Subgroups — #17046337

Order 4352.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762940	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11762866	C₂	1	1	yes	maximal, characteristic
3	#14529725	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529508	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529508	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529503	C₂	1	1	yes	maximal, characteristic, complemented
7	#14529399	C₂	1	1	yes	maximal, characteristic
8	#14529399	C₂	1	1	yes	maximal, characteristic
9	#14529392	C₂	1	1	yes	maximal, characteristic
10	#14529392	C₂	1	1	yes	maximal, characteristic
11	#14529350	C₂	1	1	yes	maximal, characteristic, complemented
12	#14529343	C₂	1	1	yes	maximal, characteristic, complemented
13	#14528764	C₂	1	1	yes	maximal, characteristic
14	#14528659	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	#11762940	—	2	4	no	—
17	#11762866	—	2	4	no	—
18	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
30	C₂×#10587474	C₂²	1	1	yes	characteristic
31	C₂×#10587474	C₂²	1	1	yes	characteristic
32	C₂×#10587474	C₂²	1	1	yes	characteristic
33	C₂×#10587474	C₂²	1	1	yes	characteristic
34	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
35	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
36	#11762564	C₂²	1	1	yes	characteristic
37	#11762564	C₂²	1	1	yes	characteristic
38	#11762564	C₂²	1	1	yes	characteristic
39	#11762564	C₂²	1	1	yes	characteristic
40	#11762564	C₂²	1	1	yes	characteristic
41	#11762564	C₂²	1	1	yes	characteristic
42	#11762564	C₂²	1	1	yes	characteristic
43	#11762564	C₂²	1	1	yes	characteristic
44	#11762564	C₂²	1	1	yes	characteristic
45	#11762564	C₂²	1	1	yes	characteristic
46	C₂×C₁₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#391	C₄	1	1	yes	characteristic
50	C₁₇×#389	C₄	1	1	yes	characteristic
51	C₁₇×#387	C₄	1	1	yes	characteristic
52	C₁₇×#387	C₄	1	1	yes	characteristic
53	C₁₇×#385	C₄	1	1	yes	characteristic
54	C₁₇×#385	C₄	1	1	yes	characteristic
55	C₁₇×#380	C₄	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
65	C₁₇×C₂²⋊Q₈	—	2	4	no	—
66	C₄×Q₈×C₁₇	—	2	2	no	—
67	C₄×Q₈×C₁₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₇	—	2	2	no	—
82	C₂×C₄²×C₁₇	—	2	2	no	—
83	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
91	C₂²×#3622	C₂³	1	1	yes	characteristic
92	C₂²×#3622	C₂³	1	1	yes	characteristic
93	C₂²×#3622	C₂³	1	1	yes	characteristic
94	C₂²×#3622	C₂³	1	1	yes	characteristic
95	C₂²×#3622	C₂³	1	1	yes	characteristic
96	C₂²×#3622	C₂³	1	1	yes	characteristic
97	C₂²×#3622	C₂³	1	1	yes	characteristic
98	C₂²×#3622	C₂³	1	1	yes	characteristic
99	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
100	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
104	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊#3622	—	2	2	no	—
