Subgroups — C₁₇×#61900 #16919644

Order 4352.

1692 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3398	C₂	1	6	yes	maximal, complemented
4	C₁₇×#3395	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3374	C₂	1	6	yes	maximal, complemented
6	C₁₇×#3359	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3218	C₂	1	3	yes	maximal
8	C₁₇×#3209	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3113	C₂	1	3	yes	maximal, complemented
10	C₁₇×#3108	C₂	1	3	yes	maximal
11	C₁₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#557	—	2	1	no	—
13	C₁₇×#557	—	2	3	no	—
14	C₁₇×#557	C₂²	1	2	yes	—
15	C₁₇×#557	C₂²	1	6	yes	—
16	C₁₇×#557	C₂²	1	1	yes	characteristic
17	C₁₇×#557	C₂²	1	3	yes	—
18	C₁₇×#556	C₂²	1	3	yes	—
19	C₁₇×#552	—	2	3	no	—
20	D₄×Q₈×C₁₇	—	2	1	no	—
21	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#541	—	2	3	no	—
23	C₁₇×#533	C₂²	1	3	yes	—
24	C₂×C₁₇×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₁₇×#529	C₂²	1	3	yes	—
26	C₂×C₁₇×#125	—	2	3	no	—
27	C₁₇×#519	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₇	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
31	C₁₇×#497	C₂²	1	6	yes	—
32	C₁₇×#494	C₂²	1	6	yes	—
33	C₁₇×#491	C₂²	1	6	yes	—
34	C₁₇×#487	C₂²	1	6	yes	—
35	C₁₇×#483	C₂²	1	3	yes	—
36	C₁₇×#480	C₂²	1	1	yes	characteristic
37	C₁₇×#479	C₂²	1	6	yes	—
38	C₁₇×#475	C₂²	1	6	yes	—
39	C₁₇×#464	C₂²	1	6	yes	—
40	C₁₇×#462	C₂²	1	12	yes	—
41	C₁₇×#462	C₂²	1	6	yes	—
42	C₁₇×#462	C₂²	1	6	yes	—
43	C₁₇×#461	C₂²	1	6	yes	—
44	C₁₇×#451	C₂²	1	3	yes	—
45	C₁₇×#451	C₂²	1	6	yes	—
46	C₁₇×#448	C₂²	1	3	yes	—
47	C₁₇×#446	C₂²	1	6	yes	—
48	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
49	C₁₇×#441	C₂²	1	12	yes	—
50	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
51	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
52	C₁₇×#432	C₂²	1	3	yes	—
53	C₁₇×#431	C₂²	1	3	yes	—
54	C₂²×Q₈×C₁₇	—	2	1	no	—
55	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₇	C₂³	1	3	yes	—
57	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
58	C₂×Q₁₆×C₁₇	C₂³	1	12	yes	—
59	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
60	C₁₇×C₄⋊Q₈	—	2	3	no	—
61	C₁₇×C₄⋊Q₈	—	2	3	no	—
62	C₁₇×C₄⋊Q₈	—	2	3	no	—
63	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
64	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
65	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
66	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₇×#126	—	2	6	no	—
68	C₁₇×#126	—	2	3	no	—
69	C₁₇×#125	—	2	6	no	—
70	C₁₇×#125	—	2	12	no	—
71	C₁₇×#125	—	2	6	no	—
72	C₁₇×#125	—	2	6	no	—
73	C₁₇×#125	—	2	3	no	—
74	C₁₇×#125	—	2	3	no	—
75	C₁₇×#125	C₂³	1	3	yes	—
76	C₁₇×#124	C₂³	1	3	yes	—
77	C₁₇×#123	—	2	3	no	—
78	C₁₇×C₂²⋊Q₈	—	2	3	no	—
79	C₁₇×C₂²⋊Q₈	—	2	3	no	—
80	C₁₇×C₂²⋊Q₈	—	2	3	no	—
81	C₁₇×C₂²⋊Q₈	C₂³	1	3	yes	—
82	C₁₇×#121	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₁₇	—	2	6	no	—
84	C₄×Q₈×C₁₇	—	2	2	no	—
85	C₄×Q₈×C₁₇	—	2	1	no	—
86	C₄×Q₈×C₁₇	—	2	3	no	—
87	C₄×Q₈×C₁₇	—	2	3	no	—
88	C₄×Q₈×C₁₇	—	2	3	no	—
89	C₄×Q₈×C₁₇	—	2	3	no	—
90	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₇	D₄	1	3	yes	—
92	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
