D₄×D₁₇	C₂²	1	4	yes	—
16	C₂²×D₄×D₁₇	C₂²	1	16	yes	—
17	C₂²×D₄×D₁₇	C₂²	1	4	yes	—
18	C₂³×C₄×D₁₇	C₂²	1	1	yes	characteristic
19	C₂³×C₄×D₁₇	C₂²	1	8	yes	complemented
20	#11763284	C₂²	1	16	yes	complemented
21	#11763283	C₂²	1	32	yes	complemented
22	#11763282	C₂²	1	64	yes	complemented
23	#11763281	C₂²	1	128	yes	complemented
24	C₂×C₄×D₆₈	C₂²	1	8	yes	complemented
25	C₂×D₄×Dic₁₇	C₂²	1	8	yes	complemented
26	C₂×#10587579	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₁₇	C₂²	1	16	yes	complemented
28	C₂×#10587567	C₂²	1	16	yes	complemented
29	C₄×D₄×D₁₇	C₂²	1	128	yes	complemented
30	C₂×#10587612	C₂²	1	2	yes	complemented
31	C₂×#10587578	C₂²	1	4	yes	complemented
32	C₂×#10587558	C₂²	1	4	yes	complemented
33	C₂×#10587563	C₂²	1	4	yes	complemented
34	#117×D₁₇	C₂²	1	32	yes	complemented
35	C₂×C₄⋊C₄×D₁₇	C₂²	1	4	yes	complemented
36	C₂²×C₂²⋊Dic₁₇	C₂²	1	4	yes	complemented
37	C₂²×#63227	C₂²	1	8	yes	complemented
38	C₂×C₂²⋊C₄×D₁₇	C₂²	1	4	yes	—
39	C₂×C₂²⋊C₄×D₁₇	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊C₄×D₁₇	C₂²	1	64	yes	complemented
41	C₂×C₂²⋊C₄×D₁₇	C₂²	1	8	yes	complemented
42	C₂×C₂²⋊C₄×D₁₇	C₂²	1	8	yes	complemented
43	C₂×C₄²×D₁₇	C₂²	1	4	yes	complemented
44	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
45	C₁₇×#518	C₂²	1	16	yes	complemented
46	C₂×C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
47	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
49	C₂⁵×C₁₇	C₂³	1	2	yes	—
50	C₂⁴×D₁₇	—	4	16	no	—
51	C₂⁴×D₁₇	C₂×C₄	1	32	yes	complemented
52	C₂⁴×D₁₇	C₂³	1	1	yes	characteristic
53	C₂⁴×D₁₇	C₂³	1	4	yes	—
54	C₂⁴×D₁₇	C₂³	1	16	yes	—
55	C₂⁴×D₁₇	C₂³	1	2	yes	—
56	C₂⁴×D₁₇	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₇	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
60	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	C₂³	1	8	yes	complemented
62	C₂²×C₂²⋊D₁₇	C₂×C₄	1	32	yes	complemented
63	C₂²×C₂²⋊D₁₇	C₂³	1	8	yes	—
64	C₂²×C₂²⋊D₁₇	C₂³	1	16	yes	—
65	C₂³×Dic₁₇	C₂³	1	1	yes	characteristic
66	C₂³×Dic₁₇	C₂³	1	8	yes	complemented
67	C₂×D₄×D₁₇	C₂×C₄	1	64	yes	complemented
68	C₂×D₄×D₁₇	C₂×C₄	1	256	yes	complemented
69	C₂×D₄×D₁₇	C₂×C₄	1	64	yes	complemented
70	C₂×D₄×D₁₇	C₂³	1	32	yes	—
71	C₂×D₄×D₁₇	C₂³	1	32	yes	—
72	C₂²×D₆₈	C₂×C₄	1	16	yes	complemented
73	C₂²×D₆₈	C₂³	1	4	yes	—
74	C₂²×D₆₈	C₂³	1	8	yes	—
75	C₂²×C₄×D₁₇	—	4	32	no	—
76	C₂²×C₄×D₁₇	C₂×C₄	1	16	yes	complemented
77	C₂²×C₄×D₁₇	C₂³	1	8	yes	—
78	C₂²×C₄×D₁₇	C₂³	1	2	yes	—
79	C₂²×C₄×D₁₇	C₂³	1	8	yes	—
80	C₂²×C₄×D₁₇	C₂³	1	2	yes	—
81	C₂²×C₄×D₁₇	C₂³	1	64	yes	complemented
82	C₂²×C₄×D₁₇	C₂³	1	16	yes	complemented
83	C₄×D₄×C₁₇	C₂³	1	64	yes	complemented
84	C₁₇×#117	C₂³	1	16	yes	complemented
85	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	complemented
