Subgroups — C₁₇×#34258 #16892002

Order 4352.

5682 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2341	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊C₄×C₁₇	C₂	1	12	yes	maximal, complemented
6	C₁₇×#2311	C₂	1	3	yes	maximal, complemented
7	C₁₇×#2309	C₂	1	3	yes	maximal, complemented
8	C₁₇×#2297	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₇×#390	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₇×H(5,𝔽₂)	—	2	8	no	—
11	C₂×C₁₇×H(5,𝔽₂)	—	2	8	no	—
12	C₂×C₁₇×H(5,𝔽₂)	C₄	1	16	yes	complemented
13	C₂²×#41×C₁₇	C₂²	1	3	yes	—
14	C₂²×#41×C₁₇	C₂²	1	2	yes	—
15	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₇	C₂²	1	3	yes	—
17	C₂³×D₄×C₁₇	C₂²	1	6	yes	—
18	C₁₇×#520	—	2	8	no	—
19	C₄×#41×C₁₇	—	2	8	no	—
20	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
21	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
22	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
23	C₂×C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
24	C₂×C₁₇×#117	C₂²	1	3	yes	complemented
25	C₂×C₁₇×#117	C₂²	1	3	yes	complemented
26	C₂²×C₄⋊C₄×C₁₇	C₂²	1	3	yes	complemented
27	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	12	yes	complemented
28	C₂²×C₄²×C₁₇	C₂²	1	3	yes	complemented
29	C₁₇×#391	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#391	C₂²	1	3	yes	complemented
31	C₁₇×#390	C₂²	1	3	yes	complemented
32	C₁₇×#390	C₂²	1	6	yes	complemented
33	C₁₇×#390	C₂²	1	12	yes	complemented
34	C₁₇×#390	C₂²	1	3	yes	complemented
35	C₁₇×#390	C₂²	1	12	yes	complemented
36	C₁₇×#386	C₂²	1	12	yes	complemented
37	C₁₇×#386	C₂²	1	12	yes	complemented
38	C₁₇×#380	C₂²	1	12	yes	complemented
39	C₁₇×#379	C₂²	1	12	yes	complemented
40	C₄×C₂²⋊C₄×C₁₇	C₂²	1	12	yes	complemented
41	C₂⁵×C₁₇	C₂³	1	6	yes	—
42	C₁₇×H(5,𝔽₂)	—	2	128	no	—
43	C₂×#41×C₁₇	—	2	8	no	—
44	C₂×#41×C₁₇	—	2	8	no	—
45	C₂×#41×C₁₇	—	2	12	no	—
46	C₂×#41×C₁₇	—	2	12	no	—
47	C₂×#41×C₁₇	C₂×C₄	1	8	yes	—
48	C₂×#41×C₁₇	C₂×C₄	1	16	yes	complemented
49	C₂×#41×C₁₇	C₂×C₄	1	24	yes	complemented
50	C₂×#41×C₁₇	D₄	1	8	yes	—
51	C₂×#41×C₁₇	D₄	1	8	yes	—
52	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₇	—	2	24	no	—
55	C₂²×D₄×C₁₇	—	2	24	no	—
56	C₂²×D₄×C₁₇	—	2	12	no	—
57	C₂²×D₄×C₁₇	—	2	12	no	—
58	C₂²×D₄×C₁₇	C₂×C₄	1	48	yes	complemented
59	C₂²×D₄×C₁₇	C₂×C₄	1	24	yes	complemented
60	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
61	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
62	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
63	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₇	C₂³	1	6	yes	—
