Subgroups — #17968963

Order 4352.

886 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊#433	C₂	1	1	yes	maximal, characteristic
2	#14545244	C₂	1	1	yes	maximal, characteristic
3	#14544585	C₂	1	1	yes	maximal, characteristic, complemented
4	#14544585	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544582	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544582	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544581	C₂	1	1	yes	maximal, characteristic, complemented
8	#14544578	C₂	1	1	yes	maximal, characteristic, complemented
9	#14544577	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊#595	C₂	1	1	yes	maximal, characteristic, complemented
11	#14544515	C₂	1	1	yes	maximal, characteristic
12	#14544515	C₂	1	1	yes	maximal, characteristic
13	#14544512	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊C₈×#595	C₂	1	1	yes	maximal, characteristic
15	D₁₇×#433	C₂	1	1	yes	maximal, characteristic
16	C₂×#10587677	C₂²	1	1	yes	characteristic
17	C₂²×C₄×#595	C₂²	1	1	yes	characteristic
18	#11763834	C₄	1	2	yes	complemented
19	#11763834	C₄	1	2	yes	complemented
20	#11763833	C₄	1	2	yes	complemented
21	#11763833	C₄	1	2	yes	complemented
22	#11763810	C₂²	1	1	yes	characteristic
23	#11763810	C₂²	1	1	yes	characteristic
24	#11763777	C₂²	1	1	yes	characteristic
25	#11763777	C₂²	1	1	yes	characteristic
26	#11763768	C₂²	1	1	yes	characteristic
27	C₂×#10587532	C₂²	1	1	yes	characteristic
28	C₂×#10587532	C₂²	1	1	yes	characteristic
29	C₂×#10587532	C₂²	1	1	yes	characteristic
30	C₂×#10587532	C₂²	1	1	yes	characteristic
31	C₄×#63242	C₂²	1	1	yes	characteristic
32	C₂×C₈×#595	C₂²	1	1	yes	characteristic
33	C₂×C₈×#595	C₂²	1	1	yes	characteristic
34	C₂×C₈×#595	C₂²	1	1	yes	characteristic
35	C₂×C₈×#595	C₂²	1	1	yes	characteristic
36	#11763760	C₄	1	2	yes	—
37	#11763760	C₄	1	2	yes	—
38	#11763756	C₄	1	2	yes	—
39	#11763756	C₄	1	2	yes	—
40	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
44	#11763674	C₂²	1	1	yes	characteristic
45	#11763674	C₂²	1	1	yes	characteristic
46	#11763674	C₂²	1	1	yes	characteristic
47	#11763674	C₂²	1	1	yes	characteristic
48	#11763674	C₂²	1	1	yes	characteristic
49	#11763674	C₂²	1	1	yes	characteristic
50	#11763674	C₂²	1	1	yes	characteristic
51	#11763674	C₂²	1	1	yes	characteristic
52	#117×D₁₇	C₂²	1	1	yes	characteristic
53	#11762871	C₄	1	1	yes	characteristic, complemented
54	#11762870	C₄	1	1	yes	characteristic, complemented
55	#11762869	C₄	1	1	yes	characteristic, complemented
56	#11762869	C₄	1	1	yes	characteristic, complemented
57	#11762868	C₄	1	1	yes	characteristic, complemented
58	#11762867	C₄	1	1	yes	characteristic, complemented
59	#11762867	C₄	1	1	yes	characteristic, complemented
60	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
61	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
