Subgroups — C₁₇×#21419 #16879163

Order 4352.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1897	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1896	C₂	1	2	yes	maximal, complemented
10	C₁₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#104	C₂	1	2	yes	maximal, complemented
12	C₁₇×#542	C₄	1	4	yes	complemented
13	C₁₇×#541	C₄	1	2	yes	complemented
14	C₁₇×#540	C₄	1	2	yes	complemented
15	C₁₇×#539	—	2	2	no	—
16	C₁₇×#538	—	2	2	no	—
17	C₁₇×#533	C₂²	1	1	yes	characteristic
18	C₁₇×#532	C₂²	1	1	yes	characteristic
19	C₁₇×#529	—	2	4	no	—
20	C₁₇×#525	C₂²	1	2	yes	—
21	C₄×#41×C₁₇	C₂²	1	2	yes	—
22	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#433	—	2	4	no	—
26	C₁₇×#423	C₂²	1	1	yes	characteristic
27	C₁₇×#423	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#104	C₂²	1	2	yes	—
29	C₂×C₁₇×#104	C₂²	1	2	yes	—
30	C₂×C₁₇×#104	C₂²	1	2	yes	—
31	C₂×C₁₇×#104	C₂²	1	2	yes	—
32	C₁₇×#407	C₂²	1	2	yes	—
33	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₇	—	2	2	no	—
35	C₄×C₂²⋊C₄×C₁₇	—	2	2	no	—
36	C₁₇×#376	C₂²	1	1	yes	characteristic
37	C₁₇×#376	C₂²	1	1	yes	characteristic
38	C₄³×C₁₇	C₂²	1	1	yes	characteristic
39	C₄³×C₁₇	C₂²	1	1	yes	characteristic
40	C₁₇×#339	C₂²	1	2	yes	—
41	C₁₇×#339	C₂²	1	2	yes	—
42	C₁₇×#339	C₂²	1	2	yes	—
43	C₁₇×#339	C₂²	1	2	yes	—
44	C₂×#41×C₁₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₇	—	2	1	no	—
46	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
48	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
49	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₁₇×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
51	C₁₇×#127	C₂×C₄	1	1	yes	characteristic, complemented
52	C₁₇×#126	—	2	4	no	—
53	C₁₇×#126	—	2	4	no	—
54	C₁₇×#125	—	2	4	no	—
55	C₁₇×#125	C₂×C₄	1	2	yes	complemented
56	C₁₇×#124	—	2	4	no	—
57	C₁₇×#124	C₂×C₄	1	2	yes	complemented
58	C₁₇×#123	—	2	2	no	—
59	C₁₇×#123	—	2	4	no	—
60	C₁₇×#123	—	2	4	no	—
61	C₁₇×C₂²⋊Q₈	—	2	2	no	—
62	C₁₇×C₂²⋊Q₈	—	2	4	no	—
63	C₁₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
64	C₁₇×#121	—	2	2	no	—
65	C₁₇×#121	—	2	4	no	—
66	C₁₇×#121	C₂×C₄	1	4	yes	—
67	C₁₇×#120	—	2	2	no	—
68	C₄×Q₈×C₁₇	—	2	2	no	—
69	C₄×Q₈×C₁₇	C₂×C₄	1	4	yes	complemented
70	C₄×D₄×C₁₇	—	2	4	no	—
71	C₄×D₄×C₁₇	—	2	4	no	—
72	C₄×D₄×C₁₇	—	2	2	no	—
73	C₄×D₄×C₁₇	C₂×C₄	1	4	yes	complemented
74	C₁₇×#117	—	2	2	no	—
75	C₁₇×#117	—	2	2	no	—
76	C₁₇×#117	—	2	2	no	—
77	C₁₇×#117	C₂×C₄	1	2	yes	—
78	C₁₇×#117	C₂×C₄	1	2	yes	—
79	C₁₇×#117	D₄	1	4	yes	—
80	C₁₇×#117	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
85	C₂×C₄²×C₁₇	—	2	1	no	—
86	C₂×C₄²×C₁₇	—	2	2	no	—