110	C₂²⋊#3622	—	2	2	no	—
111	C₂²⋊#3622	—	4	1	no	—
112	C₂²⋊#3622	—	4	1	no	—
113	C₄⋊#3622	—	2	2	no	—
114	C₄⋊#3622	—	2	2	no	—
115	C₄⋊#3622	—	2	2	no	—
116	C₄⋊#3622	—	2	2	no	—
117	C₄⋊#3622	—	2	2	no	—
118	C₄⋊#3622	—	2	2	no	—
119	C₄⋊#3622	—	4	1	no	—
120	C₄⋊#3622	—	4	1	no	—
121	#10587474	—	2	2	no	—
122	#10587474	—	2	2	no	—
123	#10587474	—	4	1	no	—
124	#10587474	D₄	1	4	yes	—
125	C₄×#3622	—	2	2	no	—
126	C₄×#3622	—	4	1	no	—
127	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₇	—	2	2	no	—
129	C₂×Q₈×C₁₇	—	2	2	no	—
130	C₂×Q₈×C₁₇	—	4	1	no	—
131	C₂²×C₄×C₁₇	—	2	2	no	—
132	C₂²×C₄×C₁₇	—	2	2	no	—
133	C₂²×C₄×C₁₇	—	2	2	no	—
134	C₂²×C₄×C₁₇	—	2	2	no	—
135	C₂²×C₄×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	—	2	1	no	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	1	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	—	4	1	no	—
142	C₂²×C₄×C₁₇	—	4	1	no	—
143	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₁₇	—	2	2	no	—
158	C₄⋊C₄×C₁₇	—	2	2	no	—
159	C₄⋊C₄×C₁₇	—	2	2	no	—
160	C₄⋊C₄×C₁₇	—	2	2	no	—
161	C₄⋊C₄×C₁₇	—	2	2	no	—
162	C₄⋊C₄×C₁₇	—	2	2	no	—
163	C₄⋊C₄×C₁₇	—	2	2	no	—
164	C₄⋊C₄×C₁₇	—	2	2	no	—
165	C₄⋊C₄×C₁₇	—	4	1	no	—
166	C₂²⋊C₄×C₁₇	—	2	2	no	—
167	C₂²⋊C₄×C₁₇	—	4	1	no	—
168	C₂²⋊C₄×C₁₇	—	4	1	no	—
169	C₂²⋊C₄×C₁₇	M₁₆	1	4	yes	—
170	C₄²×C₁₇	—	2	2	no	—
171	C₄²×C₁₇	—	2	2	no	—
172	C₄²×C₁₇	—	2	1	no	—
173	C₄²×C₁₇	—	2	1	no	—
174	C₄²×C₁₇	—	2	1	no	—
175	C₄²×C₁₇	—	2	1	no	—
176	C₄²×C₁₇	—	2	1	no	—
177	C₄²×C₁₇	—	2	1	no	—
178	C₄²×C₁₇	—	2	1	no	—
179	C₄²×C₁₇	—	2	1	no	—
180	C₄²×C₁₇	—	2	1	no	—
181	C₄²×C₁₇	—	2	1	no	—
182	C₄²×C₁₇	C₂×D₄	1	2	yes	—
183	C₄²×C₁₇	#41	1	2	yes	—
184	C₂×#3622	—	2	1	no	—
185	C₂×#3622	—	2	1	no	—
186	C₂×#3622	—	2	1	no	—
187	C₂×#3622	—	2	1	no	—
188	C₂×#3622	—	2	1	no	—
189	C₂×#3622	—	2	1	no	—
190	C₂×#3622	—	2	1	no	—
191	C₂×#3622	—	2	1	no	—
192	C₂×#3622	—	2	1	no	—
193	C₂×#3622	—	2	1	no	—
194	C₂×#3622	—	2	1	no	—
195	C₂×#3622	—	2	1	no	—
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	2	1	no	—
201	C₂×#3622	—	2	1	no	—
202	C₂×#3622	—	2	1	no	—
203	C₂×#3622	—	2	1	no	—
204	C₂×#3622	—	2	1	no	—
205	C₂×#3622	—	2	1	no	—
206	C₂×#3622	C₂×D₄	1	2	yes	—
207	C₂×#3622	C₂×D₄	1	2	yes	—
208	#22108	—	17	1	no	maximal, Sylow
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	2	1	no	—
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	—	2	1	no	—
213	C₂³×C₁₇	—	2	1	no	—
214	C₂³×C₁₇	—	2	1	no	—
215	C₂³×C₁₇	C₂×M₁₆	1	2	yes	—
216	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
217	Q₈×C₁₇	—	4	4	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	1	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	1	no	—
238	C₂×C₄×C₁₇	—	2	1	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	1	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	2	1	no	—
247	C₂×C₄×C₁₇	—	2	1	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	2	1	no	—