62	C₂²⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
63	C₂²⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
64	#97×D₁₇	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
66	C₁₇×#433	C₄	1	1	yes	characteristic, complemented
67	C₂³×#595	C₂×C₄	1	2	yes	—
68	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊#595	C₂×C₄	1	2	yes	—
70	#10587677	—	4	1	no	—
71	#10587677	—	4	1	no	—
72	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
77	C₂×C₄×#595	—	4	1	no	—
78	C₂×C₄×#595	—	4	1	no	—
79	C₂×C₄×#595	C₂×C₄	1	2	yes	—
80	C₂×C₄×#595	C₂³	1	1	yes	characteristic
81	C₂×C₄×#595	C₂³	1	1	yes	characteristic
82	C₂×C₄×#595	C₂³	1	1	yes	characteristic
83	C₂×C₄×#595	C₂³	1	1	yes	characteristic
84	C₂×#63242	C₂³	1	1	yes	characteristic
85	C₂×#63242	C₂³	1	1	yes	characteristic
86	C₂×#63242	C₂³	1	1	yes	characteristic
87	C₂×#63242	C₂³	1	1	yes	characteristic
88	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
89	#10587612	C₂×C₄	1	1	yes	characteristic
90	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
94	#10587578	C₂×C₄	1	1	yes	characteristic
95	#10587578	C₂×C₄	1	1	yes	characteristic
96	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
100	#10587563	C₂×C₄	1	1	yes	characteristic
101	#10587563	C₂×C₄	1	1	yes	characteristic
102	#10587558	C₂×C₄	1	1	yes	characteristic
103	#10587558	C₂×C₄	1	1	yes	characteristic
104	C₄²×D₁₇	C₂³	1	1	yes	characteristic
105	C₄²×D₁₇	C₂³	1	1	yes	characteristic
106	C₂²⋊#3624	C₂×C₄	1	2	yes	—
107	C₂²⋊#3624	C₂×C₄	1	2	yes	—
108	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
109	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
110	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
111	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
112	#10587544	C₂×C₄	1	2	yes	complemented
113	#10587544	C₂×C₄	1	2	yes	complemented
114	#10587543	C₂×C₄	1	2	yes	—
115	#10587543	C₂×C₄	1	2	yes	—
116	#10587542	C₂×C₄	1	2	yes	complemented
117	#10587542	C₂×C₄	1	2	yes	complemented
118	C₄⋊#3624	C₂×C₄	1	2	yes	complemented
119	C₄⋊#3624	C₂×C₄	1	2	yes	complemented
120	C₄×#3624	C₂×C₄	1	2	yes	complemented
121	C₄×#3624	C₂×C₄	1	2	yes	complemented
122	#10587532	—	4	1	no	—
123	#10587532	—	4	1	no	—
124	#10587532	—	4	1	no	—
125	#10587532	—	4	1	no	—
126	C₈×#595	—	4	1	no	—
127	C₈×#595	—	4	1	no	—
128	C₈×#595	—	4	1	no	—
129	C₈×#595	—	4	1	no	—
130	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
131	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
132	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₁₇×#97	C₂×C₄	1	1	yes	characteristic, complemented
135	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
136	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
137	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
138	#10587491	C₂×C₄	1	1	yes	characteristic
139	#10587491	C₂×C₄	1	1	yes	characteristic
140	#10587491	C₂×C₄	1	1	yes	characteristic
