Subgroups — C₁₇×#2756 #14525762

Order 2176.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#392	C₂	1	1	yes	maximal, characteristic
7	C₁₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#383	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#95	C₂²	1	1	yes	characteristic
42	C₁₇×#95	C₂²	1	1	yes	characteristic
43	C₁₇×#95	C₂²	1	1	yes	characteristic
44	C₁₇×#95	C₂²	1	1	yes	characteristic
45	C₁₇×#95	C₂²	1	1	yes	characteristic
46	C₁₇×#95	C₂²	1	1	yes	characteristic
47	C₁₇×#95	C₂²	1	1	yes	characteristic
48	C₁₇×#95	C₂²	1	1	yes	characteristic
49	C₁₇×#95	C₂²	1	1	yes	characteristic
50	C₁₇×#95	C₂²	1	1	yes	characteristic
51	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
52	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
53	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
54	C₂×D₄×C₁₇	—	2	2	no	—
55	C₂×D₄×C₁₇	—	2	2	no	—
56	C₂×D₄×C₁₇	—	2	2	no	—
57	C₂×D₄×C₁₇	—	4	1	no	—
58	C₂×D₄×C₁₇	—	4	1	no	—
59	C₂×D₄×C₁₇	—	4	1	no	—
60	C₂×D₄×C₁₇	—	4	1	no	—
61	C₂×D₄×C₁₇	—	4	1	no	—
62	C₂×D₄×C₁₇	—	4	1	no	—
63	C₂²×C₄×C₁₇	—	2	2	no	—
64	C₂²×C₄×C₁₇	—	4	1	no	—
65	C₂²×C₄×C₁₇	—	4	1	no	—
66	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₄×C₁₇	—	4	1	no	—
79	C₄⋊C₄×C₁₇	—	4	1	no	—
80	C₄⋊C₄×C₁₇	—	4	1	no	—
81	C₄⋊C₄×C₁₇	—	4	1	no	—
82	C₄⋊C₄×C₁₇	—	4	1	no	—
83	C₂²⋊C₄×C₁₇	—	2	2	no	—
84	C₂²⋊C₄×C₁₇	—	2	2	no	—
85	C₂²⋊C₄×C₁₇	—	2	2	no	—
86	C₂²⋊C₄×C₁₇	—	2	2	no	—
87	C₂²⋊C₄×C₁₇	—	4	1	no	—
88	C₂²⋊C₄×C₁₇	—	4	1	no	—
89	C₂²⋊C₄×C₁₇	—	4	1	no	—
90	C₂²⋊C₄×C₁₇	—	4	1	no	—
91	C₂²⋊C₄×C₁₇	—	4	1	no	—
92	C₂²⋊C₄×C₁₇	—	4	1	no	—
93	C₂²⋊C₄×C₁₇	—	4	1	no	—
94	C₂²⋊C₄×C₁₇	—	4	1	no	—
95	C₂²⋊C₄×C₁₇	—	4	1	no	—
96	C₂²⋊C₄×C₁₇	—	4	1	no	—
97	C₄²×C₁₇	—	2	2	no	—
98	C₄²×C₁₇	—	4	1	no	—
99	C₂³×C₁₇	—	2	1	no	—
100	C₂³×C₁₇	—	2	1	no	—
101	C₂³×C₁₇	—	2	1	no	—
102	C₂³×C₁₇	—	2	1	no	—
103	C₂³×C₁₇	—	2	1	no	—
104	C₂³×C₁₇	—	2	1	no	—
105	C₂³×C₁₇	—	2	1	no	—
106	C₂³×C₁₇	—	2	1	no	—
107	C₂³×C₁₇	—	2	1	no	—
108	C₂³×C₁₇	—	2	1	no	—
109	C₂³×C₁₇	—	2	1	no	—
110	C₂³×C₁₇	—	2	1	no	—
111	C₂³×C₁₇	—	2	1	no	—
112	C₂³×C₁₇	—	2	1	no	—
113	C₂³×C₁₇	—	2	1	no	—
114	C₂³×C₁₇	—	2	1	no	—
115	C₂³×C₁₇	—	2	1	no	—
116	C₂³×C₁₇	—	2	1	no	—
117	C₂³×C₁₇	—	2	1	no	—
118	C₂³×C₁₇	—	2	1	no	—
119	C₂³×C₁₇	#41	1	2	yes	—
120	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
121	D₄×C₁₇	—	4	4	no	—
122	D₄×C₁₇	—	4	4	no	—
123	D₄×C₁₇	—	4	4	no	—
124	C₂×C₄×C₁₇	—	2	1	no	—
125	C₂×C₄×C₁₇	—	2	1	no	—
126	C₂×C₄×C₁₇	—	2	1	no	—
127	C₂×C₄×C₁₇	—	2	1	no	—
128	C₂×C₄×C₁₇	—	2	1	no	—
129	C₂×C₄×C₁₇	—	2	1	no	—
130	C₂×C₄×C₁₇	—	2	1	no	—
131	C₂×C₄×C₁₇	—	2	1	no	—
132	C₂×C₄×C₁₇	—	2	1	no	—
133	C₂×C₄×C₁₇	—	2	1	no	—
134	C₂×C₄×C₁₇	—	2	1	no	—
135	C₂×C₄×C₁₇	—	2	1	no	—
136	C₂×C₄×C₁₇	—	2	1	no	—
137	C₂×C₄×C₁₇	—	2	1	no	—
138	C₂×C₄×C₁₇	—	2	1	no	—
139	C₂×C₄×C₁₇	—	2	1	no	—
140	C₂×C₄×C₁₇	—	2	1	no	—
