Subgroups — #17978493

Order 4352.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545152	C₂	1	2	yes	maximal, complemented
2	#14545149	C₂	1	2	yes	maximal, complemented
3	#14545147	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545146	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545143	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545142	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545117	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545114	C₂	1	1	yes	maximal, characteristic, complemented
9	#14545015	C₂	1	2	yes	maximal
10	#14544994	C₂	1	2	yes	maximal, complemented
11	#14537206	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587530	C₂²	1	2	yes	—
13	C₂×#10587529	C₂²	1	2	yes	—
14	#11763730	C₂²	1	1	yes	characteristic
15	#11763730	C₂²	1	1	yes	characteristic
16	#11763730	C₂²	1	1	yes	characteristic
17	#11763730	C₂²	1	1	yes	characteristic
18	C₄⋊#63216	C₂²	1	2	yes	—
19	C₄⋊#63216	C₂²	1	2	yes	—
20	#11763704	C₂²	1	2	yes	—
21	#11763704	C₂²	1	2	yes	—
22	C₂²⋊#63216	C₂²	1	2	yes	—
23	C₂²⋊#63216	C₂²	1	2	yes	—
24	#11763698	C₂²	1	2	yes	—
25	#11763697	C₂²	1	2	yes	—
26	#11763695	C₂²	1	2	yes	—
27	C₄×#63216	C₂²	1	2	yes	—
28	C₂×#10587593	C₂²	1	1	yes	characteristic
29	C₂×#10587587	C₄	1	1	yes	characteristic
30	#11763277	C₄	1	1	yes	characteristic
31	#11762766	C₂²	1	1	yes	characteristic
32	#11762766	C₂²	1	1	yes	characteristic
33	#11762765	C₂²	1	1	yes	characteristic
34	#11762763	C₄	1	1	yes	characteristic
35	#11762763	C₄	1	1	yes	characteristic
36	#11762761	C₄	1	1	yes	characteristic
37	#11762761	C₄	1	1	yes	characteristic
38	M₁₆×Dic₁₇	C₄	1	1	yes	characteristic
39	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#405	C₄	1	1	yes	characteristic
43	C₂×#63252	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×#63223	C₂×C₄	1	1	yes	characteristic
49	C₂²×#3622	C₂³	1	1	yes	characteristic
50	#10587593	—	2	2	no	—
51	#10587593	—	2	2	no	—
52	#10587587	—	2	4	no	—
53	C₂×#63218	C₂×C₄	1	1	yes	characteristic
54	C₂×#63218	C₂×C₄	1	1	yes	characteristic
55	C₂×#63218	C₂×C₄	1	1	yes	characteristic
56	C₂×#63218	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
61	#10587579	C₈	1	1	yes	characteristic
62	#10587579	C₈	1	1	yes	characteristic
63	#10587573	C₈	1	1	yes	characteristic
64	#10587573	C₈	1	1	yes	characteristic
65	#10587567	C₈	1	1	yes	characteristic
66	#10587567	C₈	1	1	yes	characteristic
67	#10587567	C₈	1	1	yes	characteristic
68	#10587567	C₈	1	1	yes	characteristic
69	#10587558	C₂×C₄	1	1	yes	characteristic