65	C₂³×C₄×C₁₇	C₂³	1	6	yes	—
66	C₂³×C₄×C₁₇	C₂³	1	6	yes	—
67	C₂³×C₄×C₁₇	C₂³	1	3	yes	—
68	C₄×Q₈×C₁₇	—	2	8	no	—
69	C₄×Q₈×C₁₇	—	2	8	no	—
70	C₄×D₄×C₁₇	—	2	24	no	—
71	C₄×D₄×C₁₇	—	2	24	no	—
72	C₁₇×#117	—	2	12	no	—
73	C₁₇×#117	—	2	12	no	—
74	C₂×C₄⋊C₄×C₁₇	—	2	12	no	—
75	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
76	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₁₇	—	4	24	no	—
80	C₂×C₂²⋊C₄×C₁₇	C₂³	1	12	yes	—
81	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₁₇	C₂³	1	24	yes	—
84	C₂×C₂²⋊C₄×C₁₇	C₂³	1	12	yes	—
85	C₂×C₄²×C₁₇	—	2	12	no	—
86	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
88	C₂×C₄²×C₁₇	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₇	C₂³	1	6	yes	—
90	C₁₇×#95	C₂³	1	4	yes	—
91	C₁₇×#95	C₂³	1	12	yes	—
92	C₂⁴×C₁₇	—	2	12	no	—
93	C₂⁴×C₁₇	—	2	12	no	—
94	C₂⁴×C₁₇	—	4	12	no	—
95	C₂⁴×C₁₇	—	4	12	no	—
96	C₂⁴×C₁₇	C₂²×C₄	1	24	yes	—
97	C₂⁴×C₁₇	C₂⁴	1	6	yes	—
98	C₂⁴×C₁₇	C₂⁴	1	3	yes	—
99	#41×C₁₇	—	2	64	no	—
100	#41×C₁₇	—	2	96	no	—
101	#41×C₁₇	C₂²⋊C₄	1	64	yes	complemented
102	C₂×Q₈×C₁₇	—	2	2	no	—
103	C₂×Q₈×C₁₇	—	2	2	no	—
104	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
105	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
106	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
108	C₂×D₄×C₁₇	—	2	12	no	—
109	C₂×D₄×C₁₇	—	2	12	no	—
110	C₂×D₄×C₁₇	—	2	192	no	—
111	C₂×D₄×C₁₇	—	2	96	no	—
112	C₂×D₄×C₁₇	—	2	6	no	—
113	C₂×D₄×C₁₇	—	2	12	no	—
114	C₂×D₄×C₁₇	—	2	12	no	—
115	C₂×D₄×C₁₇	—	2	6	no	—
116	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	—
117	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	—
118	C₂×D₄×C₁₇	C₂²×C₄	1	12	yes	—
119	C₂×D₄×C₁₇	C₂²×C₄	1	12	yes	—
120	C₂×D₄×C₁₇	C₂×D₄	1	12	yes	—
121	C₂×D₄×C₁₇	C₂×D₄	1	12	yes	—
122	C₂²×C₄×C₁₇	—	2	12	no	—
123	C₂²×C₄×C₁₇	—	2	12	no	—
124	C₂²×C₄×C₁₇	—	2	12	no	—
125	C₂²×C₄×C₁₇	—	2	12	no	—
126	C₂²×C₄×C₁₇	—	2	12	no	—
127	C₂²×C₄×C₁₇	—	4	6	no	—
128	C₂²×C₄×C₁₇	—	4	12	no	—
129	C₂²×C₄×C₁₇	C₂²×C₄	1	24	yes	—
130	C₂²×C₄×C₁₇	C₂²×C₄	1	12	yes	—
131	C₂²×C₄×C₁₇	C₂×D₄	1	12	yes	—
132	C₂²×C₄×C₁₇	C₂×D₄	1	12	yes	—
133	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
135	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
140	C₄⋊C₄×C₁₇	—	2	6	no	—
141	C₄⋊C₄×C₁₇	—	2	12	no	—
142	C₄⋊C₄×C₁₇	—	2	2	no	—
143	C₄⋊C₄×C₁₇	—	2	12	no	—
144	C₂²⋊C₄×C₁₇	—	2	12	no	—
145	C₂²⋊C₄×C₁₇	—	2	12	no	—
146	C₂²⋊C₄×C₁₇	—	2	24	no	—
147	C₂²⋊C₄×C₁₇	—	4	24	no	—
148	C₂²⋊C₄×C₁₇	—	4	12	no	—
149	C₄²×C₁₇	—	2	2	no	—
150	C₄²×C₁₇	—	2	6	no	—
151	C₄²×C₁₇	—	2	12	no	—
