Subgroups — #17966495

Order 4352.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545479	C₂	1	2	yes	maximal
2	#14544356	C₂	1	2	yes	maximal, complemented
3	#14544355	C₂	1	2	yes	maximal, complemented
4	#14544353	C₂	1	2	yes	maximal, complemented
5	#14544347	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544346	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544338	C₂	1	1	yes	maximal, characteristic, complemented
8	#14544334	C₂	1	1	yes	maximal, characteristic, complemented
9	#14544333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11763671	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#63254	C₂	1	1	yes	maximal, characteristic
12	#11763834	—	2	2	no	—
13	#11763833	—	2	2	no	—
14	#11763831	C₂²	1	2	yes	—
15	#11763830	C₂²	1	2	yes	—
16	#11763828	C₂²	1	2	yes	—
17	#11763825	C₂²	1	2	yes	—
18	#11763812	C₂²	1	2	yes	—
19	C₂×C₄⋊#3624	C₂²	1	2	yes	—
20	#11763782	—	2	2	no	—
21	#11763773	—	2	2	no	—
22	#11763673	C₂²	1	2	yes	—
23	#11763673	C₂²	1	2	yes	—
24	#11763672	C₂²	1	2	yes	—
25	#11763672	C₂²	1	2	yes	—
26	#11763671	C₂²	1	1	yes	characteristic
27	#11763671	C₂²	1	1	yes	characteristic
28	#11763671	C₂²	1	2	yes	—
29	#11763671	C₂²	1	1	yes	characteristic
30	#11763671	C₂²	1	1	yes	characteristic
31	#11763670	C₂²	1	2	yes	—
32	C₄×#63254	C₂²	1	1	yes	characteristic
33	C₈×Dic₃₄	C₄	1	1	yes	characteristic
34	#11762933	C₄	1	1	yes	characteristic
35	D₄×#3622	C₄	1	1	yes	characteristic
36	C₈×C₂²⋊D₁₇	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₁₇	C₄	1	1	yes	characteristic
38	#11762872	C₄	1	1	yes	characteristic
39	#11762872	C₄	1	1	yes	characteristic
40	#11762861	C₂²	1	1	yes	characteristic
41	#11762859	C₂²	1	1	yes	characteristic
42	#11762859	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₁₇	C₄	1	1	yes	characteristic
47	C₂×#63254	D₄	1	1	yes	characteristic
48	C₂×#63247	—	2	2	no	—
49	C₂²×#3624	—	2	2	no	—
50	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₁₇	Q₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
58	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
59	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
62	#10587578	D₄	1	1	yes	characteristic
63	#10587573	Q₈	1	1	yes	characteristic
64	#10587567	Q₈	1	1	yes	characteristic
65	#10587567	Q₈	1	1	yes	characteristic
66	#10587563	D₄	1	1	yes	characteristic
67	#10587563	D₄	1	1	yes	characteristic
68	C₄²×D₁₇	C₂³	1	1	yes	characteristic
69	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
70	C₂²⋊#3624	—	2	2	no	—
71	C₂²⋊#3624	—	2	2	no	—
72	#10587544	—	2	2	no	—
73	#10587543	—	2	2	no	—
74	#10587543	—	2	2	no	—
75	#10587542	—	2	2	no	—
76	#10587542	—	2	2	no	—
77	C₄⋊#3624	—	2	2	no	—
78	C₄⋊#3624	C₂³	1	2	yes	—
79	C₄⋊#3624	C₂³	1	2	yes	—
80	C₄⋊#3624	C₂³	1	2	yes	—
81	C₄⋊#3624	C₂³	1	2	yes	—
82	C₄×#3624	—	2	2	no	—
83	C₄×#3624	—	2	2	no	—
84	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
90	#10587491	C₂×C₄	1	1	yes	characteristic
91	#10587491	C₂×C₄	1	1	yes	characteristic
92	#10587485	C₂×C₄	1	1	yes	characteristic
93	#10587485	C₂×C₄	1	1	yes	characteristic
94	#10587485	C₂×C₄	1	1	yes	characteristic
95	#10587485	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
101	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
