Subgroups — #17964150

Order 4352.

782 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545595	C₂	1	2	yes	maximal
2	#14544008	C₂	1	1	yes	maximal, characteristic, complemented
3	#14544007	C₂	1	1	yes	maximal, characteristic, complemented
4	#14544004	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544003	C₂	1	1	yes	maximal, characteristic, complemented
6	#14543994	C₂	1	2	yes	maximal, complemented
7	#14543993	C₂	1	2	yes	maximal, complemented
8	#14543992	C₂	1	2	yes	maximal, complemented
9	#14543988	C₂	1	1	yes	maximal, characteristic, complemented
10	#14543978	C₂	1	1	yes	maximal, characteristic, complemented
11	#14537206	C₂	1	1	yes	maximal, characteristic
12	#11763861	C₄	1	4	yes	—
13	#11763842	C₄	1	4	yes	—
14	#11763841	C₄	1	4	yes	—
15	#11763839	C₄	1	4	yes	—
16	#11763828	C₂²	1	2	yes	—
17	#11763827	C₂²	1	2	yes	—
18	#11763826	C₂²	1	2	yes	—
19	C₄×#63243	C₂²	1	2	yes	—
20	C₄×#63247	C₂²	1	2	yes	—
21	C₄×#63242	C₂²	1	2	yes	—
22	#11763651	C₂²	1	2	yes	—
23	#11763651	C₂²	1	2	yes	—
24	#11763651	C₂²	1	2	yes	—
25	#11763651	C₂²	1	2	yes	—
26	#11763650	C₂²	1	2	yes	—
27	#11763650	C₂²	1	1	yes	characteristic
28	#11763650	C₂²	1	1	yes	characteristic
29	#11763650	C₂²	1	2	yes	—
30	C₈×#3624	C₂²	1	1	yes	characteristic
31	C₈×#3624	C₂²	1	1	yes	characteristic
32	C₂×#10587593	C₄	1	1	yes	characteristic
33	C₂×#10587587	C₄	1	1	yes	characteristic
34	#11763277	C₂²	1	1	yes	characteristic
35	#11762766	C₄	1	1	yes	characteristic
36	#11762766	C₄	1	1	yes	characteristic
37	#11762765	C₄	1	1	yes	characteristic
38	#11762763	C₄	1	1	yes	characteristic
39	#11762763	C₄	1	1	yes	characteristic
40	#11762761	C₂²	1	1	yes	characteristic
41	#11762761	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
46	C₁₇×#405	C₄	1	1	yes	characteristic
47	C₂×#63252	C₂×C₄	1	1	yes	characteristic
48	C₂×#63247	C₂×C₄	1	4	yes	—
49	C₂×#63243	C₂×C₄	1	4	yes	—
50	C₂×#63242	C₂×C₄	1	4	yes	—
51	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
55	C₂×#63223	C₂×C₄	1	1	yes	characteristic
56	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
57	#10587593	—	2	4	no	—
58	#10587587	—	2	4	no	—
59	C₂×#63218	C₂×C₄	1	1	yes	characteristic
60	C₂×#63218	C₂×C₄	1	1	yes	characteristic
61	C₂×#63218	C₂×C₄	1	1	yes	characteristic
62	C₂×#63218	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
67	#10587579	C₂×C₄	1	2	yes	—
68	#10587573	C₂×C₄	1	2	yes	—
69	#10587567	C₂×C₄	1	2	yes	—
70	#10587567	C₂×C₄	1	2	yes	—
71	#10587558	C₂×C₄	1	1	yes	characteristic
72	#10587558	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₇	C₂³	1	1	yes	characteristic
74	C₄²×D₁₇	C₂³	1	1	yes	characteristic
75	C₂²⋊#3624	C₂×C₄	1	4	yes	—
76	#10587544	C₂×C₄	1	4	yes	—
77	#10587544	C₂×C₄	1	4	yes	—
78	#10587543	C₂×C₄	1	4	yes	—
79	#10587543	C₂×C₄	1	4	yes	—
80	#10587542	C₂×C₄	1	4	yes	—
81	#10587542	C₂×C₄	1	4	yes	—
82	C₄⋊#3624	C₂×C₄	1	4	yes	—
83	C₄×#3624	C₂×C₄	1	4	yes	—
84	C₄×#3624	C₂³	1	2	yes	—
85	C₄×#3624	C₂³	1	2	yes	—
86	C₄×#3624	C₂³	1	2	yes	—
87	C₄×#3624	C₂³	1	2	yes	—
88	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
89	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
92	#10587486	C₂×C₄	1	1	yes	characteristic
93	#10587486	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