152	C₄²×C₁₇	—	2	12	no	—
153	#34258	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₇	—	2	6	no	—
155	C₂³×C₁₇	—	2	6	no	—
156	C₂³×C₁₇	—	2	6	no	—
157	C₂³×C₁₇	—	2	6	no	—
158	C₂³×C₁₇	—	2	12	no	—
159	C₂³×C₁₇	—	2	12	no	—
160	C₂³×C₁₇	—	2	48	no	—
161	C₂³×C₁₇	—	4	48	no	—
162	C₂³×C₁₇	—	8	24	no	—
163	C₂³×C₁₇	—	8	12	no	—
164	C₂³×C₁₇	—	8	12	no	—
165	C₂³×C₁₇	C₂³×C₄	1	12	yes	—
166	C₂³×C₁₇	C₂³×C₄	1	6	yes	—
167	C₂³×C₁₇	C₂²×D₄	1	6	yes	—
168	C₂³×C₁₇	C₂²×D₄	1	6	yes	—
169	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
170	Q₈×C₁₇	—	2	8	no	—
171	Q₈×C₁₇	C₂×C₂²⋊C₄	1	16	yes	complemented
172	D₄×C₁₇	—	2	48	no	—
173	D₄×C₁₇	—	2	48	no	—
174	D₄×C₁₇	—	2	24	no	—
175	D₄×C₁₇	C₂×C₂²⋊C₄	1	48	yes	complemented
176	C₂×C₄×C₁₇	—	2	2	no	—
177	C₂×C₄×C₁₇	—	2	2	no	—
178	C₂×C₄×C₁₇	—	2	2	no	—
179	C₂×C₄×C₁₇	—	2	2	no	—
180	C₂×C₄×C₁₇	—	2	48	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	6	no	—
183	C₂×C₄×C₁₇	—	2	6	no	—
184	C₂×C₄×C₁₇	—	2	12	no	—
185	C₂×C₄×C₁₇	—	2	6	no	—
186	C₂×C₄×C₁₇	—	2	4	no	—
187	C₂×C₄×C₁₇	—	2	6	no	—
188	C₂×C₄×C₁₇	—	4	24	no	—
189	C₂×C₄×C₁₇	—	8	12	no	—
190	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	48	yes	complemented
191	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
193	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₇	C₂²×D₄	1	6	yes	—
196	C₂×C₄×C₁₇	C₂²×D₄	1	6	yes	—
197	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	complemented
199	C₂²×H(5,𝔽₂)	C₂×C₁₇	1	1	yes	characteristic
200	C₂×#520	C₂×C₁₇	1	1	yes	characteristic, complemented
201	C₂×C₄×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
202	#2341	C₂×C₁₇	1	4	yes	complemented
203	D₄×C₂²⋊C₄	C₂×C₁₇	1	12	yes	complemented
204	#2311	C₂×C₁₇	1	3	yes	complemented
205	#2309	C₂×C₁₇	1	3	yes	complemented
206	#2297	C₂×C₁₇	1	3	yes	complemented
207	C₂×#390	C₂×C₁₇	1	3	yes	complemented
208	C₂²×C₁₇	—	2	12	no	—
209	C₂²×C₁₇	—	2	12	no	—
210	C₂²×C₁₇	—	2	6	no	—
211	C₂²×C₁₇	—	2	6	no	—
212	C₂²×C₁₇	—	2	12	no	—
213	C₂²×C₁₇	—	2	24	no	—
214	C₂²×C₁₇	—	4	12	no	—
215	C₂²×C₁₇	—	4	6	no	—
216	C₂²×C₁₇	—	4	6	no	—
217	C₂²×C₁₇	—	8	48	no	—
218	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	12	yes	—
219	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
220	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
221	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
222	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
223	C₂²×C₁₇	#585	1	2	yes	—
224	C₄×C₁₇	—	2	4	no	—
225	C₄×C₁₇	—	2	4	no	—
226	C₄×C₁₇	—	4	6	no	—
227	C₄×C₁₇	—	4	6	no	—
228	C₄×C₁₇	—	4	2	no	—
