Subgroups — C₂×C₁₇×#3324 #16918888

Order 4352.

2566 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3324	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₇×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#450	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₇	—	2	1	no	—
14	C₂³×D₄×C₁₇	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
17	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	complemented
18	C₁₇×#556	—	2	4	no	—
19	C₁₇×#556	C₂²	1	8	yes	complemented
20	D₄²×C₁₇	—	2	4	no	—
21	D₄²×C₁₇	C₂²	1	8	yes	—
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#126	—	2	2	no	—
25	C₂×C₁₇×#124	—	2	1	no	—
26	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₇×#121	—	2	1	no	—
28	C₂×C₁₇×#121	C₂²	1	2	yes	—
29	C₂×C₁₇×#120	—	2	2	no	—
30	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
31	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
35	C₁₇×#486	C₂²	1	8	yes	complemented
36	C₁₇×#482	C₂²	1	16	yes	complemented
37	C₁₇×#474	C₂²	1	8	yes	complemented
38	C₁₇×#468	C₂²	1	16	yes	complemented
39	C₁₇×#460	C₂²	1	8	yes	complemented
40	C₁₇×#450	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₁₇	C₂²	1	8	yes	complemented
42	C₁₇×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₇×#107	C₂²	1	2	yes	complemented
44	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#418	C₂²	1	16	yes	complemented
47	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₇×#102	C₂²	1	2	yes	—
49	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
51	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
52	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
53	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₂⁵×C₁₇	—	2	2	no	—
56	C₂²×Q₈×C₁₇	—	2	1	no	—
57	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₇	—	2	8	no	—
59	C₂²×D₄×C₁₇	—	2	2	no	—
60	C₂²×D₄×C₁₇	—	2	8	no	—
61	C₂²×D₄×C₁₇	—	2	2	no	—
62	C₂²×D₄×C₁₇	—	2	1	no	—
63	C₂²×D₄×C₁₇	—	2	4	no	—
64	C₂²×D₄×C₁₇	—	2	1	no	—
65	C₂²×D₄×C₁₇	—	4	4	no	—
66	C₂²×D₄×C₁₇	—	4	8	no	—
67	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₇	—	2	1	no	—
72	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
73	C₂×SD₁₆×C₁₇	—	2	4	no	—
74	C₂×SD₁₆×C₁₇	—	4	4	no	—
75	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
76	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	complemented
77	C₂×M₁₆×C₁₇	—	4	4	no	—
78	C₂×M₁₆×C₁₇	C₂³	1	8	yes	complemented
79	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
82	C₁₇×C₄⋊Q₈	—	2	2	no	—
83	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
84	C₁₇×#127	—	2	2	no	—
85	C₁₇×#127	C₂³	1	4	yes	—
86	C₁₇×#126	—	2	16	no	—
87	C₁₇×#124	—	2	8	no	—
88	C₁₇×C₂²⋊Q₈	—	2	4	no	—
89	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
90	C₁₇×#121	—	2	4	no	—
91	C₁₇×#121	—	2	8	no	—
92	C₁₇×#121	C₂³	1	8	yes	—
93	C₁₇×#120	—	2	16	no	—
94	C₄×Q₈×C₁₇	—	2	8	no	—
95	C₄×Q₈×C₁₇	—	2	2	no	—
96	C₄×Q₈×C₁₇	C₂³	1	4	yes	complemented
97	C₄×D₄×C₁₇	—	2	2	no	—
98	C₄×D₄×C₁₇	D₄	1	4	yes	—
99	C₄×D₄×C₁₇	C₂³	1	4	yes	—
100	C₄×D₄×C₁₇	C₂³	1	4	yes	—
101	C₁₇×#117	—	2	4	no	—
102	C₁₇×#117	C₂³	1	8	yes	complemented
103	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
115	C₂×C₄²×C₁₇	—	2	2	no	—
116	C₂×C₄²×C₁₇	—	2	1	no	—
117	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
118	C₁₇×#107	C₂³	1	8	yes	complemented