93	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
94	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
96	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
98	C₄×D₄×C₁₇	—	2	3	no	—
99	C₄×D₄×C₁₇	C₂³	1	3	yes	—
100	C₁₇×#117	—	2	3	no	—
101	C₁₇×#117	—	2	3	no	—
102	C₁₇×#117	—	2	3	no	—
103	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
104	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
105	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
106	C₂×C₄⋊C₄×C₁₇	D₄	1	3	yes	—
107	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₇	—	2	3	no	—
109	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
110	C₁₇×#107	C₂³	1	2	yes	—
111	C₁₇×#106	C₂³	1	6	yes	—
112	C₁₇×C₄⋊C₈	C₂³	1	6	yes	—
113	C₁₇×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₇×#103	C₂³	1	6	yes	—
115	C₁₇×#103	C₂³	1	12	yes	—
116	C₁₇×#103	C₂³	1	6	yes	—
117	C₁₇×#103	C₂³	1	6	yes	—
118	C₁₇×#102	C₂³	1	2	yes	—
119	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₇×C₂²⋊C₈	C₂³	1	3	yes	—
121	C₁₇×#97	C₂³	1	6	yes	—
122	C₄×C₈×C₁₇	C₂³	1	6	yes	—
123	C₂×Q₈×C₁₇	—	2	4	no	—
124	C₂×Q₈×C₁₇	—	2	3	no	—
125	C₂×Q₈×C₁₇	—	2	3	no	—
126	C₂×Q₈×C₁₇	—	4	6	no	—
127	C₂×Q₈×C₁₇	—	4	4	no	—
128	C₂×Q₈×C₁₇	C₂×D₄	1	3	yes	—
129	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
131	C₂×Q₈×C₁₇	C₂⁴	1	6	yes	—
132	C₂×D₄×C₁₇	—	2	1	no	—
133	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	—	2	3	no	—
135	C₂²×C₄×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	—	2	3	no	—
137	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
138	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
139	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₁₇	—	4	12	no	—
141	Q₁₆×C₁₇	—	4	6	no	—
142	SD₁₆×C₁₇	—	4	6	no	—
143	C₂×C₈×C₁₇	C₂⁴	1	6	yes	—
144	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₁₇	—	2	3	no	—
146	C₄⋊C₄×C₁₇	—	2	6	no	—
147	C₄⋊C₄×C₁₇	—	2	3	no	—
148	C₄⋊C₄×C₁₇	—	2	3	no	—
149	C₄⋊C₄×C₁₇	—	2	3	no	—
150	C₄⋊C₄×C₁₇	—	2	3	no	—
151	C₄⋊C₄×C₁₇	—	2	6	no	—
152	C₄⋊C₄×C₁₇	—	2	6	no	—
153	C₄⋊C₄×C₁₇	—	2	6	no	—
154	C₄⋊C₄×C₁₇	—	2	6	no	—
155	C₄⋊C₄×C₁₇	—	2	3	no	—
156	C₄⋊C₄×C₁₇	—	2	3	no	—
157	C₄⋊C₄×C₁₇	—	2	6	no	—
158	C₄⋊C₄×C₁₇	—	2	6	no	—
159	C₄⋊C₄×C₁₇	—	2	1	no	—
160	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
161	C₄⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
162	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
163	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
164	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
166	C₂²⋊C₄×C₁₇	—	2	3	no	—
167	C₂²⋊C₄×C₁₇	—	2	3	no	—
168	C₂²⋊C₄×C₁₇	—	2	3	no	—
169	C₂²⋊C₄×C₁₇	—	2	3	no	—
170	C₂²⋊C₄×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	6	no	—
172	C₄²×C₁₇	—	2	6	no	—
173	C₄²×C₁₇	—	2	6	no	—
174	C₄²×C₁₇	—	2	3	no	—
175	C₄²×C₁₇	C₂×D₄	1	3	yes	—
176	C₄²×C₁₇	C₂×D₄	1	3	yes	—
177	C₄²×C₁₇	C₂⁴	1	3	yes	—
178	C₄²×C₁₇	C₂⁴	1	3	yes	—
179	#61900	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₇	—	2	1	no	—
181	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₇	—	2	6	no	—
183	Q₈×C₁₇	—	2	6	no	—
184	Q₈×C₁₇	—	2	6	no	—
185	Q₈×C₁₇	—	2	6	no	—
186	Q₈×C₁₇	—	4	6	no	—
187	Q₈×C₁₇	—	4	6	no	—