86	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₇	C₂³	1	32	yes	complemented
88	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
89	C₂×C₄²×C₁₇	C₂³	1	4	yes	complemented
90	C₂×C₂²⋊Dic₁₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊Dic₁₇	C₂³	1	32	yes	complemented
92	C₂×C₂²⋊Dic₁₇	C₂³	1	8	yes	complemented
93	D₄×Dic₁₇	C₂³	1	64	yes	complemented
94	C₄×C₂²⋊D₁₇	C₂³	1	128	yes	complemented
95	C₂×#63227	C₂³	1	8	yes	—
96	C₂×#63227	C₂³	1	16	yes	complemented
97	C₂×#63227	C₂³	1	64	yes	complemented
98	#10587612	C₂³	1	16	yes	complemented
99	C₂×C₄⋊Dic₁₇	C₂³	1	4	yes	complemented
100	C₂×#63225	C₂³	1	8	yes	complemented
101	C₂×C₄×Dic₁₇	C₂³	1	8	yes	complemented
102	C₂×C₄×Dic₁₇	C₂³	1	4	yes	complemented
103	#10587579	C₂³	1	64	yes	complemented
104	#10587578	C₂³	1	32	yes	complemented
105	C₄⋊C₄×D₁₇	C₂³	1	32	yes	complemented
106	#10587567	C₂³	1	128	yes	complemented
107	C₂²⋊C₄×D₁₇	C₂³	1	32	yes	—
108	C₂²⋊C₄×D₁₇	C₂³	1	64	yes	complemented
109	C₂²⋊C₄×D₁₇	C₂³	1	64	yes	complemented
110	C₂²⋊C₄×D₁₇	C₂³	1	64	yes	complemented
111	#10587563	C₂³	1	32	yes	complemented
112	C₄×D₆₈	C₂³	1	64	yes	complemented
113	#10587558	C₂³	1	32	yes	complemented
114	C₄²×D₁₇	C₂³	1	32	yes	complemented
115	C₂⁴×C₁₇	—	4	8	no	—
116	C₂⁴×C₁₇	C₂²×C₄	1	16	yes	complemented
117	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
118	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
119	C₂⁴×C₁₇	C₂⁴	1	8	yes	—
120	C₂³×D₁₇	—	2	32	no	—
121	C₂³×D₁₇	—	2	8	no	—
122	C₂³×D₁₇	—	4	128	no	—
123	C₂³×D₁₇	—	4	64	no	—
124	C₂³×D₁₇	—	4	8	no	—
125	C₂³×D₁₇	—	4	16	no	—
126	C₂³×D₁₇	C₂²×C₄	1	8	yes	—
127	C₂³×D₁₇	C₂²×C₄	1	32	yes	—
128	C₂³×D₁₇	C₂²×C₄	1	128	yes	complemented
129	C₂³×D₁₇	C₂²×C₄	1	16	yes	complemented
130	C₂³×D₁₇	C₂²×C₄	1	32	yes	complemented
131	C₂³×D₁₇	C₂⁴	1	4	yes	—
132	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
133	C₂³×D₁₇	C₂⁴	1	4	yes	—
134	C₂³×D₁₇	C₂⁴	1	16	yes	—
135	C₂³×D₁₇	C₂⁴	1	8	yes	—
136	C₂³×D₁₇	C₂⁴	1	16	yes	—
137	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₇	C₂²×C₄	1	32	yes	complemented
139	C₂×D₄×C₁₇	C₂²×C₄	1	64	yes	complemented
140	C₂×D₄×C₁₇	C₂⁴	1	16	yes	—
141	C₂²×C₄×C₁₇	—	4	16	no	—
142	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	complemented
143	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₇	C₂⁴	1	32	yes	complemented
147	C₂×C₂²⋊D₁₇	C₂²×C₄	1	64	yes	complemented
148	C₂×C₂²⋊D₁₇	C₂²×C₄	1	128	yes	complemented
149	C₂×C₂²⋊D₁₇	C₂⁴	1	32	yes	—
150	C₂²×Dic₁₇	—	4	16	no	—
151	C₂²×Dic₁₇	C₂²×C₄	1	8	yes	complemented
152	C₂²×Dic₁₇	C₂⁴	1	8	yes	—
153	C₂²×Dic₁₇	C₂⁴	1	2	yes	—
154	C₂²×Dic₁₇	C₂⁴	1	4	yes	—
155	C₂²×Dic₁₇	C₂⁴	1	32	yes	complemented
156	D₄×D₁₇	C₂²×C₄	1	256	yes	complemented
157	D₄×D₁₇	C₂²×C₄	1	256	yes	complemented