229	C₄×C₁₇	C₂²×C₂²⋊C₄	1	12	yes	—
230	C₄×C₁₇	C₂²×C₂²⋊C₄	1	4	yes	—
231	C₂×H(5,𝔽₂)	—	2	8	no	—
232	C₂×H(5,𝔽₂)	—	2	8	no	—
233	C₂×H(5,𝔽₂)	C₄×C₁₇	1	16	yes	complemented
234	C₂²×#41	C₂²×C₁₇	1	3	yes	—
235	C₂²×#41	C₂²×C₁₇	1	2	yes	—
236	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
237	C₂³×D₄	C₂²×C₁₇	1	3	yes	—
238	C₂³×D₄	C₂²×C₁₇	1	6	yes	—
239	#520	—	2	8	no	—
240	C₄×#41	—	2	8	no	—
241	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	complemented
242	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	complemented
243	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
244	C₂×C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
245	C₂×#117	C₂²×C₁₇	1	3	yes	complemented
246	C₂×#117	C₂²×C₁₇	1	3	yes	complemented
247	C₂²×C₄⋊C₄	C₂²×C₁₇	1	3	yes	complemented
248	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	12	yes	complemented
249	C₂²×C₄²	C₂²×C₁₇	1	3	yes	complemented
250	#391	C₂²×C₁₇	1	3	yes	complemented
251	#391	C₂²×C₁₇	1	1	yes	characteristic, complemented
252	#390	C₂²×C₁₇	1	3	yes	complemented
253	#390	C₂²×C₁₇	1	6	yes	complemented
254	#390	C₂²×C₁₇	1	12	yes	complemented
255	#390	C₂²×C₁₇	1	12	yes	complemented
256	#390	C₂²×C₁₇	1	3	yes	complemented
257	#386	C₂²×C₁₇	1	12	yes	complemented
258	#386	C₂²×C₁₇	1	12	yes	complemented
259	#380	C₂²×C₁₇	1	12	yes	complemented
260	#379	C₂²×C₁₇	1	12	yes	complemented
261	C₄×C₂²⋊C₄	C₂²×C₁₇	1	12	yes	complemented
262	C₂×C₁₇	—	2	12	no	—
263	C₂×C₁₇	—	4	12	no	—
264	C₂×C₁₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₁₇	C₄×H(5,𝔽₂)	1	2	yes	—
266	C₂×C₁₇	#3488	1	2	yes	—
267	C₂×C₁₇	#3498	1	1	yes	characteristic
268	C₂×C₁₇	#3500	1	1	yes	characteristic
269	C₂⁵	C₂³×C₁₇	1	6	yes	—
270	H(5,𝔽₂)	—	2	128	no	—
271	C₂×#41	—	2	8	no	—
272	C₂×#41	—	2	8	no	—
273	C₂×#41	—	2	12	no	—
274	C₂×#41	—	2	12	no	—
275	C₂×#41	C₂×C₄×C₁₇	1	8	yes	—
276	C₂×#41	C₂×C₄×C₁₇	1	16	yes	complemented
277	C₂×#41	C₂×C₄×C₁₇	1	24	yes	complemented
278	C₂×#41	D₄×C₁₇	1	8	yes	—
279	C₂×#41	D₄×C₁₇	1	8	yes	—
280	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
282	C₂²×D₄	—	2	24	no	—
283	C₂²×D₄	—	2	24	no	—
284	C₂²×D₄	—	2	12	no	—
285	C₂²×D₄	—	2	12	no	—
286	C₂²×D₄	C₂×C₄×C₁₇	1	48	yes	complemented
287	C₂²×D₄	C₂×C₄×C₁₇	1	24	yes	complemented
288	C₂²×D₄	C₂³×C₁₇	1	6	yes	—
289	C₂²×D₄	C₂³×C₁₇	1	3	yes	—
290	C₂²×D₄	C₂³×C₁₇	1	6	yes	—
291	C₂²×D₄	C₂³×C₁₇	1	3	yes	—
292	C₂³×C₄	C₂³×C₁₇	1	6	yes	—
293	C₂³×C₄	C₂³×C₁₇	1	6	yes	—
294	C₂³×C₄	C₂³×C₁₇	1	6	yes	—
295	C₂³×C₄	C₂³×C₁₇	1	3	yes	—