188	Q₈×C₁₇	#137	1	4	yes	—
189	D₄×C₁₇	—	2	2	no	—
190	D₄×C₁₇	—	4	2	no	—
191	C₂×C₄×C₁₇	—	2	6	no	—
192	C₂×C₄×C₁₇	—	2	6	no	—
193	C₂×C₄×C₁₇	—	2	2	no	—
194	C₂×C₄×C₁₇	—	2	2	no	—
195	C₂×C₄×C₁₇	—	2	3	no	—
196	C₂×C₄×C₁₇	—	2	1	no	—
197	C₂×C₄×C₁₇	—	2	3	no	—
198	C₂×C₄×C₁₇	—	2	6	no	—
199	C₂×C₄×C₁₇	—	4	6	no	—
200	C₂×C₄×C₁₇	—	4	2	no	—
201	C₂×C₄×C₁₇	—	4	6	no	—
202	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
203	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
204	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
206	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
207	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
208	C₈×C₁₇	—	2	6	no	—
209	C₈×C₁₇	—	2	2	no	—
210	#3523	C₂×C₁₇	1	1	yes	characteristic
211	C₂×#557	C₂×C₁₇	1	1	yes	characteristic, complemented
212	#3398	C₂×C₁₇	1	6	yes	complemented
213	#3395	C₂×C₁₇	1	2	yes	complemented
214	#3374	C₂×C₁₇	1	6	yes	complemented
215	#3359	C₂×C₁₇	1	2	yes	complemented
216	#3218	C₂×C₁₇	1	3	yes	—
217	#3209	C₂×C₁₇	1	3	yes	complemented
218	#3113	C₂×C₁₇	1	3	yes	complemented
219	#3108	C₂×C₁₇	1	3	yes	—
220	#2984	C₂×C₁₇	1	1	yes	characteristic, complemented
221	C₂²×C₁₇	—	2	1	no	—
222	C₂²×C₁₇	—	2	1	no	—
223	C₂²×C₁₇	—	4	1	no	—
224	C₂²×C₁₇	—	4	1	no	—
225	C₂²×C₁₇	—	4	1	no	—
226	C₂²×C₁₇	#578	1	2	yes	—
227	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
228	C₄×C₁₇	—	2	1	no	—
229	C₄×C₁₇	—	2	3	no	—
230	C₄×C₁₇	—	2	3	no	—
231	C₄×C₁₇	—	2	3	no	—
232	C₄×C₁₇	—	4	6	no	—
233	C₄×C₁₇	—	4	3	no	—
234	C₄×C₁₇	—	4	3	no	—
235	C₄×C₁₇	—	4	2	no	—
236	C₄×C₁₇	—	4	1	no	—
237	C₄×C₁₇	C₂×#137	1	6	yes	—
238	C₄×C₁₇	#585	1	2	yes	—
239	#557	—	2	1	no	—
240	#557	—	2	3	no	—
241	#557	C₂²×C₁₇	1	2	yes	—
242	#557	C₂²×C₁₇	1	6	yes	—
243	#557	C₂²×C₁₇	1	1	yes	characteristic
244	#557	C₂²×C₁₇	1	3	yes	—
245	#556	C₂²×C₁₇	1	3	yes	—
246	#552	—	2	3	no	—
247	D₄×Q₈	—	2	1	no	—
248	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
249	#541	—	2	3	no	—
250	#533	C₂²×C₁₇	1	3	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₁₇	1	3	yes	—
252	#529	C₂²×C₁₇	1	3	yes	—
253	C₂×#125	—	2	3	no	—
254	#519	—	2	1	no	—
255	C₂×C₄×Q₈	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₁₇	1	3	yes	—
257	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
258	#497	C₂²×C₁₇	1	6	yes	—
259	#494	C₂²×C₁₇	1	6	yes	—
260	#491	C₂²×C₁₇	1	6	yes	—
261	#487	C₂²×C₁₇	1	6	yes	—
262	#483	C₂²×C₁₇	1	3	yes	—
263	#480	C₂²×C₁₇	1	1	yes	characteristic
264	#479	C₂²×C₁₇	1	6	yes	—
265	#475	C₂²×C₁₇	1	6	yes	—
266	#464	C₂²×C₁₇	1	6	yes	—
267	#462	C₂²×C₁₇	1	6	yes	—
268	#462	C₂²×C₁₇	1	6	yes	—
269	#462	C₂²×C₁₇	1	12	yes	—
270	#461	C₂²×C₁₇	1	6	yes	—
271	#451	C₂²×C₁₇	1	3	yes	—
272	#451	C₂²×C₁₇	1	6	yes	—
273	#448	C₂²×C₁₇	1	3	yes	—
274	#446	C₂²×C₁₇	1	6	yes	—
275	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
276	#441	C₂²×C₁₇	1	12	yes	—
277	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
278	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
279	#432	C₂²×C₁₇	1	3	yes	—
280	#431	C₂²×C₁₇	1	3	yes	—
281	C₂×C₁₇	—	2	2	no	—
282	C₂×C₁₇	—	8	1	no	—
283	C₂×C₁₇	#3487	1	1	yes	characteristic
284	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
