Subgroups — #17187577

Order 4352.

648 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	#14541886	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11762924	C₂	1	1	yes	maximal, characteristic
3	#14530624	C₂	1	4	yes	maximal, complemented
4	#14530619	C₂	1	4	yes	maximal, complemented
5	C₂×#11762629	C₂	1	1	yes	maximal, characteristic, complemented
6	#14530413	C₂	1	1	yes	maximal, characteristic, complemented
7	#14530412	C₂	1	1	yes	maximal, characteristic, complemented
8	M₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#3407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10587636	C₄	1	1	yes	characteristic
11	C₂×#10587587	C₂²	1	1	yes	characteristic
12	#11763227	—	2	2	no	—
13	#11763225	C₂²	1	4	yes	complemented
14	C₂×#10587483	C₂²	1	1	yes	characteristic
15	C₂×#10587483	C₂²	1	1	yes	characteristic
16	M₃₂×D₁₇	—	2	2	no	—
17	#11762924	C₄	1	2	yes	—
18	#11762924	C₄	1	2	yes	—
19	#11762924	C₂²	1	2	yes	—
20	#11762924	C₂²	1	2	yes	—
21	C₂×#10587493	C₄	1	1	yes	characteristic
22	C₂×#10587508	C₄	1	1	yes	characteristic
23	C₂×#10587496	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
25	#11762629	C₂²	1	2	yes	complemented
26	#11762629	C₂²	1	2	yes	complemented
27	#11762594	C₂²	1	4	yes	complemented
28	#11762593	C₂²	1	4	yes	complemented
29	#11762584	C₂²	1	2	yes	complemented
30	C₁₆×Dic₁₇	C₂²	1	2	yes	complemented
31	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
32	C₁₇×#504	—	2	2	no	—
33	C₁₇×#504	C₂²	1	4	yes	complemented
34	C₂×C₁₇×M₃₂	—	2	2	no	—
35	C₂×C₁₇×M₃₂	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×M₃₂	C₂²	1	1	yes	characteristic
37	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×#63252	C₂×C₄	1	1	yes	characteristic
39	C₁₇×#131	—	2	1	no	—
40	C₁₇×#131	—	2	1	no	—
41	C₁₇×#131	C₂×C₄	1	2	yes	—
42	C₁₇×#131	C₂³	1	2	yes	—
43	C₂×M₁₆×C₁₇	—	2	1	no	—
44	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	—	2	1	no	—
46	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
47	#10587636	C₈	1	2	yes	—
48	#10587636	C₈	1	2	yes	—
49	#10587636	C₂×C₄	1	2	yes	—
50	#10587636	C₂×C₄	1	2	yes	—
51	C₂×#63231	C₈	1	1	yes	characteristic
52	C₂×#63230	C₈	1	1	yes	characteristic
53	C₂×#63229	C₈	1	1	yes	characteristic
54	C₂×#63228	C₈	1	1	yes	characteristic
55	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×#63223	C₂×C₄	1	1	yes	characteristic
57	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
58	#10587587	—	2	1	no	—
59	#10587587	—	2	1	no	—
60	#10587587	C₂×C₄	1	2	yes	—
61	#10587587	C₂³	1	2	yes	—
62	C₂×#63218	—	2	1	no	—
63	C₂×C₈×D₁₇	—	2	1	no	—
64	C₁₇×M₃₂	—	2	4	no	—
65	C₁₇×M₃₂	—	2	1	no	—
66	C₁₇×M₃₂	D₄	1	2	yes	—
67	C₁₇×M₃₂	D₄	1	2	yes	—
68	C₁₇×M₃₂	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₇	—	2	4	no	—
70	C₂×C₁₆×C₁₇	—	2	1	no	—
71	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
72	#10587508	C₂×C₄	1	2	yes	—
73	#10587508	C₂×C₄	1	2	yes	—
74	#10587496	C₂×C₄	1	2	yes	—
75	#10587496	C₂×C₄	1	2	yes	—
76	#10587493	C₂×C₄	1	2	yes	—
77	#10587493	C₂×C₄	1	2	yes	—
78	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
81	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
82	#10587483	—	2	1	no	—
83	#10587483	—	2	1	no	—
84	#10587483	—	2	1	no	—
85	#10587483	C₂³	1	2	yes	—
86	C₂×#63214	—	2	1	no	—
87	C₂×#63214	C₂³	1	2	yes	—
88	#10587469	—	2	4	no	—
89	C₁₆×D₁₇	—	2	4	no	—
90	#41×C₁₇	—	2	1	no	—
91	#41×C₁₇	—	2	1	no	—
