Subgroups — #17054021

Order 4352.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537450	C₂	1	2	yes	maximal, complemented
2	#14529673	C₂	1	2	yes	maximal
3	#14529434	C₂	1	4	yes	maximal, complemented
4	#14528956	C₂	1	1	yes	maximal, characteristic, complemented
5	#14528804	C₂	1	2	yes	maximal, complemented
6	#14528665	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic
9	#11762870	—	2	4	no	—
10	#11762866	—	2	2	no	—
11	#11762862	—	2	2	no	—
12	C₂×#10587490	C₂²	1	2	yes	—
13	C₂×#10587490	C₂²	1	2	yes	—
14	#11762833	C₂²	1	2	yes	—
15	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
16	C₂×#10587508	C₂²	1	4	yes	—
17	#11762776	C₂²	1	4	yes	—
18	#11762765	C₂²	1	4	yes	—
19	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
21	#11762568	C₂²	1	4	yes	—
22	#11762563	C₂²	1	2	yes	—
23	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₇	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₁₇	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₁₇	C₄	1	2	yes	complemented
29	C₄×D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
31	C₁₇×#427	C₂²	1	1	yes	characteristic
32	C₁₇×#416	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
34	C₂×#41×C₁₇	C₂³	1	2	yes	—
35	C₁₇×#135	—	2	2	no	—
36	C₁₇×#135	—	2	2	no	—
37	C₂×Q₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×SD₁₆×C₁₇	C₂×C₄	1	2	yes	—
39	C₂×D₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₁₇	C₂×C₄	1	2	yes	—
43	C₄×Q₈×C₁₇	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₁₇	—	2	2	no	—
45	C₄×D₄×C₁₇	—	2	2	no	—
46	C₄×D₄×C₁₇	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₇	C₂×C₄	1	2	yes	—
48	C₁₇×#117	—	2	2	no	—
49	C₁₇×#117	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₇	—	2	2	no	—
51	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₇	—	2	1	no	—
53	C₂×C₄×Dic₁₇	C₂³	1	2	yes	—
54	C₂×#63223	C₂³	1	4	yes	—
55	C₂²×#3622	C₂³	1	2	yes	—
56	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
57	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
58	C₁₇×#106	C₂×C₄	1	2	yes	—
59	C₁₇×#103	C₂×C₄	1	2	yes	—
60	C₁₇×#103	C₂×C₄	1	2	yes	—
61	C₁₇×#102	C₂×C₄	1	2	yes	—
62	C₁₇×#102	C₂×C₄	1	2	yes	—
63	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
67	#10587508	—	4	4	no	—
68	#10587502	—	2	1	no	—
69	C₂²⋊#3622	—	2	4	no	—
70	C₂²⋊#3622	—	2	4	no	—
71	#10587490	—	2	4	no	—
72	#10587490	—	4	2	no	—
73	C₈×Dic₁₇	—	2	4	no	—
74	C₄⋊#3622	—	2	2	no	—
75	C₄⋊#3622	—	2	2	no	—
76	C₄⋊#3622	D₄	1	1	yes	characteristic
77	C₄⋊#3622	D₄	1	1	yes	characteristic
78	C₄⋊#3622	D₄	1	2	yes	—
79	#10587474	—	2	4	no	—
80	C₄×#3622	—	2	4	no	—
81	#41×C₁₇	—	2	2	no	—
82	#41×C₁₇	—	2	2	no	—
83	#41×C₁₇	—	2	2	no	—
84	#41×C₁₇	—	2	2	no	—
85	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₁₇	—	2	2	no	—
87	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₇	—	2	2	no	—
89	C₂²×C₄×C₁₇	—	2	2	no	—
90	C₂²×C₄×C₁₇	—	2	2	no	—
