Subgroups — #17060821

Order 4352.

758 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14529725	C₂	1	1	yes	maximal, characteristic, complemented
2	#14529721	C₂	1	1	yes	maximal, characteristic, complemented
3	#14529399	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529399	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529392	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529392	C₂	1	1	yes	maximal, characteristic, complemented
7	#14529082	C₂	1	1	yes	maximal, characteristic
8	#14529077	C₂	1	1	yes	maximal, characteristic
9	#14528969	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528969	C₂	1	1	yes	maximal, characteristic, complemented
11	#14528964	C₂	1	1	yes	maximal, characteristic, complemented
12	#14528964	C₂	1	1	yes	maximal, characteristic, complemented
13	#14528901	C₂	1	1	yes	maximal, characteristic, complemented
14	#14528901	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₇×#124	C₂	1	1	yes	maximal, characteristic
16	C₂²×#63223	C₂²	1	1	yes	characteristic
17	C₂³×#3622	C₂²	1	1	yes	characteristic
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×C₂²⋊#3622	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#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×C₄×#3622	C₂²	1	1	yes	characteristic
32	#11762564	C₂²	1	1	yes	characteristic
33	#11762564	C₂²	1	1	yes	characteristic
34	#11762564	C₂²	1	1	yes	characteristic
35	#11762564	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	C₂×C₁₇×#124	C₄	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#391	C₄	1	1	yes	characteristic
48	C₁₇×#390	C₄	1	1	yes	characteristic
49	C₁₇×#388	C₄	1	1	yes	characteristic
50	C₁₇×#388	C₄	1	1	yes	characteristic
51	C₁₇×#388	C₄	1	1	yes	characteristic
52	C₁₇×#388	C₄	1	1	yes	characteristic
53	C₁₇×#382	C₄	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
58	C₄³×C₁₇	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₁₇×#124	—	2	4	no	—
64	C₄×Q₈×C₁₇	—	4	1	no	—
65	C₄×Q₈×C₁₇	—	4	1	no	—
66	C₄×D₄×C₁₇	—	4	1	no	—
67	C₄×D₄×C₁₇	—	4	1	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×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊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×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₇	C₂×C₄	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	C₂×#63223	—	4	1	no	—
92	C₂×#63223	—	4	1	no	—
93	C₂×#63223	—	4	1	no	—
94	C₂²×#3622	—	4	1	no	—
95	C₂²×#3622	—	4	1	no	—
96	C₂²×#3622	—	4	1	no	—
97	C₂²×#3622	C₂³	1	1	yes	characteristic
98	C₂²×#3622	C₂³	1	1	yes	characteristic
99	C₂²×#3622	C₂³	1	1	yes	characteristic
100	C₂²×#3622	C₂³	1	1	yes	characteristic
101	C₂²×#3622	C₂³	1	1	yes	characteristic
102	C₂²×#3622	C₂³	1	1	yes	characteristic
103	C₂²×#3622	C₂³	1	1	yes	characteristic
104	C₂²×#3622	C₂³	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	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#3622	—	4	1	no	—
