Subgroups — #17968587

Order 4352.

1010 conjugacy classes of subgroups.

The subgroup lattice has 526 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	#14545347	C₂	1	2	yes	maximal
4	#14544590	C₂	1	4	yes	maximal, complemented
5	#14544586	C₂	1	4	yes	maximal, complemented
6	#14544465	C₂	1	2	yes	maximal
7	D₁₇×#405	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₇⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#10587677	C₂²	1	2	yes	—
10	C₂×#10587536	C₄	1	2	yes	complemented
11	D₁₇⋊#108	C₄	1	2	yes	complemented
12	D₁₇⋊#108	C₄	1	2	yes	complemented
13	D₁₇⋊#108	C₂²	1	2	yes	—
14	D₁₇⋊#108	C₂²	1	2	yes	—
15	C₂×#10587535	C₄	1	2	yes	complemented
16	#11763819	C₄	1	2	yes	complemented
17	#11763819	C₄	1	2	yes	complemented
18	#11763819	C₂²	1	2	yes	—
19	#11763819	C₂²	1	2	yes	—
20	C₂×#10587534	C₄	1	2	yes	complemented
21	C₂×#10587533	C₄	1	2	yes	complemented
22	#11763775	—	2	4	no	—
23	#11763772	C₂²	1	8	yes	—
24	M₁₆×#595	—	2	4	no	—
25	#11763680	C₂²	1	8	yes	—
26	C₂×M₁₆×D₁₇	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
28	#117×D₁₇	C₂²	1	1	yes	characteristic
29	#11762767	C₄	1	1	yes	characteristic, complemented
30	#11762766	C₄	1	2	yes	complemented
31	#11762765	C₄	1	1	yes	characteristic, complemented
32	#11762764	C₄	1	1	yes	characteristic, complemented
33	#11762763	C₄	1	2	yes	complemented
34	#97×D₁₇	C₂²	1	2	yes	—
35	C₄×C₈×D₁₇	C₂²	1	2	yes	—
36	C₁₇×#405	C₄	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊#595	—	2	2	no	—
39	C₂×#63247	—	2	2	no	—
40	#10587677	—	2	2	no	—
41	#10587677	—	2	2	no	—
42	#10587677	C₂×C₄	1	4	yes	—
43	#10587677	C₂³	1	4	yes	—
44	C₂×C₄⋊#595	C₂×C₄	1	4	yes	—
45	C₂×C₄×#595	—	2	2	no	—
46	D₁₇⋊M₁₆	—	2	2	no	—
47	D₁₇⋊M₁₆	—	2	2	no	—
48	D₁₇⋊M₁₆	C₂×C₄	1	4	yes	—
49	D₁₇⋊M₁₆	C₂³	1	4	yes	—
50	C₂×#63243	C₂×C₄	1	4	yes	—
51	C₂×#63242	—	2	2	no	—
52	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
55	#10587612	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	M₁₆×D₁₇	D₄	1	2	yes	—
59	M₁₆×D₁₇	D₄	1	2	yes	—
60	M₁₆×D₁₇	Q₈	1	2	yes	—
61	M₁₆×D₁₇	Q₈	1	2	yes	—
62	C₂×#63218	C₂×C₄	1	2	yes	—
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	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₁₇	C₂³	1	2	yes	—
76	#10587578	—	2	1	no	—
77	C₄⋊C₄×D₁₇	—	2	1	no	—
78	C₂²⋊C₄×D₁₇	—	2	1	no	—
79	#10587563	—	2	1	no	—
80	#10587558	C₂×C₄	1	2	yes	—
81	C₄²×D₁₇	C₂³	1	2	yes	—
82	#10587536	C₂×C₄	1	4	yes	complemented
83	#10587536	C₂×C₄	1	4	yes	complemented
84	#10587535	C₂×C₄	1	4	yes	complemented
85	#10587535	C₂×C₄	1	4	yes	complemented
86	#10587534	C₂×C₄	1	4	yes	—
87	#10587534	C₂×C₄	1	4	yes	—
88	#10587533	C₂×C₄	1	4	yes	—
89	#10587533	C₂×C₄	1	4	yes	—
90	#10587532	—	2	8	no	—
91	C₈×#595	—	2	8	no	—
