Subgroups — #17005124

Order 4352.

578 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14539384	C₂	1	1	yes	maximal, characteristic
2	#14537759	C₂	1	1	yes	maximal, characteristic
3	#14527662	C₂	1	2	yes	maximal, complemented
4	#14527655	C₂	1	2	yes	maximal, complemented
5	#14527632	C₂	1	2	yes	maximal, complemented
6	#14527618	C₂	1	2	yes	maximal, complemented
7	#14527549	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527257	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527247	C₂	1	1	yes	maximal, characteristic
10	#14527073	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763343	C₂²	1	1	yes	characteristic
13	#11763215	C₄	1	1	yes	characteristic
14	#11763201	C₄	1	1	yes	characteristic
15	#11763177	C₄	1	1	yes	characteristic
16	#11763171	C₄	1	1	yes	characteristic
17	#11763065	C₄	1	2	yes	—
18	#11763057	C₄	1	2	yes	—
19	#11762939	C₂²	1	1	yes	characteristic
20	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
21	C₄×#63231	C₂²	1	2	yes	—
22	C₄×#63230	C₂²	1	2	yes	—
23	#11762888	C₂²	1	1	yes	characteristic
24	#11762880	—	2	1	no	—
25	C₈×D₆₈	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₁₇	—	2	1	no	—
27	#11762868	—	2	1	no	—
28	#11762866	C₂²	1	1	yes	characteristic
29	#11762862	C₂²	1	1	yes	characteristic
30	#11762763	—	2	1	no	—
31	C₄×#63223	C₂²	1	1	yes	characteristic
32	#11762561	C₂²	1	2	yes	—
33	#11762559	C₂²	1	2	yes	—
34	Q₈⋊#3622	C₂²	1	2	yes	—
35	Q₈⋊#3622	C₂²	1	2	yes	—
36	#11762539	C₂²	1	2	yes	—
37	#11762536	C₂²	1	2	yes	—
38	#11762531	C₂²	1	2	yes	—
39	#11762530	C₂²	1	2	yes	—
40	C₁₇×#533	C₂²	1	1	yes	characteristic
41	C₁₇×#446	—	2	1	no	—
42	C₁₇×#446	C₂²	1	2	yes	—
43	C₈×Q₈×C₁₇	—	2	1	no	—
44	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
45	C₁₇×#424	—	2	1	no	—
46	C₁₇×#423	C₂²	1	1	yes	characteristic
47	C₁₇×#405	—	2	1	no	—
48	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₂×M₁₆×C₁₇	—	2	1	no	—
50	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
52	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₇×#125	—	2	1	no	—
55	C₁₇×C₂²⋊Q₈	—	2	1	no	—
56	C₁₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₁₇	—	2	1	no	—
58	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
59	C₁₇×#117	—	2	1	no	—
60	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
61	C₂×#63231	C₂×C₄	1	2	yes	—
62	C₂×#63230	C₂×C₄	1	2	yes	—
63	#10587616	C₂×C₄	1	1	yes	characteristic
64	#10587615	—	2	1	no	—
65	C₄×C₂²⋊D₁₇	—	2	1	no	—
66	#10587610	C₂×C₄	1	1	yes	characteristic
67	C₂×#63223	C₂×C₄	1	2	yes	—
68	C₂×#63218	—	2	1	no	—
69	C₂×C₈×D₁₇	—	2	1	no	—
70	#10587562	—	2	1	no	—
71	#10587561	C₂×C₄	1	1	yes	characteristic
72	C₄×D₆₈	C₂³	1	1	yes	characteristic
73	#10587558	—	2	1	no	—
74	#10587556	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
76	C₁₇×C₄⋊C₈	—	2	2	no	—
77	C₁₇×C₄⋊C₈	—	2	2	no	—
78	C₁₇×C₄⋊C₈	—	2	1	no	—
79	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₇×#97	—	2	2	no	—
81	C₄×C₈×C₁₇	—	2	2	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	C₂×C₄	1	2	yes	—
87	#10587506	C₂×C₄	1	2	yes	—
88	C₂²⋊#3622	—	2	1	no	—