141	#10587491	C₂×C₄	1	1	yes	characteristic
142	#10587486	C₂×C₄	1	1	yes	characteristic, complemented
143	#10587486	C₂×C₄	1	1	yes	characteristic, complemented
144	#10587485	C₂×C₄	1	1	yes	characteristic, complemented
145	#10587485	C₂×C₄	1	1	yes	characteristic, complemented
146	#10587485	C₂×C₄	1	1	yes	characteristic, complemented
147	#10587485	C₂×C₄	1	1	yes	characteristic, complemented
148	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
149	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
150	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic, complemented
151	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic, complemented
152	#10587474	C₂×C₄	1	1	yes	characteristic, complemented
153	C₄×#3622	C₂×C₄	1	1	yes	characteristic, complemented
154	C₂³×D₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×#595	—	2	4	no	—
156	C₂²×#595	—	4	2	no	—
157	C₂²×#595	—	4	2	no	—
158	C₂²×#595	C₂²×C₄	1	2	yes	—
159	C₂²×#595	C₂²×C₄	1	2	yes	—
160	C₂²×#595	C₂²×C₄	1	2	yes	—
161	C₂²×#595	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₁₇	—	2	1	no	—
165	C₂×C₄×D₁₇	—	2	1	no	—
166	C₂×C₄×D₁₇	—	2	1	no	—
167	C₂×C₄×D₁₇	—	2	1	no	—
168	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
176	C₂²⋊#595	—	4	2	no	—
177	C₂×#3624	C₂²×C₄	1	2	yes	—
178	C₂×#3624	C₂²×C₄	1	2	yes	—
179	C₂×#3624	C₂²×C₄	1	2	yes	—
180	C₂×#3624	C₂²×C₄	1	2	yes	—
181	C₄⋊#595	—	2	4	no	—
182	C₄⋊#595	—	2	4	no	—
183	C₄⋊#595	—	4	2	no	—
184	C₄⋊#595	—	4	2	no	—
185	C₄⋊#595	—	4	2	no	—
186	C₄×#595	—	2	1	no	—
187	C₄×#595	—	2	1	no	—
188	C₄×#595	—	2	1	no	—
189	C₄×#595	—	2	1	no	—
190	C₄×#595	—	2	1	no	—
191	C₄×#595	—	2	1	no	—
192	C₄×#595	—	2	1	no	—
193	C₄×#595	—	2	1	no	—
194	C₄×#595	—	4	2	no	—
195	#63242	—	2	1	no	—
196	#63242	—	2	1	no	—
197	#63242	—	2	1	no	—
198	#63242	—	2	1	no	—
199	#63242	—	2	1	no	—
200	#63242	—	2	1	no	—
201	#63242	—	2	1	no	—
202	#63242	—	2	1	no	—
203	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
208	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
209	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
211	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
213	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
214	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
215	#63227	C₄²	1	1	yes	characteristic
216	#63227	C₄²	1	1	yes	characteristic
217	#63227	C₄²	1	1	yes	characteristic
218	#63227	C₄²	1	1	yes	characteristic
219	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
220	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
221	#63225	C₄²	1	1	yes	characteristic
222	#63225	C₄²	1	1	yes	characteristic
223	#63225	C₄²	1	1	yes	characteristic
224	#63225	C₄²	1	1	yes	characteristic
225	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
226	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
228	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
