Subgroups — C₂×C₁₇×#3341 #16918976

Order 4352.

1982 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#555	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3341	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#482	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₇×#476	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₇×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₇	C₂²	1	2	yes	—
12	C₁₇×#555	—	2	8	no	—
13	C₁₇×#555	C₂²	1	16	yes	complemented
14	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₇×#124	—	2	4	no	—
16	C₂×C₁₇×#121	—	2	2	no	—
17	C₂×C₁₇×#121	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#117	—	2	2	no	—
21	C₂×C₁₇×#117	C₂²	1	4	yes	—
22	C₁₇×#500	C₂²	1	8	yes	complemented
23	C₁₇×#482	C₂²	1	32	yes	complemented
24	C₁₇×#476	C₂²	1	16	yes	complemented
25	C₁₇×#466	C₂²	1	16	yes	complemented
26	C₄×D₈×C₁₇	C₂²	1	8	yes	complemented
27	C₈×D₄×C₁₇	C₂²	1	8	yes	complemented
28	C₁₇×#427	C₂²	1	16	yes	complemented
29	C₂×C₁₇×#107	C₂²	1	2	yes	—
30	C₂×C₁₇×#107	C₂²	1	2	yes	—
31	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#106	C₂²	1	4	yes	—
33	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#102	C₂²	1	4	yes	—
35	C₂×C₁₇×#102	C₂²	1	2	yes	—
36	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₁₇	—	2	2	no	—
39	C₂²×D₄×C₁₇	—	2	4	no	—
40	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₇	—	2	2	no	—
43	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
44	C₂×D₈×C₁₇	—	2	4	no	—
45	C₂×D₈×C₁₇	C₂³	1	4	yes	—
46	C₂²×C₈×C₁₇	—	2	8	no	—
47	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
49	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
51	C₁₇×C₄⋊Q₈	—	2	4	no	—
52	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
53	C₁₇×#124	—	2	32	no	—
54	C₁₇×#121	—	2	16	no	—
55	C₁₇×#121	—	2	8	no	—
56	C₁₇×#121	C₂³	1	16	yes	—
57	C₄×D₄×C₁₇	—	2	4	no	—
58	C₄×D₄×C₁₇	D₄	1	4	yes	—
59	C₄×D₄×C₁₇	C₂³	1	8	yes	—
60	C₄×D₄×C₁₇	C₂³	1	4	yes	—
61	C₁₇×#117	—	2	8	no	—
62	C₁₇×#117	—	2	16	no	—
63	C₁₇×#117	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
72	C₂×C₄²×C₁₇	—	2	4	no	—
73	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
74	C₁₇×#107	C₂³	1	8	yes	—
75	C₁₇×#107	C₂³	1	8	yes	—
76	C₁₇×#107	C₂³	1	4	yes	—
77	C₁₇×#106	C₂³	1	16	yes	—
78	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₇×#102	C₂³	1	8	yes	—
80	C₁₇×#102	C₂³	1	16	yes	—
81	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₁₇	C₂³	1	4	yes	—
83	C₂⁴×C₁₇	—	2	2	no	—
84	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
85	C₂×Q₈×C₁₇	—	2	8	no	—
86	C₂×Q₈×C₁₇	—	8	4	no	—
87	C₂×D₄×C₁₇	—	2	16	no	—
88	C₂×D₄×C₁₇	—	2	4	no	—
89	C₂×D₄×C₁₇	—	2	2	no	—
90	C₂×D₄×C₁₇	—	2	4	no	—
91	C₂×D₄×C₁₇	—	2	4	no	—
92	C₂×D₄×C₁₇	—	8	8	no	—
93	C₂×D₄×C₁₇	C₂×D₄	1	4	yes	—
94	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₁₇	—	2	4	no	—
96	C₂²×C₄×C₁₇	—	2	4	no	—
97	C₂²×C₄×C₁₇	—	2	2	no	—
98	C₂²×C₄×C₁₇	—	2	4	no	—
99	C₂²×C₄×C₁₇	—	2	8	no	—
100	C₂²×C₄×C₁₇	—	4	8	no	—
101	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
107	D₈×C₁₇	—	2	8	no	—
108	C₂×C₈×C₁₇	—	2	4	no	—
109	C₂×C₈×C₁₇	—	2	2	no	—
110	C₂×C₈×C₁₇	—	2	16	no	—
111	C₂×C₈×C₁₇	#41	1	4	yes	—
112	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
113	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
114	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₁₇	—	2	4	no	—
116	C₄⋊C₄×C₁₇	—	2	8	no	—
117	C₄⋊C₄×C₁₇	—	2	2	no	—
118	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
119	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
120	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
121	C₂²⋊C₄×C₁₇	—	2	16	no	—
122	C₂²⋊C₄×C₁₇	—	2	8	no	—
123	C₂²⋊C₄×C₁₇	—	2	16	no	—
124	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
125	C₄²×C₁₇	—	2	16	no	—
126	C₄²×C₁₇	C₂×D₄	1	2	yes	—
127	C₄²×C₁₇	C₂⁴	1	2	yes	—
128	C₂×#3341	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₇	—	2	4	no	—
130	C₂³×C₁₇	—	2	4	no	—
