Subgroups — C₄×C₁₇×#525 #16891775

Order 4352.

3902 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₇×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
5	C₄×C₁₇×#123	C₂	1	4	yes	maximal, complemented
6	C₄×C₁₇×#121	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₇×#120	C₂	1	4	yes	maximal, complemented
8	C₁₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2290	C₂	1	4	yes	maximal, complemented
11	C₁₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×D₄×C₁₇	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
17	C₁₇×#525	C₄	1	16	yes	direct product factor
18	C₂×C₁₇×#123	C₂²	1	2	yes	—
19	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₇×#121	C₂²	1	2	yes	—
21	C₂×C₁₇×#120	C₂²	1	2	yes	—
22	C₄×#41×C₁₇	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₇	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
28	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₇	—	2	8	no	—
33	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₇	C₂²	1	4	yes	—
36	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₇	C₂²	1	2	yes	complemented
40	C₁₇×#391	C₂²	1	2	yes	complemented
41	C₁₇×#390	C₂²	1	2	yes	complemented
42	C₁₇×#389	C₂²	1	4	yes	complemented
43	C₁₇×#388	C₂²	1	8	yes	complemented
44	C₁₇×#387	C₂²	1	8	yes	complemented
45	C₁₇×#386	C₂²	1	8	yes	—
46	C₁₇×#386	C₂²	1	4	yes	—
47	C₁₇×#385	C₂²	1	8	yes	—
48	C₁₇×#385	C₂²	1	4	yes	—
49	C₁₇×#381	C₂²	1	2	yes	—
50	C₁₇×#380	C₂²	1	4	yes	—
51	C₁₇×#379	C₂²	1	2	yes	—
52	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	complemented
53	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	complemented
54	C₄×C₄⋊C₄×C₁₇	C₂²	1	8	yes	complemented
55	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
56	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
57	C₄×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
58	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	complemented
60	C₁₇×#376	C₂²	1	2	yes	complemented
61	C₄³×C₁₇	C₂²	1	2	yes	complemented
62	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
63	C₂×#41×C₁₇	—	2	4	no	—
64	C₂×#41×C₁₇	—	2	4	no	—
65	C₂×#41×C₁₇	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₇	—	2	8	no	—
71	C₂³×C₄×C₁₇	—	2	4	no	—
72	C₂³×C₄×C₁₇	—	2	4	no	—
73	C₂³×C₄×C₁₇	—	2	16	no	—
74	C₂³×C₄×C₁₇	C₂×C₄	1	8	yes	complemented
75	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₁₇×#123	C₂×C₄	1	16	yes	complemented
86	C₁₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
87	C₁₇×#121	C₂×C₄	1	16	yes	complemented
88	C₁₇×#120	C₂×C₄	1	16	yes	complemented
89	C₄×Q₈×C₁₇	—	2	8	no	—
90	C₄×D₄×C₁₇	—	2	16	no	—
91	C₄×D₄×C₁₇	—	2	32	no	—
92	C₄×D₄×C₁₇	—	2	8	no	—
93	C₄×D₄×C₁₇	C₂×C₄	1	32	yes	complemented
94	C₁₇×#117	—	2	4	no	—
95	C₁₇×#117	—	2	4	no	—
96	C₁₇×#117	—	2	8	no	—
97	C₁₇×#117	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₇	—	2	8	no	—
113	C₂×C₄²×C₁₇	—	2	4	no	—
114	C₂×C₄²×C₁₇	—	2	8	no	—
115	C₂×C₄²×C₁₇	—	2	8	no	—
116	C₂×C₄²×C₁₇	—	2	16	no	—
117	C₂×C₄²×C₁₇	—	2	8	no	—
118	C₂×C₄²×C₁₇	D₄	1	8	yes	complemented
119	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
127	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
131	C₁₇×#95	C₂³	1	8	yes	—
132	C₁₇×#95	C₂³	1	8	yes	—
133	C₁₇×#95	C₂³	1	8	yes	—
134	C₁₇×#95	C₂³	1	8	yes	—
135	C₂⁴×C₁₇	—	2	2	no	—
136	C₂⁴×C₁₇	—	2	8	no	—
137	C₂⁴×C₁₇	—	2	2	no	—
138	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
139	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
140	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
141	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
142	#41×C₁₇	—	2	32	no	—