229	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
230	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
231	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
232	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
233	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
234	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
235	C₈×D₁₇	—	2	1	no	—
236	C₈×D₁₇	—	2	1	no	—
237	C₈×D₁₇	—	2	1	no	—
238	C₈×D₁₇	—	2	1	no	—
239	C₈×D₁₇	—	2	1	no	—
240	C₈×D₁₇	—	2	1	no	—
241	C₈×D₁₇	—	2	1	no	—
242	C₈×D₁₇	—	2	1	no	—
243	#20541	—	17	1	no	maximal, Sylow
244	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
245	C₂²×D₁₇	—	2	1	no	—
246	C₂²×D₁₇	—	2	1	no	—
247	C₂²×D₁₇	—	2	2	no	—
248	C₂²×D₁₇	—	2	2	no	—
249	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
250	C₂²×D₁₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×#595	—	2	2	no	—
252	C₂×#595	—	2	2	no	—
253	C₂×#595	—	2	2	no	—
254	C₂×#595	—	2	2	no	—
255	C₂×#595	—	2	2	no	—
256	C₂×#595	—	2	2	no	—
257	C₂×#595	—	2	2	no	—
258	C₂×#595	—	2	2	no	—
259	C₂×#595	—	2	2	no	—
260	C₂×#595	—	2	2	no	—
261	C₂×#595	—	2	2	no	—
262	C₂×#595	—	4	8	no	—
263	C₂×#595	#131	1	4	yes	—
264	C₂×C₄×C₁₇	—	2	1	no	—
265	C₂×C₄×C₁₇	—	2	1	no	—
266	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
267	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
268	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
269	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
270	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
271	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
272	C₂×Dic₁₇	—	2	1	no	—
273	C₂×Dic₁₇	—	2	1	no	—
274	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
275	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
276	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
277	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
278	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
279	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
280	C₄×D₁₇	—	2	1	no	—
281	C₄×D₁₇	—	2	1	no	—
282	C₄×D₁₇	—	2	2	no	—
283	C₄×D₁₇	—	2	2	no	—
284	C₄×D₁₇	—	2	2	no	—
285	C₄×D₁₇	—	2	2	no	—
286	C₄×D₁₇	—	2	1	no	—
287	C₄×D₁₇	—	2	1	no	—
288	C₄×D₁₇	—	2	1	no	—
289	C₄×D₁₇	—	2	1	no	—
290	C₄×D₁₇	H(5,𝔽₂)	1	1	yes	characteristic
291	C₄×D₁₇	H(5,𝔽₂)	1	1	yes	characteristic
292	C₄×D₁₇	2₋¹⁺⁴	1	1	yes	characteristic
293	C₄×D₁₇	2₋¹⁺⁴	1	1	yes	characteristic
294	#3624	—	2	2	no	—
295	#3624	—	2	2	no	—
296	#3624	—	2	2	no	—
297	#3624	—	2	2	no	—
298	C₈×C₁₇	—	2	1	no	—
299	C₈×C₁₇	—	2	1	no	—
300	C₈×C₁₇	—	2	1	no	—
301	C₈×C₁₇	—	2	1	no	—
302	#3622	—	2	1	no	—
303	#3622	—	2	1	no	—
304	#3622	—	2	1	no	—
305	#3622	—	2	1	no	—
306	C₂×#433	—	17	1	no	—
307	C₂×#433	—	17	1	no	—
308	#2296	—	17	1	no	—
309	#1771	—	17	1	no	—
310	#1771	—	17	1	no	—
311	#1771	—	17	1	no	—
312	#1771	—	17	1	no	—