91	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₁₇	—	2	2	no	—
95	Q₁₆×C₁₇	—	2	2	no	—
96	SD₁₆×C₁₇	—	2	4	no	—
97	D₈×C₁₇	—	2	2	no	—
98	C₂×C₈×C₁₇	—	2	1	no	—
99	C₂×C₈×C₁₇	—	2	1	no	—
100	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₇	#41	1	2	yes	—
105	C₂×C₈×C₁₇	#41	1	2	yes	—
106	C₄⋊C₄×C₁₇	—	2	2	no	—
107	C₄⋊C₄×C₁₇	—	2	2	no	—
108	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
109	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
110	C₂²⋊C₄×C₁₇	—	2	2	no	—
111	C₂²⋊C₄×C₁₇	—	2	2	no	—
112	C₂²⋊C₄×C₁₇	—	2	2	no	—
113	C₄²×C₁₇	—	2	2	no	—
114	C₄²×C₁₇	—	2	2	no	—
115	C₄²×C₁₇	—	2	2	no	—
116	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
120	C₄⋊Dic₁₇	—	2	4	no	—
121	C₄×Dic₁₇	—	2	2	no	—
122	C₄×Dic₁₇	—	2	2	no	—
123	#63223	—	2	4	no	—
124	#63223	—	2	4	no	—
125	C₂×#3622	—	2	2	no	—
126	C₂×#3622	—	2	2	no	—
127	C₂×#3622	—	2	4	no	—
128	C₂×#3622	C₂×D₄	1	2	yes	—
129	C₂×#3622	C₂×D₄	1	2	yes	—
130	#22802	—	17	1	no	maximal, Sylow
131	C₂³×C₁₇	—	2	2	no	—
132	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
133	Q₈×C₁₇	—	2	2	no	—
134	Q₈×C₁₇	—	2	2	no	—
135	D₄×C₁₇	—	2	2	no	—
136	D₄×C₁₇	—	2	2	no	—
137	D₄×C₁₇	—	4	2	no	—
138	D₄×C₁₇	—	4	2	no	—
139	C₂×C₄×C₁₇	—	2	2	no	—
140	C₂×C₄×C₁₇	—	2	2	no	—
141	C₂×C₄×C₁₇	—	2	2	no	—
142	C₂×C₄×C₁₇	—	2	2	no	—
143	C₂×C₄×C₁₇	—	4	1	no	—
144	C₂×C₄×C₁₇	—	4	2	no	—
145	C₂×C₄×C₁₇	—	4	2	no	—
146	C₂×C₄×C₁₇	—	4	4	no	—
147	C₂×C₄×C₁₇	—	8	2	no	—
148	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×Dic₁₇	—	2	4	no	—
159	C₂×Dic₁₇	—	4	2	no	—
160	C₂×Dic₁₇	—	4	2	no	—
161	C₈×C₁₇	—	2	1	no	—
162	C₈×C₁₇	—	2	1	no	—
163	C₈×C₁₇	#117	1	2	yes	—
164	C₈×C₁₇	#117	1	2	yes	—
165	#3622	—	2	2	no	—
166	#3622	—	2	2	no	—
167	#3622	—	4	4	no	—
168	C₄×#135	D₁₇	1	1	yes	characteristic
169	#2925	—	17	2	no	—
170	#1974	—	17	2	no	—
171	#1929	—	17	4	no	—
172	#1848	—	17	1	no	—
173	#1806	—	17	2	no	—
174	#1772	—	17	2	no	—
175	C₈×C₄⋊C₄	—	17	1	no	—
176	C₂²×C₁₇	—	2	1	no	—
177	C₂²×C₁₇	—	2	1	no	—
178	C₂²×C₁₇	—	4	2	no	—
179	C₂²×C₁₇	—	4	2	no	—
180	C₂²×C₁₇	—	4	2	no	—
181	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₁₇	#555	1	1	yes	characteristic
183	C₂²×C₁₇	#556	1	1	yes	characteristic
184	C₄×C₁₇	—	2	1	no	—
185	C₄×C₁₇	—	2	1	no	—
186	C₄×C₁₇	—	2	1	no	—
187	C₄×C₁₇	—	4	2	no	—
188	C₄×C₁₇	—	4	2	no	—
189	C₄×C₁₇	—	4	2	no	—
190	C₄×C₁₇	#443	1	2	yes	—
191	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
192	C₄×C₁₇	#520	1	1	yes	characteristic
193	C₄×C₁₇	#547	1	1	yes	characteristic
194	C₄×C₁₇	#550	1	1	yes	characteristic
195	Dic₁₇	—	4	4	no	—
196	C₂×#135	C₂×D₁₇	1	1	yes	characteristic
197	C₄×#41	C₂×D₁₇	1	2	yes	—
198	C₄×Q₁₆	Dic₁₇	1	1	yes	characteristic, complemented
199	C₄×Q₁₆	Dic₁₇	1	1	yes	characteristic, complemented
200	C₄×SD₁₆	Dic₁₇	1	2	yes	complemented
201	C₄×SD₁₆	Dic₁₇	1	2	yes	complemented
202	C₄×D₈	Dic₁₇	1	1	yes	characteristic, complemented