119	C₁₇×#106	C₂³	1	4	yes	complemented
120	C₁₇×C₄⋊C₈	C₂³	1	4	yes	complemented
121	C₁₇×#103	C₂³	1	4	yes	complemented
122	C₁₇×#102	C₂³	1	4	yes	—
123	C₁₇×#102	C₂³	1	8	yes	—
124	C₁₇×#102	C₂³	1	8	yes	complemented
125	C₁₇×#102	C₂³	1	8	yes	complemented
126	C₁₇×#102	C₂³	1	8	yes	complemented
127	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
128	C₄×C₈×C₁₇	C₂³	1	4	yes	complemented
129	C₂⁴×C₁₇	—	2	1	no	—
130	C₂⁴×C₁₇	—	2	2	no	—
131	C₂⁴×C₁₇	—	2	8	no	—
132	C₂⁴×C₁₇	—	4	8	no	—
133	C₂⁴×C₁₇	—	4	8	no	—
134	C₂⁴×C₁₇	—	8	4	no	—
135	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₁₇	—	2	1	no	—
137	C₂×Q₈×C₁₇	—	2	4	no	—
138	C₂×Q₈×C₁₇	—	2	2	no	—
139	C₂×Q₈×C₁₇	—	2	2	no	—
140	C₂×Q₈×C₁₇	—	4	4	no	—
141	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
142	C₂×D₄×C₁₇	—	2	16	no	—
143	C₂×D₄×C₁₇	—	2	8	no	—
144	C₂×D₄×C₁₇	—	2	4	no	—
145	C₂×D₄×C₁₇	—	2	1	no	—
146	C₂×D₄×C₁₇	—	2	2	no	—
147	C₂×D₄×C₁₇	—	2	4	no	—
148	C₂×D₄×C₁₇	—	2	8	no	—
149	C₂×D₄×C₁₇	—	2	4	no	—
150	C₂×D₄×C₁₇	—	2	4	no	—
151	C₂×D₄×C₁₇	—	2	2	no	—
152	C₂×D₄×C₁₇	—	2	4	no	—
153	C₂×D₄×C₁₇	—	4	8	no	—
154	C₂×D₄×C₁₇	—	4	16	no	—
155	C₂×D₄×C₁₇	—	4	8	no	—
156	C₂×D₄×C₁₇	—	4	32	no	—
157	C₂×D₄×C₁₇	—	4	8	no	—
158	C₂×D₄×C₁₇	—	4	4	no	—
159	C₂×D₄×C₁₇	—	8	2	no	—
160	C₂×D₄×C₁₇	C₂×D₄	1	4	yes	—
161	C₂×D₄×C₁₇	#41	1	4	yes	—
162	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
163	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₇	—	2	4	no	—
165	C₂²×C₄×C₁₇	—	2	4	no	—
166	C₂²×C₄×C₁₇	—	2	1	no	—
167	C₂²×C₄×C₁₇	—	2	2	no	—
168	C₂²×C₄×C₁₇	—	2	1	no	—
169	C₂²×C₄×C₁₇	—	2	1	no	—
170	C₂²×C₄×C₁₇	—	2	4	no	—
171	C₂²×C₄×C₁₇	—	4	4	no	—
172	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
178	SD₁₆×C₁₇	—	2	8	no	—
179	SD₁₆×C₁₇	—	4	8	no	—
180	M₁₆×C₁₇	—	4	8	no	—
181	C₂×C₈×C₁₇	—	2	2	no	—
182	C₂×C₈×C₁₇	—	2	2	no	—
183	C₂×C₈×C₁₇	—	2	4	no	—
184	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
185	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
186	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
187	C₄⋊C₄×C₁₇	—	2	2	no	—
188	C₄⋊C₄×C₁₇	—	2	8	no	—
189	C₄⋊C₄×C₁₇	—	2	4	no	—
190	C₄⋊C₄×C₁₇	—	2	4	no	—
191	C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₄⋊C₄×C₁₇	—	2	1	no	—
193	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
194	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
195	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
196	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
197	C₂²⋊C₄×C₁₇	—	2	8	no	—
198	C₂²⋊C₄×C₁₇	—	2	8	no	—
199	C₂²⋊C₄×C₁₇	—	2	4	no	—
200	C₂²⋊C₄×C₁₇	—	2	8	no	—
201	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
202	C₄²×C₁₇	—	2	4	no	—
203	C₄²×C₁₇	—	2	8	no	—
204	C₄²×C₁₇	C₂×D₄	1	2	yes	—
205	C₄²×C₁₇	C₂⁴	1	2	yes	—
206	C₂×#3324	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₇	—	2	4	no	—
208	C₂³×C₁₇	—	2	4	no	—
209	C₂³×C₁₇	—	2	4	no	—
210	C₂³×C₁₇	—	2	4	no	—
211	C₂³×C₁₇	—	2	2	no	—
212	C₂³×C₁₇	—	2	4	no	—
213	C₂³×C₁₇	—	4	16	no	—
214	C₂³×C₁₇	—	4	16	no	—
215	C₂³×C₁₇	—	4	2	no	—
216	C₂³×C₁₇	—	4	2	no	—
217	C₂³×C₁₇	—	4	4	no	—
218	C₂³×C₁₇	—	4	4	no	—
219	C₂³×C₁₇	—	4	4	no	—
220	C₂³×C₁₇	—	8	8	no	—
221	C₂³×C₁₇	—	8	32	no	—
222	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
223	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₇	—	2	2	no	—