87	C₂×C₄²×C₁₇	—	2	2	no	—
88	C₂×C₄²×C₁₇	—	2	2	no	—
89	C₂×C₄²×C₁₇	—	2	2	no	—
90	C₂×C₄²×C₁₇	—	2	2	no	—
91	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	—	2	2	no	—
98	C₁₇×C₄⋊C₈	—	2	2	no	—
99	C₁₇×#104	—	2	4	no	—
100	C₁₇×#104	—	2	4	no	—
101	C₁₇×#104	—	2	4	no	—
102	C₁₇×#104	—	2	4	no	—
103	C₁₇×C₂²⋊C₈	—	2	4	no	—
104	C₁₇×#97	—	2	2	no	—
105	C₄×C₈×C₁₇	—	2	2	no	—
106	C₁₇×#95	—	2	2	no	—
107	C₁₇×#95	—	2	2	no	—
108	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
109	#41×C₁₇	—	2	2	no	—
110	#41×C₁₇	—	2	2	no	—
111	#41×C₁₇	—	2	2	no	—
112	#41×C₁₇	—	2	2	no	—
113	C₂×Q₈×C₁₇	—	2	2	no	—
114	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₁₇	—	2	2	no	—
116	C₂×D₄×C₁₇	—	2	4	no	—
117	C₂×D₄×C₁₇	—	2	2	no	—
118	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₇	—	2	1	no	—
120	C₂²×C₄×C₁₇	—	2	1	no	—
121	C₂²×C₄×C₁₇	—	2	1	no	—
122	C₂²×C₄×C₁₇	—	2	1	no	—
123	C₂²×C₄×C₁₇	—	2	1	no	—
124	C₂²×C₄×C₁₇	—	2	4	no	—
125	C₂²×C₄×C₁₇	—	2	1	no	—
126	C₂²×C₄×C₁₇	—	2	1	no	—
127	C₂²×C₄×C₁₇	—	2	1	no	—
128	C₂²×C₄×C₁₇	—	2	2	no	—
129	C₂²×C₄×C₁₇	—	2	4	no	—
130	C₂²×C₄×C₁₇	—	4	4	no	—
131	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₁₇	—	2	2	no	—
138	M₁₆×C₁₇	—	2	2	no	—
139	M₁₆×C₁₇	—	2	2	no	—
140	M₁₆×C₁₇	—	2	2	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	2	2	no	—
143	C₄⋊C₄×C₁₇	—	2	4	no	—
144	C₄⋊C₄×C₁₇	—	2	4	no	—
145	C₄⋊C₄×C₁₇	—	2	2	no	—
146	C₄⋊C₄×C₁₇	—	2	4	no	—
147	C₄⋊C₄×C₁₇	—	2	4	no	—
148	C₄⋊C₄×C₁₇	—	2	2	no	—
149	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
150	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
151	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
152	C₂²⋊C₄×C₁₇	—	2	4	no	—
153	C₂²⋊C₄×C₁₇	—	2	4	no	—
154	C₂²⋊C₄×C₁₇	—	2	2	no	—
155	C₂²⋊C₄×C₁₇	—	2	4	no	—
156	C₂²⋊C₄×C₁₇	—	2	4	no	—
157	C₂²⋊C₄×C₁₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
159	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	4	yes	—
160	C₄²×C₁₇	—	2	4	no	—
161	C₄²×C₁₇	—	2	4	no	—
162	C₄²×C₁₇	—	2	2	no	—
163	C₄²×C₁₇	—	2	1	no	—
164	C₄²×C₁₇	—	2	1	no	—
165	C₄²×C₁₇	—	2	1	no	—
166	C₄²×C₁₇	—	2	1	no	—
167	C₄²×C₁₇	—	4	4	no	—
168	C₄²×C₁₇	—	4	4	no	—
169	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
172	C₄²×C₁₇	C₂×D₄	1	2	yes	—
173	C₄²×C₁₇	C₂×D₄	1	2	yes	—
174	C₄²×C₁₇	#41	1	2	yes	—
175	C₄²×C₁₇	#41	1	2	yes	—
176	C₄²×C₁₇	#41	1	2	yes	—
177	C₄²×C₁₇	#41	1	2	yes	—
178	#21419	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₇	—	2	1	no	—
180	C₂³×C₁₇	—	2	1	no	—
181	C₂³×C₁₇	—	2	2	no	—
182	C₂³×C₁₇	—	4	2	no	—
183	C₂³×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₇	—	2	2	no	—
186	Q₈×C₁₇	—	2	2	no	—
187	Q₈×C₁₇	—	8	2	no	—