143	C₂×Q₈×C₁₇	—	2	2	no	—
144	C₂×Q₈×C₁₇	—	2	2	no	—
145	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	complemented
146	C₂×D₄×C₁₇	—	2	4	no	—
147	C₂×D₄×C₁₇	—	2	4	no	—
148	C₂×D₄×C₁₇	—	2	16	no	—
149	C₂×D₄×C₁₇	—	2	2	no	—
150	C₂×D₄×C₁₇	—	2	2	no	—
151	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
152	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	—
153	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	complemented
154	C₂²×C₄×C₁₇	—	2	64	no	—
155	C₂²×C₄×C₁₇	—	2	4	no	—
156	C₂²×C₄×C₁₇	—	2	2	no	—
157	C₂²×C₄×C₁₇	—	2	8	no	—
158	C₂²×C₄×C₁₇	—	2	2	no	—
159	C₂²×C₄×C₁₇	—	2	32	no	—
160	C₂²×C₄×C₁₇	—	2	8	no	—
161	C₂²×C₄×C₁₇	—	2	4	no	—
162	C₂²×C₄×C₁₇	—	2	4	no	—
163	C₂²×C₄×C₁₇	—	2	8	no	—
164	C₂²×C₄×C₁₇	—	2	4	no	—
165	C₂²×C₄×C₁₇	—	2	8	no	—
166	C₂²×C₄×C₁₇	—	2	8	no	—
167	C₂²×C₄×C₁₇	—	2	4	no	—
168	C₂²×C₄×C₁₇	—	2	4	no	—
169	C₂²×C₄×C₁₇	—	2	8	no	—
170	C₂²×C₄×C₁₇	—	2	8	no	—
171	C₂²×C₄×C₁₇	—	2	4	no	—
172	C₂²×C₄×C₁₇	—	2	8	no	—
173	C₂²×C₄×C₁₇	—	2	16	no	—
174	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
175	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
177	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	complemented
179	C₂²×C₄×C₁₇	C₂×D₄	1	8	yes	—
180	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₇	#41	1	4	yes	—
182	C₂²×C₄×C₁₇	#41	1	16	yes	complemented
183	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
193	C₄⋊C₄×C₁₇	—	2	8	no	—
194	C₄⋊C₄×C₁₇	—	2	4	no	—
195	C₄⋊C₄×C₁₇	—	2	4	no	—
196	C₄⋊C₄×C₁₇	—	2	16	no	—
197	C₄⋊C₄×C₁₇	C₂²×C₄	1	16	yes	complemented
198	C₄⋊C₄×C₁₇	C₂²×C₄	1	8	yes	complemented
199	C₂²⋊C₄×C₁₇	—	2	4	no	—
200	C₂²⋊C₄×C₁₇	—	2	4	no	—
201	C₂²⋊C₄×C₁₇	—	2	16	no	—
202	C₂²⋊C₄×C₁₇	—	2	8	no	—
203	C₂²⋊C₄×C₁₇	—	2	16	no	—
204	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
205	C₂²⋊C₄×C₁₇	C₂²×C₄	1	8	yes	—
206	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	complemented
207	C₄²×C₁₇	—	2	8	no	—
208	C₄²×C₁₇	—	2	4	no	—
209	C₄²×C₁₇	—	2	4	no	—
210	C₄²×C₁₇	—	2	8	no	—
211	C₄²×C₁₇	—	2	4	no	—
212	C₄²×C₁₇	—	2	8	no	—
213	C₄²×C₁₇	—	2	4	no	—
214	C₄²×C₁₇	—	2	16	no	—
215	C₄²×C₁₇	C₂²×C₄	1	8	yes	complemented
216	C₄²×C₁₇	C₂×D₄	1	4	yes	—
217	C₄²×C₁₇	C₂×D₄	1	4	yes	—
218	C₄²×C₁₇	C₂×D₄	1	8	yes	—
219	C₄×#525	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₁₇	—	2	16	no	—
221	C₂³×C₁₇	—	2	16	no	—
222	C₂³×C₁₇	—	2	8	no	—
223	C₂³×C₁₇	—	2	16	no	—
224	C₂³×C₁₇	—	2	2	no	—
225	C₂³×C₁₇	—	2	2	no	—
226	C₂³×C₁₇	—	2	4	no	—
227	C₂³×C₁₇	—	2	4	no	—
228	C₂³×C₁₇	—	2	2	no	—
229	C₂³×C₁₇	—	2	8	no	—
230	C₂³×C₁₇	—	2	2	no	—
231	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
232	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
233	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
234	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
235	C₂³×C₁₇	C₂×#41	1	2	yes	—
236	C₂³×C₁₇	C₂×#41	1	8	yes	—
237	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
238	Q₈×C₁₇	—	2	8	no	—
239	D₄×C₁₇	—	2	16	no	—
240	D₄×C₁₇	—	2	32	no	—
241	D₄×C₁₇	—	2	8	no	—
242	C₂×C₄×C₁₇	—	2	32	no	—
243	C₂×C₄×C₁₇	—	2	16	no	—
244	C₂×C₄×C₁₇	—	2	8	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	—	2	8	no	—
249	C₂×C₄×C₁₇	—	2	2	no	—
250	C₂×C₄×C₁₇	—	2	4	no	—
251	C₂×C₄×C₁₇	—	2	4	no	—
252	C₂×C₄×C₁₇	—	2	2	no	—
253	C₂×C₄×C₁₇	—	2	16	no	—
254	C₂×C₄×C₁₇	—	2	16	no	—
255	C₂×C₄×C₁₇	—	2	16	no	—
256	C₂×C₄×C₁₇	—	2	16	no	—
257	C₂×C₄×C₁₇	—	2	32	no	—
258	C₂×C₄×C₁₇	—	2	4	no	—
259	C₂×C₄×C₁₇	—	2	8	no	—
260	C₂×C₄×C₁₇	—	2	4	no	—
261	C₂×C₄×C₁₇	—	2	8	no	—
262	C₂×C₄×C₁₇	—	4	16	no	—
263	C₂×C₄×C₁₇	C₄×D₄	1	16	yes	complemented
