Subgroups — #17966546

Order 4352.

616 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545709	C₂	1	2	yes	maximal
2	#14544360	C₂	1	2	yes	maximal, complemented
3	#14544359	C₂	1	2	yes	maximal, complemented
4	#14544358	C₂	1	2	yes	maximal, complemented
5	#14544347	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544344	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544341	C₂	1	1	yes	maximal, characteristic, complemented
8	#14544333	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11763673	C₂	1	1	yes	maximal, characteristic, complemented
10	#14544329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#63254	C₂	1	1	yes	maximal, characteristic
12	#11763861	—	2	2	no	—
13	#11763841	—	2	2	no	—
14	#11763840	—	2	2	no	—
15	#11763836	—	2	2	no	—
16	#11763831	C₂²	1	2	yes	—
17	#11763830	C₂²	1	2	yes	—
18	#11763825	C₂²	1	2	yes	—
19	#11763812	C₂²	1	2	yes	—
20	#11763810	C₂²	1	2	yes	—
21	C₂×C₄⋊#3624	C₂²	1	2	yes	—
22	#11763673	C₂²	1	1	yes	characteristic
23	#11763673	C₂²	1	1	yes	characteristic
24	#11763673	C₂²	1	1	yes	characteristic
25	#11763673	C₂²	1	2	yes	—
26	#11763673	C₂²	1	1	yes	characteristic
27	#11763672	C₂²	1	2	yes	—
28	#11763672	C₂²	1	2	yes	—
29	#11763671	C₂²	1	2	yes	—
30	#11763671	C₂²	1	2	yes	—
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	Q₈	1	1	yes	characteristic
48	C₂×#63247	—	2	2	no	—
49	C₂²×#3624	—	2	2	no	—
50	C₂×#63242	—	2	2	no	—
51	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
54	D₄×Dic₁₇	D₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
59	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
60	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
63	#10587578	Q₈	1	1	yes	characteristic
64	#10587573	D₄	1	1	yes	characteristic
65	#10587567	D₄	1	1	yes	characteristic
66	#10587567	D₄	1	1	yes	characteristic
67	#10587563	Q₈	1	1	yes	characteristic
68	#10587563	Q₈	1	1	yes	characteristic
69	C₄²×D₁₇	C₂³	1	1	yes	characteristic
70	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊#3624	—	2	2	no	—
72	C₂²⋊#3624	—	2	2	no	—
73	#10587544	—	2	2	no	—
74	#10587544	—	2	2	no	—
75	#10587543	—	2	2	no	—
76	#10587542	—	2	2	no	—
77	#10587542	—	2	2	no	—
78	C₄⋊#3624	—	2	2	no	—
79	C₄⋊#3624	C₂³	1	2	yes	—
80	C₄⋊#3624	C₂³	1	2	yes	—
81	C₄⋊#3624	C₂³	1	2	yes	—
82	C₄⋊#3624	C₂³	1	2	yes	—
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	—	8	2	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	—	8	2	no	—
126	#63242	—	8	2	no	—
127	C₂×C₈×C₁₇	—	4	1	no	—
128	C₂×C₈×C₁₇	—	4	1	no	—
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	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
136	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²⋊Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
139	#63227	C₄⋊C₄	1	1	yes	characteristic
