Subgroups — D₁₇⋊#2155 #17978427

Order 4352.

658 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763819	C₂	1	1	yes	maximal, characteristic
3	#14545132	C₂	1	4	yes	maximal, complemented
4	#14545131	C₂	1	4	yes	maximal, complemented
5	D₁₇⋊#365	C₂	1	4	yes	maximal, complemented
6	C₂×M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
7	C₂×D₁₇⋊M₁₆	—	2	1	no	—
8	C₂×#10587677	—	2	1	no	—
9	C₂×#10587536	—	2	1	no	—
10	D₁₇⋊#108	—	2	1	no	—
11	D₁₇⋊#108	—	2	1	no	—
12	D₁₇⋊#108	C₂²	1	2	yes	—
13	D₁₇⋊#108	C₂²	1	2	yes	—
14	C₂×#10587535	C₂²	1	2	yes	—
15	#11763819	—	2	1	no	—
16	#11763819	—	2	1	no	—
17	#11763819	C₂²	1	2	yes	—
18	#11763819	C₂²	1	2	yes	—
19	C₂×#10587534	—	2	1	no	—
20	C₂×#10587533	C₂²	1	2	yes	—
21	#11763734	C₂²	1	8	yes	complemented
22	#11763733	C₂²	1	8	yes	complemented
23	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
24	C₂×#10587483	C₄	1	1	yes	characteristic, complemented
25	C₂×#10587469	C₂²	1	2	yes	—
26	M₃₂×D₁₇	C₄	1	2	yes	complemented
27	M₃₂×D₁₇	C₄	1	2	yes	complemented
28	M₃₂×D₁₇	C₂²	1	2	yes	—
29	M₃₂×D₁₇	C₂²	1	2	yes	—
30	C₂×C₁₆×D₁₇	C₄	1	2	yes	complemented
31	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊#595	—	4	1	no	—
34	C₂×#63247	—	4	1	no	—
35	#10587677	—	2	2	no	—
36	#10587677	—	2	2	no	—
37	#10587677	—	4	1	no	—
38	#10587677	—	4	1	no	—
39	C₂×C₄⋊#595	—	2	2	no	—
40	C₂×C₄×#595	—	4	1	no	—
41	D₁₇⋊M₁₆	—	2	2	no	—
42	D₁₇⋊M₁₆	—	2	2	no	—
43	D₁₇⋊M₁₆	—	4	1	no	—
44	D₁₇⋊M₁₆	—	4	1	no	—
45	C₂×#63243	—	2	2	no	—
46	C₂×#63242	—	4	1	no	—
47	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×#3622	Q₈	1	1	yes	characteristic
49	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
58	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
61	#10587536	—	2	2	no	—
62	#10587536	—	2	2	no	—
63	#10587535	—	2	2	no	—
64	#10587535	C₂³	1	4	yes	—
65	#10587534	—	2	2	no	—
66	#10587534	—	2	2	no	—
67	#10587533	—	2	2	no	—
68	#10587533	C₂³	1	4	yes	—
69	C₁₇×M₃₂	C₂×C₄	1	2	yes	—
70	C₁₇×M₃₂	C₂×C₄	1	2	yes	complemented
71	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	complemented
72	#10587483	C₂×C₄	1	2	yes	—
73	#10587483	C₂×C₄	1	2	yes	complemented
74	C₂×#63214	C₂×C₄	1	2	yes	complemented
75	#10587469	C₂×C₄	1	4	yes	complemented
76	#10587469	C₂³	1	4	yes	—
77	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
78	C₁₆×D₁₇	C₂×C₄	1	4	yes	complemented
79	C₂³×D₁₇	SD₁₆	1	1	yes	characteristic
80	C₂²×#595	—	4	2	no	—
81	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₁₇	SD₁₆	1	1	yes	characteristic
83	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
89	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
90	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