158	C₂×D₆₈	C₂²×C₄	1	32	yes	complemented
159	C₂×D₆₈	C₂²×C₄	1	64	yes	complemented
160	C₂×D₆₈	C₂⁴	1	16	yes	—
161	C₂×C₄×D₁₇	—	2	32	no	—
162	C₂×C₄×D₁₇	—	4	128	no	—
163	C₂×C₄×D₁₇	—	4	32	no	—
164	C₂×C₄×D₁₇	C₂²×C₄	1	16	yes	—
165	C₂×C₄×D₁₇	C₂²×C₄	1	64	yes	complemented
166	C₂×C₄×D₁₇	C₂²×C₄	1	16	yes	complemented
167	C₂×C₄×D₁₇	C₂⁴	1	32	yes	—
168	C₂×C₄×D₁₇	C₂⁴	1	8	yes	—
169	C₂×C₄×D₁₇	C₂⁴	1	8	yes	—
170	C₂×C₄×D₁₇	C₂⁴	1	64	yes	complemented
171	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	complemented
172	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
173	C₂²⋊C₄×C₁₇	C₂⁴	1	32	yes	complemented
174	C₄²×C₁₇	C₂⁴	1	16	yes	complemented
175	C₂²⋊Dic₁₇	C₂⁴	1	16	yes	—
176	C₂²⋊Dic₁₇	C₂⁴	1	32	yes	complemented
177	#63227	C₂⁴	1	32	yes	—
178	#63227	C₂⁴	1	64	yes	complemented
179	C₄⋊Dic₁₇	C₂⁴	1	16	yes	complemented
180	#63225	C₂⁴	1	32	yes	complemented
181	C₄×Dic₁₇	C₂⁴	1	16	yes	complemented
182	C₄×Dic₁₇	C₂⁴	1	32	yes	complemented
183	C₂²×#518	—	17	1	no	maximal, Sylow
184	C₂³×C₁₇	—	2	16	no	—
185	C₂³×C₁₇	—	2	4	no	—
186	C₂³×C₁₇	—	4	32	no	—
187	C₂³×C₁₇	—	4	16	no	—
188	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
189	C₂³×C₁₇	C₂³×C₄	1	16	yes	—
190	C₂³×C₁₇	C₂³×C₄	1	32	yes	complemented
191	C₂³×C₁₇	C₂⁵	1	2	yes	—
192	C₂³×C₁₇	C₂⁵	1	8	yes	—
193	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
194	C₂²×D₁₇	—	2	16	no	—
195	C₂²×D₁₇	—	2	4	no	—
196	C₂²×D₁₇	—	2	32	no	—
197	C₂²×D₁₇	—	2	128	no	—
198	C₂²×D₁₇	—	2	64	no	—
199	C₂²×D₁₇	—	2	16	no	—
200	C₂²×D₁₇	—	4	256	no	—
201	C₂²×D₁₇	—	4	64	no	—
202	C₂²×D₁₇	—	4	32	no	—
203	C₂²×D₁₇	—	4	16	no	—
204	C₂²×D₁₇	—	4	32	no	—
205	C₂²×D₁₇	C₂³×C₄	1	4	yes	—
206	C₂²×D₁₇	C₂³×C₄	1	16	yes	—
207	C₂²×D₁₇	C₂³×C₄	1	16	yes	—
208	C₂²×D₁₇	C₂³×C₄	1	64	yes	—
209	C₂²×D₁₇	C₂³×C₄	1	4	yes	—
210	C₂²×D₁₇	C₂³×C₄	1	32	yes	complemented
211	C₂²×D₁₇	C₂³×C₄	1	64	yes	complemented
212	C₂²×D₁₇	H(5,𝔽₂)	1	8	yes	—
213	C₂²×D₁₇	C₂⁵	1	2	yes	—
214	C₂²×D₁₇	C₂⁵	1	8	yes	—
215	C₂²×D₁₇	C₂⁵	1	2	yes	—
216	D₄×C₁₇	C₂³×C₄	1	64	yes	complemented
217	C₂×C₄×C₁₇	—	2	16	no	—
218	C₂×C₄×C₁₇	—	4	32	no	—
219	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
220	C₂×C₄×C₁₇	C₂³×C₄	1	16	yes	complemented
221	C₂×C₄×C₁₇	C₂⁵	1	16	yes	—
222	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
223	C₂²⋊D₁₇	C₂³×C₄	1	128	yes	complemented
224	C₂×Dic₁₇	—	2	16	no	—
225	C₂×Dic₁₇	—	4	32	no	—
226	C₂×Dic₁₇	C₂³×C₄	1	8	yes	—
227	C₂×Dic₁₇	C₂³×C₄	1	16	yes	complemented
228	C₂×Dic₁₇	C₂⁵	1	16	yes	—
229	C₂×Dic₁₇	C₂⁵	1	4	yes	—
230	D₆₈	C₂³×C₄	1	64	yes	complemented
231	C₄×D₁₇	—	2	64	no	—
232	C₄×D₁₇	—	4	64	no	—
233	C₄×D₁₇	C₂³×C₄	1	32	yes	—
234	C₄×D₁₇	C₂³×C₄	1	32	yes	complemented
235	C₂⁴×D₄	—	17	1	no	—
236	C₂×#518	—	17	1	no	—
237	C₂×#518	—	17	32	no	—
238	C₂×#518	—	17	8	no	—