188	D₄×C₁₇	—	2	2	no	—
189	D₄×C₁₇	—	2	2	no	—
190	D₄×C₁₇	—	4	2	no	—
191	D₄×C₁₇	—	4	2	no	—
192	D₄×C₁₇	—	8	2	no	—
193	D₄×C₁₇	—	8	4	no	—
194	C₂×C₄×C₁₇	—	2	4	no	—
195	C₂×C₄×C₁₇	—	2	1	no	—
196	C₂×C₄×C₁₇	—	2	2	no	—
197	C₂×C₄×C₁₇	—	2	1	no	—
198	C₂×C₄×C₁₇	—	2	2	no	—
199	C₂×C₄×C₁₇	—	2	2	no	—
200	C₂×C₄×C₁₇	—	2	2	no	—
201	C₂×C₄×C₁₇	—	2	2	no	—
202	C₂×C₄×C₁₇	—	2	2	no	—
203	C₂×C₄×C₁₇	—	2	4	no	—
204	C₂×C₄×C₁₇	—	2	2	no	—
205	C₂×C₄×C₁₇	—	2	2	no	—
206	C₂×C₄×C₁₇	—	2	2	no	—
207	C₂×C₄×C₁₇	—	4	2	no	—
208	C₂×C₄×C₁₇	—	4	2	no	—
209	C₂×C₄×C₁₇	—	4	8	no	—
210	C₂×C₄×C₁₇	—	4	2	no	—
211	C₂×C₄×C₁₇	—	4	2	no	—
212	C₂×C₄×C₁₇	—	4	2	no	—
213	C₂×C₄×C₁₇	—	4	2	no	—
214	C₂×C₄×C₁₇	—	4	2	no	—
215	C₂×C₄×C₁₇	—	8	4	no	—
216	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	4	yes	—
217	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
226	C₈×C₁₇	—	4	2	no	—
227	C₈×C₁₇	—	4	2	no	—
228	#3455	C₂×C₁₇	1	1	yes	characteristic
229	#2921	C₂×C₁₇	1	1	yes	characteristic, complemented
230	C₄×#117	C₂×C₁₇	1	1	yes	characteristic, complemented
231	#1995	C₂×C₁₇	1	1	yes	characteristic, complemented
232	#1994	C₂×C₁₇	1	1	yes	characteristic, complemented
233	#1963	C₂×C₁₇	1	1	yes	characteristic, complemented
234	#1962	C₂×C₁₇	1	1	yes	characteristic, complemented
235	#1897	C₂×C₁₇	1	2	yes	complemented
236	#1896	C₂×C₁₇	1	2	yes	complemented
237	#1759	C₂×C₁₇	1	2	yes	complemented
238	C₄×#104	C₂×C₁₇	1	2	yes	complemented
239	C₂²×C₁₇	—	2	2	no	—
240	C₂²×C₁₇	—	2	4	no	—
241	C₂²×C₁₇	—	2	2	no	—
242	C₂²×C₁₇	—	4	2	no	—
243	C₂²×C₁₇	—	4	2	no	—
244	C₂²×C₁₇	—	4	4	no	—
245	C₂²×C₁₇	—	4	2	no	—
246	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₁₇	#525	1	1	yes	characteristic
248	C₂²×C₁₇	#525	1	1	yes	characteristic
249	C₄×C₁₇	—	2	4	no	—
250	C₄×C₁₇	—	2	4	no	—
251	C₄×C₁₇	—	2	2	no	—
252	C₄×C₁₇	—	2	2	no	—
253	C₄×C₁₇	—	2	2	no	—
254	C₄×C₁₇	—	4	2	no	—
255	C₄×C₁₇	—	4	2	no	—
256	C₄×C₁₇	—	4	2	no	—
257	C₄×C₁₇	—	4	4	no	—
258	C₄×C₁₇	—	4	2	no	—
259	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
260	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
261	C₄×C₁₇	#532	1	1	yes	characteristic
262	C₄×C₁₇	#532	1	1	yes	characteristic
263	#542	C₄×C₁₇	1	4	yes	complemented
264	#541	C₄×C₁₇	1	2	yes	complemented
265	#540	C₄×C₁₇	1	2	yes	complemented
266	#539	—	2	2	no	—
267	#538	—	2	2	no	—
268	#533	C₂²×C₁₇	1	1	yes	characteristic
269	#532	C₂²×C₁₇	1	1	yes	characteristic
270	#529	—	2	4	no	—
271	#525	C₂²×C₁₇	1	2	yes	—
272	C₄×#41	C₂²×C₁₇	1	2	yes	—
273	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
274	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