251	C₂×C₄×C₁₇	—	2	1	no	—
252	C₂×C₄×C₁₇	—	4	4	no	—
253	C₂×C₄×C₁₇	—	4	4	no	—
254	C₂×C₄×C₁₇	—	4	1	no	—
255	C₂×C₄×C₁₇	—	4	1	no	—
256	C₂×C₄×C₁₇	—	4	1	no	—
257	C₂×C₄×C₁₇	—	4	1	no	—
258	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
260	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
261	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
262	C₂×C₄×C₁₇	#131	1	2	yes	—
263	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
269	#3622	—	2	2	no	—
270	#3622	—	2	2	no	—
271	#3622	—	4	1	no	—
272	#3622	—	4	1	no	—
273	#3622	—	4	1	no	—
274	#3622	—	4	1	no	—
275	#3622	—	4	1	no	—
276	#3622	—	4	1	no	—
277	C₂×#446	—	17	1	no	—
278	C₂×#432	—	17	1	no	—
279	C₄×C₂²⋊Q₈	D₁₇	1	1	yes	characteristic
280	#1985	—	17	1	no	—
281	#1940	—	17	1	no	—
282	#1940	—	17	1	no	—
283	#1939	—	17	1	no	—
284	#1924	—	17	1	no	—
285	#1924	—	17	1	no	—
286	#1923	—	17	1	no	—
287	#1923	—	17	1	no	—
288	#1917	—	17	1	no	—
289	#1916	—	17	1	no	—
290	#1797	—	17	1	no	—
291	#1771	—	17	1	no	—
292	C₂²×C₁₇	—	2	2	no	—
293	C₂²×C₁₇	—	2	2	no	—
294	C₂²×C₁₇	—	2	2	no	—
295	C₂²×C₁₇	—	4	1	no	—
296	C₂²×C₁₇	—	4	1	no	—
297	C₂²×C₁₇	—	4	1	no	—
298	C₂²×C₁₇	—	4	1	no	—
299	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₁₇	#519	1	1	yes	characteristic
301	C₂²×C₁₇	#520	1	1	yes	characteristic
302	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
303	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
304	C₂²×C₁₇	#568	1	1	yes	characteristic
305	C₂²×C₁₇	#568	1	1	yes	characteristic
306	C₄×C₁₇	—	2	2	no	—
307	C₄×C₁₇	—	2	2	no	—
308	C₄×C₁₇	—	2	2	no	—
309	C₄×C₁₇	—	2	2	no	—
310	C₄×C₁₇	—	2	2	no	—
311	C₄×C₁₇	—	4	1	no	—
312	C₄×C₁₇	—	4	1	no	—
313	C₄×C₁₇	—	4	1	no	—
314	C₄×C₁₇	—	4	1	no	—
315	C₄×C₁₇	—	4	1	no	—
316	C₄×C₁₇	—	4	1	no	—
317	C₄×C₁₇	—	4	1	no	—
318	C₄×C₁₇	—	4	1	no	—
319	C₄×C₁₇	#536	1	1	yes	characteristic
320	C₄×C₁₇	#537	1	1	yes	characteristic
321	C₄×C₁₇	#541	1	1	yes	characteristic
322	C₄×C₁₇	#542	1	1	yes	characteristic
323	C₂×C₂²⋊Q₈	Dic₁₇	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
325	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
326	#446	—	34	4	no	—
327	#432	—	34	4	no	—
328	C₂×C₄⋊C₈	—	17	1	no	—
329	C₂×C₄⋊C₈	—	17	1	no	—
330	C₂×C₄⋊C₈	—	17	1	no	—
331	C₂×C₄⋊C₈	—	17	1	no	—
332	C₂×C₄⋊C₈	—	17	1	no	—
333	C₂×C₄⋊C₈	—	17	1	no	—
334	C₂×C₄⋊C₈	—	17	1	no	—
335	C₂×C₄⋊C₈	—	17	1	no	—
336	C₂×C₂²⋊C₈	—	17	1	no	—
337	C₂×C₂²⋊C₈	—	17	1	no	—
338	C₂×C₂²⋊C₈	—	17	1	no	—
339	C₂×C₂²⋊C₈	—	17	1	no	—
340	C₂×#97	—	17	1	no	—
341	C₂×#97	—	17	1	no	—
342	C₂×#97	—	17	1	no	—
343	C₂×#97	—	17	1	no	—
344	C₂×C₄×C₈	—	17	1	no	—
345	C₂×C₄×C₈	—	17	1	no	—
346	#391	Dic₁₇	1	1	yes	characteristic
347	#389	Dic₁₇	1	1	yes	characteristic
348	#387	Dic₁₇	1	1	yes	characteristic
349	#387	Dic₁₇	1	1	yes	characteristic
350	#385	Dic₁₇	1	1	yes	characteristic