264	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
265	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
266	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
270	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₁₇	C₂×#41	1	8	yes	—
274	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₇	C₂×#41	1	8	yes	—
277	C₂×#525	C₂×C₁₇	1	1	yes	characteristic
278	C₂×C₄×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
279	C₂³×C₄²	C₂×C₁₇	1	1	yes	characteristic, complemented
280	C₄×C₂²⋊Q₈	C₂×C₁₇	1	4	yes	complemented
281	C₄×#123	C₂×C₁₇	1	4	yes	complemented
282	C₄×#121	C₂×C₁₇	1	4	yes	complemented
283	C₄×#120	C₂×C₁₇	1	4	yes	complemented
284	#2297	C₂×C₁₇	1	1	yes	characteristic, complemented
285	#2296	C₂×C₁₇	1	1	yes	characteristic, complemented
286	#2290	C₂×C₁₇	1	4	yes	complemented
287	#2280	C₂×C₁₇	1	1	yes	characteristic, complemented
288	C₄²×D₄	C₂×C₁₇	1	4	yes	complemented
289	C₄×#117	C₂×C₁₇	1	1	yes	characteristic, complemented
290	C₂²×C₁₇	—	2	32	no	—
291	C₂²×C₁₇	—	2	4	no	—
292	C₂²×C₁₇	—	2	4	no	—
293	C₂²×C₁₇	—	2	4	no	—
294	C₂²×C₁₇	—	2	4	no	—
295	C₂²×C₁₇	—	2	8	no	—
296	C₂²×C₁₇	—	2	4	no	—
297	C₂²×C₁₇	—	2	8	no	—
298	C₂²×C₁₇	—	2	4	no	—
299	C₂²×C₁₇	—	2	8	no	—
300	C₂²×C₁₇	—	4	4	no	—
301	C₂²×C₁₇	—	4	4	no	—
302	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
303	C₂²×C₁₇	C₄×#41	1	8	yes	complemented
304	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
305	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
306	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
307	C₂²×C₁₇	C₂²×#41	1	4	yes	—
308	C₄×C₁₇	—	2	4	no	—
309	C₄×C₁₇	—	2	4	no	—
310	C₄×C₁₇	—	2	8	no	—
311	C₄×C₁₇	—	2	4	no	—
312	C₄×C₁₇	—	2	8	no	—
313	C₄×C₁₇	—	4	4	no	—
314	C₄×C₁₇	—	4	4	no	—
315	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
316	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
317	C₄×C₁₇	#525	1	8	yes	direct product factor
318	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
319	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
320	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic
321	#525	C₄×C₁₇	1	16	yes	direct product factor
322	C₂×#123	C₂²×C₁₇	1	2	yes	—
323	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
324	C₂×#121	C₂²×C₁₇	1	2	yes	—
325	C₂×#120	C₂²×C₁₇	1	2	yes	—
326	C₄×#41	—	2	8	no	—
327	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	complemented
328	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
329	C₂×C₄×D₄	C₂²×C₁₇	1	8	yes	—
330	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
331	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	complemented
332	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
334	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
335	C₂×#117	C₂²×C₁₇	1	2	yes	complemented
336	C₂²×C₄²	—	2	8	no	—
337	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
338	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
339	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
340	C₂²×C₄²	C₂²×C₁₇	1	4	yes	—
341	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
342	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×C₁₇	1	2	yes	complemented
344	#391	C₂²×C₁₇	1	2	yes	complemented
345	#390	C₂²×C₁₇	1	2	yes	complemented
346	#389	C₂²×C₁₇	1	4	yes	complemented
347	#388	C₂²×C₁₇	1	8	yes	complemented
348	#387	C₂²×C₁₇	1	8	yes	complemented
349	#386	C₂²×C₁₇	1	8	yes	—
350	#386	C₂²×C₁₇	1	4	yes	—
351	#385	C₂²×C₁₇	1	8	yes	—
352	#385	C₂²×C₁₇	1	4	yes	—
353	#381	C₂²×C₁₇	1	2	yes	—
354	#380	C₂²×C₁₇	1	4	yes	—
355	#379	C₂²×C₁₇	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	complemented