114	C₂²⋊#3622	—	4	1	no	—
115	C₂²⋊#3622	—	4	1	no	—
116	C₂²⋊#3622	—	4	1	no	—
117	C₂²⋊#3622	—	4	1	no	—
118	C₂²⋊#3622	—	4	1	no	—
119	C₄⋊#3622	—	4	1	no	—
120	C₄⋊#3622	—	4	1	no	—
121	C₄⋊#3622	—	4	1	no	—
122	C₄⋊#3622	—	4	1	no	—
123	C₄⋊#3622	—	4	1	no	—
124	C₄⋊#3622	—	4	1	no	—
125	#10587474	—	4	1	no	—
126	C₄×#3622	—	4	1	no	—
127	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×Q₈×C₁₇	—	2	2	no	—
130	C₂×Q₈×C₁₇	—	2	2	no	—
131	C₂×Q₈×C₁₇	—	4	1	no	—
132	C₂×D₄×C₁₇	—	2	2	no	—
133	C₂×D₄×C₁₇	—	2	2	no	—
134	C₂×D₄×C₁₇	—	4	1	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	—	2	1	no	—
142	C₂²×C₄×C₁₇	—	2	1	no	—
143	C₂²×C₄×C₁₇	—	2	1	no	—
144	C₂²×C₄×C₁₇	—	2	1	no	—
145	C₂²×C₄×C₁₇	—	2	1	no	—
146	C₂²×C₄×C₁₇	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₁₇	—	4	1	no	—
161	C₄⋊C₄×C₁₇	—	4	1	no	—
162	C₄⋊C₄×C₁₇	—	4	1	no	—
163	C₄⋊C₄×C₁₇	—	4	1	no	—
164	C₂²⋊C₄×C₁₇	—	2	2	no	—
165	C₂²⋊C₄×C₁₇	—	2	2	no	—
166	C₂²⋊C₄×C₁₇	—	2	2	no	—
167	C₂²⋊C₄×C₁₇	—	2	2	no	—
168	C₂²⋊C₄×C₁₇	—	2	2	no	—
169	C₂²⋊C₄×C₁₇	—	4	1	no	—
170	C₂²⋊C₄×C₁₇	—	4	1	no	—
171	C₂²⋊C₄×C₁₇	—	4	1	no	—
172	C₂²⋊C₄×C₁₇	—	4	1	no	—
173	C₂²⋊C₄×C₁₇	M₁₆	1	4	yes	complemented
174	C₄²×C₁₇	—	2	2	no	—
175	C₄²×C₁₇	—	2	2	no	—
176	C₄²×C₁₇	—	2	2	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	—	2	1	no	—
183	C₄²×C₁₇	—	2	1	no	—
184	C₄²×C₁₇	—	2	1	no	—
185	C₄²×C₁₇	—	2	1	no	—
186	C₄²×C₁₇	—	2	1	no	—
187	C₄²×C₁₇	—	4	1	no	—
188	#63223	—	4	4	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	—	2	1	no	—
207	C₂×#3622	—	2	1	no	—
208	C₂×#3622	—	2	1	no	—
209	C₂×#3622	—	2	1	no	—
210	C₂×#3622	—	2	1	no	—
211	C₂×#3622	—	2	1	no	—
212	C₂×#3622	—	2	1	no	—
213	C₂×#3622	—	4	4	no	—
214	#23349	—	17	1	no	maximal, Sylow
215	C₂³×C₁₇	—	2	1	no	—
216	C₂³×C₁₇	—	2	1	no	—
217	C₂³×C₁₇	—	2	1	no	—
218	C₂³×C₁₇	—	2	1	no	—
219	C₂³×C₁₇	—	2	1	no	—
220	C₂³×C₁₇	—	2	1	no	—
221	C₂³×C₁₇	—	2	1	no	—
222	C₂³×C₁₇	—	2	1	no	—
223	C₂³×C₁₇	—	2	1	no	—
224	C₂³×C₁₇	—	2	1	no	—
225	C₂³×C₁₇	—	2	1	no	—
226	C₂³×C₁₇	—	2	1	no	—
227	C₂³×C₁₇	—	2	1	no	—
228	C₂³×C₁₇	C₂×M₁₆	1	2	yes	—
229	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
230	Q₈×C₁₇	—	4	4	no	—
231	D₄×C₁₇	—	4	4	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	—	2	1	no	—
253	C₂×C₄×C₁₇	—	2	1	no	—
254	C₂×C₄×C₁₇	—	2	1	no	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	1	no	—
257	C₂×C₄×C₁₇	—	2	1	no	—
258	C₂×C₄×C₁₇	—	2	1	no	—
259	C₂×C₄×C₁₇	—	2	1	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	1	no	—
262	C₂×C₄×C₁₇	—	2	1	no	—
263	C₂×C₄×C₁₇	—	2	1	no	—
264	C₂×C₄×C₁₇	—	4	1	no	—
265	C₂×C₄×C₁₇	—	4	1	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	4	1	no	—
270	C₂×C₄×C₁₇	—	4	1	no	—
271	C₂×C₄×C₁₇	—	4	1	no	—
272	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
273	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
274	C₂×C₄×C₁₇	#131	1	2	yes	—