98	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
99	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
100	#10587474	C₂×C₄	1	1	yes	characteristic
101	#10587474	C₂×C₄	1	1	yes	characteristic
102	C₄×#3622	C₂×C₄	1	1	yes	characteristic
103	C₄×#3622	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₇	C₂²×C₄	1	2	yes	—
108	#63252	—	2	2	no	—
109	#63252	—	2	2	no	—
110	C₂×D₆₈	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₇	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₁₇	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
116	#63247	—	4	4	no	—
117	C₂×#3624	C₂²×C₄	1	4	yes	—
118	C₂×#3624	C₂²×C₄	1	4	yes	—
119	C₂×#3624	C₂²×C₄	1	4	yes	—
120	C₂×#3624	C₂²×C₄	1	4	yes	—
121	#63243	—	4	4	no	—
122	#63242	—	4	4	no	—
123	M₁₆×C₁₇	—	2	2	no	—
124	C₂×C₈×C₁₇	—	2	2	no	—
125	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊C₄×C₁₇	C₄²	1	2	yes	—
130	C₂²⋊C₄×C₁₇	C₄²	1	2	yes	—
131	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	#63227	C₄²	1	2	yes	—
134	#63227	C₄²	1	2	yes	—
135	#63225	C₄²	1	2	yes	—
136	#63225	C₄²	1	2	yes	—
137	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
139	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
140	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
141	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
142	#63223	—	2	2	no	—
143	C₂×#3622	—	2	2	no	—
144	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
145	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
146	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
147	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
148	#63218	—	2	2	no	—
149	#63218	—	2	2	no	—
150	#63218	—	2	2	no	—
151	#63218	—	2	2	no	—
152	C₈×D₁₇	—	2	2	no	—
153	C₈×D₁₇	—	2	2	no	—
154	C₈×D₁₇	M₁₆	1	4	yes	complemented
155	C₈×D₁₇	M₁₆	1	4	yes	complemented
156	#17336	—	17	1	no	maximal, Sylow
157	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
159	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₇	—	2	1	no	—
161	C₂×C₄×C₁₇	—	2	1	no	—
162	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
164	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
166	C₂²⋊D₁₇	—	2	2	no	—
167	C₂²⋊D₁₇	—	2	2	no	—
168	C₂×Dic₁₇	—	2	4	no	—
169	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₁₇	C₂×C₄²	1	2	yes	—
171	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₁₇	C₂³×C₄	1	2	yes	—
173	D₆₈	—	2	2	no	—
174	C₄×D₁₇	—	2	1	no	—
175	C₄×D₁₇	—	2	1	no	—
176	C₄×D₁₇	—	2	4	no	—
177	C₄×D₁₇	—	2	4	no	—
178	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
179	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
180	Dic₃₄	—	2	2	no	—
181	#3624	—	2	4	no	—
182	#3624	—	2	4	no	—
183	#3624	—	2	4	no	—
184	#3624	—	2	4	no	—
185	C₈×C₁₇	—	2	1	no	—
186	C₈×C₁₇	—	2	1	no	—
187	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
188	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
189	#3622	—	2	1	no	—
190	#3622	—	2	1	no	—
191	#3622	C₂×M₁₆	1	2	yes	—
192	#3622	C₂×M₁₆	1	2	yes	—
193	#2965	—	17	2	no	—
194	C₄×#131	—	17	1	no	—
195	#1455	—	17	1	no	—
196	#1455	—	17	1	no	—
197	#1453	—	17	1	no	—
198	#1453	—	17	1	no	—
199	#1451	—	17	2	no	—
200	#1451	—	17	2	no	—
201	#1451	—	17	2	no	—
202	#1450	—	17	1	no	—