357	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	complemented
358	C₄×C₄⋊C₄	C₂²×C₁₇	1	8	yes	complemented
359	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	complemented
363	C₄×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	complemented
364	#376	C₂²×C₁₇	1	2	yes	complemented
365	C₄³	C₂²×C₁₇	1	2	yes	complemented
366	C₂×C₁₇	—	2	4	no	—
367	C₂×C₁₇	—	2	8	no	—
368	C₂×C₁₇	—	4	4	no	—
369	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
370	C₂×C₁₇	C₂×C₄×#41	1	2	yes	—
371	C₂×C₁₇	C₂×#525	1	2	yes	—
372	C₂×C₁₇	#3444	1	2	yes	—
373	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
374	C₂×#41	—	2	4	no	—
375	C₂×#41	—	2	4	no	—
376	C₂×#41	C₂×C₄×C₁₇	1	8	yes	complemented
377	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
379	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
380	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
381	C₂³×C₄	—	2	8	no	—
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	16	no	—
385	C₂³×C₄	C₂×C₄×C₁₇	1	8	yes	complemented
386	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
387	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
389	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
395	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
396	#123	C₂×C₄×C₁₇	1	16	yes	complemented
397	C₂²⋊Q₈	C₂×C₄×C₁₇	1	16	yes	complemented
398	#121	C₂×C₄×C₁₇	1	16	yes	complemented
399	#120	C₂×C₄×C₁₇	1	16	yes	complemented
400	C₄×Q₈	—	2	8	no	—
401	C₄×D₄	—	2	16	no	—
402	C₄×D₄	—	2	32	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	C₂×C₄×C₁₇	1	32	yes	complemented
405	#117	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	8	no	—
408	#117	C₂×C₄×C₁₇	1	8	yes	complemented
409	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
423	C₂×C₄²	—	2	8	no	—
424	C₂×C₄²	—	2	4	no	—
425	C₂×C₄²	—	2	8	no	—
426	C₂×C₄²	—	2	8	no	—
427	C₂×C₄²	—	2	8	no	—
428	C₂×C₄²	—	2	16	no	—
429	C₂×C₄²	D₄×C₁₇	1	8	yes	complemented
430	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
433	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
434	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
435	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
437	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
438	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
439	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
442	#95	C₂³×C₁₇	1	8	yes	—
443	#95	C₂³×C₁₇	1	8	yes	—
444	#95	C₂³×C₁₇	1	8	yes	—
445	#95	C₂³×C₁₇	1	8	yes	—
446	C₁₇	C₄×#525	1	1	yes	characteristic, direct product factor, Sylow
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	8	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
451	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
452	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
454	#41	—	2	32	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	complemented
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	—
464	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
465	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	complemented
466	C₂²×C₄	—	2	64	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	32	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	2	16	no	—
486	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
488	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
489	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
490	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	complemented
491	C₂²×C₄	C₂×D₄×C₁₇	1	8	yes	—
492	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
493	C₂²×C₄	#41×C₁₇	1	4	yes	—