102	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
103	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
104	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
105	C₄×#3622	C₂×C₄	1	1	yes	characteristic
106	C₂×D₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
115	#63254	—	2	4	no	—
116	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
119	C₂×Dic₃₄	C₄⋊C₄	1	1	yes	characteristic
120	#63247	—	4	4	no	—
121	C₂×#3624	—	2	2	no	—
122	C₂×#3624	—	2	2	no	—
123	C₂×#3624	—	2	2	no	—
124	C₂×#3624	—	2	2	no	—
125	C₂×#3624	—	4	4	no	—
126	C₂×C₈×C₁₇	—	4	1	no	—
127	C₂×C₈×C₁₇	—	4	1	no	—
128	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
135	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²⋊Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
138	#63227	C₄⋊C₄	1	1	yes	characteristic
139	#63227	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
141	#63225	C₄⋊C₄	1	1	yes	characteristic
142	#63225	C₄⋊C₄	1	1	yes	characteristic
143	#63225	C₄⋊C₄	1	1	yes	characteristic
144	#63225	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
151	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
152	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
153	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
154	C₂×#3622	—	2	2	no	—
155	C₂×#3622	—	2	2	no	—
156	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
157	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
158	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
159	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
160	C₈×D₁₇	—	2	2	no	—
161	C₈×D₁₇	—	4	1	no	—
162	#17827	—	17	1	no	maximal, Sylow
163	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	D₄×C₁₇	—	2	2	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	1	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
176	C₂²⋊D₁₇	—	2	2	no	—
177	C₂²⋊D₁₇	—	2	2	no	—
178	C₂×Dic₁₇	—	2	2	no	—
179	C₂×Dic₁₇	—	4	1	no	—
180	C₂×Dic₁₇	—	4	1	no	—
181	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₇	#135	1	4	yes	—
187	C₂×Dic₁₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
189	C₄×D₁₇	—	2	1	no	—
190	C₄×D₁₇	—	2	1	no	—
191	C₄×D₁₇	—	2	2	no	—
192	C₄×D₁₇	—	4	1	no	—
193	Dic₃₄	—	2	2	no	—
194	#3624	—	4	2	no	—
195	#3624	—	4	2	no	—
196	#3624	—	4	2	no	—
197	#3624	—	4	2	no	—
198	C₈×C₁₇	—	2	1	no	—
199	C₈×C₁₇	—	2	1	no	—
200	C₈×C₁₇	—	2	1	no	—
201	C₈×C₁₇	—	2	1	no	—
202	#3622	—	2	1	no	—
203	#3622	—	2	1	no	—
204	#3622	—	2	1	no	—
205	#3622	#131	1	2	yes	—
206	C₈×#41	—	17	1	no	—
207	#2925	—	17	2	no	—
208	#1572	—	17	2	no	—
209	#1572	—	17	2	no	—
210	#1571	—	17	2	no	—
211	#1568	—	17	1	no	—
212	#1568	—	17	1	no	—
213	#1566	—	17	1	no	—
214	#1564	—	17	1	no	—
215	#1564	—	17	1	no	—
216	C₂×#334	—	17	1	no	—
217	C₂²×C₁₇	—	2	1	no	—
218	C₂²×C₁₇	—	2	1	no	—
219	C₂²×C₁₇	—	2	1	no	—
220	C₂²×C₁₇	—	2	1	no	—
221	C₂²×C₁₇	—	2	1	no	—
222	C₂²×C₁₇	#427	1	2	yes	—
223	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₂×D₁₇	—	2	1	no	—
225	C₂×D₁₇	—	2	1	no	—
226	C₂×D₁₇	—	2	1	no	—
227	C₄×C₁₇	—	2	1	no	—
228	C₄×C₁₇	—	2	1	no	—
229	C₄×C₁₇	—	2	1	no	—
230	C₄×C₁₇	—	2	1	no	—
231	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
232	C₄×C₁₇	#568	1	1	yes	characteristic
233	Dic₁₇	—	2	1	no	—