351	#385	Dic₁₇	1	1	yes	characteristic
352	#380	Dic₁₇	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
358	#336	—	17	1	no	—
359	#336	—	17	1	no	—
360	#336	—	17	1	no	—
361	#336	—	17	1	no	—
362	#336	—	17	1	no	—
363	#336	—	17	1	no	—
364	#336	—	17	1	no	—
365	#336	—	17	1	no	—
366	#336	—	17	1	no	—
367	#336	—	17	1	no	—
368	C₂×C₁₇	—	4	2	no	—
369	C₂×C₁₇	#2323	1	1	yes	characteristic
370	C₂×C₁₇	#2933	1	1	yes	characteristic
371	C₂×C₁₇	D₄×M₁₆	1	1	yes	characteristic
372	C₂×C₁₇	#2983	1	1	yes	characteristic
373	C₂×C₁₇	#2985	1	1	yes	characteristic
374	C₂×C₁₇	#2990	1	1	yes	characteristic
375	C₂×C₁₇	#2995	1	1	yes	characteristic
376	C₂²×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
377	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
378	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
379	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
380	C₂²×C₈	—	17	1	no	—
381	C₂²×C₈	—	17	1	no	—
382	C₂²×C₈	—	17	1	no	—
383	C₂²×C₈	—	17	1	no	—
384	C₂²×C₈	—	17	1	no	—
385	C₂²×C₈	—	17	1	no	—
386	C₂²×C₈	—	17	1	no	—
387	C₂²×C₈	—	17	1	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
404	C₂×C₄²	—	2	2	no	—
405	C₂×C₄²	—	2	2	no	—
406	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
407	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
410	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
411	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
412	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
413	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
414	C₄⋊C₈	—	34	2	no	—
415	C₄⋊C₈	—	34	2	no	—
416	C₄⋊C₈	—	34	2	no	—
417	C₄⋊C₈	—	34	2	no	—
418	C₄⋊C₈	—	34	2	no	—
419	C₄⋊C₈	—	34	2	no	—
420	C₄⋊C₈	—	68	1	no	—
421	C₄⋊C₈	—	68	1	no	—
422	C₂²⋊C₈	—	34	2	no	—
423	C₂²⋊C₈	—	34	2	no	—
424	C₂²⋊C₈	—	68	1	no	—
425	C₂²⋊C₈	—	68	1	no	—
426	#97	—	17	4	no	—
427	#97	—	34	2	no	—
428	#97	—	34	2	no	—
429	#97	—	68	1	no	—
430	C₄×C₈	—	34	2	no	—
431	C₄×C₈	—	68	1	no	—
432	#95	C₂×Dic₁₇	1	1	yes	characteristic
433	#95	C₂×Dic₁₇	1	1	yes	characteristic
434	#95	C₂×Dic₁₇	1	1	yes	characteristic
435	#95	C₂×Dic₁₇	1	1	yes	characteristic
436	#95	C₂×Dic₁₇	1	1	yes	characteristic
437	#95	C₂×Dic₁₇	1	1	yes	characteristic
438	#95	C₂×Dic₁₇	1	1	yes	characteristic
439	#95	C₂×Dic₁₇	1	1	yes	characteristic
440	#95	C₂×Dic₁₇	1	1	yes	characteristic
441	#95	C₂×Dic₁₇	1	1	yes	characteristic
442	C₁₇	#22108	1	1	yes	characteristic, complemented, Sylow
443	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	4	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
462	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
472	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
473	C₂×C₈	—	17	2	no	—
474	C₂×C₈	—	17	2	no	—
475	C₂×C₈	—	34	1	no	—
476	C₂×C₈	—	34	1	no	—
477	C₂×C₈	—	34	1	no	—
478	C₂×C₈	—	34	1	no	—
479	C₂×C₈	—	34	1	no	—
480	C₂×C₈	—	34	1	no	—