285	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₇	1	3	yes	—
289	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
290	C₂×Q₁₆	C₂³×C₁₇	1	12	yes	—
291	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
292	C₄⋊Q₈	—	2	3	no	—
293	C₄⋊Q₈	—	2	3	no	—
294	C₄⋊Q₈	—	2	3	no	—
295	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
296	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
297	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
298	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
299	#126	—	2	6	no	—
300	#126	—	2	3	no	—
301	#125	—	2	6	no	—
302	#125	—	2	6	no	—
303	#125	—	2	12	no	—
304	#125	—	2	6	no	—
305	#125	—	2	3	no	—
306	#125	—	2	3	no	—
307	#125	C₂³×C₁₇	1	3	yes	—
308	#124	C₂³×C₁₇	1	3	yes	—
309	#123	—	2	3	no	—
310	C₂²⋊Q₈	—	2	3	no	—
311	C₂²⋊Q₈	—	2	3	no	—
312	C₂²⋊Q₈	—	2	3	no	—
313	C₂²⋊Q₈	C₂³×C₁₇	1	3	yes	—
314	#121	C₂³×C₁₇	1	1	yes	characteristic
315	C₄×Q₈	—	2	6	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	3	no	—
319	C₄×Q₈	—	2	3	no	—
320	C₄×Q₈	—	2	3	no	—
321	C₄×Q₈	—	2	3	no	—
322	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
323	C₄×Q₈	D₄×C₁₇	1	3	yes	—
324	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
325	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
326	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
327	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
328	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
329	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
330	C₄×D₄	—	2	3	no	—
331	C₄×D₄	C₂³×C₁₇	1	3	yes	—
332	#117	—	2	3	no	—
333	#117	—	2	3	no	—
334	#117	—	2	3	no	—
335	C₂×C₄⋊C₄	—	2	3	no	—
336	C₂×C₄⋊C₄	—	2	3	no	—
337	C₂×C₄⋊C₄	—	2	3	no	—
338	C₂×C₄⋊C₄	D₄×C₁₇	1	3	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
340	C₂×C₄²	—	2	3	no	—
341	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
342	#107	C₂³×C₁₇	1	2	yes	—
343	#106	C₂³×C₁₇	1	6	yes	—
344	C₄⋊C₈	C₂³×C₁₇	1	6	yes	—
345	C₄⋊C₈	C₂³×C₁₇	1	6	yes	—
346	#103	C₂³×C₁₇	1	6	yes	—
347	#103	C₂³×C₁₇	1	6	yes	—
348	#103	C₂³×C₁₇	1	6	yes	—
349	#103	C₂³×C₁₇	1	12	yes	—
350	#102	C₂³×C₁₇	1	2	yes	—
351	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
352	C₂²⋊C₈	C₂³×C₁₇	1	3	yes	—
353	#97	C₂³×C₁₇	1	6	yes	—
354	C₄×C₈	C₂³×C₁₇	1	6	yes	—
355	C₁₇	#61900	1	1	yes	characteristic, direct product factor, Sylow
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	3	no	—
358	C₂×Q₈	—	2	3	no	—
359	C₂×Q₈	—	4	6	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	C₂×D₄×C₁₇	1	3	yes	—
362	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
363	C₂×Q₈	C₂⁴×C₁₇	1	6	yes	—
364	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	3	no	—
369	C₂²×C₄	—	2	3	no	—
370	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
371	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
372	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
373	Q₁₆	—	4	12	no	—
374	Q₁₆	—	4	6	no	—
375	SD₁₆	—	4	6	no	—
376	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
377	C₂×C₈	C₂⁴×C₁₇	1	6	yes	—
378	C₄⋊C₄	—	2	6	no	—
379	C₄⋊C₄	—	2	6	no	—
380	C₄⋊C₄	—	2	6	no	—
381	C₄⋊C₄	—	2	6	no	—
382	C₄⋊C₄	—	2	6	no	—