234	Dic₁₇	—	2	1	no	—
235	Dic₁₇	—	2	1	no	—
236	Dic₁₇	—	2	1	no	—
237	Dic₁₇	—	2	1	no	—
238	Dic₁₇	#427	1	2	yes	—
239	Dic₁₇	C₂×#135	1	2	yes	—
240	C₄×#41	—	17	1	no	—
241	C₈×Q₈	—	17	1	no	—
242	C₈×Q₈	—	17	1	no	—
243	C₈×D₄	—	17	1	no	—
244	C₈×D₄	—	17	1	no	—
245	C₈×D₄	—	17	1	no	—
246	C₈×D₄	—	17	1	no	—
247	C₈×D₄	—	17	1	no	—
248	C₈×D₄	#595	1	1	yes	characteristic
249	#433	—	34	2	no	—
250	#433	—	34	2	no	—
251	#432	—	17	2	no	—
252	#432	—	17	2	no	—
253	#431	—	17	1	no	—
254	#431	—	17	1	no	—
255	#431	—	17	1	no	—
256	#431	—	17	2	no	—
257	#431	—	17	2	no	—
258	#423	—	17	2	no	—
259	C₂×C₄⋊C₈	—	17	2	no	—
260	#408	—	34	2	no	—
261	#405	—	34	2	no	—
262	C₂×C₄×C₈	—	17	1	no	—
263	C₂×C₄×C₈	—	17	1	no	—
264	C₂×C₄×C₈	—	17	1	no	—
265	#335	—	17	2	no	—
266	#335	—	17	2	no	—
267	#335	—	17	2	no	—
268	#335	—	17	2	no	—
269	#334	—	17	1	no	—
270	#334	—	17	1	no	—
271	#334	—	17	2	no	—
272	#334	—	17	1	no	—
273	#334	—	17	1	no	—
274	#334	—	17	2	no	—
275	C₂×C₁₇	—	2	2	no	—
276	C₂×C₁₇	—	4	1	no	—
277	C₂×C₁₇	#2906	1	1	yes	characteristic
278	C₂×C₁₇	C₂×#427	1	1	yes	characteristic
279	C₂×C₁₇	#2916	1	1	yes	characteristic
280	D₁₇	—	4	1	no	—
281	C₂×#41	—	17	1	no	—
282	C₂×M₁₆	—	34	2	no	—
283	C₂²×C₈	—	17	1	no	—
284	C₂²×C₈	—	17	1	no	—
285	C₂²×C₈	—	17	1	no	—
286	C₂²×C₈	—	17	1	no	—
287	C₂²×C₈	—	34	2	no	—
288	C₂²×C₈	C₂×#595	1	1	yes	characteristic
289	C₂²×C₈	C₂×#595	1	1	yes	characteristic
290	C₄×Q₈	—	17	1	no	—
291	C₄×Q₈	—	17	1	no	—
292	C₄×D₄	—	17	1	no	—
293	C₄×D₄	—	17	1	no	—
294	C₄×D₄	—	17	1	no	—
295	C₄×D₄	—	17	1	no	—
296	C₄×D₄	—	17	1	no	—
297	C₄×D₄	C₂×#595	1	1	yes	characteristic
298	#117	—	17	1	no	—
299	#117	—	17	1	no	—
300	#117	—	17	1	no	—
301	C₂×C₄²	—	17	1	no	—
302	C₂×C₄²	—	17	1	no	—
303	C₂×C₄²	—	17	1	no	—
304	C₄⋊C₈	—	17	1	no	—
305	C₄⋊C₈	—	17	1	no	—
306	C₄⋊C₈	—	17	1	no	—
307	C₄⋊C₈	—	17	1	no	—
308	C₄⋊C₈	—	17	2	no	—
309	C₄⋊C₈	—	17	2	no	—
310	C₄⋊C₈	—	17	2	no	—
311	C₄⋊C₈	—	17	2	no	—
312	C₄⋊C₈	—	17	1	no	—
313	C₄⋊C₈	—	34	2	no	—
314	C₄⋊C₈	—	34	2	no	—
315	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
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	—	34	2	no	—
321	C₂²⋊C₈	—	34	2	no	—
322	C₂²⋊C₈	—	34	2	no	—
323	C₂²⋊C₈	—	34	2	no	—
324	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
325	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
326	#97	—	34	2	no	—
327	#97	—	34	2	no	—
328	C₄×C₈	—	17	1	no	—
329	C₄×C₈	—	17	1	no	—
330	C₄×C₈	—	17	1	no	—
331	C₄×C₈	—	17	1	no	—
332	C₄×C₈	—	17	1	no	—
333	C₄×C₈	—	17	1	no	—
334	C₄×C₈	—	17	1	no	—
335	C₄×C₈	—	17	1	no	—
336	C₄×C₈	—	17	1	no	—
337	C₄×C₈	—	34	2	no	—
338	C₄×C₈	—	34	2	no	—
339	C₄×C₈	C₂×#595	1	1	yes	characteristic
340	C₁₇	#17827	1	1	yes	characteristic, complemented, Sylow
341	#41	—	34	4	no	—
342	C₂×Q₈	—	17	1	no	—
343	C₂×D₄	—	17	1	no	—
344	C₂×D₄	—	17	1	no	—
345	C₂×D₄	C₄⋊#595	1	1	yes	characteristic
346	C₂²×C₄	—	17	1	no	—
347	C₂²×C₄	—	17	1	no	—
348	C₂²×C₄	—	17	1	no	—
349	C₂²×C₄	—	17	1	no	—
350	C₂²×C₄	—	17	1	no	—
351	C₂²×C₄	—	17	1	no	—
352	C₂²×C₄	—	17	1	no	—
353	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
355	M₁₆	—	68	4	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	17	1	no	—
359	C₂×C₈	—	17	1	no	—
360	C₂×C₈	—	17	1	no	—
361	C₂×C₈	—	17	1	no	—
362	C₂×C₈	—	34	2	no	—
363	C₂×C₈	—	34	2	no	—