275	C₂×C₄×C₁₇	#131	1	2	yes	—
276	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
281	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
282	#3622	—	4	1	no	—
283	#3622	—	4	1	no	—
284	#3622	—	4	1	no	—
285	#3622	—	4	1	no	—
286	#3622	—	4	1	no	—
287	#3622	—	4	1	no	—
288	#3622	—	4	1	no	—
289	#3622	—	4	1	no	—
290	C₄×#124	D₁₇	1	1	yes	characteristic
291	#1985	—	17	1	no	—
292	#1984	—	17	1	no	—
293	#1924	—	17	1	no	—
294	#1924	—	17	1	no	—
295	#1923	—	17	1	no	—
296	#1923	—	17	1	no	—
297	#1870	—	17	1	no	—
298	#1869	—	17	1	no	—
299	#1851	—	17	1	no	—
300	#1851	—	17	1	no	—
301	#1850	—	17	1	no	—
302	#1850	—	17	1	no	—
303	#1831	—	17	1	no	—
304	#1831	—	17	1	no	—
305	C₂²×C₁₇	—	2	2	no	—
306	C₂²×C₁₇	—	2	2	no	—
307	C₂²×C₁₇	—	2	2	no	—
308	C₂²×C₁₇	—	4	1	no	—
309	C₂²×C₁₇	—	4	1	no	—
310	C₂²×C₁₇	—	4	1	no	—
311	C₂²×C₁₇	—	4	1	no	—
312	C₂²×C₁₇	—	4	1	no	—
313	C₂²×C₁₇	—	4	1	no	—
314	C₂²×C₁₇	—	4	1	no	—
315	C₂²×C₁₇	—	4	1	no	—
316	C₂²×C₁₇	—	4	1	no	—
317	C₂²×C₁₇	—	4	1	no	—
318	C₂²×C₁₇	—	4	1	no	—
319	C₂²×C₁₇	#518	1	1	yes	characteristic
320	C₂²×C₁₇	#520	1	1	yes	characteristic
321	C₂²×C₁₇	#520	1	1	yes	characteristic
322	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
323	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
324	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
325	C₂²×C₁₇	#568	1	1	yes	characteristic
326	C₄×C₁₇	—	2	2	no	—
327	C₄×C₁₇	—	2	2	no	—
328	C₄×C₁₇	—	2	2	no	—
329	C₄×C₁₇	—	2	2	no	—
330	C₄×C₁₇	—	4	1	no	—
331	C₄×C₁₇	—	4	1	no	—
332	C₄×C₁₇	—	4	1	no	—
333	C₄×C₁₇	—	4	1	no	—
334	C₄×C₁₇	—	4	1	no	—
335	C₄×C₁₇	—	4	1	no	—
336	C₄×C₁₇	—	4	1	no	—
337	C₄×C₁₇	—	4	1	no	—
338	C₄×C₁₇	H(3,𝔽₄)	1	1	yes	characteristic
339	C₄×C₁₇	#562	1	1	yes	characteristic
340	C₄×C₁₇	#562	1	1	yes	characteristic
341	C₄×C₁₇	#563	1	1	yes	characteristic
342	C₂²×M₁₆	—	17	1	no	—
343	C₂³×C₈	—	17	1	no	—
344	C₂×#124	Dic₁₇	1	1	yes	characteristic
345	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
347	C₂×C₄⋊C₈	—	17	1	no	—
348	C₂×C₄⋊C₈	—	17	1	no	—
349	C₂×C₄⋊C₈	—	17	1	no	—
350	C₂×C₄⋊C₈	—	17	1	no	—
351	C₂×C₄⋊C₈	—	17	1	no	—
352	C₂×C₄⋊C₈	—	17	1	no	—
353	C₂×C₂²⋊C₈	—	17	1	no	—
354	C₂×C₂²⋊C₈	—	17	1	no	—
355	C₂×C₂²⋊C₈	—	17	1	no	—
356	C₂×C₂²⋊C₈	—	17	1	no	—
357	C₂×C₂²⋊C₈	—	17	1	no	—
358	C₂×C₂²⋊C₈	—	17	1	no	—
359	C₂×#97	—	17	1	no	—
360	C₂×C₄×C₈	—	17	1	no	—
361	#391	Dic₁₇	1	1	yes	characteristic
362	#390	Dic₁₇	1	1	yes	characteristic
363	#388	Dic₁₇	1	1	yes	characteristic
364	#388	Dic₁₇	1	1	yes	characteristic
365	#388	Dic₁₇	1	1	yes	characteristic
366	#388	Dic₁₇	1	1	yes	characteristic
367	#382	Dic₁₇	1	1	yes	characteristic
368	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
369	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂×D₁₇	1	1	yes	characteristic
372	C₄³	C₂×D₁₇	1	1	yes	characteristic
373	#336	—	17	1	no	—
374	#336	—	17	1	no	—
375	#336	—	17	1	no	—
376	#336	—	17	1	no	—
377	#336	—	17	1	no	—