383	C₄⋊C₄	—	2	6	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	3	no	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	3	no	—
388	C₄⋊C₄	—	2	3	no	—
389	C₄⋊C₄	—	2	3	no	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	6	no	—
392	C₄⋊C₄	—	2	3	no	—
393	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
394	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
395	C₄⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
396	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
397	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
398	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	3	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	3	no	—
402	C₂²⋊C₄	—	2	3	no	—
403	C₂²⋊C₄	—	2	3	no	—
404	C₄²	—	2	6	no	—
405	C₄²	—	2	6	no	—
406	C₄²	—	2	6	no	—
407	C₄²	—	2	3	no	—
408	C₄²	C₂×D₄×C₁₇	1	3	yes	—
409	C₄²	C₂×D₄×C₁₇	1	3	yes	—
410	C₄²	C₂⁴×C₁₇	1	3	yes	—
411	C₄²	C₂⁴×C₁₇	1	3	yes	—
412	C₂³	—	2	1	no	—
413	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
414	Q₈	—	2	6	no	—
415	Q₈	—	2	6	no	—
416	Q₈	—	2	6	no	—
417	Q₈	—	2	6	no	—
418	Q₈	—	4	6	no	—
419	Q₈	—	4	6	no	—
420	Q₈	C₁₇×#137	1	4	yes	—
421	D₄	—	2	2	no	—
422	D₄	—	4	2	no	—
423	C₂×C₄	—	2	6	no	—
424	C₂×C₄	—	2	6	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	3	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	3	no	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	4	6	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	6	no	—
434	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
435	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
436	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
438	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
439	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
440	C₈	—	2	6	no	—
441	C₈	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	C₁₇×#578	1	2	yes	—
448	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	3	no	—
451	C₄	—	2	3	no	—
452	C₄	—	2	3	no	—
453	C₄	—	4	6	no	—
454	C₄	—	4	3	no	—
455	C₄	—	4	3	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	1	no	—
458	C₄	C₂×C₁₇×#137	1	6	yes	—
459	C₄	C₁₇×#585	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	8	1	no	—
462	C₂	C₁₇×#3487	1	1	yes	characteristic
463	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
464	C₂	C₂×C₁₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#557	C₂	semidirect
3. C₁₇×#3398	C₂	semidirect
4. C₁₇×#3395	C₂	semidirect
5. C₁₇×#3374	C₂	semidirect
6. C₁₇×#3359	C₂	semidirect
8. C₁₇×#3209	C₂	semidirect
9. C₁₇×#3113	C₂	semidirect
11. C₁₇×#2984	C₂	semidirect
179. #61900	C₁₇	direct (N × H)
211. C₂×#557	C₂×C₁₇	semidirect
212. #3398	C₂×C₁₇	semidirect
213. #3395	C₂×C₁₇	semidirect
214. #3374	C₂×C₁₇	semidirect
215. #3359	C₂×C₁₇	semidirect
217. #3209	C₂×C₁₇	semidirect
218. #3113	C₂×C₁₇	semidirect
220. #2984	C₂×C₁₇	semidirect
355. C₁₇	#61900	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×#3523	2
C₂×C₁₇×#557	2
C₁₇×#3398	2
C₁₇×#3395	2
C₁₇×#3374	2
C₁₇×#3359	2
C₁₇×#3218	2
C₁₇×#3209	2
C₁₇×#3113	2
C₁₇×#3108	2
C₁₇×#2984	2
#61900	17

Subgroups — C17×#61900 #16919644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61900 #16919644