275	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
276	#433	—	2	4	no	—
277	#423	C₂²×C₁₇	1	1	yes	characteristic
278	#423	C₂²×C₁₇	1	1	yes	characteristic
279	C₂×#104	C₂²×C₁₇	1	2	yes	—
280	C₂×#104	C₂²×C₁₇	1	2	yes	—
281	C₂×#104	C₂²×C₁₇	1	2	yes	—
282	C₂×#104	C₂²×C₁₇	1	2	yes	—
283	#407	C₂²×C₁₇	1	2	yes	—
284	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
285	C₄×C₄⋊C₄	—	2	2	no	—
286	C₄×C₂²⋊C₄	—	2	2	no	—
287	#376	C₂²×C₁₇	1	1	yes	characteristic
288	#376	C₂²×C₁₇	1	1	yes	characteristic
289	C₄³	C₂²×C₁₇	1	1	yes	characteristic
290	C₄³	C₂²×C₁₇	1	1	yes	characteristic
291	#339	C₂²×C₁₇	1	2	yes	—
292	#339	C₂²×C₁₇	1	2	yes	—
293	#339	C₂²×C₁₇	1	2	yes	—
294	#339	C₂²×C₁₇	1	2	yes	—
295	C₂×C₁₇	—	2	1	no	—
296	C₂×C₁₇	—	2	1	no	—
297	C₂×C₁₇	—	4	2	no	—
298	C₂×C₁₇	—	8	2	no	—
299	C₂×C₁₇	#2297	1	1	yes	characteristic
300	C₂×C₁₇	#2901	1	2	yes	—
301	C₂×#41	C₂³×C₁₇	1	2	yes	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
304	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
306	C₄⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
307	C₄⋊Q₈	C₂×C₄×C₁₇	1	2	yes	complemented
308	#127	C₂×C₄×C₁₇	1	1	yes	characteristic, complemented
309	#126	—	2	4	no	—
310	#126	—	2	4	no	—
311	#125	—	2	4	no	—
312	#125	C₂×C₄×C₁₇	1	2	yes	complemented
313	#124	—	2	4	no	—
314	#124	C₂×C₄×C₁₇	1	2	yes	complemented
315	#123	—	2	2	no	—
316	#123	—	2	4	no	—
317	#123	—	2	4	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
321	#121	—	2	2	no	—
322	#121	—	2	4	no	—
323	#121	C₂×C₄×C₁₇	1	4	yes	—
324	#120	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	C₂×C₄×C₁₇	1	4	yes	complemented
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	C₂×C₄×C₁₇	1	4	yes	complemented
331	#117	—	2	2	no	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	C₂×C₄×C₁₇	1	2	yes	—
335	#117	C₂×C₄×C₁₇	1	2	yes	—
336	#117	D₄×C₁₇	1	4	yes	—
337	#117	C₂³×C₁₇	1	2	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	2	2	no	—
356	#104	—	2	4	no	—
357	#104	—	2	4	no	—
358	#104	—	2	4	no	—
359	#104	—	2	4	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	#97	—	2	2	no	—
362	C₄×C₈	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	—	2	2	no	—
365	C₁₇	#21419	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
408	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
409	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
417	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	4	yes	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	4	4	no	—
426	C₄²	—	4	4	no	—
427	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
428	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