239	C₂×#518	—	17	2	no	—
240	C₂×#518	—	17	4	no	—
241	C₂×#518	D₁₇	1	1	yes	characteristic, direct product factor
242	C₂²×C₄×D₄	—	17	8	no	—
243	C₂²×#117	—	17	2	no	—
244	C₂³×C₂²⋊C₄	—	17	4	no	—
245	C₂²×C₁₇	—	2	16	no	—
246	C₂²×C₁₇	—	2	4	no	—
247	C₂²×C₁₇	—	2	8	no	—
248	C₂²×C₁₇	—	2	32	no	—
249	C₂²×C₁₇	—	4	32	no	—
250	C₂²×C₁₇	C₂⁴×C₄	1	4	yes	—
251	C₂²×C₁₇	C₂⁴×C₄	1	16	yes	—
252	C₂²×C₁₇	C₂⁴×C₄	1	2	yes	—
253	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	4	yes	—
254	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
255	C₂×D₁₇	—	2	16	no	—
256	C₂×D₁₇	—	2	4	no	—
257	C₂×D₁₇	—	2	8	no	—
258	C₂×D₁₇	—	2	32	no	—
259	C₂×D₁₇	—	2	32	no	—
260	C₂×D₁₇	—	2	128	no	—
261	C₂×D₁₇	—	4	64	no	—
262	C₂×D₁₇	—	4	32	no	—
263	C₂×D₁₇	#518	1	16	yes	direct product factor
264	C₂×D₁₇	C₂⁴×C₄	1	4	yes	—
265	C₂×D₁₇	C₂⁴×C₄	1	16	yes	—
266	C₂×D₁₇	C₂⁴×C₄	1	4	yes	—
267	C₂×D₁₇	C₂×H(5,𝔽₂)	1	8	yes	—
268	C₄×C₁₇	—	2	16	no	—
269	C₄×C₁₇	C₂⁴×C₄	1	8	yes	—
270	Dic₁₇	—	2	16	no	—
271	Dic₁₇	C₂⁴×C₄	1	8	yes	—
272	C₂⁶	—	17	2	no	—
273	C₂³×D₄	—	17	2	no	—
274	C₂³×D₄	—	17	32	no	—
275	C₂³×D₄	—	17	4	no	—
276	C₂³×D₄	—	17	4	no	—
277	C₂³×D₄	—	17	16	no	—
278	C₂³×D₄	—	17	1	no	—
279	C₂³×D₄	C₂×D₁₇	1	1	yes	characteristic
280	C₂⁴×C₄	—	17	1	no	—
281	C₂⁴×C₄	—	17	8	no	—
282	#518	—	17	16	no	—
283	#518	—	17	128	no	—
284	#518	—	17	32	no	—
285	#518	—	17	64	no	—
286	#518	C₂×D₁₇	1	16	yes	direct product factor
287	C₂×C₄×D₄	—	17	8	no	—
288	C₂×C₄×D₄	—	17	16	no	—
289	C₂×C₄×D₄	—	17	128	no	—
290	C₂×C₄×D₄	—	17	8	no	—
291	C₂×C₄×D₄	—	17	16	no	—
292	C₂×C₄×D₄	—	17	8	no	—
293	C₂×C₄×D₄	C₂×D₁₇	1	8	yes	complemented
294	C₂×#117	—	17	2	no	—
295	C₂×#117	—	17	32	no	—
296	C₂×#117	—	17	4	no	—
297	C₂×#117	—	17	4	no	—
298	C₂×#117	—	17	4	no	—
299	C₂×#117	C₂×D₁₇	1	2	yes	complemented
300	C₂²×C₄⋊C₄	—	17	4	no	—
301	C₂²×C₂²⋊C₄	—	17	4	no	—
302	C₂²×C₂²⋊C₄	—	17	8	no	—
303	C₂²×C₂²⋊C₄	—	17	4	no	—
304	C₂²×C₂²⋊C₄	—	17	8	no	—
305	C₂²×C₂²⋊C₄	—	17	8	no	—
306	C₂²×C₂²⋊C₄	—	17	8	no	—
307	C₂²×C₂²⋊C₄	—	17	64	no	—
308	C₂²×C₂²⋊C₄	C₂×D₁₇	1	4	yes	complemented
309	C₂²×C₄²	—	17	4	no	—
310	C₂×C₁₇	—	2	4	no	—
311	C₂×C₁₇	—	2	16	no	—
312	C₂×C₁₇	C₂×#518	1	4	yes	complemented
313	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
314	C₂×C₁₇	C₂²×H(5,𝔽₂)	1	2	yes	—
315	D₁₇	—	2	4	no	—
316	D₁₇	—	2	16	no	—
317	D₁₇	C₂×#518	1	8	yes	direct product factor
318	C₂⁵	—	17	1	no	—
319	C₂⁵	—	17	4	no	—
320	C₂⁵	—	17	32	no	—
321	C₂⁵	—	17	16	no	—
322	C₂⁵	—	17	4	no	—
323	C₂⁵	—	17	2	no	—
324	C₂⁵	—	68	16	no	—
325	C₂⁵	C₂²×D₁₇	1	2	yes	—
326	C₂²×D₄	—	17	32	no	—
327	C₂²×D₄	—	17	8	no	—
328	C₂²×D₄	—	17	16	no	—
329	C₂²×D₄	—	17	64	no	—
330	C₂²×D₄	—	17	64	no	—
331	C₂²×D₄	—	17	256	no	—
332	C₂²×D₄	—	17	32	no	—
333	C₂²×D₄	—	17	32	no	—
334	C₂²×D₄	—	17	16	no	—
335	C₂²×D₄	—	17	4	no	—
