Subgroups — #17018269

Order 4352.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14539298	C₂	1	1	yes	maximal, characteristic, complemented
2	#14538946	C₂	1	2	yes	maximal
3	#14528188	C₂	1	1	yes	maximal, characteristic, complemented
4	#14528183	C₂	1	1	yes	maximal, characteristic, complemented
5	#14528178	C₂	1	1	yes	maximal, characteristic, complemented
6	#14528173	C₂	1	1	yes	maximal, characteristic, complemented
7	#14528166	C₂	1	2	yes	maximal, complemented
8	#14528159	C₂	1	2	yes	maximal, complemented
9	#14527547	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527492	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic
12	#11763366	C₂²	1	2	yes	—
13	#11763214	C₂²	1	1	yes	characteristic
14	#11763214	C₂²	1	1	yes	characteristic
15	#11763211	—	2	1	no	—
16	#11763211	—	2	1	no	—
17	#11763207	C₂²	1	2	yes	—
18	#11763150	—	2	2	no	—
19	#11763104	C₂²	1	2	yes	—
20	#11763099	C₂²	1	2	yes	—
21	#11763019	C₂²	1	2	yes	—
22	#11763014	C₂²	1	2	yes	—
23	#11762971	—	2	2	no	—
24	#11762914	—	2	2	no	—
25	#11762909	—	2	2	no	—
26	#11762866	C₂²	1	2	yes	—
27	#11762847	—	2	1	no	—
28	#11762847	—	2	1	no	—
29	#11762562	C₂²	1	1	yes	characteristic
30	#11762562	C₂²	1	1	yes	characteristic
31	#11762560	C₂²	1	2	yes	—
32	#11762557	C₂²	1	2	yes	—
33	#11762557	C₂²	1	2	yes	—
34	#11762554	C₂²	1	2	yes	—
35	#11762554	C₂²	1	2	yes	—
36	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₇	—	2	1	no	—
40	C₈×D₄×C₁₇	—	2	1	no	—
41	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
43	C₁₇×#431	—	2	1	no	—
44	C₁₇×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₇	—	2	1	no	—
46	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₇	—	2	1	no	—
49	C₂²×C₈×C₁₇	—	2	1	no	—
50	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
54	C₄×D₄×C₁₇	—	2	1	no	—
55	C₄×D₄×C₁₇	—	2	1	no	—
56	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
57	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
58	C₁₇×#117	—	2	1	no	—
59	C₁₇×#117	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₇	—	2	1	no	—
61	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×#63231	—	2	2	no	—
63	C₂×#63229	—	2	2	no	—
64	#10587612	—	2	2	no	—
65	#10587610	—	2	2	no	—
66	#10587610	—	2	2	no	—
67	#10587556	—	2	2	no	—
68	#10587555	C₂³	1	2	yes	—
69	#10587555	C₂³	1	2	yes	—
70	C₄×Dic₃₄	—	2	2	no	—
71	C₄×Dic₃₄	—	2	2	no	—
72	C₁₇×C₄⋊C₈	—	2	1	no	—
73	C₁₇×C₄⋊C₈	—	2	1	no	—
74	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₇×C₂²⋊C₈	—	2	1	no	—
77	C₁₇×C₂²⋊C₈	—	2	1	no	—
78	C₁₇×C₂²⋊C₈	—	2	1	no	—
79	C₄×C₈×C₁₇	—	2	1	no	—
80	C₄×C₈×C₁₇	—	2	1	no	—
81	C₄×C₈×C₁₇	—	2	1	no	—
82	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
86	#10587506	—	2	2	no	—
87	#10587503	—	2	2	no	—
88	C₂²⋊#3622	—	2	2	no	—
89	#10587489	—	2	1	no	—
90	#10587489	—	2	1	no	—
91	#10587489	—	2	1	no	—
92	#10587489	—	2	1	no	—
93	#10587488	—	2	2	no	—
94	#10587488	—	2	2	no	—
95	#10587481	—	2	2	no	—
96	#10587481	—	2	2	no	—
97	#10587479	—	2	2	no	—
98	#10587478	—	2	2	no	—
99	C₄⋊#3622	C₂³	1	2	yes	—
100	C₄⋊#3622	C₂³	1	2	yes	—
101	#10587474	—	2	2	no	—
102	#41×C₁₇	—	2	2	no	—
103	#41×C₁₇	—	2	2	no	—
104	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₇	—	2	1	no	—
106	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	—	2	1	no	—
108	C₂²×C₄×C₁₇	—	2	1	no	—
109	C₂²×C₄×C₁₇	—	2	1	no	—
110	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
113	C₂×Dic₃₄	—	2	2	no	—
114	C₂×Dic₃₄	—	2	2	no	—
115	C₂×C₈×C₁₇	—	2	2	no	—
116	C₂×C₈×C₁₇	—	2	2	no	—
117	C₂×C₈×C₁₇	—	2	1	no	—
118	C₂×C₈×C₁₇	—	2	1	no	—
119	C₂×C₈×C₁₇	—	4	2	no	—
120	C₂×C₈×C₁₇	—	4	2	no	—
121	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₇	—	2	1	no	—
126	C₄⋊C₄×C₁₇	—	2	1	no	—
127	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₇	—	2	1	no	—
