Subgroups — #17966372

Order 4352.

666 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545706	C₂	1	2	yes	maximal
2	#14544349	C₂	1	2	yes	maximal, complemented
3	#14544348	C₂	1	2	yes	maximal, complemented
4	#14544347	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544346	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544340	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544338	C₂	1	1	yes	maximal, characteristic, complemented
8	#14544336	C₂	1	2	yes	maximal, complemented
9	#14544334	C₂	1	1	yes	maximal, characteristic, complemented
10	#14544326	C₂	1	1	yes	maximal, characteristic, complemented
11	#14537206	C₂	1	1	yes	maximal, characteristic
12	#11763861	—	2	2	no	—
13	#11763842	—	2	2	no	—
14	#11763841	—	2	2	no	—
15	#11763839	—	2	2	no	—
16	#11763831	C₂²	1	2	yes	—
17	#11763830	C₂²	1	2	yes	—
18	#11763828	C₂²	1	2	yes	—
19	#11763813	C₂²	1	2	yes	—
20	#11763812	C₂²	1	2	yes	—
21	#11763810	C₂²	1	2	yes	—
22	#11763673	C₂²	1	2	yes	—
23	#11763672	C₂²	1	2	yes	—
24	#11763672	C₂²	1	2	yes	—
25	#11763671	C₂²	1	1	yes	characteristic
26	#11763671	C₂²	1	1	yes	characteristic
27	#11763671	C₂²	1	1	yes	characteristic
28	#11763671	C₂²	1	1	yes	characteristic
29	#11763671	C₂²	1	2	yes	—
30	#11763670	C₂²	1	2	yes	—
31	#11763670	C₂²	1	2	yes	—
32	C₂×#10587593	C₄	1	1	yes	characteristic
33	C₂×#10587587	C₄	1	1	yes	characteristic
34	#11763277	C₂²	1	1	yes	characteristic
35	#11762766	C₄	1	1	yes	characteristic
36	#11762766	C₄	1	1	yes	characteristic
37	#11762765	C₄	1	1	yes	characteristic
38	#11762763	C₄	1	1	yes	characteristic
39	#11762763	C₄	1	1	yes	characteristic
40	#11762761	C₂²	1	1	yes	characteristic
41	#11762761	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
46	C₁₇×#405	C₄	1	1	yes	characteristic
47	C₂×#63252	C₂×C₄	1	1	yes	characteristic
48	C₂×#63247	—	2	2	no	—
49	C₂×#63243	—	2	2	no	—
50	C₂×#63242	—	2	2	no	—
51	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
55	C₂×#63223	C₂×C₄	1	1	yes	characteristic
56	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
57	#10587593	—	2	4	no	—
58	#10587587	—	2	4	no	—
59	C₂×#63218	C₂×C₄	1	1	yes	characteristic
60	C₂×#63218	C₂×C₄	1	1	yes	characteristic
61	C₂×#63218	C₂×C₄	1	1	yes	characteristic
62	C₂×#63218	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
67	#10587579	D₄	1	1	yes	characteristic
68	#10587579	Q₈	1	1	yes	characteristic
69	#10587573	D₄	1	1	yes	characteristic
70	#10587573	Q₈	1	1	yes	characteristic
71	#10587567	D₄	1	1	yes	characteristic
72	#10587567	D₄	1	1	yes	characteristic
73	#10587567	Q₈	1	1	yes	characteristic
74	#10587567	Q₈	1	1	yes	characteristic
75	#10587558	C₂×C₄	1	1	yes	characteristic