89	C₂²⋊#3622	—	2	1	no	—
90	#10587491	—	2	1	no	—
91	#10587491	—	2	1	no	—
92	#10587486	—	2	1	no	—
93	#10587485	—	2	1	no	—
94	#10587485	—	2	1	no	—
95	C₈×Dic₁₇	—	2	1	no	—
96	#10587481	C₂×C₄	1	2	yes	—
97	#10587480	C₂×C₄	1	2	yes	—
98	#10587479	C₂×C₄	1	2	yes	—
99	#10587478	C₂×C₄	1	2	yes	—
100	C₄⋊#3622	—	2	1	no	—
101	C₄⋊#3622	C₂³	1	1	yes	characteristic
102	C₄⋊#3622	C₂³	1	1	yes	characteristic
103	#10587474	—	2	1	no	—
104	#10587474	C₂×C₄	1	1	yes	characteristic
105	#10587474	C₂×C₄	1	1	yes	characteristic
106	C₄×#3622	C₂³	1	2	yes	—
107	C₄×#3622	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₇	—	2	1	no	—
109	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₇	C₂²×C₄	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×C₂²⋊D₁₇	—	2	1	no	—
114	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₇	—	2	1	no	—
116	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₁₇	—	4	2	no	—
118	C₂×C₈×C₁₇	—	2	2	no	—
119	C₂×C₈×C₁₇	—	2	2	no	—
120	C₂×C₈×C₁₇	—	4	1	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	2	no	—
127	C₄⋊C₄×C₁₇	—	2	1	no	—
128	C₄⋊C₄×C₁₇	—	2	1	no	—
129	C₄⋊C₄×C₁₇	—	2	2	no	—
130	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₁₇	—	2	2	no	—
132	C₄²×C₁₇	—	2	2	no	—
133	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₇	#41	1	1	yes	characteristic
136	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₁₇	—	2	1	no	—
138	#63231	—	4	2	no	—
139	#63230	—	4	2	no	—
140	#63227	—	2	1	no	—
141	#63227	—	2	1	no	—
142	#63227	—	2	1	no	—
143	#63227	—	2	1	no	—
144	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
146	#63225	—	2	1	no	—
147	#63225	—	2	1	no	—
148	#63225	—	2	1	no	—
149	#63225	—	2	1	no	—
150	C₄×Dic₁₇	—	2	1	no	—
151	#63223	—	4	2	no	—
152	C₂×#3622	—	2	1	no	—
153	C₂×#3622	—	2	1	no	—
154	C₂×#3622	—	2	2	no	—
155	C₂×#3622	C₂²×C₄	1	2	yes	—
156	C₂×#3622	C₂²×C₄	1	2	yes	—
157	#63218	—	4	2	no	—
158	C₈×D₁₇	—	4	2	no	—
159	#17986	—	17	1	no	maximal, Sylow
160	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₁₇	—	2	1	no	—
162	Q₈×C₁₇	—	2	2	no	—
163	Q₈×C₁₇	—	2	2	no	—
164	Q₈×C₁₇	—	4	2	no	—
165	C₂×C₄×C₁₇	—	2	2	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	2	no	—
169	C₂×C₄×C₁₇	—	2	2	no	—
170	C₂×C₄×C₁₇	—	4	1	no	—
171	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₇	C₂³×C₄	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	C₂²⋊D₁₇	—	4	2	no	—
178	C₂×Dic₁₇	—	2	1	no	—
179	C₂×Dic₁₇	—	2	1	no	—
180	C₂×Dic₁₇	—	2	1	no	—
181	D₆₈	—	2	2	no	—
182	C₄×D₁₇	—	4	1	no	—
183	C₄×D₁₇	—	4	1	no	—
184	Dic₃₄	—	2	2	no	—
185	C₈×C₁₇	—	2	1	no	—
186	C₈×C₁₇	—	2	1	no	—
187	C₈×C₁₇	—	2	1	no	—
188	C₈×C₁₇	—	4	2	no	—
189	C₈×C₁₇	#137	1	2	yes	—
190	#3622	—	2	2	no	—
191	#3622	—	2	2	no	—
192	#3622	—	4	2	no	—
193	#3622	—	4	1	no	—
194	#3622	—	4	1	no	—
195	#3172	—	17	1	no	—
196	#2966	—	17	1	no	—
197	#2960	D₁₇	1	1	yes	characteristic, complemented
198	#1588	—	17	2	no	—
199	#1587	—	17	2	no	—
200	#1584	—	17	2	no	—
201	#1582	—	17	2	no	—
202	#1569	—	17	1	no	—
203	#1497	—	17	1	no	—
204	#1495	—	17	1	no	—