140	#63227	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₁₇	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	#63225	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₇	C₂²×C₄	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×D₄	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	C₂×Q₈	1	1	yes	characteristic
154	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
155	C₂×#3622	—	2	2	no	—
156	C₂×#3622	—	2	2	no	—
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	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
161	C₈×D₁₇	—	2	2	no	—
162	C₈×D₁₇	—	4	1	no	—
163	#17836	—	17	1	no	maximal, Sylow
164	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	D₄×C₁₇	—	2	2	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	—	2	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
177	C₂²⋊D₁₇	—	2	2	no	—
178	C₂²⋊D₁₇	#108	1	4	yes	—
179	C₂×Dic₁₇	—	2	2	no	—
180	C₂×Dic₁₇	—	2	1	no	—
181	C₂×Dic₁₇	—	2	1	no	—
182	C₂×Dic₁₇	—	2	1	no	—
183	C₂×Dic₁₇	—	2	1	no	—
184	C₂×Dic₁₇	—	2	2	no	—
185	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
192	C₄×D₁₇	—	2	2	no	—
193	C₄×D₁₇	—	2	1	no	—
194	C₄×D₁₇	—	2	1	no	—
195	C₄×D₁₇	—	2	1	no	—
196	C₄×D₁₇	—	2	1	no	—
197	Dic₃₄	—	2	2	no	—
198	#3624	—	4	2	no	—
199	#3624	—	4	2	no	—
200	#3624	—	4	2	no	—
201	#3624	—	4	2	no	—
202	C₈×C₁₇	—	2	1	no	—
203	C₈×C₁₇	—	2	1	no	—
204	C₈×C₁₇	—	2	1	no	—
205	C₈×C₁₇	—	2	1	no	—
206	#3622	—	2	1	no	—
207	#3622	—	2	1	no	—
208	#3622	—	2	1	no	—
209	#3622	#131	1	2	yes	—
210	#2990	—	17	2	no	—
211	C₈×#41	—	17	1	no	—
212	#1574	—	17	2	no	—
213	#1573	—	17	2	no	—
214	#1573	—	17	2	no	—
215	#1568	—	17	1	no	—
216	#1568	—	17	1	no	—
217	#1567	—	17	1	no	—
218	#1564	—	17	1	no	—
219	C₂×#335	—	17	1	no	—
220	C₂×#335	—	17	1	no	—
221	C₂²×C₁₇	—	2	1	no	—
222	C₂²×C₁₇	—	2	1	no	—
223	C₂²×C₁₇	—	2	1	no	—
224	C₂²×C₁₇	—	2	1	no	—
225	C₂²×C₁₇	—	2	1	no	—
226	C₂²×C₁₇	C₂×#108	1	2	yes	—
227	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂×D₁₇	—	2	1	no	—
229	C₂×D₁₇	—	2	1	no	—
230	C₂×D₁₇	C₂×#108	1	2	yes	—
231	C₄×C₁₇	—	2	1	no	—
232	C₄×C₁₇	—	2	1	no	—
233	C₄×C₁₇	—	2	1	no	—
234	C₄×C₁₇	—	2	1	no	—
235	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
236	C₄×C₁₇	#568	1	1	yes	characteristic
237	Dic₁₇	—	2	1	no	—
238	Dic₁₇	—	2	1	no	—
239	Dic₁₇	—	2	1	no	—
240	Dic₁₇	—	2	1	no	—
241	Dic₁₇	—	2	1	no	—
242	Dic₁₇	C₂×#108	1	2	yes	—
243	Dic₁₇	#576	1	1	yes	characteristic
244	Dic₁₇	#578	1	1	yes	characteristic
245	C₄×#41	—	17	1	no	—
246	#446	—	34	2	no	—
247	C₈×Q₈	—	17	1	no	—
248	C₈×Q₈	—	17	1	no	—
249	#435	—	34	2	no	—
250	#435	—	34	2	no	—
251	C₈×D₄	—	17	1	no	—
252	C₈×D₄	—	17	1	no	—
253	C₈×D₄	—	17	1	no	—
254	C₈×D₄	—	17	1	no	—
255	C₈×D₄	—	17	1	no	—
256	C₈×D₄	—	34	2	no	—
257	C₈×D₄	#595	1	1	yes	characteristic
258	#432	—	17	2	no	—
259	#432	—	17	2	no	—
260	#431	—	17	1	no	—
261	#431	—	17	1	no	—
262	#431	—	17	1	no	—
263	#431	—	17	2	no	—
264	#423	—	17	2	no	—
265	C₂×C₄⋊C₈	—	17	2	no	—
266	C₂×C₄⋊C₈	—	17	2	no	—
267	C₂×C₄×C₈	—	17	1	no	—
268	C₂×C₄×C₈	—	17	1	no	—
269	C₂×C₄×C₈	—	17	1	no	—
270	#335	—	17	1	no	—
271	#335	—	17	1	no	—
272	#335	—	17	1	no	—