92	#41×C₁₇	C₂×C₈	1	2	yes	—
93	#41×C₁₇	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₇	—	2	1	no	—
96	C₂×D₄×C₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₇	—	2	1	no	—
98	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₇	—	2	1	no	—
100	C₂²×Dic₁₇	—	2	1	no	—
101	#63252	—	2	1	no	—
102	#63252	—	2	1	no	—
103	#63252	C₂×C₈	1	2	yes	—
104	#63252	C₂²×C₄	1	2	yes	—
105	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₇	—	2	1	no	—
107	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
108	M₁₆×C₁₇	—	2	1	no	—
109	M₁₆×C₁₇	—	2	2	no	—
110	M₁₆×C₁₇	—	2	2	no	—
111	M₁₆×C₁₇	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₇	—	2	1	no	—
113	C₂×C₈×C₁₇	—	2	2	no	—
114	C₂×C₈×C₁₇	—	2	2	no	—
115	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
119	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
120	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
121	#63231	C₂×C₈	1	2	yes	—
122	#63231	C₂×C₈	1	2	yes	—
123	#63230	C₂×C₈	1	2	yes	—
124	#63230	C₂×C₈	1	2	yes	—
125	#63229	C₂×C₈	1	2	yes	—
126	#63229	C₂×C₈	1	2	yes	—
127	#63228	C₂×C₈	1	2	yes	—
128	#63228	C₂×C₈	1	2	yes	—
129	C₄×Dic₁₇	—	2	1	no	—
130	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
132	#63223	—	2	1	no	—
133	#63223	C₂²×C₄	1	2	yes	—
134	C₂×#3622	—	2	1	no	—
135	C₂×#3622	C₂×C₈	1	1	yes	characteristic
136	C₂×#3622	C₂×C₈	1	1	yes	characteristic
137	C₂×#3622	C₂×C₈	1	1	yes	characteristic
138	C₂×#3622	C₂×C₈	1	1	yes	characteristic
139	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
140	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
141	#63218	—	2	2	no	—
142	#63218	—	2	2	no	—
143	C₈×D₁₇	—	2	2	no	—
144	C₈×D₁₇	—	2	2	no	—
145	C₁₆×C₁₇	—	2	2	no	—
146	C₁₆×C₁₇	C₂×D₄	1	4	yes	—
147	#63214	—	2	2	no	—
148	#63214	—	2	2	no	—
149	#33443	—	17	1	no	maximal, Sylow
150	C₂³×C₁₇	—	2	1	no	—
151	C₂³×C₁₇	#131	1	1	yes	characteristic
152	C₂²×D₁₇	—	2	1	no	—
153	Q₈×C₁₇	—	2	1	no	—
154	Q₈×C₁₇	C₂²×C₈	1	2	yes	—
155	D₄×C₁₇	—	2	2	no	—
156	D₄×C₁₇	—	2	2	no	—
157	D₄×C₁₇	—	2	1	no	—
158	D₄×C₁₇	C₂²×C₈	1	2	yes	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	2	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	#131	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
168	C₂²⋊D₁₇	—	2	2	no	—
169	C₂²⋊D₁₇	—	2	2	no	—
170	C₂×Dic₁₇	—	2	1	no	—
171	C₂×Dic₁₇	—	2	1	no	—
172	C₂×Dic₁₇	—	2	1	no	—
173	C₂×Dic₁₇	—	4	2	no	—
174	D₆₈	—	2	1	no	—
175	D₆₈	C₂²×C₈	1	2	yes	—
176	C₄×D₁₇	—	2	2	no	—
177	C₄×D₁₇	—	2	2	no	—
178	Dic₃₄	—	2	1	no	—
179	Dic₃₄	C₂²×C₈	1	2	yes	—
180	C₈×C₁₇	—	2	2	no	—
181	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
182	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
183	C₈×C₁₇	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₇	C₂×#41	1	1	yes	characteristic
185	#3622	—	2	2	no	—
186	#3622	C₂²×C₈	1	1	yes	characteristic
187	#3622	C₂²×C₈	1	1	yes	characteristic
188	#3622	C₂²×C₈	1	1	yes	characteristic
189	#3622	C₂²×C₈	1	1	yes	characteristic
190	#3407	—	17	1	no	—
191	#3407	D₁₇	1	1	yes	characteristic, complemented
192	C₂×#443	—	17	1	no	—
193	#2171	—	17	4	no	—
194	#2170	—	17	4	no	—
195	C₂×#364	—	17	1	no	—
196	#2117	—	17	1	no	—
197	#2117	—	17	1	no	—
198	C₄×M₃₂	—	17	1	no	—
199	C₂²×C₁₇	—	2	2	no	—
200	C₂²×C₁₇	—	4	1	no	—
201	C₂²×C₁₇	—	8	1	no	—
202	C₂²×C₁₇	C₈×D₄	1	1	yes	characteristic
203	C₂²×C₁₇	C₈×D₄	1	1	yes	characteristic
204	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