95	C₂²⋊#595	—	4	2	no	—
96	C₂²⋊#595	—	4	2	no	—
97	#63247	—	4	2	no	—
98	#63247	—	4	2	no	—
99	C₂×#3624	—	4	2	no	—
100	C₄⋊#595	—	2	4	no	—
101	C₄⋊#595	—	4	2	no	—
102	C₄×#595	—	4	2	no	—
103	C₄×#595	—	4	2	no	—
104	#63243	—	2	4	no	—
105	#63243	—	4	2	no	—
106	#63242	—	4	2	no	—
107	#63242	—	4	2	no	—
108	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
116	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
117	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
118	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
119	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
120	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
121	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
122	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
123	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
124	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
125	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
130	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
131	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
133	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
134	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
135	C₈×D₁₇	C₂⁴	1	1	yes	characteristic
136	C₁₆×C₁₇	C₂²×C₄	1	4	yes	—
137	#63214	C₂²×C₄	1	4	yes	—
138	C₂×#2155	—	17	1	no	maximal, Sylow
139	C₂³×C₁₇	#106	1	1	yes	characteristic
140	C₂²×D₁₇	—	4	2	no	—
141	C₂²×D₁₇	#106	1	1	yes	characteristic
142	C₂²×D₁₇	#106	1	1	yes	characteristic
143	C₂²×D₁₇	#106	1	1	yes	characteristic
144	C₂²×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
145	C₂²×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂²×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×#595	—	4	4	no	—
148	C₂×#595	—	8	4	no	—
149	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₇	#106	1	1	yes	characteristic
156	C₂×Dic₁₇	#106	1	1	yes	characteristic
157	C₂×Dic₁₇	#106	1	1	yes	characteristic
158	C₂×Dic₁₇	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×Dic₁₇	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×Dic₁₇	C₂×SD₁₆	1	1	yes	characteristic
161	C₄×D₁₇	#106	1	1	yes	characteristic
162	C₄×D₁₇	#106	1	1	yes	characteristic
163	C₄×D₁₇	#106	1	1	yes	characteristic
164	C₄×D₁₇	#106	1	1	yes	characteristic
165	C₄×D₁₇	#106	1	1	yes	characteristic
166	C₄×D₁₇	#106	1	1	yes	characteristic
167	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
171	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
172	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
173	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
174	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
175	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