76	#10587558	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₇	C₂³	1	1	yes	characteristic
78	C₄²×D₁₇	C₂³	1	1	yes	characteristic
79	C₂²⋊#3624	—	2	2	no	—
80	#10587544	—	2	2	no	—
81	#10587544	—	2	2	no	—
82	#10587543	—	2	2	no	—
83	#10587543	—	2	2	no	—
84	#10587542	—	2	2	no	—
85	#10587542	—	2	2	no	—
86	C₄⋊#3624	—	2	2	no	—
87	C₄⋊#3624	C₂³	1	2	yes	—
88	C₄⋊#3624	C₂³	1	2	yes	—
89	C₄⋊#3624	C₂³	1	2	yes	—
90	C₄⋊#3624	C₂³	1	2	yes	—
91	C₄×#3624	—	2	2	no	—
92	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
93	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
96	#10587486	C₂×C₄	1	1	yes	characteristic
97	#10587486	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	#10587474	C₂×C₄	1	1	yes	characteristic
105	#10587474	C₂×C₄	1	1	yes	characteristic
106	C₄×#3622	C₂×C₄	1	1	yes	characteristic
107	C₄×#3622	C₂×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×Q₈	1	1	yes	characteristic
113	#63252	—	2	2	no	—
114	#63252	—	2	2	no	—
115	C₂×D₆₈	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
122	C₂×Dic₃₄	C₄⋊C₄	1	1	yes	characteristic
123	#63247	—	8	2	no	—
124	C₂×#3624	—	2	2	no	—
125	C₂×#3624	—	2	2	no	—
126	C₂×#3624	—	2	2	no	—
127	C₂×#3624	—	2	2	no	—
128	#63243	—	8	2	no	—
129	#63242	—	8	2	no	—
130	M₁₆×C₁₇	—	2	2	no	—
131	C₂×C₈×C₁₇	—	2	2	no	—
132	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
140	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
142	#63227	C₄⋊C₄	1	1	yes	characteristic
143	#63227	C₄⋊C₄	1	1	yes	characteristic
144	#63227	C₄⋊C₄	1	1	yes	characteristic
145	#63227	C₄⋊C₄	1	1	yes	characteristic
146	#63225	C₄⋊C₄	1	1	yes	characteristic
147	#63225	C₄⋊C₄	1	1	yes	characteristic
148	#63225	C₄⋊C₄	1	1	yes	characteristic
149	#63225	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
158	#63223	—	2	2	no	—
159	C₂×#3622	—	2	2	no	—
160	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
161	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
162	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
163	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
164	#63218	—	2	2	no	—
165	#63218	—	2	2	no	—
166	#63218	—	2	2	no	—
167	#63218	M₁₆	1	4	yes	complemented
168	C₈×D₁₇	—	2	2	no	—
169	C₈×D₁₇	—	2	2	no	—
170	C₈×D₁₇	—	2	2	no	—
171	C₈×D₁₇	M₁₆	1	4	yes	complemented
172	#17798	—	17	1	no	maximal, Sylow
173	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	—	2	1	no	—
177	C₂×C₄×C₁₇	—	2	1	no	—
178	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
184	C₂²⋊D₁₇	—	2	2	no	—
185	C₂²⋊D₁₇	—	2	2	no	—
186	C₂×Dic₁₇	—	2	2	no	—
187	C₂×Dic₁₇	—	4	1	no	—
188	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₁₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