313	#1770	—	17	1	no	—
314	#1770	—	17	1	no	—
315	C₈×C₄⋊C₄	—	17	1	no	—
316	C₈×C₄⋊C₄	—	17	1	no	—
317	#1750	—	17	1	no	—
318	#1750	—	17	1	no	—
319	#1749	—	17	1	no	—
320	C₄×C₂²⋊C₈	—	17	1	no	—
321	C₂²×C₁₇	—	2	1	no	—
322	C₂²×C₁₇	—	2	1	no	—
323	C₂²×C₁₇	—	2	1	no	—
324	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
325	C₂×D₁₇	—	2	1	no	—
326	C₂×D₁₇	—	2	1	no	—
327	C₂×D₁₇	—	2	1	no	—
328	C₂×D₁₇	—	4	2	no	—
329	C₂×D₁₇	—	4	2	no	—
330	C₂×D₁₇	#518	1	1	yes	characteristic
331	C₂×D₁₇	#519	1	1	yes	characteristic
332	C₂×D₁₇	C₂×#131	1	2	yes	—
333	C₂×D₁₇	#568	1	2	yes	—
334	#595	—	2	4	no	—
335	#595	—	4	2	no	—
336	#595	—	4	2	no	—
337	#595	—	4	2	no	—
338	C₄×C₁₇	—	2	1	no	—
339	C₄×C₁₇	—	2	1	no	—
340	C₄×C₁₇	—	2	1	no	—
341	C₄×C₁₇	—	2	1	no	—
342	C₄×C₁₇	—	2	1	no	—
343	C₄×C₁₇	#520	1	1	yes	characteristic
344	C₄×C₁₇	#520	1	1	yes	characteristic
345	Dic₁₇	—	2	1	no	—
346	Dic₁₇	—	2	1	no	—
347	Dic₁₇	—	2	1	no	—
348	Dic₁₇	—	2	1	no	—
349	Dic₁₇	—	2	1	no	—
350	Dic₁₇	#520	1	1	yes	characteristic
351	Dic₁₇	#520	1	1	yes	characteristic
352	C₂×#117	—	17	1	no	—
353	C₂×#117	—	17	1	no	—
354	C₂²×C₄²	—	17	1	no	—
355	#433	—	17	2	no	—
356	#433	—	17	2	no	—
357	#433	—	17	2	no	—
358	#433	—	17	2	no	—
359	#433	—	17	1	no	—
360	#433	—	17	1	no	—
361	#433	—	17	1	no	—
362	#433	—	17	1	no	—
363	#433	—	17	1	no	—
364	#433	—	17	1	no	—
365	#433	—	17	1	no	—
366	#433	#595	1	1	yes	characteristic, complemented
367	C₂×C₄⋊C₈	—	17	1	no	—
368	C₂×C₄⋊C₈	—	17	1	no	—
369	C₂×C₄⋊C₈	—	17	1	no	—
370	C₂×C₄⋊C₈	—	17	1	no	—
371	C₂×C₂²⋊C₈	—	17	1	no	—
372	C₂×C₂²⋊C₈	—	17	1	no	—
373	C₂×C₂²⋊C₈	—	17	1	no	—
374	C₂×C₂²⋊C₈	—	17	1	no	—
375	C₂×#97	—	17	1	no	—
376	C₂×#97	—	17	1	no	—
377	C₂×#97	—	17	1	no	—
378	C₂×#97	—	17	1	no	—
379	C₂×#97	—	17	1	no	—
380	C₂×#97	—	17	1	no	—
381	C₂×C₄×C₈	—	17	1	no	—
382	C₂×C₄×C₈	—	17	1	no	—
383	C₂×C₄×C₈	—	17	1	no	—
384	C₂×C₄×C₈	—	17	1	no	—
385	C₂×C₄×C₈	—	17	1	no	—
386	C₂×C₄×C₈	—	17	1	no	—
387	#389	—	17	2	no	—
388	#389	—	17	2	no	—
389	#385	—	17	2	no	—
390	#385	—	17	2	no	—
391	C₄×C₄⋊C₄	—	17	1	no	—
392	C₄×C₄⋊C₄	—	17	1	no	—
393	C₄×C₄⋊C₄	—	17	1	no	—
394	C₄×C₄⋊C₄	—	17	1	no	—
395	#336	—	17	1	no	—
396	#336	—	17	1	no	—
397	#336	—	17	1	no	—
398	#336	—	17	1	no	—
399	#336	—	17	1	no	—
400	#336	—	17	1	no	—
401	#336	—	17	1	no	—
402	#336	—	17	1	no	—
403	C₂×C₁₇	—	4	1	no	—
404	C₂×C₁₇	#2274	1	1	yes	characteristic
405	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
406	C₂×C₁₇	#2875	1	1	yes	characteristic
407	D₁₇	—	4	1	no	—
408	D₁₇	#2976	1	2	yes	—
409	D₁₇	#2985	1	2	yes	—
410	C₂³×C₄	—	17	1	no	—
411	C₂³×C₄	—	17	2	no	—
412	C₂²×C₈	—	17	1	no	—
413	C₂²×C₈	—	17	1	no	—
414	C₂²×C₈	—	17	1	no	—
415	C₂²×C₈	—	17	1	no	—
416	C₂²×C₈	—	17	1	no	—
417	C₂²×C₈	—	17	1	no	—
418	C₂²×C₈	—	17	1	no	—
419	C₂²×C₈	—	17	1	no	—
420	#117	—	17	1	no	—
421	#117	—	17	1	no	—
422	#117	—	17	1	no	—
423	#117	—	17	1	no	—
424	#117	—	17	1	no	—