70	#10587558	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×#63216	C₂³	1	2	yes	—
74	C₂×#63216	C₂³	1	2	yes	—
75	C₂×#63216	C₂³	1	2	yes	—
76	C₂×#63216	C₂³	1	2	yes	—
77	#10587530	—	2	4	no	—
78	#10587529	—	2	4	no	—
79	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
80	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
83	#10587486	C₂×C₄	1	1	yes	characteristic
84	#10587486	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
90	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
91	#10587474	C₂×C₄	1	1	yes	characteristic
92	#10587474	C₂×C₄	1	1	yes	characteristic
93	C₄×#3622	C₂³	1	1	yes	characteristic
94	C₄×#3622	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
98	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
100	#63252	—	2	2	no	—
101	#63252	—	2	2	no	—
102	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂×C₈	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×Dic₃₄	C₂×C₈	1	1	yes	characteristic
110	M₁₆×C₁₇	—	2	2	no	—
111	C₂×C₈×C₁₇	—	2	2	no	—
112	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
117	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
120	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
122	#63227	C₂×C₈	1	1	yes	characteristic
123	#63227	C₂×C₈	1	1	yes	characteristic
124	#63227	C₂×C₈	1	1	yes	characteristic
125	#63227	C₂×C₈	1	1	yes	characteristic
126	#63225	C₂×C₈	1	1	yes	characteristic
127	#63225	C₂×C₈	1	1	yes	characteristic
128	#63225	C₂×C₈	1	1	yes	characteristic
129	#63225	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
138	#63223	—	2	2	no	—
139	C₂×#3622	—	2	1	no	—
140	C₂×#3622	—	2	1	no	—
141	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
142	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
143	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
144	C₂×#3622	C₂⁴	1	1	yes	characteristic
145	#63218	—	2	2	no	—
146	#63218	—	2	2	no	—
147	#63218	—	2	2	no	—
148	#63218	M₁₆	1	4	yes	—
149	C₈×D₁₇	—	2	2	no	—
150	C₈×D₁₇	—	2	2	no	—
151	C₈×D₁₇	—	2	1	no	—
152	C₈×D₁₇	—	2	1	no	—
153	C₈×D₁₇	#41	1	2	yes	—
154	C₈×D₁₇	#41	1	2	yes	—
155	#63216	—	2	2	no	—
156	#63216	—	2	2	no	—
157	#63216	—	2	2	no	—
158	#63216	—	2	2	no	—
159	#33423	—	17	1	no	maximal, Sylow
160	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
162	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	—	2	1	no	—
164	C₂×C₄×C₁₇	—	2	1	no	—
165	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
171	C₂²⋊D₁₇	—	2	2	no	—
172	C₂²⋊D₁₇	—	2	2	no	—
173	C₂×Dic₁₇	—	2	2	no	—
174	C₂×Dic₁₇	—	4	1	no	—
175	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
181	D₆₈	—	2	2	no	—