194	D₆₈	—	2	2	no	—
195	C₄×D₁₇	—	2	1	no	—
196	C₄×D₁₇	—	2	1	no	—
197	C₄×D₁₇	—	2	2	no	—
198	C₄×D₁₇	—	2	2	no	—
199	C₄×D₁₇	—	4	1	no	—
200	C₄×D₁₇	—	4	1	no	—
201	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
202	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
203	Dic₃₄	—	2	2	no	—
204	#3624	—	4	2	no	—
205	#3624	—	4	2	no	—
206	#3624	—	4	2	no	—
207	#3624	—	4	2	no	—
208	C₈×C₁₇	—	2	1	no	—
209	C₈×C₁₇	—	2	1	no	—
210	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
211	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
212	#3622	—	2	1	no	—
213	#3622	—	2	1	no	—
214	#3622	C₂×M₁₆	1	2	yes	—
215	#3622	C₂×M₁₆	1	2	yes	—
216	#2989	—	17	2	no	—
217	C₄×#131	—	17	1	no	—
218	#1569	—	17	2	no	—
219	#1569	—	17	2	no	—
220	#1568	—	17	1	no	—
221	#1568	—	17	1	no	—
222	#1566	—	17	1	no	—
223	#1566	—	17	1	no	—
224	#1565	—	17	2	no	—
225	#1564	—	17	1	no	—
226	C₂×#334	—	17	1	no	—
227	C₂²×C₁₇	—	2	1	no	—
228	C₂²×C₁₇	—	2	1	no	—
229	C₂²×C₁₇	—	2	1	no	—
230	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
231	C₂×D₁₇	—	2	1	no	—
232	C₂×D₁₇	—	2	1	no	—
233	C₂×D₁₇	—	2	1	no	—
234	C₂×D₁₇	—	2	1	no	—
235	C₂×D₁₇	—	2	1	no	—
236	C₂×D₁₇	#423	1	2	yes	—
237	C₄×C₁₇	—	2	1	no	—
238	C₄×C₁₇	—	2	1	no	—
239	C₄×C₁₇	—	2	1	no	—
240	C₄×C₁₇	—	2	1	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
243	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
244	Dic₁₇	—	2	1	no	—
245	Dic₁₇	—	2	1	no	—
246	Dic₁₇	—	2	1	no	—
247	Dic₁₇	—	2	1	no	—
248	Dic₁₇	#423	1	2	yes	—
249	Dic₁₇	#577	1	2	yes	—
250	C₂×#131	—	17	1	no	—
251	C₂×#131	—	17	1	no	—
252	C₄×#41	—	17	1	no	—
253	#446	—	34	2	no	—
254	#436	—	34	2	no	—
255	#435	—	34	2	no	—
256	#435	—	34	2	no	—
257	#432	—	17	2	no	—
258	#432	—	17	2	no	—
259	#431	—	17	2	no	—
260	#423	—	17	2	no	—
261	#423	—	17	2	no	—
262	C₂×C₄⋊C₈	—	17	2	no	—
263	#405	—	17	1	no	—
264	#405	—	17	1	no	—
265	#405	—	17	1	no	—
266	#405	—	17	1	no	—
267	#405	—	17	1	no	—
268	#405	#595	1	1	yes	characteristic
269	C₄×M₁₆	—	17	1	no	—
270	C₄×M₁₆	—	17	1	no	—
271	C₄×M₁₆	—	17	1	no	—
272	C₂×C₄×C₈	—	17	1	no	—
273	C₂×C₄×C₈	—	17	1	no	—
274	C₂×C₄×C₈	—	17	1	no	—
275	#335	—	17	2	no	—
276	#335	—	17	2	no	—
277	#335	—	17	2	no	—
278	#334	—	17	1	no	—
279	#334	—	17	1	no	—
280	#334	—	17	2	no	—
281	#334	—	17	1	no	—
282	#334	—	17	1	no	—
283	#334	—	17	2	no	—
284	#334	—	17	2	no	—
285	C₂×C₁₇	—	4	1	no	—
286	C₂×C₁₇	C₂×#423	1	1	yes	characteristic
287	C₂×C₁₇	#2912	1	1	yes	characteristic
288	C₂×C₁₇	#2916	1	1	yes	characteristic
289	D₁₇	—	2	2	no	—
290	D₁₇	—	4	1	no	—
291	C₂×#41	—	17	1	no	—
292	#131	—	34	4	no	—
293	#131	—	34	4	no	—
294	C₂×M₁₆	—	17	1	no	—
295	C₂×M₁₆	—	17	1	no	—
296	C₂×M₁₆	—	17	1	no	—
297	C₂×M₁₆	—	17	1	no	—