494	C₂²×C₄	#41×C₁₇	1	16	yes	complemented
495	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	16	no	—
509	C₄⋊C₄	C₂²×C₄×C₁₇	1	8	yes	complemented
510	C₄⋊C₄	C₂²×C₄×C₁₇	1	16	yes	complemented
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	16	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	16	no	—
516	C₂²⋊C₄	C₂²×C₄×C₁₇	1	8	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
518	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	complemented
519	C₄²	—	2	8	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	8	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	8	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	16	no	—
527	C₄²	C₂²×C₄×C₁₇	1	8	yes	complemented
528	C₄²	C₂×D₄×C₁₇	1	4	yes	—
529	C₄²	C₂×D₄×C₁₇	1	4	yes	—
530	C₄²	C₂×D₄×C₁₇	1	8	yes	—
531	C₂³	—	2	16	no	—
532	C₂³	—	2	16	no	—
533	C₂³	—	2	8	no	—
534	C₂³	—	2	16	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
543	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
544	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
545	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
546	C₂³	C₂×#41×C₁₇	1	2	yes	—
547	C₂³	C₂×#41×C₁₇	1	8	yes	—
548	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
549	Q₈	—	2	8	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	32	no	—
552	D₄	—	2	8	no	—
553	C₂×C₄	—	2	32	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	16	no	—
565	C₂×C₄	—	2	16	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	16	no	—
568	C₂×C₄	—	2	32	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	4	16	no	—
574	C₂×C₄	C₄×D₄×C₁₇	1	16	yes	complemented
575	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
576	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
577	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
578	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
579	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
581	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
583	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
584	C₂×C₄	C₂×#41×C₁₇	1	8	yes	—
585	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
586	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
587	C₂×C₄	C₂×#41×C₁₇	1	8	yes	—
588	C₂²	—	2	32	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	8	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
601	C₂²	C₄×#41×C₁₇	1	8	yes	complemented
602	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
603	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
604	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
605	C₂²	C₂²×#41×C₁₇	1	4	yes	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	2	8	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	8	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	4	no	—
613	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
614	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
615	C₄	C₁₇×#525	1	8	yes	direct product factor
616	C₂	—	2	4	no	—
617	C₂	—	2	8	no	—
618	C₂	—	4	4	no	—
619	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
620	C₂	C₂×C₄×#41×C₁₇	1	2	yes	—
621	C₂	C₂×C₁₇×#525	1	2	yes	—
622	C₂	C₁₇×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂⁵
prime radical	C₂×C₁₇×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₁₇	C₂	semidirect
3. C₂³×C₄²×C₁₇	C₂	semidirect
4. C₄×C₁₇×C₂²⋊Q₈	C₂	semidirect
5. C₄×C₁₇×#123	C₂	semidirect
6. C₄×C₁₇×#121	C₂	semidirect
7. C₄×C₁₇×#120	C₂	semidirect
8. C₁₇×#2297	C₂	semidirect
9. C₁₇×#2296	C₂	semidirect
10. C₁₇×#2290	C₂	semidirect
11. C₁₇×#2280	C₂	semidirect
12. C₄²×D₄×C₁₇	C₂	semidirect