92	C₁₇×#97	C₂×C₄	1	2	yes	complemented
93	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	complemented
94	#10587486	C₂×C₄	1	2	yes	complemented
95	#10587486	C₂×C₄	1	2	yes	complemented
96	C₈×Dic₁₇	C₂×C₄	1	2	yes	complemented
97	C₈×Dic₁₇	C₂×C₄	1	2	yes	complemented
98	#10587474	C₂×C₄	1	2	yes	complemented
99	C₄×#3622	C₂×C₄	1	2	yes	complemented
100	C₂³×D₁₇	#41	1	1	yes	characteristic
101	C₂²×#595	—	2	4	no	—
102	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₁₇	#41	1	1	yes	characteristic
104	C₂×C₄×D₁₇	—	2	2	no	—
105	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
115	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
116	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
117	C₂²⋊#595	—	2	4	no	—
118	C₂²⋊#595	—	2	4	no	—
119	#63247	—	2	4	no	—
120	#63247	—	2	4	no	—
121	C₂×#3624	—	2	4	no	—
122	C₄⋊#595	—	2	4	no	—
123	C₄⋊#595	C₂²×C₄	1	8	yes	—
124	C₄×#595	—	2	4	no	—
125	C₄×#595	—	2	4	no	—
126	#63243	—	2	4	no	—
127	#63243	C₂²×C₄	1	8	yes	—
128	#63242	—	2	4	no	—
129	#63242	—	2	4	no	—
130	M₁₆×C₁₇	C₄⋊C₄	1	2	yes	—
131	M₁₆×C₁₇	C₄⋊C₄	1	2	yes	—
132	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
133	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
135	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₁₇	—	2	1	no	—
140	C₂²⋊C₄×C₁₇	—	2	1	no	—
141	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
142	C₂²⋊Dic₁₇	—	2	1	no	—
143	#63227	—	2	2	no	—
144	C₄⋊Dic₁₇	—	2	1	no	—
145	#63225	—	2	2	no	—
146	C₄×Dic₁₇	—	2	2	no	—
147	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
148	#63223	C₄⋊C₄	1	2	yes	—
149	#63223	C₄⋊C₄	1	2	yes	—
150	C₂×#3622	C₄²	1	1	yes	characteristic
151	C₂×#3622	C₄²	1	1	yes	characteristic
152	C₂×#3622	C₄²	1	1	yes	characteristic
153	C₂×#3622	C₄²	1	1	yes	characteristic
154	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
155	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
156	C₂×#3622	C₂²×C₄	1	2	yes	—
157	#63218	C₄⋊C₄	1	4	yes	—
158	#63218	C₄⋊C₄	1	4	yes	—
159	C₈×D₁₇	C₄²	1	1	yes	characteristic
160	C₈×D₁₇	C₄²	1	1	yes	characteristic
161	C₈×D₁₇	C₄²	1	1	yes	characteristic
162	C₈×D₁₇	C₄²	1	1	yes	characteristic
163	C₈×D₁₇	C₄²	1	1	yes	characteristic
164	C₈×D₁₇	C₄²	1	1	yes	characteristic
165	C₈×D₁₇	C₄²	1	1	yes	characteristic
166	C₈×D₁₇	C₄²	1	1	yes	characteristic
167	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₈×D₁₇	C₂×D₄	1	4	yes	—
176	C₈×D₁₇	C₂×Q₈	1	4	yes	—
177	#20446	—	17	1	no	maximal, Sylow
178	C₂³×C₁₇	#117	1	1	yes	characteristic
179	C₂²×D₁₇	—	4	2	no	—
180	C₂²×D₁₇	#117	1	1	yes	characteristic
181	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
182	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
183	C₂²×D₁₇	C₄×Q₈	1	1	yes	characteristic