298	C₂×M₁₆	—	17	1	no	—
299	C₂×M₁₆	—	34	2	no	—
300	C₂×M₁₆	—	34	2	no	—
301	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
302	C₂²×C₈	—	17	1	no	—
303	C₂²×C₈	—	17	1	no	—
304	C₂²×C₈	—	17	1	no	—
305	C₂²×C₈	—	17	1	no	—
306	C₂²×C₈	—	17	1	no	—
307	C₂²×C₈	—	34	2	no	—
308	C₂²×C₈	C₂×#595	1	1	yes	characteristic
309	C₄×Q₈	—	17	1	no	—
310	C₄×Q₈	—	17	1	no	—
311	C₄×D₄	—	17	1	no	—
312	C₄×D₄	—	17	1	no	—
313	C₄×D₄	—	17	1	no	—
314	C₄×D₄	—	17	1	no	—
315	C₄×D₄	—	17	1	no	—
316	C₄×D₄	—	17	1	no	—
317	#117	—	17	1	no	—
318	#117	—	17	1	no	—
319	#117	C₂×#595	1	1	yes	characteristic
320	C₂×C₄²	—	17	1	no	—
321	C₂×C₄²	—	17	1	no	—
322	C₂×C₄²	—	17	1	no	—
323	C₄⋊C₈	—	17	2	no	—
324	C₄⋊C₈	—	17	2	no	—
325	C₄⋊C₈	—	17	2	no	—
326	C₄⋊C₈	—	17	2	no	—
327	C₄⋊C₈	—	34	2	no	—
328	C₄⋊C₈	—	34	2	no	—
329	C₄⋊C₈	—	34	2	no	—
330	C₂²⋊C₈	—	34	2	no	—
331	C₂²⋊C₈	—	34	2	no	—
332	C₂²⋊C₈	—	34	2	no	—
333	#97	—	17	1	no	—
334	#97	—	17	1	no	—
335	#97	—	17	1	no	—
336	#97	—	17	1	no	—
337	#97	—	34	2	no	—
338	#97	—	34	2	no	—
339	#97	C₂×#595	1	1	yes	characteristic
340	#97	C₂×#595	1	1	yes	characteristic
341	C₄×C₈	—	17	1	no	—
342	C₄×C₈	—	17	1	no	—
343	C₄×C₈	—	17	1	no	—
344	C₄×C₈	—	17	1	no	—
345	C₄×C₈	—	17	1	no	—
346	C₄×C₈	—	17	1	no	—
347	C₄×C₈	—	17	1	no	—
348	C₄×C₈	—	17	1	no	—
349	C₄×C₈	—	34	2	no	—
350	C₄×C₈	C₂×#595	1	1	yes	characteristic
351	C₄×C₈	C₂×#595	1	1	yes	characteristic
352	C₁₇	#17798	1	1	yes	characteristic, complemented, Sylow
353	#41	—	34	2	no	—
354	#41	—	34	2	no	—
355	C₂×Q₈	—	17	1	no	—
356	C₂×D₄	—	17	1	no	—
357	C₂×D₄	—	17	1	no	—
358	C₂×D₄	—	17	1	no	—
359	C₂²×C₄	—	17	1	no	—
360	C₂²×C₄	—	17	1	no	—
361	C₂²×C₄	—	17	1	no	—
362	C₂²×C₄	—	17	1	no	—
363	C₂²×C₄	—	17	1	no	—
364	C₂²×C₄	—	17	1	no	—
365	C₂²×C₄	—	17	1	no	—
366	C₂²×C₄	—	17	1	no	—
367	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	17	4	no	—
370	M₁₆	—	34	2	no	—
371	M₁₆	—	34	2	no	—
372	M₁₆	—	34	2	no	—
373	M₁₆	—	34	2	no	—
374	M₁₆	—	136	2	no	—
375	M₁₆	—	136	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	17	1	no	—
378	C₂×C₈	—	17	1	no	—
379	C₂×C₈	—	17	4	no	—
380	C₂×C₈	—	17	1	no	—
381	C₂×C₈	—	17	1	no	—
382	C₂×C₈	—	34	2	no	—
383	C₂×C₈	—	34	2	no	—
384	C₂×C₈	—	34	2	no	—
385	C₂×C₈	—	34	2	no	—
386	C₂×C₈	—	34	2	no	—
387	C₂×C₈	—	34	2	no	—
388	C₂×C₈	—	34	2	no	—
389	C₂×C₈	—	34	2	no	—
390	C₂×C₈	—	136	2	no	—
391	C₂×C₈	C₂²×#595	1	1	yes	characteristic
392	C₂×C₈	C₂²×#595	1	1	yes	characteristic
393	C₂×C₈	C₂²×#595	1	1	yes	characteristic
394	C₂×C₈	C₂²×#595	1	1	yes	characteristic
395	C₄⋊C₄	—	17	1	no	—
396	C₄⋊C₄	—	17	1	no	—
397	C₄⋊C₄	—	17	1	no	—
398	C₄⋊C₄	—	17	1	no	—
399	C₄⋊C₄	C₄⋊#595	1	1	yes	characteristic
400	C₄⋊C₄	C₄⋊#595	1	1	yes	characteristic
