Subgroups — #17044759

Order 4352.

662 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537421	C₂	1	1	yes	maximal, characteristic
2	#14537420	C₂	1	1	yes	maximal, characteristic
3	C₂×#11762834	C₂	1	1	yes	maximal, characteristic
4	#14529560	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529559	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529558	C₂	1	1	yes	maximal, characteristic, complemented
7	#14529558	C₂	1	1	yes	maximal, characteristic, complemented
8	#14529557	C₂	1	1	yes	maximal, characteristic, complemented
9	#14529556	C₂	1	1	yes	maximal, characteristic, complemented
10	#14529556	C₂	1	1	yes	maximal, characteristic, complemented
11	#14528825	C₂	1	1	yes	maximal, characteristic
12	#14528823	C₂	1	1	yes	maximal, characteristic
13	#14528821	C₂	1	1	yes	maximal, characteristic
14	#14528819	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#63218	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
18	C₂×#10587558	C₂²	1	1	yes	characteristic
19	#11762871	—	2	1	no	—
20	#11762871	—	2	1	no	—
21	#11762869	—	2	1	no	—
22	#11762869	—	2	1	no	—
23	#11762869	—	2	1	no	—
24	#11762869	—	2	1	no	—
25	#11762868	—	2	1	no	—
26	#11762868	—	2	1	no	—
27	C₂×#10587490	C₂²	1	1	yes	characteristic
28	C₂×#10587490	C₂²	1	1	yes	characteristic
29	C₂×#10587493	C₂²	1	1	yes	characteristic
30	C₂×#10587493	C₂²	1	1	yes	characteristic
31	C₂×#10587493	C₂²	1	1	yes	characteristic
32	C₂×#10587493	C₂²	1	1	yes	characteristic
33	#11762834	C₄	1	2	yes	—
34	#11762834	C₄	1	2	yes	—
35	#11762834	C₄	1	2	yes	—
36	#11762834	C₄	1	2	yes	—
37	#11762833	C₂²	1	1	yes	characteristic
38	#11762832	C₂²	1	1	yes	characteristic
39	#11762832	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
41	C₂×#10587485	C₂²	1	1	yes	characteristic
42	C₂×#10587485	C₂²	1	1	yes	characteristic
43	#11762772	C₂²	1	1	yes	characteristic
44	#11762772	C₂²	1	1	yes	characteristic
45	#11762772	C₂²	1	1	yes	characteristic
46	#11762772	C₂²	1	1	yes	characteristic
47	C₄×#63223	C₂²	1	1	yes	characteristic
48	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
49	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
50	#11762574	C₂²	1	1	yes	characteristic
51	#11762574	C₂²	1	1	yes	characteristic
52	#11762573	C₂²	1	1	yes	characteristic
53	#11762573	C₂²	1	1	yes	characteristic
54	#11762573	C₂²	1	1	yes	characteristic
55	#11762573	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
57	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
58	C₁₇×#423	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
61	C₁₇×#341	C₂²	1	1	yes	characteristic
62	C₁₇×#341	C₂²	1	1	yes	characteristic
63	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×#63227	Q₈	1	1	yes	characteristic
72	C₂×#63227	Q₈	1	1	yes	characteristic
73	C₂×#63225	Q₈	1	1	yes	characteristic