141	C₂×C₄×C₁₇	—	2	1	no	—
142	C₂×C₄×C₁₇	—	2	1	no	—
143	C₂×C₄×C₁₇	—	2	1	no	—
144	C₂×C₄×C₁₇	—	2	1	no	—
145	C₂×C₄×C₁₇	—	2	1	no	—
146	C₂×C₄×C₁₇	—	2	1	no	—
147	C₂×C₄×C₁₇	—	2	1	no	—
148	C₂×C₄×C₁₇	—	2	1	no	—
149	C₂×C₄×C₁₇	—	2	1	no	—
150	C₂×C₄×C₁₇	—	2	1	no	—
151	C₂×C₄×C₁₇	—	2	1	no	—
152	C₂×C₄×C₁₇	—	2	1	no	—
153	C₂×C₄×C₁₇	—	2	1	no	—
154	C₂×C₄×C₁₇	—	2	1	no	—
155	C₂×C₄×C₁₇	—	2	1	no	—
156	C₂×C₄×C₁₇	—	2	1	no	—
157	C₂×C₄×C₁₇	—	2	1	no	—
158	C₂×C₄×C₁₇	—	4	4	no	—
159	C₂×C₄×C₁₇	#41	1	2	yes	—
160	C₂×C₄×C₁₇	#41	1	2	yes	—
161	#2756	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₁₇	—	2	2	no	—
163	C₂²×C₁₇	—	2	2	no	—
164	C₂²×C₁₇	—	2	2	no	—
165	C₂²×C₁₇	—	4	1	no	—
166	C₂²×C₁₇	—	4	1	no	—
167	C₂²×C₁₇	—	4	1	no	—
168	C₂²×C₁₇	—	4	1	no	—
169	C₂²×C₁₇	—	4	1	no	—
170	C₂²×C₁₇	—	4	1	no	—
171	C₂²×C₁₇	—	4	1	no	—
172	C₂²×C₁₇	—	4	1	no	—
173	C₂²×C₁₇	—	4	1	no	—
174	C₂²×C₁₇	—	4	1	no	—
175	C₂²×C₁₇	—	4	1	no	—
176	C₂²×C₁₇	—	4	1	no	—
177	C₂²×C₁₇	—	4	1	no	—
178	C₂²×C₁₇	—	4	1	no	—
179	C₂²×C₁₇	—	4	1	no	—
180	C₂²×C₁₇	—	4	1	no	—
181	C₂²×C₁₇	—	4	1	no	—
182	C₂²×C₁₇	—	4	1	no	—
183	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
184	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
185	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
186	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₄×C₁₇	—	2	2	no	—
191	C₄×C₁₇	—	2	2	no	—
192	C₄×C₁₇	—	4	1	no	—
193	C₄×C₁₇	—	4	1	no	—
194	C₄×C₁₇	—	4	1	no	—
195	C₄×C₁₇	—	4	1	no	—
196	C₄×C₁₇	—	4	1	no	—
197	C₄×C₁₇	—	4	1	no	—
198	C₄×C₁₇	—	4	1	no	—
199	C₄×C₁₇	—	4	1	no	—
200	C₄×C₁₇	—	4	1	no	—
201	C₄×C₁₇	—	4	1	no	—
202	#398	C₂×C₁₇	1	1	yes	characteristic, complemented
203	#397	C₂×C₁₇	1	1	yes	characteristic, complemented
204	#394	C₂×C₁₇	1	1	yes	characteristic, complemented
205	#394	C₂×C₁₇	1	1	yes	characteristic, complemented
206	#394	C₂×C₁₇	1	1	yes	characteristic, complemented
207	#392	C₂×C₁₇	1	1	yes	characteristic
208	#390	C₂×C₁₇	1	1	yes	characteristic, complemented
209	#388	C₂×C₁₇	1	1	yes	characteristic, complemented
210	#388	C₂×C₁₇	1	1	yes	characteristic, complemented
211	#388	C₂×C₁₇	1	1	yes	characteristic, complemented
212	#388	C₂×C₁₇	1	1	yes	characteristic, complemented
213	#386	C₂×C₁₇	1	1	yes	characteristic, complemented
214	#386	C₂×C₁₇	1	1	yes	characteristic, complemented
215	#383	C₂×C₁₇	1	1	yes	characteristic, complemented
216	#380	C₂×C₁₇	1	1	yes	characteristic, complemented
217	C₂×C₁₇	—	4	2	no	—
218	C₂×C₁₇	—	8	1	no	—
219	C₂×C₁₇	—	8	1	no	—
220	C₂×C₁₇	#538	1	1	yes	characteristic
221	C₂×C₁₇	#538	1	1	yes	characteristic
222	C₂×C₁₇	#540	1	1	yes	characteristic
223	C₂×C₁₇	#551	1	1	yes	characteristic
224	C₂×C₁₇	#553	1	1	yes	characteristic
225	C₂×C₁₇	#555	1	1	yes	characteristic
226	C₂×C₁₇	#560	1	1	yes	characteristic
227	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