184	C₂²×D₁₇	C₄×Q₈	1	1	yes	characteristic
185	C₂²×D₁₇	C₂×#41	1	1	yes	characteristic
186	C₂×#595	—	2	8	no	—
187	C₂×#595	—	8	4	no	—
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
194	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×Dic₁₇	—	2	2	no	—
196	C₂×Dic₁₇	#117	1	1	yes	characteristic
197	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
199	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
200	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
201	C₂×Dic₁₇	C₂×#41	1	1	yes	characteristic
202	C₄×D₁₇	—	4	4	no	—
203	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
204	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
205	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
208	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
209	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
210	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
211	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
212	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
213	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
214	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
215	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
216	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
217	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
218	C₄×D₁₇	C₂²×Q₈	1	1	yes	characteristic
219	#3624	—	2	8	no	—
220	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
221	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
222	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
223	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
224	C₈×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
225	#3622	C₂×C₄²	1	1	yes	characteristic
226	#3622	C₂×C₄²	1	1	yes	characteristic
227	#3622	C₂×C₄²	1	1	yes	characteristic
228	#3622	C₂×C₄²	1	1	yes	characteristic
229	#3622	C₂×C₄⋊C₄	1	4	yes	—
230	C₂²×#108	—	17	1	no	—
231	C₂×#427	—	17	1	no	—
232	#2873	—	17	2	no	—
233	C₂×#405	—	17	1	no	—
234	#1773	—	17	4	no	—
235	#1772	—	17	4	no	—
236	#1733	—	17	2	no	—
237	C₂²×C₁₇	—	4	1	no	—
238	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
241	C₂×D₁₇	—	2	2	no	—
242	C₂×D₁₇	—	2	2	no	—
243	C₂×D₁₇	—	2	2	no	—
244	C₂×D₁₇	—	4	1	no	—
245	C₂×D₁₇	—	4	1	no	—
246	C₂×D₁₇	—	4	1	no	—
247	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
248	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
249	C₂×D₁₇	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
251	#595	—	4	8	no	—
252	C₄×C₁₇	—	4	2	no	—
253	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
254	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
255	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
256	C₄×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