74	C₂×#63225	Q₈	1	1	yes	characteristic
75	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
76	C₂×#63223	C₂³	1	1	yes	characteristic
77	C₂×#63223	C₂³	1	1	yes	characteristic
78	C₂×#63223	C₂³	1	1	yes	characteristic
79	C₂×#63223	C₂³	1	1	yes	characteristic
80	C₂²×#3622	C₂³	1	1	yes	characteristic
81	C₂²×#3622	C₂³	1	1	yes	characteristic
82	C₂×#63218	—	4	1	no	—
83	C₂×#63218	—	4	1	no	—
84	C₂×#63218	C₂×C₄	1	2	yes	—
85	C₂×#63218	C₂×C₄	1	2	yes	—
86	C₂×C₈×D₁₇	—	4	1	no	—
87	C₂×C₈×D₁₇	—	4	1	no	—
88	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
89	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
90	#10587558	C₂×C₄	1	1	yes	characteristic
91	#10587558	C₂×C₄	1	1	yes	characteristic
92	#10587558	C₂×C₄	1	1	yes	characteristic
93	#10587558	C₂×C₄	1	1	yes	characteristic
94	#10587558	D₄	1	1	yes	characteristic
95	#10587558	D₄	1	1	yes	characteristic
96	#10587558	D₄	1	1	yes	characteristic
97	#10587558	D₄	1	1	yes	characteristic
98	C₁₇×#108	—	4	1	no	—
99	C₁₇×#108	—	4	1	no	—
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	—	2	1	no	—
102	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
103	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
104	C₁₇×#97	—	2	1	no	—
105	C₄×C₈×C₁₇	—	2	1	no	—
106	#10587493	—	4	1	no	—
107	#10587493	—	4	1	no	—
108	#10587493	—	4	1	no	—
109	#10587493	—	4	1	no	—
110	#10587491	—	2	1	no	—
111	#10587491	—	2	1	no	—
112	#10587491	—	2	1	no	—
113	#10587491	—	2	1	no	—
114	#10587491	—	2	1	no	—
115	#10587491	—	2	1	no	—
116	#10587491	—	2	1	no	—
117	#10587491	—	2	1	no	—
118	#10587490	—	4	1	no	—
119	#10587490	—	4	1	no	—
120	#10587486	—	2	1	no	—
121	#10587486	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	#10587485	—	2	1	no	—
125	#10587485	—	2	1	no	—
126	#10587485	C₂×C₄	1	2	yes	—
127	#10587485	C₂×C₄	1	2	yes	—
128	#10587485	C₂×C₄	1	2	yes	—
129	#10587485	C₂×C₄	1	2	yes	—
130	C₈×Dic₁₇	—	2	1	no	—
131	C₈×Dic₁₇	—	2	1	no	—
132	C₄⋊#3622	—	2	1	no	—
133	C₄⋊#3622	—	2	1	no	—
134	C₄⋊#3622	C₂×C₄	1	2	yes	—
135	C₄⋊#3622	C₂×C₄	1	2	yes	—
136	#10587474	—	2	1	no	—
137	C₄×#3622	—	2	1	no	—
138	C₂³×D₁₇	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
142	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
143	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
144	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
145	C₂×C₄×D₁₇	—	2	1	no	—
146	C₂×C₄×D₁₇	—	2	1	no	—
147	C₂×C₄×D₁₇	—	2	1	no	—
148	C₂×C₄×D₁₇	—	2	1	no	—
149	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
153	M₁₆×C₁₇	—	2	1	no	—
154	M₁₆×C₁₇	—	2	1	no	—
155	M₁₆×C₁₇	—	2	1	no	—
156	M₁₆×C₁₇	—	2	1	no	—
157	M₁₆×C₁₇	—	2	1	no	—
158	M₁₆×C₁₇	—	2	1	no	—
159	M₁₆×C₁₇	—	2	1	no	—
160	M₁₆×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
171	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