364	C₂×C₈	—	34	2	no	—
365	C₂×C₈	—	34	2	no	—
366	C₂×C₈	—	34	2	no	—
367	C₂×C₈	—	34	2	no	—
368	C₂×C₈	—	34	2	no	—
369	C₂×C₈	—	68	1	no	—
370	C₂×C₈	—	68	4	no	—
371	C₂×C₈	C₂²×#595	1	1	yes	characteristic
372	C₂×C₈	C₂²×#595	1	1	yes	characteristic
373	C₂×C₈	C₂²×#595	1	1	yes	characteristic
374	C₂×C₈	C₂²×#595	1	1	yes	characteristic
375	C₄⋊C₄	—	17	1	no	—
376	C₄⋊C₄	—	17	1	no	—
377	C₄⋊C₄	—	17	1	no	—
378	C₄⋊C₄	—	17	1	no	—
379	C₄⋊C₄	—	17	1	no	—
380	C₄⋊C₄	C₄⋊#595	1	1	yes	characteristic
381	C₂²⋊C₄	—	17	1	no	—
382	C₂²⋊C₄	—	17	1	no	—
383	C₂²⋊C₄	—	17	1	no	—
384	C₂²⋊C₄	—	17	1	no	—
385	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
386	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
387	C₄²	—	17	1	no	—
388	C₄²	—	17	1	no	—
389	C₄²	—	17	1	no	—
390	C₄²	—	17	1	no	—
391	C₄²	—	17	1	no	—
392	C₄²	—	17	1	no	—
393	C₄²	—	17	1	no	—
394	C₄²	—	17	1	no	—
395	C₄²	—	17	1	no	—
396	C₄²	C₂²×#595	1	1	yes	characteristic
397	C₂³	—	17	1	no	—
398	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
399	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
400	Q₈	—	34	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	34	2	no	—
403	D₄	—	34	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	17	4	no	—
409	C₂×C₄	—	17	1	no	—
410	C₂×C₄	—	17	1	no	—
411	C₂×C₄	—	17	1	no	—
412	C₂×C₄	—	17	1	no	—
413	C₂×C₄	—	17	1	no	—
414	C₂×C₄	—	17	1	no	—
415	C₂×C₄	—	17	1	no	—
416	C₂×C₄	—	34	2	no	—
417	C₂×C₄	—	34	2	no	—
418	C₂×C₄	—	34	1	no	—
419	C₂×C₄	—	34	1	no	—
420	C₂×C₄	—	68	1	no	—
421	C₂×C₄	—	68	1	no	—
422	C₂×C₄	—	68	1	no	—
423	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
427	C₂×C₄	C₂³×#595	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	17	2	no	—
433	C₈	—	34	1	no	—
434	C₈	—	34	1	no	—
435	C₈	—	34	1	no	—
436	C₈	—	68	2	no	—
437	C₈	—	68	2	no	—
438	C₈	—	68	2	no	—
439	C₈	—	68	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	34	1	no	—
446	C₂²	—	34	1	no	—
447	C₂²	—	34	1	no	—
448	C₂²	#11763819	1	2	yes	—
449	C₂²	C₂²×C₄⋊#595	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	17	2	no	—
455	C₄	—	17	2	no	—
456	C₄	—	34	1	no	—
457	C₄	—	34	1	no	—
458	C₄	—	34	1	no	—
459	C₄	—	34	1	no	—
460	C₄	—	34	1	no	—
461	C₄	D₁₇⋊#131	1	1	yes	characteristic
462	C₄	#11763887	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	1	no	—
465	C₂	—	68	1	no	—
466	C₂	#14545431	1	1	yes	characteristic
467	C₂	C₂×#11763819	1	1	yes	characteristic
468	C₂	#14545446	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×#595
Fitting	C₈×D₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂×#63254	D₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	C₈×D₄	#595
hypocenter	C₁₇	#17827
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #14544356	C₂	semidirect
3. #14544355	C₂	semidirect
4. #14544353	C₂	semidirect
5. #14544347	C₂	semidirect
6. #14544346	C₂	semidirect
7. #14544338	C₂	semidirect
8. #14544334	C₂	semidirect
9. #14544333	C₂	semidirect
10. C₂×#11763671	C₂	semidirect
340. C₁₇	#17827	semidirect

Maximal subgroups

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

subgroup	index
#14545479	2
#14544356	2
#14544355	2
#14544353	2
#14544347	2
#14544346	2
#14544338	2
#14544334	2
#14544333	2
C₂×#11763671	2
C₈×#63254	2
#17827	17