273	#335	—	17	2	no	—
274	#335	—	17	2	no	—
275	#335	—	17	1	no	—
276	#335	—	17	2	no	—
277	#334	—	17	2	no	—
278	#334	—	17	2	no	—
279	#334	—	17	2	no	—
280	C₂×C₁₇	—	2	2	no	—
281	C₂×C₁₇	—	4	1	no	—
282	C₂×C₁₇	#2906	1	1	yes	characteristic
283	C₂×C₁₇	#2913	1	1	yes	characteristic
284	C₂×C₁₇	C₂²×#108	1	1	yes	characteristic
285	D₁₇	—	2	2	no	—
286	C₂×#41	—	17	1	no	—
287	C₂×M₁₆	—	34	2	no	—
288	C₂²×C₈	—	17	1	no	—
289	C₂²×C₈	—	17	1	no	—
290	C₂²×C₈	—	17	1	no	—
291	C₂²×C₈	—	17	1	no	—
292	C₂²×C₈	—	34	2	no	—
293	C₂²×C₈	—	34	2	no	—
294	C₂²×C₈	C₂×#595	1	1	yes	characteristic
295	C₂²×C₈	C₂×#595	1	1	yes	characteristic
296	C₄×Q₈	—	17	1	no	—
297	C₄×Q₈	—	17	1	no	—
298	C₄×D₄	—	17	1	no	—
299	C₄×D₄	—	17	1	no	—
300	C₄×D₄	—	17	1	no	—
301	C₄×D₄	—	17	1	no	—
302	C₄×D₄	—	17	1	no	—
303	C₄×D₄	C₂×#595	1	1	yes	characteristic
304	#117	—	17	1	no	—
305	#117	—	17	1	no	—
306	#117	—	17	1	no	—
307	C₂×C₄²	—	17	1	no	—
308	C₂×C₄²	—	17	1	no	—
309	C₂×C₄²	—	17	1	no	—
310	C₄⋊C₈	—	17	1	no	—
311	C₄⋊C₈	—	17	1	no	—
312	C₄⋊C₈	—	17	1	no	—
313	C₄⋊C₈	—	17	1	no	—
314	C₄⋊C₈	—	17	2	no	—
315	C₄⋊C₈	—	17	2	no	—
316	C₄⋊C₈	—	17	2	no	—
317	C₄⋊C₈	—	17	2	no	—
318	C₄⋊C₈	—	17	1	no	—
319	C₄⋊C₈	—	34	2	no	—
320	C₄⋊C₈	—	34	2	no	—
321	C₄⋊C₈	—	34	2	no	—
322	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
323	C₂²⋊C₈	—	17	1	no	—
324	C₂²⋊C₈	—	17	1	no	—
325	C₂²⋊C₈	—	17	1	no	—
326	C₂²⋊C₈	—	17	1	no	—
327	C₂²⋊C₈	—	34	2	no	—
328	C₂²⋊C₈	—	34	2	no	—
329	C₂²⋊C₈	—	34	2	no	—
330	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
331	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
332	#97	—	34	2	no	—
333	#97	—	34	2	no	—
334	C₄×C₈	—	17	1	no	—
335	C₄×C₈	—	17	1	no	—
336	C₄×C₈	—	17	1	no	—
337	C₄×C₈	—	17	1	no	—
338	C₄×C₈	—	17	1	no	—
339	C₄×C₈	—	17	1	no	—
340	C₄×C₈	—	17	1	no	—
341	C₄×C₈	—	17	1	no	—
342	C₄×C₈	—	17	1	no	—
343	C₄×C₈	—	34	2	no	—
344	C₄×C₈	C₂×#595	1	1	yes	characteristic
345	C₁₇	#17836	1	1	yes	characteristic, complemented, Sylow
346	#41	—	34	4	no	—
347	C₂×Q₈	—	17	1	no	—
348	C₂×D₄	—	17	1	no	—
349	C₂×D₄	—	17	1	no	—
350	C₂×D₄	C₄⋊#595	1	1	yes	characteristic
351	C₂²×C₄	—	17	1	no	—
352	C₂²×C₄	—	17	1	no	—
353	C₂²×C₄	—	17	1	no	—
354	C₂²×C₄	—	17	1	no	—
355	C₂²×C₄	—	17	1	no	—
356	C₂²×C₄	—	17	1	no	—
357	C₂²×C₄	—	17	1	no	—
358	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
359	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
360	M₁₆	—	136	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	17	1	no	—
364	C₂×C₈	—	17	1	no	—
365	C₂×C₈	—	17	1	no	—
366	C₂×C₈	—	17	1	no	—
367	C₂×C₈	—	34	2	no	—
368	C₂×C₈	—	34	2	no	—
369	C₂×C₈	—	34	2	no	—
370	C₂×C₈	—	34	2	no	—
371	C₂×C₈	—	34	2	no	—
372	C₂×C₈	—	34	2	no	—
373	C₂×C₈	—	34	2	no	—
374	C₂×C₈	—	68	1	no	—
375	C₂×C₈	—	136	2	no	—
376	C₂×C₈	—	136	2	no	—
377	C₂×C₈	C₂²×#595	1	1	yes	characteristic
378	C₂×C₈	C₂²×#595	1	1	yes	characteristic
379	C₂×C₈	C₂²×#595	1	1	yes	characteristic
380	C₂×C₈	C₂²×#595	1	1	yes	characteristic
381	C₄⋊C₄	—	17	1	no	—