175	#63227	C₄⋊C₄	1	1	yes	characteristic
176	#63227	C₄⋊C₄	1	1	yes	characteristic
177	#63227	C₄⋊C₄	1	1	yes	characteristic
178	#63227	C₄⋊C₄	1	1	yes	characteristic
179	#63227	C₄⋊C₄	1	1	yes	characteristic
180	#63227	C₄⋊C₄	1	1	yes	characteristic
181	#63227	C₄⋊C₄	1	1	yes	characteristic
182	#63227	C₄⋊C₄	1	1	yes	characteristic
183	#63225	C₄⋊C₄	1	1	yes	characteristic
184	#63225	C₄⋊C₄	1	1	yes	characteristic
185	#63225	C₄⋊C₄	1	1	yes	characteristic
186	#63225	C₄⋊C₄	1	1	yes	characteristic
187	#63225	C₄⋊C₄	1	1	yes	characteristic
188	#63225	C₄⋊C₄	1	1	yes	characteristic
189	#63225	C₄⋊C₄	1	1	yes	characteristic
190	#63225	C₄⋊C₄	1	1	yes	characteristic
191	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
195	#63223	—	2	1	no	—
196	#63223	—	2	1	no	—
197	#63223	—	2	1	no	—
198	#63223	—	2	1	no	—
199	#63223	—	2	1	no	—
200	#63223	—	2	1	no	—
201	#63223	—	2	1	no	—
202	#63223	—	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	C₂²×C₄	1	2	yes	—
212	C₂×#3622	C₂²×C₄	1	2	yes	—
213	#63218	—	4	2	no	—
214	#63218	—	4	2	no	—
215	C₈×D₁₇	—	4	2	no	—
216	C₈×D₁₇	—	4	2	no	—
217	#21971	—	17	1	no	maximal, Sylow
218	C₂³×C₁₇	C₂²×Q₈	1	1	yes	characteristic
219	C₂²×D₁₇	—	2	1	no	—
220	C₂²×D₁₇	—	2	1	no	—
221	C₂²×D₁₇	—	4	1	no	—
222	C₂²×D₁₇	—	4	1	no	—
223	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₇	—	4	1	no	—
226	C₂×C₄×C₁₇	—	4	1	no	—
227	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×Dic₁₇	—	2	1	no	—
238	C₂×Dic₁₇	—	2	1	no	—
239	C₂×Dic₁₇	—	4	1	no	—
240	C₂×Dic₁₇	—	4	1	no	—
241	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₄×D₁₇	—	2	1	no	—
248	C₄×D₁₇	—	2	1	no	—
249	C₄×D₁₇	—	2	1	no	—
250	C₄×D₁₇	—	2	1	no	—
251	C₄×D₁₇	—	2	1	no	—
252	C₄×D₁₇	—	2	1	no	—
253	C₄×D₁₇	—	2	1	no	—
254	C₄×D₁₇	—	2	1	no	—
255	C₈×C₁₇	—	2	2	no	—
256	C₈×C₁₇	—	2	2	no	—
257	C₈×C₁₇	—	4	1	no	—
258	C₈×C₁₇	—	4	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	#3622	—	2	2	no	—
262	#3622	—	2	2	no	—
263	#3622	—	4	1	no	—
264	#3622	—	4	1	no	—
265	#3622	—	4	1	no	—
266	#3622	—	4	1	no	—
267	#2921	—	17	1	no	—
268	#2921	—	17	1	no	—
269	C₂×#424	—	17	1	no	—
270	#1950	—	17	1	no	—
271	#1950	—	17	1	no	—
272	#1950	—	17	1	no	—
273	#1950	—	17	1	no	—
274	#1950	—	17	1	no	—
275	#1950	—	17	1	no	—
276	#1950	—	17	1	no	—
277	#1950	D₁₇	1	1	yes	characteristic, complemented
278	#1811	—	17	1	no	—
279	#1811	—	17	1	no	—
280	#1810	—	17	1	no	—
281	#1810	—	17	1	no	—
282	C₂²×C₁₇	—	2	1	no	—
283	C₂²×C₁₇	—	2	1	no	—
284	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
285	C₂²×C₁₇	#544	1	1	yes	characteristic
286	C₂²×C₁₇	#544	1	1	yes	characteristic
287	C₂×D₁₇	—	2	1	no	—
288	C₂×D₁₇	—	2	1	no	—
289	C₂×D₁₇	—	2	1	no	—
290	C₂×D₁₇	—	2	1	no	—
291	C₂×D₁₇	—	2	1	no	—
292	C₂×D₁₇	—	2	1	no	—
293	C₂×D₁₇	—	4	2	no	—
294	C₂×D₁₇	—	4	2	no	—
295	C₄×C₁₇	—	2	1	no	—