130	C₂²⋊C₄×C₁₇	—	2	1	no	—
131	C₂²⋊C₄×C₁₇	—	2	1	no	—
132	C₄²×C₁₇	—	2	1	no	—
133	C₄²×C₁₇	—	2	1	no	—
134	C₄²×C₁₇	—	2	1	no	—
135	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₇	#41	1	1	yes	characteristic
138	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₁₇	—	4	2	no	—
140	#63231	—	4	4	no	—
141	#63229	—	4	4	no	—
142	C₄⋊Dic₁₇	—	2	2	no	—
143	C₄⋊Dic₁₇	—	2	2	no	—
144	C₄⋊Dic₁₇	—	2	2	no	—
145	C₄⋊Dic₁₇	—	2	2	no	—
146	#63225	—	4	2	no	—
147	#63225	—	4	2	no	—
148	C₄×Dic₁₇	—	4	2	no	—
149	C₂×#3622	—	2	2	no	—
150	C₂×#3622	—	2	2	no	—
151	#19273	—	17	1	no	maximal, Sylow
152	C₂³×C₁₇	—	2	1	no	—
153	C₂³×C₁₇	#121	1	1	yes	characteristic
154	Q₈×C₁₇	—	2	1	no	—
155	Q₈×C₁₇	#135	1	2	yes	—
156	D₄×C₁₇	—	2	4	no	—
157	D₄×C₁₇	—	2	1	no	—
158	D₄×C₁₇	#135	1	2	yes	—
159	C₂×C₄×C₁₇	—	2	4	no	—
160	C₂×C₄×C₁₇	—	2	1	no	—
161	C₂×C₄×C₁₇	—	2	1	no	—
162	C₂×C₄×C₁₇	—	2	1	no	—
163	C₂×C₄×C₁₇	—	2	1	no	—
164	C₂×C₄×C₁₇	—	2	1	no	—
165	C₂×C₄×C₁₇	—	2	1	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	4	1	no	—
168	C₂×C₄×C₁₇	—	4	2	no	—
169	C₂×C₄×C₁₇	—	4	1	no	—
170	C₂×C₄×C₁₇	—	4	1	no	—
171	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₁₇	—	4	2	no	—
178	C₂×Dic₁₇	—	4	2	no	—
179	Dic₃₄	—	4	2	no	—
180	Dic₃₄	—	4	2	no	—
181	Dic₃₄	—	8	2	no	—
182	C₈×C₁₇	—	2	1	no	—
183	C₈×C₁₇	—	2	1	no	—
184	C₈×C₁₇	—	4	1	no	—
185	C₈×C₁₇	—	4	1	no	—
186	C₈×C₁₇	#137	1	2	yes	—
187	C₈×C₁₇	#137	1	2	yes	—
188	#3622	—	4	2	no	—
189	#3622	—	4	2	no	—
190	#3160	—	17	1	no	—
191	#3116	—	17	2	no	—
192	C₈×#41	D₁₇	1	1	yes	characteristic
193	#1676	—	17	1	no	—
194	#1675	—	17	1	no	—
195	#1674	—	17	1	no	—
196	#1673	—	17	1	no	—
197	#1672	—	17	2	no	—
198	#1671	—	17	2	no	—
199	#1568	—	17	1	no	—
200	#1554	—	17	2	no	—
201	C₂²×C₁₇	—	2	1	no	—
202	C₂²×C₁₇	—	2	1	no	—
203	C₂²×C₁₇	—	2	2	no	—
204	C₂²×C₁₇	—	2	1	no	—
205	C₂²×C₁₇	—	4	1	no	—
206	C₂²×C₁₇	—	4	1	no	—
207	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
208	C₄×C₁₇	—	2	1	no	—
209	C₄×C₁₇	—	2	1	no	—
210	C₄×C₁₇	—	2	2	no	—
211	C₄×C₁₇	—	2	1	no	—
212	C₄×C₁₇	—	2	1	no	—
213	C₄×C₁₇	—	4	1	no	—
214	C₄×C₁₇	—	4	1	no	—
215	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
217	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
218	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
219	Dic₁₇	—	8	2	no	—
220	Dic₁₇	—	8	2	no	—
221	#533	—	17	2	no	—
222	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
223	#500	—	17	1	no	—
224	#500	—	17	1	no	—
225	#499	—	34	1	no	—
226	#499	—	34	1	no	—
227	#498	—	17	2	no	—
228	#485	—	34	2	no	—
229	#477	—	17	2	no	—
230	#476	—	17	2	no	—
231	#462	—	17	2	no	—
232	#461	—	17	2	no	—
233	#452	—	34	2	no	—
234	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
235	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
236	#441	—	34	2	no	—
237	#440	—	34	2	no	—
238	C₈×D₄	—	2	1	no	—
239	C₈×D₄	—	2	1	no	—
240	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
241	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
242	#432	—	17	2	no	—
243	#431	—	2	1	no	—
244	#431	C₂×D₁₇	1	1	yes	characteristic
245	#427	—	34	1	no	—
246	#427	—	34	1	no	—
247	C₂×C₄×C₈	—	2	1	no	—
248	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
249	#335	—	17	1	no	—
250	#335	—	17	1	no	—
251	#334	—	17	2	no	—
252	#333	—	17	2	no	—
253	#333	—	17	2	no	—
254	#332	—	17	2	no	—
255	#332	—	17	2	no	—
256	C₂×C₁₇	—	4	1	no	—
257	C₂×C₁₇	—	4	2	no	—
258	C₂×C₁₇	#3039	1	1	yes	characteristic
259	C₂×C₁₇	#3050	1	1	yes	characteristic
260	C₂×C₁₇	#3067	1	1	yes	characteristic
261	C₂×#41	D₆₈	1	1	yes	characteristic
262	C₂×Q₁₆	—	34	2	no	—
263	C₂×SD₁₆	—	34	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
268	C₄⋊Q₈	—	17	2	no	—
269	C₄⋊Q₈	—	17	2	no	—
270	#125	—	34	2	no	—
271	C₂²⋊Q₈	—	34	2	no	—
272	C₂²⋊Q₈	—	34	2	no	—
273	C₄×Q₈	—	34	2	no	—