336	C₂²×D₄	—	17	8	no	—
337	C₂²×D₄	C₄×D₁₇	1	16	yes	complemented
338	C₂²×D₄	C₂²×D₁₇	1	4	yes	—
339	C₂²×D₄	C₂²×D₁₇	1	8	yes	—
340	C₂³×C₄	—	17	1	no	—
341	C₂³×C₄	—	17	16	no	—
342	C₂³×C₄	—	17	2	no	—
343	C₂³×C₄	—	17	8	no	—
344	C₂³×C₄	—	17	2	no	—
345	C₂³×C₄	—	17	8	no	—
346	C₂³×C₄	—	17	8	no	—
347	C₂³×C₄	—	17	16	no	—
348	C₂³×C₄	—	17	64	no	—
349	C₂³×C₄	—	68	32	no	—
350	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
351	C₂³×C₄	C₂²×D₁₇	1	8	yes	complemented
352	C₄×D₄	—	17	64	no	—
353	C₄×D₄	—	17	128	no	—
354	C₄×D₄	—	17	64	no	—
355	C₄×D₄	—	17	128	no	—
356	C₄×D₄	—	17	64	no	—
357	C₄×D₄	C₂²×D₁₇	1	64	yes	complemented
358	#117	—	17	16	no	—
359	#117	—	17	32	no	—
360	#117	—	17	32	no	—
361	#117	—	17	32	no	—
362	#117	C₂²×D₁₇	1	16	yes	complemented
363	C₂×C₄⋊C₄	—	17	8	no	—
364	C₂×C₄⋊C₄	—	17	4	no	—
365	C₂×C₄⋊C₄	—	17	32	no	—
366	C₂×C₄⋊C₄	C₂²×D₁₇	1	4	yes	complemented
367	C₂×C₂²⋊C₄	—	17	4	no	—
368	C₂×C₂²⋊C₄	—	17	8	no	—
369	C₂×C₂²⋊C₄	—	17	32	no	—
370	C₂×C₂²⋊C₄	—	17	8	no	—
371	C₂×C₂²⋊C₄	—	17	16	no	—
372	C₂×C₂²⋊C₄	—	17	64	no	—
373	C₂×C₂²⋊C₄	—	17	32	no	—
374	C₂×C₂²⋊C₄	—	17	64	no	—
375	C₂×C₂²⋊C₄	—	17	64	no	—
376	C₂×C₂²⋊C₄	—	17	64	no	—
377	C₂×C₂²⋊C₄	C₂²×D₁₇	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂²×D₁₇	1	32	yes	complemented
379	C₂×C₂²⋊C₄	C₂²×D₁₇	1	8	yes	complemented
380	C₂×C₄²	—	17	8	no	—
381	C₂×C₄²	—	17	4	no	—
382	C₂×C₄²	—	17	32	no	—
383	C₂×C₄²	C₂²×D₁₇	1	4	yes	complemented
384	C₁₇	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
385	C₂⁴	—	4	8	no	—
386	C₂⁴	—	17	1	no	—
387	C₂⁴	—	17	8	no	—
388	C₂⁴	—	17	32	no	—
389	C₂⁴	—	17	4	no	—
390	C₂⁴	—	17	16	no	—
391	C₂⁴	—	17	1	no	—
392	C₂⁴	—	17	4	no	—
393	C₂⁴	—	17	32	no	—
394	C₂⁴	—	17	16	no	—
395	C₂⁴	—	17	128	no	—
396	C₂⁴	—	17	16	no	—
397	C₂⁴	—	17	8	no	—
398	C₂⁴	—	34	32	no	—
399	C₂⁴	—	34	8	no	—
400	C₂⁴	—	68	16	no	—
401	C₂⁴	—	68	8	no	—
402	C₂⁴	—	68	128	no	—
403	C₂⁴	—	68	64	no	—
404	C₂⁴	C₂×C₄×D₁₇	1	16	yes	complemented
405	C₂⁴	C₂³×D₁₇	1	1	yes	characteristic
406	C₂⁴	C₂³×D₁₇	1	4	yes	—
407	C₂⁴	C₂³×D₁₇	1	8	yes	—
408	C₂×D₄	—	17	64	no	—
409	C₂×D₄	—	17	128	no	—
410	C₂×D₄	—	17	32	no	—
411	C₂×D₄	—	17	256	no	—
412	C₂×D₄	—	17	256	no	—
413	C₂×D₄	—	17	32	no	—
414	C₂×D₄	—	17	64	no	—
415	C₂×D₄	—	17	16	no	—
416	C₂×D₄	C₂×C₄×D₁₇	1	32	yes	complemented
417	C₂×D₄	C₂×C₄×D₁₇	1	64	yes	complemented
418	C₂×D₄	C₂³×D₁₇	1	16	yes	—
419	C₂²×C₄	—	4	16	no	—
420	C₂²×C₄	—	17	8	no	—
421	C₂²×C₄	—	17	4	no	—
422	C₂²×C₄	—	17	2	no	—
423	C₂²×C₄	—	17	16	no	—
424	C₂²×C₄	—	17	16	no	—
425	C₂²×C₄	—	17	64	no	—
426	C₂²×C₄	—	17	8	no	—
427	C₂²×C₄	—	17	8	no	—
428	C₂²×C₄	—	17	8	no	—
429	C₂²×C₄	—	17	32	no	—
430	C₂²×C₄	—	17	32	no	—
431	C₂²×C₄	—	17	64	no	—
432	C₂²×C₄	—	34	32	no	—
433	C₂²×C₄	—	68	32	no	—
434	C₂²×C₄	—	68	128	no	—