296	C₄×C₁₇	—	2	1	no	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	#518	1	1	yes	characteristic
300	C₄×C₁₇	#519	1	1	yes	characteristic
301	C₄×C₁₇	#537	1	1	yes	characteristic
302	C₄×C₁₇	#537	1	1	yes	characteristic
303	Dic₁₇	—	2	1	no	—
304	Dic₁₇	—	2	1	no	—
305	Dic₁₇	—	2	1	no	—
306	Dic₁₇	—	2	1	no	—
307	Dic₁₇	—	2	1	no	—
308	Dic₁₇	—	2	1	no	—
309	C₂²×M₁₆	—	17	1	no	—
310	C₂³×C₈	—	17	1	no	—
311	C₂×#117	—	17	1	no	—
312	#433	—	34	1	no	—
313	#433	—	34	1	no	—
314	#433	—	34	1	no	—
315	#433	—	34	1	no	—
316	#433	—	34	1	no	—
317	#433	—	34	1	no	—
318	#433	—	34	1	no	—
319	#433	—	34	1	no	—
320	C₂×#108	—	17	1	no	—
321	C₂×#108	—	17	1	no	—
322	C₂×#108	—	17	1	no	—
323	C₂×#108	—	17	1	no	—
324	C₂×#108	—	17	1	no	—
325	C₂×#108	—	17	1	no	—
326	C₂×#108	C₂×D₁₇	1	1	yes	characteristic
327	C₂×#108	C₂×D₁₇	1	1	yes	characteristic
328	#424	—	17	2	no	—
329	#424	—	17	2	no	—
330	#424	—	17	2	no	—
331	#424	—	17	2	no	—
332	#423	—	17	1	no	—
333	#423	—	17	1	no	—
334	#423	—	17	1	no	—
335	#423	C₂×D₁₇	1	1	yes	characteristic
336	C₂×C₄⋊C₈	—	17	1	no	—
337	C₂×C₄⋊C₈	—	17	1	no	—
338	C₂×C₄⋊C₈	—	17	1	no	—
339	C₂×C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
340	#407	—	17	1	no	—
341	#407	—	17	1	no	—
342	#407	—	17	1	no	—
343	#407	—	17	1	no	—
344	C₄×M₁₆	—	17	1	no	—
345	C₄×M₁₆	—	17	1	no	—
346	C₄×M₁₆	—	17	1	no	—
347	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
348	#341	—	17	1	no	—
349	#341	—	17	1	no	—
350	#341	—	17	1	no	—
351	#341	—	17	1	no	—
352	#341	—	17	1	no	—
353	#341	—	17	1	no	—
354	#341	C₂×D₁₇	1	1	yes	characteristic
355	#341	C₂×D₁₇	1	1	yes	characteristic
356	C₂×C₁₇	—	2	1	no	—
357	C₂×C₁₇	—	2	1	no	—
358	C₂×C₁₇	#2316	1	1	yes	characteristic
359	C₂×C₁₇	#2916	1	1	yes	characteristic
360	C₂×C₁₇	#2916	1	1	yes	characteristic
361	D₁₇	—	4	1	no	—
362	D₁₇	—	4	1	no	—
363	C₂³×C₄	—	17	1	no	—
364	C₂×M₁₆	—	17	2	no	—
365	C₂×M₁₆	—	17	2	no	—
366	C₂×M₁₆	—	17	1	no	—
367	C₂×M₁₆	—	17	1	no	—
368	C₂×M₁₆	—	17	1	no	—
369	C₂×M₁₆	—	17	1	no	—
370	C₂×M₁₆	—	68	1	no	—
371	C₂×M₁₆	—	68	1	no	—
372	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
373	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
374	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
375	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
376	C₂²×C₈	—	17	1	no	—
377	C₂²×C₈	—	17	1	no	—
378	C₂²×C₈	—	17	2	no	—
379	C₂²×C₈	—	17	2	no	—
380	C₂²×C₈	—	68	1	no	—
381	C₂²×C₈	—	68	1	no	—
382	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
383	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
384	#117	—	17	1	no	—
385	#117	—	17	1	no	—
386	#117	—	17	1	no	—
387	#117	—	17	1	no	—
388	#117	—	17	1	no	—
389	#117	—	17	1	no	—
390	#117	—	17	1	no	—
391	#117	—	17	1	no	—
392	C₂×C₄⋊C₄	—	17	1	no	—
393	C₂×C₄⋊C₄	—	17	1	no	—
394	C₂×C₂²⋊C₄	—	17	1	no	—
395	C₂×C₂²⋊C₄	—	17	1	no	—