203	C₂×#322	—	17	1	no	—
204	C₂²×C₁₇	—	2	1	no	—
205	C₂²×C₁₇	—	2	2	no	—
206	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
207	C₂×D₁₇	—	2	2	no	—
208	C₂×D₁₇	—	2	1	no	—
209	C₂×D₁₇	—	2	2	no	—
210	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
211	C₄×C₁₇	—	2	1	no	—
212	C₄×C₁₇	—	2	2	no	—
213	C₄×C₁₇	—	2	2	no	—
214	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
215	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
216	Dic₁₇	—	2	1	no	—
217	Dic₁₇	—	2	2	no	—
218	Dic₁₇	C₄×M₁₆	1	2	yes	—
219	Dic₁₇	#568	1	4	yes	—
220	C₂×#131	—	17	1	no	—
221	C₂×#131	—	17	1	no	—
222	C₄×#41	—	17	1	no	—
223	#446	—	17	4	no	—
224	#436	—	17	4	no	—
225	#435	—	17	4	no	—
226	#435	—	17	4	no	—
227	#431	—	17	2	no	—
228	#431	—	17	2	no	—
229	#431	—	17	2	no	—
230	#405	—	17	1	no	—
231	#405	—	17	1	no	—
232	#405	—	17	1	no	—
233	#405	—	17	1	no	—
234	#405	—	17	1	no	—
235	#405	#595	1	1	yes	characteristic
236	C₄×M₁₆	—	17	2	no	—
237	C₄×M₁₆	—	17	2	no	—
238	C₄×M₁₆	—	17	1	no	—
239	C₄×M₁₆	—	17	1	no	—
240	C₄×M₁₆	—	17	1	no	—
241	C₂×C₄×C₈	—	17	2	no	—
242	C₂×C₄×C₈	—	17	1	no	—
243	C₂×C₄×C₈	—	17	1	no	—
244	C₂×C₄×C₈	—	17	1	no	—
245	#322	—	17	2	no	—
246	#322	—	17	1	no	—
247	#322	—	17	1	no	—
248	#322	—	17	2	no	—
249	#322	—	17	2	no	—
250	#322	—	17	2	no	—
251	#322	—	17	2	no	—
252	#322	—	17	2	no	—
253	C₈²	—	17	1	no	—
254	C₈²	—	17	1	no	—
255	C₂×C₁₇	—	4	1	no	—
256	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
257	C₂×C₁₇	#2875	1	2	yes	—
258	D₁₇	—	2	2	no	—
259	D₁₇	—	4	1	no	—
260	C₂×#41	—	17	1	no	—
261	#131	—	34	4	no	—
262	#131	—	34	4	no	—
263	C₂×M₁₆	—	17	1	no	—
264	C₂×M₁₆	—	17	4	no	—
265	C₂×M₁₆	—	17	4	no	—
266	C₂×M₁₆	—	17	1	no	—
267	C₂×M₁₆	—	17	1	no	—
268	C₂×M₁₆	—	17	1	no	—
269	C₂×M₁₆	—	17	1	no	—
270	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
271	C₂²×C₈	—	17	1	no	—
272	C₂²×C₈	—	17	1	no	—
273	C₂²×C₈	—	17	1	no	—
274	C₂²×C₈	—	17	4	no	—
275	C₂²×C₈	—	17	1	no	—
276	C₂²×C₈	—	17	1	no	—
277	C₂²×C₈	C₂×#595	1	1	yes	characteristic
278	C₄×Q₈	—	17	2	no	—
279	C₄×D₄	—	17	2	no	—
280	C₄×D₄	—	17	2	no	—
281	C₄×D₄	—	17	2	no	—
282	#117	—	17	1	no	—
283	#117	—	17	1	no	—
284	#117	C₂×#595	1	1	yes	characteristic
285	C₂×C₄²	—	17	1	no	—
286	C₂×C₄²	—	17	1	no	—
287	C₂×C₄²	—	17	1	no	—
288	C₄⋊C₈	—	17	4	no	—
289	C₄⋊C₈	—	17	4	no	—
290	C₄⋊C₈	—	17	4	no	—
291	C₂²⋊C₈	—	17	4	no	—
292	C₂²⋊C₈	—	17	4	no	—
293	C₂²⋊C₈	—	17	4	no	—
294	#97	—	17	4	no	—
295	#97	—	17	4	no	—
296	#97	—	17	1	no	—
297	#97	—	17	1	no	—
298	#97	—	17	1	no	—
299	#97	—	17	1	no	—
300	#97	C₂×#595	1	1	yes	characteristic
301	#97	C₂×#595	1	1	yes	characteristic
302	C₄×C₈	—	17	2	no	—
303	C₄×C₈	—	17	2	no	—
304	C₄×C₈	—	17	2	no	—
305	C₄×C₈	—	17	2	no	—
306	C₄×C₈	—	17	4	no	—
307	C₄×C₈	—	17	1	no	—
308	C₄×C₈	—	17	1	no	—
309	C₄×C₈	—	17	1	no	—
310	C₄×C₈	—	17	1	no	—
311	C₄×C₈	—	17	1	no	—
312	C₄×C₈	—	17	1	no	—
313	C₄×C₈	—	17	1	no	—
314	C₄×C₈	—	17	1	no	—
315	C₄×C₈	C₂×#595	1	1	yes	characteristic
316	C₄×C₈	C₂×#595	1	1	yes	characteristic
317	C₁₇	#17336	1	1	yes	characteristic, complemented, Sylow
318	#41	—	34	2	no	—
319	#41	—	34	2	no	—
320	C₂×Q₈	—	17	1	no	—
321	C₂×D₄	—	17	1	no	—
322	C₂×D₄	—	17	1	no	—
323	C₂×D₄	—	17	1	no	—
324	C₂²×C₄	—	17	1	no	—
325	C₂²×C₄	—	17	2	no	—