378	#336	—	17	1	no	—
379	#336	—	17	1	no	—
380	#336	—	17	1	no	—
381	#336	—	17	1	no	—
382	#336	—	17	1	no	—
383	#336	—	17	1	no	—
384	#336	—	17	1	no	—
385	C₂×C₁₇	—	4	2	no	—
386	C₂×C₁₇	—	8	1	no	—
387	C₂×C₁₇	#2379	1	1	yes	characteristic
388	C₂×C₁₇	#2974	1	1	yes	characteristic
389	C₂×C₁₇	#2981	1	1	yes	characteristic
390	C₂×C₁₇	#2989	1	1	yes	characteristic
391	C₂×C₁₇	#2990	1	1	yes	characteristic
392	C₂×C₁₇	#2993	1	1	yes	characteristic
393	C₂×C₁₇	#2994	1	1	yes	characteristic
394	C₂²×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
395	C₂²×D₄	C₂×Dic₁₇	1	1	yes	characteristic
396	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
397	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
398	C₂×M₁₆	—	68	1	no	—
399	C₂×M₁₆	—	68	1	no	—
400	C₂×M₁₆	—	68	1	no	—
401	C₂²×C₈	—	17	1	no	—
402	C₂²×C₈	—	17	1	no	—
403	C₂²×C₈	—	17	1	no	—
404	C₂²×C₈	—	17	1	no	—
405	C₂²×C₈	—	17	1	no	—
406	C₂²×C₈	—	17	1	no	—
407	C₂²×C₈	—	17	1	no	—
408	C₂²×C₈	—	17	1	no	—
409	C₂²×C₈	—	68	1	no	—
410	C₂²×C₈	—	68	1	no	—
411	C₂²×C₈	—	68	1	no	—
412	#124	—	2	4	no	—
413	C₄×Q₈	—	4	1	no	—
414	C₄×Q₈	—	4	1	no	—
415	C₄×D₄	—	4	1	no	—
416	C₄×D₄	—	4	1	no	—
417	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
431	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
432	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
433	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
434	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
435	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
440	C₄⋊C₈	—	68	1	no	—
441	C₄⋊C₈	—	68	1	no	—
442	C₄⋊C₈	—	68	1	no	—
443	C₄⋊C₈	—	68	1	no	—
444	C₄⋊C₈	—	68	1	no	—
445	C₄⋊C₈	—	68	1	no	—
446	C₂²⋊C₈	—	68	1	no	—
447	C₂²⋊C₈	—	68	1	no	—
448	C₂²⋊C₈	—	68	1	no	—
449	C₂²⋊C₈	—	68	1	no	—
450	C₂²⋊C₈	—	68	1	no	—
451	C₂²⋊C₈	—	68	1	no	—
452	#97	—	68	1	no	—
453	C₄×C₈	—	68	1	no	—
454	#95	C₂×Dic₁₇	1	1	yes	characteristic
455	#95	C₂×Dic₁₇	1	1	yes	characteristic
456	#95	C₂×Dic₁₇	1	1	yes	characteristic
457	#95	C₂×Dic₁₇	1	1	yes	characteristic
458	#95	C₂×Dic₁₇	1	1	yes	characteristic
459	#95	C₂×Dic₁₇	1	1	yes	characteristic
460	#95	C₂×Dic₁₇	1	1	yes	characteristic
461	#95	C₂×Dic₁₇	1	1	yes	characteristic
462	C₁₇	#23349	1	1	yes	characteristic, complemented, Sylow
463	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
464	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	4	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
495	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
496	M₁₆	—	68	4	no	—
497	C₂×C₈	—	34	1	no	—
498	C₂×C₈	—	34	1	no	—
499	C₂×C₈	—	34	1	no	—
500	C₂×C₈	—	34	1	no	—
501	C₂×C₈	—	34	1	no	—
502	C₂×C₈	—	34	1	no	—
503	C₂×C₈	—	34	1	no	—
504	C₂×C₈	—	34	1	no	—
505	C₂×C₈	—	34	1	no	—
506	C₂×C₈	—	34	1	no	—
507	C₂×C₈	—	34	1	no	—
508	C₂×C₈	—	34	1	no	—
509	C₂×C₈	—	34	1	no	—
510	C₂×C₈	—	34	1	no	—
511	C₂×C₈	—	34	1	no	—
512	C₂×C₈	—	34	1	no	—
513	C₂×C₈	—	34	1	no	—