481	C₂×C₈	—	34	1	no	—
482	C₂×C₈	—	34	1	no	—
483	C₂×C₈	—	34	1	no	—
484	C₂×C₈	—	34	1	no	—
485	C₂×C₈	—	34	1	no	—
486	C₂×C₈	—	34	1	no	—
487	C₂×C₈	—	34	1	no	—
488	C₂×C₈	—	34	1	no	—
489	C₂×C₈	—	34	1	no	—
490	C₂×C₈	—	34	1	no	—
491	C₂×C₈	—	34	1	no	—
492	C₂×C₈	—	34	1	no	—
493	C₂×C₈	—	34	1	no	—
494	C₂×C₈	—	34	1	no	—
495	C₂×C₈	—	34	1	no	—
496	C₂×C₈	—	34	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	#63223	1	4	yes	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	D₄×D₁₇	1	2	yes	—
523	C₄²	#63254	1	2	yes	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	C₂×#63223	1	2	yes	—
531	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
532	Q₈	—	4	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	C₂×#63223	1	2	yes	—
574	C₂×C₄	C₂×#63223	1	2	yes	—
575	C₂×C₄	D₄×Dic₁₇	1	2	yes	—
576	C₂×C₄	D₄×Dic₁₇	1	2	yes	—
577	C₂×C₄	#10587634	1	2	yes	—
578	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
579	C₂×C₄	C₂×#63254	1	1	yes	characteristic
580	C₂×C₄	#10587694	1	1	yes	characteristic
581	C₂×C₄	#10587694	1	1	yes	characteristic
582	C₂×C₄	#10587696	1	1	yes	characteristic
583	C₂×C₄	#10587697	1	1	yes	characteristic
584	C₈	—	34	2	no	—
585	C₈	—	34	2	no	—
586	C₈	—	68	1	no	—
587	C₈	—	68	1	no	—
588	C₈	—	68	1	no	—
589	C₈	—	68	1	no	—
590	C₈	—	68	1	no	—
591	C₈	—	68	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	C₂×D₄×Dic₁₇	1	1	yes	characteristic
600	C₂²	#11763287	1	1	yes	characteristic
601	C₂²	#11763292	1	1	yes	characteristic
602	C₂²	C₂²×#63223	1	1	yes	characteristic
603	C₂²	C₂×#10587634	1	1	yes	characteristic
604	C₂²	#11763576	1	1	yes	characteristic
605	C₂²	#11763576	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	#11763382	1	1	yes	characteristic
620	C₄	#11763389	1	1	yes	characteristic
621	C₄	#11763419	1	1	yes	characteristic
622	C₄	#11763432	1	1	yes	characteristic
623	C₂	—	4	2	no	—
624	C₂	#14531468	1	1	yes	characteristic
625	C₂	#14537511	1	1	yes	characteristic
626	C₂	D₄×#63223	1	1	yes	characteristic
627	C₂	#14537869	1	1	yes	characteristic
628	C₂	#14537879	1	1	yes	characteristic
629	C₂	#14537909	1	1	yes	characteristic
630	C₂	#14537954	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator, socle	C₂³×C₁₇	C₂³×C₄
Fitting	C₄×C₁₇×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₁₇
hypocenter	C₁₇	#22108
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11762940	C₂	semidirect
3. #14529725	C₂	semidirect
4. #14529508	C₂	semidirect
5. #14529508	C₂	semidirect
6. #14529503	C₂	semidirect
11. #14529350	C₂	semidirect
12. #14529343	C₂	semidirect
14. #14528659	C₂	semidirect
442. C₁₇	#22108	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762940	2
C₂×#11762866	2
#14529725	2
#14529508	2
#14529503	2
#14529399	2
#14529392	2
#14529350	2
#14529343	2
#14528764	2
#14528659	2
C₄×C₁₇×C₂²⋊Q₈	2
#22108	17