203	C₄×D₈	Dic₁₇	1	1	yes	characteristic, complemented
204	#433	—	34	4	no	—
205	#432	—	34	2	no	—
206	#431	—	34	2	no	—
207	C₂×#108	—	17	2	no	—
208	C₂×#108	—	17	2	no	—
209	#427	C₂×D₁₇	1	1	yes	characteristic
210	#423	—	17	2	no	—
211	C₂×C₄⋊C₈	—	17	1	no	—
212	C₂×#104	—	17	4	no	—
213	#416	C₂×D₁₇	1	2	yes	—
214	#408	—	17	4	no	—
215	#405	—	17	4	no	—
216	C₂×C₄×C₈	—	17	2	no	—
217	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
218	C₄×C₄⋊C₄	—	17	1	no	—
219	#339	—	17	4	no	—
220	#336	—	17	2	no	—
221	C₂×C₁₇	—	2	1	no	—
222	C₂×C₁₇	—	2	1	no	—
223	C₂×C₁₇	—	8	2	no	—
224	C₂×C₁₇	#2354	1	1	yes	characteristic
225	C₂×C₁₇	C₂×#443	1	1	yes	characteristic
226	C₂×C₁₇	#2957	1	1	yes	characteristic
227	C₂×#41	C₂²×D₁₇	1	2	yes	—
228	#135	—	2	2	no	—
229	#135	—	2	2	no	—
230	C₂×Q₁₆	C₂×Dic₁₇	1	1	yes	characteristic
231	C₂×SD₁₆	C₂×Dic₁₇	1	2	yes	—
232	C₂×D₈	C₂×Dic₁₇	1	1	yes	characteristic
233	C₂×M₁₆	—	17	4	no	—
234	C₂²×C₈	—	17	2	no	—
235	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
236	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
237	C₄×Q₈	C₂×Dic₁₇	1	2	yes	—
238	C₄×Q₈	C₂×Dic₁₇	1	2	yes	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	C₂×Dic₁₇	1	2	yes	—
242	C₄×D₄	C₂×Dic₁₇	1	2	yes	—
243	#117	—	2	2	no	—
244	#117	C₂²×D₁₇	1	2	yes	—
245	C₂×C₄⋊C₄	—	34	1	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	17	2	no	—
248	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
249	#108	—	34	4	no	—
250	#108	—	68	2	no	—
251	#107	C₂×Dic₁₇	1	1	yes	characteristic
252	#107	C₂×Dic₁₇	1	1	yes	characteristic
253	#106	C₂×Dic₁₇	1	2	yes	—
254	C₄⋊C₈	—	17	1	no	—
255	C₄⋊C₈	—	17	1	no	—
256	C₄⋊C₈	—	17	2	no	—
257	C₄⋊C₈	—	34	2	no	—
258	C₄⋊C₈	—	34	2	no	—
259	#104	—	68	4	no	—
260	#103	C₂×Dic₁₇	1	2	yes	—
261	#103	C₂×Dic₁₇	1	2	yes	—
262	#102	C₂×Dic₁₇	1	2	yes	—
263	#102	C₂×Dic₁₇	1	2	yes	—
264	C₂²⋊C₈	—	34	4	no	—
265	C₂²⋊C₈	—	34	4	no	—
266	#97	—	34	4	no	—
267	C₄×C₈	—	34	4	no	—
268	C₄×C₈	—	34	4	no	—
269	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
270	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
271	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
272	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
273	#95	—	34	1	no	—
274	C₁₇	#22802	1	1	yes	characteristic, complemented, Sylow
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	#41	—	2	2	no	—
279	C₂×Q₈	C₂²×Dic₁₇	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²×Dic₁₇	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	34	2	no	—
286	C₂²×C₄	#63254	1	1	yes	characteristic
287	C₂²×C₄	#63254	1	1	yes	characteristic
288	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	SD₁₆	—	2	4	no	—
291	D₈	—	2	2	no	—
292	M₁₆	—	34	4	no	—
293	M₁₆	—	34	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	17	2	no	—
297	C₂×C₈	—	17	2	no	—
298	C₂×C₈	—	34	2	no	—
299	C₂×C₈	—	34	2	no	—
300	C₂×C₈	—	34	4	no	—
301	C₂×C₈	#63252	1	2	yes	—