296	C₄×Q₈	—	2	8	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×D₄	—	2	24	no	—
299	C₄×D₄	—	2	24	no	—
300	#117	—	2	12	no	—
301	#117	—	2	12	no	—
302	C₂×C₄⋊C₄	—	2	12	no	—
303	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
307	C₂×C₂²⋊C₄	—	4	24	no	—
308	C₂×C₂²⋊C₄	C₂³×C₁₇	1	12	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₇	1	24	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₇	1	12	yes	—
313	C₂×C₄²	—	2	12	no	—
314	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
315	C₂×C₄²	C₂³×C₁₇	1	6	yes	—
316	C₂×C₄²	C₂³×C₁₇	1	6	yes	—
317	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
318	#95	C₂³×C₁₇	1	4	yes	—
319	#95	C₂³×C₁₇	1	12	yes	—
320	C₁₇	#34258	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	12	no	—
322	C₂⁴	—	2	12	no	—
323	C₂⁴	—	4	12	no	—
324	C₂⁴	—	4	12	no	—
325	C₂⁴	C₂²×C₄×C₁₇	1	24	yes	—
326	C₂⁴	C₂⁴×C₁₇	1	6	yes	—
327	C₂⁴	C₂⁴×C₁₇	1	3	yes	—
328	#41	—	2	64	no	—
329	#41	—	2	96	no	—
330	#41	C₂²⋊C₄×C₁₇	1	64	yes	complemented
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
334	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
335	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
336	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
337	C₂×D₄	—	2	12	no	—
338	C₂×D₄	—	2	12	no	—
339	C₂×D₄	—	2	192	no	—
340	C₂×D₄	—	2	6	no	—
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	—	2	6	no	—
344	C₂×D₄	—	2	96	no	—
345	C₂×D₄	C₂²×C₄×C₁₇	1	24	yes	—
346	C₂×D₄	C₂²×C₄×C₁₇	1	24	yes	—
347	C₂×D₄	C₂²×C₄×C₁₇	1	12	yes	—
348	C₂×D₄	C₂²×C₄×C₁₇	1	12	yes	—
349	C₂×D₄	C₂×D₄×C₁₇	1	12	yes	—
350	C₂×D₄	C₂×D₄×C₁₇	1	12	yes	—
351	C₂²×C₄	—	2	12	no	—
352	C₂²×C₄	—	2	12	no	—
353	C₂²×C₄	—	2	12	no	—
354	C₂²×C₄	—	2	12	no	—
355	C₂²×C₄	—	2	12	no	—
356	C₂²×C₄	—	4	6	no	—
357	C₂²×C₄	—	4	12	no	—
358	C₂²×C₄	C₂²×C₄×C₁₇	1	24	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₇	1	12	yes	—
360	C₂²×C₄	C₂×D₄×C₁₇	1	12	yes	—
361	C₂²×C₄	C₂×D₄×C₁₇	1	12	yes	—
362	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₇	1	6	yes	—
364	C₂²×C₄	C₂⁴×C₁₇	1	6	yes	—
365	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
369	C₄⋊C₄	—	2	6	no	—
370	C₄⋊C₄	—	2	12	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	12	no	—
373	C₂²⋊C₄	—	2	12	no	—
374	C₂²⋊C₄	—	2	12	no	—
375	C₂²⋊C₄	—	2	24	no	—
376	C₂²⋊C₄	—	4	24	no	—
377	C₂²⋊C₄	—	4	12	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	6	no	—
380	C₄²	—	2	12	no	—
381	C₄²	—	2	12	no	—
382	C₂³	—	2	6	no	—
383	C₂³	—	2	6	no	—
384	C₂³	—	2	6	no	—
385	C₂³	—	2	6	no	—
386	C₂³	—	2	12	no	—
387	C₂³	—	2	12	no	—
388	C₂³	—	2	48	no	—