205	C₂×D₁₇	—	2	2	no	—
206	C₂×D₁₇	—	8	1	no	—
207	C₄×C₁₇	—	2	2	no	—
208	C₄×C₁₇	C₈×D₄	1	1	yes	characteristic
209	C₄×C₁₇	C₈×D₄	1	1	yes	characteristic
210	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
212	Dic₁₇	—	2	2	no	—
213	Dic₁₇	—	2	2	no	—
214	Dic₁₇	—	4	1	no	—
215	C₂×#135	—	17	1	no	—
216	C₂×#131	—	17	1	no	—
217	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
218	#504	—	2	2	no	—
219	#504	—	17	4	no	—
220	#504	—	34	2	no	—
221	#504	C₂×D₁₇	1	4	yes	complemented
222	C₂×M₃₂	—	2	2	no	—
223	C₂×M₃₂	—	17	1	no	—
224	C₂×M₃₂	—	17	1	no	—
225	C₂×M₃₂	—	34	2	no	—
226	C₂×M₃₂	C₂×D₁₇	1	1	yes	characteristic
227	C₂×M₃₂	C₂×D₁₇	1	1	yes	characteristic
228	#443	—	17	2	no	—
229	#443	—	17	2	no	—
230	#443	—	17	2	no	—
231	#443	—	17	2	no	—
232	C₂×#108	—	17	1	no	—
233	C₂×#104	—	17	1	no	—
234	C₂×#104	—	17	1	no	—
235	C₂×C₄×C₈	—	17	1	no	—
236	#364	—	17	2	no	—
237	#364	—	17	2	no	—
238	#350	—	17	4	no	—
239	#350	—	17	4	no	—
240	#346	—	17	2	no	—
241	C₄×C₁₆	—	17	2	no	—
242	C₂×C₁₇	—	2	1	no	—
243	C₂×C₁₇	—	2	1	no	—
244	C₂×C₁₇	—	2	1	no	—
245	C₂×C₁₇	—	4	2	no	—
246	C₂×C₁₇	C₂×C₈×D₄	1	1	yes	characteristic
247	D₁₇	—	4	2	no	—
248	C₂×#41	—	17	1	no	—
249	C₂×#41	C₄×D₁₇	1	1	yes	characteristic
250	#135	—	17	2	no	—
251	#135	—	17	2	no	—
252	#135	—	17	2	no	—
253	#135	—	17	2	no	—
254	C₂×Q₁₆	—	17	1	no	—
255	C₂×SD₁₆	—	17	1	no	—
256	C₂×SD₁₆	—	17	1	no	—
257	C₂×D₈	—	17	1	no	—
258	#131	—	2	1	no	—
259	#131	—	2	1	no	—
260	#131	—	17	2	no	—
261	#131	—	17	2	no	—
262	#131	—	34	1	no	—
263	#131	—	34	1	no	—
264	#131	C₄×D₁₇	1	2	yes	—
265	#131	C₂²×D₁₇	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	17	1	no	—
268	C₂×M₁₆	—	34	1	no	—
269	C₂×M₁₆	C₄×D₁₇	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	17	1	no	—
272	C₂²×C₈	—	34	1	no	—
273	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
274	C₂×C₄²	—	17	1	no	—
275	M₃₂	—	2	1	no	—
276	M₃₂	—	2	4	no	—
277	M₃₂	—	17	2	no	—
278	M₃₂	—	34	1	no	—
279	M₃₂	—	34	1	no	—
280	M₃₂	—	34	1	no	—
281	M₃₂	—	34	4	no	—
282	M₃₂	C₂²⋊D₁₇	1	2	yes	—
283	M₃₂	C₂²⋊D₁₇	1	2	yes	—
284	M₃₂	C₂²×D₁₇	1	2	yes	—
285	C₂×C₁₆	—	2	1	no	—
286	C₂×C₁₆	—	2	4	no	—
287	C₂×C₁₆	—	17	2	no	—
288	C₂×C₁₆	—	34	1	no	—
289	C₂×C₁₆	—	34	4	no	—
290	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
291	#108	—	17	2	no	—
292	#108	—	17	2	no	—
293	#104	—	17	2	no	—
294	#104	—	17	2	no	—
295	#104	—	17	2	no	—
296	#104	—	17	2	no	—
297	C₄×C₈	—	17	1	no	—
298	C₄×C₈	—	17	1	no	—
299	C₄×C₈	—	17	1	no	—
300	C₄×C₈	—	17	1	no	—
301	C₁₇	#33443	1	1	yes	characteristic, complemented, Sylow
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	17	2	no	—
305	#41	—	17	2	no	—
306	#41	—	34	1	no	—
307	#41	—	34	1	no	—
308	#41	C₈×D₁₇	1	2	yes	—
309	#41	C₂×C₄×D₁₇	1	2	yes	—
310	C₂×Q₈	—	17	1	no	—
311	C₂×Q₈	C₈×D₁₇	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	17	1	no	—
314	C₂×D₄	—	34	1	no	—
315	C₂×D₄	C₈×D₁₇	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	34	1	no	—
318	C₂²×C₄	—	34	1	no	—
319	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
320	Q₁₆	—	17	2	no	—
321	Q₁₆	—	17	2	no	—
322	SD₁₆	—	17	2	no	—
323	SD₁₆	—	17	2	no	—
324	SD₁₆	—	17	2	no	—
325	SD₁₆	—	17	2	no	—
326	D₈	—	17	2	no	—
327	D₈	—	17	2	no	—
328	M₁₆	—	2	1	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	17	2	no	—
332	M₁₆	—	34	1	no	—