182	C₄×D₁₇	—	2	1	no	—
183	C₄×D₁₇	—	2	1	no	—
184	C₄×D₁₇	—	2	2	no	—
185	C₄×D₁₇	—	2	2	no	—
186	C₄×D₁₇	—	4	1	no	—
187	C₄×D₁₇	—	4	1	no	—
188	C₄×D₁₇	#117	1	2	yes	—
189	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
190	Dic₃₄	—	2	2	no	—
191	C₈×C₁₇	—	2	1	no	—
192	C₈×C₁₇	—	2	1	no	—
193	C₈×C₁₇	#117	1	2	yes	—
194	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
195	#3622	—	2	1	no	—
196	#3622	—	2	1	no	—
197	#3622	C₂×M₁₆	1	2	yes	—
198	#3622	C₂×#41	1	1	yes	characteristic
199	#3622	C₂×#41	1	1	yes	characteristic
200	C₄×#131	—	17	1	no	—
201	#2164	—	17	2	no	—
202	#2164	—	17	2	no	—
203	#2163	—	17	1	no	—
204	#2163	—	17	1	no	—
205	#2162	—	17	1	no	—
206	#2162	—	17	1	no	—
207	#2150	—	17	1	no	—
208	C₂×C₄⋊C₁₆	—	17	1	no	—
209	#2113	—	17	2	no	—
210	#2108	—	17	2	no	—
211	C₂²×C₁₇	—	2	1	no	—
212	C₂²×C₁₇	—	2	1	no	—
213	C₂²×C₁₇	—	2	1	no	—
214	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
215	C₂×D₁₇	—	2	1	no	—
216	C₂×D₁₇	—	2	1	no	—
217	C₂×D₁₇	—	2	1	no	—
218	C₂×D₁₇	—	2	1	no	—
219	C₂×D₁₇	—	2	1	no	—
220	C₂×D₁₇	#431	1	2	yes	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	—	2	1	no	—
223	C₄×C₁₇	—	2	1	no	—
224	C₄×C₁₇	—	2	1	no	—
225	C₄×C₁₇	—	2	1	no	—
226	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
227	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
228	Dic₁₇	—	2	1	no	—
229	Dic₁₇	—	2	1	no	—
230	Dic₁₇	—	2	1	no	—
231	Dic₁₇	—	2	1	no	—
232	Dic₁₇	#431	1	2	yes	—
233	Dic₁₇	#504	1	2	yes	—
234	C₂×#131	—	17	1	no	—
235	C₂×#131	—	17	1	no	—
236	C₄×#41	—	17	1	no	—
237	C₂×M₃₂	—	17	2	no	—
238	C₂²×C₁₆	—	17	2	no	—
239	#405	—	17	1	no	—
240	#405	—	17	1	no	—
241	#405	—	17	1	no	—
242	#405	—	17	1	no	—
243	#405	—	17	1	no	—
244	#405	#595	1	1	yes	characteristic
245	C₄×M₁₆	—	17	1	no	—
246	C₄×M₁₆	—	17	1	no	—
247	C₄×M₁₆	—	17	1	no	—
248	C₂×C₄×C₈	—	17	1	no	—
249	C₂×C₄×C₈	—	17	1	no	—
250	C₂×C₄×C₈	—	17	1	no	—
251	C₄⋊C₁₆	—	17	2	no	—
252	C₄⋊C₁₆	—	17	2	no	—
253	C₄⋊C₁₆	—	17	1	no	—
254	C₄⋊C₁₆	—	17	1	no	—
255	C₄⋊C₁₆	—	17	1	no	—
256	C₄⋊C₁₆	—	17	1	no	—
257	C₂²⋊C₁₆	—	17	2	no	—
258	C₂²⋊C₁₆	—	17	2	no	—
259	C₂²⋊C₁₆	—	17	2	no	—
260	C₂²⋊C₁₆	—	17	2	no	—
261	#346	—	17	2	no	—
262	#346	—	17	2	no	—
263	C₄×C₁₆	—	17	2	no	—
264	C₄×C₁₆	—	17	2	no	—
265	C₂×C₁₇	—	4	1	no	—
266	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
267	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
268	C₂×C₁₇	#3407	1	1	yes	characteristic
269	D₁₇	—	2	2	no	—
270	D₁₇	—	4	1	no	—
271	C₂×#41	—	17	1	no	—
272	#131	—	34	4	no	—
273	#131	—	34	2	no	—
274	#131	—	34	2	no	—
275	C₂×M₁₆	—	17	1	no	—
276	C₂×M₁₆	—	17	1	no	—
277	C₂×M₁₆	—	17	1	no	—