225	Q₈×C₁₇	—	2	2	no	—
226	Q₈×C₁₇	—	4	2	no	—
227	Q₈×C₁₇	—	4	8	no	—
228	D₄×C₁₇	—	2	4	no	—
229	D₄×C₁₇	—	2	8	no	—
230	D₄×C₁₇	—	2	4	no	—
231	D₄×C₁₇	—	2	2	no	—
232	D₄×C₁₇	—	2	4	no	—
233	D₄×C₁₇	—	4	16	no	—
234	D₄×C₁₇	—	4	16	no	—
235	D₄×C₁₇	—	4	4	no	—
236	D₄×C₁₇	—	4	8	no	—
237	D₄×C₁₇	—	8	4	no	—
238	D₄×C₁₇	C₂×#41	1	4	yes	—
239	C₂×C₄×C₁₇	—	2	4	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	2	8	no	—
242	C₂×C₄×C₁₇	—	2	4	no	—
243	C₂×C₄×C₁₇	—	2	4	no	—
244	C₂×C₄×C₁₇	—	2	2	no	—
245	C₂×C₄×C₁₇	—	2	2	no	—
246	C₂×C₄×C₁₇	—	2	4	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	4	2	no	—
249	C₂×C₄×C₁₇	—	4	2	no	—
250	C₂×C₄×C₁₇	—	4	4	no	—
251	C₂×C₄×C₁₇	—	4	2	no	—
252	C₂×C₄×C₁₇	—	4	8	no	—
253	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	4	yes	—
254	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
260	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
261	C₈×C₁₇	—	2	2	no	—
262	C₈×C₁₇	—	2	2	no	—
263	C₈×C₁₇	—	2	4	no	—
264	C₂×#556	C₂×C₁₇	1	1	yes	characteristic, complemented
265	C₂×D₄²	C₂×C₁₇	1	1	yes	characteristic
266	#3324	C₂×C₁₇	1	16	yes	direct product factor
267	C₂×#486	C₂×C₁₇	1	1	yes	characteristic, complemented
268	C₂×#482	C₂×C₁₇	1	2	yes	complemented
269	C₂×#474	C₂×C₁₇	1	1	yes	characteristic, complemented
270	C₂×#468	C₂×C₁₇	1	2	yes	complemented
271	C₂×#460	C₂×C₁₇	1	1	yes	characteristic, complemented
272	C₂×#450	C₂×C₁₇	1	2	yes	complemented
273	C₂×C₄×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₂×#436	C₂×C₁₇	1	1	yes	characteristic, complemented
275	C₂×#418	C₂×C₁₇	1	2	yes	complemented
276	C₂²×C₁₇	—	2	4	no	—
277	C₂²×C₁₇	—	2	4	no	—
278	C₂²×C₁₇	—	2	4	no	—
279	C₂²×C₁₇	—	2	4	no	—
280	C₂²×C₁₇	—	4	2	no	—
281	C₂²×C₁₇	—	4	8	no	—
282	C₂²×C₁₇	—	4	8	no	—
283	C₂²×C₁₇	—	4	2	no	—
284	C₂²×C₁₇	—	4	4	no	—
285	C₂²×C₁₇	—	4	4	no	—
286	C₂²×C₁₇	—	4	4	no	—
287	C₂²×C₁₇	—	8	32	no	—
288	C₂²×C₁₇	—	8	8	no	—
289	C₂²×C₁₇	#546	1	2	yes	—
290	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
291	C₂²×C₁₇	#577	1	2	yes	—
292	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₁₇	—	2	4	no	—
294	C₄×C₁₇	—	2	2	no	—
295	C₄×C₁₇	—	4	2	no	—
296	C₄×C₁₇	—	4	2	no	—
297	C₄×C₁₇	—	4	4	no	—
298	C₄×C₁₇	—	4	2	no	—
299	C₄×C₁₇	#546	1	2	yes	—
300	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
301	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
302	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂³×D₄	—	2	1	no	—
304	C₂³×D₄	C₂²×C₁₇	1	2	yes	—
305	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
306	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
307	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	complemented
308	#556	—	2	4	no	—
309	#556	C₂²×C₁₇	1	8	yes	complemented
310	D₄²	—	2	4	no	—
311	D₄²	C₂²×C₁₇	1	8	yes	—
312	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
313	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
314	C₂×#126	—	2	2	no	—
315	C₂×#124	—	2	1	no	—
316	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	complemented
317	C₂×#121	—	2	1	no	—
318	C₂×#121	C₂²×C₁₇	1	2	yes	—
319	C₂×#120	—	2	2	no	—
320	C₂×C₄×Q₈	—	2	1	no	—
321	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
322	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
324	C₂×#117	C₂²×C₁₇	1	2	yes	complemented
325	#486	C₂²×C₁₇	1	8	yes	complemented