131	C₂³×C₁₇	—	2	4	no	—
132	C₂³×C₁₇	—	2	4	no	—
133	C₂³×C₁₇	—	4	4	no	—
134	C₂³×C₁₇	—	4	4	no	—
135	C₂³×C₁₇	—	4	4	no	—
136	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
137	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₁₇	—	8	8	no	—
139	D₄×C₁₇	—	2	8	no	—
140	D₄×C₁₇	—	2	4	no	—
141	D₄×C₁₇	—	2	4	no	—
142	D₄×C₁₇	—	4	4	no	—
143	D₄×C₁₇	—	8	16	no	—
144	C₂×C₄×C₁₇	—	2	4	no	—
145	C₂×C₄×C₁₇	—	2	2	no	—
146	C₂×C₄×C₁₇	—	2	8	no	—
147	C₂×C₄×C₁₇	—	2	4	no	—
148	C₂×C₄×C₁₇	—	2	4	no	—
149	C₂×C₄×C₁₇	—	2	4	no	—
150	C₂×C₄×C₁₇	—	2	8	no	—
151	C₂×C₄×C₁₇	—	4	4	no	—
152	C₂×C₄×C₁₇	—	4	8	no	—
153	C₂×C₄×C₁₇	—	4	16	no	—
154	C₂×C₄×C₁₇	#135	1	4	yes	—
155	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
156	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
160	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
161	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
162	C₈×C₁₇	—	2	4	no	—
163	C₈×C₁₇	—	2	2	no	—
164	C₈×C₁₇	C₂×#41	1	4	yes	—
165	C₂×#555	C₂×C₁₇	1	2	yes	complemented
166	#3341	C₂×C₁₇	1	16	yes	direct product factor
167	C₂×#500	C₂×C₁₇	1	1	yes	characteristic, complemented
168	C₂×#482	C₂×C₁₇	1	4	yes	complemented
169	C₂×#476	C₂×C₁₇	1	2	yes	complemented
170	C₂×#466	C₂×C₁₇	1	2	yes	complemented
171	C₂×C₄×D₈	C₂×C₁₇	1	1	yes	characteristic, complemented
172	C₂×C₈×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
173	C₂×#427	C₂×C₁₇	1	2	yes	complemented
174	C₂²×C₁₇	—	2	4	no	—
175	C₂²×C₁₇	—	2	4	no	—
176	C₂²×C₁₇	—	2	4	no	—
177	C₂²×C₁₇	—	4	8	no	—
178	C₂²×C₁₇	—	4	4	no	—
179	C₂²×C₁₇	—	4	4	no	—
180	C₂²×C₁₇	—	4	4	no	—
181	C₂²×C₁₇	—	8	8	no	—
182	C₂²×C₁₇	#547	1	2	yes	—
183	C₂²×C₁₇	C₂×#135	1	2	yes	—
184	C₂²×C₁₇	#576	1	2	yes	—
185	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
186	C₄×C₁₇	—	2	4	no	—
187	C₄×C₁₇	—	2	2	no	—
188	C₄×C₁₇	—	4	4	no	—
189	C₄×C₁₇	—	4	8	no	—
190	C₄×C₁₇	#547	1	2	yes	—
191	C₄×C₁₇	C₂×#135	1	4	yes	—
192	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
193	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
194	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₁₇	1	2	yes	—
196	#555	—	2	8	no	—
197	#555	C₂²×C₁₇	1	16	yes	complemented
198	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
199	C₂×#124	—	2	4	no	—
200	C₂×#121	—	2	2	no	—
201	C₂×#121	C₂²×C₁₇	1	4	yes	—
202	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
203	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
204	C₂×#117	—	2	2	no	—
205	C₂×#117	C₂²×C₁₇	1	4	yes	—
206	#500	C₂²×C₁₇	1	8	yes	complemented
207	#482	C₂²×C₁₇	1	32	yes	complemented
208	#476	C₂²×C₁₇	1	16	yes	complemented
209	#466	C₂²×C₁₇	1	16	yes	complemented
210	C₄×D₈	C₂²×C₁₇	1	8	yes	complemented
211	C₈×D₄	C₂²×C₁₇	1	8	yes	complemented
212	#427	C₂²×C₁₇	1	16	yes	complemented
213	C₂×#107	C₂²×C₁₇	1	2	yes	—
214	C₂×#107	C₂²×C₁₇	1	2	yes	—
215	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₇	1	4	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
218	C₂×#102	C₂²×C₁₇	1	2	yes	—
219	C₂×#102	C₂²×C₁₇	1	4	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
222	C₂×C₁₇	—	4	4	no	—
223	C₂×C₁₇	—	8	4	no	—
224	C₂×C₁₇	#3341	1	4	yes	direct product factor
225	C₂×C₁₇	C₂×#547	1	1	yes	characteristic
226	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
227	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×D₄	—	2	4	no	—
230	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
231	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
234	C₂×D₈	—	2	4	no	—
235	C₂×D₈	C₂³×C₁₇	1	4	yes	—
236	C₂²×C₈	—	2	8	no	—
237	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
239	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	4	no	—
242	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
243	#124	—	2	32	no	—
244	#121	—	2	16	no	—
245	#121	—	2	8	no	—
246	#121	C₂³×C₁₇	1	16	yes	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	D₄×C₁₇	1	4	yes	—
249	C₄×D₄	C₂³×C₁₇	1	8	yes	—