278	C₂×M₁₆	—	17	1	no	—
279	C₂×M₁₆	—	17	1	no	—
280	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
281	C₂²×C₈	—	17	1	no	—
282	C₂²×C₈	—	17	1	no	—
283	C₂²×C₈	—	17	1	no	—
284	C₂²×C₈	—	17	1	no	—
285	C₂²×C₈	—	17	1	no	—
286	C₂²×C₈	C₂×#595	1	1	yes	characteristic
287	C₄×Q₈	—	17	1	no	—
288	C₄×Q₈	—	17	1	no	—
289	C₄×D₄	—	17	1	no	—
290	C₄×D₄	—	17	1	no	—
291	C₄×D₄	—	17	1	no	—
292	C₄×D₄	—	17	1	no	—
293	C₄×D₄	—	17	1	no	—
294	C₄×D₄	—	17	1	no	—
295	#117	—	17	1	no	—
296	#117	—	17	1	no	—
297	#117	C₂×#595	1	1	yes	characteristic
298	C₂×C₄²	—	17	1	no	—
299	C₂×C₄²	—	17	1	no	—
300	C₂×C₄²	—	17	1	no	—
301	M₃₂	—	34	4	no	—
302	C₂×C₁₆	—	17	2	no	—
303	C₂×C₁₆	—	17	2	no	—
304	C₂×C₁₆	—	17	2	no	—
305	C₂×C₁₆	—	17	2	no	—
306	C₂×C₁₆	—	34	4	no	—
307	#97	—	17	1	no	—
308	#97	—	17	1	no	—
309	#97	—	17	1	no	—
310	#97	—	17	1	no	—
311	#97	C₂×#595	1	1	yes	characteristic
312	#97	C₂×#595	1	1	yes	characteristic
313	C₄×C₈	—	17	1	no	—
314	C₄×C₈	—	17	1	no	—
315	C₄×C₈	—	17	1	no	—
316	C₄×C₈	—	17	1	no	—
317	C₄×C₈	—	17	1	no	—
318	C₄×C₈	—	17	1	no	—
319	C₄×C₈	—	17	1	no	—
320	C₄×C₈	—	17	1	no	—
321	C₄×C₈	C₂×#595	1	1	yes	characteristic
322	C₄×C₈	C₂×#595	1	1	yes	characteristic
323	C₁₇	#33423	1	1	yes	characteristic, complemented, Sylow
324	#41	—	34	2	no	—
325	#41	—	34	2	no	—
326	C₂×Q₈	—	17	1	no	—
327	C₂×D₄	—	17	1	no	—
328	C₂×D₄	—	17	1	no	—
329	C₂×D₄	—	17	1	no	—
330	C₂²×C₄	—	17	1	no	—
331	C₂²×C₄	—	17	1	no	—
332	C₂²×C₄	—	17	1	no	—
333	C₂²×C₄	—	17	1	no	—
334	C₂²×C₄	—	17	1	no	—
335	C₂²×C₄	—	17	1	no	—
336	C₂²×C₄	—	17	1	no	—
337	C₂²×C₄	—	17	1	no	—
338	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
339	M₁₆	—	2	2	no	—
340	M₁₆	—	17	4	no	—
341	M₁₆	—	34	2	no	—
342	M₁₆	—	34	2	no	—
343	M₁₆	—	34	2	no	—
344	M₁₆	—	34	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	17	2	no	—
349	C₂×C₈	—	17	2	no	—
350	C₂×C₈	—	17	1	no	—
351	C₂×C₈	—	17	1	no	—
352	C₂×C₈	—	34	1	no	—
353	C₂×C₈	—	34	1	no	—
354	C₂×C₈	—	34	2	no	—
355	C₂×C₈	—	34	2	no	—
356	C₂×C₈	—	34	1	no	—
357	C₂×C₈	—	34	1	no	—
358	C₂×C₈	C₂²×#595	1	1	yes	characteristic
359	C₂×C₈	C₂²×#595	1	1	yes	characteristic
360	C₂×C₈	C₂²×#595	1	1	yes	characteristic
361	C₂×C₈	C₂²×#595	1	1	yes	characteristic
362	C₄⋊C₄	—	17	1	no	—
363	C₄⋊C₄	—	17	1	no	—
364	C₄⋊C₄	—	17	1	no	—
365	C₄⋊C₄	—	17	1	no	—
366	C₄⋊C₄	#63242	1	1	yes	characteristic
367	C₄⋊C₄	#63242	1	1	yes	characteristic
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	#63242	1	1	yes	characteristic
373	C₂²⋊C₄	#63242	1	1	yes	characteristic
374	C₄²	—	17	1	no	—
375	C₄²	—	17	1	no	—
376	C₄²	—	17	1	no	—
377	C₄²	—	17	1	no	—