257	Dic₁₇	—	4	2	no	—
258	Dic₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
259	Dic₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
260	Dic₁₇	C₂×C₄×D₄	1	1	yes	characteristic
261	Dic₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
262	C₂²×M₁₆	—	17	1	no	—
263	C₂²×M₁₆	—	17	2	no	—
264	C₂³×C₈	—	17	1	no	—
265	C₂×#117	—	17	1	no	—
266	C₂×#117	—	17	2	no	—
267	C₂×#108	—	17	2	no	—
268	C₂×#108	—	17	2	no	—
269	C₂×#108	—	17	2	no	—
270	C₂×#108	—	17	2	no	—
271	C₂×#108	—	17	2	no	—
272	C₂×#108	—	17	2	no	—
273	#427	—	17	2	no	—
274	#427	—	17	2	no	—
275	#427	—	17	2	no	—
276	#427	—	17	2	no	—
277	C₂×#107	—	17	2	no	—
278	C₂×#106	—	17	2	no	—
279	#405	—	17	1	no	—
280	#405	—	17	1	no	—
281	#405	—	17	1	no	—
282	#405	—	17	2	no	—
283	#405	—	17	2	no	—
284	#405	—	17	8	no	—
285	#405	—	34	4	no	—
286	#405	#595	1	1	yes	characteristic, complemented
287	C₄×M₁₆	—	34	4	no	—
288	C₂×#97	—	17	2	no	—
289	C₂×C₄×C₈	—	17	2	no	—
290	#339	—	17	8	no	—
291	C₂×C₁₇	—	2	1	no	—
292	C₂×C₁₇	—	2	1	no	—
293	C₂×C₁₇	—	2	1	no	—
294	C₂×C₁₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
295	D₁₇	—	2	1	no	—
296	D₁₇	—	2	1	no	—
297	D₁₇	—	2	1	no	—
298	D₁₇	#2957	1	2	yes	—
299	C₂³×C₄	—	17	1	no	—
300	C₂×M₁₆	—	17	1	no	—
301	C₂×M₁₆	—	17	2	no	—
302	C₂×M₁₆	—	17	2	no	—
303	C₂×M₁₆	—	17	2	no	—
304	C₂×M₁₆	—	17	2	no	—
305	C₂×M₁₆	—	17	2	no	—
306	C₂×M₁₆	—	17	4	no	—
307	C₂×M₁₆	—	17	4	no	—
308	C₂×M₁₆	—	17	4	no	—
309	C₂×M₁₆	—	34	2	no	—
310	C₂×M₁₆	—	34	2	no	—
311	C₂×M₁₆	—	34	2	no	—
312	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
313	C₂²×C₈	—	17	1	no	—
314	C₂²×C₈	—	17	1	no	—
315	C₂²×C₈	—	17	1	no	—
316	C₂²×C₈	—	17	1	no	—
317	C₂²×C₈	—	17	1	no	—
318	C₂²×C₈	—	17	1	no	—
319	C₂²×C₈	—	17	1	no	—
320	C₂²×C₈	—	17	1	no	—
321	C₂²×C₈	—	17	1	no	—
322	C₂²×C₈	—	17	1	no	—
323	C₂²×C₈	—	17	1	no	—
324	C₂²×C₈	—	17	1	no	—
325	C₂²×C₈	—	17	1	no	—
326	C₂²×C₈	—	17	2	no	—
327	C₂²×C₈	—	34	2	no	—
328	C₂²×C₈	C₂×#595	1	1	yes	characteristic
329	#117	—	17	1	no	—
330	#117	—	17	2	no	—
331	#117	—	17	4	no	—
332	#117	—	17	4	no	—
333	#117	—	34	1	no	—
334	#117	—	34	1	no	—
335	#117	—	34	2	no	—
336	#117	—	34	2	no	—
337	#117	C₂×#595	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	17	4	no	—
339	C₂×C₄⋊C₄	—	34	1	no	—
340	C₂×C₂²⋊C₄	—	34	1	no	—
341	C₂×C₂²⋊C₄	—	34	2	no	—
342	C₂×C₄²	—	17	2	no	—
343	C₂×C₄²	—	34	2	no	—
344	#108	—	17	4	no	—
345	#108	—	17	4	no	—
346	#108	—	17	4	no	—
347	#108	—	17	4	no	—
348	#107	—	17	4	no	—
349	#107	—	17	4	no	—
350	#106	—	17	4	no	—
351	#106	—	17	4	no	—
352	#97	—	17	2	no	—
353	#97	—	17	2	no	—
354	#97	—	17	2	no	—
355	#97	—	34	8	no	—
356	#97	C₂×#595	1	2	yes	complemented
357	C₄×C₈	—	17	2	no	—
358	C₄×C₈	—	17	2	no	—