429	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₁₇	1	2	yes	—
431	C₄²	C₂×D₄×C₁₇	1	2	yes	—
432	C₄²	#41×C₁₇	1	2	yes	—
433	C₄²	#41×C₁₇	1	2	yes	—
434	C₄²	#41×C₁₇	1	2	yes	—
435	C₄²	#41×C₁₇	1	2	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	4	yes	—
474	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
475	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
476	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
480	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
493	C₂²	C₁₇×#525	1	1	yes	characteristic
494	C₂²	C₁₇×#525	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	4	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
506	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
507	C₄	C₁₇×#532	1	1	yes	characteristic
508	C₄	C₁₇×#532	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	2	no	—
513	C₂	C₁₇×#2297	1	1	yes	characteristic
514	C₂	C₁₇×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×C₂²⋊C₄
prime radical	C₁₇×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2921	C₂	semidirect
3. C₄×C₁₇×#117	C₂	semidirect
4. C₁₇×#1995	C₂	semidirect
5. C₁₇×#1994	C₂	semidirect
6. C₁₇×#1963	C₂	semidirect
7. C₁₇×#1962	C₂	semidirect
8. C₁₇×#1897	C₂	semidirect
9. C₁₇×#1896	C₂	semidirect
10. C₁₇×#1759	C₂	semidirect
11. C₄×C₁₇×#104	C₂	semidirect
12. C₁₇×#542	C₄	semidirect
13. C₁₇×#541	C₄	semidirect
14. C₁₇×#540	C₄	semidirect
49. C₁₇×C₄⋊Q₈	C₂×C₄	semidirect
50. C₁₇×C₄⋊Q₈	C₂×C₄	semidirect
51. C₁₇×#127	C₂×C₄	semidirect
55. C₁₇×#125	C₂×C₄	semidirect
57. C₁₇×#124	C₂×C₄	semidirect
69. C₄×Q₈×C₁₇	C₂×C₄	semidirect
73. C₄×D₄×C₁₇	C₂×C₄	semidirect
178. #21419	C₁₇	direct (N × H)
229. #2921	C₂×C₁₇	semidirect
230. C₄×#117	C₂×C₁₇	semidirect
231. #1995	C₂×C₁₇	semidirect
232. #1994	C₂×C₁₇	semidirect
233. #1963	C₂×C₁₇	semidirect
234. #1962	C₂×C₁₇	semidirect
235. #1897	C₂×C₁₇	semidirect
236. #1896	C₂×C₁₇	semidirect
237. #1759	C₂×C₁₇	semidirect
238. C₄×#104	C₂×C₁₇	semidirect
263. #542	C₄×C₁₇	semidirect
264. #541	C₄×C₁₇	semidirect
265. #540	C₄×C₁₇	semidirect
306. C₄⋊Q₈	C₂×C₄×C₁₇	semidirect
307. C₄⋊Q₈	C₂×C₄×C₁₇	semidirect
308. #127	C₂×C₄×C₁₇	semidirect
312. #125	C₂×C₄×C₁₇	semidirect
314. #124	C₂×C₄×C₁₇	semidirect
326. C₄×Q₈	C₂×C₄×C₁₇	semidirect
330. C₄×D₄	C₂×C₄×C₁₇	semidirect
365. C₁₇	#21419	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×#3455	2
C₁₇×#2921	2
C₄×C₁₇×#117	2
C₁₇×#1995	2
C₁₇×#1994	2
C₁₇×#1963	2
C₁₇×#1962	2
C₁₇×#1897	2
C₁₇×#1896	2
C₁₇×#1759	2
C₄×C₁₇×#104	2
#21419	17

Subgroups — C17×#21419 #16879163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21419 #16879163