326	#482	C₂²×C₁₇	1	16	yes	complemented
327	#474	C₂²×C₁₇	1	8	yes	complemented
328	#468	C₂²×C₁₇	1	16	yes	complemented
329	#460	C₂²×C₁₇	1	8	yes	complemented
330	#450	C₂²×C₁₇	1	16	yes	complemented
331	C₄×SD₁₆	C₂²×C₁₇	1	8	yes	complemented
332	#436	C₂²×C₁₇	1	8	yes	complemented
333	C₂×#107	C₂²×C₁₇	1	2	yes	complemented
334	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic, complemented
335	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
336	#418	C₂²×C₁₇	1	16	yes	complemented
337	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic, complemented
338	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₇	1	2	yes	—
340	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
341	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
342	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
343	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
344	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
345	C₂×C₁₇	—	4	4	no	—
346	C₂×C₁₇	—	4	4	no	—
347	C₂×C₁₇	—	8	4	no	—
348	C₂×C₁₇	#3324	1	4	yes	direct product factor
349	C₂×C₁₇	C₂×#546	1	1	yes	characteristic
350	C₂×C₁₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
352	C₂⁵	—	2	2	no	—
353	C₂²×Q₈	—	2	1	no	—
354	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
355	C₂²×D₄	—	2	8	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	8	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	4	4	no	—
363	C₂²×D₄	—	4	8	no	—
364	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
366	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
367	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
370	C₂×SD₁₆	—	2	4	no	—
371	C₂×SD₁₆	—	4	4	no	—
372	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
373	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	complemented
374	C₂×M₁₆	—	4	4	no	—
375	C₂×M₁₆	C₂³×C₁₇	1	8	yes	complemented
376	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
378	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
379	C₄⋊Q₈	—	2	2	no	—
380	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	complemented
381	#127	—	2	2	no	—
382	#127	C₂³×C₁₇	1	4	yes	—
383	#126	—	2	16	no	—
384	#124	—	2	8	no	—
385	C₂²⋊Q₈	—	2	4	no	—
386	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	complemented
387	#121	—	2	4	no	—
388	#121	—	2	8	no	—
389	#121	C₂³×C₁₇	1	8	yes	—
390	#120	—	2	16	no	—
391	C₄×Q₈	—	2	8	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	C₂³×C₁₇	1	4	yes	complemented
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	D₄×C₁₇	1	4	yes	—
396	C₄×D₄	C₂³×C₁₇	1	4	yes	—
397	C₄×D₄	C₂³×C₁₇	1	4	yes	—
398	#117	—	2	4	no	—
399	#117	C₂³×C₁₇	1	8	yes	complemented
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
415	#107	C₂³×C₁₇	1	8	yes	complemented
416	#106	C₂³×C₁₇	1	4	yes	complemented
417	C₄⋊C₈	C₂³×C₁₇	1	4	yes	complemented
418	#103	C₂³×C₁₇	1	4	yes	complemented
419	#102	C₂³×C₁₇	1	4	yes	—
420	#102	C₂³×C₁₇	1	8	yes	—
421	#102	C₂³×C₁₇	1	8	yes	complemented
422	#102	C₂³×C₁₇	1	8	yes	complemented
423	#102	C₂³×C₁₇	1	8	yes	complemented
424	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	complemented
425	C₄×C₈	C₂³×C₁₇	1	4	yes	complemented
426	C₁₇	C₂×#3324	1	1	yes	characteristic, direct product factor, Sylow
427	C₂⁴	—	2	1	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	—	2	8	no	—