302	C₂×C₈	#63252	1	2	yes	—
303	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
306	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	34	4	no	—
310	C₄⋊C₄	C₂²×Dic₁₇	1	2	yes	—
311	C₄⋊C₄	C₂²×Dic₁₇	1	2	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	34	2	no	—
319	C₄²	—	34	2	no	—
320	C₄²	D₄×D₁₇	1	1	yes	characteristic
321	C₄²	D₄×D₁₇	1	1	yes	characteristic
322	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
323	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	C₂×#63254	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	34	4	no	—
342	C₂×C₄	—	68	2	no	—
343	C₂×C₄	—	68	2	no	—
344	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
345	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
346	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
347	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
348	C₂×C₄	C₂×#63252	1	1	yes	characteristic
349	C₂×C₄	C₂×#63252	1	1	yes	characteristic
350	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
351	C₂×C₄	#10587696	1	1	yes	characteristic
352	C₂×C₄	#10587697	1	1	yes	characteristic
353	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	34	2	no	—
357	C₈	—	34	2	no	—
358	C₈	—	68	4	no	—
359	C₈	#10587612	1	2	yes	—
360	C₈	#10587612	1	2	yes	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₂×D₄×Dic₁₇	1	1	yes	characteristic
367	C₂²	#11763524	1	1	yes	characteristic
368	C₂²	#11763529	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	68	4	no	—
376	C₄	#11762926	1	2	yes	—
377	C₄	C₂×#10587612	1	1	yes	characteristic
378	C₄	#11763292	1	1	yes	characteristic
379	C₄	#11763464	1	1	yes	characteristic
380	C₄	#11763480	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	2	no	—
384	C₂	#14531733	1	1	yes	characteristic
385	C₂	C₂×#11762926	1	1	yes	characteristic
386	C₂	#14537701	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₄×C₁₇×#135	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×C₁₇×#135	C₂²
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×#135	D₁₇
hypocenter	C₁₇	#22802
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #14537450	C₂	semidirect
3. #14529434	C₂	semidirect
4. #14528956	C₂	semidirect
5. #14528804	C₂	semidirect
6. #14528665	C₂	semidirect
7. C₈×C₄⋊Dic₁₇	C₂	semidirect
25. C₄×Q₁₆×C₁₇	C₄	semidirect
26. C₄×Q₁₆×C₁₇	C₄	semidirect
27. C₄×SD₁₆×C₁₇	C₄	semidirect
28. C₄×SD₁₆×C₁₇	C₄	semidirect
29. C₄×D₈×C₁₇	C₄	semidirect
30. C₄×D₈×C₁₇	C₄	semidirect
198. C₄×Q₁₆	Dic₁₇	semidirect
199. C₄×Q₁₆	Dic₁₇	semidirect
200. C₄×SD₁₆	Dic₁₇	semidirect
201. C₄×SD₁₆	Dic₁₇	semidirect
202. C₄×D₈	Dic₁₇	semidirect
203. C₄×D₈	Dic₁₇	semidirect
274. C₁₇	#22802	semidirect

Maximal subgroups

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

subgroup	index
#14537450	2
#14529673	2
#14529434	2
#14528956	2
#14528804	2
#14528665	2
C₈×C₄⋊Dic₁₇	2
C₄×C₁₇×#135	2
#22802	17