425	#117	—	17	1	no	—
426	#117	—	17	1	no	—
427	#117	—	68	1	no	—
428	#117	—	68	1	no	—
429	#117	C₂×#595	1	1	yes	characteristic
430	C₂×C₄⋊C₄	—	17	1	no	—
431	C₂×C₄⋊C₄	—	17	1	no	—
432	C₂×C₄⋊C₄	—	17	2	no	—
433	C₂×C₄⋊C₄	—	17	2	no	—
434	C₂×C₄⋊C₄	—	17	2	no	—
435	C₂×C₄⋊C₄	—	17	2	no	—
436	C₂×C₄⋊C₄	—	17	2	no	—
437	C₂×C₂²⋊C₄	—	17	1	no	—
438	C₂×C₂²⋊C₄	—	17	1	no	—
439	C₂×C₂²⋊C₄	—	17	2	no	—
440	C₂×C₄²	—	17	1	no	—
441	C₂×C₄²	—	17	1	no	—
442	C₂×C₄²	—	17	1	no	—
443	C₂×C₄²	—	17	1	no	—
444	C₂×C₄²	—	17	1	no	—
445	C₂×C₄²	—	17	1	no	—
446	C₂×C₄²	—	17	2	no	—
447	C₂×C₄²	—	68	1	no	—
448	C₂×C₄²	—	68	1	no	—
449	C₄⋊C₈	—	17	2	no	—
450	C₄⋊C₈	—	17	2	no	—
451	C₄⋊C₈	—	17	2	no	—
452	C₄⋊C₈	—	17	2	no	—
453	C₄⋊C₈	—	17	1	no	—
454	C₄⋊C₈	—	17	1	no	—
455	C₄⋊C₈	—	17	1	no	—
456	C₄⋊C₈	—	17	1	no	—
457	C₄⋊C₈	—	17	1	no	—
458	C₄⋊C₈	—	17	1	no	—
459	C₄⋊C₈	C₂×#595	1	1	yes	characteristic, complemented
460	C₄⋊C₈	C₂×#595	1	1	yes	characteristic, complemented
461	C₂²⋊C₈	—	17	2	no	—
462	C₂²⋊C₈	—	17	2	no	—
463	C₂²⋊C₈	—	17	2	no	—
464	C₂²⋊C₈	—	17	2	no	—
465	C₂²⋊C₈	—	17	1	no	—
466	C₂²⋊C₈	—	17	1	no	—
467	C₂²⋊C₈	—	17	1	no	—
468	C₂²⋊C₈	—	17	1	no	—
469	C₂²⋊C₈	—	17	1	no	—
470	C₂²⋊C₈	—	17	1	no	—
471	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
472	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
473	#97	—	17	2	no	—
474	#97	—	17	2	no	—
475	#97	—	17	1	no	—
476	#97	—	17	1	no	—
477	#97	—	17	1	no	—
478	#97	—	68	1	no	—
479	#97	—	68	1	no	—
480	#97	—	68	1	no	—
481	#97	—	68	1	no	—
482	#97	C₂×#595	1	1	yes	characteristic, complemented
483	C₄×C₈	—	17	2	no	—
484	C₄×C₈	—	17	2	no	—
485	C₄×C₈	—	17	1	no	—
486	C₄×C₈	—	17	1	no	—
487	C₄×C₈	—	17	1	no	—
488	C₄×C₈	—	68	1	no	—
489	C₄×C₈	—	68	1	no	—
490	C₄×C₈	—	68	1	no	—
491	C₄×C₈	—	68	1	no	—
492	C₄×C₈	C₂×#595	1	1	yes	characteristic, complemented
493	#95	—	17	2	no	—
494	#95	—	17	2	no	—
495	#95	—	17	2	no	—
496	#95	—	17	2	no	—
497	C₁₇	#20541	1	1	yes	characteristic, complemented, Sylow
498	C₂⁴	—	17	1	no	—
499	C₂²×C₄	—	17	1	no	—
500	C₂²×C₄	—	17	2	no	—
501	C₂²×C₄	—	17	1	no	—
502	C₂²×C₄	—	17	1	no	—
503	C₂²×C₄	—	17	1	no	—
504	C₂²×C₄	—	17	1	no	—
505	C₂²×C₄	—	17	1	no	—
506	C₂²×C₄	—	17	1	no	—
507	C₂²×C₄	—	17	1	no	—
508	C₂²×C₄	—	17	1	no	—
509	C₂²×C₄	—	17	2	no	—
510	C₂²×C₄	—	17	2	no	—
511	C₂²×C₄	—	17	2	no	—
512	C₂²×C₄	—	34	1	no	—
513	C₂²×C₄	—	34	1	no	—
514	C₂²×C₄	—	34	1	no	—
515	C₂²×C₄	—	34	1	no	—
516	C₂²×C₄	—	34	4	no	—
517	C₂²×C₄	—	68	2	no	—
518	C₂²×C₄	—	68	2	no	—
519	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
520	C₂×C₈	—	17	2	no	—
521	C₂×C₈	—	17	2	no	—
522	C₂×C₈	—	17	2	no	—
523	C₂×C₈	—	17	2	no	—
524	C₂×C₈	—	17	1	no	—
525	C₂×C₈	—	17	1	no	—
526	C₂×C₈	—	17	1	no	—
527	C₂×C₈	—	17	1	no	—
528	C₂×C₈	—	34	1	no	—
529	C₂×C₈	—	34	1	no	—
530	C₂×C₈	—	34	1	no	—
531	C₂×C₈	—	34	1	no	—
532	C₂×C₈	—	34	1	no	—
533	C₂×C₈	—	34	1	no	—
534	C₂×C₈	—	34	1	no	—