389	C₂³	—	4	48	no	—
390	C₂³	—	8	24	no	—
391	C₂³	—	8	12	no	—
392	C₂³	—	8	12	no	—
393	C₂³	C₂³×C₄×C₁₇	1	12	yes	—
394	C₂³	C₂³×C₄×C₁₇	1	6	yes	—
395	C₂³	C₂²×D₄×C₁₇	1	6	yes	—
396	C₂³	C₂²×D₄×C₁₇	1	6	yes	—
397	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	C₂×C₂²⋊C₄×C₁₇	1	16	yes	complemented
400	D₄	—	2	48	no	—
401	D₄	—	2	48	no	—
402	D₄	—	2	24	no	—
403	D₄	C₂×C₂²⋊C₄×C₁₇	1	48	yes	complemented
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	48	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	2	12	no	—
413	C₂×C₄	—	2	6	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	4	24	no	—
417	C₂×C₄	—	8	12	no	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	48	yes	complemented
419	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
420	C₂×C₄	C₂³×C₄×C₁₇	1	6	yes	—
421	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₇	1	6	yes	—
424	C₂×C₄	C₂²×D₄×C₁₇	1	6	yes	—
425	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
426	C₂×C₄	C₁₇×H(5,𝔽₂)	1	4	yes	complemented
427	C₂²	—	2	12	no	—
428	C₂²	—	2	6	no	—
429	C₂²	—	2	6	no	—
430	C₂²	—	2	12	no	—
431	C₂²	—	2	12	no	—
432	C₂²	—	2	24	no	—
433	C₂²	—	4	12	no	—
434	C₂²	—	4	6	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	8	48	no	—
437	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	12	yes	—
438	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
439	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
440	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
441	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
442	C₂²	C₁₇×#585	1	2	yes	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	6	no	—
446	C₄	—	4	6	no	—
447	C₄	—	4	2	no	—
448	C₄	C₂²×C₂²⋊C₄×C₁₇	1	12	yes	—
449	C₄	C₂²×C₂²⋊C₄×C₁₇	1	4	yes	—
450	C₂	—	2	12	no	—
451	C₂	—	4	12	no	—
452	C₂	C₂³×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
453	C₂	C₄×C₁₇×H(5,𝔽₂)	1	2	yes	—
454	C₂	C₁₇×#3488	1	2	yes	—
455	C₂	C₁₇×#3498	1	1	yes	characteristic
456	C₂	C₁₇×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂²×C₁₇×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#520	C₂	semidirect
3. C₂×C₄×#41×C₁₇	C₂	semidirect
4. C₁₇×#2341	C₂	semidirect
5. D₄×C₂²⋊C₄×C₁₇	C₂	semidirect
6. C₁₇×#2311	C₂	semidirect
7. C₁₇×#2309	C₂	semidirect
8. C₁₇×#2297	C₂	semidirect
9. C₂×C₁₇×#390	C₂	semidirect
12. C₂×C₁₇×H(5,𝔽₂)	C₄	semidirect
20. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
21. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
22. C₂×C₄×D₄×C₁₇	C₂²	semidirect
23. C₂×C₄×D₄×C₁₇	C₂²	semidirect