435	C₂²×C₄	—	68	16	no	—
436	C₂²×C₄	C₂×C₄×D₁₇	1	8	yes	complemented
437	C₂²×C₄	C₂³×D₁₇	1	8	yes	—
438	C₂²×C₄	C₂³×D₁₇	1	2	yes	—
439	C₂²×C₄	C₂³×D₁₇	1	4	yes	—
440	C₂²×C₄	C₂³×D₁₇	1	32	yes	complemented
441	C₄⋊C₄	—	17	32	no	—
442	C₄⋊C₄	—	17	16	no	—
443	C₄⋊C₄	C₂³×D₁₇	1	16	yes	complemented
444	C₂²⋊C₄	—	17	16	no	—
445	C₂²⋊C₄	—	17	32	no	—
446	C₂²⋊C₄	—	17	32	no	—
447	C₂²⋊C₄	—	17	64	no	—
448	C₂²⋊C₄	C₂³×D₁₇	1	16	yes	—
449	C₂²⋊C₄	C₂³×D₁₇	1	32	yes	complemented
450	C₄²	—	17	32	no	—
451	C₄²	—	17	16	no	—
452	C₄²	C₂³×D₁₇	1	16	yes	complemented
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	4	32	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	17	4	no	—
458	C₂³	—	17	8	no	—
459	C₂³	—	17	2	no	—
460	C₂³	—	17	16	no	—
461	C₂³	—	17	4	no	—
462	C₂³	—	17	64	no	—
463	C₂³	—	17	16	no	—
464	C₂³	—	17	2	no	—
465	C₂³	—	17	8	no	—
466	C₂³	—	17	64	no	—
467	C₂³	—	17	32	no	—
468	C₂³	—	34	64	no	—
469	C₂³	—	34	32	no	—
470	C₂³	—	34	16	no	—
471	C₂³	—	34	128	no	—
472	C₂³	—	34	16	no	—
473	C₂³	—	34	4	no	—
474	C₂³	—	68	32	no	—
475	C₂³	—	68	64	no	—
476	C₂³	—	68	32	no	—
477	C₂³	—	68	16	no	—
478	C₂³	—	68	256	no	—
479	C₂³	C₂²×C₄×D₁₇	1	4	yes	—
480	C₂³	C₂²×C₄×D₁₇	1	16	yes	—
481	C₂³	C₂²×C₄×D₁₇	1	32	yes	complemented
482	C₂³	C₂⁴×D₁₇	1	2	yes	—
483	C₂³	C₂⁴×D₁₇	1	8	yes	—
484	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
485	D₄	—	17	128	no	—
486	D₄	—	17	64	no	—
487	D₄	C₂²×C₄×D₁₇	1	64	yes	complemented
488	C₂×C₄	—	2	16	no	—
489	C₂×C₄	—	4	32	no	—
490	C₂×C₄	—	17	8	no	—
491	C₂×C₄	—	17	16	no	—
492	C₂×C₄	—	17	4	no	—
493	C₂×C₄	—	17	32	no	—
494	C₂×C₄	—	17	32	no	—
495	C₂×C₄	—	17	16	no	—
496	C₂×C₄	—	34	64	no	—
497	C₂×C₄	—	34	16	no	—
498	C₂×C₄	—	68	64	no	—
499	C₂×C₄	—	68	32	no	—
500	C₂×C₄	C₂²×C₄×D₁₇	1	8	yes	—
501	C₂×C₄	C₂²×C₄×D₁₇	1	16	yes	complemented
502	C₂×C₄	C₂⁴×D₁₇	1	16	yes	—
503	C₂×C₄	C₂⁴×D₁₇	1	4	yes	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	32	no	—
506	C₂²	—	2	16	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	4	32	no	—
509	C₂²	—	17	16	no	—
510	C₂²	—	17	4	no	—
511	C₂²	—	17	8	no	—
512	C₂²	—	17	4	no	—
513	C₂²	—	17	16	no	—
514	C₂²	—	34	32	no	—
515	C₂²	—	34	128	no	—
516	C₂²	—	34	8	no	—
517	C₂²	—	34	32	no	—
518	C₂²	—	34	16	no	—
519	C₂²	—	34	4	no	—
520	C₂²	—	68	32	no	—
521	C₂²	—	68	64	no	—
522	C₂²	C₂³×C₄×D₁₇	1	4	yes	—
523	C₂²	C₂³×C₄×D₁₇	1	16	yes	—
524	C₂²	C₂³×C₄×D₁₇	1	2	yes	—
525	C₂²	H(5,𝔽₂)×D₁₇	1	4	yes	—
526	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
527	C₄	—	2	16	no	—
528	C₄	—	17	8	no	—
529	C₄	—	34	16	no	—
530	C₄	C₂³×C₄×D₁₇	1	8	yes	—
531	C₂	—	2	4	no	—
532	C₂	—	2	16	no	—
533	C₂	—	17	8	no	—
534	C₂	—	34	4	no	—
535	C₂	—	34	16	no	—
536	C₂	D₁₇×#518	1	4	yes	direct product factor
537	C₂	C₂⁴×C₄×D₁₇	1	1	yes	characteristic