514	C₂×C₈	—	34	1	no	—
515	C₂×C₈	—	34	1	no	—
516	C₂×C₈	—	34	1	no	—
517	C₂×C₈	—	34	1	no	—
518	C₂×C₈	—	34	1	no	—
519	C₂×C₈	—	34	1	no	—
520	C₂×C₈	—	34	1	no	—
521	C₂×C₈	—	68	4	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	#63223	1	4	yes	complemented
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	4	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	C₂×#63223	1	2	yes	—
564	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
565	Q₈	—	4	4	no	—
566	D₄	—	4	4	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	C₂×#63223	1	2	yes	—
608	C₂×C₄	C₂×#63223	1	2	yes	—
609	C₂×C₄	#10587634	1	2	yes	—
610	C₂×C₄	#10587634	1	2	yes	—
611	C₂×C₄	#10587691	1	1	yes	characteristic
612	C₂×C₄	#10587691	1	1	yes	characteristic
613	C₂×C₄	#10587696	1	1	yes	characteristic
614	C₂×C₄	#10587696	1	1	yes	characteristic
615	C₂×C₄	#10587697	1	1	yes	characteristic
616	C₂×C₄	#10587697	1	1	yes	characteristic
617	C₈	—	68	1	no	—
618	C₈	—	68	1	no	—
619	C₈	—	68	1	no	—
620	C₈	—	68	1	no	—
621	C₈	—	68	1	no	—
622	C₈	—	68	1	no	—
623	C₈	—	68	1	no	—
624	C₈	—	68	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	#11763284	1	1	yes	characteristic
640	C₂²	#11763292	1	1	yes	characteristic
641	C₂²	#11763292	1	1	yes	characteristic
642	C₂²	C₂²×#63223	1	1	yes	characteristic
643	C₂²	C₂×#10587634	1	1	yes	characteristic
644	C₂²	C₂×#10587634	1	1	yes	characteristic
645	C₂²	#11763576	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	#11763551	1	1	yes	characteristic
659	C₄	#11763553	1	1	yes	characteristic
660	C₄	#11763553	1	1	yes	characteristic
661	C₄	#11763559	1	1	yes	characteristic
662	C₂	—	4	2	no	—
663	C₂	—	8	1	no	—
664	C₂	#14531958	1	1	yes	characteristic
665	C₂	#14537819	1	1	yes	characteristic
666	C₂	#14537860	1	1	yes	characteristic
667	C₂	#14537901	1	1	yes	characteristic
668	C₂	#14537909	1	1	yes	characteristic
669	C₂	#14537933	1	1	yes	characteristic
670	C₂	#14537944	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator, socle	C₂³×C₁₇	C₂³×C₄
Fitting	C₄×C₁₇×#124	C₂
prime radical	C₂²×D₄×C₁₇	C₂×C₄
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×#124	D₁₇
hypocenter	C₁₇	#23349
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. #14529725	C₂	semidirect
2. #14529721	C₂	semidirect
3. #14529399	C₂	semidirect
4. #14529399	C₂	semidirect
5. #14529392	C₂	semidirect
6. #14529392	C₂	semidirect
9. #14528969	C₂	semidirect
10. #14528969	C₂	semidirect
11. #14528964	C₂	semidirect
12. #14528964	C₂	semidirect
13. #14528901	C₂	semidirect
14. #14528901	C₂	semidirect
173. C₂²⋊C₄×C₁₇	M₁₆	semidirect
462. C₁₇	#23349	semidirect
535. C₂²⋊C₄	#63223	semidirect

Maximal subgroups

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

subgroup	index
#14529725	2
#14529721	2
#14529399	2
#14529392	2
#14529082	2
#14529077	2
#14528969	2
#14528964	2
#14528901	2
C₄×C₁₇×#124	2
#23349	17