205	#1451	—	17	1	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂×D₁₇	—	4	1	no	—
211	C₂×D₁₇	—	4	1	no	—
212	C₂×D₁₇	—	4	1	no	—
213	C₄×C₁₇	—	2	1	no	—
214	C₄×C₁₇	—	2	1	no	—
215	C₄×C₁₇	—	2	1	no	—
216	C₄×C₁₇	—	2	1	no	—
217	C₄×C₁₇	—	4	2	no	—
218	C₄×C₁₇	—	4	2	no	—
219	C₄×C₁₇	#568	1	2	yes	—
220	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
221	C₄×C₁₇	#575	1	1	yes	characteristic
222	Dic₁₇	—	4	1	no	—
223	Dic₁₇	—	4	1	no	—
224	Dic₁₇	—	4	1	no	—
225	#533	C₂×D₁₇	1	1	yes	characteristic
226	#529	—	17	1	no	—
227	#501	—	17	1	no	—
228	#497	—	17	1	no	—
229	#491	—	17	1	no	—
230	#489	—	17	1	no	—
231	#470	—	17	2	no	—
232	#468	—	17	2	no	—
233	#446	—	2	1	no	—
234	#446	—	17	1	no	—
235	#446	C₂×D₁₇	1	2	yes	—
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	—	17	1	no	—
238	C₈×Q₈	C₂×D₁₇	1	2	yes	—
239	C₄×Q₁₆	—	17	2	no	—
240	C₄×SD₁₆	—	17	2	no	—
241	#436	—	17	1	no	—
242	#435	—	34	1	no	—
243	C₈×D₄	—	17	1	no	—
244	C₈×D₄	—	34	1	no	—
245	#433	—	34	1	no	—
246	#432	—	17	1	no	—
247	#431	—	17	1	no	—
248	#424	—	2	1	no	—
249	#423	C₂×D₁₇	1	1	yes	characteristic
250	#405	—	2	1	no	—
251	#405	—	34	1	no	—
252	C₄×M₁₆	—	17	1	no	—
253	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
254	#335	—	17	2	no	—
255	#334	—	17	2	no	—
256	Q₈⋊C₈	—	17	2	no	—
257	Q₈⋊C₈	—	17	2	no	—
258	Q₈⋊C₈	—	17	2	no	—
259	D₄⋊C₈	—	17	2	no	—
260	#322	—	17	2	no	—
261	#322	—	17	2	no	—
262	C₂×C₁₇	—	4	1	no	—
263	C₂×C₁₇	#2932	1	1	yes	characteristic
264	C₂×C₁₇	C₄×#137	1	1	yes	characteristic
265	C₂×C₁₇	#2955	1	1	yes	characteristic
266	D₁₇	—	8	1	no	—
267	C₂×Q₁₆	—	17	2	no	—
268	C₂×SD₁₆	—	17	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	17	2	no	—
271	C₂×M₁₆	—	34	1	no	—
272	C₂²×C₈	—	34	1	no	—
273	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
275	C₄⋊Q₈	C₄×D₁₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₄×D₁₇	1	1	yes	characteristic
277	#126	—	34	1	no	—
278	#125	—	2	1	no	—
279	#125	—	17	1	no	—
280	#124	—	17	1	no	—
281	#123	—	34	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	17	1	no	—
284	C₂²⋊Q₈	C₄×D₁₇	1	2	yes	—
285	#121	—	17	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	17	1	no	—
288	C₄×Q₈	C₂²×D₁₇	1	2	yes	—
289	C₄×D₄	—	17	1	no	—
290	C₄×D₄	—	34	1	no	—
291	#117	—	2	1	no	—
292	#117	—	34	1	no	—
293	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
294	#107	—	17	2	no	—
295	#106	—	17	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	17	1	no	—
300	C₄⋊C₈	—	17	1	no	—
301	C₄⋊C₈	—	34	1	no	—
302	C₄⋊C₈	—	34	1	no	—
303	C₄⋊C₈	—	34	1	no	—
304	C₄⋊C₈	C₂²×D₁₇	1	2	yes	—
305	#103	—	17	2	no	—
306	#103	—	17	2	no	—
307	#103	—	17	2	no	—
308	#102	—	17	2	no	—
309	C₂²⋊C₈	—	34	1	no	—
310	C₂²⋊C₈	—	34	1	no	—
311	C₂²⋊C₈	—	34	1	no	—
312	C₂²⋊C₈	—	34	1	no	—
313	#97	—	2	2	no	—
314	#97	—	17	1	no	—
315	#97	—	17	1	no	—
316	#97	—	34	1	no	—
317	#97	—	34	1	no	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	17	2	no	—
320	C₄×C₈	—	17	2	no	—
321	C₄×C₈	—	34	1	no	—
322	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
323	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
326	C₁₇	#17986	1	1	yes	characteristic, complemented, Sylow