24. C₂×C₁₇×#117	C₂²	semidirect
25. C₂×C₁₇×#117	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₁₇	C₂²	semidirect
28. C₂²×C₄²×C₁₇	C₂²	semidirect
29. C₁₇×#391	C₂²	semidirect
30. C₁₇×#391	C₂²	semidirect
31. C₁₇×#390	C₂²	semidirect
32. C₁₇×#390	C₂²	semidirect
33. C₁₇×#390	C₂²	semidirect
34. C₁₇×#390	C₂²	semidirect
35. C₁₇×#390	C₂²	semidirect
36. C₁₇×#386	C₂²	semidirect
37. C₁₇×#386	C₂²	semidirect
38. C₁₇×#380	C₂²	semidirect
39. C₁₇×#379	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
48. C₂×#41×C₁₇	C₂×C₄	semidirect
49. C₂×#41×C₁₇	C₂×C₄	semidirect
58. C₂²×D₄×C₁₇	C₂×C₄	semidirect
59. C₂²×D₄×C₁₇	C₂×C₄	semidirect
101. #41×C₁₇	C₂²⋊C₄	semidirect
153. #34258	C₁₇	direct (N × H)
171. Q₈×C₁₇	C₂×C₂²⋊C₄	semidirect
175. D₄×C₁₇	C₂×C₂²⋊C₄	semidirect
190. C₂×C₄×C₁₇	C₂×C₂²⋊C₄	semidirect
198. C₂×C₄×C₁₇	H(5,𝔽₂)	semidirect
200. C₂×#520	C₂×C₁₇	semidirect
201. C₂×C₄×#41	C₂×C₁₇	semidirect
202. #2341	C₂×C₁₇	semidirect
203. D₄×C₂²⋊C₄	C₂×C₁₇	semidirect
204. #2311	C₂×C₁₇	semidirect
205. #2309	C₂×C₁₇	semidirect
206. #2297	C₂×C₁₇	semidirect
207. C₂×#390	C₂×C₁₇	semidirect
233. C₂×H(5,𝔽₂)	C₄×C₁₇	semidirect
241. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
242. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
243. C₂×C₄×D₄	C₂²×C₁₇	semidirect
244. C₂×C₄×D₄	C₂²×C₁₇	semidirect
245. C₂×#117	C₂²×C₁₇	semidirect
246. C₂×#117	C₂²×C₁₇	semidirect
247. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
248. C₂²×C₂²⋊C₄	C₂²×C₁₇	semidirect
249. C₂²×C₄²	C₂²×C₁₇	semidirect
250. #391	C₂²×C₁₇	semidirect
251. #391	C₂²×C₁₇	semidirect
252. #390	C₂²×C₁₇	semidirect
253. #390	C₂²×C₁₇	semidirect
254. #390	C₂²×C₁₇	semidirect
255. #390	C₂²×C₁₇	semidirect
256. #390	C₂²×C₁₇	semidirect
257. #386	C₂²×C₁₇	semidirect
258. #386	C₂²×C₁₇	semidirect
259. #380	C₂²×C₁₇	semidirect
260. #379	C₂²×C₁₇	semidirect
261. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
276. C₂×#41	C₂×C₄×C₁₇	semidirect
277. C₂×#41	C₂×C₄×C₁₇	semidirect
286. C₂²×D₄	C₂×C₄×C₁₇	semidirect
287. C₂²×D₄	C₂×C₄×C₁₇	semidirect
320. C₁₇	#34258	direct (N × H)
330. #41	C₂²⋊C₄×C₁₇	semidirect
399. Q₈	C₂×C₂²⋊C₄×C₁₇	semidirect
403. D₄	C₂×C₂²⋊C₄×C₁₇	semidirect
418. C₂×C₄	C₂×C₂²⋊C₄×C₁₇	semidirect
426. C₂×C₄	C₁₇×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₇×H(5,𝔽₂)	2
C₂×C₁₇×#520	2
C₂×C₄×#41×C₁₇	2
C₁₇×#2341	2
D₄×C₂²⋊C₄×C₁₇	2
C₁₇×#2311	2
C₁₇×#2309	2
C₁₇×#2297	2
C₂×C₁₇×#390	2
#34258	17

Subgroups — C17×#34258 #16892002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34258 #16892002