250	C₄×D₄	C₂³×C₁₇	1	4	yes	—
251	#117	—	2	8	no	—
252	#117	—	2	16	no	—
253	#117	C₂³×C₁₇	1	16	yes	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
264	#107	C₂³×C₁₇	1	4	yes	—
265	#107	C₂³×C₁₇	1	8	yes	—
266	#107	C₂³×C₁₇	1	8	yes	—
267	#106	C₂³×C₁₇	1	16	yes	—
268	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
269	#102	C₂³×C₁₇	1	8	yes	—
270	#102	C₂³×C₁₇	1	16	yes	—
271	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
272	C₄×C₈	C₂³×C₁₇	1	4	yes	—
273	C₁₇	C₂×#3341	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	2	no	—
275	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	8	4	no	—
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	8	8	no	—
284	C₂×D₄	C₂×D₄×C₁₇	1	4	yes	—
285	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
298	D₈	—	2	8	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	16	no	—
302	C₂×C₈	#41×C₁₇	1	4	yes	—
303	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
304	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
305	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
310	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
311	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
316	C₄²	—	2	16	no	—
317	C₄²	C₂×D₄×C₁₇	1	2	yes	—
318	C₄²	C₂⁴×C₁₇	1	2	yes	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
327	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
328	Q₈	—	8	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	8	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	C₁₇×#135	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
349	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
350	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
351	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	C₂×#41×C₁₇	1	4	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	C₁₇×#547	1	2	yes	—
364	C₂²	C₂×C₁₇×#135	1	2	yes	—
365	C₂²	C₁₇×#576	1	2	yes	—
366	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	8	no	—
371	C₄	C₁₇×#547	1	2	yes	—
372	C₄	C₂×C₁₇×#135	1	4	yes	—
373	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
374	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂	—	4	4	no	—
376	C₂	—	8	4	no	—
377	C₂	C₁₇×#3341	1	4	yes	direct product factor
378	C₂	C₂×C₁₇×#547	1	1	yes	characteristic
379	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
380	C₂	C₂×C₁₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
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×#555	C₂	semidirect
2. C₁₇×#3341	C₂	direct (N × H)
3. C₂×C₁₇×#500	C₂	semidirect
4. C₂×C₁₇×#482	C₂	semidirect
5. C₂×C₁₇×#476	C₂	semidirect
6. C₂×C₁₇×#466	C₂	semidirect
7. C₂×C₄×D₈×C₁₇	C₂	semidirect
8. C₂×C₈×D₄×C₁₇	C₂	semidirect
9. C₂×C₁₇×#427	C₂	semidirect
13. C₁₇×#555	C₂²	semidirect
22. C₁₇×#500	C₂²	semidirect
23. C₁₇×#482	C₂²	semidirect
24. C₁₇×#476	C₂²	semidirect
25. C₁₇×#466	C₂²	semidirect
26. C₄×D₈×C₁₇	C₂²	semidirect
27. C₈×D₄×C₁₇	C₂²	semidirect
28. C₁₇×#427	C₂²	semidirect
128. C₂×#3341	C₁₇	direct (N × H)
165. C₂×#555	C₂×C₁₇	semidirect
166. #3341	C₂×C₁₇	direct (N × H)
167. C₂×#500	C₂×C₁₇	semidirect
168. C₂×#482	C₂×C₁₇	semidirect
169. C₂×#476	C₂×C₁₇	semidirect
170. C₂×#466	C₂×C₁₇	semidirect
171. C₂×C₄×D₈	C₂×C₁₇	semidirect
172. C₂×C₈×D₄	C₂×C₁₇	semidirect
173. C₂×#427	C₂×C₁₇	semidirect
197. #555	C₂²×C₁₇	semidirect
206. #500	C₂²×C₁₇	semidirect
207. #482	C₂²×C₁₇	semidirect
208. #476	C₂²×C₁₇	semidirect
209. #466	C₂²×C₁₇	semidirect
210. C₄×D₈	C₂²×C₁₇	semidirect
211. C₈×D₄	C₂²×C₁₇	semidirect
212. #427	C₂²×C₁₇	semidirect
224. C₂×C₁₇	#3341	direct (N × H)
273. C₁₇	C₂×#3341	direct (N × H)
377. C₂	C₁₇×#3341	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×#555	2
C₁₇×#3341	2
C₂×C₁₇×#500	2
C₂×C₁₇×#482	2
C₂×C₁₇×#476	2
C₂×C₁₇×#466	2
C₂×C₄×D₈×C₁₇	2
C₂×C₈×D₄×C₁₇	2
C₂×C₁₇×#427	2
C₂×#3341	17

Subgroups — C2×C17×#3341 #16918976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3341 #16918976