359	C₄×C₈	—	17	2	no	—
360	C₄×C₈	—	34	8	no	—
361	C₄×C₈	C₂×#595	1	2	yes	complemented
362	C₁₇	#20446	1	1	yes	characteristic, complemented, Sylow
363	C₂⁴	—	17	1	no	—
364	C₂²×C₄	—	17	1	no	—
365	C₂²×C₄	—	17	1	no	—
366	C₂²×C₄	—	17	1	no	—
367	C₂²×C₄	—	17	1	no	—
368	C₂²×C₄	—	17	1	no	—
369	C₂²×C₄	—	17	1	no	—
370	C₂²×C₄	—	17	1	no	—
371	C₂²×C₄	—	17	1	no	—
372	C₂²×C₄	—	17	1	no	—
373	C₂²×C₄	—	17	1	no	—
374	C₂²×C₄	—	17	1	no	—
375	C₂²×C₄	—	17	1	no	—
376	C₂²×C₄	—	17	1	no	—
377	C₂²×C₄	—	34	2	no	—
378	C₂²×C₄	—	34	4	no	—
379	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
380	M₁₆	—	17	2	no	—
381	M₁₆	—	17	2	no	—
382	M₁₆	—	17	4	no	—
383	M₁₆	—	17	4	no	—
384	M₁₆	—	17	8	no	—
385	M₁₆	—	34	4	no	—
386	M₁₆	—	34	4	no	—
387	M₁₆	—	34	4	no	—
388	M₁₆	C₄⋊#595	1	2	yes	—
389	M₁₆	C₄⋊#595	1	2	yes	—
390	C₂×C₈	—	17	1	no	—
391	C₂×C₈	—	17	1	no	—
392	C₂×C₈	—	17	1	no	—
393	C₂×C₈	—	17	1	no	—
394	C₂×C₈	—	17	1	no	—
395	C₂×C₈	—	17	2	no	—
396	C₂×C₈	—	17	1	no	—
397	C₂×C₈	—	17	1	no	—
398	C₂×C₈	—	17	1	no	—
399	C₂×C₈	—	17	1	no	—
400	C₂×C₈	—	17	1	no	—
401	C₂×C₈	—	17	1	no	—
402	C₂×C₈	—	17	1	no	—
403	C₂×C₈	—	17	1	no	—
404	C₂×C₈	—	17	1	no	—
405	C₂×C₈	—	17	1	no	—
406	C₂×C₈	—	17	1	no	—
407	C₂×C₈	—	17	1	no	—
408	C₂×C₈	—	17	1	no	—
409	C₂×C₈	—	17	1	no	—
410	C₂×C₈	—	17	1	no	—
411	C₂×C₈	—	17	1	no	—
412	C₂×C₈	—	17	1	no	—
413	C₂×C₈	—	17	4	no	—
414	C₂×C₈	—	17	4	no	—
415	C₂×C₈	—	34	4	no	—
416	C₂×C₈	—	34	4	no	—
417	C₂×C₈	—	34	4	no	—
418	C₂×C₈	C₄×#595	1	1	yes	characteristic
419	C₂×C₈	C₄×#595	1	1	yes	characteristic
420	C₂×C₈	C₄×#595	1	1	yes	characteristic
421	C₂×C₈	C₄×#595	1	1	yes	characteristic
422	C₂×C₈	C₂²×#595	1	1	yes	characteristic
423	C₂×C₈	C₂²×#595	1	1	yes	characteristic
424	C₂×C₈	C₂²×#595	1	2	yes	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	17	8	no	—
427	C₄⋊C₄	—	34	2	no	—
428	C₄⋊C₄	—	34	4	no	—
429	C₄⋊C₄	—	34	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	34	2	no	—
432	C₂²⋊C₄	—	34	4	no	—
433	C₂²⋊C₄	—	34	4	no	—
434	C₂²⋊C₄	—	34	1	no	—
435	C₄²	—	17	2	no	—
436	C₄²	—	34	2	no	—
437	C₄²	—	34	4	no	—
438	C₄²	—	34	4	no	—
439	C₄²	C₂²×#595	1	2	yes	—
440	C₂³	—	17	1	no	—
441	C₂³	—	17	1	no	—
442	C₂³	—	17	1	no	—
443	C₂³	—	17	1	no	—
444	C₂³	—	17	1	no	—
445	C₂³	—	17	1	no	—
446	C₂³	—	68	2	no	—
447	C₂³	#10587677	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	17	1	no	—
450	C₂×C₄	—	17	1	no	—
451	C₂×C₄	—	17	1	no	—
452	C₂×C₄	—	17	1	no	—
453	C₂×C₄	—	17	1	no	—
454	C₂×C₄	—	17	1	no	—
455	C₂×C₄	—	17	1	no	—
456	C₂×C₄	—	17	1	no	—
457	C₂×C₄	—	17	1	no	—
458	C₂×C₄	—	17	1	no	—
459	C₂×C₄	—	17	1	no	—
460	C₂×C₄	—	17	1	no	—
461	C₂×C₄	—	17	1	no	—
462	C₂×C₄	—	17	1	no	—
463	C₂×C₄	—	17	1	no	—
464	C₂×C₄	—	17	1	no	—
465	C₂×C₄	—	17	1	no	—
466	C₂×C₄	—	17	1	no	—