382	C₄⋊C₄	—	17	1	no	—
383	C₄⋊C₄	—	17	1	no	—
384	C₄⋊C₄	—	17	1	no	—
385	C₄⋊C₄	—	17	1	no	—
386	C₄⋊C₄	C₄⋊#595	1	1	yes	characteristic
387	C₂²⋊C₄	—	17	1	no	—
388	C₂²⋊C₄	—	17	1	no	—
389	C₂²⋊C₄	—	17	1	no	—
390	C₂²⋊C₄	—	17	1	no	—
391	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
392	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
393	C₄²	—	17	1	no	—
394	C₄²	—	17	1	no	—
395	C₄²	—	17	1	no	—
396	C₄²	—	17	1	no	—
397	C₄²	—	17	1	no	—
398	C₄²	—	17	1	no	—
399	C₄²	—	17	1	no	—
400	C₄²	—	17	1	no	—
401	C₄²	—	17	1	no	—
402	C₄²	C₂²×#595	1	1	yes	characteristic
403	C₂³	—	17	1	no	—
404	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
405	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
406	Q₈	—	34	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	17	4	no	—
409	D₄	—	34	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	17	1	no	—
415	C₂×C₄	—	17	1	no	—
416	C₂×C₄	—	17	1	no	—
417	C₂×C₄	—	17	1	no	—
418	C₂×C₄	—	17	1	no	—
419	C₂×C₄	—	17	1	no	—
420	C₂×C₄	—	17	1	no	—
421	C₂×C₄	—	34	1	no	—
422	C₂×C₄	—	34	1	no	—
423	C₂×C₄	—	34	2	no	—
424	C₂×C₄	—	34	1	no	—
425	C₂×C₄	—	34	1	no	—
426	C₂×C₄	—	34	2	no	—
427	C₂×C₄	—	34	1	no	—
428	C₂×C₄	—	34	1	no	—
429	C₂×C₄	—	34	2	no	—
430	C₂×C₄	—	34	1	no	—
431	C₂×C₄	—	34	1	no	—
432	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
435	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
436	C₂×C₄	C₂³×#595	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	2	1	no	—
441	C₈	—	17	2	no	—
442	C₈	—	34	1	no	—
443	C₈	—	34	1	no	—
444	C₈	—	34	1	no	—
445	C₈	—	68	2	no	—
446	C₈	—	68	2	no	—
447	C₈	—	68	2	no	—
448	C₈	—	68	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	17	2	no	—
455	C₂²	—	34	1	no	—
456	C₂²	—	34	1	no	—
457	C₂²	D₁₇⋊#108	1	2	yes	—
458	C₂²	C₂²×C₄⋊#595	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	17	1	no	—
464	C₄	—	17	1	no	—
465	C₄	—	17	2	no	—
466	C₄	—	34	1	no	—
467	C₄	—	34	1	no	—
468	C₄	—	34	1	no	—
469	C₄	—	34	1	no	—
470	C₄	—	34	1	no	—
471	C₄	D₁₇⋊#131	1	1	yes	characteristic
472	C₄	#11763887	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	34	2	no	—
476	C₂	#14545431	1	1	yes	characteristic
477	C₂	#14545439	1	1	yes	characteristic
478	C₂	C₂×D₁₇⋊#108	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	Q₈
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	C₈×D₄	#595
hypocenter	C₁₇	#17836
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. #14544360	C₂	semidirect
3. #14544359	C₂	semidirect
4. #14544358	C₂	semidirect
5. #14544347	C₂	semidirect
6. #14544344	C₂	semidirect
7. #14544341	C₂	semidirect
8. #14544333	C₂	semidirect
9. C₂×#11763673	C₂	semidirect
10. #14544329	C₂	semidirect
345. C₁₇	#17836	semidirect

Maximal subgroups

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

subgroup	index
#14545709	2
#14544360	2
#14544359	2
#14544358	2
#14544347	2
#14544344	2
#14544341	2
#14544333	2
C₂×#11763673	2
#14544329	2
C₈×#63254	2
#17836	17