176	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
177	#3624	—	4	4	no	—
178	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
182	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
184	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
185	#3622	C₂²×Q₈	1	1	yes	characteristic
186	C₂²×M₃₂	—	17	1	no	—
187	C₂²×#108	—	17	1	no	—
188	C₂×#427	—	17	1	no	—
189	#2155	—	17	4	no	—
190	#2155	—	17	4	no	—
191	C₂×#365	—	17	4	no	—
192	C₂²×C₁₇	—	4	1	no	—
193	C₂²×C₁₇	C₂×#106	1	1	yes	characteristic
194	C₂²×C₁₇	C₂×#106	1	1	yes	characteristic
195	C₂²×C₁₇	C₂×#106	1	1	yes	characteristic
196	C₂×D₁₇	—	2	2	no	—
197	C₂×D₁₇	—	2	2	no	—
198	C₂×D₁₇	—	2	2	no	—
199	C₂×D₁₇	—	4	1	no	—
200	C₂×D₁₇	—	4	1	no	—
201	C₂×D₁₇	—	4	1	no	—
202	C₂×D₁₇	C₂×#106	1	1	yes	characteristic
203	C₂×D₁₇	C₂×#106	1	1	yes	characteristic
204	C₂×D₁₇	C₂×#106	1	1	yes	characteristic
205	C₂×D₁₇	C₂²×SD₁₆	1	1	yes	characteristic
206	#595	—	8	4	no	—
207	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
208	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
209	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
210	C₄×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	Dic₁₇	C₂×#106	1	1	yes	characteristic
212	Dic₁₇	C₂×#106	1	1	yes	characteristic
213	Dic₁₇	C₂×#106	1	1	yes	characteristic
214	Dic₁₇	C₂²×SD₁₆	1	1	yes	characteristic
215	C₂²×M₁₆	—	34	1	no	—
216	C₂³×C₈	—	17	1	no	—
217	C₂×#117	—	34	1	no	—
218	C₂×M₃₂	—	17	1	no	—
219	C₂×M₃₂	—	17	2	no	—
220	C₂×M₃₂	—	17	2	no	—
221	C₂×M₃₂	—	17	2	no	—
222	C₂×M₃₂	—	17	2	no	—
223	C₂×M₃₂	—	17	2	no	—
224	C₂×M₃₂	#595	1	1	yes	characteristic, complemented
225	C₂²×C₁₆	—	17	2	no	—
226	C₂×#108	—	17	2	no	—
227	C₂×#108	—	17	2	no	—
228	C₂×#108	—	17	2	no	—
229	C₂×#108	—	34	1	no	—
230	C₂×#108	—	34	1	no	—
231	C₂×#108	—	34	1	no	—
232	#427	—	17	2	no	—
233	#427	—	17	2	no	—
234	#427	—	34	1	no	—
235	#427	—	34	1	no	—
236	C₂×#107	—	34	1	no	—
237	C₂×#106	—	17	2	no	—
238	#365	—	17	8	no	—
239	#365	—	17	8	no	—
240	C₂×C₁₇	—	2	1	no	—
241	C₂×C₁₇	—	2	1	no	—
242	C₂×C₁₇	—	2	1	no	—
243	C₂×C₁₇	C₂²×#106	1	1	yes	characteristic
244	D₁₇	—	2	1	no	—
245	D₁₇	—	2	1	no	—
246	D₁₇	—	2	1	no	—
247	D₁₇	#2155	1	2	yes	complemented
248	C₂³×C₄	—	17	1	no	—
249	C₂×M₁₆	—	34	2	no	—
250	C₂×M₁₆	—	34	2	no	—
251	C₂×M₁₆	—	34	2	no	—
252	C₂×M₁₆	—	68	1	no	—
253	C₂×M₁₆	—	68	1	no	—
254	C₂×M₁₆	—	68	1	no	—
255	C₂²×C₈	—	17	1	no	—
256	C₂²×C₈	—	17	1	no	—
257	C₂²×C₈	—	17	1	no	—
258	C₂²×C₈	—	17	1	no	—
259	C₂²×C₈	—	17	1	no	—
260	C₂²×C₈	—	17	1	no	—
261	C₂²×C₈	—	17	1	no	—
262	C₂²×C₈	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	1	no	—
265	C₂²×C₈	—	17	1	no	—
266	C₂²×C₈	—	17	1	no	—
267	C₂²×C₈	—	17	1	no	—