538	C₂	C₂×H(5,𝔽₂)×D₁₇	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₇
commutator	C₂×C₁₇	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂×C₁₇×#518	C₂
socle	C₂³×C₁₇	C₂⁵
prime radical	C₂³×D₄×D₁₇	C₂
cosocle	C₂²×C₁₇	C₂⁶
hypercenter	C₂×#518	D₁₇
hypocenter	C₁₇	C₂²×#518
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
2. C₂×#11763284	C₂	semidirect
3. C₂×#11763283	C₂	semidirect
4. C₂×#11763282	C₂	semidirect
5. C₂×#11763281	C₂	semidirect
6. D₁₇×#518	C₂	direct (N × H)
7. C₂×C₄×D₄×D₁₇	C₂	semidirect
8. C₂×#117×D₁₇	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₁₇	C₂	semidirect
10. C₂×C₁₇×#518	C₂	semidirect
14. C₂²×D₄×D₁₇	C₄	semidirect
19. C₂³×C₄×D₁₇	C₂²	semidirect
20. #11763284	C₂²	semidirect
21. #11763283	C₂²	semidirect
22. #11763282	C₂²	semidirect
23. #11763281	C₂²	semidirect
24. C₂×C₄×D₆₈	C₂²	semidirect
25. C₂×D₄×Dic₁₇	C₂²	semidirect
26. C₂×#10587579	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
28. C₂×#10587567	C₂²	semidirect
29. C₄×D₄×D₁₇	C₂²	semidirect
30. C₂×#10587612	C₂²	semidirect
31. C₂×#10587578	C₂²	semidirect
32. C₂×#10587558	C₂²	semidirect
33. C₂×#10587563	C₂²	semidirect
34. #117×D₁₇	C₂²	semidirect
35. C₂×C₄⋊C₄×D₁₇	C₂²	semidirect
36. C₂²×C₂²⋊Dic₁₇	C₂²	semidirect
37. C₂²×#63227	C₂²	semidirect
39. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
40. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
41. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
42. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
43. C₂×C₄²×D₁₇	C₂²	semidirect
45. C₁₇×#518	C₂²	semidirect
46. C₂×C₄×D₄×C₁₇	C₂²	semidirect
47. C₂×C₁₇×#117	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₁₇	C₂²	semidirect
51. C₂⁴×D₁₇	C₂×C₄	semidirect
57. C₂²×D₄×C₁₇	C₂×C₄	semidirect
61. C₂³×C₄×C₁₇	C₂³	semidirect
62. C₂²×C₂²⋊D₁₇	C₂×C₄	semidirect
66. C₂³×Dic₁₇	C₂³	semidirect
67. C₂×D₄×D₁₇	C₂×C₄	semidirect
68. C₂×D₄×D₁₇	C₂×C₄	semidirect
69. C₂×D₄×D₁₇	C₂×C₄	semidirect
72. C₂²×D₆₈	C₂×C₄	semidirect
76. C₂²×C₄×D₁₇	C₂×C₄	semidirect
81. C₂²×C₄×D₁₇	C₂³	semidirect
82. C₂²×C₄×D₁₇	C₂³	semidirect
83. C₄×D₄×C₁₇	C₂³	semidirect
84. C₁₇×#117	C₂³	semidirect
85. C₂×C₄⋊C₄×C₁₇	C₂³	semidirect
87. C₂×C₂²⋊C₄×C₁₇	C₂³	semidirect
88. C₂×C₂²⋊C₄×C₁₇	C₂³	semidirect
89. C₂×C₄²×C₁₇	C₂³	semidirect
91. C₂×C₂²⋊Dic₁₇	C₂³	semidirect
92. C₂×C₂²⋊Dic₁₇	C₂³	semidirect
93. D₄×Dic₁₇	C₂³	semidirect
94. C₄×C₂²⋊D₁₇	C₂³	semidirect
96. C₂×#63227	C₂³	semidirect
97. C₂×#63227	C₂³	semidirect
98. #10587612	C₂³	semidirect
99. C₂×C₄⋊Dic₁₇	C₂³	semidirect
100. C₂×#63225	C₂³	semidirect
101. C₂×C₄×Dic₁₇	C₂³	semidirect
102. C₂×C₄×Dic₁₇	C₂³	semidirect
103. #10587579	C₂³	semidirect
104. #10587578	C₂³	semidirect
105. C₄⋊C₄×D₁₇	C₂³	semidirect