274	C₄×Q₈	—	34	2	no	—
275	C₄×Q₈	D₆₈	1	1	yes	characteristic
276	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	D₆₈	1	1	yes	characteristic
280	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	34	2	no	—
283	#117	D₆₈	1	1	yes	characteristic
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
286	#107	—	34	1	no	—
287	#107	—	34	1	no	—
288	#107	—	34	1	no	—
289	#107	—	34	1	no	—
290	#107	—	34	2	no	—
291	#106	—	34	2	no	—
292	#106	—	34	2	no	—
293	#106	—	34	2	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	17	2	no	—
297	C₄⋊C₈	—	17	2	no	—
298	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
300	#103	—	34	2	no	—
301	#103	—	34	2	no	—
302	#103	—	34	2	no	—
303	#102	—	34	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	34	2	no	—
308	#97	—	34	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
313	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
316	C₁₇	#19273	1	1	yes	characteristic, complemented, Sylow
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	—	34	2	no	—
320	C₂×Q₈	—	34	2	no	—
321	C₂×Q₈	C₂×D₆₈	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
328	C₂²×C₄	#63252	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
330	Q₁₆	—	68	4	no	—
331	SD₁₆	—	68	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	34	2	no	—
339	C₂×C₈	—	34	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	34	2	no	—
347	C₄⋊C₄	—	34	2	no	—
348	C₄⋊C₄	—	34	2	no	—
349	C₄⋊C₄	—	34	2	no	—
350	C₄⋊C₄	—	68	2	no	—
351	C₄⋊C₄	—	68	2	no	—
352	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
353	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	68	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	68	2	no	—
362	C₄²	C₂×D₆₈	1	1	yes	characteristic
363	C₄²	#63252	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
365	C₄²	C₂³×D₁₇	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	#10587616	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	68	2	no	—
370	Q₈	—	68	2	no	—
371	Q₈	—	136	2	no	—
372	Q₈	#10587590	1	2	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	#10587590	1	2	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	68	2	no	—
389	C₂×C₄	—	68	2	no	—
390	C₂×C₄	#10587616	1	1	yes	characteristic
391	C₂×C₄	#10587616	1	1	yes	characteristic
392	C₂×C₄	#10587616	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
394	C₂×C₄	C₂×#63252	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	68	2	no	—
401	C₈	—	68	2	no	—
402	C₈	#10587637	1	2	yes	—
403	C₈	#10587637	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#10587616	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	136	2	no	—
419	C₄	—	136	2	no	—
420	C₄	C₂×#10587590	1	1	yes	characteristic
421	C₄	C₂×#10587590	1	1	yes	characteristic
422	C₄	C₂×#10587637	1	1	yes	characteristic
423	C₄	C₂×#10587637	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#14538271	1	1	yes	characteristic
427	C₂	#14538365	1	1	yes	characteristic
428	C₂	#14538504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10587616
commutator, cosocle	C₄²×C₁₇	C₂⁴
Frattini	C₄²	C₂³×D₁₇
Fitting	C₈×#41×C₁₇	C₂
socle	C₂²×C₁₇	C₂×#121
prime radical	C₂×#41×C₁₇	D₄
hypercenter	C₈×#41	D₁₇
hypocenter	C₁₇	#19273
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #14539298	C₂	semidirect
3. #14528188	C₂	semidirect
4. #14528183	C₂	semidirect
5. #14528178	C₂	semidirect
6. #14528173	C₂	semidirect
7. #14528166	C₂	semidirect
8. #14528159	C₂	semidirect
9. #14527547	C₂	semidirect
10. #14527492	C₂	semidirect
316. C₁₇	#19273	semidirect

Maximal subgroups

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

subgroup	index
#14539298	2
#14538946	2
#14528188	2
#14528183	2
#14528178	2
#14528173	2
#14528166	2
#14528159	2
#14527547	2
#14527492	2
C₈×#41×C₁₇	2
#19273	17