326	C₂²×C₄	—	17	2	no	—
327	C₂²×C₄	—	17	2	no	—
328	C₂²×C₄	—	17	1	no	—
329	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	34	2	no	—
332	M₁₆	—	34	2	no	—
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	2	no	—
336	M₁₆	—	68	4	no	—
337	M₁₆	—	68	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	17	1	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	4	no	—
342	C₂×C₈	—	17	4	no	—
343	C₂×C₈	—	17	4	no	—
344	C₂×C₈	—	17	4	no	—
345	C₂×C₈	—	17	4	no	—
346	C₂×C₈	—	17	4	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	17	1	no	—
349	C₂×C₈	—	34	2	no	—
350	C₂×C₈	—	34	2	no	—
351	C₂×C₈	—	34	2	no	—
352	C₂×C₈	—	68	4	no	—
353	C₂×C₈	C₂²×#595	1	1	yes	characteristic
354	C₂×C₈	C₂²×#595	1	1	yes	characteristic
355	C₂×C₈	C₂²×#595	1	1	yes	characteristic
356	C₂×C₈	C₂²×#595	1	1	yes	characteristic
357	C₄⋊C₄	—	17	2	no	—
358	C₄⋊C₄	—	17	2	no	—
359	C₄⋊C₄	C₄×#595	1	2	yes	—
360	C₂²⋊C₄	—	17	2	no	—
361	C₂²⋊C₄	—	17	2	no	—
362	C₂²⋊C₄	C₄×#595	1	2	yes	—
363	C₄²	—	17	2	no	—
364	C₄²	—	17	2	no	—
365	C₄²	—	17	2	no	—
366	C₄²	—	17	1	no	—
367	C₄²	—	17	1	no	—
368	C₄²	C₂²×#595	1	1	yes	characteristic
369	C₄²	C₂²×#595	1	1	yes	characteristic
370	C₂³	—	17	1	no	—
371	C₂³	—	17	1	no	—
372	C₂³	C₂×C₄×#595	1	1	yes	characteristic
373	Q₈	—	34	2	no	—
374	D₄	—	34	2	no	—
375	D₄	—	34	2	no	—
376	D₄	—	34	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	17	2	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	2	no	—
382	C₂×C₄	—	17	2	no	—
383	C₂×C₄	—	17	2	no	—
384	C₂×C₄	—	17	1	no	—
385	C₂×C₄	—	34	4	no	—
386	C₂×C₄	—	34	4	no	—
387	C₂×C₄	—	34	4	no	—
388	C₂×C₄	—	34	1	no	—
389	C₂×C₄	—	34	1	no	—
390	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#595	1	2	yes	—
392	C₂×C₄	C₂×C₄×#595	1	2	yes	—
393	C₂×C₄	C₂³×#595	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	17	2	no	—
397	C₈	—	17	2	no	—
398	C₈	—	34	4	no	—
399	C₈	—	34	4	no	—
400	C₈	—	34	4	no	—
401	C₈	—	34	4	no	—
402	C₈	—	34	1	no	—
403	C₈	—	34	1	no	—
404	C₈	D₁₇⋊M₁₆	1	2	yes	—
405	C₈	D₁₇⋊M₁₆	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	17	2	no	—
409	C₂²	—	34	2	no	—
410	C₂²	—	34	1	no	—
411	C₂²	—	34	2	no	—
412	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	17	2	no	—
417	C₄	—	17	4	no	—
418	C₄	—	34	1	no	—
419	C₄	—	34	2	no	—
420	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
421	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	34	2	no	—
424	C₂	—	68	1	no	—
425	C₂	C₄×D₁₇⋊M₁₆	1	1	yes	characteristic
426	C₂	#14545354	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#405	C₄
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#17336
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #14544008	C₂	semidirect
3. #14544007	C₂	semidirect
4. #14544004	C₂	semidirect
5. #14544003	C₂	semidirect
6. #14543994	C₂	semidirect
7. #14543993	C₂	semidirect
8. #14543992	C₂	semidirect
9. #14543988	C₂	semidirect
10. #14543978	C₂	semidirect
154. C₈×D₁₇	M₁₆	semidirect
155. C₈×D₁₇	M₁₆	semidirect
317. C₁₇	#17336	semidirect

Maximal subgroups

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

subgroup	index
#14545595	2
#14544008	2
#14544007	2
#14544004	2
#14544003	2
#14543994	2
#14543993	2
#14543992	2
#14543988	2
#14543978	2
#14537206	2
#17336	17