396	C₂×C₄²	—	17	1	no	—
397	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
398	#108	—	4	1	no	—
399	#108	—	4	1	no	—
400	#108	—	68	1	no	—
401	#108	—	68	1	no	—
402	#108	—	68	1	no	—
403	#108	—	68	1	no	—
404	#108	—	68	1	no	—
405	#108	—	68	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	17	2	no	—
409	C₄⋊C₈	—	17	2	no	—
410	C₄⋊C₈	—	17	2	no	—
411	C₄⋊C₈	—	17	2	no	—
412	C₄⋊C₈	—	17	2	no	—
413	C₄⋊C₈	—	17	2	no	—
414	C₄⋊C₈	—	34	1	no	—
415	C₄⋊C₈	—	34	1	no	—
416	C₄⋊C₈	—	34	1	no	—
417	C₄⋊C₈	—	34	1	no	—
418	C₄⋊C₈	—	34	1	no	—
419	C₄⋊C₈	—	34	1	no	—
420	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
421	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
422	C₂²⋊C₈	—	34	1	no	—
423	C₂²⋊C₈	—	34	1	no	—
424	C₂²⋊C₈	—	34	1	no	—
425	C₂²⋊C₈	—	34	1	no	—
426	C₂²⋊C₈	—	34	1	no	—
427	C₂²⋊C₈	—	34	1	no	—
428	C₂²⋊C₈	—	34	1	no	—
429	C₂²⋊C₈	—	34	1	no	—
430	#97	—	2	1	no	—
431	#97	—	34	1	no	—
432	#97	—	34	1	no	—
433	#97	—	34	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	34	1	no	—
436	C₄×C₈	—	34	1	no	—
437	C₄×C₈	—	34	1	no	—
438	C₁₇	#21971	1	1	yes	characteristic, complemented, Sylow
439	C₂⁴	—	17	1	no	—
440	C₂²×C₄	—	17	1	no	—
441	C₂²×C₄	—	17	1	no	—
442	C₂²×C₄	—	17	1	no	—
443	C₂²×C₄	—	17	1	no	—
444	C₂²×C₄	—	17	1	no	—
445	C₂²×C₄	—	17	1	no	—
446	C₂²×C₄	—	17	1	no	—
447	C₂²×C₄	—	34	1	no	—
448	C₂²×C₄	—	34	1	no	—
449	C₂²×C₄	—	34	1	no	—
450	C₂²×C₄	—	34	1	no	—
451	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
452	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	2	1	no	—
461	M₁₆	—	2	1	no	—
462	M₁₆	—	34	1	no	—
463	M₁₆	—	34	1	no	—
464	M₁₆	—	34	1	no	—
465	M₁₆	—	34	1	no	—
466	M₁₆	—	34	1	no	—
467	M₁₆	—	34	1	no	—
468	M₁₆	—	34	1	no	—
469	M₁₆	—	34	1	no	—
470	M₁₆	—	68	2	no	—
471	M₁₆	—	68	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	17	2	no	—
481	C₂×C₈	—	17	2	no	—
482	C₂×C₈	—	34	1	no	—
483	C₂×C₈	—	34	1	no	—
484	C₂×C₈	—	34	1	no	—
485	C₂×C₈	—	34	1	no	—
486	C₂×C₈	—	34	1	no	—
487	C₂×C₈	—	34	1	no	—
488	C₂×C₈	—	34	1	no	—
489	C₂×C₈	—	34	1	no	—
490	C₂×C₈	—	68	2	no	—
491	C₂×C₈	—	68	2	no	—
492	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
493	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
494	C₄⋊C₄	—	17	1	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	17	1	no	—
497	C₄⋊C₄	—	17	1	no	—
498	C₄⋊C₄	—	17	1	no	—
499	C₄⋊C₄	—	17	1	no	—
500	C₄⋊C₄	—	17	1	no	—
501	C₄⋊C₄	—	17	1	no	—
502	C₂²⋊C₄	—	17	1	no	—
503	C₂²⋊C₄	—	17	1	no	—
504	C₂²⋊C₄	—	17	1	no	—
505	C₂²⋊C₄	—	17	1	no	—
506	C₂²⋊C₄	—	17	1	no	—
507	C₂²⋊C₄	—	17	1	no	—
508	C₂²⋊C₄	—	17	1	no	—
509	C₂²⋊C₄	—	17	1	no	—
510	C₄²	—	17	1	no	—
511	C₄²	—	17	1	no	—
512	C₄²	—	17	1	no	—
513	C₄²	—	17	1	no	—
514	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
515	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