467	C₂×C₄	—	17	1	no	—
468	C₂×C₄	—	17	1	no	—
469	C₂×C₄	—	17	1	no	—
470	C₂×C₄	—	17	1	no	—
471	C₂×C₄	—	34	8	no	—
472	C₂×C₄	—	34	2	no	—
473	C₂×C₄	—	68	4	no	—
474	C₂×C₄	—	136	4	no	—
475	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
479	C₂×C₄	#10587677	1	1	yes	characteristic
480	C₂×C₄	C₂³×#595	1	1	yes	characteristic
481	C₈	—	17	1	no	—
482	C₈	—	17	1	no	—
483	C₈	—	17	1	no	—
484	C₈	—	17	1	no	—
485	C₈	—	17	4	no	—
486	C₈	—	34	8	no	—
487	C₈	C₂×C₄×#595	1	1	yes	characteristic
488	C₈	C₂×C₄×#595	1	1	yes	characteristic
489	C₈	C₂×C₄×#595	1	1	yes	characteristic
490	C₈	C₂×C₄×#595	1	1	yes	characteristic
491	C₈	C₂×C₄⋊#595	1	4	yes	—
492	C₂²	—	4	1	no	—
493	C₂²	—	17	1	no	—
494	C₂²	—	17	1	no	—
495	C₂²	—	17	1	no	—
496	C₂²	—	17	1	no	—
497	C₂²	—	34	2	no	—
498	C₂²	—	34	2	no	—
499	C₂²	—	34	2	no	—
500	C₂²	—	68	1	no	—
501	C₂²	—	68	1	no	—
502	C₂²	—	68	1	no	—
503	C₂²	C₄×C₄⋊#595	1	1	yes	characteristic
504	C₂²	C₄×C₄⋊#595	1	1	yes	characteristic
505	C₂²	C₂×#10587677	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	17	1	no	—
508	C₄	—	17	1	no	—
509	C₄	—	17	1	no	—
510	C₄	—	17	1	no	—
511	C₄	—	68	2	no	—
512	C₄	—	68	8	no	—
513	C₄	C₄×C₄⋊#595	1	1	yes	characteristic
514	C₄	C₄×C₄⋊#595	1	1	yes	characteristic
515	C₄	C₂²×C₄×#595	1	1	yes	characteristic
516	C₄	C₂²×C₄⋊#595	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	17	2	no	—
521	C₂	—	34	1	no	—
522	C₂	—	34	1	no	—
523	C₂	—	34	1	no	—
524	C₂	C₂×C₄×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#595
Fitting	C₁₇×#405	C₄
socle	C₂×C₁₇	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#20446
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #14544590	C₂	semidirect
5. #14544586	C₂	semidirect
10. C₂×#10587536	C₄	semidirect
11. D₁₇⋊#108	C₄	semidirect
12. D₁₇⋊#108	C₄	semidirect
15. C₂×#10587535	C₄	semidirect
16. #11763819	C₄	semidirect
17. #11763819	C₄	semidirect
20. C₂×#10587534	C₄	semidirect
21. C₂×#10587533	C₄	semidirect
29. #11762767	C₄	semidirect
30. #11762766	C₄	semidirect
31. #11762765	C₄	semidirect
32. #11762764	C₄	semidirect
33. #11762763	C₄	semidirect
36. C₁₇×#405	C₄	semidirect
82. #10587536	C₂×C₄	semidirect
83. #10587536	C₂×C₄	semidirect
84. #10587535	C₂×C₄	semidirect
85. #10587535	C₂×C₄	semidirect
92. C₁₇×#97	C₂×C₄	semidirect
93. C₄×C₈×C₁₇	C₂×C₄	semidirect
94. #10587486	C₂×C₄	semidirect
95. #10587486	C₂×C₄	semidirect
96. C₈×Dic₁₇	C₂×C₄	semidirect
97. C₈×Dic₁₇	C₂×C₄	semidirect
98. #10587474	C₂×C₄	semidirect
99. C₄×#3622	C₂×C₄	semidirect
286. #405	#595	semidirect
356. #97	C₂×#595	semidirect
361. C₄×C₈	C₂×#595	semidirect
362. C₁₇	#20446	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
#14545347	2
#14544590	2
#14544586	2
#14544465	2
D₁₇×#405	2
#20446	17