430	C₂⁴	—	4	8	no	—
431	C₂⁴	—	4	8	no	—
432	C₂⁴	—	8	4	no	—
433	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
440	C₂×D₄	—	2	16	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	16	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	32	no	—
455	C₂×D₄	—	4	8	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	8	2	no	—
458	C₂×D₄	C₂×D₄×C₁₇	1	4	yes	—
459	C₂×D₄	#41×C₁₇	1	4	yes	—
460	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
461	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
473	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
476	SD₁₆	—	2	8	no	—
477	SD₁₆	—	4	8	no	—
478	M₁₆	—	4	8	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	4	no	—
482	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
483	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
484	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
492	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
493	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	2	8	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
500	C₄²	—	2	8	no	—
501	C₄²	—	2	4	no	—
502	C₄²	C₂×D₄×C₁₇	1	2	yes	—
503	C₄²	C₂⁴×C₁₇	1	2	yes	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	16	no	—
511	C₂³	—	4	16	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	8	8	no	—
518	C₂³	—	8	32	no	—
519	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
520	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	8	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	16	no	—
531	D₄	—	4	16	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	8	no	—
534	D₄	—	8	4	no	—
535	D₄	C₂×#41×C₁₇	1	4	yes	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
552	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
555	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
556	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
557	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	8	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	8	32	no	—
573	C₂²	—	8	8	no	—
574	C₂²	C₁₇×#546	1	2	yes	—
575	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	2	yes	—
576	C₂²	C₁₇×#577	1	2	yes	—
577	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
578	C₄	—	2	4	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	2	no	—
584	C₄	C₁₇×#546	1	2	yes	—
585	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	4	yes	—
586	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
587	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂	—	4	4	no	—
589	C₂	—	4	4	no	—
590	C₂	—	8	4	no	—
591	C₂	C₁₇×#3324	1	4	yes	direct product factor
592	C₂	C₂×C₁₇×#546	1	1	yes	characteristic
593	C₂	C₂²×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
594	C₂	C₂×C₁₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂×D₄²×C₁₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#556	C₂	semidirect
3. C₁₇×#3324	C₂	direct (N × H)
4. C₂×C₁₇×#486	C₂	semidirect
5. C₂×C₁₇×#482	C₂	semidirect
6. C₂×C₁₇×#474	C₂	semidirect
7. C₂×C₁₇×#468	C₂	semidirect
8. C₂×C₁₇×#460	C₂	semidirect
9. C₂×C₁₇×#450	C₂	semidirect
10. C₂×C₄×SD₁₆×C₁₇	C₂	semidirect
11. C₂×C₁₇×#436	C₂	semidirect
12. C₂×C₁₇×#418	C₂	semidirect
16. C₂²×SD₁₆×C₁₇	C₂²	semidirect
17. C₂²×M₁₆×C₁₇	C₂²	semidirect
19. C₁₇×#556	C₂²	semidirect