516	C₄²	D₄×D₁₇	1	1	yes	characteristic
517	C₄²	D₄×D₁₇	1	1	yes	characteristic
518	C₂³	—	17	1	no	—
519	C₂³	—	17	1	no	—
520	C₂³	—	34	1	no	—
521	C₂³	—	34	1	no	—
522	C₂³	—	68	1	no	—
523	C₂³	—	68	1	no	—
524	C₂³	C₂×Q₈×D₁₇	1	1	yes	characteristic
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	17	1	no	—
528	C₂×C₄	—	17	1	no	—
529	C₂×C₄	—	17	1	no	—
530	C₂×C₄	—	17	1	no	—
531	C₂×C₄	—	17	1	no	—
532	C₂×C₄	—	17	1	no	—
533	C₂×C₄	—	34	1	no	—
534	C₂×C₄	—	34	1	no	—
535	C₂×C₄	—	34	1	no	—
536	C₂×C₄	—	34	1	no	—
537	C₂×C₄	—	34	1	no	—
538	C₂×C₄	—	34	1	no	—
539	C₂×C₄	—	34	1	no	—
540	C₂×C₄	—	34	1	no	—
541	C₂×C₄	—	34	1	no	—
542	C₂×C₄	—	34	1	no	—
543	C₂×C₄	—	68	1	no	—
544	C₂×C₄	—	68	1	no	—
545	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
546	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
547	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
548	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
551	C₂×C₄	#10587691	1	1	yes	characteristic
552	C₂×C₄	#10587694	1	1	yes	characteristic
553	C₂×C₄	#10587696	1	1	yes	characteristic
554	C₂×C₄	#10587697	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	34	2	no	—
562	C₈	—	34	2	no	—
563	C₈	—	68	1	no	—
564	C₈	—	68	1	no	—
565	C₈	—	68	1	no	—
566	C₈	—	68	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	34	1	no	—
570	C₂²	—	34	1	no	—
571	C₂²	—	34	1	no	—
572	C₂²	—	34	1	no	—
573	C₂²	—	34	1	no	—
574	C₂²	—	34	1	no	—
575	C₂²	—	68	2	no	—
576	C₂²	—	68	2	no	—
577	C₂²	C₂×C₄⋊C₄×D₁₇	1	1	yes	characteristic
578	C₂²	#11763436	1	1	yes	characteristic
579	C₂²	#11763439	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	34	1	no	—
585	C₄	—	34	1	no	—
586	C₄	—	34	1	no	—
587	C₄	—	34	1	no	—
588	C₄	—	34	1	no	—
589	C₄	—	34	1	no	—
590	C₄	#11763281	1	1	yes	characteristic
591	C₄	#11763285	1	1	yes	characteristic
592	C₄	#11763388	1	1	yes	characteristic
593	C₄	#11763389	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	68	1	no	—
597	C₂	—	68	1	no	—
598	C₂	#14531399	1	1	yes	characteristic
599	C₂	#14537392	1	1	yes	characteristic
600	C₂	#14537394	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₁₇×#1950	C₂
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#1950	D₁₇
hypocenter	C₁₇	#21971
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #14529560	C₂	semidirect
5. #14529559	C₂	semidirect
6. #14529558	C₂	semidirect
7. #14529558	C₂	semidirect
8. #14529557	C₂	semidirect
9. #14529556	C₂	semidirect
10. #14529556	C₂	semidirect
15. C₁₇×#1950	C₂	semidirect
277. #1950	D₁₇	semidirect
438. C₁₇	#21971	semidirect

Maximal subgroups

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

subgroup	index
#14537421	2
#14537420	2
C₂×#11762834	2
#14529560	2
#14529559	2
#14529558	2
#14529557	2
#14529556	2
#14528825	2
#14528823	2
#14528821	2
#14528819	2
C₁₇×#1950	2
#21971	17