268	C₂²×C₈	—	68	1	no	—
269	C₂²×C₈	C₂×#595	1	1	yes	characteristic
270	#117	—	34	2	no	—
271	#117	—	34	2	no	—
272	#117	—	68	1	no	—
273	#117	—	68	1	no	—
274	C₂×C₄⋊C₄	—	34	2	no	—
275	C₂×C₂²⋊C₄	—	68	1	no	—
276	C₂×C₄²	—	68	1	no	—
277	M₃₂	—	17	2	no	—
278	M₃₂	—	17	2	no	—
279	M₃₂	—	17	4	no	—
280	M₃₂	—	17	4	no	—
281	M₃₂	C₂×#595	1	2	yes	—
282	M₃₂	C₂×#595	1	2	yes	complemented
283	C₂×C₁₆	—	17	2	no	—
284	C₂×C₁₆	—	17	4	no	—
285	C₂×C₁₆	—	17	4	no	—
286	C₂×C₁₆	C₂×#595	1	2	yes	complemented
287	#108	—	17	4	no	—
288	#108	—	34	2	no	—
289	#108	—	34	2	no	—
290	#108	—	34	2	no	—
291	#107	—	34	2	no	—
292	#107	—	34	2	no	—
293	#106	—	17	4	no	—
294	#106	—	34	2	no	—
295	C₁₇	C₂×#2155	1	1	yes	characteristic, complemented, Sylow
296	C₂⁴	—	17	1	no	—
297	C₂²×C₄	—	17	1	no	—
298	C₂²×C₄	—	17	1	no	—
299	C₂²×C₄	—	17	1	no	—
300	C₂²×C₄	—	17	1	no	—
301	C₂²×C₄	—	17	1	no	—
302	C₂²×C₄	—	17	1	no	—
303	C₂²×C₄	—	17	1	no	—
304	C₂²×C₄	—	17	1	no	—
305	C₂²×C₄	—	17	1	no	—
306	C₂²×C₄	—	17	1	no	—
307	C₂²×C₄	—	17	1	no	—
308	C₂²×C₄	—	17	1	no	—
309	C₂²×C₄	—	17	1	no	—
310	C₂²×C₄	—	68	2	no	—
311	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
312	M₁₆	—	34	4	no	—
313	M₁₆	—	68	2	no	—
314	M₁₆	—	68	2	no	—
315	M₁₆	—	68	2	no	—
316	C₂×C₈	—	17	1	no	—
317	C₂×C₈	—	17	1	no	—
318	C₂×C₈	—	17	1	no	—
319	C₂×C₈	—	17	1	no	—
320	C₂×C₈	—	17	1	no	—
321	C₂×C₈	—	17	1	no	—
322	C₂×C₈	—	17	1	no	—
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	17	1	no	—
327	C₂×C₈	—	17	1	no	—
328	C₂×C₈	—	17	1	no	—
329	C₂×C₈	—	17	1	no	—
330	C₂×C₈	—	17	1	no	—
331	C₂×C₈	—	17	1	no	—
332	C₂×C₈	—	17	1	no	—
333	C₂×C₈	—	17	1	no	—
334	C₂×C₈	—	17	1	no	—
335	C₂×C₈	—	17	1	no	—
336	C₂×C₈	—	17	1	no	—
337	C₂×C₈	—	17	1	no	—
338	C₂×C₈	—	68	2	no	—
339	C₂×C₈	—	68	2	no	—
340	C₂×C₈	—	68	2	no	—
341	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
342	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
343	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
344	C₂×C₈	C₂²×#595	1	1	yes	characteristic
345	C₂×C₈	C₂²×#595	1	1	yes	characteristic
346	C₂×C₈	C₂²×#595	1	1	yes	characteristic
347	C₄⋊C₄	—	34	4	no	—
348	C₄⋊C₄	—	68	2	no	—
349	C₂²⋊C₄	—	68	2	no	—
350	C₂²⋊C₄	—	68	2	no	—
351	C₄²	—	68	2	no	—
352	C₄²	—	68	2	no	—
353	C₁₆	—	17	4	no	—
354	C₁₆	C₂²×#595	1	4	yes	—
355	C₂³	—	17	1	no	—
356	C₂³	—	17	1	no	—
357	C₂³	—	17	1	no	—
358	C₂³	—	17	1	no	—
359	C₂³	—	17	1	no	—
360	C₂³	—	17	1	no	—
361	C₂³	—	68	2	no	—
362	C₂³	#10587533	1	1	yes	characteristic
363	C₂×C₄	—	17	1	no	—
364	C₂×C₄	—	17	1	no	—
365	C₂×C₄	—	17	1	no	—
366	C₂×C₄	—	17	1	no	—
367	C₂×C₄	—	17	1	no	—
368	C₂×C₄	—	17	1	no	—
369	C₂×C₄	—	17	1	no	—
370	C₂×C₄	—	17	1	no	—
371	C₂×C₄	—	17	1	no	—
372	C₂×C₄	—	17	1	no	—