535	C₂×C₈	—	34	1	no	—
536	C₂×C₈	—	34	1	no	—
537	C₂×C₈	—	34	1	no	—
538	C₂×C₈	—	34	1	no	—
539	C₂×C₈	—	34	1	no	—
540	C₂×C₈	—	34	1	no	—
541	C₂×C₈	—	34	1	no	—
542	C₂×C₈	—	34	1	no	—
543	C₂×C₈	—	34	1	no	—
544	C₂×C₈	C₂²×#595	1	1	yes	characteristic
545	C₂×C₈	C₂²×#595	1	1	yes	characteristic
546	C₂×C₈	C₂²×#595	1	1	yes	characteristic
547	C₂×C₈	C₂²×#595	1	1	yes	characteristic
548	C₄⋊C₄	—	17	1	no	—
549	C₄⋊C₄	—	17	1	no	—
550	C₄⋊C₄	—	17	1	no	—
551	C₄⋊C₄	—	17	1	no	—
552	C₄⋊C₄	—	17	1	no	—
553	C₄⋊C₄	—	17	1	no	—
554	C₄⋊C₄	—	34	4	no	—
555	C₄⋊C₄	—	34	4	no	—
556	C₄⋊C₄	—	68	2	no	—
557	C₄⋊C₄	—	68	2	no	—
558	C₄⋊C₄	—	68	2	no	—
559	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
560	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
561	C₂²⋊C₄	—	17	1	no	—
562	C₂²⋊C₄	—	17	1	no	—
563	C₂²⋊C₄	—	17	1	no	—
564	C₂²⋊C₄	—	17	1	no	—
565	C₂²⋊C₄	—	17	1	no	—
566	C₂²⋊C₄	—	17	1	no	—
567	C₂²⋊C₄	—	68	2	no	—
568	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
569	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
570	C₄²	—	17	1	no	—
571	C₄²	—	17	1	no	—
572	C₄²	—	17	1	no	—
573	C₄²	—	17	1	no	—
574	C₄²	—	17	1	no	—
575	C₄²	—	17	1	no	—
576	C₄²	—	34	1	no	—
577	C₄²	—	34	1	no	—
578	C₄²	—	34	1	no	—
579	C₄²	—	34	1	no	—
580	C₄²	—	34	1	no	—
581	C₄²	—	34	1	no	—
582	C₄²	—	34	1	no	—
583	C₄²	—	34	1	no	—
584	C₄²	—	68	2	no	—
585	C₄²	C₂²×#595	1	1	yes	characteristic
586	C₄²	C₂²×#595	1	1	yes	characteristic
587	C₂³	—	17	1	no	—
588	C₂³	—	17	1	no	—
589	C₂³	—	34	1	no	—
590	C₂³	—	34	1	no	—
591	C₂³	—	34	2	no	—
592	C₂³	—	34	2	no	—
593	C₂³	C₂×C₄×#595	1	1	yes	characteristic
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	17	1	no	—
597	C₂×C₄	—	17	1	no	—
598	C₂×C₄	—	17	1	no	—
599	C₂×C₄	—	17	1	no	—
600	C₂×C₄	—	17	1	no	—
601	C₂×C₄	—	17	4	no	—
602	C₂×C₄	—	17	1	no	—
603	C₂×C₄	—	17	1	no	—
604	C₂×C₄	—	17	1	no	—
605	C₂×C₄	—	17	1	no	—
606	C₂×C₄	—	17	1	no	—
607	C₂×C₄	—	34	1	no	—
608	C₂×C₄	—	34	1	no	—
609	C₂×C₄	—	34	1	no	—
610	C₂×C₄	—	34	2	no	—
611	C₂×C₄	—	34	2	no	—
612	C₂×C₄	—	34	2	no	—
613	C₂×C₄	—	34	2	no	—
614	C₂×C₄	—	34	1	no	—
615	C₂×C₄	—	34	1	no	—
616	C₂×C₄	—	34	1	no	—
617	C₂×C₄	—	34	2	no	—
618	C₂×C₄	—	34	2	no	—
619	C₂×C₄	—	34	1	no	—
620	C₂×C₄	—	34	1	no	—
621	C₂×C₄	—	34	2	no	—
622	C₂×C₄	—	34	2	no	—
623	C₂×C₄	—	34	2	no	—
624	C₂×C₄	—	34	2	no	—
625	C₂×C₄	—	34	2	no	—
626	C₂×C₄	—	34	2	no	—
627	C₂×C₄	—	34	2	no	—
628	C₂×C₄	—	34	2	no	—
629	C₂×C₄	—	34	2	no	—
630	C₂×C₄	—	68	8	no	—
631	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
632	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
633	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
634	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
635	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
636	C₂×C₄	C₂³×#595	1	1	yes	characteristic
637	C₈	—	2	1	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	34	2	no	—