22. C₂×C₁₇×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
34. C₂×C₁₇×#117	C₂²	semidirect
35. C₁₇×#486	C₂²	semidirect
36. C₁₇×#482	C₂²	semidirect
37. C₁₇×#474	C₂²	semidirect
38. C₁₇×#468	C₂²	semidirect
39. C₁₇×#460	C₂²	semidirect
40. C₁₇×#450	C₂²	semidirect
41. C₄×SD₁₆×C₁₇	C₂²	semidirect
42. C₁₇×#436	C₂²	semidirect
43. C₂×C₁₇×#107	C₂²	semidirect
44. C₂×C₁₇×#106	C₂²	semidirect
45. C₂×C₁₇×C₄⋊C₈	C₂²	semidirect
46. C₁₇×#418	C₂²	semidirect
47. C₂×C₁₇×#103	C₂²	semidirect
50. C₂×C₁₇×#102	C₂²	semidirect
51. C₂×C₁₇×#102	C₂²	semidirect
52. C₂×C₁₇×#102	C₂²	semidirect
53. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₈×C₁₇	C₂²	semidirect
76. C₂×SD₁₆×C₁₇	C₂³	semidirect
78. C₂×M₁₆×C₁₇	C₂³	semidirect
83. C₁₇×C₄⋊Q₈	C₂³	semidirect
89. C₁₇×C₂²⋊Q₈	C₂³	semidirect
96. C₄×Q₈×C₁₇	C₂³	semidirect
102. C₁₇×#117	C₂³	semidirect
118. C₁₇×#107	C₂³	semidirect
119. C₁₇×#106	C₂³	semidirect
120. C₁₇×C₄⋊C₈	C₂³	semidirect
121. C₁₇×#103	C₂³	semidirect
124. C₁₇×#102	C₂³	semidirect
125. C₁₇×#102	C₂³	semidirect
126. C₁₇×#102	C₂³	semidirect
127. C₁₇×C₂²⋊C₈	C₂³	semidirect
128. C₄×C₈×C₁₇	C₂³	semidirect
206. C₂×#3324	C₁₇	direct (N × H)
264. C₂×#556	C₂×C₁₇	semidirect
266. #3324	C₂×C₁₇	direct (N × H)
267. C₂×#486	C₂×C₁₇	semidirect
268. C₂×#482	C₂×C₁₇	semidirect
269. C₂×#474	C₂×C₁₇	semidirect
270. C₂×#468	C₂×C₁₇	semidirect
271. C₂×#460	C₂×C₁₇	semidirect
272. C₂×#450	C₂×C₁₇	semidirect
273. C₂×C₄×SD₁₆	C₂×C₁₇	semidirect
274. C₂×#436	C₂×C₁₇	semidirect
275. C₂×#418	C₂×C₁₇	semidirect
306. C₂²×SD₁₆	C₂²×C₁₇	semidirect
307. C₂²×M₁₆	C₂²×C₁₇	semidirect
309. #556	C₂²×C₁₇	semidirect
312. C₂×C₄⋊Q₈	C₂²×C₁₇	semidirect
316. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
321. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
324. C₂×#117	C₂²×C₁₇	semidirect
325. #486	C₂²×C₁₇	semidirect
326. #482	C₂²×C₁₇	semidirect
327. #474	C₂²×C₁₇	semidirect
328. #468	C₂²×C₁₇	semidirect
329. #460	C₂²×C₁₇	semidirect
330. #450	C₂²×C₁₇	semidirect
331. C₄×SD₁₆	C₂²×C₁₇	semidirect
332. #436	C₂²×C₁₇	semidirect
333. C₂×#107	C₂²×C₁₇	semidirect
334. C₂×#106	C₂²×C₁₇	semidirect
335. C₂×C₄⋊C₈	C₂²×C₁₇	semidirect
336. #418	C₂²×C₁₇	semidirect
337. C₂×#103	C₂²×C₁₇	semidirect
340. C₂×#102	C₂²×C₁₇	semidirect
341. C₂×#102	C₂²×C₁₇	semidirect
342. C₂×#102	C₂²×C₁₇	semidirect
343. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
344. C₂×C₄×C₈	C₂²×C₁₇	semidirect
348. C₂×C₁₇	#3324	direct (N × H)
373. C₂×SD₁₆	C₂³×C₁₇	semidirect
375. C₂×M₁₆	C₂³×C₁₇	semidirect
380. C₄⋊Q₈	C₂³×C₁₇	semidirect
386. C₂²⋊Q₈	C₂³×C₁₇	semidirect
393. C₄×Q₈	C₂³×C₁₇	semidirect
399. #117	C₂³×C₁₇	semidirect
415. #107	C₂³×C₁₇	semidirect
416. #106	C₂³×C₁₇	semidirect
417. C₄⋊C₈	C₂³×C₁₇	semidirect
418. #103	C₂³×C₁₇	semidirect
421. #102	C₂³×C₁₇	semidirect
422. #102	C₂³×C₁₇	semidirect
423. #102	C₂³×C₁₇	semidirect
424. C₂²⋊C₈	C₂³×C₁₇	semidirect
425. C₄×C₈	C₂³×C₁₇	semidirect
426. C₁₇	C₂×#3324	direct (N × H)
591. C₂	C₁₇×#3324	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×C₁₇×#556	2
C₂×D₄²×C₁₇	2
C₁₇×#3324	2
C₂×C₁₇×#486	2
C₂×C₁₇×#482	2
C₂×C₁₇×#474	2
C₂×C₁₇×#468	2
C₂×C₁₇×#460	2
C₂×C₁₇×#450	2
C₂×C₄×SD₁₆×C₁₇	2
C₂×C₁₇×#436	2
C₂×C₁₇×#418	2
C₂×#3324	17

Subgroups — C2×C17×#3324 #16918888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3324 #16918888