228	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
229	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
230	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
252	#95	C₂²×C₁₇	1	1	yes	characteristic
253	#95	C₂²×C₁₇	1	1	yes	characteristic
254	#95	C₂²×C₁₇	1	1	yes	characteristic
255	#95	C₂²×C₁₇	1	1	yes	characteristic
256	#95	C₂²×C₁₇	1	1	yes	characteristic
257	#95	C₂²×C₁₇	1	1	yes	characteristic
258	#95	C₂²×C₁₇	1	1	yes	characteristic
259	#95	C₂²×C₁₇	1	1	yes	characteristic
260	#95	C₂²×C₁₇	1	1	yes	characteristic
261	#95	C₂²×C₁₇	1	1	yes	characteristic
262	C₁₇	#2756	1	1	yes	characteristic, direct product factor, Sylow
263	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
264	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
265	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	4	1	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	#41×C₁₇	1	2	yes	—
332	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	#41×C₁₇	1	2	yes	—
372	C₂×C₄	#41×C₁₇	1	2	yes	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
395	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
396	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
397	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₂	—	4	2	no	—
414	C₂	—	8	1	no	—
415	C₂	—	8	1	no	—
416	C₂	C₁₇×#538	1	1	yes	characteristic
417	C₂	C₁₇×#538	1	1	yes	characteristic
418	C₂	C₁₇×#540	1	1	yes	characteristic
419	C₂	C₁₇×#551	1	1	yes	characteristic
420	C₂	C₁₇×#553	1	1	yes	characteristic
421	C₂	C₁₇×#555	1	1	yes	characteristic
422	C₂	C₁₇×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₁₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#398	C₂	semidirect
2. C₁₇×#397	C₂	semidirect
3. C₁₇×#394	C₂	semidirect
4. C₁₇×#394	C₂	semidirect
5. C₁₇×#394	C₂	semidirect
7. C₁₇×#390	C₂	semidirect
8. C₁₇×#388	C₂	semidirect
9. C₁₇×#388	C₂	semidirect
10. C₁₇×#388	C₂	semidirect
11. C₁₇×#388	C₂	semidirect
12. C₁₇×#386	C₂	semidirect
13. C₁₇×#386	C₂	semidirect
14. C₁₇×#383	C₂	semidirect
15. C₁₇×#380	C₂	semidirect
161. #2756	C₁₇	direct (N × H)
202. #398	C₂×C₁₇	semidirect
203. #397	C₂×C₁₇	semidirect
204. #394	C₂×C₁₇	semidirect
205. #394	C₂×C₁₇	semidirect
206. #394	C₂×C₁₇	semidirect
208. #390	C₂×C₁₇	semidirect
209. #388	C₂×C₁₇	semidirect
210. #388	C₂×C₁₇	semidirect
211. #388	C₂×C₁₇	semidirect
212. #388	C₂×C₁₇	semidirect
213. #386	C₂×C₁₇	semidirect
214. #386	C₂×C₁₇	semidirect
215. #383	C₂×C₁₇	semidirect
216. #380	C₂×C₁₇	semidirect
262. C₁₇	#2756	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#398	2
C₁₇×#397	2
C₁₇×#394	2
C₁₇×#392	2
C₁₇×#390	2
C₁₇×#388	2
C₁₇×#386	2
C₁₇×#383	2
C₁₇×#380	2
#2756	17

Subgroups — C17×#2756 #14525762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#2756 #14525762