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	C₂×C₄×D₁₇	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	17	1	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	1	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	34	1	no	—
346	C₂×C₈	—	34	2	no	—
347	C₂×C₈	—	34	2	no	—
348	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
349	C₂×C₈	#63252	1	1	yes	characteristic
350	C₂×C₈	#63252	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
354	C₄²	—	17	1	no	—
355	C₄²	—	17	1	no	—
356	C₄²	—	34	1	no	—
357	C₁₆	—	2	2	no	—
358	C₁₆	—	34	2	no	—
359	C₁₆	—	34	2	no	—
360	C₁₆	C₂×C₂²⋊D₁₇	1	4	yes	—
361	C₂³	—	2	1	no	—
362	C₂³	—	34	1	no	—
363	C₂³	#10587587	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	17	2	no	—
366	Q₈	—	34	1	no	—
367	Q₈	C₂×C₈×D₁₇	1	2	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	1	no	—
371	D₄	—	17	2	no	—
372	D₄	—	34	2	no	—
373	D₄	—	34	2	no	—
374	D₄	—	34	1	no	—
375	D₄	C₂×C₈×D₁₇	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	34	1	no	—
380	C₂×C₄	—	34	1	no	—
381	C₂×C₄	—	34	2	no	—
382	C₂×C₄	—	34	2	no	—
383	C₂×C₄	—	34	1	no	—
384	C₂×C₄	—	68	2	no	—
385	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
386	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
387	C₂×C₄	#10587587	1	1	yes	characteristic
388	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
389	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	17	1	no	—
393	C₈	—	17	1	no	—
394	C₈	—	17	1	no	—
395	C₈	—	17	1	no	—
396	C₈	—	34	2	no	—
397	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
398	C₈	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
399	C₈	C₂×#63252	1	1	yes	characteristic
400	C₈	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
401	C₂²	—	2	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	34	2	no	—
405	C₂²	—	136	1	no	—
406	C₂²	C₈×C₂²⋊D₁₇	1	1	yes	characteristic
407	C₂²	C₈×C₂²⋊D₁₇	1	1	yes	characteristic
408	C₂²	C₂×#10587587	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	34	2	no	—
411	C₄	—	34	2	no	—
412	C₄	—	68	1	no	—
413	C₄	C₈×C₂²⋊D₁₇	1	1	yes	characteristic
414	C₄	C₈×C₂²⋊D₁₇	1	1	yes	characteristic
415	C₄	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
416	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	68	2	no	—
422	C₂	C₂×C₈×C₂²⋊D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×C₂²⋊D₁₇
commutator	C₄×C₁₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₁₇×#3407	C₂
socle	C₂×C₁₇	C₂×C₈×D₄
prime radical	C₂×#10587636	C₄
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	#3407	D₁₇
hypocenter	C₁₇	#33443
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂ ◁ #3407

Complements

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

N	H ≅ G/N	type
1. #14541886	C₂	semidirect
3. #14530624	C₂	semidirect
4. #14530619	C₂	semidirect
5. C₂×#11762629	C₂	semidirect
6. #14530413	C₂	semidirect
7. #14530412	C₂	semidirect
8. M₃₂×Dic₁₇	C₂	semidirect
9. C₁₇×#3407	C₂	semidirect
13. #11763225	C₂²	semidirect
25. #11762629	C₂²	semidirect
26. #11762629	C₂²	semidirect
27. #11762594	C₂²	semidirect
28. #11762593	C₂²	semidirect
29. #11762584	C₂²	semidirect
30. C₁₆×Dic₁₇	C₂²	semidirect
33. C₁₇×#504	C₂²	semidirect
191. #3407	D₁₇	semidirect
221. #504	C₂×D₁₇	semidirect
301. C₁₇	#33443	semidirect

Maximal subgroups

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

subgroup	index
#14541886	2
C₂×#11762924	2
#14530624	2
#14530619	2
C₂×#11762629	2
#14530413	2
#14530412	2
M₃₂×Dic₁₇	2
C₁₇×#3407	2
#33443	17