642	C₈	—	34	2	no	—
643	C₈	—	34	2	no	—
644	C₈	—	34	2	no	—
645	C₈	—	34	1	no	—
646	C₈	—	34	1	no	—
647	C₈	—	34	1	no	—
648	C₈	—	34	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	17	1	no	—
653	C₂²	—	17	1	no	—
654	C₂²	—	17	2	no	—
655	C₂²	—	17	2	no	—
656	C₂²	—	34	1	no	—
657	C₂²	—	34	1	no	—
658	C₂²	—	34	1	no	—
659	C₂²	—	68	2	no	—
660	C₂²	—	68	2	no	—
661	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	17	1	no	—
668	C₄	—	17	1	no	—
669	C₄	—	34	4	no	—
670	C₄	—	34	1	no	—
671	C₄	—	34	1	no	—
672	C₄	—	34	1	no	—
673	C₄	—	34	1	no	—
674	C₄	—	34	1	no	—
675	C₄	—	68	2	no	—
676	C₄	—	68	2	no	—
677	C₄	—	68	2	no	—
678	C₄	#11763878	1	1	yes	characteristic
679	C₄	#11763878	1	1	yes	characteristic
680	C₂	—	4	1	no	—
681	C₂	—	17	2	no	—
682	C₂	—	17	2	no	—
683	C₂	—	68	1	no	—
684	C₂	#14545221	1	1	yes	characteristic
685	C₂	#131×#595	1	1	yes	characteristic
686	C₂	#14545354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#433	C₄
prime radical	C₂³×D₁₇	C₂²×C₄
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#433	#595
hypocenter	C₁₇	#20541
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
3. #14544585	C₂	semidirect
4. #14544585	C₂	semidirect
5. #14544582	C₂	semidirect
6. #14544582	C₂	semidirect
7. #14544581	C₂	semidirect
8. #14544578	C₂	semidirect
9. #14544577	C₂	semidirect
10. C₈×C₄⋊#595	C₂	semidirect
18. #11763834	C₄	semidirect
19. #11763834	C₄	semidirect
20. #11763833	C₄	semidirect
21. #11763833	C₄	semidirect
53. #11762871	C₄	semidirect
54. #11762870	C₄	semidirect
55. #11762869	C₄	semidirect
56. #11762869	C₄	semidirect
57. #11762868	C₄	semidirect
58. #11762867	C₄	semidirect
59. #11762867	C₄	semidirect
66. C₁₇×#433	C₄	semidirect
112. #10587544	C₂×C₄	semidirect
113. #10587544	C₂×C₄	semidirect
116. #10587542	C₂×C₄	semidirect
117. #10587542	C₂×C₄	semidirect
118. C₄⋊#3624	C₂×C₄	semidirect
119. C₄⋊#3624	C₂×C₄	semidirect
120. C₄×#3624	C₂×C₄	semidirect
121. C₄×#3624	C₂×C₄	semidirect
130. C₁₇×C₄⋊C₈	C₂×C₄	semidirect
131. C₁₇×C₄⋊C₈	C₂×C₄	semidirect
134. C₁₇×#97	C₂×C₄	semidirect
135. C₄×C₈×C₁₇	C₂×C₄	semidirect
142. #10587486	C₂×C₄	semidirect
143. #10587486	C₂×C₄	semidirect
144. #10587485	C₂×C₄	semidirect
145. #10587485	C₂×C₄	semidirect
146. #10587485	C₂×C₄	semidirect
147. #10587485	C₂×C₄	semidirect
148. C₈×Dic₁₇	C₂×C₄	semidirect
149. C₈×Dic₁₇	C₂×C₄	semidirect
150. C₄⋊#3622	C₂×C₄	semidirect
151. C₄⋊#3622	C₂×C₄	semidirect
152. #10587474	C₂×C₄	semidirect
153. C₄×#3622	C₂×C₄	semidirect
366. #433	#595	semidirect
459. C₄⋊C₈	C₂×#595	semidirect
460. C₄⋊C₈	C₂×#595	semidirect
482. #97	C₂×#595	semidirect
492. C₄×C₈	C₂×#595	semidirect
497. C₁₇	#20541	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊#433	2
#14545244	2
#14544585	2
#14544582	2
#14544581	2
#14544578	2
#14544577	2
C₈×C₄⋊#595	2
#14544515	2
#14544512	2
C₂²⋊C₈×#595	2
D₁₇×#433	2
#20541	17