401	C₂²⋊C₄	—	17	1	no	—
402	C₂²⋊C₄	—	17	1	no	—
403	C₂²⋊C₄	—	17	1	no	—
404	C₂²⋊C₄	—	17	1	no	—
405	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
406	C₂²⋊C₄	C₄⋊#595	1	1	yes	characteristic
407	C₄²	—	17	1	no	—
408	C₄²	—	17	1	no	—
409	C₄²	—	17	1	no	—
410	C₄²	—	17	1	no	—
411	C₄²	—	17	1	no	—
412	C₄²	—	17	1	no	—
413	C₄²	—	17	1	no	—
414	C₄²	—	17	1	no	—
415	C₄²	C₂²×#595	1	1	yes	characteristic
416	C₄²	C₂²×#595	1	1	yes	characteristic
417	C₂³	—	17	1	no	—
418	C₂³	—	17	1	no	—
419	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
420	Q₈	—	34	2	no	—
421	D₄	—	34	2	no	—
422	D₄	—	34	2	no	—
423	D₄	—	34	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	17	1	no	—
427	C₂×C₄	—	17	1	no	—
428	C₂×C₄	—	17	2	no	—
429	C₂×C₄	—	17	2	no	—
430	C₂×C₄	—	17	1	no	—
431	C₂×C₄	—	17	1	no	—
432	C₂×C₄	—	17	1	no	—
433	C₂×C₄	—	17	1	no	—
434	C₂×C₄	—	34	2	no	—
435	C₂×C₄	—	34	2	no	—
436	C₂×C₄	—	34	2	no	—
437	C₂×C₄	—	34	1	no	—
438	C₂×C₄	—	34	1	no	—
439	C₂×C₄	—	68	1	no	—
440	C₂×C₄	—	68	1	no	—
441	C₂×C₄	—	68	1	no	—
442	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
447	C₂×C₄	C₂³×#595	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	17	2	no	—
451	C₈	—	17	2	no	—
452	C₈	—	34	1	no	—
453	C₈	—	34	1	no	—
454	C₈	—	68	2	no	—
455	C₈	—	68	2	no	—
456	C₈	—	68	2	no	—
457	C₈	—	68	2	no	—
458	C₈	D₁₇⋊M₁₆	1	2	yes	—
459	C₈	D₁₇⋊M₁₆	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	17	2	no	—
464	C₂²	—	34	1	no	—
465	C₂²	—	34	1	no	—
466	C₂²	—	34	1	no	—
467	C₂²	—	34	1	no	—
468	C₂²	—	34	1	no	—
469	C₂²	C₂²×C₄⋊#595	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	17	2	no	—
476	C₄	—	17	2	no	—
477	C₄	—	34	1	no	—
478	C₄	—	34	1	no	—
479	C₄	—	34	1	no	—
480	C₄	—	34	1	no	—
481	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
483	C₂	—	4	1	no	—
484	C₂	—	34	2	no	—
485	C₂	—	68	1	no	—
486	C₂	D₁₇⋊#423	1	1	yes	characteristic
487	C₂	#14545438	1	1	yes	characteristic
488	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	C₁₇×#405	C₄
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#17798
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #14544349	C₂	semidirect
3. #14544348	C₂	semidirect
4. #14544347	C₂	semidirect
5. #14544346	C₂	semidirect
6. #14544340	C₂	semidirect
7. #14544338	C₂	semidirect
8. #14544336	C₂	semidirect
9. #14544334	C₂	semidirect
10. #14544326	C₂	semidirect
167. #63218	M₁₆	semidirect
171. C₈×D₁₇	M₁₆	semidirect
352. C₁₇	#17798	semidirect

Maximal subgroups

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

subgroup	index
#14545706	2
#14544349	2
#14544348	2
#14544347	2
#14544346	2
#14544340	2
#14544338	2
#14544336	2
#14544334	2
#14544326	2
#14537206	2
#17798	17