378	C₄²	—	17	1	no	—
379	C₄²	—	17	1	no	—
380	C₄²	—	17	1	no	—
381	C₄²	—	17	1	no	—
382	C₄²	C₂²×#595	1	1	yes	characteristic
383	C₄²	C₂²×#595	1	1	yes	characteristic
384	C₁₆	—	34	2	no	—
385	C₁₆	—	34	2	no	—
386	C₁₆	—	34	2	no	—
387	C₁₆	—	34	2	no	—
388	C₂³	—	17	1	no	—
389	C₂³	—	17	1	no	—
390	C₂³	C₂×#63242	1	1	yes	characteristic
391	Q₈	—	34	2	no	—
392	D₄	—	34	2	no	—
393	D₄	—	34	2	no	—
394	D₄	—	34	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	17	1	no	—
398	C₂×C₄	—	17	1	no	—
399	C₂×C₄	—	17	2	no	—
400	C₂×C₄	—	17	2	no	—
401	C₂×C₄	—	17	1	no	—
402	C₂×C₄	—	17	1	no	—
403	C₂×C₄	—	17	1	no	—
404	C₂×C₄	—	17	1	no	—
405	C₂×C₄	—	34	2	no	—
406	C₂×C₄	—	34	2	no	—
407	C₂×C₄	—	34	2	no	—
408	C₂×C₄	—	34	1	no	—
409	C₂×C₄	—	34	1	no	—
410	C₂×C₄	—	68	1	no	—
411	C₂×C₄	—	68	1	no	—
412	C₂×C₄	—	68	1	no	—
413	C₂×C₄	C₂×#63242	1	1	yes	characteristic
414	C₂×C₄	C₂×#63242	1	1	yes	characteristic
415	C₂×C₄	C₂×#63242	1	1	yes	characteristic
416	C₂×C₄	C₂×#63242	1	1	yes	characteristic
417	C₂×C₄	C₂×#63242	1	1	yes	characteristic
418	C₂×C₄	C₂³×#595	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	17	1	no	—
422	C₈	—	17	1	no	—
423	C₈	—	17	2	no	—
424	C₈	—	34	1	no	—
425	C₈	—	34	1	no	—
426	C₈	D₁₇⋊M₁₆	1	2	yes	—
427	C₈	#10587677	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	17	2	no	—
432	C₂²	—	34	1	no	—
433	C₂²	—	34	1	no	—
434	C₂²	—	34	1	no	—
435	C₂²	—	34	1	no	—
436	C₂²	—	34	1	no	—
437	C₂²	C₂²×#63242	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	17	2	no	—
444	C₄	—	17	2	no	—
445	C₄	—	34	1	no	—
446	C₄	—	34	1	no	—
447	C₄	—	34	1	no	—
448	C₄	—	34	1	no	—
449	C₄	C₂×#10587677	1	1	yes	characteristic
450	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	34	2	no	—
453	C₂	—	68	1	no	—
454	C₂	#14545448	1	1	yes	characteristic
455	C₂	#14545749	1	1	yes	characteristic
456	C₂	#14545752	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#405	C₄
prime radical	C₂×#63252	C₂×C₄
cosocle	C₂×#3622	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#33423
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
1. #14545152	C₂	semidirect
2. #14545149	C₂	semidirect
3. #14545147	C₂	semidirect
4. #14545146	C₂	semidirect
5. #14545143	C₂	semidirect
6. #14545142	C₂	semidirect
7. #14545117	C₂	semidirect
8. #14545114	C₂	semidirect
10. #14544994	C₂	semidirect
323. C₁₇	#33423	semidirect

Maximal subgroups

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

subgroup	index
#14545152	2
#14545149	2
#14545147	2
#14545146	2
#14545143	2
#14545142	2
#14545117	2
#14545114	2
#14545015	2
#14544994	2
#14537206	2
#33423	17