106. #10587567	C₂³	semidirect
108. C₂²⋊C₄×D₁₇	C₂³	semidirect
109. C₂²⋊C₄×D₁₇	C₂³	semidirect
110. C₂²⋊C₄×D₁₇	C₂³	semidirect
111. #10587563	C₂³	semidirect
112. C₄×D₆₈	C₂³	semidirect
113. #10587558	C₂³	semidirect
114. C₄²×D₁₇	C₂³	semidirect
116. C₂⁴×C₁₇	C₂²×C₄	semidirect
128. C₂³×D₁₇	C₂²×C₄	semidirect
129. C₂³×D₁₇	C₂²×C₄	semidirect
130. C₂³×D₁₇	C₂²×C₄	semidirect
138. C₂×D₄×C₁₇	C₂²×C₄	semidirect
139. C₂×D₄×C₁₇	C₂²×C₄	semidirect
142. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
146. C₂²×C₄×C₁₇	C₂⁴	semidirect
147. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
148. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
151. C₂²×Dic₁₇	C₂²×C₄	semidirect
155. C₂²×Dic₁₇	C₂⁴	semidirect
156. D₄×D₁₇	C₂²×C₄	semidirect
157. D₄×D₁₇	C₂²×C₄	semidirect
158. C₂×D₆₈	C₂²×C₄	semidirect
159. C₂×D₆₈	C₂²×C₄	semidirect
165. C₂×C₄×D₁₇	C₂²×C₄	semidirect
166. C₂×C₄×D₁₇	C₂²×C₄	semidirect
170. C₂×C₄×D₁₇	C₂⁴	semidirect
171. C₄⋊C₄×C₁₇	C₂⁴	semidirect
173. C₂²⋊C₄×C₁₇	C₂⁴	semidirect
174. C₄²×C₁₇	C₂⁴	semidirect
176. C₂²⋊Dic₁₇	C₂⁴	semidirect
178. #63227	C₂⁴	semidirect
179. C₄⋊Dic₁₇	C₂⁴	semidirect
180. #63225	C₂⁴	semidirect
181. C₄×Dic₁₇	C₂⁴	semidirect
182. C₄×Dic₁₇	C₂⁴	semidirect
190. C₂³×C₁₇	C₂³×C₄	semidirect
210. C₂²×D₁₇	C₂³×C₄	semidirect
211. C₂²×D₁₇	C₂³×C₄	semidirect
216. D₄×C₁₇	C₂³×C₄	semidirect
220. C₂×C₄×C₁₇	C₂³×C₄	semidirect
223. C₂²⋊D₁₇	C₂³×C₄	semidirect
227. C₂×Dic₁₇	C₂³×C₄	semidirect
230. D₆₈	C₂³×C₄	semidirect
234. C₄×D₁₇	C₂³×C₄	semidirect
241. C₂×#518	D₁₇	direct (N × H)
263. C₂×D₁₇	#518	direct (N × H)
286. #518	C₂×D₁₇	direct (N × H)
293. C₂×C₄×D₄	C₂×D₁₇	semidirect
299. C₂×#117	C₂×D₁₇	semidirect
308. C₂²×C₂²⋊C₄	C₂×D₁₇	semidirect
312. C₂×C₁₇	C₂×#518	semidirect
317. D₁₇	C₂×#518	direct (N × H)
337. C₂²×D₄	C₄×D₁₇	semidirect
351. C₂³×C₄	C₂²×D₁₇	semidirect
357. C₄×D₄	C₂²×D₁₇	semidirect
362. #117	C₂²×D₁₇	semidirect
366. C₂×C₄⋊C₄	C₂²×D₁₇	semidirect
378. C₂×C₂²⋊C₄	C₂²×D₁₇	semidirect
379. C₂×C₂²⋊C₄	C₂²×D₁₇	semidirect
383. C₂×C₄²	C₂²×D₁₇	semidirect
384. C₁₇	C₂²×#518	semidirect
404. C₂⁴	C₂×C₄×D₁₇	semidirect
416. C₂×D₄	C₂×C₄×D₁₇	semidirect
417. C₂×D₄	C₂×C₄×D₁₇	semidirect
436. C₂²×C₄	C₂×C₄×D₁₇	semidirect
440. C₂²×C₄	C₂³×D₁₇	semidirect
443. C₄⋊C₄	C₂³×D₁₇	semidirect
449. C₂²⋊C₄	C₂³×D₁₇	semidirect
452. C₄²	C₂³×D₁₇	semidirect
481. C₂³	C₂²×C₄×D₁₇	semidirect
487. D₄	C₂²×C₄×D₁₇	semidirect
501. C₂×C₄	C₂²×C₄×D₁₇	semidirect
536. C₂	D₁₇×#518	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₁₇	2
C₂×#11763284	2
C₂×#11763283	2
C₂×#11763282	2
C₂×#11763281	2
D₁₇×#518	2
C₂×C₄×D₄×D₁₇	2
C₂×#117×D₁₇	2
C₂²×C₂²⋊C₄×D₁₇	2
C₂×C₁₇×#518	2
C₂²×#518	17

Subgroups — C2×D17×#518 #17940901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₇×#518 #17940901