373	C₂×C₄	—	17	1	no	—
374	C₂×C₄	—	17	1	no	—
375	C₂×C₄	—	17	1	no	—
376	C₂×C₄	—	17	1	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	17	1	no	—
383	C₂×C₄	—	17	1	no	—
384	C₂×C₄	—	17	1	no	—
385	C₂×C₄	—	68	4	no	—
386	C₂×C₄	—	136	4	no	—
387	C₂×C₄	#10587533	1	1	yes	characteristic
388	C₂×C₄	#10587533	1	1	yes	characteristic
389	C₂×C₄	#10587533	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
393	C₈	—	17	1	no	—
394	C₈	—	17	1	no	—
395	C₈	—	17	1	no	—
396	C₈	—	17	1	no	—
397	C₈	—	68	4	no	—
398	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
399	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
400	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
401	C₈	C₂³×#595	1	1	yes	characteristic
402	C₂²	—	4	1	no	—
403	C₂²	—	17	1	no	—
404	C₂²	—	17	1	no	—
405	C₂²	—	17	1	no	—
406	C₂²	—	17	1	no	—
407	C₂²	—	34	2	no	—
408	C₂²	—	34	2	no	—
409	C₂²	—	34	2	no	—
410	C₂²	—	68	1	no	—
411	C₂²	—	68	1	no	—
412	C₂²	—	68	1	no	—
413	C₂²	C₂×#10587533	1	1	yes	characteristic
414	C₂²	C₂×#10587533	1	1	yes	characteristic
415	C₂²	C₂×#10587533	1	1	yes	characteristic
416	C₄	—	17	1	no	—
417	C₄	—	17	1	no	—
418	C₄	—	17	1	no	—
419	C₄	—	17	1	no	—
420	C₄	—	136	4	no	—
421	C₄	C₂×#10587533	1	1	yes	characteristic
422	C₄	C₂×#10587533	1	1	yes	characteristic
423	C₄	C₂×#10587533	1	1	yes	characteristic
424	C₄	C₂²×C₄⋊#595	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	17	2	no	—
429	C₂	—	34	1	no	—
430	C₂	—	34	1	no	—
431	C₂	—	34	1	no	—
432	C₂	C₂²×#10587533	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#10587533
commutator	C₈×C₁₇	C₂³×C₄
Frattini	C₈	C₂³×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂×C₁₇	C₂²×#106
prime radical	C₂³×D₁₇	SD₁₆
cosocle	C₈×D₁₇	C₂⁴
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₂×#2155
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14545132	C₂	semidirect
4. #14545131	C₂	semidirect
5. D₁₇⋊#365	C₂	semidirect
21. #11763734	C₂²	semidirect
22. #11763733	C₂²	semidirect
24. C₂×#10587483	C₄	semidirect
26. M₃₂×D₁₇	C₄	semidirect
27. M₃₂×D₁₇	C₄	semidirect
30. C₂×C₁₆×D₁₇	C₄	semidirect
31. C₂×C₁₇×M₃₂	C₄	semidirect
70. C₁₇×M₃₂	C₂×C₄	semidirect
71. C₂×C₁₆×C₁₇	C₂×C₄	semidirect
73. #10587483	C₂×C₄	semidirect
74. C₂×#63214	C₂×C₄	semidirect
75. #10587469	C₂×C₄	semidirect
78. C₁₆×D₁₇	C₂×C₄	semidirect
224. C₂×M₃₂	#595	semidirect
247. D₁₇	#2155	semidirect
282. M₃₂	C₂×#595	semidirect
286. C₂×C₁₆	C₂×#595	semidirect
295. C₁₇	C₂×#2155	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₇⋊#108	2
C₂×#11763819	2
#14545132	2
#14545131	2
D₁₇⋊#365	2
C₂×M₃₂×D₁₇	2
C₂×#2155	17

Subgroups — D17⋊#2155 #17978427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇⋊#2155 #17978427