13. C₄×C₁₇×#117	C₂	semidirect
17. C₁₇×#525	C₄	direct (N × H)
23. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
27. C₂×C₄×D₄×C₁₇	C₂²	semidirect
31. C₂×C₁₇×#117	C₂²	semidirect
39. C₂²×C₄²×C₁₇	C₂²	semidirect
40. C₁₇×#391	C₂²	semidirect
41. C₁₇×#390	C₂²	semidirect
42. C₁₇×#389	C₂²	semidirect
43. C₁₇×#388	C₂²	semidirect
44. C₁₇×#387	C₂²	semidirect
52. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
53. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
54. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
58. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
59. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
60. C₁₇×#376	C₂²	semidirect
61. C₄³×C₁₇	C₂²	semidirect
65. C₂×#41×C₁₇	C₂×C₄	semidirect
74. C₂³×C₄×C₁₇	C₂×C₄	semidirect
85. C₁₇×#123	C₂×C₄	semidirect
86. C₁₇×C₂²⋊Q₈	C₂×C₄	semidirect
87. C₁₇×#121	C₂×C₄	semidirect
88. C₁₇×#120	C₂×C₄	semidirect
93. C₄×D₄×C₁₇	C₂×C₄	semidirect
97. C₁₇×#117	C₂×C₄	semidirect
118. C₂×C₄²×C₁₇	D₄	semidirect
145. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
153. C₂×D₄×C₁₇	C₂²×C₄	semidirect
178. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
182. C₂²×C₄×C₁₇	#41	semidirect
197. C₄⋊C₄×C₁₇	C₂²×C₄	semidirect
198. C₄⋊C₄×C₁₇	C₂²×C₄	semidirect
206. C₂²⋊C₄×C₁₇	C₂²×C₄	semidirect
215. C₄²×C₁₇	C₂²×C₄	semidirect
219. C₄×#525	C₁₇	direct (N × H)
263. C₂×C₄×C₁₇	C₄×D₄	semidirect
278. C₂×C₄×#41	C₂×C₁₇	semidirect
279. C₂³×C₄²	C₂×C₁₇	semidirect
280. C₄×C₂²⋊Q₈	C₂×C₁₇	semidirect
281. C₄×#123	C₂×C₁₇	semidirect
282. C₄×#121	C₂×C₁₇	semidirect
283. C₄×#120	C₂×C₁₇	semidirect
284. #2297	C₂×C₁₇	semidirect
285. #2296	C₂×C₁₇	semidirect
286. #2290	C₂×C₁₇	semidirect
287. #2280	C₂×C₁₇	semidirect
288. C₄²×D₄	C₂×C₁₇	semidirect
289. C₄×#117	C₂×C₁₇	semidirect
303. C₂²×C₁₇	C₄×#41	semidirect
317. C₄×C₁₇	#525	direct (N × H)
321. #525	C₄×C₁₇	direct (N × H)
327. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
331. C₂×C₄×D₄	C₂²×C₁₇	semidirect
335. C₂×#117	C₂²×C₁₇	semidirect
343. C₂²×C₄²	C₂²×C₁₇	semidirect
344. #391	C₂²×C₁₇	semidirect
345. #390	C₂²×C₁₇	semidirect
346. #389	C₂²×C₁₇	semidirect
347. #388	C₂²×C₁₇	semidirect
348. #387	C₂²×C₁₇	semidirect
356. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
357. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
358. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
362. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
363. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
364. #376	C₂²×C₁₇	semidirect
365. C₄³	C₂²×C₁₇	semidirect
376. C₂×#41	C₂×C₄×C₁₇	semidirect
385. C₂³×C₄	C₂×C₄×C₁₇	semidirect
396. #123	C₂×C₄×C₁₇	semidirect
397. C₂²⋊Q₈	C₂×C₄×C₁₇	semidirect
398. #121	C₂×C₄×C₁₇	semidirect
399. #120	C₂×C₄×C₁₇	semidirect
404. C₄×D₄	C₂×C₄×C₁₇	semidirect
408. #117	C₂×C₄×C₁₇	semidirect
429. C₂×C₄²	D₄×C₁₇	semidirect
446. C₁₇	C₄×#525	direct (N × H)
457. C₂×Q₈	C₂²×C₄×C₁₇	semidirect
465. C₂×D₄	C₂²×C₄×C₁₇	semidirect
490. C₂²×C₄	C₂²×C₄×C₁₇	semidirect
494. C₂²×C₄	#41×C₁₇	semidirect
509. C₄⋊C₄	C₂²×C₄×C₁₇	semidirect
510. C₄⋊C₄	C₂²×C₄×C₁₇	semidirect
518. C₂²⋊C₄	C₂²×C₄×C₁₇	semidirect
527. C₄²	C₂²×C₄×C₁₇	semidirect
574. C₂×C₄	C₄×D₄×C₁₇	semidirect
601. C₂²	C₄×#41×C₁₇	semidirect
615. C₄	C₁₇×#525	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×#525	2
C₂×C₄×#41×C₁₇	2
C₂³×C₄²×C₁₇	2
C₄×C₁₇×C₂²⋊Q₈	2
C₄×C₁₇×#123	2
C₄×C₁₇×#121	2
C₄×C₁₇×#120	2
C₁₇×#2297	2
C₁₇×#2296	2
C₁₇×#2290	2
C₁₇×#2280	2
C₄²×D₄×C₁₇	2
C₄×C₁₇×#117	2
C₄×#525	17

Subgroups — C4×C17×#525 #16891775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₇×#525 #16891775