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	17	1	no	—
329	C₂×Q₈	C₂×C₄×D₁₇	1	2	yes	—
330	C₂×D₄	—	17	1	no	—
331	C₂×D₄	—	34	1	no	—
332	C₂²×C₄	—	34	1	no	—
333	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
334	C₂²×C₄	#63252	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
336	Q₁₆	—	68	2	no	—
337	SD₁₆	—	68	2	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	68	2	no	—
340	M₁₆	—	68	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	17	2	no	—
345	C₂×C₈	—	17	2	no	—
346	C₂×C₈	—	34	2	no	—
347	C₂×C₈	—	34	1	no	—
348	C₂×C₈	—	34	1	no	—
349	C₂×C₈	—	68	2	no	—
350	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	17	1	no	—
360	C₄⋊C₄	—	17	1	no	—
361	C₄⋊C₄	—	34	1	no	—
362	C₄⋊C₄	—	34	1	no	—
363	C₄⋊C₄	—	34	1	no	—
364	C₄⋊C₄	—	34	1	no	—
365	C₄⋊C₄	C₂×C₄×D₁₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	34	1	no	—
368	C₂²⋊C₄	—	34	1	no	—
369	C₂²⋊C₄	—	34	1	no	—
370	C₂²⋊C₄	—	34	1	no	—
371	C₂²⋊C₄	—	34	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	34	1	no	—
374	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
375	C₄²	#63252	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
377	C₄²	C₂³×D₁₇	1	1	yes	characteristic
378	C₂³	—	34	1	no	—
379	C₂³	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	34	2	no	—
384	D₄	—	34	2	no	—
385	D₄	—	68	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	34	1	no	—
393	C₂×C₄	—	34	1	no	—
394	C₂×C₄	—	34	1	no	—
395	C₂×C₄	—	68	1	no	—
396	C₂×C₄	—	68	1	no	—
397	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
399	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#63252	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	34	2	no	—
408	C₈	—	34	2	no	—
409	C₈	—	68	2	no	—
410	C₈	—	68	1	no	—
411	C₈	—	68	1	no	—
412	C₈	#10587628	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	68	1	no	—
417	C₂²	—	68	1	no	—
418	C₂²	—	68	1	no	—
419	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	68	1	no	—
427	C₄	—	68	1	no	—
428	C₄	—	68	1	no	—
429	C₄	#11763574	1	2	yes	—
430	C₄	C₂×#10587628	1	1	yes	characteristic
431	C₄	#11763607	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	136	1	no	—
434	C₂	#14537500	1	1	yes	characteristic
435	C₂	C₄×#10587628	1	1	yes	characteristic
436	C₂	#14537685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#2960	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#10587616	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2960	D₁₇
hypocenter	C₁₇	#17986
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #14527662	C₂	semidirect
4. #14527655	C₂	semidirect
5. #14527632	C₂	semidirect
6. #14527618	C₂	semidirect
7. #14527549	C₂	semidirect
8. #14527257	C₂	semidirect
10. #14527073	C₂	semidirect
11. C₁₇×#2960	C₂	semidirect
197. #2960	D₁₇	semidirect
326. C₁₇	#17986	semidirect

Maximal subgroups

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

subgroup	index
#14539384	2
#14537759	2
#14527662	2
#14527655	2
#14527632	2
#14527618	2
#14527549	2
#14527257	2
#14527247	2
#14527073	2
C₁₇×#2960	2
#17986	17